Open with one click!
(File too big to render nicely. Download...)

R<x>:=PolynomialRing(Rationals());
S<a> := PolynomialRing(Rationals());
T<q> := PowerSeriesRing(S);

J := [rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> : 
         i in [1..500]];

J[1] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.141 seconds




J[2] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.18 seconds




J[3] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.16 seconds




J[5] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.16 seconds




J[6] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.181 seconds




J[7] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.149 seconds




J[10] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.169 seconds




J[11] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 11 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -2, -1, 1, -2, 1, 4, -2, 0, -1, 0, 7, 3 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 5 ]
], tamagawa_numbers := [
[ 5 ]
], torsion_upper_bounds := [ 5 ], torsion_lower_bounds := [ 5 ], l_ratios := [ 1/5 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -2, -1, 1, -2, 1, 4, -2, 0, -1, 0, 7, 3 ]
*], q_expansions := [*
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 - 2*q^10 + q^11 - 2*q^12 + 4*q^13 + 4*q^14 - q^15 - 4*q^16 - 2*q^17 + 4*q^18 + 2*q^20 + 2*q^21 - 2*q^22 - q^23 - 4*q^25 - 8*q^26 + 5*q^27 - 4*q^28 + 2*q^30 + 7*q^31 + 8*q^32 - q^33 + 4*q^34 - 2*q^35 - 4*q^36 + 3*q^37 + O(q^38)
*]> ;  // time = 0.52 seconds




J[13] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [], new_dimensions := [], dimensions := [], intersection_graph := [], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.16 seconds




J[14] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 14 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, -2, 0, 1, 0, -4, 6, 2, 0, -6, -4, 2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1 ]
], component_group_orders := [
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 3 ]
], torsion_upper_bounds := [ 3 ], torsion_lower_bounds := [ 3 ], l_ratios := [ 1/3 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, -2, 0, 1, 0, -4, 6, 2, 0, -6, -4, 2 ]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 + 2*q^6 + q^7 - q^8 + q^9 - 2*q^12 - 4*q^13 - q^14 + q^16 + 6*q^17 - q^18 + 2*q^19 - 2*q^21 + 2*q^24 - 5*q^25 + 4*q^26 + 4*q^27 + q^28 - 6*q^29 - 4*q^31 - q^32 - 6*q^34 + q^36 + 2*q^37 + O(q^38)
*]> ;  // time = 2.601 seconds




J[15] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 15 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, -1, 1, 0, -4, -2, 2, 4, 0, -2, 0, -10 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, -1, 1, 0, -4, -2, 2, 4, 0, -2, 0, -10 ]
*], q_expansions := [*
q - q^2 - q^3 - q^4 + q^5 + q^6 + 3*q^8 + q^9 - q^10 - 4*q^11 + q^12 - 2*q^13 - q^15 - q^16 + 2*q^17 - q^18 + 4*q^19 - q^20 + 4*q^22 - 3*q^24 + q^25 + 2*q^26 - q^27 - 2*q^29 + q^30 - 5*q^32 + 4*q^33 - 2*q^34 - q^36 - 10*q^37 + O(q^38)
*]> ;  // time = 1.81 seconds




J[17] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 17 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, 0, -2, 4, 0, -2, 1, -4, 4, 6, 4, -2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 1 ]
], tamagawa_numbers := [
[ 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, 0, -2, 4, 0, -2, 1, -4, 4, 6, 4, -2 ]
*], q_expansions := [*
q - q^2 - q^4 - 2*q^5 + 4*q^7 + 3*q^8 - 3*q^9 + 2*q^10 - 2*q^13 - 4*q^14 - q^16 + q^17 + 3*q^18 - 4*q^19 + 2*q^20 + 4*q^23 - q^25 + 2*q^26 - 4*q^28 + 6*q^29 + 4*q^31 - 5*q^32 - q^34 - 8*q^35 + 3*q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 0.509 seconds




J[19] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 19 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ 0, -2, 3, -1, 3, -4, -3, 1, 0, 6, -4, 2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 3 ]
], tamagawa_numbers := [
[ 3 ]
], torsion_upper_bounds := [ 3 ], torsion_lower_bounds := [ 3 ], l_ratios := [ 1/3 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 0, -2, 3, -1, 3, -4, -3, 1, 0, 6, -4, 2 ]
*], q_expansions := [*
q - 2*q^3 - 2*q^4 + 3*q^5 - q^7 + q^9 + 3*q^11 + 4*q^12 - 4*q^13 - 6*q^15 + 4*q^16 - 3*q^17 + q^19 - 6*q^20 + 2*q^21 + 4*q^25 + 4*q^27 + 2*q^28 + 6*q^29 - 4*q^31 - 6*q^33 - 3*q^35 - 2*q^36 + 2*q^37 + O(q^38)
*]> ;  // time = 0.52 seconds




J[21] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 21 ], new_dimensions := [ 1 ], dimensions := [ 1 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, 1, -2, -1, 4, -2, -6, 4, 0, -2, 0, 6 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, 1, -2, -1, 4, -2, -6, 4, 0, -2, 0, 6 ]
*], q_expansions := [*
q - q^2 + q^3 - q^4 - 2*q^5 - q^6 - q^7 + 3*q^8 + q^9 + 2*q^10 + 4*q^11 - q^12 - 2*q^13 + q^14 - 2*q^15 - q^16 - 6*q^17 - q^18 + 4*q^19 + 2*q^20 - q^21 - 4*q^22 + 3*q^24 - q^25 + 2*q^26 + q^27 + q^28 - 2*q^29 + 2*q^30 - 5*q^32 + 4*q^33 + 6*q^34 + 2*q^35 - q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 1.821 seconds




J[22] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 11 ], new_dimensions := [ 1 ], dimensions := [ 2 ], intersection_graph := [ 0 ], ap_traces := [], hecke_fields := [], atkin_lehners := [], component_group_orders := [], tamagawa_numbers := [], torsion_upper_bounds := [], torsion_lower_bounds := [], l_ratios := [], analytic_sha_upper_bounds := [], analytic_sha_lower_bounds := [], eigenvalues := [**], q_expansions := [**]> ;  // time = 0.66 seconds




J[23] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 23 ], new_dimensions := [ 2 ], dimensions := [ 2 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, 0, -2, 2, -6, 6, 6, -4, 2, -6, 0, 2 ]
], hecke_fields := [
x^2 + x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 11 ]
], tamagawa_numbers := [
[ 11 ]
], torsion_upper_bounds := [ 11 ], torsion_lower_bounds := [ 11 ], l_ratios := [ 1/11 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-2*a - 1,
2*a,
2*a + 2,
-2*a - 4,
3,
-2*a + 2,
-2,
1,
-3,
6*a + 3,
-2*a
]
*], q_expansions := [*
q + a*q^2 + (-2*a - 1)*q^3 + (-a - 1)*q^4 + 2*a*q^5 + (a - 2)*q^6 + (2*a + 2)*q^7 + (-2*a - 1)*q^8 + 2*q^9 + (-2*a + 2)*q^10 + (-2*a - 4)*q^11 + (a + 3)*q^12 + 3*q^13 + 2*q^14 + (2*a - 4)*q^15 + 3*a*q^16 + (-2*a + 2)*q^17 + 2*a*q^18 - 2*q^19 - 2*q^20 + (-2*a - 6)*q^21 + (-2*a - 2)*q^22 + q^23 + 5*q^24 + (-4*a - 1)*q^25 + 3*a*q^26 + (2*a + 1)*q^27 + (-2*a - 4)*q^28 - 3*q^29 + (-6*a + 2)*q^30 + (6*a + 3)*q^31 + (a + 5)*q^32 + (6*a + 8)*q^33 + (4*a - 2)*q^34 + 4*q^35 + (-2*a - 2)*q^36 - 2*a*q^37 + O(q^38)
*]> ;  // time = 0.56 seconds




J[26] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 26, 26 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 1 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, 1, -3, -1, 6, 1, -3, 2, 0, 6, -4, -7 ],
[ 1, -3, -1, 1, -2, -1, -3, 6, -4, 2, 4, 3 ]
], hecke_fields := [
x - 1,
x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 3 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 3, 7 ], torsion_lower_bounds := [ 3, 7 ], l_ratios := [ 1/3, 1/7 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ -1, 1, -3, -1, 6, 1, -3, 2, 0, 6, -4, -7 ],
[ 1, -3, -1, 1, -2, -1, -3, 6, -4, 2, 4, 3 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - 3*q^5 - q^6 - q^7 - q^8 - 2*q^9 + 3*q^10 + 6*q^11 + q^12 + q^13 + q^14 - 3*q^15 + q^16 - 3*q^17 + 2*q^18 + 2*q^19 - 3*q^20 - q^21 - 6*q^22 - q^24 + 4*q^25 - q^26 - 5*q^27 - q^28 + 6*q^29 + 3*q^30 - 4*q^31 - q^32 + 6*q^33 + 3*q^34 + 3*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - q^5 - 3*q^6 + q^7 + q^8 + 6*q^9 - q^10 - 2*q^11 - 3*q^12 - q^13 + q^14 + 3*q^15 + q^16 - 3*q^17 + 6*q^18 + 6*q^19 - q^20 - 3*q^21 - 2*q^22 - 4*q^23 - 3*q^24 - 4*q^25 - q^26 - 9*q^27 + q^28 + 2*q^29 + 3*q^30 + 4*q^31 + q^32 + 6*q^33 - 3*q^34 - q^35 + 6*q^36 + 3*q^37 + O(q^38)
*]> ;  // time = 3.819 seconds




J[29] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 29 ], new_dimensions := [ 2 ], dimensions := [ 2 ], intersection_graph := [ 0 ], ap_traces := [
[ -2, 2, -2, 0, 2, -2, -4, 12, -4, 2, 6, -8 ]
], hecke_fields := [
x^2 + 2*x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 7 ]
], tamagawa_numbers := [
[ 7 ]
], torsion_upper_bounds := [ 7 ], torsion_lower_bounds := [ 7 ], l_ratios := [ 1/7 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-a,
-1,
2*a + 2,
a + 2,
2*a + 1,
-2*a - 4,
6,
-4*a - 6,
1,
-5*a - 2,
-4
]
*], q_expansions := [*
q + a*q^2 - a*q^3 + (-2*a - 1)*q^4 - q^5 + (2*a - 1)*q^6 + (2*a + 2)*q^7 + (a - 2)*q^8 + (-2*a - 2)*q^9 - a*q^10 + (a + 2)*q^11 + (-3*a + 2)*q^12 + (2*a + 1)*q^13 + (-2*a + 2)*q^14 + a*q^15 + 3*q^16 + (-2*a - 4)*q^17 + (2*a - 2)*q^18 + 6*q^19 + (2*a + 1)*q^20 + (2*a - 2)*q^21 + q^22 + (-4*a - 6)*q^23 + (4*a - 1)*q^24 - 4*q^25 + (-3*a + 2)*q^26 + (a + 2)*q^27 + (2*a - 6)*q^28 + q^29 + (-2*a + 1)*q^30 + (-5*a - 2)*q^31 + (a + 4)*q^32 - q^33 - 2*q^34 + (-2*a - 2)*q^35 + (-2*a + 6)*q^36 - 4*q^37 + O(q^38)
*]> ;  // time = 0.58 seconds




J[30] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 30, 15 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, 1, -1, -4, 0, 2, 6, -4, 0, -6, 8, 2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1, 1 ]
], component_group_orders := [
[ 1, 3, 1 ]
], tamagawa_numbers := [
[ 1, 3, 1 ]
], torsion_upper_bounds := [ 3 ], torsion_lower_bounds := [ 3 ], l_ratios := [ 1/3 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, 1, -1, -4, 0, 2, 6, -4, 0, -6, 8, 2 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - q^5 - q^6 - 4*q^7 - q^8 + q^9 + q^10 + q^12 + 2*q^13 + 4*q^14 - q^15 + q^16 + 6*q^17 - q^18 - 4*q^19 - q^20 - 4*q^21 - q^24 + q^25 - 2*q^26 + q^27 - 4*q^28 - 6*q^29 + q^30 + 8*q^31 - q^32 - 6*q^34 + 4*q^35 + q^36 + 2*q^37 + O(q^38)
*]> ;  // time = 10.479 seconds




J[31] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 31 ], new_dimensions := [ 2 ], dimensions := [ 2 ], intersection_graph := [ 0 ], ap_traces := [
[ 1, -2, 2, -4, 4, -2, 6, 0, -2, 10, 2, -4 ]
], hecke_fields := [
x^2 - x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 5 ]
], tamagawa_numbers := [
[ 5 ]
], torsion_upper_bounds := [ 5 ], torsion_lower_bounds := [ 5 ], l_ratios := [ 1/5 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-2*a,
1,
2*a - 3,
2,
-2*a,
-2*a + 4,
-2*a + 1,
6*a - 4,
-2*a + 6,
1,
-2
]
*], q_expansions := [*
q + a*q^2 - 2*a*q^3 + (a - 1)*q^4 + q^5 + (-2*a - 2)*q^6 + (2*a - 3)*q^7 + (-2*a + 1)*q^8 + (4*a + 1)*q^9 + a*q^10 + 2*q^11 - 2*q^12 - 2*a*q^13 + (-a + 2)*q^14 - 2*a*q^15 - 3*a*q^16 + (-2*a + 4)*q^17 + (5*a + 4)*q^18 + (-2*a + 1)*q^19 + (a - 1)*q^20 + (2*a - 4)*q^21 + 2*a*q^22 + (6*a - 4)*q^23 + (2*a + 4)*q^24 - 4*q^25 + (-2*a - 2)*q^26 + (-4*a - 8)*q^27 + (-3*a + 5)*q^28 + (-2*a + 6)*q^29 + (-2*a - 2)*q^30 + q^31 + (a - 5)*q^32 - 4*a*q^33 + (2*a - 2)*q^34 + (2*a - 3)*q^35 + (a + 3)*q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 0.56 seconds




J[33] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 33, 11 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 3, 3, 0 ], ap_traces := [
[ 1, -1, -2, 4, 1, -2, -2, 0, 8, -6, -8, 6 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ]
], tamagawa_numbers := [
[ 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 1, -1, -2, 4, 1, -2, -2, 0, 8, -6, -8, 6 ]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - 2*q^5 - q^6 + 4*q^7 - 3*q^8 + q^9 - 2*q^10 + q^11 + q^12 - 2*q^13 + 4*q^14 + 2*q^15 - q^16 - 2*q^17 + q^18 + 2*q^20 - 4*q^21 + q^22 + 8*q^23 + 3*q^24 - q^25 - 2*q^26 - q^27 - 4*q^28 - 6*q^29 + 2*q^30 - 8*q^31 + 5*q^32 - q^33 - 2*q^34 - 8*q^35 - q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 2.76 seconds




J[34] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 34, 17 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 1, -2, 0, -4, 6, 2, -1, -4, 0, 0, -4, -4 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ]
], tamagawa_numbers := [
[ 3, 1 ]
], torsion_upper_bounds := [ 3 ], torsion_lower_bounds := [ 3 ], l_ratios := [ 1/3 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 1, -2, 0, -4, 6, 2, -1, -4, 0, 0, -4, -4 ]
*], q_expansions := [*
q + q^2 - 2*q^3 + q^4 - 2*q^6 - 4*q^7 + q^8 + q^9 + 6*q^11 - 2*q^12 + 2*q^13 - 4*q^14 + q^16 - q^17 + q^18 - 4*q^19 + 8*q^21 + 6*q^22 - 2*q^24 - 5*q^25 + 2*q^26 + 4*q^27 - 4*q^28 - 4*q^31 + q^32 - 12*q^33 - q^34 + q^36 - 4*q^37 + O(q^38)
*]> ;  // time = 3.571 seconds




J[35] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 35, 35 ], new_dimensions := [ 1, 2 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 0, 1, -1, 1, -3, 5, 3, 2, -6, 3, -4, 2 ],
[ -1, -1, 2, -2, 1, 5, -5, -6, -2, 1, 0, 12 ]
], hecke_fields := [
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 3 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 3, 1 ], torsion_lower_bounds := [ 3, 1 ], l_ratios := [ 1/3, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 0, 1, -1, 1, -3, 5, 3, 2, -6, 3, -4, 2 ],
[
a,
-a - 1,
1,
-1,
a + 1,
a + 3,
-a - 3,
2*a - 2,
-2*a - 2,
-3*a - 1,
0,
6
]
*], q_expansions := [*
q + q^3 - 2*q^4 - q^5 + q^7 - 2*q^9 - 3*q^11 - 2*q^12 + 5*q^13 - q^15 + 4*q^16 + 3*q^17 + 2*q^19 + 2*q^20 + q^21 - 6*q^23 + q^25 - 5*q^27 - 2*q^28 + 3*q^29 - 4*q^31 - 3*q^33 - q^35 + 4*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (-a + 2)*q^4 + q^5 - 4*q^6 - q^7 + (a - 4)*q^8 + (a + 2)*q^9 + a*q^10 + (a + 1)*q^11 + (-2*a + 2)*q^12 + (a + 3)*q^13 - a*q^14 + (-a - 1)*q^15 - 3*a*q^16 + (-a - 3)*q^17 + (a + 4)*q^18 + (2*a - 2)*q^19 + (-a + 2)*q^20 + (a + 1)*q^21 + 4*q^22 + (-2*a - 2)*q^23 + 4*a*q^24 + q^25 + (2*a + 4)*q^26 + (a - 3)*q^27 + (a - 2)*q^28 + (-3*a - 1)*q^29 - 4*q^30 + (a - 4)*q^32 + (-a - 5)*q^33 + (-2*a - 4)*q^34 - q^35 + a*q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 3.46 seconds




J[37] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 37, 37 ], new_dimensions := [ 1, 1 ], dimensions := [ 1, 1 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -3, -2, -1, -5, -2, 0, 0, 2, 6, -4, -1 ],
[ 0, 1, 0, -1, 3, -4, 6, 2, 6, -6, -4, 1 ]
], hecke_fields := [
x - 1,
x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 3 ]
], tamagawa_numbers := [
[ 1 ],
[ 3 ]
], torsion_upper_bounds := [ 1, 3 ], torsion_lower_bounds := [ 1, 3 ], l_ratios := [ 0, 1/3 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -2, -3, -2, -1, -5, -2, 0, 0, 2, 6, -4, -1 ],
[ 0, 1, 0, -1, 3, -4, 6, 2, 6, -6, -4, 1 ]
*], q_expansions := [*
q - 2*q^2 - 3*q^3 + 2*q^4 - 2*q^5 + 6*q^6 - q^7 + 6*q^9 + 4*q^10 - 5*q^11 - 6*q^12 - 2*q^13 + 2*q^14 + 6*q^15 - 4*q^16 - 12*q^18 - 4*q^20 + 3*q^21 + 10*q^22 + 2*q^23 - q^25 + 4*q^26 - 9*q^27 - 2*q^28 + 6*q^29 - 12*q^30 - 4*q^31 + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + O(q^38),
q + q^3 - 2*q^4 - q^7 - 2*q^9 + 3*q^11 - 2*q^12 - 4*q^13 + 4*q^16 + 6*q^17 + 2*q^19 - q^21 + 6*q^23 - 5*q^25 - 5*q^27 + 2*q^28 - 6*q^29 - 4*q^31 + 3*q^33 + 4*q^36 + q^37 + O(q^38)
*]> ;  // time = 0.64 seconds




J[38] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 38, 38, 19 ], new_dimensions := [ 1, 1, 1 ], dimensions := [ 1, 1, 2 ], intersection_graph := [ 0, 1, 3, 1, 0, 1, 3, 1, 0 ], ap_traces := [
[ -1, 1, 0, -1, -6, 5, 3, 1, 3, 9, -4, 2 ],
[ 1, -1, -4, 3, 2, -1, 3, -1, -1, -5, -8, -2 ]
], hecke_fields := [
x - 1,
x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 3 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 3, 5 ], torsion_lower_bounds := [ 3, 5 ], l_ratios := [ 1/3, 1/5 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ -1, 1, 0, -1, -6, 5, 3, 1, 3, 9, -4, 2 ],
[ 1, -1, -4, 3, 2, -1, 3, -1, -1, -5, -8, -2 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - q^6 - q^7 - q^8 - 2*q^9 - 6*q^11 + q^12 + 5*q^13 + q^14 + q^16 + 3*q^17 + 2*q^18 + q^19 - q^21 + 6*q^22 + 3*q^23 - q^24 - 5*q^25 - 5*q^26 - 5*q^27 - q^28 + 9*q^29 - 4*q^31 - q^32 - 6*q^33 - 3*q^34 - 2*q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 4*q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 - 4*q^10 + 2*q^11 - q^12 - q^13 + 3*q^14 + 4*q^15 + q^16 + 3*q^17 - 2*q^18 - q^19 - 4*q^20 - 3*q^21 + 2*q^22 - q^23 - q^24 + 11*q^25 - q^26 + 5*q^27 + 3*q^28 - 5*q^29 + 4*q^30 - 8*q^31 + q^32 - 2*q^33 + 3*q^34 - 12*q^35 - 2*q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 4.451 seconds




J[39] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 39, 39 ], new_dimensions := [ 1, 2 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 1, -1, 2, -4, 4, 1, 2, 0, 0, -10, 4, -2 ],
[ -2, 2, 0, 0, -4, -2, 4, 0, -8, 4, -8, -4 ]
], hecke_fields := [
x - 1,
x^2 + 2*x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 7 ], torsion_lower_bounds := [ 1, 7 ], l_ratios := [ 1, 1/7 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, -1, 2, -4, 4, 1, 2, 0, 0, -10, 4, -2 ],
[
a,
1,
-2*a - 2,
2*a + 2,
-2,
-1,
4*a + 6,
-2*a - 2,
-4,
2,
2*a - 2,
-4*a - 6
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 + 2*q^5 - q^6 - 4*q^7 - 3*q^8 + q^9 + 2*q^10 + 4*q^11 + q^12 + q^13 - 4*q^14 - 2*q^15 - q^16 + 2*q^17 + q^18 - 2*q^20 + 4*q^21 + 4*q^22 + 3*q^24 - q^25 + q^26 - q^27 + 4*q^28 - 10*q^29 - 2*q^30 + 4*q^31 + 5*q^32 - 4*q^33 + 2*q^34 - 8*q^35 - q^36 - 2*q^37 + O(q^38),
q + a*q^2 + q^3 + (-2*a - 1)*q^4 + (-2*a - 2)*q^5 + a*q^6 + (2*a + 2)*q^7 + (a - 2)*q^8 + q^9 + (2*a - 2)*q^10 - 2*q^11 + (-2*a - 1)*q^12 - q^13 + (-2*a + 2)*q^14 + (-2*a - 2)*q^15 + 3*q^16 + (4*a + 6)*q^17 + a*q^18 + (-2*a - 2)*q^19 + (-2*a + 6)*q^20 + (2*a + 2)*q^21 - 2*a*q^22 - 4*q^23 + (a - 2)*q^24 + 3*q^25 - a*q^26 + q^27 + (2*a - 6)*q^28 + 2*q^29 + (2*a - 2)*q^30 + (2*a - 2)*q^31 + (a + 4)*q^32 - 2*q^33 + (-2*a + 4)*q^34 - 8*q^35 + (-2*a - 1)*q^36 + (-4*a - 6)*q^37 + O(q^38)
*]> ;  // time = 3.229 seconds




J[41] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 41 ], new_dimensions := [ 3 ], dimensions := [ 3 ], intersection_graph := [ 0 ], ap_traces := [
[ -1, 0, -2, 6, 2, -2, -6, 4, 4, -6, 16, -6 ]
], hecke_fields := [
x^3 + x^2 - 5*x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 5 ]
], tamagawa_numbers := [
[ 5 ]
], torsion_upper_bounds := [ 5 ], torsion_lower_bounds := [ 5 ], l_ratios := [ 1/5 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-1/2*a^2 - a + 3/2,
-a - 1,
1/2*a^2 + a + 1/2,
3/2*a^2 + a - 9/2,
-a^2 + 3,
-2,
-3/2*a^2 - a + 13/2,
-2*a^2 - 2*a + 8,
a^2 + 2*a - 5,
2*a + 6,
-3*a - 3
]
*], q_expansions := [*
q + a*q^2 + (-1/2*a^2 - a + 3/2)*q^3 + (a^2 - 2)*q^4 + (-a - 1)*q^5 + (-1/2*a^2 - a - 1/2)*q^6 + (1/2*a^2 + a + 1/2)*q^7 + (-a^2 + a + 1)*q^8 + a*q^9 + (-a^2 - a)*q^10 + (3/2*a^2 + a - 9/2)*q^11 + (1/2*a^2 - a - 7/2)*q^12 + (-a^2 + 3)*q^13 + (1/2*a^2 + 3*a + 1/2)*q^14 + (a^2 + 2*a - 1)*q^15 + (-4*a + 3)*q^16 - 2*q^17 + a^2*q^18 + (-3/2*a^2 - a + 13/2)*q^19 + (-3*a + 1)*q^20 + (-a^2 - 3*a)*q^21 + (-1/2*a^2 + 3*a + 3/2)*q^22 + (-2*a^2 - 2*a + 8)*q^23 + (-1/2*a^2 + a + 3/2)*q^24 + (a^2 + 2*a - 4)*q^25 + (a^2 - 2*a - 1)*q^26 + (a^2 + 2*a - 5)*q^27 + (3/2*a^2 + a - 1/2)*q^28 + (a^2 + 2*a - 5)*q^29 + (a^2 + 4*a + 1)*q^30 + (2*a + 6)*q^31 + (-2*a^2 + a - 2)*q^32 + (a^2 - a - 8)*q^33 - 2*a*q^34 + (-a^2 - 4*a - 1)*q^35 + (-a^2 + 3*a + 1)*q^36 + (-3*a - 3)*q^37 + O(q^38)
*]> ;  // time = 0.649 seconds




J[42] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 42, 21, 14 ], new_dimensions := [ 1, 1, 1 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ 1, -1, -2, -1, -4, 6, 2, -4, 8, -2, 0, -10 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 1, -1, -2, -1, -4, 6, 2, -4, 8, -2, 0, -10 ]
*], q_expansions := [*
q + q^2 - q^3 + q^4 - 2*q^5 - q^6 - q^7 + q^8 + q^9 - 2*q^10 - 4*q^11 - q^12 + 6*q^13 - q^14 + 2*q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 - 2*q^20 + q^21 - 4*q^22 + 8*q^23 - q^24 - q^25 + 6*q^26 - q^27 - q^28 - 2*q^29 + 2*q^30 + q^32 + 4*q^33 + 2*q^34 + 2*q^35 + q^36 - 10*q^37 + O(q^38)
*]> ;  // time = 11.65 seconds




J[43] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 43, 43 ], new_dimensions := [ 1, 2 ], dimensions := [ 1, 2 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -2, -4, 0, 3, -5, -3, -2, -1, -6, -1, 0 ],
[ 0, 0, 4, -4, -2, 2, 10, -4, 2, 0, -6, 0 ]
], hecke_fields := [
x - 1,
x^2 - 2
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 7 ]
], tamagawa_numbers := [
[ 1 ],
[ 7 ]
], torsion_upper_bounds := [ 1, 7 ], torsion_lower_bounds := [ 1, 7 ], l_ratios := [ 0, 1/7 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -2, -2, -4, 0, 3, -5, -3, -2, -1, -6, -1, 0 ],
[
a,
-a,
-a + 2,
a - 2,
2*a - 1,
2*a + 1,
2*a + 5,
-2*a - 2,
-4*a + 1,
3*a,
-3,
-6*a
]
*], q_expansions := [*
q - 2*q^2 - 2*q^3 + 2*q^4 - 4*q^5 + 4*q^6 + q^9 + 8*q^10 + 3*q^11 - 4*q^12 - 5*q^13 + 8*q^15 - 4*q^16 - 3*q^17 - 2*q^18 - 2*q^19 - 8*q^20 - 6*q^22 - q^23 + 11*q^25 + 10*q^26 + 4*q^27 - 6*q^29 - 16*q^30 - q^31 + 8*q^32 - 6*q^33 + 6*q^34 + 2*q^36 + O(q^38),
q + a*q^2 - a*q^3 + (-a + 2)*q^5 - 2*q^6 + (a - 2)*q^7 - 2*a*q^8 - q^9 + (2*a - 2)*q^10 + (2*a - 1)*q^11 + (2*a + 1)*q^13 + (-2*a + 2)*q^14 + (-2*a + 2)*q^15 - 4*q^16 + (2*a + 5)*q^17 - a*q^18 + (-2*a - 2)*q^19 + (2*a - 2)*q^21 + (-a + 4)*q^22 + (-4*a + 1)*q^23 + 4*q^24 + (-4*a + 1)*q^25 + (a + 4)*q^26 + 4*a*q^27 + 3*a*q^29 + (2*a - 4)*q^30 - 3*q^31 + (a - 4)*q^33 + (5*a + 4)*q^34 + (4*a - 6)*q^35 - 6*a*q^37 + O(q^38)
*]> ;  // time = 0.699 seconds




J[46] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 46, 23 ], new_dimensions := [ 1, 2 ], dimensions := [ 1, 4 ], intersection_graph := [ 0, 5, 5, 0 ], ap_traces := [
[ -1, 0, 4, -4, 2, -2, -2, -2, 1, 2, 0, -4 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, 0, 4, -4, 2, -2, -2, -2, 1, 2, 0, -4 ]
*], q_expansions := [*
q - q^2 + q^4 + 4*q^5 - 4*q^7 - q^8 - 3*q^9 - 4*q^10 + 2*q^11 - 2*q^13 + 4*q^14 + q^16 - 2*q^17 + 3*q^18 - 2*q^19 + 4*q^20 - 2*q^22 + q^23 + 11*q^25 + 2*q^26 - 4*q^28 + 2*q^29 - q^32 + 2*q^34 - 16*q^35 - 3*q^36 - 4*q^37 + O(q^38)
*]> ;  // time = 4.579 seconds




J[47] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 47 ], new_dimensions := [ 4 ], dimensions := [ 4 ], intersection_graph := [ 0 ], ap_traces := [
[ 1, 0, -2, 4, -6, 8, 6, 0, -6, -10, -8, 10 ]
], hecke_fields := [
x^4 - x^3 - 5*x^2 + 5*x - 1
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 23 ]
], tamagawa_numbers := [
[ 23 ]
], torsion_upper_bounds := [ 23 ], torsion_lower_bounds := [ 23 ], l_ratios := [ 1/23 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
a^3 - a^2 - 6*a + 4,
-4*a^3 + 2*a^2 + 20*a - 10,
3*a^3 - a^2 - 16*a + 7,
2*a^3 - 2*a^2 - 10*a + 6,
-4*a^3 + 2*a^2 + 22*a - 8,
a^3 + a^2 - 6*a,
-2*a^3 + 10*a - 2,
-2*a^3 + 12*a - 4,
-2*a^3 + 2*a^2 + 10*a - 10,
4*a^3 - 2*a^2 - 22*a + 8,
3*a^3 - a^2 - 14*a + 8
]
*], q_expansions := [*
q + a*q^2 + (a^3 - a^2 - 6*a + 4)*q^3 + (a^2 - 2)*q^4 + (-4*a^3 + 2*a^2 + 20*a - 10)*q^5 + (-a^2 - a + 1)*q^6 + (3*a^3 - a^2 - 16*a + 7)*q^7 + (a^3 - 4*a)*q^8 + (3*a^3 - a^2 - 14*a + 6)*q^9 + (-2*a^3 + 10*a - 4)*q^10 + (2*a^3 - 2*a^2 - 10*a + 6)*q^11 + (-3*a^3 + a^2 + 13*a - 8)*q^12 + (-4*a^3 + 2*a^2 + 22*a - 8)*q^13 + (2*a^3 - a^2 - 8*a + 3)*q^14 + (-4*a^3 + 4*a^2 + 22*a - 16)*q^15 + (a^3 - a^2 - 5*a + 5)*q^16 + (a^3 + a^2 - 6*a)*q^17 + (2*a^3 + a^2 - 9*a + 3)*q^18 + (-2*a^3 + 10*a - 2)*q^19 + (6*a^3 - 4*a^2 - 34*a + 18)*q^20 + (2*a^3 - 2*a^2 - 12*a + 9)*q^21 + (-4*a + 2)*q^22 + (-2*a^3 + 12*a - 4)*q^23 + (-2*a^3 + 9*a - 5)*q^24 + (4*a^3 - 4*a^2 - 20*a + 19)*q^25 + (-2*a^3 + 2*a^2 + 12*a - 4)*q^26 + (-2*a^3 + 10*a - 5)*q^27 + (-5*a^3 + 4*a^2 + 25*a - 12)*q^28 + (-2*a^3 + 2*a^2 + 10*a - 10)*q^29 + (2*a^2 + 4*a - 4)*q^30 + (4*a^3 - 2*a^2 - 22*a + 8)*q^31 + (-2*a^3 + 8*a + 1)*q^32 + (4*a^3 - 2*a^2 - 18*a + 12)*q^33 + (2*a^3 - a^2 - 5*a + 1)*q^34 + (2*a^2 - 2*a - 10)*q^35 + (-3*a^3 + 3*a^2 + 21*a - 10)*q^36 + (3*a^3 - a^2 - 14*a + 8)*q^37 + O(q^38)
*]> ;  // time = 0.701 seconds




J[51] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 51, 51, 17 ], new_dimensions := [ 1, 2, 1 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ 0, 1, 3, -4, -3, -1, -1, -1, 9, 6, 2, -4 ],
[ -1, -2, 3, 0, -1, 5, 2, 3, -9, 0, -2, -2 ]
], hecke_fields := [
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 3, 1 ], torsion_lower_bounds := [ 3, 1 ], l_ratios := [ 1/3, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 0, 1, 3, -4, -3, -1, -1, -1, 9, 6, 2, -4 ],
[
a,
-1,
-a + 1,
0,
-a - 1,
a + 3,
1,
3*a + 3,
-a - 5,
4*a + 2,
-2*a - 2,
2*a
]
*], q_expansions := [*
q + q^3 - 2*q^4 + 3*q^5 - 4*q^7 + q^9 - 3*q^11 - 2*q^12 - q^13 + 3*q^15 + 4*q^16 - q^17 - q^19 - 6*q^20 - 4*q^21 + 9*q^23 + 4*q^25 + q^27 + 8*q^28 + 6*q^29 + 2*q^31 - 3*q^33 - 12*q^35 - 2*q^36 - 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a + 2)*q^4 + (-a + 1)*q^5 - a*q^6 + (a - 4)*q^8 + q^9 + (2*a - 4)*q^10 + (-a - 1)*q^11 + (a - 2)*q^12 + (a + 3)*q^13 + (a - 1)*q^15 - 3*a*q^16 + q^17 + a*q^18 + (3*a + 3)*q^19 + (-4*a + 6)*q^20 - 4*q^22 + (-a - 5)*q^23 + (-a + 4)*q^24 - 3*a*q^25 + (2*a + 4)*q^26 - q^27 + (4*a + 2)*q^29 + (-2*a + 4)*q^30 + (-2*a - 2)*q^31 + (a - 4)*q^32 + (a + 1)*q^33 + a*q^34 + (-a + 2)*q^36 + 2*a*q^37 + O(q^38)
*]> ;  // time = 4.25 seconds




J[53] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 53, 53 ], new_dimensions := [ 1, 3 ], dimensions := [ 1, 3 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -3, 0, -4, 0, -3, -3, -5, 7, -7, 4, 5 ],
[ -1, 3, -2, 4, -4, 3, -5, 11, 3, -5, -2, -5 ]
], hecke_fields := [
x - 1,
x^3 + x^2 - 3*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 13 ]
], tamagawa_numbers := [
[ 1 ],
[ 13 ]
], torsion_upper_bounds := [ 1, 13 ], torsion_lower_bounds := [ 1, 13 ], l_ratios := [ 0, 1/13 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -3, 0, -4, 0, -3, -3, -5, 7, -7, 4, 5 ],
[
a,
-a^2 - a + 3,
a^2 - 3,
a^2 - 1,
a^2 + 2*a - 3,
1,
2*a - 1,
a + 4,
2*a^2 - a - 4,
-3*a^2 - 4*a + 4,
-a^2 + 4*a + 3,
a^2 + 6*a - 2
]
*], q_expansions := [*
q - q^2 - 3*q^3 - q^4 + 3*q^6 - 4*q^7 + 3*q^8 + 6*q^9 + 3*q^12 - 3*q^13 + 4*q^14 - q^16 - 3*q^17 - 6*q^18 - 5*q^19 + 12*q^21 + 7*q^23 - 9*q^24 - 5*q^25 + 3*q^26 - 9*q^27 + 4*q^28 - 7*q^29 + 4*q^31 - 5*q^32 + 3*q^34 - 6*q^36 + 5*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 3)*q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 - q^6 + (a^2 - 1)*q^7 + (-a^2 - a + 1)*q^8 + (-3*a^2 - 2*a + 7)*q^9 + (-a^2 + 1)*q^10 + (a^2 + 2*a - 3)*q^11 + (2*a^2 + a - 6)*q^12 + q^13 + (-a^2 + 2*a + 1)*q^14 + (3*a^2 + 2*a - 9)*q^15 + (-2*a^2 - 2*a + 3)*q^16 + (2*a - 1)*q^17 + (a^2 - 2*a - 3)*q^18 + (a + 4)*q^19 + (-a^2 - 2*a + 5)*q^20 + (a^2 - 3)*q^21 + (a^2 + 1)*q^22 + (2*a^2 - a - 4)*q^23 + (-a^2 + 4)*q^24 + (-2*a^2 - 2*a + 3)*q^25 + a*q^26 + (-4*a^2 - a + 14)*q^27 + (a^2 - 2*a + 1)*q^28 + (-3*a^2 - 4*a + 4)*q^29 + (-a^2 + 3)*q^30 + (-a^2 + 4*a + 3)*q^31 + (2*a^2 - a - 4)*q^32 + (3*a^2 + 2*a - 11)*q^33 + (2*a^2 - a)*q^34 + (-2*a + 2)*q^35 + (3*a^2 + 4*a - 13)*q^36 + (a^2 + 6*a - 2)*q^37 + O(q^38)
*]> ;  // time = 0.79 seconds




J[55] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 55, 55, 11 ], new_dimensions := [ 1, 2, 1 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 7, 1, 7, 0 ], ap_traces := [
[ 1, 0, 1, 0, -1, 2, 6, -4, 4, 6, -8, -2 ],
[ 2, 0, -2, -4, 2, -8, 8, 0, 0, 4, 0, -4 ]
], hecke_fields := [
x - 1,
x^2 - 2*x - 1
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 1, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 0, 1, 0, -1, 2, 6, -4, 4, 6, -8, -2 ],
[
a,
-2*a + 2,
-1,
-2,
1,
2*a - 6,
2*a + 2,
0,
-2*a + 2,
-4*a + 6,
0,
-4*a + 2
]
*], q_expansions := [*
q + q^2 - q^4 + q^5 - 3*q^8 - 3*q^9 + q^10 - q^11 + 2*q^13 - q^16 + 6*q^17 - 3*q^18 - 4*q^19 - q^20 - q^22 + 4*q^23 + q^25 + 2*q^26 + 6*q^29 - 8*q^31 + 5*q^32 + 6*q^34 + 3*q^36 - 2*q^37 + O(q^38),
q + a*q^2 + (-2*a + 2)*q^3 + (2*a - 1)*q^4 - q^5 + (-2*a - 2)*q^6 - 2*q^7 + (a + 2)*q^8 + 5*q^9 - a*q^10 + q^11 + (-2*a - 6)*q^12 + (2*a - 6)*q^13 - 2*a*q^14 + (2*a - 2)*q^15 + 3*q^16 + (2*a + 2)*q^17 + 5*a*q^18 + (-2*a + 1)*q^20 + (4*a - 4)*q^21 + a*q^22 + (-2*a + 2)*q^23 + (-6*a + 2)*q^24 + q^25 + (-2*a + 2)*q^26 + (-4*a + 4)*q^27 + (-4*a + 2)*q^28 + (-4*a + 6)*q^29 + (2*a + 2)*q^30 + (a - 4)*q^32 + (-2*a + 2)*q^33 + (6*a + 2)*q^34 + 2*q^35 + (10*a - 5)*q^36 + (-4*a + 2)*q^37 + O(q^38)
*]> ;  // time = 4.151 seconds




J[57] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 57, 57, 57, 19 ], new_dimensions := [ 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 3, 1, 1, 3, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ -2, -1, -3, -5, 1, 2, -1, -1, -4, -2, -6, 0 ],
[ 1, 1, -2, 0, 0, 6, -6, -1, 4, 2, 8, -10 ],
[ -2, 1, 1, 3, -3, -6, 3, -1, 4, -10, 2, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 5 ], l_ratios := [ 0, 1, 1/5 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -2, -1, -3, -5, 1, 2, -1, -1, -4, -2, -6, 0 ],
[ 1, 1, -2, 0, 0, 6, -6, -1, 4, 2, 8, -10 ],
[ -2, 1, 1, 3, -3, -6, 3, -1, 4, -10, 2, 8 ]
*], q_expansions := [*
q - 2*q^2 - q^3 + 2*q^4 - 3*q^5 + 2*q^6 - 5*q^7 + q^9 + 6*q^10 + q^11 - 2*q^12 + 2*q^13 + 10*q^14 + 3*q^15 - 4*q^16 - q^17 - 2*q^18 - q^19 - 6*q^20 + 5*q^21 - 2*q^22 - 4*q^23 + 4*q^25 - 4*q^26 - q^27 - 10*q^28 - 2*q^29 - 6*q^30 - 6*q^31 + 8*q^32 - q^33 + 2*q^34 + 15*q^35 + 2*q^36 + O(q^38),
q + q^2 + q^3 - q^4 - 2*q^5 + q^6 - 3*q^8 + q^9 - 2*q^10 - q^12 + 6*q^13 - 2*q^15 - q^16 - 6*q^17 + q^18 - q^19 + 2*q^20 + 4*q^23 - 3*q^24 - q^25 + 6*q^26 + q^27 + 2*q^29 - 2*q^30 + 8*q^31 + 5*q^32 - 6*q^34 - q^36 - 10*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 + q^5 - 2*q^6 + 3*q^7 + q^9 - 2*q^10 - 3*q^11 + 2*q^12 - 6*q^13 - 6*q^14 + q^15 - 4*q^16 + 3*q^17 - 2*q^18 - q^19 + 2*q^20 + 3*q^21 + 6*q^22 + 4*q^23 - 4*q^25 + 12*q^26 + q^27 + 6*q^28 - 10*q^29 - 2*q^30 + 2*q^31 + 8*q^32 - 3*q^33 - 6*q^34 + 3*q^35 + 2*q^36 + 8*q^37 + O(q^38)
*]> ;  // time = 4.781 seconds




J[58] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 58, 58, 29 ], new_dimensions := [ 1, 1, 2 ], dimensions := [ 1, 1, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, -3, -3, -2, -1, 3, -4, -8, 0, -1, 3, -8 ],
[ 1, -1, 1, -2, -3, -1, 8, 0, 4, -1, -3, 8 ]
], hecke_fields := [
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 5 ], torsion_lower_bounds := [ 1, 5 ], l_ratios := [ 0, 1/5 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -3, -3, -2, -1, 3, -4, -8, 0, -1, 3, -8 ],
[ 1, -1, 1, -2, -3, -1, 8, 0, 4, -1, -3, 8 ]
*], q_expansions := [*
q - q^2 - 3*q^3 + q^4 - 3*q^5 + 3*q^6 - 2*q^7 - q^8 + 6*q^9 + 3*q^10 - q^11 - 3*q^12 + 3*q^13 + 2*q^14 + 9*q^15 + q^16 - 4*q^17 - 6*q^18 - 8*q^19 - 3*q^20 + 6*q^21 + q^22 + 3*q^24 + 4*q^25 - 3*q^26 - 9*q^27 - 2*q^28 - q^29 - 9*q^30 + 3*q^31 - q^32 + 3*q^33 + 4*q^34 + 6*q^35 + 6*q^36 - 8*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 - 2*q^7 + q^8 - 2*q^9 + q^10 - 3*q^11 - q^12 - q^13 - 2*q^14 - q^15 + q^16 + 8*q^17 - 2*q^18 + q^20 + 2*q^21 - 3*q^22 + 4*q^23 - q^24 - 4*q^25 - q^26 + 5*q^27 - 2*q^28 - q^29 - q^30 - 3*q^31 + q^32 + 3*q^33 + 8*q^34 - 2*q^35 - 2*q^36 + 8*q^37 + O(q^38)
*]> ;  // time = 6.101 seconds




J[59] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 59 ], new_dimensions := [ 5 ], dimensions := [ 5 ], intersection_graph := [ 0 ], ap_traces := [
[ 0, -2, 2, 2, -2, 8, -1, 6, -8, 14, 0, 18 ]
], hecke_fields := [
x^5 - 9*x^3 + 2*x^2 + 16*x - 8
], atkin_lehners := [
[ -1 ]
], component_group_orders := [
[ 29 ]
], tamagawa_numbers := [
[ 29 ]
], torsion_upper_bounds := [ 29 ], torsion_lower_bounds := [ 29 ], l_ratios := [ 1/29 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[
a,
-1/4*a^4 + 5/4*a^2 - 1/2*a,
3/4*a^4 + 1/2*a^3 - 23/4*a^2 - 3*a + 7,
-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 3/2*a - 3,
-1/2*a^4 - a^3 + 9/2*a^2 + 6*a - 8,
-1/2*a^4 - a^3 + 9/2*a^2 + 6*a - 6,
a^4 - 8*a^2 + 9,
3/4*a^4 + 3/2*a^3 - 23/4*a^2 - 8*a + 9,
-1/2*a^4 + 9/2*a^2 + a - 8,
-a^4 - 1/2*a^3 + 8*a^2 + 1/2*a - 7,
a^4 + a^3 - 9*a^2 - 3*a + 14,
-a^4 + 7*a^2 - 2
]
*], q_expansions := [*
q + a*q^2 + (-1/4*a^4 + 5/4*a^2 - 1/2*a)*q^3 + (a^2 - 2)*q^4 + (3/4*a^4 + 1/2*a^3 - 23/4*a^2 - 3*a + 7)*q^5 + (-a^3 + 4*a - 2)*q^6 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 3/2*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^3 + a^2 - 5/2*a - 2)*q^9 + (1/2*a^4 + a^3 - 9/2*a^2 - 5*a + 6)*q^10 + (-1/2*a^4 - a^3 + 9/2*a^2 + 6*a - 8)*q^11 + (-1/2*a^4 + 3/2*a^2 - a)*q^12 + (-1/2*a^4 - a^3 + 9/2*a^2 + 6*a - 6)*q^13 + (-1/2*a^4 - a^3 + 5/2*a^2 + 5*a - 4)*q^14 + (1/4*a^4 + 1/2*a^3 - 9/4*a^2 - 2*a + 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - 8*a^2 + 9)*q^17 + (1/2*a^4 + a^3 - 5/2*a^2 - 2*a)*q^18 + (3/4*a^4 + 3/2*a^3 - 23/4*a^2 - 8*a + 9)*q^19 + (-1/2*a^4 - a^3 + 11/2*a^2 + 4*a - 10)*q^20 + (-1/4*a^4 + a^3 + 9/4*a^2 - 7/2*a + 1)*q^21 + (-a^4 + 7*a^2 - 4)*q^22 + (-1/2*a^4 + 9/2*a^2 + a - 8)*q^23 - a^3*q^24 + (1/4*a^4 - a^3 - 13/4*a^2 + 11/2*a + 7)*q^25 + (-a^4 + 7*a^2 + 2*a - 4)*q^26 + (1/4*a^4 - 9/4*a^2 - 3/2*a + 1)*q^27 + (-a^3 - a^2 + a + 2)*q^28 + (-a^4 - 1/2*a^3 + 8*a^2 + 1/2*a - 7)*q^29 + (1/2*a^4 - 5/2*a^2 - 2*a + 2)*q^30 + (a^4 + a^3 - 9*a^2 - 3*a + 14)*q^31 + (a^3 - 2*a^2 - 4*a + 8)*q^32 + (-a^3 + 7*a - 4)*q^33 + (a^3 - 2*a^2 - 7*a + 8)*q^34 + (1/2*a^4 + 1/2*a^3 - 5/2*a^2 - 7/2*a - 2)*q^35 + (a^4 + a^3 - 5*a^2 - 3*a + 8)*q^36 + (-a^4 + 7*a^2 - 2)*q^37 + O(q^38)
*]> ;  // time = 0.759 seconds




J[61] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 61, 61 ], new_dimensions := [ 1, 3 ], dimensions := [ 1, 3 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -2, -3, 1, -5, 1, 4, -4, -9, -6, 0, 8 ],
[ 1, 2, -1, -3, 13, -9, -2, 0, 5, 4, -2, -6 ]
], hecke_fields := [
x - 1,
x^3 - x^2 - 3*x + 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 5 ]
], tamagawa_numbers := [
[ 1 ],
[ 5 ]
], torsion_upper_bounds := [ 1, 5 ], torsion_lower_bounds := [ 1, 5 ], l_ratios := [ 0, 1/5 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -2, -3, 1, -5, 1, 4, -4, -9, -6, 0, 8 ],
[
a,
-a^2 + 3,
a^2 - 2*a - 2,
a^2 - a - 3,
a + 4,
-2*a^2 + 2*a + 1,
-a^2 + 2*a + 1,
3*a^2 - 7,
-a + 2,
-a^2 + 2*a + 3,
-a^2 - 4*a + 3,
3*a^2 - 9
]
*], q_expansions := [*
q - q^2 - 2*q^3 - q^4 - 3*q^5 + 2*q^6 + q^7 + 3*q^8 + q^9 + 3*q^10 - 5*q^11 + 2*q^12 + q^13 - q^14 + 6*q^15 - q^16 + 4*q^17 - q^18 - 4*q^19 + 3*q^20 - 2*q^21 + 5*q^22 - 9*q^23 - 6*q^24 + 4*q^25 - q^26 + 4*q^27 - q^28 - 6*q^29 - 6*q^30 - 5*q^32 + 10*q^33 - 4*q^34 - 3*q^35 - q^36 + 8*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 3)*q^3 + (a^2 - 2)*q^4 + (a^2 - 2*a - 2)*q^5 + (-a^2 + 1)*q^6 + (a^2 - a - 3)*q^7 + (a^2 - a - 1)*q^8 + (-2*a^2 + 2*a + 5)*q^9 + (-a^2 + a - 1)*q^10 + (a + 4)*q^11 + (a^2 - 2*a - 5)*q^12 + (-2*a^2 + 2*a + 1)*q^13 - q^14 + (3*a^2 - 2*a - 7)*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-a^2 + 2*a + 1)*q^17 + (-a + 2)*q^18 + (3*a^2 - 7)*q^19 + (-2*a^2 + 5)*q^20 + (3*a^2 - 2*a - 9)*q^21 + (a^2 + 4*a)*q^22 + (-a + 2)*q^23 + (a^2 - 2*a - 3)*q^24 + (-2*a + 2)*q^25 + (-5*a + 2)*q^26 + (-2*a^2 + 4*a + 6)*q^27 + (-2*a^2 + a + 6)*q^28 + (-a^2 + 2*a + 3)*q^29 + (a^2 + 2*a - 3)*q^30 + (-a^2 - 4*a + 3)*q^31 + (-2*a^2 - a + 4)*q^32 + (-5*a^2 + 13)*q^33 + (a^2 - 2*a + 1)*q^34 + (-2*a^2 + a + 8)*q^35 + (3*a^2 - 2*a - 10)*q^36 + (3*a^2 - 9)*q^37 + O(q^38)
*]> ;  // time = 0.81 seconds




J[62] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 62, 62, 31 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 11, 1, 11, 0 ], ap_traces := [
[ 1, 0, -2, 0, 0, 2, -6, 4, 8, 2, -1, 10 ],
[ -2, 2, 0, 4, -6, -2, 0, -8, 0, -6, 2, 10 ]
], hecke_fields := [
x - 1,
x^2 - 2*x - 2
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 33, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 3 ], torsion_lower_bounds := [ 1, 3 ], l_ratios := [ 1, 1/3 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 0, -2, 0, 0, 2, -6, 4, 8, 2, -1, 10 ],
[
-1,
a,
-2*a + 2,
2,
a - 4,
-3*a + 2,
2*a - 2,
-4,
0,
3*a - 6,
1,
3*a + 2
]
*], q_expansions := [*
q + q^2 + q^4 - 2*q^5 + q^8 - 3*q^9 - 2*q^10 + 2*q^13 + q^16 - 6*q^17 - 3*q^18 + 4*q^19 - 2*q^20 + 8*q^23 - q^25 + 2*q^26 + 2*q^29 - q^31 + q^32 - 6*q^34 - 3*q^36 + 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-2*a + 2)*q^5 - a*q^6 + 2*q^7 - q^8 + (2*a - 1)*q^9 + (2*a - 2)*q^10 + (a - 4)*q^11 + a*q^12 + (-3*a + 2)*q^13 - 2*q^14 + (-2*a - 4)*q^15 + q^16 + (2*a - 2)*q^17 + (-2*a + 1)*q^18 - 4*q^19 + (-2*a + 2)*q^20 + 2*a*q^21 + (-a + 4)*q^22 - a*q^24 + 7*q^25 + (3*a - 2)*q^26 + 4*q^27 + 2*q^28 + (3*a - 6)*q^29 + (2*a + 4)*q^30 + q^31 - q^32 + (-2*a + 2)*q^33 + (-2*a + 2)*q^34 + (-4*a + 4)*q^35 + (2*a - 1)*q^36 + (3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 6.84 seconds




J[65] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 65, 65, 65 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, -2, -1, -4, 2, -1, 2, -6, -6, 2, -10, -2 ],
[ 0, 2, -2, 4, -6, 2, 0, -2, 6, -12, 10, -8 ],
[ -2, 0, 2, 4, 4, -2, -4, 4, 0, 0, 12, 0 ]
], hecke_fields := [
x - 1,
x^2 - 3,
x^2 + 2*x - 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 3 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 3, 7 ], torsion_lower_bounds := [ 1, 3, 7 ], l_ratios := [ 0, 1/3, 1/7 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -2, -1, -4, 2, -1, 2, -6, -6, 2, -10, -2 ],
[
a,
-a + 1,
-1,
2,
a - 3,
1,
2*a,
3*a - 1,
a + 3,
-2*a - 6,
-3*a + 5,
-4
],
[
a,
a + 1,
1,
-2*a,
-a + 1,
-1,
-2*a - 4,
a + 3,
-a - 1,
4*a + 4,
3*a + 9,
6*a + 6
]
*], q_expansions := [*
q - q^2 - 2*q^3 - q^4 - q^5 + 2*q^6 - 4*q^7 + 3*q^8 + q^9 + q^10 + 2*q^11 + 2*q^12 - q^13 + 4*q^14 + 2*q^15 - q^16 + 2*q^17 - q^18 - 6*q^19 + q^20 + 8*q^21 - 2*q^22 - 6*q^23 - 6*q^24 + q^25 + q^26 + 4*q^27 + 4*q^28 + 2*q^29 - 2*q^30 - 10*q^31 - 5*q^32 - 4*q^33 - 2*q^34 + 4*q^35 - q^36 - 2*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + q^4 - q^5 + (a - 3)*q^6 + 2*q^7 - a*q^8 + (-2*a + 1)*q^9 - a*q^10 + (a - 3)*q^11 + (-a + 1)*q^12 + q^13 + 2*a*q^14 + (a - 1)*q^15 - 5*q^16 + 2*a*q^17 + (a - 6)*q^18 + (3*a - 1)*q^19 - q^20 + (-2*a + 2)*q^21 + (-3*a + 3)*q^22 + (a + 3)*q^23 + (-a + 3)*q^24 + q^25 + a*q^26 + 4*q^27 + 2*q^28 + (-2*a - 6)*q^29 + (-a + 3)*q^30 + (-3*a + 5)*q^31 - 3*a*q^32 + (4*a - 6)*q^33 + 6*q^34 - 2*q^35 + (-2*a + 1)*q^36 - 4*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-2*a - 1)*q^4 + q^5 + (-a + 1)*q^6 - 2*a*q^7 + (a - 2)*q^8 - q^9 + a*q^10 + (-a + 1)*q^11 + (a - 3)*q^12 - q^13 + (4*a - 2)*q^14 + (a + 1)*q^15 + 3*q^16 + (-2*a - 4)*q^17 - a*q^18 + (a + 3)*q^19 + (-2*a - 1)*q^20 + (2*a - 2)*q^21 + (3*a - 1)*q^22 + (-a - 1)*q^23 + (-3*a - 1)*q^24 + q^25 - a*q^26 + (-4*a - 4)*q^27 + (-6*a + 4)*q^28 + (4*a + 4)*q^29 + (-a + 1)*q^30 + (3*a + 9)*q^31 + (a + 4)*q^32 + 2*a*q^33 - 2*q^34 - 2*a*q^35 + (2*a + 1)*q^36 + (6*a + 6)*q^37 + O(q^38)
*]> ;  // time = 5.169 seconds




J[66] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 66, 66, 66, 33, 11 ], new_dimensions := [ 1, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 5, 1, 1, 1, 0, 9, 1, 1, 5, 9, 0 ], ap_traces := [
[ -1, 1, 0, 2, -1, -4, -6, -4, 6, 6, 8, -10 ],
[ 1, -1, 2, -4, -1, -6, 2, 4, 4, 6, 0, 6 ],
[ 1, 1, -4, -2, 1, 4, -2, 0, -6, 10, -8, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ]
], tamagawa_numbers := [
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ]
], torsion_upper_bounds := [ 3, 1, 5 ], torsion_lower_bounds := [ 3, 1, 1 ], l_ratios := [ 1/3, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/25 ], eigenvalues := [*
[ -1, 1, 0, 2, -1, -4, -6, -4, 6, 6, 8, -10 ],
[ 1, -1, 2, -4, -1, -6, 2, 4, 4, 6, 0, 6 ],
[ 1, 1, -4, -2, 1, 4, -2, 0, -6, 10, -8, -2 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - q^6 + 2*q^7 - q^8 + q^9 - q^11 + q^12 - 4*q^13 - 2*q^14 + q^16 - 6*q^17 - q^18 - 4*q^19 + 2*q^21 + q^22 + 6*q^23 - q^24 - 5*q^25 + 4*q^26 + q^27 + 2*q^28 + 6*q^29 + 8*q^31 - q^32 - q^33 + 6*q^34 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 2*q^5 - q^6 - 4*q^7 + q^8 + q^9 + 2*q^10 - q^11 - q^12 - 6*q^13 - 4*q^14 - 2*q^15 + q^16 + 2*q^17 + q^18 + 4*q^19 + 2*q^20 + 4*q^21 - q^22 + 4*q^23 - q^24 - q^25 - 6*q^26 - q^27 - 4*q^28 + 6*q^29 - 2*q^30 + q^32 + q^33 + 2*q^34 - 8*q^35 + q^36 + 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - 4*q^5 + q^6 - 2*q^7 + q^8 + q^9 - 4*q^10 + q^11 + q^12 + 4*q^13 - 2*q^14 - 4*q^15 + q^16 - 2*q^17 + q^18 - 4*q^20 - 2*q^21 + q^22 - 6*q^23 + q^24 + 11*q^25 + 4*q^26 + q^27 - 2*q^28 + 10*q^29 - 4*q^30 - 8*q^31 + q^32 + q^33 - 2*q^34 + 8*q^35 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 19.689 seconds




J[67] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 67, 67, 67 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 5, 1, 0, 1, 5, 1, 0 ], ap_traces := [
[ 2, -2, 2, -2, -4, 2, 3, 7, 9, -5, -10, -1 ],
[ -3, -3, -6, -1, 0, -7, -6, 1, 6, -6, -2, -1 ],
[ -1, 1, 4, 1, 2, -1, 6, -11, -2, 10, 0, 3 ]
], hecke_fields := [
x - 1,
x^2 + 3*x + 1,
x^2 + x - 1
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 11 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 11 ]
], torsion_upper_bounds := [ 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 11 ], l_ratios := [ 1, 0, 1/11 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 2, -2, 2, -2, -4, 2, 3, 7, 9, -5, -10, -1 ],
[
a,
-a - 3,
-3,
3*a + 4,
-2*a - 3,
-3*a - 8,
-2*a - 6,
3*a + 5,
-4*a - 3,
4*a + 3,
-1,
3*a + 4
],
[
a,
a + 1,
-2*a + 1,
-a,
1,
a,
-2*a + 2,
a - 5,
4*a + 1,
4*a + 7,
6*a + 3,
a + 2
]
*], q_expansions := [*
q + 2*q^2 - 2*q^3 + 2*q^4 + 2*q^5 - 4*q^6 - 2*q^7 + q^9 + 4*q^10 - 4*q^11 - 4*q^12 + 2*q^13 - 4*q^14 - 4*q^15 - 4*q^16 + 3*q^17 + 2*q^18 + 7*q^19 + 4*q^20 + 4*q^21 - 8*q^22 + 9*q^23 - q^25 + 4*q^26 + 4*q^27 - 4*q^28 - 5*q^29 - 8*q^30 - 10*q^31 - 8*q^32 + 8*q^33 + 6*q^34 - 4*q^35 + 2*q^36 - q^37 + O(q^38),
q + a*q^2 + (-a - 3)*q^3 + (-3*a - 3)*q^4 - 3*q^5 + q^6 + (3*a + 4)*q^7 + (4*a + 3)*q^8 + (3*a + 5)*q^9 - 3*a*q^10 + (-2*a - 3)*q^11 + (3*a + 6)*q^12 + (-3*a - 8)*q^13 + (-5*a - 3)*q^14 + (3*a + 9)*q^15 + (-3*a + 2)*q^16 + (-2*a - 6)*q^17 + (-4*a - 3)*q^18 + (3*a + 5)*q^19 + (9*a + 9)*q^20 + (-4*a - 9)*q^21 + (3*a + 2)*q^22 + (-4*a - 3)*q^23 + (-3*a - 5)*q^24 + 4*q^25 + (a + 3)*q^26 + (-2*a - 3)*q^27 + (6*a - 3)*q^28 + (4*a + 3)*q^29 - 3*q^30 - q^31 + (3*a - 3)*q^32 + (3*a + 7)*q^33 + 2*q^34 + (-9*a - 12)*q^35 + (3*a - 6)*q^36 + (3*a + 4)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-a - 1)*q^4 + (-2*a + 1)*q^5 + q^6 - a*q^7 + (-2*a - 1)*q^8 + (a - 1)*q^9 + (3*a - 2)*q^10 + q^11 + (-a - 2)*q^12 + a*q^13 + (a - 1)*q^14 + (a - 1)*q^15 + 3*a*q^16 + (-2*a + 2)*q^17 + (-2*a + 1)*q^18 + (a - 5)*q^19 + (-a + 1)*q^20 - q^21 + a*q^22 + (4*a + 1)*q^23 + (-a - 3)*q^24 - 8*a*q^25 + (-a + 1)*q^26 + (-4*a - 3)*q^27 + q^28 + (4*a + 7)*q^29 + (-2*a + 1)*q^30 + (6*a + 3)*q^31 + (a + 5)*q^32 + (a + 1)*q^33 + (4*a - 2)*q^34 + (-3*a + 2)*q^35 + a*q^36 + (a + 2)*q^37 + O(q^38)
*]> ;  // time = 0.94 seconds




J[69] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 69, 69, 23 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 11, 1, 11, 0 ], ap_traces := [
[ 1, 1, 0, -2, 4, -6, 4, 2, -1, 2, 4, 2 ],
[ 0, -2, -2, 2, 8, 0, -10, 10, 2, 0, -4, 0 ]
], hecke_fields := [
x - 1,
x^2 - 5
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 1, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 1, 0, -2, 4, -6, 4, 2, -1, 2, 4, 2 ],
[
a,
-1,
-a - 1,
-a + 1,
4,
2*a,
-a - 5,
-a + 5,
1,
-2*a,
2*a - 2,
-2*a
]
*], q_expansions := [*
q + q^2 + q^3 - q^4 + q^6 - 2*q^7 - 3*q^8 + q^9 + 4*q^11 - q^12 - 6*q^13 - 2*q^14 - q^16 + 4*q^17 + q^18 + 2*q^19 - 2*q^21 + 4*q^22 - q^23 - 3*q^24 - 5*q^25 - 6*q^26 + q^27 + 2*q^28 + 2*q^29 + 4*q^31 + 5*q^32 + 4*q^33 + 4*q^34 - q^36 + 2*q^37 + O(q^38),
q + a*q^2 - q^3 + 3*q^4 + (-a - 1)*q^5 - a*q^6 + (-a + 1)*q^7 + a*q^8 + q^9 + (-a - 5)*q^10 + 4*q^11 - 3*q^12 + 2*a*q^13 + (a - 5)*q^14 + (a + 1)*q^15 - q^16 + (-a - 5)*q^17 + a*q^18 + (-a + 5)*q^19 + (-3*a - 3)*q^20 + (a - 1)*q^21 + 4*a*q^22 + q^23 - a*q^24 + (2*a + 1)*q^25 + 10*q^26 - q^27 + (-3*a + 3)*q^28 - 2*a*q^29 + (a + 5)*q^30 + (2*a - 2)*q^31 - 3*a*q^32 - 4*q^33 + (-5*a - 5)*q^34 + 4*q^35 + 3*q^36 - 2*a*q^37 + O(q^38)
*]> ;  // time = 5.06 seconds




J[70] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 70, 35, 35, 14 ], new_dimensions := [ 1, 1, 2, 1 ], dimensions := [ 1, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 1, 3, 1, 1, 0, 1, 1, 3, 1, 0 ], ap_traces := [
[ 1, 0, -1, -1, 4, -6, 2, 0, 0, 6, 8, -10 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ 1, 0, -1, -1, 4, -6, 2, 0, 0, 6, 8, -10 ]
*], q_expansions := [*
q + q^2 + q^4 - q^5 - q^7 + q^8 - 3*q^9 - q^10 + 4*q^11 - 6*q^13 - q^14 + q^16 + 2*q^17 - 3*q^18 - q^20 + 4*q^22 + q^25 - 6*q^26 - q^28 + 6*q^29 + 8*q^31 + q^32 + 2*q^34 + q^35 - 3*q^36 - 10*q^37 + O(q^38)
*]> ;  // time = 14.431 seconds




J[71] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 71, 71 ], new_dimensions := [ 3, 3 ], dimensions := [ 3, 3 ], intersection_graph := [ 0, 9, 9, 0 ], ap_traces := [
[ 0, -1, -3, 2, -2, 12, 2, 11, 8, -5, -6, 9 ],
[ -1, 1, 5, 2, 0, -6, -2, 1, -12, 11, 12, -15 ]
], hecke_fields := [
x^3 - 5*x + 3,
x^3 + x^2 - 4*x - 3
], atkin_lehners := [
[ -1 ],
[ -1 ]
], component_group_orders := [
[ 5 ],
[ 7 ]
], tamagawa_numbers := [
[ 5 ],
[ 7 ]
], torsion_upper_bounds := [ 5, 7 ], torsion_lower_bounds := [ 5, 7 ], l_ratios := [ 1/5, 1/7 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
-a^2 + 3,
-a - 1,
2*a^2 + 2*a - 6,
-2*a^2 - 2*a + 6,
4,
2*a^2 + 2*a - 6,
-a^2 - a + 7,
2*a^2 - 4,
a^2 + 2*a - 5,
-2*a - 2,
-3*a^2 - a + 13
],
[
a,
-a,
-a^2 + a + 5,
-2*a,
2*a^2 - 6,
-2*a^2 + 4,
2*a^2 + 2*a - 6,
a^2 + 2*a - 2,
-4,
-2*a^2 + a + 10,
4,
-a^2 - 2
]
*], q_expansions := [*
q + a*q^2 + (-a^2 + 3)*q^3 + (a^2 - 2)*q^4 + (-a - 1)*q^5 + (-2*a + 3)*q^6 + (2*a^2 + 2*a - 6)*q^7 + (a - 3)*q^8 + (-a^2 - 3*a + 6)*q^9 + (-a^2 - a)*q^10 + (-2*a^2 - 2*a + 6)*q^11 + (3*a - 6)*q^12 + 4*q^13 + (2*a^2 + 4*a - 6)*q^14 + (a^2 + 2*a - 6)*q^15 + (-a^2 - 3*a + 4)*q^16 + (2*a^2 + 2*a - 6)*q^17 + (-3*a^2 + a + 3)*q^18 + (-a^2 - a + 7)*q^19 + (-a^2 - 3*a + 5)*q^20 + (2*a^2 + 2*a - 12)*q^21 + (-2*a^2 - 4*a + 6)*q^22 + (2*a^2 - 4)*q^23 + (3*a^2 - 2*a - 6)*q^24 + (a^2 + 2*a - 4)*q^25 + 4*a*q^26 + (-a^2 + 3*a)*q^27 + 6*q^28 + (a^2 + 2*a - 5)*q^29 + (2*a^2 - a - 3)*q^30 + (-2*a - 2)*q^31 + (-3*a^2 - 3*a + 9)*q^32 + (-2*a^2 - 2*a + 12)*q^33 + (2*a^2 + 4*a - 6)*q^34 + (-4*a^2 - 6*a + 12)*q^35 + (3*a^2 - 6*a - 3)*q^36 + (-3*a^2 - a + 13)*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 5)*q^5 - a^2*q^6 - 2*a*q^7 + (-a^2 + 3)*q^8 + (a^2 - 3)*q^9 + (2*a^2 + a - 3)*q^10 + (2*a^2 - 6)*q^11 + (a^2 - 2*a - 3)*q^12 + (-2*a^2 + 4)*q^13 - 2*a^2*q^14 + (-2*a^2 - a + 3)*q^15 + (-a^2 - a + 1)*q^16 + (2*a^2 + 2*a - 6)*q^17 + (-a^2 + a + 3)*q^18 + (a^2 + 2*a - 2)*q^19 + (a^2 + 3*a - 4)*q^20 + 2*a^2*q^21 + (-2*a^2 + 2*a + 6)*q^22 - 4*q^23 + (-a^2 + a + 3)*q^24 + (-2*a^2 + a + 11)*q^25 + (2*a^2 - 4*a - 6)*q^26 + (a^2 + 2*a - 3)*q^27 + (2*a^2 - 4*a - 6)*q^28 + (-2*a^2 + a + 10)*q^29 + (a^2 - 5*a - 6)*q^30 + 4*q^31 + (2*a^2 - 3*a - 9)*q^32 + (2*a^2 - 2*a - 6)*q^33 + (2*a + 6)*q^34 + (-4*a^2 - 2*a + 6)*q^35 + (-a + 3)*q^36 + (-a^2 - 2)*q^37 + O(q^38)
*]> ;  // time = 0.941 seconds




J[73] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 73, 73, 73 ], new_dimensions := [ 1, 2, 2 ], dimensions := [ 1, 2, 2 ], intersection_graph := [ 0, 1, 3, 1, 0, 1, 3, 1, 0 ], ap_traces := [
[ 1, 0, 2, 2, -2, -6, 2, 8, 4, 2, -2, -6 ],
[ -3, -3, -3, -6, -3, 1, 0, 2, -15, 6, 2, -4 ],
[ 1, 1, -1, -2, 7, -1, -4, -14, 13, 2, 6, 8 ]
], hecke_fields := [
x - 1,
x^2 + 3*x + 1,
x^2 - x - 3
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 3 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 3 ]
], torsion_upper_bounds := [ 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 3 ], l_ratios := [ 1, 0, 1/3 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, 0, 2, 2, -2, -6, 2, 8, 4, 2, -2, -6 ],
[
a,
-a - 3,
a,
-3,
-a - 3,
3*a + 5,
-6*a - 9,
1,
a - 6,
-4*a - 3,
6*a + 10,
-6*a - 11
],
[
a,
-a + 1,
-a,
-1,
a + 3,
a - 1,
2*a - 3,
-7,
a + 6,
-4*a + 3,
2*a + 2,
-2*a + 5
]
*], q_expansions := [*
q + q^2 - q^4 + 2*q^5 + 2*q^7 - 3*q^8 - 3*q^9 + 2*q^10 - 2*q^11 - 6*q^13 + 2*q^14 - q^16 + 2*q^17 - 3*q^18 + 8*q^19 - 2*q^20 - 2*q^22 + 4*q^23 - q^25 - 6*q^26 - 2*q^28 + 2*q^29 - 2*q^31 + 5*q^32 + 2*q^34 + 4*q^35 + 3*q^36 - 6*q^37 + O(q^38),
q + a*q^2 + (-a - 3)*q^3 + (-3*a - 3)*q^4 + a*q^5 + q^6 - 3*q^7 + (4*a + 3)*q^8 + (3*a + 5)*q^9 + (-3*a - 1)*q^10 + (-a - 3)*q^11 + (3*a + 6)*q^12 + (3*a + 5)*q^13 - 3*a*q^14 + q^15 + (-3*a + 2)*q^16 + (-6*a - 9)*q^17 + (-4*a - 3)*q^18 + q^19 + (6*a + 3)*q^20 + (3*a + 9)*q^21 + q^22 + (a - 6)*q^23 + (-3*a - 5)*q^24 + (-3*a - 6)*q^25 + (-4*a - 3)*q^26 + (-2*a - 3)*q^27 + (9*a + 9)*q^28 + (-4*a - 3)*q^29 + a*q^30 + (6*a + 10)*q^31 + (3*a - 3)*q^32 + (3*a + 8)*q^33 + (9*a + 6)*q^34 - 3*a*q^35 + (3*a - 6)*q^36 + (-6*a - 11)*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + (a + 1)*q^4 - a*q^5 - 3*q^6 - q^7 + 3*q^8 + (-a + 1)*q^9 + (-a - 3)*q^10 + (a + 3)*q^11 + (-a - 2)*q^12 + (a - 1)*q^13 - a*q^14 + 3*q^15 + (a - 2)*q^16 + (2*a - 3)*q^17 - 3*q^18 - 7*q^19 + (-2*a - 3)*q^20 + (a - 1)*q^21 + (4*a + 3)*q^22 + (a + 6)*q^23 + (-3*a + 3)*q^24 + (a - 2)*q^25 + 3*q^26 + (2*a + 1)*q^27 + (-a - 1)*q^28 + (-4*a + 3)*q^29 + 3*a*q^30 + (2*a + 2)*q^31 + (-a - 3)*q^32 - 3*a*q^33 + (-a + 6)*q^34 + a*q^35 + (-a - 2)*q^36 + (-2*a + 5)*q^37 + O(q^38)
*]> ;  // time = 0.96 seconds




J[74] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 74, 74, 37, 37 ], new_dimensions := [ 2, 2, 1, 1 ], dimensions := [ 2, 2, 2, 2 ], intersection_graph := [ 0, 1, 1, 3, 1, 0, 5, 1, 1, 5, 0, 1, 3, 1, 1, 0 ], ap_traces := [
[ -2, 3, -1, 2, -1, -1, -12, 4, -3, 3, 3, 2 ],
[ 2, -1, 1, -2, -5, 1, 0, 0, -1, -3, 17, -2 ]
], hecke_fields := [
x^2 - 3*x - 1,
x^2 + x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 3 ],
[ 95, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 95, 1 ]
], torsion_upper_bounds := [ 3, 19 ], torsion_lower_bounds := [ 3, 19 ], l_ratios := [ 1/3, 5/19 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
-1,
a,
-a + 1,
-2*a + 4,
-a + 1,
a - 2,
-6,
2,
3*a - 6,
-3*a + 6,
-a + 3,
1
],
[
1,
a,
-3*a - 1,
2*a,
-a - 3,
3*a + 2,
4*a + 2,
-4*a - 2,
-3*a - 2,
7*a + 2,
a + 9,
-1
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (-a + 1)*q^5 - a*q^6 + (-2*a + 4)*q^7 - q^8 + (3*a - 2)*q^9 + (a - 1)*q^10 + (-a + 1)*q^11 + a*q^12 + (a - 2)*q^13 + (2*a - 4)*q^14 + (-2*a - 1)*q^15 + q^16 - 6*q^17 + (-3*a + 2)*q^18 + 2*q^19 + (-a + 1)*q^20 + (-2*a - 2)*q^21 + (a - 1)*q^22 + (3*a - 6)*q^23 - a*q^24 + (a - 3)*q^25 + (-a + 2)*q^26 + (4*a + 3)*q^27 + (-2*a + 4)*q^28 + (-3*a + 6)*q^29 + (2*a + 1)*q^30 + (-a + 3)*q^31 - q^32 + (-2*a - 1)*q^33 + 6*q^34 + 6*q^35 + (3*a - 2)*q^36 + q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-3*a - 1)*q^5 + a*q^6 + 2*a*q^7 + q^8 + (-a - 2)*q^9 + (-3*a - 1)*q^10 + (-a - 3)*q^11 + a*q^12 + (3*a + 2)*q^13 + 2*a*q^14 + (2*a - 3)*q^15 + q^16 + (4*a + 2)*q^17 + (-a - 2)*q^18 + (-4*a - 2)*q^19 + (-3*a - 1)*q^20 + (-2*a + 2)*q^21 + (-a - 3)*q^22 + (-3*a - 2)*q^23 + a*q^24 + (-3*a + 5)*q^25 + (3*a + 2)*q^26 + (-4*a - 1)*q^27 + 2*a*q^28 + (7*a + 2)*q^29 + (2*a - 3)*q^30 + (a + 9)*q^31 + q^32 + (-2*a - 1)*q^33 + (4*a + 2)*q^34 + (4*a - 6)*q^35 + (-a - 2)*q^36 - q^37 + O(q^38)
*]> ;  // time = 9.699 seconds




J[77] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 77, 77, 77, 77, 11 ], new_dimensions := [ 1, 1, 1, 2, 1 ], dimensions := [ 1, 1, 1, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 0, 5, 1, 1, 1, 5, 0, 1, 1, 3, 1, 1, 0 ], ap_traces := [
[ 0, -3, -1, -1, -1, -4, 2, -6, -5, 10, 1, -5 ],
[ 1, 2, -2, -1, 1, 4, 4, 0, -4, -6, 10, -6 ],
[ 0, 1, 3, 1, -1, -4, -6, 2, 3, -6, 5, 11 ],
[ 0, 2, -4, 2, -2, 2, -2, 4, -4, 8, -10, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 5
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 3, 3 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 3, 1 ], l_ratios := [ 0, 1, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ 0, -3, -1, -1, -1, -4, 2, -6, -5, 10, 1, -5 ],
[ 1, 2, -2, -1, 1, 4, 4, 0, -4, -6, 10, -6 ],
[ 0, 1, 3, 1, -1, -4, -6, 2, 3, -6, 5, 11 ],
[
a,
-a + 1,
-2,
1,
-1,
a + 1,
-a - 1,
2*a + 2,
2*a - 2,
2*a + 4,
a - 5,
-2*a - 4
]
*], q_expansions := [*
q - 3*q^3 - 2*q^4 - q^5 - q^7 + 6*q^9 - q^11 + 6*q^12 - 4*q^13 + 3*q^15 + 4*q^16 + 2*q^17 - 6*q^19 + 2*q^20 + 3*q^21 - 5*q^23 - 4*q^25 - 9*q^27 + 2*q^28 + 10*q^29 + q^31 + 3*q^33 + q^35 - 12*q^36 - 5*q^37 + O(q^38),
q + q^2 + 2*q^3 - q^4 - 2*q^5 + 2*q^6 - q^7 - 3*q^8 + q^9 - 2*q^10 + q^11 - 2*q^12 + 4*q^13 - q^14 - 4*q^15 - q^16 + 4*q^17 + q^18 + 2*q^20 - 2*q^21 + q^22 - 4*q^23 - 6*q^24 - q^25 + 4*q^26 - 4*q^27 + q^28 - 6*q^29 - 4*q^30 + 10*q^31 + 5*q^32 + 2*q^33 + 4*q^34 + 2*q^35 - q^36 - 6*q^37 + O(q^38),
q + q^3 - 2*q^4 + 3*q^5 + q^7 - 2*q^9 - q^11 - 2*q^12 - 4*q^13 + 3*q^15 + 4*q^16 - 6*q^17 + 2*q^19 - 6*q^20 + q^21 + 3*q^23 + 4*q^25 - 5*q^27 - 2*q^28 - 6*q^29 + 5*q^31 - q^33 + 3*q^35 + 4*q^36 + 11*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + 3*q^4 - 2*q^5 + (a - 5)*q^6 + q^7 + a*q^8 + (-2*a + 3)*q^9 - 2*a*q^10 - q^11 + (-3*a + 3)*q^12 + (a + 1)*q^13 + a*q^14 + (2*a - 2)*q^15 - q^16 + (-a - 1)*q^17 + (3*a - 10)*q^18 + (2*a + 2)*q^19 - 6*q^20 + (-a + 1)*q^21 - a*q^22 + (2*a - 2)*q^23 + (a - 5)*q^24 - q^25 + (a + 5)*q^26 + (-2*a + 10)*q^27 + 3*q^28 + (2*a + 4)*q^29 + (-2*a + 10)*q^30 + (a - 5)*q^31 - 3*a*q^32 + (a - 1)*q^33 + (-a - 5)*q^34 - 2*q^35 + (-6*a + 9)*q^36 + (-2*a - 4)*q^37 + O(q^38)
*]> ;  // time = 6.4 seconds




J[78] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 78, 39, 39, 26, 26 ], new_dimensions := [ 1, 1, 2, 1, 1 ], dimensions := [ 1, 2, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 7, 5, 1, 1, 0, 1, 1, 1, 7, 1, 0 ], ap_traces := [
[ -1, -1, 2, 4, -4, 1, 2, -8, 0, 6, -4, -2 ]
], hecke_fields := [
x - 1
], atkin_lehners := [
[ 1, 1, -1 ]
], component_group_orders := [
[ 1, 5, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1 ], torsion_lower_bounds := [ 1 ], l_ratios := [ 1 ], analytic_sha_upper_bounds := [ 1 ], analytic_sha_lower_bounds := [ 1 ], eigenvalues := [*
[ -1, -1, 2, 4, -4, 1, 2, -8, 0, 6, -4, -2 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + 2*q^5 + q^6 + 4*q^7 - q^8 + q^9 - 2*q^10 - 4*q^11 - q^12 + q^13 - 4*q^14 - 2*q^15 + q^16 + 2*q^17 - q^18 - 8*q^19 + 2*q^20 - 4*q^21 + 4*q^22 + q^24 - q^25 - q^26 - q^27 + 4*q^28 + 6*q^29 + 2*q^30 - 4*q^31 - q^32 + 4*q^33 - 2*q^34 + 8*q^35 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 25.54 seconds




J[79] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 79, 79 ], new_dimensions := [ 1, 5 ], dimensions := [ 1, 5 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -1, -3, -1, -2, 3, -6, 4, 2, -6, -10, -2 ],
[ 0, 1, 7, -5, 2, -3, 10, -4, 2, 6, 2, 0 ]
], hecke_fields := [
x - 1,
x^5 - 6*x^3 + 8*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 13 ]
], tamagawa_numbers := [
[ 1 ],
[ 13 ]
], torsion_upper_bounds := [ 1, 13 ], torsion_lower_bounds := [ 1, 13 ], l_ratios := [ 0, 1/13 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -1, -3, -1, -2, 3, -6, 4, 2, -6, -10, -2 ],
[
a,
-a^4 + a^3 + 3*a^2 - 3*a + 1,
a^4 - 4*a^2 - a + 3,
a^4 - a^3 - 5*a^2 + 3*a + 3,
-a^4 - 2*a^3 + 6*a^2 + 7*a - 6,
a^3 + a^2 - 2*a - 3,
-2*a^3 + 6*a + 2,
-3*a^3 + 3*a^2 + 10*a - 8,
2*a^4 + a^3 - 9*a^2 - 4*a + 6,
2*a^3 - 2*a^2 - 4*a + 6,
-a^4 + 2*a^3 + 6*a^2 - 5*a - 6,
2*a^4 - 2*a^3 - 10*a^2 + 4*a + 8
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - 3*q^5 + q^6 - q^7 + 3*q^8 - 2*q^9 + 3*q^10 - 2*q^11 + q^12 + 3*q^13 + q^14 + 3*q^15 - q^16 - 6*q^17 + 2*q^18 + 4*q^19 + 3*q^20 + q^21 + 2*q^22 + 2*q^23 - 3*q^24 + 4*q^25 - 3*q^26 + 5*q^27 + q^28 - 6*q^29 - 3*q^30 - 10*q^31 - 5*q^32 + 2*q^33 + 6*q^34 + 3*q^35 + 2*q^36 - 2*q^37 + O(q^38),
q + a*q^2 + (-a^4 + a^3 + 3*a^2 - 3*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^4 - 4*a^2 - a + 3)*q^5 + (a^4 - 3*a^3 - 3*a^2 + 9*a - 1)*q^6 + (a^4 - a^3 - 5*a^2 + 3*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 + a^3 + 5*a^2 - 5*a - 2)*q^9 + (2*a^3 - a^2 - 5*a + 1)*q^10 + (-a^4 - 2*a^3 + 6*a^2 + 7*a - 6)*q^11 + (-a^4 + a^3 + 3*a^2 - 3*a - 1)*q^12 + (a^3 + a^2 - 2*a - 3)*q^13 + (-a^4 + a^3 + 3*a^2 - 5*a + 1)*q^14 + (-a^4 + 3*a^3 + a^2 - 9*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-2*a^3 + 6*a + 2)*q^17 + (a^4 - a^3 - 5*a^2 + 6*a - 1)*q^18 + (-3*a^3 + 3*a^2 + 10*a - 8)*q^19 + (-a^3 + 3*a^2 + 3*a - 6)*q^20 + (3*a^4 - 3*a^3 - 11*a^2 + 11*a + 1)*q^21 + (-2*a^4 + 7*a^2 + 2*a - 1)*q^22 + (2*a^4 + a^3 - 9*a^2 - 4*a + 6)*q^23 + (-a^4 + 3*a^3 + 3*a^2 - 11*a + 1)*q^24 + (2*a^4 - 3*a^3 - 7*a^2 + 8*a + 2)*q^25 + (a^4 + a^3 - 2*a^2 - 3*a)*q^26 + (-3*a^4 + 7*a^3 + 11*a^2 - 23*a - 1)*q^27 + (-a^4 - a^3 + 5*a^2 + 3*a - 7)*q^28 + (2*a^3 - 2*a^2 - 4*a + 6)*q^29 + (3*a^4 - 5*a^3 - 9*a^2 + 11*a - 1)*q^30 + (-a^4 + 2*a^3 + 6*a^2 - 5*a - 6)*q^31 + (-2*a^3 + 4*a + 1)*q^32 + (-2*a^4 + 8*a^2 + 4*a - 4)*q^33 + (-2*a^4 + 6*a^2 + 2*a)*q^34 + (a^4 - a^3 - 7*a^2 + 3*a + 9)*q^35 + (a^4 - a^3 - 4*a^2 + a + 5)*q^36 + (2*a^4 - 2*a^3 - 10*a^2 + 4*a + 8)*q^37 + O(q^38)
*]> ;  // time = 1.02 seconds




J[82] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 82, 82, 41 ], new_dimensions := [ 1, 2, 3 ], dimensions := [ 1, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, -2, -2, -4, -2, 4, -2, 6, -8, 0, -8, 2 ],
[ 2, 0, 0, -4, 0, 0, 4, -8, 8, 8, -8, 0 ]
], hecke_fields := [
x - 1,
x^2 - 2
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 7 ], torsion_lower_bounds := [ 1, 7 ], l_ratios := [ 0, 1/7 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -2, -2, -4, -2, 4, -2, 6, -8, 0, -8, 2 ],
[
1,
a,
-2*a,
-a - 2,
3*a,
0,
4*a + 2,
-a - 4,
-2*a + 4,
-4*a + 4,
2*a - 4,
6*a
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 - 2*q^5 + 2*q^6 - 4*q^7 - q^8 + q^9 + 2*q^10 - 2*q^11 - 2*q^12 + 4*q^13 + 4*q^14 + 4*q^15 + q^16 - 2*q^17 - q^18 + 6*q^19 - 2*q^20 + 8*q^21 + 2*q^22 - 8*q^23 + 2*q^24 - q^25 - 4*q^26 + 4*q^27 - 4*q^28 - 4*q^30 - 8*q^31 - q^32 + 4*q^33 + 2*q^34 + 8*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - 2*a*q^5 + a*q^6 + (-a - 2)*q^7 + q^8 - q^9 - 2*a*q^10 + 3*a*q^11 + a*q^12 + (-a - 2)*q^14 - 4*q^15 + q^16 + (4*a + 2)*q^17 - q^18 + (-a - 4)*q^19 - 2*a*q^20 + (-2*a - 2)*q^21 + 3*a*q^22 + (-2*a + 4)*q^23 + a*q^24 + 3*q^25 - 4*a*q^27 + (-a - 2)*q^28 + (-4*a + 4)*q^29 - 4*q^30 + (2*a - 4)*q^31 + q^32 + 6*q^33 + (4*a + 2)*q^34 + (4*a + 4)*q^35 - q^36 + 6*a*q^37 + O(q^38)
*]> ;  // time = 8.95 seconds




J[83] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 83, 83 ], new_dimensions := [ 1, 6 ], dimensions := [ 1, 6 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, -3, 3, -6, 5, 2, -4, -7, 5, -11 ],
[ 1, 1, 2, 3, -3, 14, -5, -4, -5, -1, 3, 39 ]
], hecke_fields := [
x - 1,
x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2 - 12*x - 8
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 41 ]
], tamagawa_numbers := [
[ 1 ],
[ 41 ]
], torsion_upper_bounds := [ 1, 41 ], torsion_lower_bounds := [ 1, 41 ], l_ratios := [ 0, 1/41 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ -1, -1, -2, -3, 3, -6, 5, 2, -4, -7, 5, -11 ],
[
a,
1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 3/2*a + 4,
-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + 7/2*a^2 - 8*a - 2,
3/4*a^5 - 1/4*a^4 - 25/4*a^3 + 3/4*a^2 + 19/2*a,
-1/4*a^5 + 1/4*a^4 + 5/4*a^3 + 1/4*a^2 - 4,
a^3 - 5*a + 2,
1/4*a^5 - 3/4*a^4 - 7/4*a^3 + 17/4*a^2 + 7/2*a - 4,
3/2*a^5 - 1/2*a^4 - 23/2*a^3 - 1/2*a^2 + 16*a + 4,
-a^5 + 7*a^3 + 3*a^2 - 8*a - 7,
3/2*a^5 - 12*a^3 - 4*a^2 + 39/2*a + 8,
-3/4*a^5 + 3/4*a^4 + 23/4*a^3 - 21/4*a^2 - 8*a + 8,
-3/4*a^5 + 3/4*a^4 + 19/4*a^3 - 13/4*a^2 - 3*a + 8
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - 2*q^5 + q^6 - 3*q^7 + 3*q^8 - 2*q^9 + 2*q^10 + 3*q^11 + q^12 - 6*q^13 + 3*q^14 + 2*q^15 - q^16 + 5*q^17 + 2*q^18 + 2*q^19 + 2*q^20 + 3*q^21 - 3*q^22 - 4*q^23 - 3*q^24 - q^25 + 6*q^26 + 5*q^27 + 3*q^28 - 7*q^29 - 2*q^30 + 5*q^31 - 5*q^32 - 3*q^33 - 5*q^34 + 6*q^35 + 2*q^36 - 11*q^37 + O(q^38),
q + a*q^2 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 3/2*a + 4)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + 7/2*a^2 - 8*a - 2)*q^5 + (1/2*a^5 - 1/2*a^4 - 7/2*a^3 + 3/2*a^2 + 4*a)*q^6 + (3/4*a^5 - 1/4*a^4 - 25/4*a^3 + 3/4*a^2 + 19/2*a)*q^7 + (a^3 - 4*a)*q^8 + (-1/4*a^5 + 1/4*a^4 + 9/4*a^3 - 7/4*a^2 - 5*a + 3)*q^9 + (-a^5 + 7*a^3 + 2*a^2 - 8*a - 4)*q^10 + (-1/4*a^5 + 1/4*a^4 + 5/4*a^3 + 1/4*a^2 - 4)*q^11 + (-a^3 + a^2 + 3*a - 4)*q^12 + (a^3 - 5*a + 2)*q^13 + (1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 11/2*a^2 + 9*a + 6)*q^14 + (a^4 - 7*a^2 + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/4*a^5 - 3/4*a^4 - 7/4*a^3 + 17/4*a^2 + 7/2*a - 4)*q^17 - 2*q^18 + (3/2*a^5 - 1/2*a^4 - 23/2*a^3 - 1/2*a^2 + 16*a + 4)*q^19 + (-a^4 + 5*a^2 - 4)*q^20 + (1/4*a^5 + 1/4*a^4 - 15/4*a^3 + 1/4*a^2 + 23/2*a - 5)*q^21 + (-a^4 + 2*a^3 + 5*a^2 - 7*a - 2)*q^22 + (-a^5 + 7*a^3 + 3*a^2 - 8*a - 7)*q^23 + (-a^5 + 8*a^3 - 12*a)*q^24 + (-a^5 - a^4 + 9*a^3 + 9*a^2 - 14*a - 9)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 + (-a^5 - 1/2*a^4 + 19/2*a^3 + 9/2*a^2 - 35/2*a - 3)*q^27 + (-1/2*a^5 + 1/2*a^4 + 7/2*a^3 - 5/2*a^2 - 7*a + 4)*q^28 + (3/2*a^5 - 12*a^3 - 4*a^2 + 39/2*a + 8)*q^29 + (a^5 - 7*a^3 + 6*a)*q^30 + (-3/4*a^5 + 3/4*a^4 + 23/4*a^3 - 21/4*a^2 - 8*a + 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^5 - a^4 - 4*a^3 + 8*a^2 + 9/2*a - 11)*q^33 + (-1/2*a^5 + 1/2*a^4 + 5/2*a^3 - 3/2*a^2 - a + 2)*q^34 + (a^5 - a^4 - 6*a^3 + 5*a^2 + 3*a - 6)*q^35 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 7/2*a^2 + 8*a - 6)*q^36 + (-3/4*a^5 + 3/4*a^4 + 19/4*a^3 - 13/4*a^2 - 3*a + 8)*q^37 + O(q^38)
*]> ;  // time = 1.029 seconds




J[85] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 85, 85, 85, 17 ], new_dimensions := [ 1, 2, 2, 1 ], dimensions := [ 1, 2, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, 2, -1, -2, 2, 2, 1, 0, 6, -6, -10, 2 ],
[ -2, -4, -2, -4, -8, 0, -2, 0, -4, -4, 0, -4 ],
[ 0, 2, 2, -2, 6, -8, -2, 4, -6, 0, 10, -8 ]
], hecke_fields := [
x - 1,
x^2 + 2*x - 1,
x^2 - 3
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 3 ], l_ratios := [ 1, 0, 1/3 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, 2, -1, -2, 2, 2, 1, 0, 6, -6, -10, 2 ],
[
a,
-a - 3,
-1,
a - 1,
a - 3,
-2*a - 2,
-1,
-2*a - 2,
-a - 3,
-2*a - 4,
3*a + 3,
6*a + 4
],
[
a,
-a + 1,
1,
a - 1,
-a + 3,
-4,
-1,
2*a + 2,
3*a - 3,
2*a,
a + 5,
-2*a - 4
]
*], q_expansions := [*
q + q^2 + 2*q^3 - q^4 - q^5 + 2*q^6 - 2*q^7 - 3*q^8 + q^9 - q^10 + 2*q^11 - 2*q^12 + 2*q^13 - 2*q^14 - 2*q^15 - q^16 + q^17 + q^18 + q^20 - 4*q^21 + 2*q^22 + 6*q^23 - 6*q^24 + q^25 + 2*q^26 - 4*q^27 + 2*q^28 - 6*q^29 - 2*q^30 - 10*q^31 + 5*q^32 + 4*q^33 + q^34 + 2*q^35 - q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 3)*q^3 + (-2*a - 1)*q^4 - q^5 + (-a - 1)*q^6 + (a - 1)*q^7 + (a - 2)*q^8 + (4*a + 7)*q^9 - a*q^10 + (a - 3)*q^11 + (3*a + 5)*q^12 + (-2*a - 2)*q^13 + (-3*a + 1)*q^14 + (a + 3)*q^15 + 3*q^16 - q^17 + (-a + 4)*q^18 + (-2*a - 2)*q^19 + (2*a + 1)*q^20 + 2*q^21 + (-5*a + 1)*q^22 + (-a - 3)*q^23 + (a + 5)*q^24 + q^25 + (2*a - 2)*q^26 + (-8*a - 16)*q^27 + (5*a - 1)*q^28 + (-2*a - 4)*q^29 + (a + 1)*q^30 + (3*a + 3)*q^31 + (a + 4)*q^32 + (2*a + 8)*q^33 - a*q^34 + (-a + 1)*q^35 + (-2*a - 15)*q^36 + (6*a + 4)*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + q^4 + q^5 + (a - 3)*q^6 + (a - 1)*q^7 - a*q^8 + (-2*a + 1)*q^9 + a*q^10 + (-a + 3)*q^11 + (-a + 1)*q^12 - 4*q^13 + (-a + 3)*q^14 + (-a + 1)*q^15 - 5*q^16 - q^17 + (a - 6)*q^18 + (2*a + 2)*q^19 + q^20 + (2*a - 4)*q^21 + (3*a - 3)*q^22 + (3*a - 3)*q^23 + (-a + 3)*q^24 + q^25 - 4*a*q^26 + 4*q^27 + (a - 1)*q^28 + 2*a*q^29 + (a - 3)*q^30 + (a + 5)*q^31 - 3*a*q^32 + (-4*a + 6)*q^33 - a*q^34 + (a - 1)*q^35 + (-2*a + 1)*q^36 + (-2*a - 4)*q^37 + O(q^38)
*]> ;  // time = 6.431 seconds




J[86] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 86, 86, 43, 43 ], new_dimensions := [ 2, 2, 1, 2 ], dimensions := [ 2, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 7, 1, 0, 5, 1, 1, 5, 0, 1, 7, 1, 1, 0 ], ap_traces := [
[ -2, -1, 3, 4, 0, 4, -9, 1, -9, 3, 1, 1 ],
[ 2, 1, -3, 0, -4, 0, -1, 11, 3, -7, 13, -5 ]
], hecke_fields := [
x^2 + x - 5,
x^2 - x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 21, 3 ],
[ 55, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 55, 1 ]
], torsion_upper_bounds := [ 3, 11 ], torsion_lower_bounds := [ 3, 11 ], l_ratios := [ 1/3, 5/11 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
-1,
a,
-a + 1,
2,
0,
2,
a - 4,
-3*a - 1,
-a - 5,
a + 2,
3*a + 2,
3*a + 2
],
[
1,
a,
-a - 1,
-4*a + 2,
4*a - 4,
4*a - 2,
-a,
a + 5,
-3*a + 3,
-3*a - 2,
a + 6,
-a - 2
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (-a + 1)*q^5 - a*q^6 + 2*q^7 - q^8 + (-a + 2)*q^9 + (a - 1)*q^10 + a*q^12 + 2*q^13 - 2*q^14 + (2*a - 5)*q^15 + q^16 + (a - 4)*q^17 + (a - 2)*q^18 + (-3*a - 1)*q^19 + (-a + 1)*q^20 + 2*a*q^21 + (-a - 5)*q^23 - a*q^24 + (-3*a + 1)*q^25 - 2*q^26 - 5*q^27 + 2*q^28 + (a + 2)*q^29 + (-2*a + 5)*q^30 + (3*a + 2)*q^31 - q^32 + (-a + 4)*q^34 + (-2*a + 2)*q^35 + (-a + 2)*q^36 + (3*a + 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a - 1)*q^5 + a*q^6 + (-4*a + 2)*q^7 + q^8 + (a - 2)*q^9 + (-a - 1)*q^10 + (4*a - 4)*q^11 + a*q^12 + (4*a - 2)*q^13 + (-4*a + 2)*q^14 + (-2*a - 1)*q^15 + q^16 - a*q^17 + (a - 2)*q^18 + (a + 5)*q^19 + (-a - 1)*q^20 + (-2*a - 4)*q^21 + (4*a - 4)*q^22 + (-3*a + 3)*q^23 + a*q^24 + (3*a - 3)*q^25 + (4*a - 2)*q^26 + (-4*a + 1)*q^27 + (-4*a + 2)*q^28 + (-3*a - 2)*q^29 + (-2*a - 1)*q^30 + (a + 6)*q^31 + q^32 + 4*q^33 - a*q^34 + (6*a + 2)*q^35 + (a - 2)*q^36 + (-a - 2)*q^37 + O(q^38)
*]> ;  // time = 10.201 seconds




J[87] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 87, 87, 29 ], new_dimensions := [ 2, 3, 2 ], dimensions := [ 2, 3, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 23, 1, 23, 0 ], ap_traces := [
[ 1, 2, 2, -4, 4, -2, 6, -10, -2, -2, -6, 6 ],
[ 2, -3, 0, 4, -8, 4, 4, -2, 6, 3, 6, 8 ]
], hecke_fields := [
x^2 - x - 1,
x^3 - 2*x^2 - 4*x + 7
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ],
[ 23, 1 ]
], tamagawa_numbers := [
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 5, 1 ], torsion_lower_bounds := [ 5, 1 ], l_ratios := [ 1/5, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
1,
-2*a + 2,
-2*a - 1,
2*a + 1,
4*a - 3,
3,
2*a - 6,
6*a - 4,
-1,
-6*a,
-2*a + 4
],
[
a,
-1,
-2*a^2 + 8,
a^2 - a - 2,
a^2 - a - 6,
-a^2 - a + 6,
3*a^2 - a - 10,
2*a - 2,
-2*a^2 + 10,
1,
-2*a^2 + 10,
-2*a + 4
]
*], q_expansions := [*
q + a*q^2 + q^3 + (a - 1)*q^4 + (-2*a + 2)*q^5 + a*q^6 + (-2*a - 1)*q^7 + (-2*a + 1)*q^8 + q^9 - 2*q^10 + (2*a + 1)*q^11 + (a - 1)*q^12 + (4*a - 3)*q^13 + (-3*a - 2)*q^14 + (-2*a + 2)*q^15 - 3*a*q^16 + 3*q^17 + a*q^18 + (2*a - 6)*q^19 + (2*a - 4)*q^20 + (-2*a - 1)*q^21 + (3*a + 2)*q^22 + (6*a - 4)*q^23 + (-2*a + 1)*q^24 + (-4*a + 3)*q^25 + (a + 4)*q^26 + q^27 + (-a - 1)*q^28 - q^29 - 2*q^30 - 6*a*q^31 + (a - 5)*q^32 + (2*a + 1)*q^33 + 3*a*q^34 + (2*a + 2)*q^35 + (a - 1)*q^36 + (-2*a + 4)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-2*a^2 + 8)*q^5 - a*q^6 + (a^2 - a - 2)*q^7 + (2*a^2 - 7)*q^8 + q^9 + (-4*a^2 + 14)*q^10 + (a^2 - a - 6)*q^11 + (-a^2 + 2)*q^12 + (-a^2 - a + 6)*q^13 + (a^2 + 2*a - 7)*q^14 + (2*a^2 - 8)*q^15 + (2*a^2 + a - 10)*q^16 + (3*a^2 - a - 10)*q^17 + a*q^18 + (2*a - 2)*q^19 + (-4*a^2 - 2*a + 12)*q^20 + (-a^2 + a + 2)*q^21 + (a^2 - 2*a - 7)*q^22 + (-2*a^2 + 10)*q^23 + (-2*a^2 + 7)*q^24 + (4*a + 3)*q^25 + (-3*a^2 + 2*a + 7)*q^26 - q^27 + (2*a^2 - a - 3)*q^28 + q^29 + (4*a^2 - 14)*q^30 + (-2*a^2 + 10)*q^31 + (a^2 - 2*a)*q^32 + (-a^2 + a + 6)*q^33 + (5*a^2 + 2*a - 21)*q^34 + (-2*a - 2)*q^35 + (a^2 - 2)*q^36 + (-2*a + 4)*q^37 + O(q^38)
*]> ;  // time = 6.941 seconds




J[89] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 89, 89, 89 ], new_dimensions := [ 1, 1, 5 ], dimensions := [ 1, 1, 5 ], intersection_graph := [ 0, 1, 1, 1, 0, 5, 1, 5, 0 ], ap_traces := [
[ -1, -1, -1, -4, -2, 2, 3, -5, 7, 0, -9, -2 ],
[ 1, 2, -2, 2, -4, 2, 6, -2, 2, -6, 6, 10 ],
[ -1, -3, -1, 8, 6, 0, -13, 13, 1, 2, 19, -14 ]
], hecke_fields := [
x - 1,
x - 1,
x^5 + x^4 - 10*x^3 - 10*x^2 + 21*x + 17
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 11 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 11 ]
], torsion_upper_bounds := [ 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 11 ], l_ratios := [ 0, 1, 1/11 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -1, -1, -4, -2, 2, 3, -5, 7, 0, -9, -2 ],
[ 1, 2, -2, 2, -4, 2, 6, -2, 2, -6, 6, 10 ],
[
a,
-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 5/2*a - 4,
-a^2 + 4,
1/2*a^4 - 4*a^2 - a + 13/2,
-a^3 + 5*a + 2,
-a^4 + a^3 + 8*a^2 - 5*a - 11,
a^4 - a^3 - 7*a^2 + 4*a + 4,
1/2*a^3 - 1/2*a^2 - 3/2*a + 9/2,
a^4 - 3/2*a^3 - 13/2*a^2 + 17/2*a + 11/2,
-a^4 + 9*a^2 - 14,
1/2*a^4 - 3/2*a^3 - 7/2*a^2 + 15/2*a + 8,
a^4 - 2*a^3 - 8*a^2 + 10*a + 9
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - q^5 + q^6 - 4*q^7 + 3*q^8 - 2*q^9 + q^10 - 2*q^11 + q^12 + 2*q^13 + 4*q^14 + q^15 - q^16 + 3*q^17 + 2*q^18 - 5*q^19 + q^20 + 4*q^21 + 2*q^22 + 7*q^23 - 3*q^24 - 4*q^25 - 2*q^26 + 5*q^27 + 4*q^28 - q^30 - 9*q^31 - 5*q^32 + 2*q^33 - 3*q^34 + 4*q^35 + 2*q^36 - 2*q^37 + O(q^38),
q + q^2 + 2*q^3 - q^4 - 2*q^5 + 2*q^6 + 2*q^7 - 3*q^8 + q^9 - 2*q^10 - 4*q^11 - 2*q^12 + 2*q^13 + 2*q^14 - 4*q^15 - q^16 + 6*q^17 + q^18 - 2*q^19 + 2*q^20 + 4*q^21 - 4*q^22 + 2*q^23 - 6*q^24 - q^25 + 2*q^26 - 4*q^27 - 2*q^28 - 6*q^29 - 4*q^30 + 6*q^31 + 5*q^32 - 8*q^33 + 6*q^34 - 4*q^35 - q^36 + 10*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 5/2*a - 4)*q^3 + (a^2 - 2)*q^4 + (-a^2 + 4)*q^5 + (a^4 - 3/2*a^3 - 15/2*a^2 + 13/2*a + 17/2)*q^6 + (1/2*a^4 - 4*a^2 - a + 13/2)*q^7 + (a^3 - 4*a)*q^8 + (a^2 - a - 4)*q^9 + (-a^3 + 4*a)*q^10 + (-a^3 + 5*a + 2)*q^11 + (-3/2*a^4 + 3/2*a^3 + 19/2*a^2 - 15/2*a - 9)*q^12 + (-a^4 + a^3 + 8*a^2 - 5*a - 11)*q^13 + (-1/2*a^4 + a^3 + 4*a^2 - 4*a - 17/2)*q^14 + (1/2*a^4 - 1/2*a^3 - 5/2*a^2 + 5/2*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - a^3 - 7*a^2 + 4*a + 4)*q^17 + (a^3 - a^2 - 4*a)*q^18 + (1/2*a^3 - 1/2*a^2 - 3/2*a + 9/2)*q^19 + (-a^4 + 6*a^2 - 8)*q^20 + (-a^4 + a^3 + 7*a^2 - 4*a - 9)*q^21 + (-a^4 + 5*a^2 + 2*a)*q^22 + (a^4 - 3/2*a^3 - 13/2*a^2 + 17/2*a + 11/2)*q^23 + (a^4 - 5/2*a^3 - 15/2*a^2 + 19/2*a + 17/2)*q^24 + (a^4 - 8*a^2 + 11)*q^25 + (2*a^4 - 2*a^3 - 15*a^2 + 10*a + 17)*q^26 + (1/2*a^3 - 1/2*a^2 - 3/2*a + 5/2)*q^27 + (1/2*a^4 - a^3 - a^2 + 4*a - 9/2)*q^28 + (-a^4 + 9*a^2 - 14)*q^29 + (-a^4 + 5/2*a^3 + 15/2*a^2 - 19/2*a - 17/2)*q^30 + (1/2*a^4 - 3/2*a^3 - 7/2*a^2 + 15/2*a + 8)*q^31 + (-a^4 + 2*a^3 + 10*a^2 - 9*a - 17)*q^32 + (-a^4 + 2*a^3 + 7*a^2 - 8*a - 8)*q^33 + (-2*a^4 + 3*a^3 + 14*a^2 - 17*a - 17)*q^34 + (1/2*a^4 + a^3 - 7*a^2 - 6*a + 35/2)*q^35 + (a^4 - a^3 - 6*a^2 + 2*a + 8)*q^36 + (a^4 - 2*a^3 - 8*a^2 + 10*a + 9)*q^37 + O(q^38)
*]> ;  // time = 1.161 seconds




J[91] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 91, 91, 91, 91 ], new_dimensions := [ 1, 1, 2, 3 ], dimensions := [ 1, 1, 2, 3 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ -2, 0, -3, -1, -6, -1, 4, 5, 3, -5, -3, -4 ],
[ 0, -2, -3, 1, 0, 1, -6, -7, 3, -9, 5, 2 ],
[ 0, 0, 6, 2, 0, -2, 0, -6, -6, 6, -2, -4 ],
[ 1, -2, 2, -3, 2, 3, 4, -4, 10, 24, -4, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2,
x^3 - x^2 - 4*x + 2
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 7, 1 ], torsion_lower_bounds := [ 1, 1, 7, 1 ], l_ratios := [ 0, 0, 1/7, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ -2, 0, -3, -1, -6, -1, 4, 5, 3, -5, -3, -4 ],
[ 0, -2, -3, 1, 0, 1, -6, -7, 3, -9, 5, 2 ],
[
a,
-a,
a + 3,
1,
-3*a,
-1,
-a,
3*a - 3,
2*a - 3,
2*a + 3,
-3*a - 1,
-3*a - 2
],
[
a,
-a^2 + a + 2,
-a + 1,
-1,
a^2 - a - 2,
1,
a^2 + a - 2,
-a - 1,
-a^2 - 2*a + 7,
a^2 + 5,
2*a^2 - a - 7,
a^2 + 3*a - 4
]
*], q_expansions := [*
q - 2*q^2 + 2*q^4 - 3*q^5 - q^7 - 3*q^9 + 6*q^10 - 6*q^11 - q^13 + 2*q^14 - 4*q^16 + 4*q^17 + 6*q^18 + 5*q^19 - 6*q^20 + 12*q^22 + 3*q^23 + 4*q^25 + 2*q^26 - 2*q^28 - 5*q^29 - 3*q^31 + 8*q^32 - 8*q^34 + 3*q^35 - 6*q^36 - 4*q^37 + O(q^38),
q - 2*q^3 - 2*q^4 - 3*q^5 + q^7 + q^9 + 4*q^12 + q^13 + 6*q^15 + 4*q^16 - 6*q^17 - 7*q^19 + 6*q^20 - 2*q^21 + 3*q^23 + 4*q^25 + 4*q^27 - 2*q^28 - 9*q^29 + 5*q^31 - 3*q^35 - 2*q^36 + 2*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a + 3)*q^5 - 2*q^6 + q^7 - 2*a*q^8 - q^9 + (3*a + 2)*q^10 - 3*a*q^11 - q^13 + a*q^14 + (-3*a - 2)*q^15 - 4*q^16 - a*q^17 - a*q^18 + (3*a - 3)*q^19 - a*q^21 - 6*q^22 + (2*a - 3)*q^23 + 4*q^24 + (6*a + 6)*q^25 - a*q^26 + 4*a*q^27 + (2*a + 3)*q^29 + (-2*a - 6)*q^30 + (-3*a - 1)*q^31 + 6*q^33 - 2*q^34 + (a + 3)*q^35 + (-3*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 2)*q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + (-2*a + 2)*q^6 - q^7 + (a^2 - 2)*q^8 + (-2*a + 3)*q^9 + (-a^2 + a)*q^10 + (a^2 - a - 2)*q^11 - 4*q^12 + q^13 - a*q^14 + (-a^2 + 3*a)*q^15 + (-a^2 + 2*a + 2)*q^16 + (a^2 + a - 2)*q^17 + (-2*a^2 + 3*a)*q^18 + (-a - 1)*q^19 - 2*a*q^20 + (a^2 - a - 2)*q^21 + (2*a - 2)*q^22 + (-a^2 - 2*a + 7)*q^23 - 4*q^24 + (a^2 - 2*a - 4)*q^25 + a*q^26 + (4*a - 4)*q^27 + (-a^2 + 2)*q^28 + (a^2 + 5)*q^29 + (2*a^2 - 4*a + 2)*q^30 + (2*a^2 - a - 7)*q^31 + (-a^2 - 2*a + 6)*q^32 + (2*a - 6)*q^33 + (2*a^2 + 2*a - 2)*q^34 + (a - 1)*q^35 + (a^2 - 4*a - 2)*q^36 + (a^2 + 3*a - 4)*q^37 + O(q^38)
*]> ;  // time = 7.149 seconds




J[93] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 93, 93, 31 ], new_dimensions := [ 2, 3, 2 ], dimensions := [ 2, 3, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -3, -2, -4, -4, -6, -2, -4, -8, 2, 2, -2, 2 ],
[ 0, 3, -2, 4, -2, 4, -2, 4, -6, -8, -3, 0 ]
], hecke_fields := [
x^2 + 3*x + 1,
x^3 - 4*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 0, 1 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-1,
-2*a - 5,
2*a + 1,
2*a,
2*a + 2,
-4*a - 8,
-2*a - 7,
-2*a - 2,
2*a + 4,
-1,
-6*a - 8
],
[
a,
1,
-a^2 - a + 2,
-a^2 - a + 4,
2*a^2 - 6,
2*a^2 - 4,
2*a^2 + 2*a - 6,
-a^2 + 3*a + 4,
-2*a - 2,
-4*a^2 - 2*a + 8,
-1,
2*a
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-3*a - 3)*q^4 + (-2*a - 5)*q^5 - a*q^6 + (2*a + 1)*q^7 + (4*a + 3)*q^8 + q^9 + (a + 2)*q^10 + 2*a*q^11 + (3*a + 3)*q^12 + (2*a + 2)*q^13 + (-5*a - 2)*q^14 + (2*a + 5)*q^15 + (-3*a + 2)*q^16 + (-4*a - 8)*q^17 + a*q^18 + (-2*a - 7)*q^19 + (3*a + 9)*q^20 + (-2*a - 1)*q^21 + (-6*a - 2)*q^22 + (-2*a - 2)*q^23 + (-4*a - 3)*q^24 + (8*a + 16)*q^25 + (-4*a - 2)*q^26 - q^27 + (9*a + 3)*q^28 + (2*a + 4)*q^29 + (-a - 2)*q^30 - q^31 + (3*a - 3)*q^32 - 2*a*q^33 + (4*a + 4)*q^34 - q^35 + (-3*a - 3)*q^36 + (-6*a - 8)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 2)*q^5 + a*q^6 + (-a^2 - a + 4)*q^7 - q^8 + q^9 + (-a^2 - 2*a + 1)*q^10 + (2*a^2 - 6)*q^11 + (a^2 - 2)*q^12 + (2*a^2 - 4)*q^13 + (-a^2 + 1)*q^14 + (-a^2 - a + 2)*q^15 + (-2*a^2 - a + 4)*q^16 + (2*a^2 + 2*a - 6)*q^17 + a*q^18 + (-a^2 + 3*a + 4)*q^19 + (-a - 3)*q^20 + (-a^2 - a + 4)*q^21 + (2*a - 2)*q^22 + (-2*a - 2)*q^23 - q^24 + (a^2 + 3*a - 3)*q^25 + (4*a - 2)*q^26 + q^27 + (2*a^2 - a - 7)*q^28 + (-4*a^2 - 2*a + 8)*q^29 + (-a^2 - 2*a + 1)*q^30 - q^31 + (-a^2 - 4*a + 4)*q^32 + (2*a^2 - 6)*q^33 + (2*a^2 + 2*a - 2)*q^34 + (-a^2 + a + 6)*q^35 + (a^2 - 2)*q^36 + 2*a*q^37 + O(q^38)
*]> ;  // time = 7.289 seconds




J[94] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 94, 94, 47 ], new_dimensions := [ 1, 2, 4 ], dimensions := [ 1, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 0, 47, 1, 47, 0 ], ap_traces := [
[ 1, 0, 0, 0, 2, -4, -2, -2, 4, 4, 4, 2 ],
[ -2, 0, 4, -4, 8, -4, 0, -8, 0, 12, 0, 4 ]
], hecke_fields := [
x - 1,
x^2 - 8
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 47, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 1, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 0, 0, 0, 2, -4, -2, -2, 4, 4, 4, 2 ],
[
-1,
a,
-1/2*a + 2,
-a - 2,
-1/2*a + 4,
-1/2*a - 2,
0,
3/2*a - 4,
-a,
3/2*a + 6,
-3*a,
3*a + 2
]
*], q_expansions := [*
q + q^2 + q^4 + q^8 - 3*q^9 + 2*q^11 - 4*q^13 + q^16 - 2*q^17 - 3*q^18 - 2*q^19 + 2*q^22 + 4*q^23 - 5*q^25 - 4*q^26 + 4*q^29 + 4*q^31 + q^32 - 2*q^34 - 3*q^36 + 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a + 2)*q^5 - a*q^6 + (-a - 2)*q^7 - q^8 + 5*q^9 + (1/2*a - 2)*q^10 + (-1/2*a + 4)*q^11 + a*q^12 + (-1/2*a - 2)*q^13 + (a + 2)*q^14 + (2*a - 4)*q^15 + q^16 - 5*q^18 + (3/2*a - 4)*q^19 + (-1/2*a + 2)*q^20 + (-2*a - 8)*q^21 + (1/2*a - 4)*q^22 - a*q^23 - a*q^24 + (-2*a + 1)*q^25 + (1/2*a + 2)*q^26 + 2*a*q^27 + (-a - 2)*q^28 + (3/2*a + 6)*q^29 + (-2*a + 4)*q^30 - 3*a*q^31 - q^32 + (4*a - 4)*q^33 - a*q^35 + 5*q^36 + (3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 9.529 seconds




J[95] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 95, 95, 19 ], new_dimensions := [ 3, 4, 1 ], dimensions := [ 3, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 9, 1, 9, 0 ], ap_traces := [
[ 1, 2, 3, 0, -8, 8, 2, -3, -4, -10, 4, 20 ],
[ -2, 2, -4, 4, 4, 2, 4, 4, -8, 4, 4, -6 ]
], hecke_fields := [
x^3 - x^2 - 3*x + 1,
x^4 + 2*x^3 - 6*x^2 - 8*x + 9
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ],
[ 27, 3 ]
], tamagawa_numbers := [
[ 5, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 5, 3 ], torsion_lower_bounds := [ 5, 3 ], l_ratios := [ 1/5, 1/3 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
-a^2 + 3,
1,
2*a^2 - 2*a - 4,
-2*a - 2,
a^2 - 2*a + 1,
-2*a^2 + 4*a + 4,
-1,
2*a - 2,
2*a^2 - 8,
4*a,
a^2 - 2*a + 5
],
[
a,
-a^3 + 5*a - 2,
-1,
-2*a^2 - 2*a + 8,
2*a^2 + 2*a - 6,
a^3 + 2*a^2 - 3*a - 4,
2*a^3 - 10*a + 6,
1,
-2*a^3 - 2*a^2 + 8*a,
2*a^3 - 10*a + 6,
2*a^3 - 2*a^2 - 10*a + 14,
a^3 - 3*a + 2
]
*], q_expansions := [*
q + a*q^2 + (-a^2 + 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 + 1)*q^6 + (2*a^2 - 2*a - 4)*q^7 + (a^2 - a - 1)*q^8 + (-2*a^2 + 2*a + 5)*q^9 + a*q^10 + (-2*a - 2)*q^11 + (a^2 - 2*a - 5)*q^12 + (a^2 - 2*a + 1)*q^13 + (2*a - 2)*q^14 + (-a^2 + 3)*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-2*a^2 + 4*a + 4)*q^17 + (-a + 2)*q^18 - q^19 + (a^2 - 2)*q^20 + (4*a^2 - 4*a - 12)*q^21 + (-2*a^2 - 2*a)*q^22 + (2*a - 2)*q^23 + (a^2 - 2*a - 3)*q^24 + q^25 + (-a^2 + 4*a - 1)*q^26 + (-2*a^2 + 4*a + 6)*q^27 + (-2*a^2 + 2*a + 8)*q^28 + (2*a^2 - 8)*q^29 + (-a^2 + 1)*q^30 + 4*a*q^31 + (-2*a^2 - a + 4)*q^32 + (4*a^2 - 8)*q^33 + (2*a^2 - 2*a + 2)*q^34 + (2*a^2 - 2*a - 4)*q^35 + (3*a^2 - 2*a - 10)*q^36 + (a^2 - 2*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 5*a - 2)*q^3 + (a^2 - 2)*q^4 - q^5 + (2*a^3 - a^2 - 10*a + 9)*q^6 + (-2*a^2 - 2*a + 8)*q^7 + (a^3 - 4*a)*q^8 + (-2*a + 1)*q^9 - a*q^10 + (2*a^2 + 2*a - 6)*q^11 + (-3*a^3 + 2*a^2 + 15*a - 14)*q^12 + (a^3 + 2*a^2 - 3*a - 4)*q^13 + (-2*a^3 - 2*a^2 + 8*a)*q^14 + (a^3 - 5*a + 2)*q^15 + (-2*a^3 + 8*a - 5)*q^16 + (2*a^3 - 10*a + 6)*q^17 + (-2*a^2 + a)*q^18 + q^19 + (-a^2 + 2)*q^20 + (-2*a^3 - 2*a^2 + 10*a + 2)*q^21 + (2*a^3 + 2*a^2 - 6*a)*q^22 + (-2*a^3 - 2*a^2 + 8*a)*q^23 + (4*a^3 - a^2 - 18*a + 9)*q^24 + q^25 + (3*a^2 + 4*a - 9)*q^26 + (-2*a^3 + 2*a^2 + 10*a - 14)*q^27 + (2*a^3 - 12*a + 2)*q^28 + (2*a^3 - 10*a + 6)*q^29 + (-2*a^3 + a^2 + 10*a - 9)*q^30 + (2*a^3 - 2*a^2 - 10*a + 14)*q^31 + (2*a^3 - 4*a^2 - 13*a + 18)*q^32 + (2*a^2 - 6)*q^33 + (-4*a^3 + 2*a^2 + 22*a - 18)*q^34 + (2*a^2 + 2*a - 8)*q^35 + (-2*a^3 + a^2 + 4*a - 2)*q^36 + (a^3 - 3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 7.601 seconds




J[97] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 97, 97 ], new_dimensions := [ 3, 4 ], dimensions := [ 3, 4 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -4, -4, -3, -7, -7, -2, -3, 5, -12, 1, -8, -2 ],
[ 3, 0, 1, 3, 5, -6, 3, -3, 22, 7, -4, -6 ]
], hecke_fields := [
x^3 + 4*x^2 + 3*x - 1,
x^4 - 3*x^3 - x^2 + 6*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 0, 1 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - 3*a - 2,
2*a^2 + 5*a - 1,
-a^2 - 3*a - 3,
a - 1,
-a - 2,
a^2 + 4*a + 1,
-4*a^2 - 6*a + 7,
-3*a - 8,
-4*a^2 - 14*a - 5,
a^2 - 6,
6*a^2 + 17*a + 2
],
[
a,
-a^2 + a + 2,
-a + 1,
a^3 - a^2 - 4*a + 2,
-2*a^3 + 4*a^2 + 3*a - 3,
-3*a^3 + 4*a^2 + 8*a - 5,
2*a^3 - 3*a^2 - 4*a + 3,
-a^3 + 2*a^2 + 3*a - 4,
-a^3 + 4*a^2 - 1,
a^3 - 2*a^2 + a + 2,
3*a^3 - 7*a^2 - 3*a + 7,
-3*a^3 + 6*a^2 + 6*a - 9
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - 3*a - 2)*q^3 + (a^2 - 2)*q^4 + (2*a^2 + 5*a - 1)*q^5 + (a^2 + a - 1)*q^6 + (-a^2 - 3*a - 3)*q^7 + (-4*a^2 - 7*a + 1)*q^8 + (2*a^2 + 7*a + 3)*q^9 + (-3*a^2 - 7*a + 2)*q^10 + (a - 1)*q^11 + (-a^2 + 2*a + 5)*q^12 + (-a - 2)*q^13 + (a^2 - 1)*q^14 - q^15 + (7*a^2 + 13*a)*q^16 + (a^2 + 4*a + 1)*q^17 + (-a^2 - 3*a + 2)*q^18 + (-4*a^2 - 6*a + 7)*q^19 + (a^2 + a - 1)*q^20 + (3*a^2 + 10*a + 8)*q^21 + (a^2 - a)*q^22 + (-3*a - 8)*q^23 + (4*a^2 + 6*a + 1)*q^24 + (-7*a^2 - 18*a)*q^25 + (-a^2 - 2*a)*q^26 + (a^2 - a - 5)*q^27 + (-2*a^2 + 2*a + 7)*q^28 + (-4*a^2 - 14*a - 5)*q^29 - a*q^30 + (a^2 - 6)*q^31 + (-7*a^2 - 7*a + 5)*q^32 + (2*a^2 + 4*a + 1)*q^33 + (-2*a + 1)*q^34 + (-2*a^2 - 5*a)*q^35 + (-3*a^2 - 9*a - 7)*q^36 + (6*a^2 + 17*a + 2)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 2)*q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + (-a^3 + a^2 + 2*a)*q^6 + (a^3 - a^2 - 4*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 - 2*a^2 - 2*a + 2)*q^9 + (-a^2 + a)*q^10 + (-2*a^3 + 4*a^2 + 3*a - 3)*q^11 + (-2*a^3 + 3*a^2 + 4*a - 5)*q^12 + (-3*a^3 + 4*a^2 + 8*a - 5)*q^13 + (2*a^3 - 3*a^2 - 4*a + 1)*q^14 + (a^3 - 2*a^2 - a + 2)*q^15 + (3*a^3 - 5*a^2 - 6*a + 5)*q^16 + (2*a^3 - 3*a^2 - 4*a + 3)*q^17 + (a^3 - a^2 - 4*a + 1)*q^18 + (-a^3 + 2*a^2 + 3*a - 4)*q^19 + (-a^3 + a^2 + 2*a - 2)*q^20 + (a^3 - 3*a^2 - a + 3)*q^21 + (-2*a^3 + a^2 + 9*a - 2)*q^22 + (-a^3 + 4*a^2 - 1)*q^23 + (-a^3 + 3*a - 2)*q^24 + (a^2 - 2*a - 4)*q^25 + (-5*a^3 + 5*a^2 + 13*a - 3)*q^26 + (a^3 + a^2 - 6*a - 2)*q^27 + (a^3 - 3*a - 2)*q^28 + (a^3 - 2*a^2 + a + 2)*q^29 + (a^3 - 4*a + 1)*q^30 + (3*a^3 - 7*a^2 - 3*a + 7)*q^31 + (2*a^3 - 3*a^2 - 5*a + 3)*q^32 + (-a^3 + 2*a^2 + 5*a - 6)*q^33 + (3*a^3 - 2*a^2 - 9*a + 2)*q^34 + (-a^3 + 2*a^2 + 1)*q^35 + (a^2 - a - 3)*q^36 + (-3*a^3 + 6*a^2 + 6*a - 9)*q^37 + O(q^38)
*]> ;  // time = 1.069 seconds




J[101] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 101, 101 ], new_dimensions := [ 1, 7 ], dimensions := [ 1, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 0, -2, -1, -2, -2, 1, 3, -5, 1, -4, -9, -2 ],
[ 0, 4, -3, 2, 8, -1, -7, 19, -7, -2, 7, 0 ]
], hecke_fields := [
x - 1,
x^7 - 13*x^5 + 2*x^4 + 47*x^3 - 16*x^2 - 43*x + 14
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 25 ]
], tamagawa_numbers := [
[ 1 ],
[ 25 ]
], torsion_upper_bounds := [ 1, 25 ], torsion_lower_bounds := [ 1, 25 ], l_ratios := [ 0, 1/25 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ 0, -2, -1, -2, -2, 1, 3, -5, 1, -4, -9, -2 ],
[
a,
1/4*a^6 + 1/4*a^5 - 5/2*a^4 - 5/2*a^3 + 19/4*a^2 + 17/4*a + 1/2,
-1/2*a^6 - 3/4*a^5 + 11/2*a^4 + 7*a^3 - 29/2*a^2 - 45/4*a + 15/2,
-1/4*a^5 - 1/2*a^4 + 5/2*a^3 + 4*a^2 - 21/4*a - 7/2,
-1/4*a^6 + 3*a^4 - 35/4*a^2 + 5,
3/4*a^6 + a^5 - 17/2*a^4 - 9*a^3 + 91/4*a^2 + 12*a - 10,
3/4*a^6 + 3/4*a^5 - 8*a^4 - 7*a^3 + 79/4*a^2 + 45/4*a - 21/2,
1/2*a^5 - 5*a^3 + 21/2*a + 2,
-1/2*a^6 - 1/2*a^5 + 5*a^4 + 4*a^3 - 21/2*a^2 - 7/2*a + 2,
-1/2*a^6 - 1/2*a^5 + 5*a^4 + 4*a^3 - 19/2*a^2 - 7/2*a - 1,
-a^6 - 3/2*a^5 + 11*a^4 + 15*a^3 - 28*a^2 - 55/2*a + 14,
-5/4*a^6 - 9/4*a^5 + 13*a^4 + 21*a^3 - 113/4*a^2 - 135/4*a + 13/2
]
*], q_expansions := [*
q - 2*q^3 - 2*q^4 - q^5 - 2*q^7 + q^9 - 2*q^11 + 4*q^12 + q^13 + 2*q^15 + 4*q^16 + 3*q^17 - 5*q^19 + 2*q^20 + 4*q^21 + q^23 - 4*q^25 + 4*q^27 + 4*q^28 - 4*q^29 - 9*q^31 + 4*q^33 + 2*q^35 - 2*q^36 - 2*q^37 + O(q^38),
q + a*q^2 + (1/4*a^6 + 1/4*a^5 - 5/2*a^4 - 5/2*a^3 + 19/4*a^2 + 17/4*a + 1/2)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^6 - 3/4*a^5 + 11/2*a^4 + 7*a^3 - 29/2*a^2 - 45/4*a + 15/2)*q^5 + (1/4*a^6 + 3/4*a^5 - 3*a^4 - 7*a^3 + 33/4*a^2 + 45/4*a - 7/2)*q^6 + (-1/4*a^5 - 1/2*a^4 + 5/2*a^3 + 4*a^2 - 21/4*a - 7/2)*q^7 + (a^3 - 4*a)*q^8 + (1/4*a^6 + 1/2*a^5 - 5/2*a^4 - 5*a^3 + 21/4*a^2 + 17/2*a - 1)*q^9 + (-3/4*a^6 - a^5 + 8*a^4 + 9*a^3 - 77/4*a^2 - 14*a + 7)*q^10 + (-1/4*a^6 + 3*a^4 - 35/4*a^2 + 5)*q^11 + (1/4*a^6 - 1/4*a^5 - 5/2*a^4 + 3/2*a^3 + 23/4*a^2 - 5/4*a - 9/2)*q^12 + (3/4*a^6 + a^5 - 17/2*a^4 - 9*a^3 + 91/4*a^2 + 12*a - 10)*q^13 + (-1/4*a^6 - 1/2*a^5 + 5/2*a^4 + 4*a^3 - 21/4*a^2 - 7/2*a)*q^14 + (-3/4*a^6 - 3/4*a^5 + 17/2*a^4 + 15/2*a^3 - 93/4*a^2 - 55/4*a + 25/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3/4*a^6 + 3/4*a^5 - 8*a^4 - 7*a^3 + 79/4*a^2 + 45/4*a - 21/2)*q^17 + (1/2*a^6 + 3/4*a^5 - 11/2*a^4 - 13/2*a^3 + 25/2*a^2 + 39/4*a - 7/2)*q^18 + (1/2*a^5 - 5*a^3 + 21/2*a + 2)*q^19 + (-1/4*a^5 - 1/2*a^4 + 2*a^3 + 3*a^2 - 11/4*a - 9/2)*q^20 + (3/4*a^6 + 1/2*a^5 - 17/2*a^4 - 4*a^3 + 95/4*a^2 + 7/2*a - 14)*q^21 + (-1/4*a^5 + 1/2*a^4 + 3*a^3 - 4*a^2 - 23/4*a + 7/2)*q^22 + (-1/2*a^6 - 1/2*a^5 + 5*a^4 + 4*a^3 - 21/2*a^2 - 7/2*a + 2)*q^23 + (-3/4*a^6 - 3/4*a^5 + 7*a^4 + 8*a^3 - 55/4*a^2 - 65/4*a + 7/2)*q^24 + (3/4*a^6 + 5/4*a^5 - 8*a^4 - 12*a^3 + 75/4*a^2 + 87/4*a - 13/2)*q^25 + (a^6 + 5/4*a^5 - 21/2*a^4 - 25/2*a^3 + 24*a^2 + 89/4*a - 21/2)*q^26 + (-1/2*a^6 - 3/4*a^5 + 11/2*a^4 + 13/2*a^3 - 25/2*a^2 - 31/4*a + 3/2)*q^27 + (-1/2*a^6 - 1/4*a^5 + 11/2*a^4 + 3/2*a^3 - 31/2*a^2 - 1/4*a + 21/2)*q^28 + (-1/2*a^6 - 1/2*a^5 + 5*a^4 + 4*a^3 - 19/2*a^2 - 7/2*a - 1)*q^29 + (-3/4*a^6 - 5/4*a^5 + 9*a^4 + 12*a^3 - 103/4*a^2 - 79/4*a + 21/2)*q^30 + (-a^6 - 3/2*a^5 + 11*a^4 + 15*a^3 - 28*a^2 - 55/2*a + 14)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3/4*a^6 - 5/4*a^5 + 9*a^4 + 11*a^3 - 111/4*a^2 - 59/4*a + 33/2)*q^33 + (3/4*a^6 + 7/4*a^5 - 17/2*a^4 - 31/2*a^3 + 93/4*a^2 + 87/4*a - 21/2)*q^34 + (-1/4*a^6 - a^5 + 2*a^4 + 10*a^3 + 1/4*a^2 - 18*a - 7)*q^35 + (1/4*a^6 - 5/2*a^4 - a^3 + 29/4*a^2 + a - 5)*q^36 + (-5/4*a^6 - 9/4*a^5 + 13*a^4 + 21*a^3 - 113/4*a^2 - 135/4*a + 13/2)*q^37 + O(q^38)
*]> ;  // time = 1.149 seconds




J[102] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 102, 102, 102, 51, 51, 34, 17 ], new_dimensions := [ 1, 1, 1, 1, 2, 1, 1 ], dimensions := [ 1, 1, 1, 2, 4, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 0, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, -1, -4, -2, 0, -6, -1, 4, 6, -4, -6, -4 ],
[ -1, 1, 0, 2, 0, 2, -1, -4, -6, 0, -10, 8 ],
[ 1, 1, -2, 0, -4, -2, 1, 4, 0, -10, 8, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 3, 3, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1 ], torsion_lower_bounds := [ 1, 3, 1 ], l_ratios := [ 0, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -1, -4, -2, 0, -6, -1, 4, 6, -4, -6, -4 ],
[ -1, 1, 0, 2, 0, 2, -1, -4, -6, 0, -10, 8 ],
[ 1, 1, -2, 0, -4, -2, 1, 4, 0, -10, 8, -2 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 4*q^5 + q^6 - 2*q^7 - q^8 + q^9 + 4*q^10 - q^12 - 6*q^13 + 2*q^14 + 4*q^15 + q^16 - q^17 - q^18 + 4*q^19 - 4*q^20 + 2*q^21 + 6*q^23 + q^24 + 11*q^25 + 6*q^26 - q^27 - 2*q^28 - 4*q^29 - 4*q^30 - 6*q^31 - q^32 + q^34 + 8*q^35 + q^36 - 4*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - q^6 + 2*q^7 - q^8 + q^9 + q^12 + 2*q^13 - 2*q^14 + q^16 - q^17 - q^18 - 4*q^19 + 2*q^21 - 6*q^23 - q^24 - 5*q^25 - 2*q^26 + q^27 + 2*q^28 - 10*q^31 - q^32 + q^34 + q^36 + 8*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - 2*q^5 + q^6 + q^8 + q^9 - 2*q^10 - 4*q^11 + q^12 - 2*q^13 - 2*q^15 + q^16 + q^17 + q^18 + 4*q^19 - 2*q^20 - 4*q^22 + q^24 - q^25 - 2*q^26 + q^27 - 10*q^29 - 2*q^30 + 8*q^31 + q^32 - 4*q^33 + q^34 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 37.689 seconds




J[103] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 103, 103 ], new_dimensions := [ 2, 6 ], dimensions := [ 2, 6 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -2, -3, -2, -3, -3, -9, 5, 0, -6, 0, 0 ],
[ 4, 0, 3, -2, -1, -1, 21, -7, 12, 12, -16, 0 ]
], hecke_fields := [
x^2 + 3*x + 1,
x^6 - 4*x^5 - x^4 + 17*x^3 - 9*x^2 - 16*x + 11
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 17 ]
], tamagawa_numbers := [
[ 1 ],
[ 17 ]
], torsion_upper_bounds := [ 1, 17 ], torsion_lower_bounds := [ 1, 17 ], l_ratios := [ 0, 1/17 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-1,
-a - 3,
-1,
a,
3*a + 3,
a - 3,
-3*a - 2,
-4*a - 6,
2*a,
6*a + 9,
-6*a - 9
],
[
a,
-a^5 + 3*a^4 + 3*a^3 - 11*a^2 - a + 8,
2*a^5 - 5*a^4 - 9*a^3 + 19*a^2 + 9*a - 13,
-a^4 + 2*a^3 + 4*a^2 - 5*a - 3,
-a^5 + 2*a^4 + 4*a^3 - 4*a^2 - 4*a - 1,
2*a^5 - 4*a^4 - 11*a^3 + 15*a^2 + 14*a - 11,
-3*a^5 + 7*a^4 + 16*a^3 - 30*a^2 - 21*a + 30,
-a^5 + 3*a^4 + 4*a^3 - 14*a^2 - 3*a + 13,
-4*a^5 + 9*a^4 + 22*a^3 - 38*a^2 - 29*a + 34,
3*a^5 - 8*a^4 - 13*a^3 + 31*a^2 + 14*a - 21,
a^5 - 3*a^4 - 3*a^3 + 11*a^2 + 3*a - 12,
5*a^5 - 13*a^4 - 23*a^3 + 53*a^2 + 27*a - 44
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-3*a - 3)*q^4 + (-a - 3)*q^5 - a*q^6 - q^7 + (4*a + 3)*q^8 - 2*q^9 + q^10 + a*q^11 + (3*a + 3)*q^12 + (3*a + 3)*q^13 - a*q^14 + (a + 3)*q^15 + (-3*a + 2)*q^16 + (a - 3)*q^17 - 2*a*q^18 + (-3*a - 2)*q^19 + (3*a + 6)*q^20 + q^21 + (-3*a - 1)*q^22 + (-4*a - 6)*q^23 + (-4*a - 3)*q^24 + (3*a + 3)*q^25 + (-6*a - 3)*q^26 + 5*q^27 + (3*a + 3)*q^28 + 2*a*q^29 - q^30 + (6*a + 9)*q^31 + (3*a - 3)*q^32 - a*q^33 + (-6*a - 1)*q^34 + (a + 3)*q^35 + (6*a + 6)*q^36 + (-6*a - 9)*q^37 + O(q^38),
q + a*q^2 + (-a^5 + 3*a^4 + 3*a^3 - 11*a^2 - a + 8)*q^3 + (a^2 - 2)*q^4 + (2*a^5 - 5*a^4 - 9*a^3 + 19*a^2 + 9*a - 13)*q^5 + (-a^5 + 2*a^4 + 6*a^3 - 10*a^2 - 8*a + 11)*q^6 + (-a^4 + 2*a^3 + 4*a^2 - 5*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 + 3*a^4 + 5*a^3 - 15*a^2 - 7*a + 17)*q^9 + (3*a^5 - 7*a^4 - 15*a^3 + 27*a^2 + 19*a - 22)*q^10 + (-a^5 + 2*a^4 + 4*a^3 - 4*a^2 - 4*a - 1)*q^11 + (-a^4 + a^3 + 5*a^2 - 3*a - 5)*q^12 + (2*a^5 - 4*a^4 - 11*a^3 + 15*a^2 + 14*a - 11)*q^13 + (-a^5 + 2*a^4 + 4*a^3 - 5*a^2 - 3*a)*q^14 + (a^4 - 3*a^3 - a^2 + 7*a - 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^5 + 7*a^4 + 16*a^3 - 30*a^2 - 21*a + 30)*q^17 + (-a^5 + 4*a^4 + 2*a^3 - 16*a^2 + a + 11)*q^18 + (-a^5 + 3*a^4 + 4*a^3 - 14*a^2 - 3*a + 13)*q^19 + (a^5 - 2*a^4 - 6*a^3 + 8*a^2 + 8*a - 7)*q^20 + (a^5 - 3*a^4 - 5*a^3 + 17*a^2 + 7*a - 24)*q^21 + (-2*a^5 + 3*a^4 + 13*a^3 - 13*a^2 - 17*a + 11)*q^22 + (-4*a^5 + 9*a^4 + 22*a^3 - 38*a^2 - 29*a + 34)*q^23 + (a^5 - 3*a^4 - 7*a^3 + 17*a^2 + 11*a - 22)*q^24 + (a^5 - 4*a^4 - 2*a^3 + 16*a^2 - 12)*q^25 + (4*a^5 - 9*a^4 - 19*a^3 + 32*a^2 + 21*a - 22)*q^26 + (a^5 - a^4 - 7*a^3 + a^2 + 13*a + 2)*q^27 + (-2*a^5 + 5*a^4 + 8*a^3 - 20*a^2 - 6*a + 17)*q^28 + (3*a^5 - 8*a^4 - 13*a^3 + 31*a^2 + 14*a - 21)*q^29 + (a^5 - 3*a^4 - a^3 + 7*a^2 - 5*a)*q^30 + (a^5 - 3*a^4 - 3*a^3 + 11*a^2 + 3*a - 12)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^5 - 4*a^4 - 2*a^3 + 20*a^2 - 4*a - 19)*q^33 + (-5*a^5 + 13*a^4 + 21*a^3 - 48*a^2 - 18*a + 33)*q^34 + (2*a^5 - 5*a^4 - 7*a^3 + 15*a^2 + 3*a - 5)*q^35 + (2*a^5 - 5*a^4 - 9*a^3 + 22*a^2 + 9*a - 23)*q^36 + (5*a^5 - 13*a^4 - 23*a^3 + 53*a^2 + 27*a - 44)*q^37 + O(q^38)
*]> ;  // time = 1.171 seconds




J[105] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 105, 105, 35, 35, 21, 15 ], new_dimensions := [ 1, 2, 1, 2, 1, 1 ], dimensions := [ 1, 2, 2, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 5, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, 1, 1, 1, 0, -6, 2, -8, 8, -2, 4, -2 ],
[ 0, -2, -2, 2, 4, 0, -4, 4, 8, -4, 12, 4 ]
], hecke_fields := [
x - 1,
x^2 - 5
], atkin_lehners := [
[ -1, -1, -1 ],
[ 1, 1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 5, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 1, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[ 1, 1, 1, 1, 0, -6, 2, -8, 8, -2, 4, -2 ],
[
a,
-1,
-1,
1,
-2*a + 2,
-2*a,
-2,
2*a + 2,
4,
-2,
2*a + 6,
4*a + 2
]
*], q_expansions := [*
q + q^2 + q^3 - q^4 + q^5 + q^6 + q^7 - 3*q^8 + q^9 + q^10 - q^12 - 6*q^13 + q^14 + q^15 - q^16 + 2*q^17 + q^18 - 8*q^19 - q^20 + q^21 + 8*q^23 - 3*q^24 + q^25 - 6*q^26 + q^27 - q^28 - 2*q^29 + q^30 + 4*q^31 + 5*q^32 + 2*q^34 + q^35 - q^36 - 2*q^37 + O(q^38),
q + a*q^2 - q^3 + 3*q^4 - q^5 - a*q^6 + q^7 + a*q^8 + q^9 - a*q^10 + (-2*a + 2)*q^11 - 3*q^12 - 2*a*q^13 + a*q^14 + q^15 - q^16 - 2*q^17 + a*q^18 + (2*a + 2)*q^19 - 3*q^20 - q^21 + (2*a - 10)*q^22 + 4*q^23 - a*q^24 + q^25 - 10*q^26 - q^27 + 3*q^28 - 2*q^29 + a*q^30 + (2*a + 6)*q^31 - 3*a*q^32 + (2*a - 2)*q^33 - 2*a*q^34 - q^35 + 3*q^36 + (4*a + 2)*q^37 + O(q^38)
*]> ;  // time = 17.341 seconds




J[106] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 106, 106, 106, 106, 53, 53 ], new_dimensions := [ 1, 1, 1, 1, 1, 3 ], dimensions := [ 1, 1, 1, 1, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 0, 3, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 0 ], ap_traces := [
[ -1, -1, -4, 0, -4, 1, 5, -7, 1, 5, -4, 1 ],
[ -1, 2, 1, -2, 5, -4, 3, -4, -3, -6, 7, -6 ],
[ 1, 1, 0, -4, 0, 5, -3, -1, 3, 9, -4, 5 ],
[ 1, -2, 3, 2, -3, -4, 3, -4, -9, 6, 5, -10 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 3, 1 ],
[ 3, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 3 ], torsion_lower_bounds := [ 1, 1, 3, 3 ], l_ratios := [ 0, 1, 1/3, 1/3 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ -1, -1, -4, 0, -4, 1, 5, -7, 1, 5, -4, 1 ],
[ -1, 2, 1, -2, 5, -4, 3, -4, -3, -6, 7, -6 ],
[ 1, 1, 0, -4, 0, 5, -3, -1, 3, 9, -4, 5 ],
[ 1, -2, 3, 2, -3, -4, 3, -4, -9, 6, 5, -10 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 4*q^5 + q^6 - q^8 - 2*q^9 + 4*q^10 - 4*q^11 - q^12 + q^13 + 4*q^15 + q^16 + 5*q^17 + 2*q^18 - 7*q^19 - 4*q^20 + 4*q^22 + q^23 + q^24 + 11*q^25 - q^26 + 5*q^27 + 5*q^29 - 4*q^30 - 4*q^31 - q^32 + 4*q^33 - 5*q^34 - 2*q^36 + q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + q^5 - 2*q^6 - 2*q^7 - q^8 + q^9 - q^10 + 5*q^11 + 2*q^12 - 4*q^13 + 2*q^14 + 2*q^15 + q^16 + 3*q^17 - q^18 - 4*q^19 + q^20 - 4*q^21 - 5*q^22 - 3*q^23 - 2*q^24 - 4*q^25 + 4*q^26 - 4*q^27 - 2*q^28 - 6*q^29 - 2*q^30 + 7*q^31 - q^32 + 10*q^33 - 3*q^34 - 2*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 - 4*q^7 + q^8 - 2*q^9 + q^12 + 5*q^13 - 4*q^14 + q^16 - 3*q^17 - 2*q^18 - q^19 - 4*q^21 + 3*q^23 + q^24 - 5*q^25 + 5*q^26 - 5*q^27 - 4*q^28 + 9*q^29 - 4*q^31 + q^32 - 3*q^34 - 2*q^36 + 5*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 + 3*q^5 - 2*q^6 + 2*q^7 + q^8 + q^9 + 3*q^10 - 3*q^11 - 2*q^12 - 4*q^13 + 2*q^14 - 6*q^15 + q^16 + 3*q^17 + q^18 - 4*q^19 + 3*q^20 - 4*q^21 - 3*q^22 - 9*q^23 - 2*q^24 + 4*q^25 - 4*q^26 + 4*q^27 + 2*q^28 + 6*q^29 - 6*q^30 + 5*q^31 + q^32 + 6*q^33 + 3*q^34 + 6*q^35 + q^36 - 10*q^37 + O(q^38)
*]> ;  // time = 12.181 seconds




J[107] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 107, 107 ], new_dimensions := [ 2, 7 ], dimensions := [ 2, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -3, -3, -4, 4, -12, -3, 2, 6, -2, -2, -13 ],
[ -1, 3, 5, 4, -2, 18, -1, -4, 0, -3, 4, 25 ]
], hecke_fields := [
x^2 + x - 1,
x^7 + x^6 - 10*x^5 - 7*x^4 + 29*x^3 + 12*x^2 - 20*x - 8
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 53 ]
], tamagawa_numbers := [
[ 1 ],
[ 53 ]
], torsion_upper_bounds := [ 1, 53 ], torsion_lower_bounds := [ 1, 53 ], l_ratios := [ 0, 1/53 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a - 2,
-a - 2,
2*a - 1,
2*a + 3,
-6,
a - 1,
-6*a - 2,
-4*a + 1,
-4*a - 3,
4*a + 1,
-3*a - 8
],
[
a,
-1/4*a^6 - 1/4*a^5 + 5/2*a^4 + 3/4*a^3 - 29/4*a^2 + 2*a + 4,
1/2*a^6 + 1/2*a^5 - 4*a^4 - 5/2*a^3 + 15/2*a^2 + a,
-1/2*a^6 - 1/2*a^5 + 4*a^4 + 7/2*a^3 - 15/2*a^2 - 6*a + 2,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 11/2*a,
1/2*a^6 - 11/2*a^4 + 1/2*a^3 + 17*a^2 - 7/2*a - 8,
a^5 + a^4 - 7*a^3 - 5*a^2 + 10*a + 4,
-3/4*a^6 - 5/4*a^5 + 6*a^4 + 33/4*a^3 - 45/4*a^2 - 19/2*a,
3/4*a^6 - 3/4*a^5 - 9*a^4 + 23/4*a^3 + 113/4*a^2 - 21/2*a - 16,
a^5 + a^4 - 7*a^3 - 4*a^2 + 12*a + 1,
a^4 - 7*a^2 + 2*a + 8,
-1/4*a^6 + 3/4*a^5 + 7/2*a^4 - 21/4*a^3 - 49/4*a^2 + 7*a + 12
]
*], q_expansions := [*
q + a*q^2 + (-a - 2)*q^3 + (-a - 1)*q^4 + (-a - 2)*q^5 + (-a - 1)*q^6 + (2*a - 1)*q^7 + (-2*a - 1)*q^8 + (3*a + 2)*q^9 + (-a - 1)*q^10 + (2*a + 3)*q^11 + (2*a + 3)*q^12 - 6*q^13 + (-3*a + 2)*q^14 + (3*a + 5)*q^15 + 3*a*q^16 + (a - 1)*q^17 + (-a + 3)*q^18 + (-6*a - 2)*q^19 + (2*a + 3)*q^20 - a*q^21 + (a + 2)*q^22 + (-4*a + 1)*q^23 + (3*a + 4)*q^24 + 3*a*q^25 - 6*a*q^26 + (-2*a - 1)*q^27 + (a - 1)*q^28 + (-4*a - 3)*q^29 + (2*a + 3)*q^30 + (4*a + 1)*q^31 + (a + 5)*q^32 + (-5*a - 8)*q^33 + (-2*a + 1)*q^34 - a*q^35 + (-2*a - 5)*q^36 + (-3*a - 8)*q^37 + O(q^38),
q + a*q^2 + (-1/4*a^6 - 1/4*a^5 + 5/2*a^4 + 3/4*a^3 - 29/4*a^2 + 2*a + 4)*q^3 + (a^2 - 2)*q^4 + (1/2*a^6 + 1/2*a^5 - 4*a^4 - 5/2*a^3 + 15/2*a^2 + a)*q^5 + (-a^4 + 5*a^2 - a - 2)*q^6 + (-1/2*a^6 - 1/2*a^5 + 4*a^4 + 7/2*a^3 - 15/2*a^2 - 6*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (1/4*a^6 - 1/4*a^5 - 2*a^4 + 9/4*a^3 + 15/4*a^2 - 9/2*a - 1)*q^9 + (a^5 + a^4 - 7*a^3 - 5*a^2 + 10*a + 4)*q^10 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 11/2*a)*q^11 + (1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 27/2*a^2 - 6*a - 8)*q^12 + (1/2*a^6 - 11/2*a^4 + 1/2*a^3 + 17*a^2 - 7/2*a - 8)*q^13 + (-a^5 + 7*a^3 - 8*a - 4)*q^14 + (-1/2*a^6 + 1/2*a^5 + 6*a^4 - 11/2*a^3 - 39/2*a^2 + 14*a + 10)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 + a^4 - 7*a^3 - 5*a^2 + 10*a + 4)*q^17 + (-1/2*a^6 + 1/2*a^5 + 4*a^4 - 7/2*a^3 - 15/2*a^2 + 4*a + 2)*q^18 + (-3/4*a^6 - 5/4*a^5 + 6*a^4 + 33/4*a^3 - 45/4*a^2 - 19/2*a)*q^19 + (a^4 - 5*a^2 + 2*a)*q^20 + (-a^6 - a^5 + 9*a^4 + 6*a^3 - 22*a^2 - 5*a + 8)*q^21 + (1/2*a^6 - 1/2*a^5 - 4*a^4 + 5/2*a^3 + 11/2*a^2)*q^22 + (3/4*a^6 - 3/4*a^5 - 9*a^4 + 23/4*a^3 + 113/4*a^2 - 21/2*a - 16)*q^23 + (-a^6 + 9*a^4 - a^3 - 22*a^2 + 4*a + 8)*q^24 + (a^6 - 11*a^4 + 2*a^3 + 32*a^2 - 10*a - 13)*q^25 + (-1/2*a^6 - 1/2*a^5 + 4*a^4 + 5/2*a^3 - 19/2*a^2 + 2*a + 4)*q^26 + (1/4*a^6 + 1/4*a^5 - 3/2*a^4 - 3/4*a^3 + 13/4*a^2 - 2*a - 5)*q^27 + (a^5 - a^4 - 7*a^3 + 7*a^2 + 8*a - 4)*q^28 + (a^5 + a^4 - 7*a^3 - 4*a^2 + 12*a + 1)*q^29 + (a^6 + a^5 - 9*a^4 - 5*a^3 + 20*a^2 - 4)*q^30 + (a^4 - 7*a^2 + 2*a + 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^6 + a^5 - 9/2*a^4 - 11/2*a^3 + 11*a^2 + 11/2*a - 3)*q^33 + (a^6 + a^5 - 7*a^4 - 5*a^3 + 10*a^2 + 4*a)*q^34 + (-a^5 + 9*a^3 - 18*a - 4)*q^35 + (1/2*a^6 - 1/2*a^5 - 3*a^4 + 5/2*a^3 + 5/2*a^2 + a - 2)*q^36 + (-1/4*a^6 + 3/4*a^5 + 7/2*a^4 - 21/4*a^3 - 49/4*a^2 + 7*a + 12)*q^37 + O(q^38)
*]> ;  // time = 1.25 seconds




J[109] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 109, 109, 109 ], new_dimensions := [ 1, 3, 4 ], dimensions := [ 1, 3, 4 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ 1, 0, 3, 2, 1, 0, -8, -5, 7, -5, 6, 2 ],
[ -2, -4, -6, -1, -13, -1, 3, -5, 1, -6, -7, 0 ],
[ -1, 4, 1, -3, 12, -7, 11, 10, -2, 1, -5, -12 ]
], hecke_fields := [
x - 1,
x^3 + 2*x^2 - x - 1,
x^4 + x^3 - 5*x^2 - 4*x + 3
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 9 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 9 ]
], torsion_upper_bounds := [ 1, 1, 9 ], torsion_lower_bounds := [ 1, 1, 9 ], l_ratios := [ 1, 0, 1/9 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, 0, 3, 2, 1, 0, -8, -5, 7, -5, 6, 2 ],
[
a,
-a - 2,
-2*a^2 - 3*a,
3*a^2 + 5*a - 3,
a^2 + 2*a - 5,
-2*a^2 - a + 3,
-a^2 - 3*a + 1,
-3*a^2 - 5*a + 1,
-5*a - 3,
4*a^2 + 9*a - 4,
-2*a^2 - 7*a - 3,
a^2 - 2
],
[
a,
-a^3 + 4*a + 1,
-a,
a^3 - a^2 - 4*a + 2,
a^3 + a^2 - 5*a,
2*a^2 + a - 7,
a^3 - a^2 - 2*a + 6,
-a^2 - a + 5,
-a^3 + 2*a^2 + 4*a - 6,
2*a^3 - 2*a^2 - 7*a + 6,
2*a^3 - 7*a - 1,
-3*a^3 - 3*a^2 + 11*a + 5
]
*], q_expansions := [*
q + q^2 - q^4 + 3*q^5 + 2*q^7 - 3*q^8 - 3*q^9 + 3*q^10 + q^11 + 2*q^14 - q^16 - 8*q^17 - 3*q^18 - 5*q^19 - 3*q^20 + q^22 + 7*q^23 + 4*q^25 - 2*q^28 - 5*q^29 + 6*q^31 + 5*q^32 - 8*q^34 + 6*q^35 + 3*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 2)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 - 3*a)*q^5 + (-a^2 - 2*a)*q^6 + (3*a^2 + 5*a - 3)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (a^2 + 4*a + 1)*q^9 + (a^2 - 2*a - 2)*q^10 + (a^2 + 2*a - 5)*q^11 + (a + 3)*q^12 + (-2*a^2 - a + 3)*q^13 + (-a^2 + 3)*q^14 + (3*a^2 + 8*a + 2)*q^15 + (-a^2 - a + 2)*q^16 + (-a^2 - 3*a + 1)*q^17 + (2*a^2 + 2*a + 1)*q^18 + (-3*a^2 - 5*a + 1)*q^19 + (5*a + 1)*q^20 + (-5*a^2 - 10*a + 3)*q^21 + (-4*a + 1)*q^22 + (-5*a - 3)*q^23 + (3*a^2 + 7*a)*q^24 + (5*a^2 + 8*a - 1)*q^25 + (3*a^2 + a - 2)*q^26 + (-4*a^2 - 7*a + 3)*q^27 + (-4*a^2 - 8*a + 5)*q^28 + (4*a^2 + 9*a - 4)*q^29 + (2*a^2 + 5*a + 3)*q^30 + (-2*a^2 - 7*a - 3)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (-2*a^2 + 9)*q^33 + (-a^2 - 1)*q^34 + (-a^2 - 4*a - 7)*q^35 + (-4*a^2 - 5*a)*q^36 + (a^2 - 2)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 4*a + 1)*q^3 + (a^2 - 2)*q^4 - a*q^5 + (a^3 - a^2 - 3*a + 3)*q^6 + (a^3 - a^2 - 4*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (-a^3 - a^2 + 3*a + 4)*q^9 - a^2*q^10 + (a^3 + a^2 - 5*a)*q^11 + (2*a^2 - a - 5)*q^12 + (2*a^2 + a - 7)*q^13 + (-2*a^3 + a^2 + 6*a - 3)*q^14 + (-a^3 + a^2 + 3*a - 3)*q^15 + (-a^3 - a^2 + 4*a + 1)*q^16 + (a^3 - a^2 - 2*a + 6)*q^17 + (-2*a^2 + 3)*q^18 + (-a^2 - a + 5)*q^19 + (-a^3 + 2*a)*q^20 + (-a^2 + 2*a - 1)*q^21 + (4*a - 3)*q^22 + (-a^3 + 2*a^2 + 4*a - 6)*q^23 + (a^2 + a - 6)*q^24 + (a^2 - 5)*q^25 + (2*a^3 + a^2 - 7*a)*q^26 + (-2*a^2 - a + 7)*q^27 + (a^3 - 2*a^2 - 3*a + 2)*q^28 + (2*a^3 - 2*a^2 - 7*a + 6)*q^29 + (2*a^3 - 2*a^2 - 7*a + 3)*q^30 + (2*a^3 - 7*a - 1)*q^31 + (-2*a^3 - a^2 + 5*a + 3)*q^32 + (-3*a^3 + 4*a^2 + 11*a - 12)*q^33 + (-2*a^3 + 3*a^2 + 10*a - 3)*q^34 + (2*a^3 - a^2 - 6*a + 3)*q^35 + (2*a^2 - 3*a - 8)*q^36 + (-3*a^3 - 3*a^2 + 11*a + 5)*q^37 + O(q^38)
*]> ;  // time = 1.239 seconds




J[110] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 110, 110, 110, 110, 55, 55, 11 ], new_dimensions := [ 1, 1, 1, 2, 1, 2, 1 ], dimensions := [ 1, 1, 1, 2, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 1, 0, 49, 1, 1, 5, 1, 1, 49, 0 ], ap_traces := [
[ -1, 1, -1, 5, 1, 2, 3, -7, -6, -3, -7, -7 ],
[ 1, 1, -1, -1, -1, 2, -3, -1, 6, -9, 5, 5 ],
[ 1, -1, 1, 3, 1, -6, -7, 5, -6, 5, -3, 3 ],
[ -2, -1, 2, 1, -2, 4, -3, 7, -6, -3, 1, 13 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + x - 8
], atkin_lehners := [
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 7, 1, 3 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ],
[ 1, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 3 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ],
[ 1, 3, 1 ]
], torsion_upper_bounds := [ 3, 3, 5, 3 ], torsion_lower_bounds := [ 3, 3, 1, 3 ], l_ratios := [ 1/3, 1/3, 1, 1/3 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/25, 1 ], eigenvalues := [*
[ -1, 1, -1, 5, 1, 2, 3, -7, -6, -3, -7, -7 ],
[ 1, 1, -1, -1, -1, 2, -3, -1, 6, -9, 5, 5 ],
[ 1, -1, 1, 3, 1, -6, -7, 5, -6, 5, -3, 3 ],
[
-1,
a,
1,
-a,
-1,
2,
-a - 2,
a + 4,
-2*a - 4,
-a - 2,
-a,
-a + 6
]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - q^5 - q^6 + 5*q^7 - q^8 - 2*q^9 + q^10 + q^11 + q^12 + 2*q^13 - 5*q^14 - q^15 + q^16 + 3*q^17 + 2*q^18 - 7*q^19 - q^20 + 5*q^21 - q^22 - 6*q^23 - q^24 + q^25 - 2*q^26 - 5*q^27 + 5*q^28 - 3*q^29 + q^30 - 7*q^31 - q^32 + q^33 - 3*q^34 - 5*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 - q^7 + q^8 - 2*q^9 - q^10 - q^11 + q^12 + 2*q^13 - q^14 - q^15 + q^16 - 3*q^17 - 2*q^18 - q^19 - q^20 - q^21 - q^22 + 6*q^23 + q^24 + q^25 + 2*q^26 - 5*q^27 - q^28 - 9*q^29 - q^30 + 5*q^31 + q^32 - q^33 - 3*q^34 + q^35 - 2*q^36 + 5*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 + q^10 + q^11 - q^12 - 6*q^13 + 3*q^14 - q^15 + q^16 - 7*q^17 - 2*q^18 + 5*q^19 + q^20 - 3*q^21 + q^22 - 6*q^23 - q^24 + q^25 - 6*q^26 + 5*q^27 + 3*q^28 + 5*q^29 - q^30 - 3*q^31 + q^32 - q^33 - 7*q^34 + 3*q^35 - 2*q^36 + 3*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 - a*q^7 - q^8 + (-a + 5)*q^9 - q^10 - q^11 + a*q^12 + 2*q^13 + a*q^14 + a*q^15 + q^16 + (-a - 2)*q^17 + (a - 5)*q^18 + (a + 4)*q^19 + q^20 + (a - 8)*q^21 + q^22 + (-2*a - 4)*q^23 - a*q^24 + q^25 - 2*q^26 + (3*a - 8)*q^27 - a*q^28 + (-a - 2)*q^29 - a*q^30 - a*q^31 - q^32 - a*q^33 + (a + 2)*q^34 - a*q^35 + (-a + 5)*q^36 + (-a + 6)*q^37 + O(q^38)
*]> ;  // time = 26.111 seconds




J[111] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 111, 111, 37, 37 ], new_dimensions := [ 3, 4, 1, 1 ], dimensions := [ 3, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 5, 1, 0, 7, 1, 1, 7, 0, 1, 5, 1, 1, 0 ], ap_traces := [
[ 3, -3, 4, -4, 4, -2, 4, -8, -2, 16, -8, 3 ],
[ 0, 4, -2, 4, 0, 4, -2, 8, -10, -2, 4, -4 ]
], hecke_fields := [
x^3 - 3*x^2 - x + 5,
x^4 - 6*x^2 + 2*x + 5
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 133, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 133, 1 ]
], torsion_upper_bounds := [ 1, 19 ], torsion_lower_bounds := [ 1, 19 ], l_ratios := [ 1, 7/19 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
-1,
-a^2 + 5,
-2*a^2 + 2*a + 4,
2*a^2 - 4*a - 2,
2*a^2 - 4*a - 4,
-a^2 + 4*a + 1,
2*a^2 - 2*a - 8,
-a^2 + 2*a + 1,
-a^2 + 9,
-4*a^2 + 6*a + 6,
1
],
[
a,
1,
-a^3 - 2*a^2 + 3*a + 4,
2*a^3 + 2*a^2 - 8*a - 2,
2*a^2 - 6,
-2*a^3 - 4*a^2 + 6*a + 10,
-a^3 + 3*a - 2,
2*a^2 + 2*a - 4,
3*a^3 + 2*a^2 - 11*a - 4,
-a^3 + 7*a - 2,
-2*a^3 - 2*a^2 + 8*a + 4,
-1
]
*], q_expansions := [*
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + 5)*q^5 - a*q^6 + (-2*a^2 + 2*a + 4)*q^7 + (3*a^2 - 3*a - 5)*q^8 + q^9 + (-3*a^2 + 4*a + 5)*q^10 + (2*a^2 - 4*a - 2)*q^11 + (-a^2 + 2)*q^12 + (2*a^2 - 4*a - 4)*q^13 + (-4*a^2 + 2*a + 10)*q^14 + (a^2 - 5)*q^15 + (4*a^2 - 2*a - 11)*q^16 + (-a^2 + 4*a + 1)*q^17 + a*q^18 + (2*a^2 - 2*a - 8)*q^19 + (-3*a^2 + 2*a + 5)*q^20 + (2*a^2 - 2*a - 4)*q^21 + (2*a^2 - 10)*q^22 + (-a^2 + 2*a + 1)*q^23 + (-3*a^2 + 3*a + 5)*q^24 + (-2*a + 5)*q^25 + (2*a^2 - 2*a - 10)*q^26 - q^27 + (-6*a^2 + 2*a + 12)*q^28 + (-a^2 + 9)*q^29 + (3*a^2 - 4*a - 5)*q^30 + (-4*a^2 + 6*a + 6)*q^31 + (4*a^2 - a - 10)*q^32 + (-2*a^2 + 4*a + 2)*q^33 + (a^2 + 5)*q^34 + 4*a*q^35 + (a^2 - 2)*q^36 + q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^3 - 2*a^2 + 3*a + 4)*q^5 + a*q^6 + (2*a^3 + 2*a^2 - 8*a - 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2*a^3 - 3*a^2 + 6*a + 5)*q^10 + (2*a^2 - 6)*q^11 + (a^2 - 2)*q^12 + (-2*a^3 - 4*a^2 + 6*a + 10)*q^13 + (2*a^3 + 4*a^2 - 6*a - 10)*q^14 + (-a^3 - 2*a^2 + 3*a + 4)*q^15 + (-2*a - 1)*q^16 + (-a^3 + 3*a - 2)*q^17 + a*q^18 + (2*a^2 + 2*a - 4)*q^19 + (-a^3 - 2*a^2 + 3*a + 2)*q^20 + (2*a^3 + 2*a^2 - 8*a - 2)*q^21 + (2*a^3 - 6*a)*q^22 + (3*a^3 + 2*a^2 - 11*a - 4)*q^23 + (a^3 - 4*a)*q^24 + (2*a^3 + 4*a^2 - 4*a - 9)*q^25 + (-4*a^3 - 6*a^2 + 14*a + 10)*q^26 + q^27 + (2*a^2 + 2*a - 6)*q^28 + (-a^3 + 7*a - 2)*q^29 + (-2*a^3 - 3*a^2 + 6*a + 5)*q^30 + (-2*a^3 - 2*a^2 + 8*a + 4)*q^31 + (-2*a^3 - 2*a^2 + 7*a)*q^32 + (2*a^2 - 6)*q^33 + (-3*a^2 + 5)*q^34 + (-2*a^2 - 4*a + 2)*q^35 + (a^2 - 2)*q^36 - q^37 + O(q^38)
*]> ;  // time = 9.719 seconds




J[113] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 113, 113, 113, 113 ], new_dimensions := [ 1, 2, 3, 3 ], dimensions := [ 1, 2, 3, 3 ], intersection_graph := [ 0, 1, 1, 3, 1, 0, 1, 11, 1, 1, 0, 1, 3, 11, 1, 0 ], ap_traces := [
[ -1, 2, 2, 0, 0, 2, -6, 6, -6, -6, -4, 2 ],
[ 2, 2, 0, 8, -4, -4, -4, -6, 2, 8, 4, -8 ],
[ -2, -5, -1, -10, 2, -8, -2, -4, -6, 5, -15, -2 ],
[ -2, -1, -3, 6, 2, 8, 10, 4, 4, -7, 9, 8 ]
], hecke_fields := [
x - 1,
x^2 - 8*x - 11,
x^3 + 2*x^2 - x - 1,
x^3 + 2*x^2 - 5*x - 9
], atkin_lehners := [
[ -1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 7 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 7 ]
], torsion_upper_bounds := [ 1, 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 1, 7 ], l_ratios := [ 1, 1, 0, 1/7 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1 ], eigenvalues := [*
[ -1, 2, 2, 0, 0, 2, -6, 6, -6, -6, -4, 2 ],
[
1,
1/3*a - 1/3,
-2/3*a + 8/3,
4,
-2/3*a + 2/3,
2/3*a - 14/3,
-2,
1/3*a - 13/3,
1/3*a - 1/3,
2/3*a + 4/3,
-2/3*a + 14/3,
2/3*a - 20/3
],
[
a,
-a^2 - 2*a - 1,
2*a^2 + 2*a - 3,
-a^2 - a - 2,
-3*a^2 - 4*a + 4,
a^2 + 4*a - 2,
-a^2 - 5*a - 2,
3*a^2 + 5*a - 4,
3*a,
-a^2 + 2*a + 5,
a^2 - 3*a - 9,
-6*a^2 - 11*a + 4
],
[
a,
a^2 - 5,
-1,
-a^2 - a + 6,
a^2 - 4,
a^2 - 2,
a^2 - a - 2,
-3*a^2 + a + 16,
-2*a^2 - a + 10,
a^2 - 7,
a^2 + a - 1,
-4*a^2 + a + 22
]
*], q_expansions := [*
q - q^2 + 2*q^3 - q^4 + 2*q^5 - 2*q^6 + 3*q^8 + q^9 - 2*q^10 - 2*q^12 + 2*q^13 + 4*q^15 - q^16 - 6*q^17 - q^18 + 6*q^19 - 2*q^20 - 6*q^23 + 6*q^24 - q^25 - 2*q^26 - 4*q^27 - 6*q^29 - 4*q^30 - 4*q^31 - 5*q^32 + 6*q^34 - q^36 + 2*q^37 + O(q^38),
q + q^2 + (1/3*a - 1/3)*q^3 - q^4 + (-2/3*a + 8/3)*q^5 + (1/3*a - 1/3)*q^6 + 4*q^7 - 3*q^8 + (2/3*a - 5/3)*q^9 + (-2/3*a + 8/3)*q^10 + (-2/3*a + 2/3)*q^11 + (-1/3*a + 1/3)*q^12 + (2/3*a - 14/3)*q^13 + 4*q^14 + (-2/3*a - 10/3)*q^15 - q^16 - 2*q^17 + (2/3*a - 5/3)*q^18 + (1/3*a - 13/3)*q^19 + (2/3*a - 8/3)*q^20 + (4/3*a - 4/3)*q^21 + (-2/3*a + 2/3)*q^22 + (1/3*a - 1/3)*q^23 + (-a + 1)*q^24 + 7*q^25 + (2/3*a - 14/3)*q^26 + 4*q^27 - 4*q^28 + (2/3*a + 4/3)*q^29 + (-2/3*a - 10/3)*q^30 + (-2/3*a + 14/3)*q^31 + 5*q^32 + (-4/3*a - 8/3)*q^33 - 2*q^34 + (-8/3*a + 32/3)*q^35 + (-2/3*a + 5/3)*q^36 + (2/3*a - 20/3)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - 2*a - 1)*q^3 + (a^2 - 2)*q^4 + (2*a^2 + 2*a - 3)*q^5 + (-2*a - 1)*q^6 + (-a^2 - a - 2)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (3*a^2 + 7*a)*q^9 + (-2*a^2 - a + 2)*q^10 + (-3*a^2 - 4*a + 4)*q^11 + (3*a + 2)*q^12 + (a^2 + 4*a - 2)*q^13 + (a^2 - 3*a - 1)*q^14 + (-a^2 + 1)*q^15 + (-a^2 - a + 2)*q^16 + (-a^2 - 5*a - 2)*q^17 + (a^2 + 3*a + 3)*q^18 + (3*a^2 + 5*a - 4)*q^19 + (-a^2 - 4*a + 4)*q^20 + (4*a^2 + 7*a + 3)*q^21 + (2*a^2 + a - 3)*q^22 + 3*a*q^23 + (3*a^2 + 6*a + 2)*q^24 + (-4*a^2 - 8*a + 4)*q^25 + (2*a^2 - a + 1)*q^26 + (-3*a^2 - 11*a - 4)*q^27 + (-3*a^2 + 2*a + 5)*q^28 + (-a^2 + 2*a + 5)*q^29 + (2*a^2 - 1)*q^30 + (a^2 - 3*a - 9)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (2*a^2 + 3*a)*q^33 + (-3*a^2 - 3*a - 1)*q^34 + (-5*a^2 - 3*a + 6)*q^35 + (-5*a^2 - 10*a + 1)*q^36 + (-6*a^2 - 11*a + 4)*q^37 + O(q^38),
q + a*q^2 + (a^2 - 5)*q^3 + (a^2 - 2)*q^4 - q^5 + (-2*a^2 + 9)*q^6 + (-a^2 - a + 6)*q^7 + (-2*a^2 + a + 9)*q^8 + (-a^2 - a + 4)*q^9 - a*q^10 + (a^2 - 4)*q^11 + (2*a^2 - a - 8)*q^12 + (a^2 - 2)*q^13 + (a^2 + a - 9)*q^14 + (-a^2 + 5)*q^15 + (3*a^2 - a - 14)*q^16 + (a^2 - a - 2)*q^17 + (a^2 - a - 9)*q^18 + (-3*a^2 + a + 16)*q^19 + (-a^2 + 2)*q^20 + (4*a^2 + a - 21)*q^21 + (-2*a^2 + a + 9)*q^22 + (-2*a^2 - a + 10)*q^23 + (-a^2 + 2*a)*q^24 - 4*q^25 + (-2*a^2 + 3*a + 9)*q^26 + (-a^2 + a + 4)*q^27 + (a^2 - 2*a - 3)*q^28 + (a^2 - 7)*q^29 + (2*a^2 - 9)*q^30 + (a^2 + a - 1)*q^31 + (-3*a^2 - a + 9)*q^32 + (-a + 2)*q^33 + (-3*a^2 + 3*a + 9)*q^34 + (a^2 + a - 6)*q^35 + (-a^2 - 2*a + 1)*q^36 + (-4*a^2 + a + 22)*q^37 + O(q^38)
*]> ;  // time = 1.421 seconds




J[114] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 114, 114, 114, 57, 57, 57, 38, 38, 19 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2, 2, 2, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 5, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 5, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 9, 0, 1, 5, 1, 5, 1, 1, 1, 1, 1, 0, 1, 9, 1, 3, 1, 1, 1, 5, 1, 0, 1, 1, 1, 3, 1, 1, 1, 9, 1, 0 ], ap_traces := [
[ -1, -1, 0, 4, 4, 0, -2, 1, -2, -6, 6, -8 ],
[ 1, -1, 2, 0, -4, 2, -6, -1, -4, -2, 4, 10 ],
[ 1, 1, 0, -4, 0, -4, 6, 1, -6, 6, 2, -4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 5, 1 ],
[ 5, 3, 1 ],
[ 3, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 3, 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1 ], l_ratios := [ 1, 5, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/9 ], eigenvalues := [*
[ -1, -1, 0, 4, 4, 0, -2, 1, -2, -6, 6, -8 ],
[ 1, -1, 2, 0, -4, 2, -6, -1, -4, -2, 4, 10 ],
[ 1, 1, 0, -4, 0, -4, 6, 1, -6, 6, 2, -4 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^6 + 4*q^7 - q^8 + q^9 + 4*q^11 - q^12 - 4*q^14 + q^16 - 2*q^17 - q^18 + q^19 - 4*q^21 - 4*q^22 - 2*q^23 + q^24 - 5*q^25 - q^27 + 4*q^28 - 6*q^29 + 6*q^31 - q^32 - 4*q^33 + 2*q^34 + q^36 - 8*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 2*q^5 - q^6 + q^8 + q^9 + 2*q^10 - 4*q^11 - q^12 + 2*q^13 - 2*q^15 + q^16 - 6*q^17 + q^18 - q^19 + 2*q^20 - 4*q^22 - 4*q^23 - q^24 - q^25 + 2*q^26 - q^27 - 2*q^29 - 2*q^30 + 4*q^31 + q^32 + 4*q^33 - 6*q^34 + q^36 + 10*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 - 4*q^7 + q^8 + q^9 + q^12 - 4*q^13 - 4*q^14 + q^16 + 6*q^17 + q^18 + q^19 - 4*q^21 - 6*q^23 + q^24 - 5*q^25 - 4*q^26 + q^27 - 4*q^28 + 6*q^29 + 2*q^31 + q^32 + 6*q^34 + q^36 - 4*q^37 + O(q^38)
*]> ;  // time = 42.31 seconds




J[115] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 115, 115, 115, 23 ], new_dimensions := [ 1, 2, 4, 2 ], dimensions := [ 1, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 5, 1, 0, 1, 1, 1, 1, 0, 1, 5, 1, 1, 0 ], ap_traces := [
[ 2, 0, -1, 1, 2, -2, 3, -2, 1, 7, -5, 11 ],
[ -3, -2, -2, -2, -2, -8, -4, 2, -2, -10, 4, -6 ],
[ 2, -2, 4, -3, 4, 0, -1, -4, -4, 19, -1, -3 ]
], hecke_fields := [
x - 1,
x^2 + 3*x + 1,
x^4 - 2*x^3 - 4*x^2 + 5*x + 2
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1 ], l_ratios := [ 1, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 2, 0, -1, 1, 2, -2, 3, -2, 1, 7, -5, 11 ],
[
a,
-1,
-1,
-2*a - 4,
2*a + 2,
2*a - 1,
-4*a - 8,
6*a + 10,
-1,
-4*a - 11,
-2*a - 1,
6*a + 6
],
[
a,
-a^2 + a + 2,
1,
a^3 - 2*a^2 - 4*a + 3,
-2*a + 2,
-2*a^3 + 3*a^2 + 7*a - 4,
-a^3 + 2*a^2 + 2*a - 3,
2*a - 2,
-1,
a^3 - a^2 - 3*a + 5,
-3*a^3 + 5*a^2 + 9*a - 7,
a^3 + 2*a^2 - 8*a - 7
]
*], q_expansions := [*
q + 2*q^2 + 2*q^4 - q^5 + q^7 - 3*q^9 - 2*q^10 + 2*q^11 - 2*q^13 + 2*q^14 - 4*q^16 + 3*q^17 - 6*q^18 - 2*q^19 - 2*q^20 + 4*q^22 + q^23 + q^25 - 4*q^26 + 2*q^28 + 7*q^29 - 5*q^31 - 8*q^32 + 6*q^34 - q^35 - 6*q^36 + 11*q^37 + O(q^38),
q + a*q^2 - q^3 + (-3*a - 3)*q^4 - q^5 - a*q^6 + (-2*a - 4)*q^7 + (4*a + 3)*q^8 - 2*q^9 - a*q^10 + (2*a + 2)*q^11 + (3*a + 3)*q^12 + (2*a - 1)*q^13 + (2*a + 2)*q^14 + q^15 + (-3*a + 2)*q^16 + (-4*a - 8)*q^17 - 2*a*q^18 + (6*a + 10)*q^19 + (3*a + 3)*q^20 + (2*a + 4)*q^21 + (-4*a - 2)*q^22 - q^23 + (-4*a - 3)*q^24 + q^25 + (-7*a - 2)*q^26 + 5*q^27 + 6*q^28 + (-4*a - 11)*q^29 + a*q^30 + (-2*a - 1)*q^31 + (3*a - 3)*q^32 + (-2*a - 2)*q^33 + (4*a + 4)*q^34 + (2*a + 4)*q^35 + (6*a + 6)*q^36 + (6*a + 6)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^3 + a^2 + 2*a)*q^6 + (a^3 - 2*a^2 - 4*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (a^2 - a - 1)*q^9 + a*q^10 + (-2*a + 2)*q^11 + (-a^3 + 3*a - 2)*q^12 + (-2*a^3 + 3*a^2 + 7*a - 4)*q^13 + (-2*a - 2)*q^14 + (-a^2 + a + 2)*q^15 + (2*a^3 - 2*a^2 - 5*a + 2)*q^16 + (-a^3 + 2*a^2 + 2*a - 3)*q^17 + (a^3 - a^2 - a)*q^18 + (2*a - 2)*q^19 + (a^2 - 2)*q^20 + (2*a^3 - 2*a^2 - 8*a + 4)*q^21 + (-2*a^2 + 2*a)*q^22 - q^23 + (-3*a^2 - a + 2)*q^24 + q^25 + (-a^3 - a^2 + 6*a + 4)*q^26 + (a^2 - a - 6)*q^27 + (-2*a^3 + 2*a^2 + 6*a - 6)*q^28 + (a^3 - a^2 - 3*a + 5)*q^29 + (-a^3 + a^2 + 2*a)*q^30 + (-3*a^3 + 5*a^2 + 9*a - 7)*q^31 + (3*a^2 - 4)*q^32 + (2*a^3 - 4*a^2 - 2*a + 4)*q^33 + (-2*a^2 + 2*a + 2)*q^34 + (a^3 - 2*a^2 - 4*a + 3)*q^35 + (a^3 + a^2 - 3*a)*q^36 + (a^3 + 2*a^2 - 8*a - 7)*q^37 + O(q^38)
*]> ;  // time = 9.329 seconds




J[118] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 118, 118, 118, 118, 59 ], new_dimensions := [ 1, 1, 1, 1, 5 ], dimensions := [ 1, 1, 1, 1, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 19, 1, 1, 0, 3, 1, 1, 1, 3, 0, 1, 1, 19, 1, 1, 0 ], ap_traces := [
[ -1, -1, -3, -1, -2, -2, -2, 3, 0, -1, 10, -12 ],
[ -1, 2, 2, -3, 1, 3, -1, -8, 8, -4, -4, -1 ],
[ 1, -1, 1, 3, 2, -6, -2, -5, 4, -5, 2, 8 ],
[ 1, 2, -2, -3, -1, -3, 7, 4, 4, 4, -4, -7 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 19, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 5, 1 ], l_ratios := [ 0, 1, 1/5, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ -1, -1, -3, -1, -2, -2, -2, 3, 0, -1, 10, -12 ],
[ -1, 2, 2, -3, 1, 3, -1, -8, 8, -4, -4, -1 ],
[ 1, -1, 1, 3, 2, -6, -2, -5, 4, -5, 2, 8 ],
[ 1, 2, -2, -3, -1, -3, 7, 4, 4, 4, -4, -7 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 3*q^5 + q^6 - q^7 - q^8 - 2*q^9 + 3*q^10 - 2*q^11 - q^12 - 2*q^13 + q^14 + 3*q^15 + q^16 - 2*q^17 + 2*q^18 + 3*q^19 - 3*q^20 + q^21 + 2*q^22 + q^24 + 4*q^25 + 2*q^26 + 5*q^27 - q^28 - q^29 - 3*q^30 + 10*q^31 - q^32 + 2*q^33 + 2*q^34 + 3*q^35 - 2*q^36 - 12*q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 - 3*q^7 - q^8 + q^9 - 2*q^10 + q^11 + 2*q^12 + 3*q^13 + 3*q^14 + 4*q^15 + q^16 - q^17 - q^18 - 8*q^19 + 2*q^20 - 6*q^21 - q^22 + 8*q^23 - 2*q^24 - q^25 - 3*q^26 - 4*q^27 - 3*q^28 - 4*q^29 - 4*q^30 - 4*q^31 - q^32 + 2*q^33 + q^34 - 6*q^35 + q^36 - q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 + q^10 + 2*q^11 - q^12 - 6*q^13 + 3*q^14 - q^15 + q^16 - 2*q^17 - 2*q^18 - 5*q^19 + q^20 - 3*q^21 + 2*q^22 + 4*q^23 - q^24 - 4*q^25 - 6*q^26 + 5*q^27 + 3*q^28 - 5*q^29 - q^30 + 2*q^31 + q^32 - 2*q^33 - 2*q^34 + 3*q^35 - 2*q^36 + 8*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 - 2*q^5 + 2*q^6 - 3*q^7 + q^8 + q^9 - 2*q^10 - q^11 + 2*q^12 - 3*q^13 - 3*q^14 - 4*q^15 + q^16 + 7*q^17 + q^18 + 4*q^19 - 2*q^20 - 6*q^21 - q^22 + 4*q^23 + 2*q^24 - q^25 - 3*q^26 - 4*q^27 - 3*q^28 + 4*q^29 - 4*q^30 - 4*q^31 + q^32 - 2*q^33 + 7*q^34 + 6*q^35 + q^36 - 7*q^37 + O(q^38)
*]> ;  // time = 13.88 seconds




J[119] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 119, 119, 17 ], new_dimensions := [ 4, 5, 1 ], dimensions := [ 4, 5, 2 ], intersection_graph := [ 0, 1, 1, 1, 0, 3, 1, 3, 0 ], ap_traces := [
[ -1, 2, 2, 4, 2, 8, -4, 10, -6, 2, 12, 6 ],
[ 2, -2, 0, -5, -2, 2, 5, 6, -10, -8, 0, 8 ]
], hecke_fields := [
x^4 + x^3 - 5*x^2 - x + 3,
x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 14*x - 17
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 9, 3 ],
[ 3, 1 ]
], tamagawa_numbers := [
[ 9, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 9, 1 ], torsion_lower_bounds := [ 9, 1 ], l_ratios := [ 1/9, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
-a^3 - a^2 + 4*a + 1,
a^3 + a^2 - 4*a,
1,
-2*a,
2*a^3 + 4*a^2 - 6*a - 4,
-1,
-2*a^3 - 4*a^2 + 4*a + 8,
2*a^2 + 4*a - 6,
-2*a,
a^3 - a^2 - 4*a + 8,
2*a^3 + 4*a^2 - 4*a - 4
],
[
a,
-a^4 + 6*a^2 + a - 4,
2*a^4 + a^3 - 15*a^2 - 6*a + 18,
-1,
-2*a^4 - 2*a^3 + 14*a^2 + 12*a - 14,
-2*a^4 + 14*a^2 - 14,
1,
-2*a^4 + 14*a^2 + 2*a - 14,
2*a^2 - 10,
4*a^4 - 28*a^2 - 2*a + 28,
2*a^4 + a^3 - 13*a^2 - 6*a + 10,
-2*a^3 + 8*a + 4
]
*], q_expansions := [*
q + a*q^2 + (-a^3 - a^2 + 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^3 + a^2 - 4*a)*q^5 + (-a^2 + 3)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-a^3 - 3*a^2 + 2*a + 7)*q^9 + (a^2 + a - 3)*q^10 - 2*a*q^11 + (a^3 + 2*a^2 - 5*a - 2)*q^12 + (2*a^3 + 4*a^2 - 6*a - 4)*q^13 + a*q^14 + (2*a^2 + 2*a - 9)*q^15 + (-a^3 - a^2 + a + 1)*q^16 - q^17 + (-2*a^3 - 3*a^2 + 6*a + 3)*q^18 + (-2*a^3 - 4*a^2 + 4*a + 8)*q^19 + (-a^3 - a^2 + 5*a)*q^20 + (-a^3 - a^2 + 4*a + 1)*q^21 - 2*a^2*q^22 + (2*a^2 + 4*a - 6)*q^23 + (a^3 + 2*a^2 - a - 9)*q^24 + (a^3 - a^2 - 6*a + 4)*q^25 + (2*a^3 + 4*a^2 - 2*a - 6)*q^26 + (-2*a^3 - 4*a^2 + 8*a + 7)*q^27 + (a^2 - 2)*q^28 - 2*a*q^29 + (2*a^3 + 2*a^2 - 9*a)*q^30 + (a^3 - a^2 - 4*a + 8)*q^31 + (-2*a^3 - 4*a^2 + 8*a + 3)*q^32 + (2*a^2 - 6)*q^33 - a*q^34 + (a^3 + a^2 - 4*a)*q^35 + (a^3 + 2*a^2 - 3*a - 8)*q^36 + (2*a^3 + 4*a^2 - 4*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-a^4 + 6*a^2 + a - 4)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + a^3 - 15*a^2 - 6*a + 18)*q^5 + (-2*a^4 - 2*a^3 + 15*a^2 + 10*a - 17)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (2*a^4 + a^3 - 13*a^2 - 8*a + 13)*q^9 + (5*a^4 + a^3 - 34*a^2 - 10*a + 34)*q^10 + (-2*a^4 - 2*a^3 + 14*a^2 + 12*a - 14)*q^11 + (-4*a^4 - a^3 + 26*a^2 + 9*a - 26)*q^12 + (-2*a^4 + 14*a^2 - 14)*q^13 - a*q^14 + (-a^4 - a^3 + 7*a^2 + 3*a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + q^17 + (5*a^4 + 3*a^3 - 36*a^2 - 15*a + 34)*q^18 + (-2*a^4 + 14*a^2 + 2*a - 14)*q^19 + (7*a^4 + 4*a^3 - 50*a^2 - 24*a + 49)*q^20 + (a^4 - 6*a^2 - a + 4)*q^21 + (-6*a^4 - 2*a^3 + 40*a^2 + 14*a - 34)*q^22 + (2*a^2 - 10)*q^23 + (-5*a^4 - 2*a^3 + 35*a^2 + 10*a - 34)*q^24 + (-3*a^4 - 2*a^3 + 22*a^2 + 13*a - 21)*q^25 + (-4*a^4 - 2*a^3 + 28*a^2 + 14*a - 34)*q^26 + (-a^4 + a^3 + 5*a^2 - 3*a - 6)*q^27 + (-a^2 + 2)*q^28 + (4*a^4 - 28*a^2 - 2*a + 28)*q^29 + (-3*a^4 - a^3 + 17*a^2 + 10*a - 17)*q^30 + (2*a^4 + a^3 - 13*a^2 - 6*a + 10)*q^31 + (2*a^4 - 14*a^2 - 2*a + 17)*q^32 + (4*a^4 - 26*a^2 + 22)*q^33 + a*q^34 + (-2*a^4 - a^3 + 15*a^2 + 6*a - 18)*q^35 + (9*a^4 + 2*a^3 - 59*a^2 - 20*a + 59)*q^36 + (-2*a^3 + 8*a + 4)*q^37 + O(q^38)
*]> ;  // time = 9.91 seconds




J[122] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 122, 122, 122, 61, 61 ], new_dimensions := [ 1, 2, 3, 1, 3 ], dimensions := [ 1, 2, 3, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 13, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 13, 1, 1, 0 ], ap_traces := [
[ -1, -2, 1, -5, -3, -3, 0, 0, 5, 6, 0, -12 ],
[ -2, 1, 0, 5, 2, 6, -2, 1, -3, -11, -1, -3 ],
[ 3, -1, 1, 4, -7, -1, -6, -3, 2, 1, -3, 7 ]
], hecke_fields := [
x - 1,
x^2 - x - 3,
x^3 + x^2 - 5*x + 2
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 39, 3 ],
[ 31, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 31, 1 ]
], torsion_upper_bounds := [ 1, 3, 31 ], torsion_lower_bounds := [ 1, 3, 31 ], l_ratios := [ 0, 1/3, 1/31 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -2, 1, -5, -3, -3, 0, 0, 5, 6, 0, -12 ],
[
-1,
a,
0,
-a + 3,
-2*a + 2,
-2*a + 4,
2*a - 2,
3*a - 1,
-3*a,
-a - 5,
-a,
a - 2
],
[
1,
a,
-a^2 - 3*a + 3,
2*a^2 + 3*a - 5,
-a^2 - a + 1,
-a^2 - a + 3,
-2*a^2 - 4*a + 4,
a^2 + 2*a - 4,
3*a^2 + 4*a - 9,
a^2 + 4*a - 2,
-2*a^2 - a + 6,
-4*a^2 - 9*a + 14
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 + q^5 + 2*q^6 - 5*q^7 - q^8 + q^9 - q^10 - 3*q^11 - 2*q^12 - 3*q^13 + 5*q^14 - 2*q^15 + q^16 - q^18 + q^20 + 10*q^21 + 3*q^22 + 5*q^23 + 2*q^24 - 4*q^25 + 3*q^26 + 4*q^27 - 5*q^28 + 6*q^29 + 2*q^30 - q^32 + 6*q^33 - 5*q^35 + q^36 - 12*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - a*q^6 + (-a + 3)*q^7 - q^8 + a*q^9 + (-2*a + 2)*q^11 + a*q^12 + (-2*a + 4)*q^13 + (a - 3)*q^14 + q^16 + (2*a - 2)*q^17 - a*q^18 + (3*a - 1)*q^19 + (2*a - 3)*q^21 + (2*a - 2)*q^22 - 3*a*q^23 - a*q^24 - 5*q^25 + (2*a - 4)*q^26 + (-2*a + 3)*q^27 + (-a + 3)*q^28 + (-a - 5)*q^29 - a*q^31 - q^32 - 6*q^33 + (-2*a + 2)*q^34 + a*q^36 + (a - 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 - 3*a + 3)*q^5 + a*q^6 + (2*a^2 + 3*a - 5)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 - 3*a + 3)*q^10 + (-a^2 - a + 1)*q^11 + a*q^12 + (-a^2 - a + 3)*q^13 + (2*a^2 + 3*a - 5)*q^14 + (-2*a^2 - 2*a + 2)*q^15 + q^16 + (-2*a^2 - 4*a + 4)*q^17 + (a^2 - 3)*q^18 + (a^2 + 2*a - 4)*q^19 + (-a^2 - 3*a + 3)*q^20 + (a^2 + 5*a - 4)*q^21 + (-a^2 - a + 1)*q^22 + (3*a^2 + 4*a - 9)*q^23 + a*q^24 + (3*a^2 + 5*a - 6)*q^25 + (-a^2 - a + 3)*q^26 + (-a^2 - a - 2)*q^27 + (2*a^2 + 3*a - 5)*q^28 + (a^2 + 4*a - 2)*q^29 + (-2*a^2 - 2*a + 2)*q^30 + (-2*a^2 - a + 6)*q^31 + q^32 + (-4*a + 2)*q^33 + (-2*a^2 - 4*a + 4)*q^34 + (-a^2 - 7*a - 1)*q^35 + (a^2 - 3)*q^36 + (-4*a^2 - 9*a + 14)*q^37 + O(q^38)
*]> ;  // time = 15.78 seconds




J[123] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 123, 123, 123, 123, 41 ], new_dimensions := [ 1, 1, 2, 3, 3 ], dimensions := [ 1, 1, 2, 3, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 0, 23, 1, 5, 1, 23, 0 ], ap_traces := [
[ 0, -1, -2, -4, 5, -4, -5, -2, 4, 1, -5, -7 ],
[ -2, 1, -4, -2, -3, -6, 3, 0, -6, 5, 7, -7 ],
[ 0, 2, 4, -4, 2, 4, 2, -8, 0, 2, -6, -2 ],
[ 1, -3, 4, 2, -4, 8, 2, 2, -10, -6, -2, 20 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2,
x^3 - x^2 - 4*x + 2
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 7, 1 ],
[ 23, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 7, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 5, 7, 1 ], torsion_lower_bounds := [ 1, 1, 7, 1 ], l_ratios := [ 0, 0, 1/7, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ 0, -1, -2, -4, 5, -4, -5, -2, 4, 1, -5, -7 ],
[ -2, 1, -4, -2, -3, -6, 3, 0, -6, 5, 7, -7 ],
[
a,
1,
-a + 2,
a - 2,
-a + 1,
-3*a + 2,
a + 1,
a - 4,
a,
5*a + 1,
-3,
6*a - 1
],
[
a,
-1,
-a^2 + a + 4,
-a^2 - a + 4,
-a - 1,
a^2 - a,
2*a^2 - a - 5,
a^2 - a - 2,
a^2 - a - 6,
-3*a - 1,
a^2 + 4*a - 5,
-a^2 + 2*a + 9
]
*], q_expansions := [*
q - q^3 - 2*q^4 - 2*q^5 - 4*q^7 + q^9 + 5*q^11 + 2*q^12 - 4*q^13 + 2*q^15 + 4*q^16 - 5*q^17 - 2*q^19 + 4*q^20 + 4*q^21 + 4*q^23 - q^25 - q^27 + 8*q^28 + q^29 - 5*q^31 - 5*q^33 + 8*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - 4*q^5 - 2*q^6 - 2*q^7 + q^9 + 8*q^10 - 3*q^11 + 2*q^12 - 6*q^13 + 4*q^14 - 4*q^15 - 4*q^16 + 3*q^17 - 2*q^18 - 8*q^20 - 2*q^21 + 6*q^22 - 6*q^23 + 11*q^25 + 12*q^26 + q^27 - 4*q^28 + 5*q^29 + 8*q^30 + 7*q^31 + 8*q^32 - 3*q^33 - 6*q^34 + 8*q^35 + 2*q^36 - 7*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a + 2)*q^5 + a*q^6 + (a - 2)*q^7 - 2*a*q^8 + q^9 + (2*a - 2)*q^10 + (-a + 1)*q^11 + (-3*a + 2)*q^13 + (-2*a + 2)*q^14 + (-a + 2)*q^15 - 4*q^16 + (a + 1)*q^17 + a*q^18 + (a - 4)*q^19 + (a - 2)*q^21 + (a - 2)*q^22 + a*q^23 - 2*a*q^24 + (-4*a + 1)*q^25 + (2*a - 6)*q^26 + q^27 + (5*a + 1)*q^29 + (2*a - 2)*q^30 - 3*q^31 + (-a + 1)*q^33 + (a + 2)*q^34 + (4*a - 6)*q^35 + (6*a - 1)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 4)*q^5 - a*q^6 + (-a^2 - a + 4)*q^7 + (a^2 - 2)*q^8 + q^9 + 2*q^10 + (-a - 1)*q^11 + (-a^2 + 2)*q^12 + (a^2 - a)*q^13 + (-2*a^2 + 2)*q^14 + (a^2 - a - 4)*q^15 + (-a^2 + 2*a + 2)*q^16 + (2*a^2 - a - 5)*q^17 + a*q^18 + (a^2 - a - 2)*q^19 + (2*a^2 - 8)*q^20 + (a^2 + a - 4)*q^21 + (-a^2 - a)*q^22 + (a^2 - a - 6)*q^23 + (-a^2 + 2)*q^24 + (-4*a^2 + 2*a + 13)*q^25 + (4*a - 2)*q^26 - q^27 + (-4*a - 4)*q^28 + (-3*a - 1)*q^29 - 2*q^30 + (a^2 + 4*a - 5)*q^31 + (-a^2 - 2*a + 6)*q^32 + (a + 1)*q^33 + (a^2 + 3*a - 4)*q^34 + (-4*a^2 + 2*a + 14)*q^35 + (a^2 - 2)*q^36 + (-a^2 + 2*a + 9)*q^37 + O(q^38)
*]> ;  // time = 11.54 seconds




J[127] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 127, 127 ], new_dimensions := [ 3, 7 ], dimensions := [ 3, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -3, -6, -3, 0, -3, -18, 3, -9, 3, 12, 0 ],
[ 2, 3, 8, -3, 0, -1, 24, -5, -1, -7, -8, -6 ]
], hecke_fields := [
x^3 + 3*x^2 - 3,
x^7 - 2*x^6 - 8*x^5 + 15*x^4 + 17*x^3 - 28*x^2 - 11*x + 15
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 21 ]
], tamagawa_numbers := [
[ 1 ],
[ 21 ]
], torsion_upper_bounds := [ 1, 21 ], torsion_lower_bounds := [ 1, 21 ], l_ratios := [ 0, 1/21 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - 2*a,
a^2 + a - 4,
a^2 + a - 3,
a^2 + 4*a + 1,
-3*a^2 - 4*a + 4,
-a - 7,
a^2 + a - 1,
-2*a^2 - 3*a,
a^2 - a - 3,
-3*a^2 - 5*a + 8,
-4*a^2 - 2*a + 10
],
[
a,
a^6 - 2*a^5 - 6*a^4 + 12*a^3 + 4*a^2 - 11*a + 4,
-a^6 + a^5 + 8*a^4 - 6*a^3 - 16*a^2 + 5*a + 9,
-a^5 + a^4 + 7*a^3 - 7*a^2 - 9*a + 8,
a^6 - 2*a^5 - 6*a^4 + 13*a^3 + 3*a^2 - 15*a + 6,
-2*a^6 + 6*a^5 + 11*a^4 - 38*a^3 - 2*a^2 + 39*a - 13,
a^6 - a^5 - 9*a^4 + 6*a^3 + 24*a^2 - 6*a - 15,
2*a^6 - 5*a^5 - 11*a^4 + 32*a^3 + 2*a^2 - 33*a + 11,
3*a^5 - 6*a^4 - 20*a^3 + 36*a^2 + 24*a - 33,
-2*a^6 + 5*a^5 + 13*a^4 - 31*a^3 - 15*a^2 + 29*a,
-a^6 + 5*a^5 - 33*a^3 + 33*a^2 + 39*a - 40,
-4*a^5 + 6*a^4 + 27*a^3 - 37*a^2 - 32*a + 35
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - 2*a)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 4)*q^5 + (a^2 - 3)*q^6 + (a^2 + a - 3)*q^7 + (-3*a^2 - 4*a + 3)*q^8 + (a^2 + 3*a)*q^9 + (-2*a^2 - 4*a + 3)*q^10 + (a^2 + 4*a + 1)*q^11 + (-a^2 + a + 3)*q^12 + (-3*a^2 - 4*a + 4)*q^13 + (-2*a^2 - 3*a + 3)*q^14 + (2*a^2 + 5*a)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (-a - 7)*q^17 + 3*q^18 + (a^2 + a - 1)*q^19 + (a + 2)*q^20 + (a^2 + 3*a)*q^21 + (a^2 + a + 3)*q^22 + (-2*a^2 - 3*a)*q^23 + (2*a^2 + 3*a + 3)*q^24 + (-4*a^2 - 5*a + 8)*q^25 + (5*a^2 + 4*a - 9)*q^26 + (3*a^2 + 3*a - 6)*q^27 + (a^2 + a)*q^28 + (a^2 - a - 3)*q^29 + (-a^2 + 6)*q^30 + (-3*a^2 - 5*a + 8)*q^31 + (3*a + 3)*q^32 + (-5*a - 9)*q^33 + (-a^2 - 7*a)*q^34 + (-3*a^2 - 4*a + 9)*q^35 + (-2*a^2 - 3*a)*q^36 + (-4*a^2 - 2*a + 10)*q^37 + O(q^38),
q + a*q^2 + (a^6 - 2*a^5 - 6*a^4 + 12*a^3 + 4*a^2 - 11*a + 4)*q^3 + (a^2 - 2)*q^4 + (-a^6 + a^5 + 8*a^4 - 6*a^3 - 16*a^2 + 5*a + 9)*q^5 + (2*a^5 - 3*a^4 - 13*a^3 + 17*a^2 + 15*a - 15)*q^6 + (-a^5 + a^4 + 7*a^3 - 7*a^2 - 9*a + 8)*q^7 + (a^3 - 4*a)*q^8 + (a^5 - 3*a^4 - 7*a^3 + 19*a^2 + 9*a - 17)*q^9 + (-a^6 + 9*a^4 + a^3 - 23*a^2 - 2*a + 15)*q^10 + (a^6 - 2*a^5 - 6*a^4 + 13*a^3 + 3*a^2 - 15*a + 6)*q^11 + (a^5 - a^4 - 7*a^3 + 7*a^2 + 7*a - 8)*q^12 + (-2*a^6 + 6*a^5 + 11*a^4 - 38*a^3 - 2*a^2 + 39*a - 13)*q^13 + (-a^6 + a^5 + 7*a^4 - 7*a^3 - 9*a^2 + 8*a)*q^14 + (-a^5 + 4*a^4 + 6*a^3 - 24*a^2 - 8*a + 21)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - a^5 - 9*a^4 + 6*a^3 + 24*a^2 - 6*a - 15)*q^17 + (a^6 - 3*a^5 - 7*a^4 + 19*a^3 + 9*a^2 - 17*a)*q^18 + (2*a^6 - 5*a^5 - 11*a^4 + 32*a^3 + 2*a^2 - 33*a + 11)*q^19 + (-a^5 + 6*a^3 + 2*a^2 - 6*a - 3)*q^20 + (a^6 - 3*a^5 - 4*a^4 + 20*a^3 - 10*a^2 - 23*a + 17)*q^21 + (2*a^5 - 2*a^4 - 14*a^3 + 13*a^2 + 17*a - 15)*q^22 + (3*a^5 - 6*a^4 - 20*a^3 + 36*a^2 + 24*a - 33)*q^23 + (a^6 - 5*a^5 - a^4 + 33*a^3 - 27*a^2 - 38*a + 30)*q^24 + (-a^6 + a^5 + 7*a^4 - 7*a^3 - 9*a^2 + 10*a + 1)*q^25 + (2*a^6 - 5*a^5 - 8*a^4 + 32*a^3 - 17*a^2 - 35*a + 30)*q^26 + (a^6 + a^5 - 12*a^4 - 8*a^3 + 42*a^2 + 13*a - 35)*q^27 + (-a^6 + a^5 + 6*a^4 - 6*a^3 - 6*a^2 + 7*a - 1)*q^28 + (-2*a^6 + 5*a^5 + 13*a^4 - 31*a^3 - 15*a^2 + 29*a)*q^29 + (-a^6 + 4*a^5 + 6*a^4 - 24*a^3 - 8*a^2 + 21*a)*q^30 + (-a^6 + 5*a^5 - 33*a^3 + 33*a^2 + 39*a - 40)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^6 - 5*a^5 - 3*a^4 + 33*a^3 - 15*a^2 - 36*a + 24)*q^33 + (a^6 - a^5 - 9*a^4 + 7*a^3 + 22*a^2 - 4*a - 15)*q^34 + (-a^4 + a^3 + 5*a^2 - a - 3)*q^35 + (-a^6 - a^5 + 10*a^4 + 6*a^3 - 27*a^2 - 7*a + 19)*q^36 + (-4*a^5 + 6*a^4 + 27*a^3 - 37*a^2 - 32*a + 35)*q^37 + O(q^38)
*]> ;  // time = 1.39 seconds




J[129] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 129, 129, 129, 129, 43, 43 ], new_dimensions := [ 1, 1, 2, 3, 1, 2 ], dimensions := [ 1, 1, 2, 3, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 1, 5, 3, 1, 1, 1, 0, 1, 1, 7, 1, 5, 1, 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 7, 1, 1, 0 ], ap_traces := [
[ 0, -1, -2, -2, -5, 3, -3, 2, -1, 0, -5, 8 ],
[ 1, 1, 2, 0, 0, -2, -6, 4, -4, -6, 8, 6 ],
[ 2, -2, 2, 2, 6, -10, -4, -2, 12, 6, 8, -8 ],
[ -2, 3, -4, 4, 1, 9, 1, -4, 11, 2, -5, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2*x - 1,
x^3 + 2*x^2 - 5*x - 8
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 7, 1 ],
[ 11, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 11, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 1, 11 ], l_ratios := [ 0, 3, 1, 1/11 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ 0, -1, -2, -2, -5, 3, -3, 2, -1, 0, -5, 8 ],
[ 1, 1, 2, 0, 0, -2, -6, 4, -4, -6, 8, 6 ],
[
a,
-1,
-a + 2,
-2*a + 3,
-a + 4,
-5,
-2*a,
4*a - 5,
6,
3*a,
4,
-2*a - 2
],
[
a,
1,
-a - 2,
-a^2 + 6,
a^2 - a - 5,
3,
-a^2 + 5,
-a^2 - 2*a + 2,
3*a^2 + 2*a - 9,
-a,
a^2 + 2*a - 5,
2*a^2 + 2*a - 8
]
*], q_expansions := [*
q - q^3 - 2*q^4 - 2*q^5 - 2*q^7 + q^9 - 5*q^11 + 2*q^12 + 3*q^13 + 2*q^15 + 4*q^16 - 3*q^17 + 2*q^19 + 4*q^20 + 2*q^21 - q^23 - q^25 - q^27 + 4*q^28 - 5*q^31 + 5*q^33 + 4*q^35 - 2*q^36 + 8*q^37 + O(q^38),
q + q^2 + q^3 - q^4 + 2*q^5 + q^6 - 3*q^8 + q^9 + 2*q^10 - q^12 - 2*q^13 + 2*q^15 - q^16 - 6*q^17 + q^18 + 4*q^19 - 2*q^20 - 4*q^23 - 3*q^24 - q^25 - 2*q^26 + q^27 - 6*q^29 + 2*q^30 + 8*q^31 + 5*q^32 - 6*q^34 - q^36 + 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (2*a - 1)*q^4 + (-a + 2)*q^5 - a*q^6 + (-2*a + 3)*q^7 + (a + 2)*q^8 + q^9 - q^10 + (-a + 4)*q^11 + (-2*a + 1)*q^12 - 5*q^13 + (-a - 2)*q^14 + (a - 2)*q^15 + 3*q^16 - 2*a*q^17 + a*q^18 + (4*a - 5)*q^19 + (a - 4)*q^20 + (2*a - 3)*q^21 + (2*a - 1)*q^22 + 6*q^23 + (-a - 2)*q^24 - 2*a*q^25 - 5*a*q^26 - q^27 - 7*q^28 + 3*a*q^29 + q^30 + 4*q^31 + (a - 4)*q^32 + (a - 4)*q^33 + (-4*a - 2)*q^34 + (-3*a + 8)*q^35 + (2*a - 1)*q^36 + (-2*a - 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a - 2)*q^5 + a*q^6 + (-a^2 + 6)*q^7 + (-2*a^2 + a + 8)*q^8 + q^9 + (-a^2 - 2*a)*q^10 + (a^2 - a - 5)*q^11 + (a^2 - 2)*q^12 + 3*q^13 + (2*a^2 + a - 8)*q^14 + (-a - 2)*q^15 + (3*a^2 - 2*a - 12)*q^16 + (-a^2 + 5)*q^17 + a*q^18 + (-a^2 - 2*a + 2)*q^19 + (-3*a - 4)*q^20 + (-a^2 + 6)*q^21 + (-3*a^2 + 8)*q^22 + (3*a^2 + 2*a - 9)*q^23 + (-2*a^2 + a + 8)*q^24 + (a^2 + 4*a - 1)*q^25 + 3*a*q^26 + q^27 + (-a^2 + 2*a + 4)*q^28 - a*q^29 + (-a^2 - 2*a)*q^30 + (a^2 + 2*a - 5)*q^31 + (-4*a^2 + a + 8)*q^32 + (a^2 - a - 5)*q^33 + (2*a^2 - 8)*q^34 + (-a - 4)*q^35 + (a^2 - 2)*q^36 + (2*a^2 + 2*a - 8)*q^37 + O(q^38)
*]> ;  // time = 11.51 seconds




J[130] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 130, 130, 130, 65, 65, 65, 26, 26 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 1, 1 ], dimensions := [ 1, 1, 1, 2, 4, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 7, 3, 1, 1, 1, 3, 1, 0, 1, 1, 5, 1, 1, 1, 7, 1, 0 ], ap_traces := [
[ -1, -2, 1, -4, -6, 1, -6, 2, 6, -6, 2, 2 ],
[ 1, 2, -1, -4, -2, -1, 2, 6, 6, 2, -6, -2 ],
[ 1, 0, 1, 0, 0, 1, 2, -8, -4, -2, -4, 6 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 1, 5, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 3, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1 ], l_ratios := [ 0, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -2, 1, -4, -6, 1, -6, 2, 6, -6, 2, 2 ],
[ 1, 2, -1, -4, -2, -1, 2, 6, 6, 2, -6, -2 ],
[ 1, 0, 1, 0, 0, 1, 2, -8, -4, -2, -4, 6 ]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 + q^5 + 2*q^6 - 4*q^7 - q^8 + q^9 - q^10 - 6*q^11 - 2*q^12 + q^13 + 4*q^14 - 2*q^15 + q^16 - 6*q^17 - q^18 + 2*q^19 + q^20 + 8*q^21 + 6*q^22 + 6*q^23 + 2*q^24 + q^25 - q^26 + 4*q^27 - 4*q^28 - 6*q^29 + 2*q^30 + 2*q^31 - q^32 + 12*q^33 + 6*q^34 - 4*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 - q^5 + 2*q^6 - 4*q^7 + q^8 + q^9 - q^10 - 2*q^11 + 2*q^12 - q^13 - 4*q^14 - 2*q^15 + q^16 + 2*q^17 + q^18 + 6*q^19 - q^20 - 8*q^21 - 2*q^22 + 6*q^23 + 2*q^24 + q^25 - q^26 - 4*q^27 - 4*q^28 + 2*q^29 - 2*q^30 - 6*q^31 + q^32 - 4*q^33 + 2*q^34 + 4*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 + q^4 + q^5 + q^8 - 3*q^9 + q^10 + q^13 + q^16 + 2*q^17 - 3*q^18 - 8*q^19 + q^20 - 4*q^23 + q^25 + q^26 - 2*q^29 - 4*q^31 + q^32 + 2*q^34 - 3*q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 33.3 seconds




J[131] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 131, 131 ], new_dimensions := [ 1, 10 ], dimensions := [ 1, 10 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ 0, -1, -2, -1, 0, -3, 4, -2, -2, 0, -2, -8 ],
[ 0, 1, 4, 1, 2, 11, -2, 0, -10, 16, 6, 34 ]
], hecke_fields := [
x - 1,
x^10 - 18*x^8 + 2*x^7 + 111*x^6 - 18*x^5 - 270*x^4 + 28*x^3 + 232*x^2 + 16*x - 32
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 65 ]
], tamagawa_numbers := [
[ 1 ],
[ 65 ]
], torsion_upper_bounds := [ 1, 65 ], torsion_lower_bounds := [ 1, 65 ], l_ratios := [ 0, 1/65 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[ 0, -1, -2, -1, 0, -3, 4, -2, -2, 0, -2, -8 ],
[
a,
1/8*a^8 - 2*a^6 + 81/8*a^4 - 67/4*a^2 + 5,
-1/16*a^9 + 9/8*a^7 + 1/8*a^6 - 107/16*a^5 - 9/8*a^4 + 117/8*a^3 + 7/4*a^2 - 9*a + 1,
-1/8*a^9 - 1/4*a^8 + 7/4*a^7 + 7/2*a^6 - 57/8*a^5 - 63/4*a^4 + 11/2*a^3 + 47/2*a^2 + 15/2*a - 3,
-1/16*a^9 + 9/8*a^7 - 3/8*a^6 - 107/16*a^5 + 31/8*a^4 + 117/8*a^3 - 35/4*a^2 - 11*a + 2,
1/16*a^9 + 1/8*a^8 - 7/8*a^7 - 15/8*a^6 + 55/16*a^5 + 17/2*a^4 - 17/8*a^3 - 21/2*a^2 - 5*a + 1,
1/8*a^9 + 1/4*a^8 - 7/4*a^7 - 13/4*a^6 + 59/8*a^5 + 25/2*a^4 - 31/4*a^3 - 12*a^2 - 4*a - 4,
1/8*a^9 - 9/4*a^7 + 1/4*a^6 + 103/8*a^5 - 13/4*a^4 - 95/4*a^3 + 21/2*a^2 + 6*a - 6,
1/4*a^9 + 1/4*a^8 - 4*a^7 - 7/2*a^6 + 83/4*a^5 + 63/4*a^4 - 37*a^3 - 49/2*a^2 + 16*a + 6,
1/8*a^9 - 1/4*a^8 - 9/4*a^7 + 17/4*a^6 + 103/8*a^5 - 45/2*a^4 - 99/4*a^3 + 37*a^2 + 13*a - 10,
3/8*a^9 + 1/4*a^8 - 25/4*a^7 - 11/4*a^6 + 273/8*a^5 + 8*a^4 - 257/4*a^3 - 5*a^2 + 26*a - 2,
-1/4*a^8 + 7/2*a^6 - 1/2*a^5 - 59/4*a^4 + 7/2*a^3 + 35/2*a^2 - 2*a + 2
]
*], q_expansions := [*
q - q^3 - 2*q^4 - 2*q^5 - q^7 - 2*q^9 + 2*q^12 - 3*q^13 + 2*q^15 + 4*q^16 + 4*q^17 - 2*q^19 + 4*q^20 + q^21 - 2*q^23 - q^25 + 5*q^27 + 2*q^28 - 2*q^31 + 2*q^35 + 4*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (1/8*a^8 - 2*a^6 + 81/8*a^4 - 67/4*a^2 + 5)*q^3 + (a^2 - 2)*q^4 + (-1/16*a^9 + 9/8*a^7 + 1/8*a^6 - 107/16*a^5 - 9/8*a^4 + 117/8*a^3 + 7/4*a^2 - 9*a + 1)*q^5 + (1/8*a^9 - 2*a^7 + 81/8*a^5 - 67/4*a^3 + 5*a)*q^6 + (-1/8*a^9 - 1/4*a^8 + 7/4*a^7 + 7/2*a^6 - 57/8*a^5 - 63/4*a^4 + 11/2*a^3 + 47/2*a^2 + 15/2*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (3/16*a^9 - 25/8*a^7 + 5/8*a^6 + 273/16*a^5 - 45/8*a^4 - 261/8*a^3 + 39/4*a^2 + 31/2*a + 1)*q^9 + (1/4*a^7 + 1/4*a^6 - 9/4*a^5 - 9/4*a^4 + 7/2*a^3 + 11/2*a^2 + 2*a - 2)*q^10 + (-1/16*a^9 + 9/8*a^7 - 3/8*a^6 - 107/16*a^5 + 31/8*a^4 + 117/8*a^3 - 35/4*a^2 - 11*a + 2)*q^11 + (-1/4*a^7 + 1/4*a^6 + 9/4*a^5 - 13/4*a^4 - 7/2*a^3 + 19/2*a^2 - 2*a - 6)*q^12 + (1/16*a^9 + 1/8*a^8 - 7/8*a^7 - 15/8*a^6 + 55/16*a^5 + 17/2*a^4 - 17/8*a^3 - 21/2*a^2 - 5*a + 1)*q^13 + (-1/4*a^9 - 1/2*a^8 + 15/4*a^7 + 27/4*a^6 - 18*a^5 - 113/4*a^4 + 27*a^3 + 73/2*a^2 - a - 4)*q^14 + (-1/8*a^9 + 1/8*a^8 + 9/4*a^7 - 5/2*a^6 - 109/8*a^5 + 121/8*a^4 + 61/2*a^3 - 109/4*a^2 - 41/2*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/8*a^9 + 1/4*a^8 - 7/4*a^7 - 13/4*a^6 + 59/8*a^5 + 25/2*a^4 - 31/4*a^3 - 12*a^2 - 4*a - 4)*q^17 + (1/4*a^8 + 1/4*a^7 - 15/4*a^6 - 9/4*a^5 + 18*a^4 + 9/2*a^3 - 28*a^2 - 2*a + 6)*q^18 + (1/8*a^9 - 9/4*a^7 + 1/4*a^6 + 103/8*a^5 - 13/4*a^4 - 95/4*a^3 + 21/2*a^2 + 6*a - 6)*q^19 + (1/8*a^9 + 1/4*a^8 - 2*a^7 - 5/2*a^6 + 89/8*a^5 + 23/4*a^4 - 95/4*a^3 - 3/2*a^2 + 16*a - 2)*q^20 + (1/16*a^9 - 9/8*a^7 + 1/8*a^6 + 119/16*a^5 - 5/8*a^4 - 163/8*a^3 - 3/4*a^2 + 33/2*a + 3)*q^21 + (-1/4*a^7 + 1/4*a^6 + 11/4*a^5 - 9/4*a^4 - 7*a^3 + 7/2*a^2 + 3*a - 2)*q^22 + (1/4*a^9 + 1/4*a^8 - 4*a^7 - 7/2*a^6 + 83/4*a^5 + 63/4*a^4 - 37*a^3 - 49/2*a^2 + 16*a + 6)*q^23 + (-1/4*a^9 - 1/4*a^8 + 17/4*a^7 + 9/4*a^6 - 47/2*a^5 - 7/2*a^4 + 43*a^3 - 2*a^2 - 16*a)*q^24 + (-5/16*a^9 - 1/4*a^8 + 41/8*a^7 + 21/8*a^6 - 447/16*a^5 - 51/8*a^4 + 441/8*a^3 - 1/4*a^2 - 29*a + 5)*q^25 + (1/8*a^9 + 1/4*a^8 - 2*a^7 - 7/2*a^6 + 77/8*a^5 + 59/4*a^4 - 49/4*a^3 - 39/2*a^2 + 2)*q^26 + (-3/16*a^9 - 1/8*a^8 + 23/8*a^7 + 11/8*a^6 - 209/16*a^5 - 7/2*a^4 + 99/8*a^3 - a^2 + 16*a + 4)*q^27 + (-1/4*a^9 - 1/4*a^8 + 15/4*a^7 + 11/4*a^6 - 37/2*a^5 - 9*a^4 + 65/2*a^3 + 10*a^2 - 15*a - 2)*q^28 + (1/8*a^9 - 1/4*a^8 - 9/4*a^7 + 17/4*a^6 + 103/8*a^5 - 45/2*a^4 - 99/4*a^3 + 37*a^2 + 13*a - 10)*q^29 + (1/8*a^9 - 9/4*a^7 + 1/4*a^6 + 103/8*a^5 - 13/4*a^4 - 95/4*a^3 + 17/2*a^2 + 7*a - 4)*q^30 + (3/8*a^9 + 1/4*a^8 - 25/4*a^7 - 11/4*a^6 + 273/8*a^5 + 8*a^4 - 257/4*a^3 - 5*a^2 + 26*a - 2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/4*a^9 - 1/4*a^8 + 4*a^7 + 13/4*a^6 - 21*a^5 - 27/2*a^4 + 157/4*a^3 + 19*a^2 - 39/2*a - 4)*q^33 + (1/4*a^9 + 1/2*a^8 - 7/2*a^7 - 13/2*a^6 + 59/4*a^5 + 26*a^4 - 31/2*a^3 - 33*a^2 - 6*a + 4)*q^34 + (-1/16*a^9 - 3/8*a^8 + 7/8*a^7 + 47/8*a^6 - 55/16*a^5 - 119/4*a^4 + 1/8*a^3 + 50*a^2 + 13*a - 14)*q^35 + (-1/8*a^9 + 1/4*a^8 + 5/2*a^7 - 7/2*a^6 - 129/8*a^5 + 63/4*a^4 + 149/4*a^3 - 43/2*a^2 - 25*a - 2)*q^36 + (-1/4*a^8 + 7/2*a^6 - 1/2*a^5 - 59/4*a^4 + 7/2*a^3 + 35/2*a^2 - 2*a + 2)*q^37 + O(q^38)
*]> ;  // time = 1.479 seconds




J[133] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 133, 133, 133, 133, 19 ], new_dimensions := [ 2, 2, 2, 3, 1 ], dimensions := [ 2, 2, 2, 3, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 0, 7, 1, 1, 3, 7, 0 ], ap_traces := [
[ -3, -3, 0, -2, -9, 2, -3, -2, -6, -9, 5, -8 ],
[ 1, 3, 2, 2, -1, -2, 1, -2, -2, 5, -1, -14 ],
[ -1, -3, -6, 2, -5, -4, -7, 2, -6, 9, -1, 0 ],
[ 2, 3, -2, -3, 7, -2, 7, 3, 14, -3, -11, 0 ]
], hecke_fields := [
x^2 + 3*x + 1,
x^2 - x - 1,
x^2 + x - 3,
x^3 - 2*x^2 - 4*x + 7
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 3, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 3, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 5, 9, 1 ], torsion_lower_bounds := [ 1, 5, 1, 1 ], l_ratios := [ 0, 1/5, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1 ], eigenvalues := [*
[
a,
a,
-2*a - 3,
-1,
a - 3,
1,
3*a + 3,
-1,
-3,
a - 3,
3*a + 7,
6*a + 5
],
[
a,
-a + 2,
1,
1,
a - 1,
-1,
3*a - 1,
-1,
-4*a + 1,
-a + 3,
9*a - 5,
4*a - 9
],
[
a,
-a - 2,
-3,
1,
-a - 3,
2*a - 1,
a - 3,
1,
-3,
-3*a + 3,
-a - 1,
-2*a - 1
],
[
a,
-a^2 + 5,
a^2 - a - 4,
-1,
-a + 3,
a^2 - a - 4,
-2*a^2 - a + 11,
1,
a^2 + a,
-4*a^2 + 3*a + 13,
2*a^2 - a - 11,
-a^2 + 3*a + 2
]
*], q_expansions := [*
q + a*q^2 + a*q^3 + (-3*a - 3)*q^4 + (-2*a - 3)*q^5 + (-3*a - 1)*q^6 - q^7 + (4*a + 3)*q^8 + (-3*a - 4)*q^9 + (3*a + 2)*q^10 + (a - 3)*q^11 + (6*a + 3)*q^12 + q^13 - a*q^14 + (3*a + 2)*q^15 + (-3*a + 2)*q^16 + (3*a + 3)*q^17 + (5*a + 3)*q^18 - q^19 + (-3*a + 3)*q^20 - a*q^21 + (-6*a - 1)*q^22 - 3*q^23 + (-9*a - 4)*q^24 + a*q^26 + (2*a + 3)*q^27 + (3*a + 3)*q^28 + (a - 3)*q^29 + (-7*a - 3)*q^30 + (3*a + 7)*q^31 + (3*a - 3)*q^32 + (-6*a - 1)*q^33 + (-6*a - 3)*q^34 + (2*a + 3)*q^35 + (-6*a + 3)*q^36 + (6*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a + 2)*q^3 + (a - 1)*q^4 + q^5 + (a - 1)*q^6 + q^7 + (-2*a + 1)*q^8 + (-3*a + 2)*q^9 + a*q^10 + (a - 1)*q^11 + (2*a - 3)*q^12 - q^13 + a*q^14 + (-a + 2)*q^15 - 3*a*q^16 + (3*a - 1)*q^17 + (-a - 3)*q^18 - q^19 + (a - 1)*q^20 + (-a + 2)*q^21 + q^22 + (-4*a + 1)*q^23 + (-3*a + 4)*q^24 - 4*q^25 - a*q^26 + (-2*a + 1)*q^27 + (a - 1)*q^28 + (-a + 3)*q^29 + (a - 1)*q^30 + (9*a - 5)*q^31 + (a - 5)*q^32 + (2*a - 3)*q^33 + (2*a + 3)*q^34 + q^35 + (2*a - 5)*q^36 + (4*a - 9)*q^37 + O(q^38),
q + a*q^2 + (-a - 2)*q^3 + (-a + 1)*q^4 - 3*q^5 + (-a - 3)*q^6 + q^7 - 3*q^8 + (3*a + 4)*q^9 - 3*a*q^10 + (-a - 3)*q^11 + q^12 + (2*a - 1)*q^13 + a*q^14 + (3*a + 6)*q^15 + (-a - 2)*q^16 + (a - 3)*q^17 + (a + 9)*q^18 + q^19 + (3*a - 3)*q^20 + (-a - 2)*q^21 + (-2*a - 3)*q^22 - 3*q^23 + (3*a + 6)*q^24 + 4*q^25 + (-3*a + 6)*q^26 + (-4*a - 11)*q^27 + (-a + 1)*q^28 + (-3*a + 3)*q^29 + (3*a + 9)*q^30 + (-a - 1)*q^31 + (-a + 3)*q^32 + (4*a + 9)*q^33 + (-4*a + 3)*q^34 - 3*q^35 + (2*a - 5)*q^36 + (-2*a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 5)*q^3 + (a^2 - 2)*q^4 + (a^2 - a - 4)*q^5 + (-2*a^2 + a + 7)*q^6 - q^7 + (2*a^2 - 7)*q^8 + (-2*a^2 + a + 8)*q^9 + (a^2 - 7)*q^10 + (-a + 3)*q^11 + (-a^2 - a + 4)*q^12 + (a^2 - a - 4)*q^13 - a*q^14 + (3*a^2 - 2*a - 13)*q^15 + (2*a^2 + a - 10)*q^16 + (-2*a^2 - a + 11)*q^17 + (-3*a^2 + 14)*q^18 + q^19 + (-a + 1)*q^20 + (a^2 - 5)*q^21 + (-a^2 + 3*a)*q^22 + (a^2 + a)*q^23 + (a^2 - 2*a - 7)*q^24 + (-3*a^2 + a + 11)*q^25 + (a^2 - 7)*q^26 + (-a^2 + 3*a + 4)*q^27 + (-a^2 + 2)*q^28 + (-4*a^2 + 3*a + 13)*q^29 + (4*a^2 - a - 21)*q^30 + (2*a^2 - a - 11)*q^31 + (a^2 - 2*a)*q^32 + (-a^2 - a + 8)*q^33 + (-5*a^2 + 3*a + 14)*q^34 + (-a^2 + a + 4)*q^35 + (-2*a^2 + 5)*q^36 + (-a^2 + 3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 10.539 seconds




J[134] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 134, 134, 67, 67, 67 ], new_dimensions := [ 3, 3, 1, 2, 2 ], dimensions := [ 3, 3, 2, 4, 4 ], intersection_graph := [ 0, 1, 5, 1, 5, 1, 0, 1, 19, 1, 5, 1, 0, 1, 25, 1, 19, 1, 0, 1, 5, 1, 25, 1, 0 ], ap_traces := [
[ -3, 1, 3, 0, -1, 11, -3, 6, -11, 0, 4, 4 ],
[ 3, 3, -3, 0, -3, -3, -3, 6, -3, -12, 12, 0 ]
], hecke_fields := [
x^3 - x^2 - 8*x + 11,
x^3 - 3*x^2 + 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 75, 3 ],
[ 323, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 323, 1 ]
], torsion_upper_bounds := [ 3, 17 ], torsion_lower_bounds := [ 3, 17 ], l_ratios := [ 1/3, 19/17 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
-1,
a,
a^2 + a - 5,
-2*a^2 - 2*a + 12,
-a^2 - 2*a + 6,
a^2 - 2,
-a^2 - a + 5,
2,
a - 4,
0,
4*a^2 + 2*a - 22,
-2*a^2 - 4*a + 14
],
[
1,
a,
-a^2 + a + 1,
2*a^2 - 6*a,
-3*a^2 + 6*a + 2,
3*a^2 - 8*a - 2,
-a^2 + 5*a - 3,
-4*a^2 + 12*a + 2,
4*a^2 - 9*a - 4,
-4,
-2*a + 6,
-6*a^2 + 16*a + 2
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (a^2 + a - 5)*q^5 - a*q^6 + (-2*a^2 - 2*a + 12)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^2 - a + 5)*q^10 + (-a^2 - 2*a + 6)*q^11 + a*q^12 + (a^2 - 2)*q^13 + (2*a^2 + 2*a - 12)*q^14 + (2*a^2 + 3*a - 11)*q^15 + q^16 + (-a^2 - a + 5)*q^17 + (-a^2 + 3)*q^18 + 2*q^19 + (a^2 + a - 5)*q^20 + (-4*a^2 - 4*a + 22)*q^21 + (a^2 + 2*a - 6)*q^22 + (a - 4)*q^23 - a*q^24 + (2*a^2 + 3*a - 13)*q^25 + (-a^2 + 2)*q^26 + (a^2 + 2*a - 11)*q^27 + (-2*a^2 - 2*a + 12)*q^28 + (-2*a^2 - 3*a + 11)*q^30 + (4*a^2 + 2*a - 22)*q^31 - q^32 + (-3*a^2 - 2*a + 11)*q^33 + (a^2 + a - 5)*q^34 + (-2*a^2 - 4*a + 6)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 - 4*a + 14)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 + a + 1)*q^5 + a*q^6 + (2*a^2 - 6*a)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 + a + 1)*q^10 + (-3*a^2 + 6*a + 2)*q^11 + a*q^12 + (3*a^2 - 8*a - 2)*q^13 + (2*a^2 - 6*a)*q^14 + (-2*a^2 + a + 1)*q^15 + q^16 + (-a^2 + 5*a - 3)*q^17 + (a^2 - 3)*q^18 + (-4*a^2 + 12*a + 2)*q^19 + (-a^2 + a + 1)*q^20 - 2*q^21 + (-3*a^2 + 6*a + 2)*q^22 + (4*a^2 - 9*a - 4)*q^23 + a*q^24 + (2*a^2 + a - 5)*q^25 + (3*a^2 - 8*a - 2)*q^26 + (3*a^2 - 6*a - 1)*q^27 + (2*a^2 - 6*a)*q^28 - 4*q^29 + (-2*a^2 + a + 1)*q^30 + (-2*a + 6)*q^31 + q^32 + (-3*a^2 + 2*a + 3)*q^33 + (-a^2 + 5*a - 3)*q^34 + (2*a^2 - 4*a - 2)*q^35 + (a^2 - 3)*q^36 + (-6*a^2 + 16*a + 2)*q^37 + O(q^38)
*]> ;  // time = 17.249 seconds




J[137] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 137, 137 ], new_dimensions := [ 4, 7 ], dimensions := [ 4, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -5, -2, -13, 1, -8, -4, -10, -1, 11, -17, -4 ],
[ 0, 3, -2, 15, -3, 12, -6, 10, -3, -9, 13, -2 ]
], hecke_fields := [
x^4 + 3*x^3 - 4*x - 1,
x^7 - 10*x^5 + 28*x^3 + 3*x^2 - 19*x - 7
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 17 ]
], tamagawa_numbers := [
[ 1 ],
[ 17 ]
], torsion_upper_bounds := [ 1, 17 ], torsion_lower_bounds := [ 1, 17 ], l_ratios := [ 0, 1/17 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
a^3 + a^2 - 3*a - 2,
-2*a^3 - 3*a^2 + 3*a + 1,
-a^3 - 2*a^2 + 2*a - 1,
4*a^3 + 9*a^2 - 4*a - 8,
a^2 + 3*a - 2,
-a^3 - 5*a^2 - 2*a + 5,
-2*a^3 - 7*a^2 - a + 5,
a^2 - 2*a - 4,
-a^3 - 5*a^2 + a + 11,
5*a^3 + 9*a^2 - 7*a - 11,
2*a^3 + 7*a^2 + 3*a - 7
],
[
a,
-1/2*a^6 + 1/2*a^5 + 11/2*a^4 - 9/2*a^3 - 33/2*a^2 + 9*a + 21/2,
a^6 - a^5 - 10*a^4 + 8*a^3 + 26*a^2 - 13*a - 13,
-a^6 + 9*a^4 - a^3 - 21*a^2 + 3*a + 11,
2*a^6 - a^5 - 19*a^4 + 10*a^3 + 47*a^2 - 21*a - 22,
a^6 - 9*a^4 + 2*a^3 + 22*a^2 - 8*a - 10,
a^5 + a^4 - 7*a^3 - 5*a^2 + 9*a + 3,
a^6 - a^5 - 10*a^4 + 8*a^3 + 28*a^2 - 13*a - 17,
-1/2*a^6 + 1/2*a^5 + 7/2*a^4 - 11/2*a^3 - 9/2*a^2 + 12*a + 1/2,
-a^6 + a^5 + 11*a^4 - 8*a^3 - 32*a^2 + 15*a + 16,
1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 3/2*a^3 + 21/2*a^2 - 2*a - 3/2,
-a^6 + 10*a^4 - 3*a^3 - 28*a^2 + 12*a + 16
]
*], q_expansions := [*
q + a*q^2 + (a^3 + a^2 - 3*a - 2)*q^3 + (a^2 - 2)*q^4 + (-2*a^3 - 3*a^2 + 3*a + 1)*q^5 + (-2*a^3 - 3*a^2 + 2*a + 1)*q^6 + (-a^3 - 2*a^2 + 2*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (2*a^2 + 3*a - 1)*q^9 + (3*a^3 + 3*a^2 - 7*a - 2)*q^10 + (4*a^3 + 9*a^2 - 4*a - 8)*q^11 + (a^3 - a + 2)*q^12 + (a^2 + 3*a - 2)*q^13 + (a^3 + 2*a^2 - 5*a - 1)*q^14 + (4*a + 1)*q^15 + (-3*a^3 - 6*a^2 + 4*a + 5)*q^16 + (-a^3 - 5*a^2 - 2*a + 5)*q^17 + (2*a^3 + 3*a^2 - a)*q^18 + (-2*a^3 - 7*a^2 - a + 5)*q^19 + (-2*a^3 - a^2 + 4*a + 1)*q^20 + (-4*a^3 - 4*a^2 + 11*a + 5)*q^21 + (-3*a^3 - 4*a^2 + 8*a + 4)*q^22 + (a^2 - 2*a - 4)*q^23 + (a^3 + 5*a^2 + 2*a - 1)*q^24 + (3*a^3 + 7*a^2 - 6*a - 7)*q^25 + (a^3 + 3*a^2 - 2*a)*q^26 + (-4*a^3 - 9*a^2 + 4*a + 7)*q^27 + (a^3 - a^2 - a + 3)*q^28 + (-a^3 - 5*a^2 + a + 11)*q^29 + (4*a^2 + a)*q^30 + (5*a^3 + 9*a^2 - 7*a - 11)*q^31 + (a^3 + 4*a^2 + a - 3)*q^32 + (-a^3 - 6*a^2 - 7*a + 6)*q^33 + (-2*a^3 - 2*a^2 + a - 1)*q^34 + (9*a^3 + 13*a^2 - 16*a - 5)*q^35 + (-3*a^3 - 5*a^2 + 2*a + 4)*q^36 + (2*a^3 + 7*a^2 + 3*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^6 + 1/2*a^5 + 11/2*a^4 - 9/2*a^3 - 33/2*a^2 + 9*a + 21/2)*q^3 + (a^2 - 2)*q^4 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 26*a^2 - 13*a - 13)*q^5 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 5/2*a^3 + 21/2*a^2 + a - 7/2)*q^6 + (-a^6 + 9*a^4 - a^3 - 21*a^2 + 3*a + 11)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^6 + a^5 + 19*a^4 - 10*a^3 - 48*a^2 + 20*a + 25)*q^9 + (-a^6 + 8*a^4 - 2*a^3 - 16*a^2 + 6*a + 7)*q^10 + (2*a^6 - a^5 - 19*a^4 + 10*a^3 + 47*a^2 - 21*a - 22)*q^11 + (3/2*a^6 - 1/2*a^5 - 27/2*a^4 + 11/2*a^3 + 65/2*a^2 - 12*a - 35/2)*q^12 + (a^6 - 9*a^4 + 2*a^3 + 22*a^2 - 8*a - 10)*q^13 + (-a^5 - a^4 + 7*a^3 + 6*a^2 - 8*a - 7)*q^14 + (a^6 - 10*a^4 + a^3 + 27*a^2 - 5*a - 14)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 + a^4 - 7*a^3 - 5*a^2 + 9*a + 3)*q^17 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 26*a^2 - 13*a - 14)*q^18 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 28*a^2 - 13*a - 17)*q^19 + (-2*a^6 + 18*a^4 - 4*a^3 - 43*a^2 + 14*a + 19)*q^20 + (-3*a^6 + 2*a^5 + 31*a^4 - 18*a^3 - 87*a^2 + 34*a + 49)*q^21 + (-a^6 + a^5 + 10*a^4 - 9*a^3 - 27*a^2 + 16*a + 14)*q^22 + (-1/2*a^6 + 1/2*a^5 + 7/2*a^4 - 11/2*a^3 - 9/2*a^2 + 12*a + 1/2)*q^23 + (-3/2*a^6 + 1/2*a^5 + 29/2*a^4 - 9/2*a^3 - 75/2*a^2 + 9*a + 35/2)*q^24 + (a^6 - 9*a^4 + 3*a^3 + 22*a^2 - 11*a - 11)*q^25 + (a^5 + 2*a^4 - 6*a^3 - 11*a^2 + 9*a + 7)*q^26 + (-2*a^6 + 18*a^4 - 2*a^3 - 43*a^2 + 6*a + 21)*q^27 + (a^6 - a^5 - 11*a^4 + 8*a^3 + 34*a^2 - 13*a - 22)*q^28 + (-a^6 + a^5 + 11*a^4 - 8*a^3 - 32*a^2 + 15*a + 16)*q^29 + (a^4 - a^3 - 8*a^2 + 5*a + 7)*q^30 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 3/2*a^3 + 21/2*a^2 - 2*a - 3/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^6 - a^5 - 11*a^4 + 8*a^3 + 33*a^2 - 13*a - 21)*q^33 + (a^6 + a^5 - 7*a^4 - 5*a^3 + 9*a^2 + 3*a)*q^34 + (3*a^6 - 3*a^5 - 30*a^4 + 25*a^3 + 80*a^2 - 42*a - 45)*q^35 + (3*a^6 - 2*a^5 - 30*a^4 + 18*a^3 + 80*a^2 - 35*a - 43)*q^36 + (-a^6 + 10*a^4 - 3*a^3 - 28*a^2 + 12*a + 16)*q^37 + O(q^38)
*]> ;  // time = 1.5 seconds




J[138] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 138, 138, 138, 138, 69, 69, 46, 23 ], new_dimensions := [ 1, 1, 1, 2, 1, 2, 1, 2 ], dimensions := [ 1, 1, 1, 2, 2, 4, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 121, 1, 1, 1, 1, 1, 1, 0, 25, 1, 1, 1, 11, 1, 121, 25, 0 ], ap_traces := [
[ -1, -1, -2, -2, -6, -2, 0, 0, -1, 6, 8, 0 ],
[ -1, 1, 0, 2, 0, 2, 0, 2, -1, -6, -4, -10 ],
[ 1, -1, 2, 0, 0, -2, 2, -8, -1, -2, -8, 2 ],
[ 2, 2, -2, 0, -6, 0, -8, -2, 2, 0, 4, 18 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 11, 11, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 11, 11, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 11 ], torsion_lower_bounds := [ 1, 3, 1, 1 ], l_ratios := [ 0, 1/3, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1/121 ], eigenvalues := [*
[ -1, -1, -2, -2, -6, -2, 0, 0, -1, 6, 8, 0 ],
[ -1, 1, 0, 2, 0, 2, 0, 2, -1, -6, -4, -10 ],
[ 1, -1, 2, 0, 0, -2, 2, -8, -1, -2, -8, 2 ],
[
1,
1,
a,
-2*a - 2,
-a - 4,
2*a + 2,
-4,
3*a + 2,
1,
-2*a - 2,
-2*a,
a + 10
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 - 2*q^7 - q^8 + q^9 + 2*q^10 - 6*q^11 - q^12 - 2*q^13 + 2*q^14 + 2*q^15 + q^16 - q^18 - 2*q^20 + 2*q^21 + 6*q^22 - q^23 + q^24 - q^25 + 2*q^26 - q^27 - 2*q^28 + 6*q^29 - 2*q^30 + 8*q^31 - q^32 + 6*q^33 + 4*q^35 + q^36 + O(q^38),
q - q^2 + q^3 + q^4 - q^6 + 2*q^7 - q^8 + q^9 + q^12 + 2*q^13 - 2*q^14 + q^16 - q^18 + 2*q^19 + 2*q^21 - q^23 - q^24 - 5*q^25 - 2*q^26 + q^27 + 2*q^28 - 6*q^29 - 4*q^31 - q^32 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 2*q^5 - q^6 + q^8 + q^9 + 2*q^10 - q^12 - 2*q^13 - 2*q^15 + q^16 + 2*q^17 + q^18 - 8*q^19 + 2*q^20 - q^23 - q^24 - q^25 - 2*q^26 - q^27 - 2*q^29 - 2*q^30 - 8*q^31 + q^32 + 2*q^34 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (-2*a - 2)*q^7 + q^8 + q^9 + a*q^10 + (-a - 4)*q^11 + q^12 + (2*a + 2)*q^13 + (-2*a - 2)*q^14 + a*q^15 + q^16 - 4*q^17 + q^18 + (3*a + 2)*q^19 + a*q^20 + (-2*a - 2)*q^21 + (-a - 4)*q^22 + q^23 + q^24 + (-2*a - 1)*q^25 + (2*a + 2)*q^26 + q^27 + (-2*a - 2)*q^28 + (-2*a - 2)*q^29 + a*q^30 - 2*a*q^31 + q^32 + (-a - 4)*q^33 - 4*q^34 + (2*a - 8)*q^35 + q^36 + (a + 10)*q^37 + O(q^38)
*]> ;  // time = 52.451 seconds




J[139] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 139, 139, 139 ], new_dimensions := [ 1, 3, 7 ], dimensions := [ 1, 3, 7 ], intersection_graph := [ 0, 1, 3, 1, 0, 1, 3, 1, 0 ], ap_traces := [
[ 1, 2, -1, 3, 5, -7, -6, -2, 2, 9, 9, 2 ],
[ -2, -2, -8, 0, -7, 1, -3, -2, -7, -15, 3, -9 ],
[ 1, -2, 11, -5, 2, 6, 5, -10, -1, 30, -20, 6 ]
], hecke_fields := [
x - 1,
x^3 + 2*x^2 - x - 1,
x^7 - x^6 - 11*x^5 + 8*x^4 + 35*x^3 - 10*x^2 - 32*x - 8
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 23 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 23 ]
], torsion_upper_bounds := [ 1, 1, 23 ], torsion_lower_bounds := [ 1, 1, 23 ], l_ratios := [ 1, 0, 1/23 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, 2, -1, 3, 5, -7, -6, -2, 2, 9, 9, 2 ],
[
a,
-a^2 - 2*a,
a^2 + a - 4,
2*a^2 + 3*a - 2,
-3*a^2 - 4*a + 1,
-3*a^2 - 5*a + 3,
a^2 + 3*a - 1,
2*a^2 + 7*a,
4*a^2 + 5*a - 7,
-3*a - 7,
-3*a - 1,
-a^2 - 6*a - 5
],
[
a,
1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 4*a^3 + 19/2*a^2 - 6*a - 4,
-1/4*a^6 - 1/4*a^5 + 9/4*a^4 + 3/2*a^3 - 19/4*a^2 - a + 3,
-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - 2*a^3 - 35/4*a^2 + 7/2*a + 6,
-1/2*a^6 + a^5 + 5*a^4 - 17/2*a^3 - 25/2*a^2 + 27/2*a + 7,
1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 4*a^2 + 17/2*a + 7,
1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 4*a^3 + 17/2*a^2 + 6*a + 2,
-a^4 + 7*a^2 - 8,
1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 5*a^3 + 21/2*a^2 - 10*a - 8,
-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - a^3 - 27/4*a^2 - 7/2*a + 4,
-3/4*a^6 + 1/4*a^5 + 27/4*a^4 - 7/2*a^3 - 57/4*a^2 + 10*a + 3,
-2*a^4 + 13*a^2 - 9
]
*], q_expansions := [*
q + q^2 + 2*q^3 - q^4 - q^5 + 2*q^6 + 3*q^7 - 3*q^8 + q^9 - q^10 + 5*q^11 - 2*q^12 - 7*q^13 + 3*q^14 - 2*q^15 - q^16 - 6*q^17 + q^18 - 2*q^19 + q^20 + 6*q^21 + 5*q^22 + 2*q^23 - 6*q^24 - 4*q^25 - 7*q^26 - 4*q^27 - 3*q^28 + 9*q^29 - 2*q^30 + 9*q^31 + 5*q^32 + 10*q^33 - 6*q^34 - 3*q^35 - q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a^2 - 2*a)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 4)*q^5 + (-a - 1)*q^6 + (2*a^2 + 3*a - 2)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (a^2 + 3*a - 1)*q^9 + (-a^2 - 3*a + 1)*q^10 + (-3*a^2 - 4*a + 1)*q^11 + (a^2 + 3*a)*q^12 + (-3*a^2 - 5*a + 3)*q^13 + (-a^2 + 2)*q^14 + (3*a^2 + 6*a - 1)*q^15 + (-a^2 - a + 2)*q^16 + (a^2 + 3*a - 1)*q^17 + (a^2 + 1)*q^18 + (2*a^2 + 7*a)*q^19 + (-3*a^2 - 2*a + 7)*q^20 + (-a - 3)*q^21 + (2*a^2 - 2*a - 3)*q^22 + (4*a^2 + 5*a - 7)*q^23 + (a^2 + 3*a + 3)*q^24 + (-6*a^2 - 7*a + 11)*q^25 + (a^2 - 3)*q^26 + (3*a^2 + 4*a - 3)*q^27 + (-2*a^2 - 5*a + 3)*q^28 + (-3*a - 7)*q^29 + (2*a + 3)*q^30 + (-3*a - 1)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (2*a^2 + 5*a + 4)*q^33 + (a^2 + 1)*q^34 + (-7*a^2 - 11*a + 9)*q^35 + (-4*a^2 - 4*a + 3)*q^36 + (-a^2 - 6*a - 5)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 4*a^3 + 19/2*a^2 - 6*a - 4)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^6 - 1/4*a^5 + 9/4*a^4 + 3/2*a^3 - 19/4*a^2 - a + 3)*q^5 + (a^5 - 8*a^3 - a^2 + 12*a + 4)*q^6 + (-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - 2*a^3 - 35/4*a^2 + 7/2*a + 6)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 7)*q^9 + (-1/2*a^6 - 1/2*a^5 + 7/2*a^4 + 4*a^3 - 7/2*a^2 - 5*a - 2)*q^10 + (-1/2*a^6 + a^5 + 5*a^4 - 17/2*a^3 - 25/2*a^2 + 27/2*a + 7)*q^11 + (a^5 + a^4 - 9*a^3 - 7*a^2 + 16*a + 8)*q^12 + (1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 4*a^2 + 17/2*a + 7)*q^13 + (a^2 - 2*a - 2)*q^14 + (a^6 - 9*a^4 + 19*a^2 - a - 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 4*a^3 + 17/2*a^2 + 6*a + 2)*q^17 + (-a^6 - a^5 + 9*a^4 + 7*a^3 - 18*a^2 - 7*a)*q^18 + (-a^4 + 7*a^2 - 8)*q^19 + (-1/2*a^6 - 3/2*a^5 + 7/2*a^4 + 11*a^3 - 1/2*a^2 - 16*a - 10)*q^20 + (-a^4 + a^3 + 7*a^2 - 5*a - 8)*q^21 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 5*a^3 + 17/2*a^2 - 9*a - 4)*q^22 + (1/2*a^6 - 1/2*a^5 - 9/2*a^4 + 5*a^3 + 21/2*a^2 - 10*a - 8)*q^23 + (a^6 - a^5 - 9*a^4 + 9*a^3 + 18*a^2 - 16*a - 8)*q^24 + (-3/4*a^6 - 1/4*a^5 + 29/4*a^4 + a^3 - 65/4*a^2 + 3/2*a + 5)*q^25 + (1/2*a^6 + 1/2*a^5 - 9/2*a^4 - 4*a^3 + 17/2*a^2 + 7*a)*q^26 + (a^6 - a^5 - 8*a^4 + 9*a^3 + 11*a^2 - 16*a)*q^27 + (1/2*a^6 - 1/2*a^5 - 11/2*a^4 + 5*a^3 + 31/2*a^2 - 9*a - 12)*q^28 + (-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - a^3 - 27/4*a^2 - 7/2*a + 4)*q^29 + (a^6 + 2*a^5 - 8*a^4 - 16*a^3 + 9*a^2 + 26*a + 8)*q^30 + (-3/4*a^6 + 1/4*a^5 + 27/4*a^4 - 7/2*a^3 - 57/4*a^2 + 10*a + 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 + a^5 + 10*a^4 - 10*a^3 - 24*a^2 + 22*a + 6)*q^33 + (a^6 + a^5 - 8*a^4 - 9*a^3 + 11*a^2 + 18*a + 4)*q^34 + (-3/4*a^6 + 5/4*a^5 + 31/4*a^4 - 19/2*a^3 - 93/4*a^2 + 14*a + 18)*q^35 + (-2*a^6 + 17*a^4 - a^3 - 31*a^2 + 4*a + 6)*q^36 + (-2*a^4 + 13*a^2 - 9)*q^37 + O(q^38)
*]> ;  // time = 1.641 seconds




J[141] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 141, 141, 141, 141, 141, 141, 47 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 4 ], dimensions := [ 1, 1, 1, 1, 1, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 0, 3, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 1, 0, 43, 1, 3, 1, 1, 7, 43, 0 ], ap_traces := [
[ 0, -1, -1, -3, -3, -4, 8, -6, 3, -1, 4, 1 ],
[ -1, -1, 0, 4, 0, 6, -6, 2, 4, 8, 6, -6 ],
[ -1, 1, 2, 0, 4, -2, 2, 0, 0, -6, -4, -10 ],
[ 2, 1, -1, -3, 1, -2, 2, 6, 3, 3, 2, -7 ],
[ -2, 1, -3, -3, -5, 2, -6, -6, 9, 1, -2, 1 ],
[ -1, -2, 1, 1, 7, -6, 2, 12, -3, -15, 6, 11 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 43, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 1, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1 ], eigenvalues := [*
[ 0, -1, -1, -3, -3, -4, 8, -6, 3, -1, 4, 1 ],
[ -1, -1, 0, 4, 0, 6, -6, 2, 4, 8, 6, -6 ],
[ -1, 1, 2, 0, 4, -2, 2, 0, 0, -6, -4, -10 ],
[ 2, 1, -1, -3, 1, -2, 2, 6, 3, 3, 2, -7 ],
[ -2, 1, -3, -3, -5, 2, -6, -6, 9, 1, -2, 1 ],
[
a,
-1,
a + 1,
a + 1,
-a + 3,
-2*a - 4,
-2*a,
6,
-3*a - 3,
a - 7,
2*a + 4,
-a + 5
]
*], q_expansions := [*
q - q^3 - 2*q^4 - q^5 - 3*q^7 + q^9 - 3*q^11 + 2*q^12 - 4*q^13 + q^15 + 4*q^16 + 8*q^17 - 6*q^19 + 2*q^20 + 3*q^21 + 3*q^23 - 4*q^25 - q^27 + 6*q^28 - q^29 + 4*q^31 + 3*q^33 + 3*q^35 - 2*q^36 + q^37 + O(q^38),
q - q^2 - q^3 - q^4 + q^6 + 4*q^7 + 3*q^8 + q^9 + q^12 + 6*q^13 - 4*q^14 - q^16 - 6*q^17 - q^18 + 2*q^19 - 4*q^21 + 4*q^23 - 3*q^24 - 5*q^25 - 6*q^26 - q^27 - 4*q^28 + 8*q^29 + 6*q^31 - 5*q^32 + 6*q^34 - q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 - q^4 + 2*q^5 - q^6 + 3*q^8 + q^9 - 2*q^10 + 4*q^11 - q^12 - 2*q^13 + 2*q^15 - q^16 + 2*q^17 - q^18 - 2*q^20 - 4*q^22 + 3*q^24 - q^25 + 2*q^26 + q^27 - 6*q^29 - 2*q^30 - 4*q^31 - 5*q^32 + 4*q^33 - 2*q^34 - q^36 - 10*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 - q^5 + 2*q^6 - 3*q^7 + q^9 - 2*q^10 + q^11 + 2*q^12 - 2*q^13 - 6*q^14 - q^15 - 4*q^16 + 2*q^17 + 2*q^18 + 6*q^19 - 2*q^20 - 3*q^21 + 2*q^22 + 3*q^23 - 4*q^25 - 4*q^26 + q^27 - 6*q^28 + 3*q^29 - 2*q^30 + 2*q^31 - 8*q^32 + q^33 + 4*q^34 + 3*q^35 + 2*q^36 - 7*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - 3*q^5 - 2*q^6 - 3*q^7 + q^9 + 6*q^10 - 5*q^11 + 2*q^12 + 2*q^13 + 6*q^14 - 3*q^15 - 4*q^16 - 6*q^17 - 2*q^18 - 6*q^19 - 6*q^20 - 3*q^21 + 10*q^22 + 9*q^23 + 4*q^25 - 4*q^26 + q^27 - 6*q^28 + q^29 + 6*q^30 - 2*q^31 + 8*q^32 - 5*q^33 + 12*q^34 + 9*q^35 + 2*q^36 + q^37 + O(q^38),
q + a*q^2 - q^3 + (-a + 2)*q^4 + (a + 1)*q^5 - a*q^6 + (a + 1)*q^7 + (a - 4)*q^8 + q^9 + 4*q^10 + (-a + 3)*q^11 + (a - 2)*q^12 + (-2*a - 4)*q^13 + 4*q^14 + (-a - 1)*q^15 - 3*a*q^16 - 2*a*q^17 + a*q^18 + 6*q^19 + (2*a - 2)*q^20 + (-a - 1)*q^21 + (4*a - 4)*q^22 + (-3*a - 3)*q^23 + (-a + 4)*q^24 + a*q^25 + (-2*a - 8)*q^26 - q^27 + (2*a - 2)*q^28 + (a - 7)*q^29 - 4*q^30 + (2*a + 4)*q^31 + (a - 4)*q^32 + (a - 3)*q^33 + (2*a - 8)*q^34 + (a + 5)*q^35 + (-a + 2)*q^36 + (-a + 5)*q^37 + O(q^38)
*]> ;  // time = 12.77 seconds




J[142] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 142, 142, 142, 142, 142, 71, 71 ], new_dimensions := [ 1, 1, 1, 1, 1, 3, 3 ], dimensions := [ 1, 1, 1, 1, 1, 6, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 3, 3, 1, 3, 0, 1, 1, 9, 9, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 3, 3, 1, 3, 9, 1, 3, 0, 81, 1, 3, 9, 1, 3, 81, 0 ], ap_traces := [
[ -1, -1, -2, -1, -2, -3, -6, 5, -1, 6, 1, 6 ],
[ -1, 0, 2, 0, 6, 4, 6, -8, -4, -2, -8, 10 ],
[ -1, 3, 2, -3, -6, -5, 6, 1, 5, -2, -5, -2 ],
[ 1, 1, 0, -1, 0, -1, 0, -1, 3, 0, 5, -4 ],
[ 1, -3, -4, -3, 0, 1, 0, -5, -7, -8, 7, 4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 27, 1 ],
[ 3, 1 ],
[ 9, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 9, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1 ], l_ratios := [ 0, 1, 1, 1/3, 0 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0 ], eigenvalues := [*
[ -1, -1, -2, -1, -2, -3, -6, 5, -1, 6, 1, 6 ],
[ -1, 0, 2, 0, 6, 4, 6, -8, -4, -2, -8, 10 ],
[ -1, 3, 2, -3, -6, -5, 6, 1, 5, -2, -5, -2 ],
[ 1, 1, 0, -1, 0, -1, 0, -1, 3, 0, 5, -4 ],
[ 1, -3, -4, -3, 0, 1, 0, -5, -7, -8, 7, 4 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 - q^7 - q^8 - 2*q^9 + 2*q^10 - 2*q^11 - q^12 - 3*q^13 + q^14 + 2*q^15 + q^16 - 6*q^17 + 2*q^18 + 5*q^19 - 2*q^20 + q^21 + 2*q^22 - q^23 + q^24 - q^25 + 3*q^26 + 5*q^27 - q^28 + 6*q^29 - 2*q^30 + q^31 - q^32 + 2*q^33 + 6*q^34 + 2*q^35 - 2*q^36 + 6*q^37 + O(q^38),
q - q^2 + q^4 + 2*q^5 - q^8 - 3*q^9 - 2*q^10 + 6*q^11 + 4*q^13 + q^16 + 6*q^17 + 3*q^18 - 8*q^19 + 2*q^20 - 6*q^22 - 4*q^23 - q^25 - 4*q^26 - 2*q^29 - 8*q^31 - q^32 - 6*q^34 - 3*q^36 + 10*q^37 + O(q^38),
q - q^2 + 3*q^3 + q^4 + 2*q^5 - 3*q^6 - 3*q^7 - q^8 + 6*q^9 - 2*q^10 - 6*q^11 + 3*q^12 - 5*q^13 + 3*q^14 + 6*q^15 + q^16 + 6*q^17 - 6*q^18 + q^19 + 2*q^20 - 9*q^21 + 6*q^22 + 5*q^23 - 3*q^24 - q^25 + 5*q^26 + 9*q^27 - 3*q^28 - 2*q^29 - 6*q^30 - 5*q^31 - q^32 - 18*q^33 - 6*q^34 - 6*q^35 + 6*q^36 - 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 - q^7 + q^8 - 2*q^9 + q^12 - q^13 - q^14 + q^16 - 2*q^18 - q^19 - q^21 + 3*q^23 + q^24 - 5*q^25 - q^26 - 5*q^27 - q^28 + 5*q^31 + q^32 - 2*q^36 - 4*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - 4*q^5 - 3*q^6 - 3*q^7 + q^8 + 6*q^9 - 4*q^10 - 3*q^12 + q^13 - 3*q^14 + 12*q^15 + q^16 + 6*q^18 - 5*q^19 - 4*q^20 + 9*q^21 - 7*q^23 - 3*q^24 + 11*q^25 + q^26 - 9*q^27 - 3*q^28 - 8*q^29 + 12*q^30 + 7*q^31 + q^32 + 12*q^35 + 6*q^36 + 4*q^37 + O(q^38)
*]> ;  // time = 17.65 seconds




J[143] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 143, 143, 143, 11 ], new_dimensions := [ 1, 4, 6, 1 ], dimensions := [ 1, 4, 6, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 0, 1, 9, 1, 1, 0, 1, 1, 9, 1, 0 ], ap_traces := [
[ 0, -1, -1, -2, -1, -1, -4, 2, 7, -2, -3, -11 ],
[ 3, 0, 0, 6, 4, -4, 6, 8, -4, -10, 2, 12 ],
[ 0, 3, 1, 4, -6, 6, 0, -10, 11, 2, -9, 15 ]
], hecke_fields := [
x - 1,
x^4 - 3*x^3 - x^2 + 5*x + 1,
x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 9 ],
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 7, 3 ], torsion_lower_bounds := [ 1, 7, 3 ], l_ratios := [ 0, 1/7, 1/3 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ 0, -1, -1, -2, -1, -1, -4, 2, 7, -2, -3, -11 ],
[
a,
-a^3 + 3*a^2 - 3,
-2*a^2 + 2*a + 4,
a^3 - a^2 - 4*a + 2,
1,
-1,
-4*a^2 + 6*a + 8,
-3*a^3 + 7*a^2 + 2*a - 3,
a^3 - a^2 - 2*a - 2,
-2*a^3 + 4*a^2 + 4*a - 6,
4*a^3 - 6*a^2 - 8*a + 2,
-4*a^2 + 8*a + 8
],
[
a,
-a^5 - a^4 + 8*a^3 + 6*a^2 - 11*a - 5,
a^5 + 2*a^4 - 8*a^3 - 14*a^2 + 12*a + 15,
2*a^5 + 2*a^4 - 17*a^3 - 13*a^2 + 26*a + 14,
-1,
1,
-2*a,
-2*a^5 - 3*a^4 + 16*a^3 + 20*a^2 - 23*a - 22,
-3*a^5 - 4*a^4 + 25*a^3 + 29*a^2 - 38*a - 33,
2*a^5 + 2*a^4 - 16*a^3 - 14*a^2 + 22*a + 18,
3*a^5 + 4*a^4 - 26*a^3 - 28*a^2 + 44*a + 29,
-a^5 - 2*a^4 + 8*a^3 + 16*a^2 - 10*a - 19
]
*], q_expansions := [*
q - q^3 - 2*q^4 - q^5 - 2*q^7 - 2*q^9 - q^11 + 2*q^12 - q^13 + q^15 + 4*q^16 - 4*q^17 + 2*q^19 + 2*q^20 + 2*q^21 + 7*q^23 - 4*q^25 + 5*q^27 + 4*q^28 - 2*q^29 - 3*q^31 + q^33 + 2*q^35 + 4*q^36 - 11*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 3*a^2 - 3)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 + 2*a + 4)*q^5 + (-a^2 + 2*a + 1)*q^6 + (a^3 - a^2 - 4*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 - 3*a^2 - 2*a + 5)*q^9 + (-2*a^3 + 2*a^2 + 4*a)*q^10 + q^11 + (a^3 - 4*a^2 + a + 6)*q^12 - q^13 + (2*a^3 - 3*a^2 - 3*a - 1)*q^14 + (-2*a^3 + 6*a^2 + 2*a - 10)*q^15 + (3*a^3 - 5*a^2 - 5*a + 3)*q^16 + (-4*a^2 + 6*a + 8)*q^17 + (-a^2 - 1)*q^18 + (-3*a^3 + 7*a^2 + 2*a - 3)*q^19 + (-4*a^3 + 6*a^2 + 6*a - 6)*q^20 + (-2*a^3 + 8*a^2 - 4*a - 9)*q^21 + a*q^22 + (a^3 - a^2 - 2*a - 2)*q^23 + (-a^3 + 4*a^2 - 3*a - 3)*q^24 + (4*a^3 - 8*a^2 - 4*a + 7)*q^25 - a*q^26 + (2*a^2 - 2*a - 7)*q^27 + (a^3 + a^2 - 3*a - 6)*q^28 + (-2*a^3 + 4*a^2 + 4*a - 6)*q^29 + 2*q^30 + (4*a^3 - 6*a^2 - 8*a + 2)*q^31 + (2*a^3 - 2*a^2 - 4*a - 3)*q^32 + (-a^3 + 3*a^2 - 3)*q^33 + (-4*a^3 + 6*a^2 + 8*a)*q^34 + (2*a^3 - 8*a^2 + 10)*q^35 + (-3*a^3 + 6*a^2 + 3*a - 10)*q^36 + (-4*a^2 + 8*a + 8)*q^37 + O(q^38),
q + a*q^2 + (-a^5 - a^4 + 8*a^3 + 6*a^2 - 11*a - 5)*q^3 + (a^2 - 2)*q^4 + (a^5 + 2*a^4 - 8*a^3 - 14*a^2 + 12*a + 15)*q^5 + (-a^5 - 2*a^4 + 8*a^3 + 13*a^2 - 12*a - 12)*q^6 + (2*a^5 + 2*a^4 - 17*a^3 - 13*a^2 + 26*a + 14)*q^7 + (a^3 - 4*a)*q^8 + (-3*a^5 - 4*a^4 + 25*a^3 + 27*a^2 - 38*a - 26)*q^9 + (2*a^5 + 2*a^4 - 16*a^3 - 12*a^2 + 22*a + 12)*q^10 - q^11 + (-a^3 + 3*a - 2)*q^12 + q^13 + (2*a^5 + 3*a^4 - 17*a^3 - 22*a^2 + 28*a + 24)*q^14 + (3*a^5 + 4*a^4 - 24*a^3 - 28*a^2 + 30*a + 33)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - 2*a*q^17 + (-4*a^5 - 5*a^4 + 33*a^3 + 34*a^2 - 47*a - 36)*q^18 + (-2*a^5 - 3*a^4 + 16*a^3 + 20*a^2 - 23*a - 22)*q^19 + (2*a^2 + 2*a - 6)*q^20 + (2*a^5 + 3*a^4 - 17*a^3 - 19*a^2 + 29*a + 14)*q^21 - a*q^22 + (-3*a^5 - 4*a^4 + 25*a^3 + 29*a^2 - 38*a - 33)*q^23 + (2*a^5 + 3*a^4 - 16*a^3 - 23*a^2 + 22*a + 24)*q^24 + (-3*a^5 - 4*a^4 + 26*a^3 + 26*a^2 - 44*a - 20)*q^25 + a*q^26 + (-5*a^5 - 7*a^4 + 41*a^3 + 47*a^2 - 59*a - 47)*q^27 + (-a^5 - a^4 + 8*a^3 + 6*a^2 - 14*a - 4)*q^28 + (2*a^5 + 2*a^4 - 16*a^3 - 14*a^2 + 22*a + 18)*q^29 + (4*a^5 + 6*a^4 - 34*a^3 - 42*a^2 + 54*a + 36)*q^30 + (3*a^5 + 4*a^4 - 26*a^3 - 28*a^2 + 44*a + 29)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^5 + a^4 - 8*a^3 - 6*a^2 + 11*a + 5)*q^33 - 2*a^2*q^34 + (-2*a^3 + 12*a - 6)*q^35 + (a^5 + a^4 - 8*a^3 - 5*a^2 + 12*a + 4)*q^36 + (-a^5 - 2*a^4 + 8*a^3 + 16*a^2 - 10*a - 19)*q^37 + O(q^38)
*]> ;  // time = 12.87 seconds




J[145] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 145, 145, 145, 145, 29 ], new_dimensions := [ 1, 2, 3, 3, 2 ], dimensions := [ 1, 2, 3, 3, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 0, 1, 25, 1, 1, 1, 0, 1, 1, 7, 25, 1, 0 ], ap_traces := [
[ -1, 0, -1, -2, -6, 2, -2, -2, 2, -1, 2, 10 ],
[ -2, -4, 2, -4, -4, -4, 0, -4, -12, 2, -4, 0 ],
[ 3, -2, -3, -2, 8, -6, 0, 0, 14, 3, 12, 4 ],
[ 1, 2, 3, 4, 2, -2, -4, -10, 16, -3, -14, -8 ]
], hecke_fields := [
x - 1,
x^2 + 2*x - 1,
x^3 - 3*x^2 - x + 5,
x^3 - x^2 - 3*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 7, 1 ],
[ 25, 1 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 1, 5 ], l_ratios := [ 0, 0, 1, 1/5 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, -1, -2, -6, 2, -2, -2, 2, -1, 2, 10 ],
[
a,
-2,
1,
-2*a - 4,
2*a,
-2,
2*a + 2,
-2*a - 4,
2*a - 4,
1,
6*a + 4,
-6*a - 6
],
[
a,
-a^2 + 2*a + 1,
-1,
-a^2 + 3,
a^2 - 2*a + 1,
2*a - 4,
-3*a^2 + 2*a + 9,
3*a^2 - 4*a - 7,
a^2 - 2*a + 3,
1,
-3*a^2 + 4*a + 11,
-a^2 - 2*a + 7
],
[
a,
-a^2 + 3,
1,
a^2 - 1,
a^2 - 2*a - 1,
-2*a,
3*a^2 - 4*a - 7,
-a^2 - 1,
-a^2 + 2*a + 7,
-1,
a^2 - 7,
-3*a^2 + 4*a + 3
]
*], q_expansions := [*
q - q^2 - q^4 - q^5 - 2*q^7 + 3*q^8 - 3*q^9 + q^10 - 6*q^11 + 2*q^13 + 2*q^14 - q^16 - 2*q^17 + 3*q^18 - 2*q^19 + q^20 + 6*q^22 + 2*q^23 + q^25 - 2*q^26 + 2*q^28 - q^29 + 2*q^31 - 5*q^32 + 2*q^34 + 2*q^35 + 3*q^36 + 10*q^37 + O(q^38),
q + a*q^2 - 2*q^3 + (-2*a - 1)*q^4 + q^5 - 2*a*q^6 + (-2*a - 4)*q^7 + (a - 2)*q^8 + q^9 + a*q^10 + 2*a*q^11 + (4*a + 2)*q^12 - 2*q^13 - 2*q^14 - 2*q^15 + 3*q^16 + (2*a + 2)*q^17 + a*q^18 + (-2*a - 4)*q^19 + (-2*a - 1)*q^20 + (4*a + 8)*q^21 + (-4*a + 2)*q^22 + (2*a - 4)*q^23 + (-2*a + 4)*q^24 + q^25 - 2*a*q^26 + 4*q^27 + (2*a + 8)*q^28 + q^29 - 2*a*q^30 + (6*a + 4)*q^31 + (a + 4)*q^32 - 4*a*q^33 + (-2*a + 2)*q^34 + (-2*a - 4)*q^35 + (-2*a - 1)*q^36 + (-6*a - 6)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^2 + 5)*q^6 + (-a^2 + 3)*q^7 + (3*a^2 - 3*a - 5)*q^8 + (-2*a + 3)*q^9 - a*q^10 + (a^2 - 2*a + 1)*q^11 + (-a^2 + 3)*q^12 + (2*a - 4)*q^13 + (-3*a^2 + 2*a + 5)*q^14 + (a^2 - 2*a - 1)*q^15 + (4*a^2 - 2*a - 11)*q^16 + (-3*a^2 + 2*a + 9)*q^17 + (-2*a^2 + 3*a)*q^18 + (3*a^2 - 4*a - 7)*q^19 + (-a^2 + 2)*q^20 + (2*a - 2)*q^21 + (a^2 + 2*a - 5)*q^22 + (a^2 - 2*a + 3)*q^23 + (-a^2 + 2*a - 5)*q^24 + q^25 + (2*a^2 - 4*a)*q^26 + (2*a^2 - 10)*q^27 + (-5*a^2 + 2*a + 9)*q^28 + q^29 + (a^2 - 5)*q^30 + (-3*a^2 + 4*a + 11)*q^31 + (4*a^2 - a - 10)*q^32 + (-2*a^2 + 6*a - 4)*q^33 + (-7*a^2 + 6*a + 15)*q^34 + (a^2 - 3)*q^35 + (-3*a^2 + 2*a + 4)*q^36 + (-a^2 - 2*a + 7)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 + 1)*q^6 + (a^2 - 1)*q^7 + (a^2 - a - 1)*q^8 + (-2*a^2 + 2*a + 5)*q^9 + a*q^10 + (a^2 - 2*a - 1)*q^11 + (a^2 - 2*a - 5)*q^12 - 2*a*q^13 + (a^2 + 2*a - 1)*q^14 + (-a^2 + 3)*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (3*a^2 - 4*a - 7)*q^17 + (-a + 2)*q^18 + (-a^2 - 1)*q^19 + (a^2 - 2)*q^20 + (-2*a - 2)*q^21 + (-a^2 + 2*a - 1)*q^22 + (-a^2 + 2*a + 7)*q^23 + (a^2 - 2*a - 3)*q^24 + q^25 - 2*a^2*q^26 + (-2*a^2 + 4*a + 6)*q^27 + (a^2 + 2*a + 1)*q^28 - q^29 + (-a^2 + 1)*q^30 + (a^2 - 7)*q^31 + (-2*a^2 - a + 4)*q^32 + (2*a^2 - 2*a - 4)*q^33 + (-a^2 + 2*a - 3)*q^34 + (a^2 - 1)*q^35 + (3*a^2 - 2*a - 10)*q^36 + (-3*a^2 + 4*a + 3)*q^37 + O(q^38)
*]> ;  // time = 12.571 seconds




J[146] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 146, 146, 73, 73, 73 ], new_dimensions := [ 3, 4, 1, 2, 2 ], dimensions := [ 3, 4, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 9, 1, 0, 1, 19, 1, 1, 1, 0, 1, 9, 1, 19, 1, 0, 1, 9, 1, 9, 1, 0 ], ap_traces := [
[ -3, 0, -2, 8, 2, 4, -2, 8, 4, -6, 2, -14 ],
[ 4, 0, 2, 0, 0, -4, -4, 0, -12, 2, -6, 12 ]
], hecke_fields := [
x^3 - 8*x + 4,
x^4 - 8*x^2 + 4*x + 4
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 27, 3 ],
[ 703, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 703, 1 ]
], torsion_upper_bounds := [ 3, 37 ], torsion_lower_bounds := [ 3, 37 ], l_ratios := [ 1/3, 19/37 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
-1,
a,
-1/2*a^2 + 2,
1/2*a^2,
-a^2 - 2*a + 6,
-1/2*a^2 + 4,
a^2 + 2*a - 6,
-a^2 - 2*a + 8,
a^2 - 4,
3/2*a^2 - 2*a - 10,
1/2*a^2 + 2*a - 2,
-2*a^2 - 2*a + 6
],
[
1,
a,
-1/2*a^3 - 1/2*a^2 + 2*a + 1,
a^3 + 1/2*a^2 - 7*a + 1,
a^2 - 4,
-3/2*a^2 - a + 5,
-a^3 - a^2 + 6*a,
a^2 + 2*a - 4,
-a^3 - a^2 + 8*a - 2,
3/2*a^3 + 1/2*a^2 - 10*a + 3,
-1/2*a^3 + 1/2*a^2 + 6*a - 5,
a^3 - 8*a + 6
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (-1/2*a^2 + 2)*q^5 - a*q^6 + 1/2*a^2*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^2 - 2)*q^10 + (-a^2 - 2*a + 6)*q^11 + a*q^12 + (-1/2*a^2 + 4)*q^13 - 1/2*a^2*q^14 + (-2*a + 2)*q^15 + q^16 + (a^2 + 2*a - 6)*q^17 + (-a^2 + 3)*q^18 + (-a^2 - 2*a + 8)*q^19 + (-1/2*a^2 + 2)*q^20 + (4*a - 2)*q^21 + (a^2 + 2*a - 6)*q^22 + (a^2 - 4)*q^23 - a*q^24 + (-a - 1)*q^25 + (1/2*a^2 - 4)*q^26 + (2*a - 4)*q^27 + 1/2*a^2*q^28 + (3/2*a^2 - 2*a - 10)*q^29 + (2*a - 2)*q^30 + (1/2*a^2 + 2*a - 2)*q^31 - q^32 + (-2*a^2 - 2*a + 4)*q^33 + (-a^2 - 2*a + 6)*q^34 + (-a^2 + a)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 - 2*a + 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/2*a^3 - 1/2*a^2 + 2*a + 1)*q^5 + a*q^6 + (a^3 + 1/2*a^2 - 7*a + 1)*q^7 + q^8 + (a^2 - 3)*q^9 + (-1/2*a^3 - 1/2*a^2 + 2*a + 1)*q^10 + (a^2 - 4)*q^11 + a*q^12 + (-3/2*a^2 - a + 5)*q^13 + (a^3 + 1/2*a^2 - 7*a + 1)*q^14 + (-1/2*a^3 - 2*a^2 + 3*a + 2)*q^15 + q^16 + (-a^3 - a^2 + 6*a)*q^17 + (a^2 - 3)*q^18 + (a^2 + 2*a - 4)*q^19 + (-1/2*a^3 - 1/2*a^2 + 2*a + 1)*q^20 + (1/2*a^3 + a^2 - 3*a - 4)*q^21 + (a^2 - 4)*q^22 + (-a^3 - a^2 + 8*a - 2)*q^23 + a*q^24 + (2*a^2 + a - 5)*q^25 + (-3/2*a^2 - a + 5)*q^26 + (a^3 - 6*a)*q^27 + (a^3 + 1/2*a^2 - 7*a + 1)*q^28 + (3/2*a^3 + 1/2*a^2 - 10*a + 3)*q^29 + (-1/2*a^3 - 2*a^2 + 3*a + 2)*q^30 + (-1/2*a^3 + 1/2*a^2 + 6*a - 5)*q^31 + q^32 + (a^3 - 4*a)*q^33 + (-a^3 - a^2 + 6*a)*q^34 + (a^3 + a^2 - 7*a - 4)*q^35 + (a^2 - 3)*q^36 + (a^3 - 8*a + 6)*q^37 + O(q^38)
*]> ;  // time = 20.321 seconds




J[149] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 149, 149 ], new_dimensions := [ 3, 9 ], dimensions := [ 3, 9 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -4, -3, -5, -5, -3, 5, -18, 8, -2, -18, 3 ],
[ -1, 6, -1, 3, 5, 7, -5, 30, -4, -16, 22, -7 ]
], hecke_fields := [
x^3 + x^2 - 2*x - 1,
x^9 + x^8 - 15*x^7 - 12*x^6 + 75*x^5 + 48*x^4 - 137*x^3 - 76*x^2 + 68*x + 39
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 37 ]
], tamagawa_numbers := [
[ 1 ],
[ 37 ]
], torsion_upper_bounds := [ 1, 37 ], torsion_lower_bounds := [ 1, 37 ], l_ratios := [ 0, 1/37 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - a,
a^2 - a - 3,
a^2 + a - 3,
-2*a^2 + a + 2,
-2*a^2 - a + 2,
4*a^2 + 3*a - 4,
-2*a^2 - a - 3,
-a^2 - a + 4,
-4*a^2 - 3*a + 5,
3*a^2 - 11,
6*a + 3
],
[
a,
-3/4*a^8 - 1/4*a^7 + 23/2*a^6 + 5/4*a^5 - 233/4*a^4 + 13/4*a^3 + 209/2*a^2 - 49/4*a - 44,
-1/4*a^8 - 1/4*a^7 + 7/2*a^6 + 9/4*a^5 - 63/4*a^4 - 19/4*a^3 + 23*a^2 + 3/4*a - 13/2,
a^8 + 1/2*a^7 - 29/2*a^6 - 3*a^5 + 139/2*a^4 - 3/2*a^3 - 237/2*a^2 + 14*a + 101/2,
3/4*a^8 - 49/4*a^6 + 3/4*a^5 + 129/2*a^4 - 15/2*a^3 - 471/4*a^2 + 63/4*a + 207/4,
a^8 + 1/2*a^7 - 29/2*a^6 - 3*a^5 + 139/2*a^4 - 3/2*a^3 - 235/2*a^2 + 14*a + 95/2,
-1/4*a^8 - 1/2*a^7 + 11/4*a^6 + 19/4*a^5 - 10*a^4 - 25/2*a^3 + 59/4*a^2 + 29/4*a - 25/4,
-1/2*a^8 + 15/2*a^6 - 3/2*a^5 - 37*a^4 + 12*a^3 + 131/2*a^2 - 41/2*a - 55/2,
1/2*a^8 - 1/4*a^7 - 33/4*a^6 + 7/2*a^5 + 177/4*a^4 - 57/4*a^3 - 335/4*a^2 + 15*a + 149/4,
1/4*a^7 + 3/4*a^6 - 5/2*a^5 - 31/4*a^4 + 27/4*a^3 + 89/4*a^2 - 7/2*a - 61/4,
3/2*a^8 + 1/2*a^7 - 23*a^6 - 7/2*a^5 + 231/2*a^4 + 1/2*a^3 - 204*a^2 + 37/2*a + 88,
5/4*a^8 + 3/4*a^7 - 18*a^6 - 21/4*a^5 + 345/4*a^4 + 17/4*a^3 - 299/2*a^2 + 41/4*a + 66
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - a)*q^3 + (a^2 - 2)*q^4 + (a^2 - a - 3)*q^5 + (-2*a - 1)*q^6 + (a^2 + a - 3)*q^7 + (-a^2 - 2*a + 1)*q^8 + (2*a^2 + 3*a - 2)*q^9 + (-2*a^2 - a + 1)*q^10 + (-2*a^2 + a + 2)*q^11 + a*q^12 + (-2*a^2 - a + 2)*q^13 + (-a + 1)*q^14 + (a^2 + 4*a + 1)*q^15 + (-3*a^2 - a + 3)*q^16 + (4*a^2 + 3*a - 4)*q^17 + (a^2 + 2*a + 2)*q^18 + (-2*a^2 - a - 3)*q^19 + (-a^2 - a + 4)*q^20 + (a^2 - 1)*q^21 + (3*a^2 - 2*a - 2)*q^22 + (-a^2 - a + 4)*q^23 + (a^2 + 4*a + 2)*q^24 + (a + 1)*q^25 + (a^2 - 2*a - 2)*q^26 + (a^2 - 3*a - 3)*q^27 + (-3*a^2 - a + 6)*q^28 + (-4*a^2 - 3*a + 5)*q^29 + (3*a^2 + 3*a + 1)*q^30 + (3*a^2 - 11)*q^31 + (4*a^2 + a - 5)*q^32 + (2*a^2 - 2*a - 1)*q^33 + (-a^2 + 4*a + 4)*q^34 + (-4*a^2 - a + 8)*q^35 + (-3*a^2 - 2*a + 5)*q^36 + (6*a + 3)*q^37 + O(q^38),
q + a*q^2 + (-3/4*a^8 - 1/4*a^7 + 23/2*a^6 + 5/4*a^5 - 233/4*a^4 + 13/4*a^3 + 209/2*a^2 - 49/4*a - 44)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^8 - 1/4*a^7 + 7/2*a^6 + 9/4*a^5 - 63/4*a^4 - 19/4*a^3 + 23*a^2 + 3/4*a - 13/2)*q^5 + (1/2*a^8 + 1/4*a^7 - 31/4*a^6 - 2*a^5 + 157/4*a^4 + 7/4*a^3 - 277/4*a^2 + 7*a + 117/4)*q^6 + (a^8 + 1/2*a^7 - 29/2*a^6 - 3*a^5 + 139/2*a^4 - 3/2*a^3 - 237/2*a^2 + 14*a + 101/2)*q^7 + (a^3 - 4*a)*q^8 + (-3/4*a^8 + 47/4*a^6 - 7/4*a^5 - 121/2*a^4 + 14*a^3 + 439/4*a^2 - 93/4*a - 185/4)*q^9 + (-1/4*a^7 - 3/4*a^6 + 3*a^5 + 29/4*a^4 - 45/4*a^3 - 73/4*a^2 + 21/2*a + 39/4)*q^10 + (3/4*a^8 - 49/4*a^6 + 3/4*a^5 + 129/2*a^4 - 15/2*a^3 - 471/4*a^2 + 63/4*a + 207/4)*q^11 + (5/4*a^8 + 1/4*a^7 - 19*a^6 - 3/4*a^5 + 377/4*a^4 - 29/4*a^3 - 164*a^2 + 79/4*a + 137/2)*q^12 + (a^8 + 1/2*a^7 - 29/2*a^6 - 3*a^5 + 139/2*a^4 - 3/2*a^3 - 235/2*a^2 + 14*a + 95/2)*q^13 + (-1/2*a^8 + 1/2*a^7 + 9*a^6 - 11/2*a^5 - 99/2*a^4 + 37/2*a^3 + 90*a^2 - 35/2*a - 39)*q^14 + (-7/4*a^8 - 3/4*a^7 + 26*a^6 + 21/4*a^5 - 503/4*a^4 - 9/4*a^3 + 211*a^2 - 77/4*a - 169/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/4*a^8 - 1/2*a^7 + 11/4*a^6 + 19/4*a^5 - 10*a^4 - 25/2*a^3 + 59/4*a^2 + 29/4*a - 25/4)*q^17 + (3/4*a^8 + 1/2*a^7 - 43/4*a^6 - 17/4*a^5 + 50*a^4 + 7*a^3 - 321/4*a^2 + 19/4*a + 117/4)*q^18 + (-1/2*a^8 + 15/2*a^6 - 3/2*a^5 - 37*a^4 + 12*a^3 + 131/2*a^2 - 41/2*a - 55/2)*q^19 + (1/4*a^8 - 1/4*a^7 - 4*a^6 + 11/4*a^5 + 81/4*a^4 - 35/4*a^3 - 71/2*a^2 + 33/4*a + 13)*q^20 + (1/2*a^8 - 15/2*a^6 + 3/2*a^5 + 36*a^4 - 12*a^3 - 115/2*a^2 + 37/2*a + 41/2)*q^21 + (-3/4*a^8 - a^7 + 39/4*a^6 + 33/4*a^5 - 87/2*a^4 - 15*a^3 + 291/4*a^2 + 3/4*a - 117/4)*q^22 + (1/2*a^8 - 1/4*a^7 - 33/4*a^6 + 7/2*a^5 + 177/4*a^4 - 57/4*a^3 - 335/4*a^2 + 15*a + 149/4)*q^23 + (-2*a^8 - 3/4*a^7 + 119/4*a^6 + 9/2*a^5 - 583/4*a^4 + 15/4*a^3 + 1013/4*a^2 - 61/2*a - 429/4)*q^24 + (-1/2*a^8 + 1/4*a^7 + 33/4*a^6 - 4*a^5 - 179/4*a^4 + 71/4*a^3 + 347/4*a^2 - 19*a - 163/4)*q^25 + (-1/2*a^8 + 1/2*a^7 + 9*a^6 - 11/2*a^5 - 99/2*a^4 + 39/2*a^3 + 90*a^2 - 41/2*a - 39)*q^26 + (-7/4*a^8 + 109/4*a^6 - 15/4*a^5 - 277/2*a^4 + 61/2*a^3 + 987/4*a^2 - 203/4*a - 419/4)*q^27 + (-a^8 + 1/2*a^7 + 35/2*a^6 - 6*a^5 - 193/2*a^4 + 49/2*a^3 + 363/2*a^2 - 33*a - 163/2)*q^28 + (1/4*a^7 + 3/4*a^6 - 5/2*a^5 - 31/4*a^4 + 27/4*a^3 + 89/4*a^2 - 7/2*a - 61/4)*q^29 + (a^8 - 1/4*a^7 - 63/4*a^6 + 11/2*a^5 + 327/4*a^4 - 115/4*a^3 - 609/4*a^2 + 69/2*a + 273/4)*q^30 + (3/2*a^8 + 1/2*a^7 - 23*a^6 - 7/2*a^5 + 231/2*a^4 + 1/2*a^3 - 204*a^2 + 37/2*a + 88)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/4*a^8 + 17/4*a^6 - 1/4*a^5 - 47/2*a^4 + 2*a^3 + 185/4*a^2 - 3/4*a - 99/4)*q^33 + (-1/4*a^8 - a^7 + 7/4*a^6 + 35/4*a^5 - 1/2*a^4 - 39/2*a^3 - 47/4*a^2 + 43/4*a + 39/4)*q^34 + (3/2*a^8 + 1/2*a^7 - 23*a^6 - 5/2*a^5 + 233/2*a^4 - 15/2*a^3 - 210*a^2 + 59/2*a + 91)*q^35 + (5/4*a^8 + 1/2*a^7 - 75/4*a^6 - 11/4*a^5 + 92*a^4 - 11/2*a^3 - 631/4*a^2 + 99/4*a + 253/4)*q^36 + (5/4*a^8 + 3/4*a^7 - 18*a^6 - 21/4*a^5 + 345/4*a^4 + 17/4*a^3 - 299/2*a^2 + 41/4*a + 66)*q^37 + O(q^38)
*]> ;  // time = 1.66 seconds




J[151] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 151, 151, 151 ], new_dimensions := [ 3, 3, 6 ], dimensions := [ 3, 3, 6 ], intersection_graph := [ 0, 1, 1, 1, 0, 67, 1, 67, 0 ], ap_traces := [
[ -2, -1, -7, -3, -5, -1, -8, -3, 0, -1, -1, 13 ],
[ 0, 6, 5, -6, -1, -2, 9, 3, 0, 3, -1, 3 ],
[ 1, -5, 6, 3, 8, -1, 9, -6, -4, -2, -8, -12 ]
], hecke_fields := [
x^3 + 2*x^2 - x - 1,
x^3 - 5*x + 3,
x^6 - x^5 - 7*x^4 + 3*x^3 + 13*x^2 + 3*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 25 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 25 ]
], torsion_upper_bounds := [ 1, 1, 25 ], torsion_lower_bounds := [ 1, 1, 25 ], l_ratios := [ 0, 1, 1/25 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[
a,
-a - 1,
-a^2 - a - 1,
-1,
2*a^2 + 4*a - 3,
3*a^2 + 5*a - 3,
-3*a^2 - 5*a,
-5*a^2 - 6*a + 5,
3*a^2 + 6*a - 2,
-a^2 - 7*a - 3,
-4*a^2 - 7*a + 3,
-3*a^2 - 5*a + 7
],
[
a,
2,
-a^2 - 2*a + 5,
-2,
2*a^2 + a - 7,
-2*a^2 + 6,
-a + 3,
3*a^2 + 3*a - 9,
2*a,
3*a^2 + 5*a - 9,
-a^2 + 3,
-3*a + 1
],
[
a,
-a^5 + a^4 + 7*a^3 - 4*a^2 - 12*a - 1,
a^5 - a^4 - 6*a^3 + 3*a^2 + 9*a + 2,
-a^4 + 3*a^2 + 3*a + 3,
a^3 - 5*a,
2*a^5 - 3*a^4 - 11*a^3 + 12*a^2 + 13*a - 4,
-a^4 - 2*a^3 + 6*a^2 + 8*a,
2*a^5 - a^4 - 12*a^3 + 2*a^2 + 15*a + 1,
-a^5 + 6*a^3 - 7*a + 1,
3*a^5 - 5*a^4 - 17*a^3 + 19*a^2 + 24*a - 3,
-2*a^5 + 3*a^4 + 10*a^3 - 9*a^2 - 12*a - 3,
a^2 + 3*a - 5
]
*], q_expansions := [*
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - a - 1)*q^5 + (-a^2 - a)*q^6 - q^7 + (-2*a^2 - 3*a + 1)*q^8 + (a^2 + 2*a - 2)*q^9 + (a^2 - 2*a - 1)*q^10 + (2*a^2 + 4*a - 3)*q^11 + (a^2 + a + 1)*q^12 + (3*a^2 + 5*a - 3)*q^13 - a*q^14 + (3*a + 2)*q^15 + (-a^2 - a + 2)*q^16 + (-3*a^2 - 5*a)*q^17 + (-a + 1)*q^18 + (-5*a^2 - 6*a + 5)*q^19 + (-2*a^2 + 2*a + 3)*q^20 + (a + 1)*q^21 + (-a + 2)*q^22 + (3*a^2 + 6*a - 2)*q^23 + (a^2 + 4*a + 1)*q^24 + (4*a^2 + 3*a - 4)*q^25 + (-a^2 + 3)*q^26 + (-a^2 + 2*a + 4)*q^27 + (-a^2 + 2)*q^28 + (-a^2 - 7*a - 3)*q^29 + (3*a^2 + 2*a)*q^30 + (-4*a^2 - 7*a + 3)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (-2*a^2 - 3*a + 1)*q^33 + (a^2 - 3*a - 3)*q^34 + (a^2 + a + 1)*q^35 + (-3*a^2 - 3*a + 4)*q^36 + (-3*a^2 - 5*a + 7)*q^37 + O(q^38),
q + a*q^2 + 2*q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a + 5)*q^5 + 2*a*q^6 - 2*q^7 + (a - 3)*q^8 + q^9 + (-2*a^2 + 3)*q^10 + (2*a^2 + a - 7)*q^11 + (2*a^2 - 4)*q^12 + (-2*a^2 + 6)*q^13 - 2*a*q^14 + (-2*a^2 - 4*a + 10)*q^15 + (-a^2 - 3*a + 4)*q^16 + (-a + 3)*q^17 + a*q^18 + (3*a^2 + 3*a - 9)*q^19 + (2*a^2 - 3*a - 4)*q^20 - 4*q^21 + (a^2 + 3*a - 6)*q^22 + 2*a*q^23 + (2*a - 6)*q^24 + (-a^2 - 3*a + 8)*q^25 + (-4*a + 6)*q^26 - 4*q^27 + (-2*a^2 + 4)*q^28 + (3*a^2 + 5*a - 9)*q^29 + (-4*a^2 + 6)*q^30 + (-a^2 + 3)*q^31 + (-3*a^2 - 3*a + 9)*q^32 + (4*a^2 + 2*a - 14)*q^33 + (-a^2 + 3*a)*q^34 + (2*a^2 + 4*a - 10)*q^35 + (a^2 - 2)*q^36 + (-3*a + 1)*q^37 + O(q^38),
q + a*q^2 + (-a^5 + a^4 + 7*a^3 - 4*a^2 - 12*a - 1)*q^3 + (a^2 - 2)*q^4 + (a^5 - a^4 - 6*a^3 + 3*a^2 + 9*a + 2)*q^5 + (-a^3 + a^2 + 2*a - 1)*q^6 + (-a^4 + 3*a^2 + 3*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 + 3*a^4 + 4*a^3 - 13*a^2 - 4*a + 9)*q^9 + (a^4 - 4*a^2 - a + 1)*q^10 + (a^3 - 5*a)*q^11 + (2*a^5 - 3*a^4 - 13*a^3 + 10*a^2 + 23*a + 2)*q^12 + (2*a^5 - 3*a^4 - 11*a^3 + 12*a^2 + 13*a - 4)*q^13 + (-a^5 + 3*a^3 + 3*a^2 + 3*a)*q^14 + (-a^5 + 7*a^3 + 3*a^2 - 13*a - 10)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - 2*a^3 + 6*a^2 + 8*a)*q^17 + (2*a^5 - 3*a^4 - 10*a^3 + 9*a^2 + 12*a - 1)*q^18 + (2*a^5 - a^4 - 12*a^3 + 2*a^2 + 15*a + 1)*q^19 + (-a^5 + 2*a^4 + 8*a^3 - 7*a^2 - 17*a - 4)*q^20 + (-3*a^5 + 5*a^4 + 19*a^3 - 16*a^2 - 36*a - 5)*q^21 + (a^4 - 5*a^2)*q^22 + (-a^5 + 6*a^3 - 7*a + 1)*q^23 + (-a^5 + a^4 + 6*a^3 - 5*a^2 - 8*a + 4)*q^24 + (2*a^5 - a^4 - 13*a^3 + a^2 + 21*a + 5)*q^25 + (-a^5 + 3*a^4 + 6*a^3 - 13*a^2 - 10*a + 2)*q^26 + (-5*a^5 + 6*a^4 + 34*a^3 - 22*a^2 - 57*a - 5)*q^27 + (-a^5 - 2*a^4 + 6*a^3 + 10*a^2 - 3*a - 7)*q^28 + (3*a^5 - 5*a^4 - 17*a^3 + 19*a^2 + 24*a - 3)*q^29 + (-a^5 + 6*a^3 - 7*a - 1)*q^30 + (-2*a^5 + 3*a^4 + 10*a^3 - 9*a^2 - 12*a - 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 + a^4 + 7*a^3 - 6*a^2 - 10*a + 5)*q^33 + (-a^5 - 2*a^4 + 6*a^3 + 8*a^2)*q^34 + (2*a^5 - 3*a^4 - 15*a^3 + 10*a^2 + 29*a + 8)*q^35 + (a^5 - 2*a^4 - 5*a^3 + 12*a^2 + a - 16)*q^36 + (a^2 + 3*a - 5)*q^37 + O(q^38)
*]> ;  // time = 1.71 seconds




J[154] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 154, 154, 154, 154, 77, 77, 77, 77, 14, 11 ], new_dimensions := [ 1, 1, 1, 2, 1, 1, 1, 2, 1, 1 ], dimensions := [ 1, 1, 1, 2, 2, 2, 2, 4, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 5, 3, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 0, 25, 3, 1, 1, 1, 1, 1, 1, 1, 25, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 5, 1, 9, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -4, -1, -1, 2, -4, -6, 4, -2, -2, 10 ],
[ -1, 2, 2, -1, 1, -4, 0, 4, 4, 2, -10, -6 ],
[ 1, 0, 2, -1, -1, 2, 2, 0, -8, -2, -8, -2 ],
[ 2, -2, 2, 2, 2, -2, -4, -10, 8, 0, 4, -4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 0, 1, 3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1/25 ], eigenvalues := [*
[ -1, 0, -4, -1, -1, 2, -4, -6, 4, -2, -2, 10 ],
[ -1, 2, 2, -1, 1, -4, 0, 4, 4, 2, -10, -6 ],
[ 1, 0, 2, -1, -1, 2, 2, 0, -8, -2, -8, -2 ],
[
1,
a,
-a,
1,
1,
-a - 2,
2*a,
-a - 6,
4,
2*a + 2,
2,
4*a + 2
]
*], q_expansions := [*
q - q^2 + q^4 - 4*q^5 - q^7 - q^8 - 3*q^9 + 4*q^10 - q^11 + 2*q^13 + q^14 + q^16 - 4*q^17 + 3*q^18 - 6*q^19 - 4*q^20 + q^22 + 4*q^23 + 11*q^25 - 2*q^26 - q^28 - 2*q^29 - 2*q^31 - q^32 + 4*q^34 + 4*q^35 - 3*q^36 + 10*q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 - q^7 - q^8 + q^9 - 2*q^10 + q^11 + 2*q^12 - 4*q^13 + q^14 + 4*q^15 + q^16 - q^18 + 4*q^19 + 2*q^20 - 2*q^21 - q^22 + 4*q^23 - 2*q^24 - q^25 + 4*q^26 - 4*q^27 - q^28 + 2*q^29 - 4*q^30 - 10*q^31 - q^32 + 2*q^33 - 2*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 - q^7 + q^8 - 3*q^9 + 2*q^10 - q^11 + 2*q^13 - q^14 + q^16 + 2*q^17 - 3*q^18 + 2*q^20 - q^22 - 8*q^23 - q^25 + 2*q^26 - q^28 - 2*q^29 - 8*q^31 + q^32 + 2*q^34 - 2*q^35 - 3*q^36 - 2*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - a*q^5 + a*q^6 + q^7 + q^8 + (-2*a + 1)*q^9 - a*q^10 + q^11 + a*q^12 + (-a - 2)*q^13 + q^14 + (2*a - 4)*q^15 + q^16 + 2*a*q^17 + (-2*a + 1)*q^18 + (-a - 6)*q^19 - a*q^20 + a*q^21 + q^22 + 4*q^23 + a*q^24 + (-2*a - 1)*q^25 + (-a - 2)*q^26 + (2*a - 8)*q^27 + q^28 + (2*a + 2)*q^29 + (2*a - 4)*q^30 + 2*q^31 + q^32 + a*q^33 + 2*a*q^34 - a*q^35 + (-2*a + 1)*q^36 + (4*a + 2)*q^37 + O(q^38)
*]> ;  // time = 42.359 seconds




J[155] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 155, 155, 155, 155, 155, 31 ], new_dimensions := [ 1, 1, 1, 4, 4, 2 ], dimensions := [ 1, 1, 1, 4, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 0, 1, 49, 1, 1, 1, 1, 0, 1, 1, 1, 5, 49, 1, 0 ], ap_traces := [
[ 0, -1, -1, 0, -4, -6, 5, -1, 8, -10, -1, 1 ],
[ -1, 2, -1, 4, 4, 0, -8, 4, 2, -6, 1, -4 ],
[ -2, -1, 1, -2, 2, -6, -7, -5, 4, 0, 1, -7 ],
[ -1, -1, -4, 0, -6, 16, 1, 5, 0, 6, 4, 9 ],
[ 1, 1, 4, 2, -4, 10, 11, -3, -2, -8, -4, 3 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^4 + x^3 - 8*x^2 - 4*x + 12,
x^4 - x^3 - 6*x^2 + 4*x + 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ],
[ 147, 3 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 5, 1 ],
[ 1, 3 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1 ], l_ratios := [ 0, 1, 0, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1 ], eigenvalues := [*
[ 0, -1, -1, 0, -4, -6, 5, -1, 8, -10, -1, 1 ],
[ -1, 2, -1, 4, 4, 0, -8, 4, 2, -6, 1, -4 ],
[ -2, -1, 1, -2, 2, -6, -7, -5, 4, 0, 1, -7 ],
[
a,
-1/2*a^3 - 1/2*a^2 + 3*a + 1,
-1,
a^2 + a - 4,
a^2 - a - 6,
-a^2 - a + 8,
-1/2*a^3 + 1/2*a^2 + 2*a - 3,
a^3 + a^2 - 5*a - 1,
-a^3 - 2*a^2 + 3*a + 6,
-a^3 + 7*a,
1,
1/2*a^3 - 1/2*a^2 - 4*a + 5
],
[
a,
-1/2*a^3 + 1/2*a^2 + 2*a - 1,
1,
-a^2 - a + 4,
-a^2 + a + 2,
a^3 - 5*a + 2,
1/2*a^3 + 1/2*a^2 - 3*a + 1,
-a^3 + a^2 + 3*a - 3,
a^2 + a - 4,
a^3 - 2*a^2 - 5*a + 4,
-1,
-1/2*a^3 - 5/2*a^2 + 3*a + 9
]
*], q_expansions := [*
q - q^3 - 2*q^4 - q^5 - 2*q^9 - 4*q^11 + 2*q^12 - 6*q^13 + q^15 + 4*q^16 + 5*q^17 - q^19 + 2*q^20 + 8*q^23 + q^25 + 5*q^27 - 10*q^29 - q^31 + 4*q^33 + 4*q^36 + q^37 + O(q^38),
q - q^2 + 2*q^3 - q^4 - q^5 - 2*q^6 + 4*q^7 + 3*q^8 + q^9 + q^10 + 4*q^11 - 2*q^12 - 4*q^14 - 2*q^15 - q^16 - 8*q^17 - q^18 + 4*q^19 + q^20 + 8*q^21 - 4*q^22 + 2*q^23 + 6*q^24 + q^25 - 4*q^27 - 4*q^28 - 6*q^29 + 2*q^30 + q^31 - 5*q^32 + 8*q^33 + 8*q^34 - 4*q^35 - q^36 - 4*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 - 2*q^10 + 2*q^11 - 2*q^12 - 6*q^13 + 4*q^14 - q^15 - 4*q^16 - 7*q^17 + 4*q^18 - 5*q^19 + 2*q^20 + 2*q^21 - 4*q^22 + 4*q^23 + q^25 + 12*q^26 + 5*q^27 - 4*q^28 + 2*q^30 + q^31 + 8*q^32 - 2*q^33 + 14*q^34 - 2*q^35 - 4*q^36 - 7*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^3 - 1/2*a^2 + 3*a + 1)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^2 - a + 6)*q^6 + (a^2 + a - 4)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^2 - a + 10)*q^9 - a*q^10 + (a^2 - a - 6)*q^11 - 2*q^12 + (-a^2 - a + 8)*q^13 + (a^3 + a^2 - 4*a)*q^14 + (1/2*a^3 + 1/2*a^2 - 3*a - 1)*q^15 + (-a^3 + 2*a^2 + 4*a - 8)*q^16 + (-1/2*a^3 + 1/2*a^2 + 2*a - 3)*q^17 + (-2*a^3 - a^2 + 10*a)*q^18 + (a^3 + a^2 - 5*a - 1)*q^19 + (-a^2 + 2)*q^20 + (a^3 - 7*a + 2)*q^21 + (a^3 - a^2 - 6*a)*q^22 + (-a^3 - 2*a^2 + 3*a + 6)*q^23 + (2*a^2 - 12)*q^24 + q^25 + (-a^3 - a^2 + 8*a)*q^26 + (-3/2*a^3 - 1/2*a^2 + 10*a + 1)*q^27 + (2*a^2 + 2*a - 4)*q^28 + (-a^3 + 7*a)*q^29 + (a^2 + a - 6)*q^30 + q^31 + (a^3 - 4*a^2 - 4*a + 12)*q^32 + (2*a^3 + 3*a^2 - 11*a - 12)*q^33 + (a^3 - 2*a^2 - 5*a + 6)*q^34 + (-a^2 - a + 4)*q^35 + (a^3 - 2*a^2 - 6*a + 4)*q^36 + (1/2*a^3 - 1/2*a^2 - 4*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^3 + 1/2*a^2 + 2*a - 1)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 + a + 2)*q^6 + (-a^2 - a + 4)*q^7 + (a^3 - 4*a)*q^8 - a*q^9 + a*q^10 + (-a^2 + a + 2)*q^11 + (-2*a + 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (-a^3 - a^2 + 4*a)*q^14 + (-1/2*a^3 + 1/2*a^2 + 2*a - 1)*q^15 + (a^3 - 4*a)*q^16 + (1/2*a^3 + 1/2*a^2 - 3*a + 1)*q^17 - a^2*q^18 + (-a^3 + a^2 + 3*a - 3)*q^19 + (a^2 - 2)*q^20 + (-a^3 + 2*a^2 + 5*a - 6)*q^21 + (-a^3 + a^2 + 2*a)*q^22 + (a^2 + a - 4)*q^23 - 4*q^24 + q^25 + (a^3 + a^2 - 2*a - 4)*q^26 + (3/2*a^3 - 1/2*a^2 - 7*a + 1)*q^27 + (-2*a^3 + 6*a - 4)*q^28 + (a^3 - 2*a^2 - 5*a + 4)*q^29 + (-a^2 + a + 2)*q^30 - q^31 + (-a^3 + 2*a^2 + 4*a - 4)*q^32 + (-a^2 + 3*a)*q^33 + (a^3 - a - 2)*q^34 + (-a^2 - a + 4)*q^35 + (-a^3 + 2*a)*q^36 + (-1/2*a^3 - 5/2*a^2 + 3*a + 9)*q^37 + O(q^38)
*]> ;  // time = 15.101 seconds




J[157] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 157, 157 ], new_dimensions := [ 5, 7 ], dimensions := [ 5, 7 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -5, -7, -3, -3, -14, -7, -9, -3, -13, -2, 3, 3 ],
[ 5, 5, -1, 1, 10, -5, 5, -3, 15, 8, -13, -15 ]
], hecke_fields := [
x^5 + 5*x^4 + 5*x^3 - 6*x^2 - 7*x + 1,
x^7 - 5*x^6 + 2*x^5 + 21*x^4 - 22*x^3 - 21*x^2 + 27*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 13 ]
], tamagawa_numbers := [
[ 1 ],
[ 13 ]
], torsion_upper_bounds := [ 1, 13 ], torsion_lower_bounds := [ 1, 13 ], l_ratios := [ 0, 1/13 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^4 - 3*a^3 + 3*a - 1,
2*a^4 + 7*a^3 + a^2 - 10*a - 2,
-a^4 - 5*a^3 - 4*a^2 + 6*a + 2,
-a^4 - 2*a^3 + 4*a^2 + 5*a - 6,
a^3 + 3*a^2 + a - 3,
a^4 + a^3 - 3*a^2 + 3*a,
-a^3 - 5*a^2 - 3*a + 5,
-a^4 - 5*a^3 - 6*a^2 + 3*a + 3,
a^4 + 5*a^3 + 3*a^2 - 8*a - 2,
-2*a^4 - 2*a^3 + 14*a^2 + 9*a - 12,
a^4 - 9*a^2 - 4*a + 7
],
[
a,
a^4 - 3*a^3 - 2*a^2 + 7*a + 1,
a^6 - 4*a^5 - 2*a^4 + 18*a^3 - 2*a^2 - 20*a + 3,
-a^6 + 3*a^5 + 4*a^4 - 13*a^3 - 5*a^2 + 13*a + 2,
-a^6 + 4*a^5 + a^4 - 15*a^3 + 3*a^2 + 13*a + 1,
a^6 - 3*a^5 - 5*a^4 + 17*a^3 + 4*a^2 - 22*a + 3,
a^6 - 3*a^5 - 4*a^4 + 13*a^3 + 6*a^2 - 16*a - 2,
4*a^6 - 14*a^5 - 12*a^4 + 61*a^3 + 9*a^2 - 65*a - 3,
a^5 - 4*a^4 + 12*a^2 - 4*a - 4,
-4*a^6 + 13*a^5 + 16*a^4 - 62*a^3 - 17*a^2 + 71*a + 1,
2*a^6 - 7*a^5 - 7*a^4 + 35*a^3 + 2*a^2 - 42*a + 5,
-2*a^6 + 8*a^5 + a^4 - 30*a^3 + 13*a^2 + 28*a - 11
]
*], q_expansions := [*
q + a*q^2 + (-a^4 - 3*a^3 + 3*a - 1)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + 7*a^3 + a^2 - 10*a - 2)*q^5 + (2*a^4 + 5*a^3 - 3*a^2 - 8*a + 1)*q^6 + (-a^4 - 5*a^3 - 4*a^2 + 6*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (2*a^4 + 6*a^3 + a^2 - 5*a - 2)*q^9 + (-3*a^4 - 9*a^3 + 2*a^2 + 12*a - 2)*q^10 + (-a^4 - 2*a^3 + 4*a^2 + 5*a - 6)*q^11 + (-3*a^4 - 7*a^3 + 4*a^2 + 9*a)*q^12 + (a^3 + 3*a^2 + a - 3)*q^13 + (a^3 - 5*a + 1)*q^14 + (-a^4 - 4*a^3 - a^2 + 8*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + a^3 - 3*a^2 + 3*a)*q^17 + (-4*a^4 - 9*a^3 + 7*a^2 + 12*a - 2)*q^18 + (-a^3 - 5*a^2 - 3*a + 5)*q^19 + (2*a^4 + 3*a^3 - 8*a^2 - 3*a + 7)*q^20 + (a^4 + 6*a^3 + 6*a^2 - 6*a - 1)*q^21 + (3*a^4 + 9*a^3 - a^2 - 13*a + 1)*q^22 + (-a^4 - 5*a^3 - 6*a^2 + 3*a + 3)*q^23 + (4*a^4 + 9*a^3 - 3*a^2 - 5*a + 1)*q^24 + (-a^4 - 3*a^3 - 3*a^2 - 2*a + 6)*q^25 + (a^4 + 3*a^3 + a^2 - 3*a)*q^26 + (a^3 - a^2 - 4*a + 4)*q^27 + (3*a^4 + 10*a^3 + 3*a^2 - 11*a - 4)*q^28 + (a^4 + 5*a^3 + 3*a^2 - 8*a - 2)*q^29 + (a^4 + 4*a^3 + 2*a^2 - 6*a + 1)*q^30 + (-2*a^4 - 2*a^3 + 14*a^2 + 9*a - 12)*q^31 + (-5*a^4 - 13*a^3 + 6*a^2 + 19*a - 1)*q^32 + (3*a^4 + 8*a^3 - 4*a^2 - 13*a + 5)*q^33 + (-4*a^4 - 8*a^3 + 9*a^2 + 7*a - 1)*q^34 + (-2*a^4 - 6*a^3 + 6*a^2 + 16*a - 11)*q^35 + (7*a^4 + 15*a^3 - 14*a^2 - 20*a + 8)*q^36 + (a^4 - 9*a^2 - 4*a + 7)*q^37 + O(q^38),
q + a*q^2 + (a^4 - 3*a^3 - 2*a^2 + 7*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^6 - 4*a^5 - 2*a^4 + 18*a^3 - 2*a^2 - 20*a + 3)*q^5 + (a^5 - 3*a^4 - 2*a^3 + 7*a^2 + a)*q^6 + (-a^6 + 3*a^5 + 4*a^4 - 13*a^3 - 5*a^2 + 13*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^6 + 7*a^5 + 7*a^4 - 35*a^3 - 3*a^2 + 42*a - 3)*q^9 + (a^6 - 4*a^5 - 3*a^4 + 20*a^3 + a^2 - 24*a + 1)*q^10 + (-a^6 + 4*a^5 + a^4 - 15*a^3 + 3*a^2 + 13*a + 1)*q^11 + (a^6 - 3*a^5 - 4*a^4 + 13*a^3 + 5*a^2 - 14*a - 2)*q^12 + (a^6 - 3*a^5 - 5*a^4 + 17*a^3 + 4*a^2 - 22*a + 3)*q^13 + (-2*a^6 + 6*a^5 + 8*a^4 - 27*a^3 - 8*a^2 + 29*a - 1)*q^14 + (3*a^6 - 11*a^5 - 8*a^4 + 50*a^3 - 57*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - 3*a^5 - 4*a^4 + 13*a^3 + 6*a^2 - 16*a - 2)*q^17 + (-3*a^6 + 11*a^5 + 7*a^4 - 47*a^3 + 51*a - 2)*q^18 + (4*a^6 - 14*a^5 - 12*a^4 + 61*a^3 + 9*a^2 - 65*a - 3)*q^19 + (-a^6 + 3*a^5 + 3*a^4 - 13*a^3 + a^2 + 14*a - 5)*q^20 + (a^4 - 2*a^3 - 4*a^2 + 4*a + 3)*q^21 + (-a^6 + 3*a^5 + 6*a^4 - 19*a^3 - 8*a^2 + 28*a - 1)*q^22 + (a^5 - 4*a^4 + 12*a^2 - 4*a - 4)*q^23 + (2*a^6 - 8*a^5 - 2*a^4 + 31*a^3 - 7*a^2 - 31*a + 1)*q^24 + (-a^6 + 4*a^5 + 3*a^4 - 20*a^3 - 2*a^2 + 26*a - 1)*q^25 + (2*a^6 - 7*a^5 - 4*a^4 + 26*a^3 - a^2 - 24*a + 1)*q^26 + (-5*a^6 + 18*a^5 + 14*a^4 - 82*a^3 + 90*a - 9)*q^27 + (-2*a^6 + 6*a^5 + 7*a^4 - 26*a^3 - 3*a^2 + 27*a - 6)*q^28 + (-4*a^6 + 13*a^5 + 16*a^4 - 62*a^3 - 17*a^2 + 71*a + 1)*q^29 + (4*a^6 - 14*a^5 - 13*a^4 + 66*a^3 + 6*a^2 - 76*a + 3)*q^30 + (2*a^6 - 7*a^5 - 7*a^4 + 35*a^3 + 2*a^2 - 42*a + 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^6 + 7*a^5 + 8*a^4 - 37*a^3 - 8*a^2 + 50*a)*q^33 + (2*a^6 - 6*a^5 - 8*a^4 + 28*a^3 + 5*a^2 - 29*a + 1)*q^34 + (-a^6 + 3*a^5 + 5*a^4 - 14*a^3 - 9*a^2 + 15*a + 5)*q^35 + (-a^5 + 2*a^4 + 4*a^3 - 6*a^2 - 5*a + 3)*q^36 + (-2*a^6 + 8*a^5 + a^4 - 30*a^3 + 13*a^2 + 28*a - 11)*q^37 + O(q^38)
*]> ;  // time = 1.641 seconds




J[158] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 158, 158, 158, 158, 158, 158, 79, 79 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 1, 5 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 53, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 53, 1, 0 ], ap_traces := [
[ -1, -1, -1, -3, 4, -7, -4, -6, 6, 4, 8, 10 ],
[ -1, 1, 3, -1, 0, 5, 0, 2, -6, 0, -4, 2 ],
[ 1, -1, 1, 3, 2, -1, -2, 0, -6, -10, 2, -2 ],
[ 1, 2, -2, 0, -4, 2, -2, 0, 0, 8, 8, 4 ],
[ 1, -3, -3, -3, -2, -5, 6, 0, -2, 6, -10, -10 ],
[ -2, 0, -4, 8, 0, 4, 4, 0, 4, -4, -4, -4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 6
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 3 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 53, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 5, 1, 1, 1 ], torsion_lower_bounds := [ 1, 3, 5, 1, 1, 1 ], l_ratios := [ 0, 1/3, 1/5, 1, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1 ], eigenvalues := [*
[ -1, -1, -1, -3, 4, -7, -4, -6, 6, 4, 8, 10 ],
[ -1, 1, 3, -1, 0, 5, 0, 2, -6, 0, -4, 2 ],
[ 1, -1, 1, 3, 2, -1, -2, 0, -6, -10, 2, -2 ],
[ 1, 2, -2, 0, -4, 2, -2, 0, 0, 8, 8, 4 ],
[ 1, -3, -3, -3, -2, -5, 6, 0, -2, 6, -10, -10 ],
[
-1,
a,
-2,
4,
0,
-2*a + 2,
-2*a + 2,
2*a,
2*a + 2,
-3*a - 2,
-2*a - 2,
-a - 2
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - 3*q^7 - q^8 - 2*q^9 + q^10 + 4*q^11 - q^12 - 7*q^13 + 3*q^14 + q^15 + q^16 - 4*q^17 + 2*q^18 - 6*q^19 - q^20 + 3*q^21 - 4*q^22 + 6*q^23 + q^24 - 4*q^25 + 7*q^26 + 5*q^27 - 3*q^28 + 4*q^29 - q^30 + 8*q^31 - q^32 - 4*q^33 + 4*q^34 + 3*q^35 - 2*q^36 + 10*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 3*q^5 - q^6 - q^7 - q^8 - 2*q^9 - 3*q^10 + q^12 + 5*q^13 + q^14 + 3*q^15 + q^16 + 2*q^18 + 2*q^19 + 3*q^20 - q^21 - 6*q^23 - q^24 + 4*q^25 - 5*q^26 - 5*q^27 - q^28 - 3*q^30 - 4*q^31 - q^32 - 3*q^35 - 2*q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 + q^10 + 2*q^11 - q^12 - q^13 + 3*q^14 - q^15 + q^16 - 2*q^17 - 2*q^18 + q^20 - 3*q^21 + 2*q^22 - 6*q^23 - q^24 - 4*q^25 - q^26 + 5*q^27 + 3*q^28 - 10*q^29 - q^30 + 2*q^31 + q^32 - 2*q^33 - 2*q^34 + 3*q^35 - 2*q^36 - 2*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 - 2*q^5 + 2*q^6 + q^8 + q^9 - 2*q^10 - 4*q^11 + 2*q^12 + 2*q^13 - 4*q^15 + q^16 - 2*q^17 + q^18 - 2*q^20 - 4*q^22 + 2*q^24 - q^25 + 2*q^26 - 4*q^27 + 8*q^29 - 4*q^30 + 8*q^31 + q^32 - 8*q^33 - 2*q^34 + q^36 + 4*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - 3*q^5 - 3*q^6 - 3*q^7 + q^8 + 6*q^9 - 3*q^10 - 2*q^11 - 3*q^12 - 5*q^13 - 3*q^14 + 9*q^15 + q^16 + 6*q^17 + 6*q^18 - 3*q^20 + 9*q^21 - 2*q^22 - 2*q^23 - 3*q^24 + 4*q^25 - 5*q^26 - 9*q^27 - 3*q^28 + 6*q^29 + 9*q^30 - 10*q^31 + q^32 + 6*q^33 + 6*q^34 + 9*q^35 + 6*q^36 - 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - 2*q^5 - a*q^6 + 4*q^7 - q^8 + 3*q^9 + 2*q^10 + a*q^12 + (-2*a + 2)*q^13 - 4*q^14 - 2*a*q^15 + q^16 + (-2*a + 2)*q^17 - 3*q^18 + 2*a*q^19 - 2*q^20 + 4*a*q^21 + (2*a + 2)*q^23 - a*q^24 - q^25 + (2*a - 2)*q^26 + 4*q^28 + (-3*a - 2)*q^29 + 2*a*q^30 + (-2*a - 2)*q^31 - q^32 + (2*a - 2)*q^34 - 8*q^35 + 3*q^36 + (-a - 2)*q^37 + O(q^38)
*]> ;  // time = 21.38 seconds




J[159] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 159, 159, 53, 53 ], new_dimensions := [ 4, 5, 1, 3 ], dimensions := [ 4, 5, 2, 6 ], intersection_graph := [ 0, 1, 7, 1, 1, 0, 1, 107, 7, 1, 0, 1, 1, 107, 1, 0 ], ap_traces := [
[ 3, 4, 2, -4, 6, -6, 10, -6, 2, 6, -12, -10 ],
[ 0, -5, 0, 4, 2, 8, 0, 2, -6, 20, 8, 4 ]
], hecke_fields := [
x^4 - 3*x^3 - x^2 + 7*x - 3,
x^5 - 10*x^3 + 22*x + 5
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 63, 1 ],
[ 107, 1 ]
], tamagawa_numbers := [
[ 63, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 9, 1 ], torsion_lower_bounds := [ 9, 1 ], l_ratios := [ 7/9, 1 ], analytic_sha_upper_bounds := [ 1, 1 ], analytic_sha_lower_bounds := [ 1, 1 ], eigenvalues := [*
[
a,
1,
-a^3 + a^2 + 2*a,
a^3 - 3*a^2 - 2*a + 5,
4*a^3 - 6*a^2 - 12*a + 12,
-3*a^3 + 5*a^2 + 8*a - 10,
-4*a^3 + 8*a^2 + 10*a - 12,
2*a^2 - 4*a - 4,
-a^3 + a^2 + 6*a - 3,
4*a^3 - 6*a^2 - 12*a + 12,
2*a^2 + 2*a - 10,
a^3 - 3*a^2 - 4*a + 5
],
[
a,
-1,
-a^3 - a^2 + 6*a + 4,
1/3*a^4 + 4/3*a^3 - 2*a^2 - 7*a + 4/3,
-2/3*a^4 - 2/3*a^3 + 4*a^2 + 2*a - 2/3,
2/3*a^4 - 1/3*a^3 - 5*a^2 + 2*a + 20/3,
-2*a,
-2/3*a^4 - 2/3*a^3 + 4*a^2 + 2*a - 2/3,
1/3*a^4 + 4/3*a^3 - 7*a - 26/3,
2*a^2 - 4,
2/3*a^4 + 2/3*a^3 - 4*a^2 - 4*a + 8/3,
1/3*a^4 + 4/3*a^3 - 2*a^2 - 5*a + 4/3
]
*], q_expansions := [*
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^3 + a^2 + 2*a)*q^5 + a*q^6 + (a^3 - 3*a^2 - 2*a + 5)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2*a^3 + a^2 + 7*a - 3)*q^10 + (4*a^3 - 6*a^2 - 12*a + 12)*q^11 + (a^2 - 2)*q^12 + (-3*a^3 + 5*a^2 + 8*a - 10)*q^13 + (-a^2 - 2*a + 3)*q^14 + (-a^3 + a^2 + 2*a)*q^15 + (3*a^3 - 5*a^2 - 7*a + 7)*q^16 + (-4*a^3 + 8*a^2 + 10*a - 12)*q^17 + a*q^18 + (2*a^2 - 4*a - 4)*q^19 + (-3*a^3 + 3*a^2 + 7*a - 6)*q^20 + (a^3 - 3*a^2 - 2*a + 5)*q^21 + (6*a^3 - 8*a^2 - 16*a + 12)*q^22 + (-a^3 + a^2 + 6*a - 3)*q^23 + (a^3 - 4*a)*q^24 + (a^3 + a^2 - 4*a - 2)*q^25 + (-4*a^3 + 5*a^2 + 11*a - 9)*q^26 + q^27 + (-3*a^3 + 4*a^2 + 7*a - 10)*q^28 + (4*a^3 - 6*a^2 - 12*a + 12)*q^29 + (-2*a^3 + a^2 + 7*a - 3)*q^30 + (2*a^2 + 2*a - 10)*q^31 + (2*a^3 - 4*a^2 - 6*a + 9)*q^32 + (4*a^3 - 6*a^2 - 12*a + 12)*q^33 + (-4*a^3 + 6*a^2 + 16*a - 12)*q^34 + (4*a^3 - 6*a^2 - 8*a + 9)*q^35 + (a^2 - 2)*q^36 + (a^3 - 3*a^2 - 4*a + 5)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^3 - a^2 + 6*a + 4)*q^5 - a*q^6 + (1/3*a^4 + 4/3*a^3 - 2*a^2 - 7*a + 4/3)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 - a^3 + 6*a^2 + 4*a)*q^10 + (-2/3*a^4 - 2/3*a^3 + 4*a^2 + 2*a - 2/3)*q^11 + (-a^2 + 2)*q^12 + (2/3*a^4 - 1/3*a^3 - 5*a^2 + 2*a + 20/3)*q^13 + (4/3*a^4 + 4/3*a^3 - 7*a^2 - 6*a - 5/3)*q^14 + (a^3 + a^2 - 6*a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - 2*a*q^17 + a*q^18 + (-2/3*a^4 - 2/3*a^3 + 4*a^2 + 2*a - 2/3)*q^19 + (-a^4 - 2*a^3 + 6*a^2 + 10*a - 3)*q^20 + (-1/3*a^4 - 4/3*a^3 + 2*a^2 + 7*a - 4/3)*q^21 + (-2/3*a^4 - 8/3*a^3 + 2*a^2 + 14*a + 10/3)*q^22 + (1/3*a^4 + 4/3*a^3 - 7*a - 26/3)*q^23 + (-a^3 + 4*a)*q^24 + (-a^4 + 6*a^2 - a + 1)*q^25 + (-1/3*a^4 + 5/3*a^3 + 2*a^2 - 8*a - 10/3)*q^26 - q^27 + (2/3*a^4 + 11/3*a^3 - 2*a^2 - 17*a - 28/3)*q^28 + (2*a^2 - 4)*q^29 + (a^4 + a^3 - 6*a^2 - 4*a)*q^30 + (2/3*a^4 + 2/3*a^3 - 4*a^2 - 4*a + 8/3)*q^31 + (2*a^3 - 10*a - 5)*q^32 + (2/3*a^4 + 2/3*a^3 - 4*a^2 - 2*a + 2/3)*q^33 - 2*a^2*q^34 + (5/3*a^4 - 1/3*a^3 - 13*a^2 + 3*a + 26/3)*q^35 + (a^2 - 2)*q^36 + (1/3*a^4 + 4/3*a^3 - 2*a^2 - 5*a + 4/3)*q^37 + O(q^38)
*]> ;  // time = 15.679 seconds




J[161] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 161, 161, 161, 161, 23 ], new_dimensions := [ 1, 2, 3, 5, 2 ], dimensions := [ 1, 2, 3, 5, 4 ], intersection_graph := [ 0, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 19, 5, 1, 1, 0, 1, 1, 1, 19, 1, 0 ], ap_traces := [
[ -1, 0, 2, 1, 4, 6, -2, 4, -1, -2, -4, -2 ],
[ -1, -2, -2, -2, 0, -4, 0, -10, -2, 6, -18, 2 ],
[ -1, 2, 2, -3, 4, 2, 4, 8, 3, -2, 16, -6 ],
[ 2, 0, -4, 5, -4, -6, -12, 6, -5, -4, 30, 4 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^3 + x^2 - 5*x - 1,
x^5 - 2*x^4 - 9*x^3 + 17*x^2 + 16*x - 27
], atkin_lehners := [
[ -1, 1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 19, 1 ],
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 3 ], l_ratios := [ 1, 0, 1, 1/3 ], analytic_sha_upper_bounds := [ 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, 2, 1, 4, 6, -2, 4, -1, -2, -4, -2 ],
[
a,
-1,
-2*a - 2,
-1,
4*a + 2,
2*a - 1,
0,
-2*a - 6,
-1,
-4*a + 1,
-9,
-6*a - 2
],
[
a,
-1/2*a^2 + 5/2,
-1/2*a^2 + 5/2,
-1,
-a + 1,
a^2 - 3,
1/2*a^2 - 1/2,
2*a^2 + 2*a - 4,
1,
a^2 + a - 4,
-3/2*a^2 - 4*a + 19/2,
a^2 + 2*a - 5
],
[
a,
1/2*a^4 - 1/2*a^3 - 4*a^2 + 5/2*a + 11/2,
-1/2*a^4 - 1/2*a^3 + 5*a^2 + 5/2*a - 21/2,
1,
-a^4 + 8*a^2 + a - 12,
a^4 - 9*a^2 + 14,
1/2*a^4 + 1/2*a^3 - 3*a^2 - 5/2*a - 3/2,
-2*a + 2,
-1,
-3*a^2 + a + 12,
-1/2*a^4 + 1/2*a^3 + 4*a^2 - 5/2*a + 1/2,
a^4 - a^3 - 8*a^2 + 7*a + 11
]
*], q_expansions := [*
q - q^2 - q^4 + 2*q^5 + q^7 + 3*q^8 - 3*q^9 - 2*q^10 + 4*q^11 + 6*q^13 - q^14 - q^16 - 2*q^17 + 3*q^18 + 4*q^19 - 2*q^20 - 4*q^22 - q^23 - q^25 - 6*q^26 - q^28 - 2*q^29 - 4*q^31 - 5*q^32 + 2*q^34 + 2*q^35 + 3*q^36 - 2*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^4 + (-2*a - 2)*q^5 - a*q^6 - q^7 + (-2*a - 1)*q^8 - 2*q^9 - 2*q^10 + (4*a + 2)*q^11 + (a + 1)*q^12 + (2*a - 1)*q^13 - a*q^14 + (2*a + 2)*q^15 + 3*a*q^16 - 2*a*q^18 + (-2*a - 6)*q^19 + (2*a + 4)*q^20 + q^21 + (-2*a + 4)*q^22 - q^23 + (2*a + 1)*q^24 + (4*a + 3)*q^25 + (-3*a + 2)*q^26 + 5*q^27 + (a + 1)*q^28 + (-4*a + 1)*q^29 + 2*q^30 - 9*q^31 + (a + 5)*q^32 + (-4*a - 2)*q^33 + (2*a + 2)*q^35 + (2*a + 2)*q^36 + (-6*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^2 + 5/2)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^2 + 5/2)*q^5 + (1/2*a^2 - 1/2)*q^6 - q^7 + (-a^2 + a + 1)*q^8 + (-a^2 - a + 3)*q^9 + (1/2*a^2 - 1/2)*q^10 + (-a + 1)*q^11 + (1/2*a^2 + 2*a - 9/2)*q^12 + (a^2 - 3)*q^13 - a*q^14 + (-a^2 - a + 6)*q^15 + (-4*a + 3)*q^16 + (1/2*a^2 - 1/2)*q^17 + (-2*a - 1)*q^18 + (2*a^2 + 2*a - 4)*q^19 + (1/2*a^2 + 2*a - 9/2)*q^20 + (1/2*a^2 - 5/2)*q^21 + (-a^2 + a)*q^22 + q^23 + (1/2*a^2 - 2*a + 3/2)*q^24 + (-a^2 - a + 1)*q^25 + (-a^2 + 2*a + 1)*q^26 - 2*a*q^27 + (-a^2 + 2)*q^28 + (a^2 + a - 4)*q^29 + (a - 1)*q^30 + (-3/2*a^2 - 4*a + 19/2)*q^31 + (-2*a^2 + a - 2)*q^32 + (-a^2 + 3)*q^33 + (-1/2*a^2 + 2*a + 1/2)*q^34 + (1/2*a^2 - 5/2)*q^35 + (a - 6)*q^36 + (a^2 + 2*a - 5)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^4 - 1/2*a^3 - 4*a^2 + 5/2*a + 11/2)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^4 - 1/2*a^3 + 5*a^2 + 5/2*a - 21/2)*q^5 + (1/2*a^4 + 1/2*a^3 - 6*a^2 - 5/2*a + 27/2)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-a^2 - a + 7)*q^9 + (-3/2*a^4 + 1/2*a^3 + 11*a^2 - 5/2*a - 27/2)*q^10 + (-a^4 + 8*a^2 + a - 12)*q^11 + (1/2*a^4 - 1/2*a^3 - 3*a^2 + 1/2*a + 5/2)*q^12 + (a^4 - 9*a^2 + 14)*q^13 + a*q^14 + (a^3 - 8*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/2*a^4 + 1/2*a^3 - 3*a^2 - 5/2*a - 3/2)*q^17 + (-a^3 - a^2 + 7*a)*q^18 + (-2*a + 2)*q^19 + (-3/2*a^4 - 3/2*a^3 + 13*a^2 + 11/2*a - 39/2)*q^20 + (1/2*a^4 - 1/2*a^3 - 4*a^2 + 5/2*a + 11/2)*q^21 + (-2*a^4 - a^3 + 18*a^2 + 4*a - 27)*q^22 - q^23 + (-1/2*a^4 + 1/2*a^3 + 4*a^2 - 1/2*a - 27/2)*q^24 + (a^3 - 6*a + 4)*q^25 + (2*a^4 - 17*a^2 - 2*a + 27)*q^26 + (-a^3 + a^2 + 7*a - 5)*q^27 + (a^2 - 2)*q^28 + (-3*a^2 + a + 12)*q^29 + (a^4 - 8*a^2 + 3*a)*q^30 + (-1/2*a^4 + 1/2*a^3 + 4*a^2 - 5/2*a + 1/2)*q^31 + (2*a^4 + a^3 - 17*a^2 - 4*a + 27)*q^32 + (a^4 + a^3 - 10*a^2 - 5*a + 15)*q^33 + (3/2*a^4 + 3/2*a^3 - 11*a^2 - 19/2*a + 27/2)*q^34 + (-1/2*a^4 - 1/2*a^3 + 5*a^2 + 5/2*a - 21/2)*q^35 + (-a^4 - a^3 + 9*a^2 + 2*a - 14)*q^36 + (a^4 - a^3 - 8*a^2 + 7*a + 11)*q^37 + O(q^38)
*]> ;  // time = 15.02 seconds




J[163] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 163, 163, 163 ], new_dimensions := [ 1, 5, 7 ], dimensions := [ 1, 5, 7 ], intersection_graph := [ 0, 3, 1, 3, 0, 1, 1, 1, 0 ], ap_traces := [
[ 0, 0, -4, 2, -6, 4, 0, -6, 6, -4, -6, -8 ],
[ -5, -5, -9, -6, 2, -14, -21, 7, -8, -13, 7, -1 ],
[ 3, 1, 11, 0, 2, 10, 13, -5, 2, 7, -11, 3 ]
], hecke_fields := [
x - 1,
x^5 + 5*x^4 + 3*x^3 - 15*x^2 - 16*x + 3,
x^7 - 3*x^6 - 5*x^5 + 19*x^4 - 23*x^2 + 4*x + 6
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 27 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 27 ]
], torsion_upper_bounds := [ 1, 1, 27 ], torsion_lower_bounds := [ 1, 1, 27 ], l_ratios := [ 0, 0, 1/27 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ 0, 0, -4, 2, -6, 4, 0, -6, 6, -4, -6, -8 ],
[
a,
-2*a^4 - 5*a^3 + 6*a^2 + 13*a - 3,
2*a^4 + 5*a^3 - 7*a^2 - 15*a + 2,
3*a^4 + 8*a^3 - 8*a^2 - 22*a - 1,
-a^4 - 4*a^3 + a^2 + 13*a + 3,
-a^4 - 3*a^3 + 2*a^2 + 8*a - 2,
-a^4 - 2*a^3 + 4*a^2 + 6*a - 6,
-2*a^4 - 3*a^3 + 9*a^2 + 8*a - 3,
2*a^4 + 3*a^3 - 8*a^2 - 7*a,
-2*a^4 - 6*a^3 + 4*a^2 + 16*a - 1,
4*a^4 + 11*a^3 - 14*a^2 - 34*a + 12,
-3*a^4 - 7*a^3 + 10*a^2 + 18*a - 5
],
[
a,
a^5 - a^4 - 6*a^3 + 5*a^2 + 5*a - 2,
-a^6 + a^5 + 7*a^4 - 6*a^3 - 11*a^2 + 6*a + 6,
a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 11*a^2 - 11*a - 4,
a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 12*a^2 - 12*a - 6,
-a^6 + a^5 + 8*a^4 - 6*a^3 - 16*a^2 + 5*a + 8,
a^6 - a^5 - 6*a^4 + 5*a^3 + 6*a^2 - 3*a,
a^6 - 6*a^4 - a^3 + 4*a^2 + 3*a + 2,
a^6 - a^5 - 7*a^4 + 6*a^3 + 12*a^2 - 8*a - 6,
a^6 - 6*a^4 + 3*a^2 - a + 6,
-a^6 + a^5 + 5*a^4 - 4*a^3 + 2*a^2 - a - 10,
3*a^6 - 6*a^5 - 17*a^4 + 33*a^3 + 11*a^2 - 21*a + 2
]
*], q_expansions := [*
q - 2*q^4 - 4*q^5 + 2*q^7 - 3*q^9 - 6*q^11 + 4*q^13 + 4*q^16 - 6*q^19 + 8*q^20 + 6*q^23 + 11*q^25 - 4*q^28 - 4*q^29 - 6*q^31 - 8*q^35 + 6*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (-2*a^4 - 5*a^3 + 6*a^2 + 13*a - 3)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + 5*a^3 - 7*a^2 - 15*a + 2)*q^5 + (5*a^4 + 12*a^3 - 17*a^2 - 35*a + 6)*q^6 + (3*a^4 + 8*a^3 - 8*a^2 - 22*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (2*a^2 + 3*a - 3)*q^9 + (-5*a^4 - 13*a^3 + 15*a^2 + 34*a - 6)*q^10 + (-a^4 - 4*a^3 + a^2 + 13*a + 3)*q^11 + (-9*a^4 - 22*a^3 + 28*a^2 + 60*a - 9)*q^12 + (-a^4 - 3*a^3 + 2*a^2 + 8*a - 2)*q^13 + (-7*a^4 - 17*a^3 + 23*a^2 + 47*a - 9)*q^14 + (5*a^4 + 13*a^3 - 14*a^2 - 32*a + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - 2*a^3 + 4*a^2 + 6*a - 6)*q^17 + (2*a^3 + 3*a^2 - 3*a)*q^18 + (-2*a^4 - 3*a^3 + 9*a^2 + 8*a - 3)*q^19 + (8*a^4 + 20*a^3 - 27*a^2 - 56*a + 11)*q^20 + (2*a^4 + 5*a^3 - 8*a^2 - 14*a + 6)*q^21 + (a^4 + 4*a^3 - 2*a^2 - 13*a + 3)*q^22 + (2*a^4 + 3*a^3 - 8*a^2 - 7*a)*q^23 + (13*a^4 + 31*a^3 - 41*a^2 - 83*a + 15)*q^24 + (-9*a^4 - 22*a^3 + 32*a^2 + 65*a - 16)*q^25 + (2*a^4 + 5*a^3 - 7*a^2 - 18*a + 3)*q^26 + (a^4 + 2*a^3 - 7*a^2 - 11*a + 6)*q^27 + (12*a^4 + 28*a^3 - 42*a^2 - 77*a + 23)*q^28 + (-2*a^4 - 6*a^3 + 4*a^2 + 16*a - 1)*q^29 + (-12*a^4 - 29*a^3 + 43*a^2 + 86*a - 15)*q^30 + (4*a^4 + 11*a^3 - 14*a^2 - 34*a + 12)*q^31 + (-5*a^4 - 11*a^3 + 15*a^2 + 28*a - 3)*q^32 + (a^3 + a^2 - 5*a - 3)*q^33 + (3*a^4 + 7*a^3 - 9*a^2 - 22*a + 3)*q^34 + (-9*a^4 - 23*a^3 + 28*a^2 + 63*a - 8)*q^35 + (2*a^4 + 3*a^3 - 7*a^2 - 6*a + 6)*q^36 + (-3*a^4 - 7*a^3 + 10*a^2 + 18*a - 5)*q^37 + O(q^38),
q + a*q^2 + (a^5 - a^4 - 6*a^3 + 5*a^2 + 5*a - 2)*q^3 + (a^2 - 2)*q^4 + (-a^6 + a^5 + 7*a^4 - 6*a^3 - 11*a^2 + 6*a + 6)*q^5 + (a^6 - a^5 - 6*a^4 + 5*a^3 + 5*a^2 - 2*a)*q^6 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 11*a^2 - 11*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 12*a^2 + 2*a + 7)*q^9 + (-2*a^6 + 2*a^5 + 13*a^4 - 11*a^3 - 17*a^2 + 10*a + 6)*q^10 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 12*a^2 - 12*a - 6)*q^11 + (2*a^6 - 3*a^5 - 12*a^4 + 17*a^3 + 11*a^2 - 14*a - 2)*q^12 + (-a^6 + a^5 + 8*a^4 - 6*a^3 - 16*a^2 + 5*a + 8)*q^13 + (a^6 - 2*a^5 - 7*a^4 + 11*a^3 + 12*a^2 - 8*a - 6)*q^14 + (2*a^5 - a^4 - 13*a^3 + 4*a^2 + 14*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - a^5 - 6*a^4 + 5*a^3 + 6*a^2 - 3*a)*q^17 + (-2*a^6 + 2*a^5 + 14*a^4 - 12*a^3 - 21*a^2 + 11*a + 6)*q^18 + (a^6 - 6*a^4 - a^3 + 4*a^2 + 3*a + 2)*q^19 + (-2*a^6 + a^5 + 13*a^4 - 5*a^3 - 14*a^2 + 2*a)*q^20 + (-2*a^4 + a^3 + 12*a^2 - 4*a - 10)*q^21 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 11*a^2 - 10*a - 6)*q^22 + (a^6 - a^5 - 7*a^4 + 6*a^3 + 12*a^2 - 8*a - 6)*q^23 + (a^6 - 9*a^4 + a^3 + 22*a^2 - 6*a - 12)*q^24 + (-3*a^6 + 4*a^5 + 21*a^4 - 24*a^3 - 33*a^2 + 24*a + 13)*q^25 + (-2*a^6 + 3*a^5 + 13*a^4 - 16*a^3 - 18*a^2 + 12*a + 6)*q^26 + (-a^6 + a^5 + 6*a^4 - 5*a^3 - 5*a^2 + 2*a - 2)*q^27 + (-a^6 + 2*a^5 + 6*a^4 - 12*a^3 - 7*a^2 + 12*a + 2)*q^28 + (a^6 - 6*a^4 + 3*a^2 - a + 6)*q^29 + (2*a^6 - a^5 - 13*a^4 + 4*a^3 + 14*a^2)*q^30 + (-a^6 + a^5 + 5*a^4 - 4*a^3 + 2*a^2 - a - 10)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^6 - 2*a^5 - 8*a^4 + 13*a^3 + 18*a^2 - 16*a - 12)*q^33 + (2*a^6 - a^5 - 14*a^4 + 6*a^3 + 20*a^2 - 4*a - 6)*q^34 + (3*a^6 - 5*a^5 - 20*a^4 + 30*a^3 + 28*a^2 - 28*a - 12)*q^35 + (-2*a^6 + 2*a^5 + 12*a^4 - 11*a^3 - 11*a^2 + 10*a - 2)*q^36 + (3*a^6 - 6*a^5 - 17*a^4 + 33*a^3 + 11*a^2 - 21*a + 2)*q^37 + O(q^38)
*]> ;  // time = 1.87 seconds




J[165] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 165, 165, 165, 55, 55, 33, 15, 11 ], new_dimensions := [ 2, 2, 3, 1, 2, 1, 1, 1 ], dimensions := [ 2, 2, 3, 2, 4, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 49, 1, 1, 1, 1, 1, 0, 1, 9, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 49, 9, 1, 0 ], ap_traces := [
[ -2, -2, -2, -4, -2, 0, -8, -8, -8, -4, 0, 12 ],
[ 0, 2, -2, 4, -2, 4, 0, 4, 0, 0, -8, 4 ],
[ -1, 3, 3, 0, 3, -2, -2, 8, 0, -10, 8, -6 ]
], hecke_fields := [
x^2 + 2*x - 1,
x^2 - 3,
x^3 + x^2 - 5*x - 1
], atkin_lehners := [
[ 1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 5, 1 ]
], torsion_upper_bounds := [ 1, 3, 5 ], torsion_lower_bounds := [ 1, 3, 1 ], l_ratios := [ 0, 1/3, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1/25 ], eigenvalues := [*
[
a,
-1,
-1,
-2*a - 4,
-1,
4*a + 4,
-2*a - 6,
2*a - 2,
-4,
2*a,
0,
-4*a + 2
],
[
a,
1,
-1,
2,
-1,
-2*a + 2,
0,
-2*a + 2,
-4*a,
2*a,
4*a - 4,
4*a + 2
],
[
a,
1,
1,
-a^2 - 2*a + 3,
1,
-a^2 + 3,
a^2 - 2*a - 5,
2*a^2 + 2*a - 4,
2*a^2 + 4*a - 6,
-2*a - 4,
-2*a^2 + 10,
-2
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-2*a - 1)*q^4 - q^5 - a*q^6 + (-2*a - 4)*q^7 + (a - 2)*q^8 + q^9 - a*q^10 - q^11 + (2*a + 1)*q^12 + (4*a + 4)*q^13 - 2*q^14 + q^15 + 3*q^16 + (-2*a - 6)*q^17 + a*q^18 + (2*a - 2)*q^19 + (2*a + 1)*q^20 + (2*a + 4)*q^21 - a*q^22 - 4*q^23 + (-a + 2)*q^24 + q^25 + (-4*a + 4)*q^26 - q^27 + (2*a + 8)*q^28 + 2*a*q^29 + a*q^30 + (a + 4)*q^32 + q^33 + (-2*a - 2)*q^34 + (2*a + 4)*q^35 + (-2*a - 1)*q^36 + (-4*a + 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + q^4 - q^5 + a*q^6 + 2*q^7 - a*q^8 + q^9 - a*q^10 - q^11 + q^12 + (-2*a + 2)*q^13 + 2*a*q^14 - q^15 - 5*q^16 + a*q^18 + (-2*a + 2)*q^19 - q^20 + 2*q^21 - a*q^22 - 4*a*q^23 - a*q^24 + q^25 + (2*a - 6)*q^26 + q^27 + 2*q^28 + 2*a*q^29 - a*q^30 + (4*a - 4)*q^31 - 3*a*q^32 - q^33 - 2*q^35 + q^36 + (4*a + 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + q^5 + a*q^6 + (-a^2 - 2*a + 3)*q^7 + (-a^2 + a + 1)*q^8 + q^9 + a*q^10 + q^11 + (a^2 - 2)*q^12 + (-a^2 + 3)*q^13 + (-a^2 - 2*a - 1)*q^14 + q^15 + (-4*a + 3)*q^16 + (a^2 - 2*a - 5)*q^17 + a*q^18 + (2*a^2 + 2*a - 4)*q^19 + (a^2 - 2)*q^20 + (-a^2 - 2*a + 3)*q^21 + a*q^22 + (2*a^2 + 4*a - 6)*q^23 + (-a^2 + a + 1)*q^24 + q^25 + (a^2 - 2*a - 1)*q^26 + q^27 + (a^2 - 2*a - 7)*q^28 + (-2*a - 4)*q^29 + a*q^30 + (-2*a^2 + 10)*q^31 + (-2*a^2 + a - 2)*q^32 + q^33 + (-3*a^2 + 1)*q^34 + (-a^2 - 2*a + 3)*q^35 + (a^2 - 2)*q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 33.04 seconds




J[166] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 166, 166, 166, 83, 83 ], new_dimensions := [ 1, 2, 3, 1, 6 ], dimensions := [ 1, 2, 3, 2, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 131, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 131, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, 1, -5, -2, -3, -2, 4, -3, 1, 1 ],
[ -2, -2, 3, -3, 6, 3, 7, -1, 3, 8, -9, -4 ],
[ 3, 1, -1, 2, 5, -9, -4, -5, 7, 13, -4, -19 ]
], hecke_fields := [
x - 1,
x^2 + 2*x - 4,
x^3 - x^2 - 6*x + 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 131, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 7 ], l_ratios := [ 0, 1, 1/7 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, -1, -2, 1, -5, -2, -3, -2, 4, -3, 1, 1 ],
[
-1,
a,
1/2*a + 2,
1/2*a - 1,
-a + 2,
-1/2*a + 1,
1/2*a + 4,
-1/2*a - 1,
-3/2*a,
4,
1/2*a - 4,
-4*a - 6
],
[
1,
a,
-1/2*a^2 - 1/2*a + 2,
1/2*a^2 - 3/2*a - 1,
-a + 2,
-1/2*a^2 + 1/2*a - 1,
3/2*a^2 + 1/2*a - 8,
-5/2*a^2 + 1/2*a + 9,
1/2*a^2 + 1/2*a,
a^2,
3/2*a^2 + 1/2*a - 8,
-a^2 - 2
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 + q^7 - q^8 - 2*q^9 + 2*q^10 - 5*q^11 - q^12 - 2*q^13 - q^14 + 2*q^15 + q^16 - 3*q^17 + 2*q^18 - 2*q^19 - 2*q^20 - q^21 + 5*q^22 + 4*q^23 + q^24 - q^25 + 2*q^26 + 5*q^27 + q^28 - 3*q^29 - 2*q^30 + q^31 - q^32 + 5*q^33 + 3*q^34 - 2*q^35 - 2*q^36 + q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (1/2*a + 2)*q^5 - a*q^6 + (1/2*a - 1)*q^7 - q^8 + (-2*a + 1)*q^9 + (-1/2*a - 2)*q^10 + (-a + 2)*q^11 + a*q^12 + (-1/2*a + 1)*q^13 + (-1/2*a + 1)*q^14 + (a + 2)*q^15 + q^16 + (1/2*a + 4)*q^17 + (2*a - 1)*q^18 + (-1/2*a - 1)*q^19 + (1/2*a + 2)*q^20 + (-2*a + 2)*q^21 + (a - 2)*q^22 - 3/2*a*q^23 - a*q^24 + 3/2*a*q^25 + (1/2*a - 1)*q^26 + (2*a - 8)*q^27 + (1/2*a - 1)*q^28 + 4*q^29 + (-a - 2)*q^30 + (1/2*a - 4)*q^31 - q^32 + (4*a - 4)*q^33 + (-1/2*a - 4)*q^34 - q^35 + (-2*a + 1)*q^36 + (-4*a - 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/2*a^2 - 1/2*a + 2)*q^5 + a*q^6 + (1/2*a^2 - 3/2*a - 1)*q^7 + q^8 + (a^2 - 3)*q^9 + (-1/2*a^2 - 1/2*a + 2)*q^10 + (-a + 2)*q^11 + a*q^12 + (-1/2*a^2 + 1/2*a - 1)*q^13 + (1/2*a^2 - 3/2*a - 1)*q^14 + (-a^2 - a + 2)*q^15 + q^16 + (3/2*a^2 + 1/2*a - 8)*q^17 + (a^2 - 3)*q^18 + (-5/2*a^2 + 1/2*a + 9)*q^19 + (-1/2*a^2 - 1/2*a + 2)*q^20 + (-a^2 + 2*a - 2)*q^21 + (-a + 2)*q^22 + (1/2*a^2 + 1/2*a)*q^23 + a*q^24 + (1/2*a^2 + 3/2*a - 4)*q^25 + (-1/2*a^2 + 1/2*a - 1)*q^26 + (a^2 - 4)*q^27 + (1/2*a^2 - 3/2*a - 1)*q^28 + a^2*q^29 + (-a^2 - a + 2)*q^30 + (3/2*a^2 + 1/2*a - 8)*q^31 + q^32 + (-a^2 + 2*a)*q^33 + (3/2*a^2 + 1/2*a - 8)*q^34 + (a^2 - 3)*q^35 + (a^2 - 3)*q^36 + (-a^2 - 2)*q^37 + O(q^38)
*]> ;  // time = 22.089 seconds




J[167] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 167, 167 ], new_dimensions := [ 2, 12 ], dimensions := [ 2, 12 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, -5, 0, -5, -5, 0, 1, 8, 6, -12 ],
[ 2, 3, 4, 11, 0, 9, 3, 0, 1, -6, 2, 34 ]
], hecke_fields := [
x^2 + x - 1,
x^12 - 2*x^11 - 17*x^10 + 33*x^9 + 103*x^8 - 189*x^7 - 277*x^6 + 447*x^5 + 363*x^4 - 433*x^3 - 205*x^2 + 120*x + 9
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 83 ]
], tamagawa_numbers := [
[ 1 ],
[ 83 ]
], torsion_upper_bounds := [ 1, 83 ], torsion_lower_bounds := [ 1, 83 ], l_ratios := [ 0, 1/83 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a - 1,
-1,
a - 2,
0,
-a - 3,
a - 2,
4*a + 2,
-a,
-2*a + 3,
-2*a + 2,
2*a - 5
],
[
a,
544/933*a^11 + 157/933*a^10 - 10187/933*a^9 - 1063/311*a^8 + 68788/933*a^7 + 7637/311*a^6 - 200347/933*a^5 - 23356/311*a^4 + 76833/311*a^3 + 80543/933*a^2 - 60181/933*a - 1147/311,
-779/933*a^11 + 631/933*a^10 + 13207/933*a^9 - 2957/311*a^8 - 78341/933*a^7 + 12545/311*a^6 + 193997/933*a^5 - 13559/311*a^4 - 64281/311*a^3 - 12787/933*a^2 + 42281/933*a + 1204/311,
-98/311*a^11 - 34/311*a^10 + 1802/311*a^9 + 754/311*a^8 - 11866/311*a^7 - 5855/311*a^6 + 33461/311*a^5 + 18902/311*a^4 - 37164/311*a^3 - 21634/311*a^2 + 8350/311*a + 2112/311,
-623/933*a^11 + 628/933*a^10 + 10567/933*a^9 - 3008/311*a^8 - 62594/933*a^7 + 13132/311*a^6 + 154004/933*a^5 - 15052/311*a^4 - 49696/311*a^3 - 12775/933*a^2 + 24248/933*a + 1943/311,
652/933*a^11 - 491/933*a^10 - 11297/933*a^9 + 2227/311*a^8 + 69355/933*a^7 - 8631/311*a^6 - 182461/933*a^5 + 5275/311*a^4 + 67433/311*a^3 + 30887/933*a^2 - 59101/933*a - 755/311,
7/933*a^11 + 580/933*a^10 - 884/933*a^9 - 3202/311*a^8 + 12088/933*a^7 + 18170/311*a^6 - 54838/933*a^5 - 41428/311*a^4 + 26298/311*a^3 + 107774/933*a^2 - 19834/933*a - 3027/311,
973/933*a^11 + 382/933*a^10 - 18380/933*a^9 - 2525/311*a^8 + 125854/933*a^7 + 17726/311*a^6 - 374938/933*a^5 - 52886/311*a^4 + 149519/311*a^3 + 179474/933*a^2 - 131464/933*a - 4635/311,
125/933*a^11 - 1372/933*a^10 - 58/933*a^9 + 7154/311*a^8 - 17926/933*a^7 - 37362/311*a^6 + 112360/933*a^5 + 74590/311*a^4 - 63980/311*a^3 - 164318/933*a^2 + 79000/933*a + 2815/311,
938/933*a^11 - 1585/933*a^10 - 14893/933*a^9 + 7887/311*a^8 + 79409/933*a^7 - 37670/311*a^6 - 164192/933*a^5 + 60643/311*a^4 + 42909/311*a^3 - 78563/933*a^2 - 10835/933*a + 237/311,
1466/933*a^11 - 1021/933*a^10 - 25192/933*a^9 + 4724/311*a^8 + 152156/933*a^7 - 19272/311*a^6 - 385676/933*a^5 + 16332/311*a^4 + 130096/311*a^3 + 48868/933*a^2 - 83927/933*a - 2166/311,
91/311*a^11 - 235/311*a^10 - 1229/311*a^9 + 3565/311*a^8 + 4443/311*a^7 - 17555/311*a^6 - 393/311*a^5 + 31053/311*a^4 - 10941/311*a^3 - 19897/311*a^2 + 4953/311*a + 2304/311
]
*], q_expansions := [*
q + a*q^2 + (-a - 1)*q^3 + (-a - 1)*q^4 - q^5 - q^6 + (a - 2)*q^7 + (-2*a - 1)*q^8 + (a - 1)*q^9 - a*q^10 + (a + 2)*q^12 + (-a - 3)*q^13 + (-3*a + 1)*q^14 + (a + 1)*q^15 + 3*a*q^16 + (a - 2)*q^17 + (-2*a + 1)*q^18 + (4*a + 2)*q^19 + (a + 1)*q^20 + (2*a + 1)*q^21 - a*q^23 + (a + 3)*q^24 - 4*q^25 + (-2*a - 1)*q^26 + (4*a + 3)*q^27 + (2*a + 1)*q^28 + (-2*a + 3)*q^29 + q^30 + (-2*a + 2)*q^31 + (a + 5)*q^32 + (-3*a + 1)*q^34 + (-a + 2)*q^35 + a*q^36 + (2*a - 5)*q^37 + O(q^38),
q + a*q^2 + (544/933*a^11 + 157/933*a^10 - 10187/933*a^9 - 1063/311*a^8 + 68788/933*a^7 + 7637/311*a^6 - 200347/933*a^5 - 23356/311*a^4 + 76833/311*a^3 + 80543/933*a^2 - 60181/933*a - 1147/311)*q^3 + (a^2 - 2)*q^4 + (-779/933*a^11 + 631/933*a^10 + 13207/933*a^9 - 2957/311*a^8 - 78341/933*a^7 + 12545/311*a^6 + 193997/933*a^5 - 13559/311*a^4 - 64281/311*a^3 - 12787/933*a^2 + 42281/933*a + 1204/311)*q^5 + (415/311*a^11 - 313/311*a^10 - 7047/311*a^9 + 4252/311*a^8 + 41909/311*a^7 - 16553/311*a^6 - 104412/311*a^5 + 11009/311*a^4 + 105365/311*a^3 + 17113/311*a^2 - 22907/311*a - 1632/311)*q^6 + (-98/311*a^11 - 34/311*a^10 + 1802/311*a^9 + 754/311*a^8 - 11866/311*a^7 - 5855/311*a^6 + 33461/311*a^5 + 18902/311*a^4 - 37164/311*a^3 - 21634/311*a^2 + 8350/311*a + 2112/311)*q^7 + (a^3 - 4*a)*q^8 + (-324/311*a^11 + 78/311*a^10 + 5818/311*a^9 - 687/311*a^8 - 37466/311*a^7 - 1002/311*a^6 + 104330/311*a^5 + 19422/311*a^4 - 119105/311*a^3 - 33278/311*a^2 + 32836/311*a + 1759/311)*q^9 + (-309/311*a^11 - 12/311*a^10 + 5612/311*a^9 + 632/311*a^8 - 36532/311*a^7 - 7262/311*a^6 + 102512/311*a^5 + 29978/311*a^4 - 116698/311*a^3 - 39138/311*a^2 + 32364/311*a + 2337/311)*q^10 + (-623/933*a^11 + 628/933*a^10 + 10567/933*a^9 - 3008/311*a^8 - 62594/933*a^7 + 13132/311*a^6 + 154004/933*a^5 - 15052/311*a^4 - 49696/311*a^3 - 12775/933*a^2 + 24248/933*a + 1943/311)*q^11 + (463/933*a^11 - 290/933*a^10 - 7955/933*a^9 + 1290/311*a^8 + 48070/933*a^7 - 4731/311*a^6 - 122794/933*a^5 + 1432/311*a^4 + 43142/311*a^3 + 25418/933*a^2 - 33934/933*a - 1441/311)*q^12 + (652/933*a^11 - 491/933*a^10 - 11297/933*a^9 + 2227/311*a^8 + 69355/933*a^7 - 8631/311*a^6 - 182461/933*a^5 + 5275/311*a^4 + 67433/311*a^3 + 30887/933*a^2 - 59101/933*a - 755/311)*q^13 + (-230/311*a^11 + 136/311*a^10 + 3988/311*a^9 - 1772/311*a^8 - 24377/311*a^7 + 6315/311*a^6 + 62708/311*a^5 - 1590/311*a^4 - 64068/311*a^3 - 11740/311*a^2 + 13872/311*a + 882/311)*q^14 + (2158/933*a^11 - 2063/933*a^10 - 36209/933*a^9 + 9713/311*a^8 + 211147/933*a^7 - 41277/311*a^6 - 508297/933*a^5 + 44605/311*a^4 + 161381/311*a^3 + 35309/933*a^2 - 83227/933*a - 1647/311)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (7/933*a^11 + 580/933*a^10 - 884/933*a^9 - 3202/311*a^8 + 12088/933*a^7 + 18170/311*a^6 - 54838/933*a^5 - 41428/311*a^4 + 26298/311*a^3 + 107774/933*a^2 - 19834/933*a - 3027/311)*q^17 + (-570/311*a^11 + 310/311*a^10 + 10005/311*a^9 - 4094/311*a^8 - 62238/311*a^7 + 14582/311*a^6 + 164250/311*a^5 - 1493/311*a^4 - 173570/311*a^3 - 33584/311*a^2 + 40639/311*a + 2916/311)*q^18 + (973/933*a^11 + 382/933*a^10 - 18380/933*a^9 - 2525/311*a^8 + 125854/933*a^7 + 17726/311*a^6 - 374938/933*a^5 - 52886/311*a^4 + 149519/311*a^3 + 179474/933*a^2 - 131464/933*a - 4635/311)*q^19 + (-332/933*a^11 - 185/933*a^10 + 6073/933*a^9 + 1209/311*a^8 - 40307/933*a^7 - 8171/311*a^6 + 116309/933*a^5 + 22587/311*a^4 - 44373/311*a^3 - 67369/933*a^2 + 33689/933*a + 373/311)*q^20 + (510/311*a^11 + 50/311*a^10 - 9492/311*a^9 - 1493/311*a^8 + 63789/311*a^7 + 13879/311*a^6 - 185901/311*a^5 - 51305/311*a^4 + 218367/311*a^3 + 65732/311*a^2 - 63320/311*a - 3051/311)*q^21 + (-206/311*a^11 - 8/311*a^10 + 3845/311*a^9 + 525/311*a^8 - 26117/311*a^7 - 6189/311*a^6 + 77775/311*a^5 + 25687/311*a^4 - 94178/311*a^3 - 34489/311*a^2 + 26863/311*a + 1869/311)*q^22 + (125/933*a^11 - 1372/933*a^10 - 58/933*a^9 + 7154/311*a^8 - 17926/933*a^7 - 37362/311*a^6 + 112360/933*a^5 + 74590/311*a^4 - 63980/311*a^3 - 164318/933*a^2 + 79000/933*a + 2815/311)*q^23 + (-618/311*a^11 + 598/311*a^10 + 10291/311*a^9 - 8377/311*a^8 - 59380/311*a^7 + 34925/311*a^6 + 141269/311*a^5 - 34899/311*a^4 - 135431/311*a^3 - 13899/311*a^2 + 25853/311*a + 1875/311)*q^24 + (-2245/933*a^11 + 719/933*a^10 + 40265/933*a^9 - 2705/311*a^8 - 258487/933*a^7 + 5071/311*a^6 + 714025/933*a^5 + 25467/311*a^4 - 266529/311*a^3 - 184811/933*a^2 + 212977/933*a + 3681/311)*q^25 + (271/311*a^11 - 71/311*a^10 - 4945/311*a^9 + 733/311*a^8 + 32445/311*a^7 - 619/311*a^6 - 91873/311*a^5 - 11459/311*a^4 + 104401/311*a^3 + 24853/311*a^2 - 26835/311*a - 1956/311)*q^26 + (167/933*a^11 + 2108/933*a^10 - 6295/933*a^9 - 11125/311*a^8 + 67664/933*a^7 + 58907/311*a^6 - 277313/933*a^5 - 119864/311*a^4 + 131439/311*a^3 + 272401/933*a^2 - 137036/933*a - 5084/311)*q^27 + (-128/311*a^11 + 146/311*a^10 + 2214/311*a^9 - 2195/311*a^8 - 13423/311*a^7 + 10708/311*a^6 + 34298/311*a^5 - 18382/311*a^4 - 37002/311*a^3 + 9990/311*a^2 + 11782/311*a - 2154/311)*q^28 + (938/933*a^11 - 1585/933*a^10 - 14893/933*a^9 + 7887/311*a^8 + 79409/933*a^7 - 37670/311*a^6 - 164192/933*a^5 + 60643/311*a^4 + 42909/311*a^3 - 78563/933*a^2 - 10835/933*a + 237/311)*q^29 + (751/311*a^11 + 159/311*a^10 - 14025/311*a^9 - 3709/311*a^8 + 94677/311*a^7 + 29823/311*a^6 - 276937/311*a^5 - 99737/311*a^4 + 323241/311*a^3 + 119721/311*a^2 - 87967/311*a - 6474/311)*q^30 + (1466/933*a^11 - 1021/933*a^10 - 25192/933*a^9 + 4724/311*a^8 + 152156/933*a^7 - 19272/311*a^6 - 385676/933*a^5 + 16332/311*a^4 + 130096/311*a^3 + 48868/933*a^2 - 83927/933*a - 2166/311)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-124/311*a^11 - 500/311*a^10 + 3175/311*a^9 + 8088/311*a^8 - 28330/311*a^7 - 44557/311*a^6 + 105281/311*a^5 + 98176/311*a^4 - 144754/311*a^3 - 84147/311*a^2 + 47276/311*a + 5008/311)*q^33 + (198/311*a^11 - 255/311*a^10 - 3279/311*a^9 + 3789/311*a^8 + 18611/311*a^7 - 17633/311*a^6 - 42471/311*a^5 + 25451/311*a^4 + 36935/311*a^3 - 6133/311*a^2 - 3307/311*a - 21/311)*q^34 + (-673/311*a^11 + 306/311*a^10 + 11772/311*a^9 - 3676/311*a^8 - 72964/311*a^7 + 9466/311*a^6 + 191786/311*a^5 + 18970/311*a^4 - 201066/311*a^3 - 57826/311*a^2 + 43652/311*a + 4317/311)*q^35 + (-182/311*a^11 + 159/311*a^10 + 3080/311*a^9 - 2154/311*a^8 - 18216/311*a^7 + 8364/311*a^6 + 44637/311*a^5 - 5504/311*a^4 - 42184/311*a^3 - 9655/311*a^2 + 5644/311*a + 1612/311)*q^36 + (91/311*a^11 - 235/311*a^10 - 1229/311*a^9 + 3565/311*a^8 + 4443/311*a^7 - 17555/311*a^6 - 393/311*a^5 + 31053/311*a^4 - 10941/311*a^3 - 19897/311*a^2 + 4953/311*a + 2304/311)*q^37 + O(q^38)
*]> ;  // time = 1.961 seconds




J[170] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 170, 170, 170, 170, 170, 170, 85, 85, 85, 34, 17 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 4, 4, 2, 4 ], intersection_graph := [ 0, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, -2, -1, 2, 6, 2, 1, 8, -6, -6, 2, 2 ],
[ -1, 3, -1, 2, -4, -3, 1, 3, -6, 9, -3, -8 ],
[ -1, 1, 1, 2, 0, 5, -1, -1, 6, -9, -1, -4 ],
[ -1, -2, 1, -2, -2, -6, 1, -8, -2, 6, -2, 6 ],
[ 1, 1, -1, 2, 0, -1, -1, -1, -6, -3, 5, 8 ],
[ 2, -1, 2, 2, -8, 5, 2, -1, -2, 1, -9, -6 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 3, 3, 1 ],
[ 1, 1, 1 ],
[ 21, 3, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 3 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 21, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 3, 1, 3, 1, 3, 1 ], torsion_lower_bounds := [ 3, 1, 3, 1, 3, 1 ], l_ratios := [ 1/3, 1, 1/3, 0, 7/3, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, -2, -1, 2, 6, 2, 1, 8, -6, -6, 2, 2 ],
[ -1, 3, -1, 2, -4, -3, 1, 3, -6, 9, -3, -8 ],
[ -1, 1, 1, 2, 0, 5, -1, -1, 6, -9, -1, -4 ],
[ -1, -2, 1, -2, -2, -6, 1, -8, -2, 6, -2, 6 ],
[ 1, 1, -1, 2, 0, -1, -1, -1, -6, -3, 5, 8 ],
[
1,
a,
1,
-2*a,
-4,
-a + 2,
1,
a,
2*a,
3*a + 2,
a - 4,
2*a - 2
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 - q^5 + 2*q^6 + 2*q^7 - q^8 + q^9 + q^10 + 6*q^11 - 2*q^12 + 2*q^13 - 2*q^14 + 2*q^15 + q^16 + q^17 - q^18 + 8*q^19 - q^20 - 4*q^21 - 6*q^22 - 6*q^23 + 2*q^24 + q^25 - 2*q^26 + 4*q^27 + 2*q^28 - 6*q^29 - 2*q^30 + 2*q^31 - q^32 - 12*q^33 - q^34 - 2*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + 3*q^3 + q^4 - q^5 - 3*q^6 + 2*q^7 - q^8 + 6*q^9 + q^10 - 4*q^11 + 3*q^12 - 3*q^13 - 2*q^14 - 3*q^15 + q^16 + q^17 - 6*q^18 + 3*q^19 - q^20 + 6*q^21 + 4*q^22 - 6*q^23 - 3*q^24 + q^25 + 3*q^26 + 9*q^27 + 2*q^28 + 9*q^29 + 3*q^30 - 3*q^31 - q^32 - 12*q^33 - q^34 - 2*q^35 + 6*q^36 - 8*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + q^5 - q^6 + 2*q^7 - q^8 - 2*q^9 - q^10 + q^12 + 5*q^13 - 2*q^14 + q^15 + q^16 - q^17 + 2*q^18 - q^19 + q^20 + 2*q^21 + 6*q^23 - q^24 + q^25 - 5*q^26 - 5*q^27 + 2*q^28 - 9*q^29 - q^30 - q^31 - q^32 + q^34 + 2*q^35 - 2*q^36 - 4*q^37 + O(q^38),
q - q^2 - 2*q^3 + q^4 + q^5 + 2*q^6 - 2*q^7 - q^8 + q^9 - q^10 - 2*q^11 - 2*q^12 - 6*q^13 + 2*q^14 - 2*q^15 + q^16 + q^17 - q^18 - 8*q^19 + q^20 + 4*q^21 + 2*q^22 - 2*q^23 + 2*q^24 + q^25 + 6*q^26 + 4*q^27 - 2*q^28 + 6*q^29 + 2*q^30 - 2*q^31 - q^32 + 4*q^33 - q^34 - 2*q^35 + q^36 + 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + 2*q^7 + q^8 - 2*q^9 - q^10 + q^12 - q^13 + 2*q^14 - q^15 + q^16 - q^17 - 2*q^18 - q^19 - q^20 + 2*q^21 - 6*q^23 + q^24 + q^25 - q^26 - 5*q^27 + 2*q^28 - 3*q^29 - q^30 + 5*q^31 + q^32 - q^34 - 2*q^35 - 2*q^36 + 8*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 - 2*a*q^7 + q^8 + (-a + 1)*q^9 + q^10 - 4*q^11 + a*q^12 + (-a + 2)*q^13 - 2*a*q^14 + a*q^15 + q^16 + q^17 + (-a + 1)*q^18 + a*q^19 + q^20 + (2*a - 8)*q^21 - 4*q^22 + 2*a*q^23 + a*q^24 + q^25 + (-a + 2)*q^26 + (-a - 4)*q^27 - 2*a*q^28 + (3*a + 2)*q^29 + a*q^30 + (a - 4)*q^31 + q^32 - 4*a*q^33 + q^34 - 2*a*q^35 + (-a + 1)*q^36 + (2*a - 2)*q^37 + O(q^38)
*]> ;  // time = 50.219 seconds




J[173] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 173, 173 ], new_dimensions := [ 4, 10 ], dimensions := [ 4, 10 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -6, -1, -9, -5, -5, 2, -7, -11, 9, 3, -14 ],
[ 1, 8, 1, 11, 5, 1, -2, 7, 5, -5, 3, 8 ]
], hecke_fields := [
x^4 + x^3 - 3*x^2 - x + 1,
x^10 - x^9 - 16*x^8 + 16*x^7 + 85*x^6 - 80*x^5 - 175*x^4 + 136*x^3 + 138*x^2 - 71*x - 25
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 43 ]
], tamagawa_numbers := [
[ 1 ],
[ 43 ]
], torsion_upper_bounds := [ 1, 43 ], torsion_lower_bounds := [ 1, 43 ], l_ratios := [ 0, 1/43 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - a,
a^2 - 2,
a^3 + a^2 - 3*a - 3,
-3*a^3 - 4*a^2 + 6*a + 2,
-4*a^3 - 5*a^2 + 10*a + 3,
4*a^3 + 5*a^2 - 7*a - 3,
2*a^3 + 3*a^2 - 2*a - 4,
3*a^3 + 2*a^2 - 8*a - 3,
-2*a^3 - 2*a^2 + 3*a + 3,
2*a^3 + 4*a^2 - a - 3,
3*a^3 - a^2 - 10*a + 1
],
[
a,
9/116*a^9 - 11/58*a^8 - 69/58*a^7 + 81/29*a^6 + 645/116*a^5 - 1439/116*a^4 - 235/29*a^3 + 465/29*a^2 + 98/29*a - 303/116,
-7/58*a^9 + 15/29*a^8 + 44/29*a^7 - 213/29*a^6 - 231/58*a^5 + 1783/58*a^4 - 179/29*a^3 - 1023/29*a^2 + 376/29*a + 371/58,
-1/58*a^9 - 37/116*a^8 + 79/116*a^7 + 537/116*a^6 - 849/116*a^5 - 579/29*a^4 + 3125/116*a^3 + 2767/116*a^2 - 2913/116*a - 387/116,
23/116*a^9 + 5/116*a^8 - 343/116*a^7 - 71/116*a^6 + 400/29*a^5 + 389/116*a^4 - 2399/116*a^3 - 921/116*a^2 + 715/116*a + 275/58,
-25/116*a^9 - 13/116*a^8 + 393/116*a^7 + 173/116*a^6 - 1007/58*a^5 - 791/116*a^4 + 3755/116*a^3 + 1455/116*a^2 - 2265/116*a - 140/29,
-5/58*a^9 + 9/58*a^8 + 67/58*a^7 - 151/58*a^6 - 126/29*a^5 + 735/58*a^4 + 171/58*a^3 - 927/58*a^2 + 127/58*a + 31/29,
-47/116*a^9 + 73/116*a^8 + 653/116*a^7 - 1083/116*a^6 - 1283/58*a^5 + 4647/116*a^4 + 2141/116*a^3 - 5141/116*a^2 + 463/116*a + 224/29,
5/58*a^9 + 10/29*a^8 - 48/29*a^7 - 142/29*a^6 + 687/58*a^5 + 1237/58*a^4 - 1028/29*a^3 - 827/29*a^2 + 908/29*a + 489/58,
1/116*a^9 - 27/58*a^8 + 1/29*a^7 + 183/29*a^6 - 257/116*a^5 - 2815/116*a^4 + 338/29*a^3 + 1215/58*a^2 - 292/29*a + 179/116,
-35/58*a^9 + 17/29*a^8 + 249/29*a^7 - 253/29*a^6 - 2083/58*a^5 + 2129/58*a^4 + 1164/29*a^3 - 1026/29*a^2 - 150/29*a - 1/58,
-53/116*a^9 + 5/29*a^8 + 387/58*a^7 - 171/58*a^6 - 3489/116*a^5 + 1643/116*a^4 + 2481/58*a^3 - 515/29*a^2 - 687/58*a + 547/116
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - a)*q^3 + (a^2 - 2)*q^4 + (a^2 - 2)*q^5 + (-a^3 - a^2)*q^6 + (a^3 + a^2 - 3*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + 4*a^2 + a - 4)*q^9 + (a^3 - 2*a)*q^10 + (-3*a^3 - 4*a^2 + 6*a + 2)*q^11 + (-a^2 + a + 1)*q^12 + (-4*a^3 - 5*a^2 + 10*a + 3)*q^13 + (-2*a - 1)*q^14 + (-a^2 + a + 1)*q^15 + (-a^3 - 3*a^2 + a + 3)*q^16 + (4*a^3 + 5*a^2 - 7*a - 3)*q^17 + (3*a^3 + 4*a^2 - 3*a - 1)*q^18 + (2*a^3 + 3*a^2 - 2*a - 4)*q^19 + (-a^3 - a^2 + a + 3)*q^20 + (2*a^2 + 3*a + 1)*q^21 + (-a^3 - 3*a^2 - a + 3)*q^22 + (3*a^3 + 2*a^2 - 8*a - 3)*q^23 + (a^3 + 3*a^2 + a)*q^24 + (-a^3 - a^2 + a - 2)*q^25 + (-a^3 - 2*a^2 - a + 4)*q^26 + (-4*a^3 - 7*a^2 + 4*a + 4)*q^27 + (-2*a^3 - 4*a^2 + 5*a + 6)*q^28 + (-2*a^3 - 2*a^2 + 3*a + 3)*q^29 + (-a^3 + a^2 + a)*q^30 + (2*a^3 + 4*a^2 - a - 3)*q^31 + (-4*a^3 - 2*a^2 + 10*a + 1)*q^32 + (3*a^3 + 7*a^2 - a - 4)*q^33 + (a^3 + 5*a^2 + a - 4)*q^34 + (-2*a^3 - 4*a^2 + 5*a + 6)*q^35 + (-a^3 - 2*a^2 + 5)*q^36 + (3*a^3 - a^2 - 10*a + 1)*q^37 + O(q^38),
q + a*q^2 + (9/116*a^9 - 11/58*a^8 - 69/58*a^7 + 81/29*a^6 + 645/116*a^5 - 1439/116*a^4 - 235/29*a^3 + 465/29*a^2 + 98/29*a - 303/116)*q^3 + (a^2 - 2)*q^4 + (-7/58*a^9 + 15/29*a^8 + 44/29*a^7 - 213/29*a^6 - 231/58*a^5 + 1783/58*a^4 - 179/29*a^3 - 1023/29*a^2 + 376/29*a + 371/58)*q^5 + (-13/116*a^9 + 3/58*a^8 + 45/29*a^7 - 30/29*a^6 - 719/116*a^5 + 635/116*a^4 + 159/29*a^3 - 425/58*a^2 + 84/29*a + 225/116)*q^6 + (-1/58*a^9 - 37/116*a^8 + 79/116*a^7 + 537/116*a^6 - 849/116*a^5 - 579/29*a^4 + 3125/116*a^3 + 2767/116*a^2 - 2913/116*a - 387/116)*q^7 + (a^3 - 4*a)*q^8 + (9/29*a^9 - 59/116*a^8 - 523/116*a^7 + 861/116*a^6 + 2261/116*a^5 - 1805/58*a^4 - 2745/116*a^3 + 3641/116*a^2 + 611/116*a + 151/116)*q^9 + (23/58*a^9 - 12/29*a^8 - 157/29*a^7 + 182/29*a^6 + 1223/58*a^5 - 1583/58*a^4 - 547/29*a^3 + 859/29*a^2 - 63/29*a - 175/58)*q^10 + (23/116*a^9 + 5/116*a^8 - 343/116*a^7 - 71/116*a^6 + 400/29*a^5 + 389/116*a^4 - 2399/116*a^3 - 921/116*a^2 + 715/116*a + 275/58)*q^11 + (-25/116*a^9 + 4/29*a^8 + 91/29*a^7 - 131/58*a^6 - 1695/116*a^5 + 1239/116*a^4 + 1399/58*a^3 - 795/58*a^2 - 741/58*a + 281/116)*q^12 + (-25/116*a^9 - 13/116*a^8 + 393/116*a^7 + 173/116*a^6 - 1007/58*a^5 - 791/116*a^4 + 3755/116*a^3 + 1455/116*a^2 - 2265/116*a - 140/29)*q^13 + (-39/116*a^9 + 47/116*a^8 + 569/116*a^7 - 679/116*a^6 - 619/29*a^5 + 2775/116*a^4 + 3039/116*a^3 - 2637/116*a^2 - 529/116*a - 25/58)*q^14 + (-11/29*a^9 + 57/58*a^8 + 289/58*a^7 - 821/58*a^6 - 929/58*a^5 + 1733/29*a^4 - 251/58*a^3 - 3899/58*a^2 + 1597/58*a + 557/58)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5/58*a^9 + 9/58*a^8 + 67/58*a^7 - 151/58*a^6 - 126/29*a^5 + 735/58*a^4 + 171/58*a^3 - 927/58*a^2 + 127/58*a + 31/29)*q^17 + (-23/116*a^9 + 53/116*a^8 + 285/116*a^7 - 799/116*a^6 - 365/58*a^5 + 3555/116*a^4 - 1255/116*a^3 - 4357/116*a^2 + 2707/116*a + 225/29)*q^18 + (-47/116*a^9 + 73/116*a^8 + 653/116*a^7 - 1083/116*a^6 - 1283/58*a^5 + 4647/116*a^4 + 2141/116*a^3 - 5141/116*a^2 + 463/116*a + 224/29)*q^19 + (13/58*a^9 - 3/29*a^8 - 90/29*a^7 + 60/29*a^6 + 719/58*a^5 - 635/58*a^4 - 347/29*a^3 + 396/29*a^2 - 23/29*a - 167/58)*q^20 + (27/116*a^9 - 31/29*a^8 - 149/58*a^7 + 921/58*a^6 + 311/116*a^5 - 8261/116*a^4 + 1867/58*a^3 + 2758/29*a^2 - 2689/58*a - 3229/116)*q^21 + (7/29*a^9 + 25/116*a^8 - 439/116*a^7 - 355/116*a^6 + 2229/116*a^5 + 813/58*a^4 - 4049/116*a^3 - 2459/116*a^2 + 2183/116*a + 575/116)*q^22 + (5/58*a^9 + 10/29*a^8 - 48/29*a^7 - 142/29*a^6 + 687/58*a^5 + 1237/58*a^4 - 1028/29*a^3 - 827/29*a^2 + 908/29*a + 489/58)*q^23 + (17/116*a^9 - 12/29*a^8 - 111/58*a^7 + 335/58*a^6 + 677/116*a^5 - 2847/116*a^4 + 269/58*a^3 + 917/29*a^2 - 1083/58*a - 1075/116)*q^24 + (6/29*a^9 - 5/29*a^8 - 92/29*a^7 + 71/29*a^6 + 430/29*a^5 - 302/29*a^4 - 588/29*a^3 + 399/29*a^2 + 68/29*a - 144/29)*q^25 + (-19/58*a^9 - 7/116*a^8 + 573/116*a^7 + 111/116*a^6 - 2791/116*a^5 - 155/29*a^4 + 4855/116*a^3 + 1185/116*a^2 - 2335/116*a - 625/116)*q^26 + (111/116*a^9 - 107/116*a^8 - 1615/116*a^7 + 1589/116*a^6 + 1793/29*a^5 - 6631/116*a^4 - 9863/116*a^3 + 6207/116*a^2 + 3491/116*a + 263/58)*q^27 + (3/29*a^9 + 19/116*a^8 - 213/116*a^7 - 235/116*a^6 + 1353/116*a^5 + 423/58*a^4 - 3583/116*a^3 - 681/116*a^2 + 3007/116*a - 201/116)*q^28 + (1/116*a^9 - 27/58*a^8 + 1/29*a^7 + 183/29*a^6 - 257/116*a^5 - 2815/116*a^4 + 338/29*a^3 + 1215/58*a^2 - 292/29*a + 179/116)*q^29 + (35/58*a^9 - 63/58*a^8 - 469/58*a^7 + 941/58*a^6 + 853/29*a^5 - 4101/58*a^4 - 907/58*a^3 + 4633/58*a^2 - 1005/58*a - 275/29)*q^30 + (-35/58*a^9 + 17/29*a^8 + 249/29*a^7 - 253/29*a^6 - 2083/58*a^5 + 2129/58*a^4 + 1164/29*a^3 - 1026/29*a^2 - 150/29*a - 1/58)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (9/29*a^9 - 59/116*a^8 - 523/116*a^7 + 861/116*a^6 + 2261/116*a^5 - 1863/58*a^4 - 2629/116*a^3 + 4569/116*a^2 + 31/116*a - 1125/116)*q^33 + (2/29*a^9 - 13/58*a^8 - 71/58*a^7 + 173/58*a^6 + 335/58*a^5 - 352/29*a^4 - 247/58*a^3 + 817/58*a^2 - 293/58*a - 125/58)*q^34 + (-16/29*a^9 + 23/29*a^8 + 226/29*a^7 - 344/29*a^6 - 934/29*a^5 + 1511/29*a^4 + 988/29*a^3 - 1789/29*a^2 + 12/29*a + 239/29)*q^35 + (-21/58*a^9 + 35/116*a^8 + 615/116*a^7 - 497/116*a^6 - 2807/116*a^5 + 485/29*a^4 + 4261/116*a^3 - 1401/116*a^2 - 1955/116*a - 877/116)*q^36 + (-53/116*a^9 + 5/29*a^8 + 387/58*a^7 - 171/58*a^6 - 3489/116*a^5 + 1643/116*a^4 + 2481/58*a^3 - 515/29*a^2 - 687/58*a + 547/116)*q^37 + O(q^38)
*]> ;  // time = 1.931 seconds




J[174] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 174, 174, 174, 174, 174, 87, 87, 58, 58, 29 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 3, 1, 1, 2 ], dimensions := [ 1, 1, 1, 1, 1, 4, 6, 2, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 0, 5, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 11, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 11, 1, 1, 0, 1, 1, 5, 1, 13, 1, 1, 1, 1, 1, 0, 1, 1, 529, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 529, 1, 1, 0 ], ap_traces := [
[ -1, -1, 3, -3, 6, 0, 7, 5, -8, 1, -8, -3 ],
[ -1, 1, 2, 0, -4, 6, -2, 4, 0, -1, -4, -6 ],
[ -1, 1, -3, 5, 6, -4, 3, -1, 0, -1, -4, -1 ],
[ 1, -1, 1, 1, 6, -4, -7, -3, 4, -1, 0, -7 ],
[ 1, 1, -1, 1, -2, 0, -3, -1, -4, 1, 4, 3 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 13, 1, 1 ],
[ 1, 1, 1 ],
[ 11, 21, 1 ],
[ 1, 3, 1 ],
[ 7, 7, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 21, 1 ],
[ 1, 1, 1 ],
[ 7, 7, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 7 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1 ], l_ratios := [ 1, 1, 7/3, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1/49 ], eigenvalues := [*
[ -1, -1, 3, -3, 6, 0, 7, 5, -8, 1, -8, -3 ],
[ -1, 1, 2, 0, -4, 6, -2, 4, 0, -1, -4, -6 ],
[ -1, 1, -3, 5, 6, -4, 3, -1, 0, -1, -4, -1 ],
[ 1, -1, 1, 1, 6, -4, -7, -3, 4, -1, 0, -7 ],
[ 1, 1, -1, 1, -2, 0, -3, -1, -4, 1, 4, 3 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + 3*q^5 + q^6 - 3*q^7 - q^8 + q^9 - 3*q^10 + 6*q^11 - q^12 + 3*q^14 - 3*q^15 + q^16 + 7*q^17 - q^18 + 5*q^19 + 3*q^20 + 3*q^21 - 6*q^22 - 8*q^23 + q^24 + 4*q^25 - q^27 - 3*q^28 + q^29 + 3*q^30 - 8*q^31 - q^32 - 6*q^33 - 7*q^34 - 9*q^35 + q^36 - 3*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 2*q^5 - q^6 - q^8 + q^9 - 2*q^10 - 4*q^11 + q^12 + 6*q^13 + 2*q^15 + q^16 - 2*q^17 - q^18 + 4*q^19 + 2*q^20 + 4*q^22 - q^24 - q^25 - 6*q^26 + q^27 - q^29 - 2*q^30 - 4*q^31 - q^32 - 4*q^33 + 2*q^34 + q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 3*q^5 - q^6 + 5*q^7 - q^8 + q^9 + 3*q^10 + 6*q^11 + q^12 - 4*q^13 - 5*q^14 - 3*q^15 + q^16 + 3*q^17 - q^18 - q^19 - 3*q^20 + 5*q^21 - 6*q^22 - q^24 + 4*q^25 + 4*q^26 + q^27 + 5*q^28 - q^29 + 3*q^30 - 4*q^31 - q^32 + 6*q^33 - 3*q^34 - 15*q^35 + q^36 - q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + q^7 + q^8 + q^9 + q^10 + 6*q^11 - q^12 - 4*q^13 + q^14 - q^15 + q^16 - 7*q^17 + q^18 - 3*q^19 + q^20 - q^21 + 6*q^22 + 4*q^23 - q^24 - 4*q^25 - 4*q^26 - q^27 + q^28 - q^29 - q^30 + q^32 - 6*q^33 - 7*q^34 + q^35 + q^36 - 7*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + q^7 + q^8 + q^9 - q^10 - 2*q^11 + q^12 + q^14 - q^15 + q^16 - 3*q^17 + q^18 - q^19 - q^20 + q^21 - 2*q^22 - 4*q^23 + q^24 - 4*q^25 + q^27 + q^28 + q^29 - q^30 + 4*q^31 + q^32 - 2*q^33 - 3*q^34 - q^35 + q^36 + 3*q^37 + O(q^38)
*]> ;  // time = 71.159 seconds




J[177] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 177, 177, 177, 177, 59 ], new_dimensions := [ 2, 2, 2, 3, 5 ], dimensions := [ 2, 2, 2, 3, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 31, 1, 1, 1, 0, 229, 1, 1, 31, 229, 0 ], ap_traces := [
[ -1, -2, 0, -7, 0, -8, -3, -5, -7, 15, -1, -7 ],
[ 1, 2, 2, 1, 4, -2, 1, -5, 3, 5, -1, -9 ],
[ -3, 2, -6, -7, -2, 0, -3, -5, -5, -11, -7, -1 ],
[ 0, -3, -2, 9, -2, 4, 3, 7, 1, -11, 13, -5 ]
], hecke_fields := [
x^2 + x - 1,
x^2 - x - 1,
x^2 + 3*x + 1,
x^3 - 4*x - 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 31, 1 ],
[ 229, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 31, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 5, 1, 1 ], l_ratios := [ 0, 1/5, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1 ], eigenvalues := [*
[
a,
-1,
-2*a - 1,
a - 3,
2*a + 1,
-2*a - 5,
3*a,
5*a,
-a - 4,
-a + 7,
-9*a - 5,
3*a - 2
],
[
a,
1,
1,
-a + 1,
-2*a + 3,
-1,
-3*a + 2,
3*a - 4,
3*a,
-a + 3,
-3*a + 1,
-a - 4
],
[
a,
1,
-3,
-a - 5,
-4*a - 7,
6*a + 9,
a,
3*a + 2,
-a - 4,
-a - 7,
-a - 5,
-5*a - 8
],
[
a,
-1,
-a^2 + a + 2,
a + 3,
-a^2 - a + 2,
-a^2 - a + 4,
3*a^2 - 2*a - 7,
-a^2 + 5,
-a^2 - 2*a + 3,
2*a^2 + a - 9,
2*a^2 - a - 1,
-a^2 - 2*a + 1
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-a - 1)*q^4 + (-2*a - 1)*q^5 - a*q^6 + (a - 3)*q^7 + (-2*a - 1)*q^8 + q^9 + (a - 2)*q^10 + (2*a + 1)*q^11 + (a + 1)*q^12 + (-2*a - 5)*q^13 + (-4*a + 1)*q^14 + (2*a + 1)*q^15 + 3*a*q^16 + 3*a*q^17 + a*q^18 + 5*a*q^19 + (a + 3)*q^20 + (-a + 3)*q^21 + (-a + 2)*q^22 + (-a - 4)*q^23 + (2*a + 1)*q^24 + (-3*a - 2)*q^26 - q^27 + (3*a + 2)*q^28 + (-a + 7)*q^29 + (-a + 2)*q^30 + (-9*a - 5)*q^31 + (a + 5)*q^32 + (-2*a - 1)*q^33 + (-3*a + 3)*q^34 + (7*a + 1)*q^35 + (-a - 1)*q^36 + (3*a - 2)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a - 1)*q^4 + q^5 + a*q^6 + (-a + 1)*q^7 + (-2*a + 1)*q^8 + q^9 + a*q^10 + (-2*a + 3)*q^11 + (a - 1)*q^12 - q^13 - q^14 + q^15 - 3*a*q^16 + (-3*a + 2)*q^17 + a*q^18 + (3*a - 4)*q^19 + (a - 1)*q^20 + (-a + 1)*q^21 + (a - 2)*q^22 + 3*a*q^23 + (-2*a + 1)*q^24 - 4*q^25 - a*q^26 + q^27 + (a - 2)*q^28 + (-a + 3)*q^29 + a*q^30 + (-3*a + 1)*q^31 + (a - 5)*q^32 + (-2*a + 3)*q^33 + (-a - 3)*q^34 + (-a + 1)*q^35 + (a - 1)*q^36 + (-a - 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-3*a - 3)*q^4 - 3*q^5 + a*q^6 + (-a - 5)*q^7 + (4*a + 3)*q^8 + q^9 - 3*a*q^10 + (-4*a - 7)*q^11 + (-3*a - 3)*q^12 + (6*a + 9)*q^13 + (-2*a + 1)*q^14 - 3*q^15 + (-3*a + 2)*q^16 + a*q^17 + a*q^18 + (3*a + 2)*q^19 + (9*a + 9)*q^20 + (-a - 5)*q^21 + (5*a + 4)*q^22 + (-a - 4)*q^23 + (4*a + 3)*q^24 + 4*q^25 + (-9*a - 6)*q^26 + q^27 + (9*a + 12)*q^28 + (-a - 7)*q^29 - 3*a*q^30 + (-a - 5)*q^31 + (3*a - 3)*q^32 + (-4*a - 7)*q^33 + (-3*a - 1)*q^34 + (3*a + 15)*q^35 + (-3*a - 3)*q^36 + (-5*a - 8)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 2)*q^5 - a*q^6 + (a + 3)*q^7 + q^8 + q^9 + (a^2 - 2*a - 1)*q^10 + (-a^2 - a + 2)*q^11 + (-a^2 + 2)*q^12 + (-a^2 - a + 4)*q^13 + (a^2 + 3*a)*q^14 + (a^2 - a - 2)*q^15 + (-2*a^2 + a + 4)*q^16 + (3*a^2 - 2*a - 7)*q^17 + a*q^18 + (-a^2 + 5)*q^19 + (a - 3)*q^20 + (-a - 3)*q^21 + (-a^2 - 2*a - 1)*q^22 + (-a^2 - 2*a + 3)*q^23 - q^24 + (a^2 - 3*a - 3)*q^25 + (-a^2 - 1)*q^26 - q^27 + (3*a^2 + 2*a - 5)*q^28 + (2*a^2 + a - 9)*q^29 + (-a^2 + 2*a + 1)*q^30 + (2*a^2 - a - 1)*q^31 + (a^2 - 4*a - 4)*q^32 + (a^2 + a - 2)*q^33 + (-2*a^2 + 5*a + 3)*q^34 + (-2*a^2 + a + 5)*q^35 + (a^2 - 2)*q^36 + (-a^2 - 2*a + 1)*q^37 + O(q^38)
*]> ;  // time = 17.36 seconds




J[178] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 178, 178, 178, 178, 89, 89, 89 ], new_dimensions := [ 1, 1, 2, 3, 1, 1, 5 ], dimensions := [ 1, 1, 2, 3, 2, 2, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 25, 7, 1, 1, 1, 1, 25, 0 ], ap_traces := [
[ -1, 2, 2, 0, 0, -4, 2, -2, 8, 0, 0, 0 ],
[ 1, 1, 3, -4, -6, 2, 3, 5, -3, 0, 5, -10 ],
[ -2, -2, -2, -4, -4, -4, -6, 2, -14, 0, 6, 12 ],
[ 3, 1, -1, 0, 6, -2, -5, -11, 5, 4, -19, 10 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 1,
x^3 - x^2 - 8*x + 4
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 7, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 5 ], torsion_lower_bounds := [ 1, 3, 1, 5 ], l_ratios := [ 1, 1/3, 0, 1/5 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1 ], eigenvalues := [*
[ -1, 2, 2, 0, 0, -4, 2, -2, 8, 0, 0, 0 ],
[ 1, 1, 3, -4, -6, 2, 3, 5, -3, 0, 5, -10 ],
[
-1,
a,
-2*a - 3,
-2,
2*a,
-2,
2*a - 1,
a + 2,
-a - 8,
-4*a - 4,
-a + 2,
4*a + 10
],
[
1,
a,
-a,
-1/2*a^2 - 1/2*a + 3,
2,
1/2*a^2 - 3/2*a - 3,
-a^2 + 4,
a - 4,
3/2*a^2 + 1/2*a - 7,
-3/2*a^2 + 5/2*a + 9,
1/2*a^2 - 1/2*a - 9,
1/2*a^2 - 3/2*a + 1
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 - q^8 + q^9 - 2*q^10 + 2*q^12 - 4*q^13 + 4*q^15 + q^16 + 2*q^17 - q^18 - 2*q^19 + 2*q^20 + 8*q^23 - 2*q^24 - q^25 + 4*q^26 - 4*q^27 - 4*q^30 - q^32 - 2*q^34 + q^36 + O(q^38),
q + q^2 + q^3 + q^4 + 3*q^5 + q^6 - 4*q^7 + q^8 - 2*q^9 + 3*q^10 - 6*q^11 + q^12 + 2*q^13 - 4*q^14 + 3*q^15 + q^16 + 3*q^17 - 2*q^18 + 5*q^19 + 3*q^20 - 4*q^21 - 6*q^22 - 3*q^23 + q^24 + 4*q^25 + 2*q^26 - 5*q^27 - 4*q^28 + 3*q^30 + 5*q^31 + q^32 - 6*q^33 + 3*q^34 - 12*q^35 - 2*q^36 - 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-2*a - 3)*q^5 - a*q^6 - 2*q^7 - q^8 + (-2*a - 2)*q^9 + (2*a + 3)*q^10 + 2*a*q^11 + a*q^12 - 2*q^13 + 2*q^14 + (a - 2)*q^15 + q^16 + (2*a - 1)*q^17 + (2*a + 2)*q^18 + (a + 2)*q^19 + (-2*a - 3)*q^20 - 2*a*q^21 - 2*a*q^22 + (-a - 8)*q^23 - a*q^24 + (4*a + 8)*q^25 + 2*q^26 + (-a - 2)*q^27 - 2*q^28 + (-4*a - 4)*q^29 + (-a + 2)*q^30 + (-a + 2)*q^31 - q^32 + (-4*a + 2)*q^33 + (-2*a + 1)*q^34 + (4*a + 6)*q^35 + (-2*a - 2)*q^36 + (4*a + 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - a*q^5 + a*q^6 + (-1/2*a^2 - 1/2*a + 3)*q^7 + q^8 + (a^2 - 3)*q^9 - a*q^10 + 2*q^11 + a*q^12 + (1/2*a^2 - 3/2*a - 3)*q^13 + (-1/2*a^2 - 1/2*a + 3)*q^14 - a^2*q^15 + q^16 + (-a^2 + 4)*q^17 + (a^2 - 3)*q^18 + (a - 4)*q^19 - a*q^20 + (-a^2 - a + 2)*q^21 + 2*q^22 + (3/2*a^2 + 1/2*a - 7)*q^23 + a*q^24 + (a^2 - 5)*q^25 + (1/2*a^2 - 3/2*a - 3)*q^26 + (a^2 + 2*a - 4)*q^27 + (-1/2*a^2 - 1/2*a + 3)*q^28 + (-3/2*a^2 + 5/2*a + 9)*q^29 - a^2*q^30 + (1/2*a^2 - 1/2*a - 9)*q^31 + q^32 + 2*a*q^33 + (-a^2 + 4)*q^34 + (a^2 + a - 2)*q^35 + (a^2 - 3)*q^36 + (1/2*a^2 - 3/2*a + 1)*q^37 + O(q^38)
*]> ;  // time = 26.441 seconds




J[179] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 179, 179, 179 ], new_dimensions := [ 1, 3, 11 ], dimensions := [ 1, 3, 11 ], intersection_graph := [ 0, 1, 9, 1, 0, 1, 9, 1, 0 ], ap_traces := [
[ 2, 0, 3, -4, 4, -1, 1, -3, 6, 3, -8, 2 ],
[ -1, -2, -4, -4, -3, -11, 2, -9, 9, -1, -1, -2 ],
[ -3, 0, 3, 8, -9, 24, 7, 20, -9, 6, 13, 0 ]
], hecke_fields := [
x - 1,
x^3 + x^2 - 2*x - 1,
x^11 + 3*x^10 - 14*x^9 - 45*x^8 + 59*x^7 + 225*x^6 - 58*x^5 - 427*x^4 - 76*x^3 + 240*x^2 + 56*x - 16
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 89 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 89 ]
], torsion_upper_bounds := [ 1, 1, 89 ], torsion_lower_bounds := [ 1, 1, 89 ], l_ratios := [ 1, 0, 1/89 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 2, 0, 3, -4, 4, -1, 1, -3, 6, 3, -8, 2 ],
[
a,
-a - 1,
-a^2 - a,
a - 1,
2*a^2 + a - 4,
-a^2 - 2,
5*a^2 + 2*a - 7,
-3*a^2 + 2,
-3*a^2 + 8,
-5*a^2 + 8,
-5*a - 2,
3*a^2 - 4*a - 7
],
[
a,
-21/68*a^10 - 1/2*a^9 + 345/68*a^8 + 471/68*a^7 - 57/2*a^6 - 514/17*a^5 + 4241/68*a^4 + 2993/68*a^3 - 2895/68*a^2 - 311/34*a + 45/17,
-3/136*a^10 - 1/8*a^9 + 21/68*a^8 + 247/136*a^7 - 13/8*a^6 - 1151/136*a^5 + 309/68*a^4 + 1841/136*a^3 - 223/34*a^2 - 157/34*a + 53/17,
7/68*a^10 + 1/4*a^9 - 49/34*a^8 - 259/68*a^7 + 25/4*a^6 + 1303/68*a^5 - 279/34*a^4 - 2369/68*a^3 - 18/17*a^2 + 270/17*a + 36/17,
5/17*a^10 + 1/2*a^9 - 157/34*a^8 - 117/17*a^7 + 49/2*a^6 + 1009/34*a^5 - 1703/34*a^4 - 711/17*a^3 + 1041/34*a^2 + 123/17*a - 4/17,
-1/8*a^10 - 1/8*a^9 + 2*a^8 + 13/8*a^7 - 89/8*a^6 - 51/8*a^5 + 51/2*a^4 + 59/8*a^3 - 81/4*a^2 - a + 3,
39/136*a^10 + 3/8*a^9 - 81/17*a^8 - 695/136*a^7 + 219/8*a^6 + 3029/136*a^5 - 2119/34*a^4 - 4689/136*a^3 + 2993/68*a^2 + 375/34*a + 8/17,
79/136*a^10 + 7/8*a^9 - 319/34*a^8 - 1631/136*a^7 + 415/8*a^6 + 7065/136*a^5 - 1928/17*a^4 - 10377/136*a^3 + 5687/68*a^2 + 621/34*a - 166/17,
-22/17*a^10 - 2*a^9 + 359/17*a^8 + 474/17*a^7 - 118*a^6 - 2111/17*a^5 + 4413/17*a^4 + 3278/17*a^3 - 3164/17*a^2 - 1041/17*a + 242/17,
155/136*a^10 + 13/8*a^9 - 1289/68*a^8 - 3083/136*a^7 + 873/8*a^6 + 13727/136*a^5 - 17189/68*a^4 - 21293/136*a^3 + 3429/17*a^2 + 857/17*a - 415/17,
31/68*a^10 + 1/2*a^9 - 519/68*a^8 - 433/68*a^7 + 89/2*a^6 + 405/17*a^5 - 7219/68*a^4 - 1627/68*a^3 + 6197/68*a^2 - 161/34*a - 166/17,
13/17*a^10 + 3/2*a^9 - 415/34*a^8 - 362/17*a^7 + 133/2*a^6 + 3317/34*a^5 - 4829/34*a^4 - 2702/17*a^3 + 3305/34*a^2 + 1010/17*a - 126/17
]
*], q_expansions := [*
q + 2*q^2 + 2*q^4 + 3*q^5 - 4*q^7 - 3*q^9 + 6*q^10 + 4*q^11 - q^13 - 8*q^14 - 4*q^16 + q^17 - 6*q^18 - 3*q^19 + 6*q^20 + 8*q^22 + 6*q^23 + 4*q^25 - 2*q^26 - 8*q^28 + 3*q^29 - 8*q^31 - 8*q^32 + 2*q^34 - 12*q^35 - 6*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - a)*q^5 + (-a^2 - a)*q^6 + (a - 1)*q^7 + (-a^2 - 2*a + 1)*q^8 + (a^2 + 2*a - 2)*q^9 + (-2*a - 1)*q^10 + (2*a^2 + a - 4)*q^11 + q^12 + (-a^2 - 2)*q^13 + (a^2 - a)*q^14 + (a^2 + 3*a + 1)*q^15 + (-3*a^2 - a + 3)*q^16 + (5*a^2 + 2*a - 7)*q^17 + (a^2 + 1)*q^18 + (-3*a^2 + 2)*q^19 + a*q^20 + (-a^2 + 1)*q^21 + (-a^2 + 2)*q^22 + (-3*a^2 + 8)*q^23 + (2*a^2 + 3*a)*q^24 + (2*a^2 + 3*a - 4)*q^25 + (a^2 - 4*a - 1)*q^26 + (-2*a^2 + a + 4)*q^27 + (-2*a^2 + 3)*q^28 + (-5*a^2 + 8)*q^29 + (2*a^2 + 3*a + 1)*q^30 + (-5*a - 2)*q^31 + (4*a^2 + a - 5)*q^32 + (-a^2 - a + 2)*q^33 + (-3*a^2 + 3*a + 5)*q^34 + (a^2 - a - 1)*q^35 + (-3*a^2 - a + 5)*q^36 + (3*a^2 - 4*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-21/68*a^10 - 1/2*a^9 + 345/68*a^8 + 471/68*a^7 - 57/2*a^6 - 514/17*a^5 + 4241/68*a^4 + 2993/68*a^3 - 2895/68*a^2 - 311/34*a + 45/17)*q^3 + (a^2 - 2)*q^4 + (-3/136*a^10 - 1/8*a^9 + 21/68*a^8 + 247/136*a^7 - 13/8*a^6 - 1151/136*a^5 + 309/68*a^4 + 1841/136*a^3 - 223/34*a^2 - 157/34*a + 53/17)*q^5 + (29/68*a^10 + 3/4*a^9 - 237/34*a^8 - 699/68*a^7 + 157/4*a^6 + 3023/68*a^5 - 2987/34*a^4 - 4491/68*a^3 + 2209/34*a^2 + 339/17*a - 84/17)*q^6 + (7/68*a^10 + 1/4*a^9 - 49/34*a^8 - 259/68*a^7 + 25/4*a^6 + 1303/68*a^5 - 279/34*a^4 - 2369/68*a^3 - 18/17*a^2 + 270/17*a + 36/17)*q^7 + (a^3 - 4*a)*q^8 + (-12/17*a^10 - 5/4*a^9 + 757/68*a^8 + 599/34*a^7 - 237/4*a^6 - 5445/68*a^5 + 8205/68*a^4 + 4409/34*a^3 - 5041/68*a^2 - 1641/34*a + 115/17)*q^9 + (-1/17*a^10 + 14/17*a^8 - 11/34*a^7 - 7/2*a^6 + 111/34*a^5 + 70/17*a^4 - 140/17*a^3 + 23/34*a^2 + 74/17*a - 6/17)*q^10 + (5/17*a^10 + 1/2*a^9 - 157/34*a^8 - 117/17*a^7 + 49/2*a^6 + 1009/34*a^5 - 1703/34*a^4 - 711/17*a^3 + 1041/34*a^2 + 123/17*a - 4/17)*q^11 + (3/34*a^10 - 21/17*a^8 + 4/17*a^7 + 11/2*a^6 - 45/17*a^5 - 295/34*a^4 + 159/17*a^3 + 93/34*a^2 - 179/17*a + 26/17)*q^12 + (-1/8*a^10 - 1/8*a^9 + 2*a^8 + 13/8*a^7 - 89/8*a^6 - 51/8*a^5 + 51/2*a^4 + 59/8*a^3 - 81/4*a^2 - a + 3)*q^13 + (-1/17*a^10 + 14/17*a^8 + 3/17*a^7 - 4*a^6 - 38/17*a^5 + 155/17*a^4 + 115/17*a^3 - 150/17*a^2 - 62/17*a + 28/17)*q^14 + (35/34*a^10 + 7/4*a^9 - 1133/68*a^8 - 418/17*a^7 + 369/4*a^6 + 7573/68*a^5 - 13655/68*a^4 - 3075/17*a^3 + 9701/68*a^2 + 1170/17*a - 252/17)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (39/136*a^10 + 3/8*a^9 - 81/17*a^8 - 695/136*a^7 + 219/8*a^6 + 3029/136*a^5 - 2119/34*a^4 - 4689/136*a^3 + 2993/68*a^2 + 375/34*a + 8/17)*q^17 + (59/68*a^10 + 5/4*a^9 - 481/34*a^8 - 1197/68*a^7 + 315/4*a^6 + 5421/68*a^5 - 5839/34*a^4 - 8689/68*a^3 + 4119/34*a^2 + 787/17*a - 192/17)*q^18 + (79/136*a^10 + 7/8*a^9 - 319/34*a^8 - 1631/136*a^7 + 415/8*a^6 + 7065/136*a^5 - 1928/17*a^4 - 10377/136*a^3 + 5687/68*a^2 + 621/34*a - 166/17)*q^19 + (15/68*a^10 + 1/4*a^9 - 61/17*a^8 - 249/68*a^7 + 79/4*a^6 + 1199/68*a^5 - 1443/34*a^4 - 2099/68*a^3 + 537/17*a^2 + 207/17*a - 122/17)*q^20 + (-75/68*a^10 - 7/4*a^9 + 305/17*a^8 + 1687/68*a^7 - 399/4*a^6 - 7729/68*a^5 + 3701/17*a^4 + 12637/68*a^3 - 5251/34*a^2 - 1188/17*a + 270/17)*q^21 + (-13/34*a^10 - 1/2*a^9 + 108/17*a^8 + 243/34*a^7 - 73/2*a^6 - 1123/34*a^5 + 1424/17*a^4 + 1801/34*a^3 - 1077/17*a^2 - 284/17*a + 80/17)*q^22 + (-22/17*a^10 - 2*a^9 + 359/17*a^8 + 474/17*a^7 - 118*a^6 - 2111/17*a^5 + 4413/17*a^4 + 3278/17*a^3 - 3164/17*a^2 - 1041/17*a + 242/17)*q^23 + (-19/17*a^10 - 3/2*a^9 + 617/34*a^8 + 709/34*a^7 - 101*a^6 - 1572/17*a^5 + 7573/34*a^4 + 2406/17*a^3 - 2748/17*a^2 - 736/17*a + 192/17)*q^24 + (59/136*a^10 + 5/8*a^9 - 481/68*a^8 - 1163/136*a^7 + 313/8*a^6 + 5047/136*a^5 - 5669/68*a^4 - 7533/136*a^3 + 949/17*a^2 + 215/17*a - 62/17)*q^25 + (1/4*a^10 + 1/4*a^9 - 4*a^8 - 15/4*a^7 + 87/4*a^6 + 73/4*a^5 - 46*a^4 - 119/4*a^3 + 29*a^2 + 10*a - 2)*q^26 + (-15/34*a^10 - 1/2*a^9 + 122/17*a^8 + 215/34*a^7 - 79/2*a^6 - 791/34*a^5 + 1409/17*a^4 + 739/34*a^3 - 870/17*a^2 + 147/17*a - 11/17)*q^27 + (-1/34*a^10 - 1/2*a^9 + 7/17*a^8 + 241/34*a^7 - 3/2*a^6 - 1109/34*a^5 - 33/17*a^4 + 1917/34*a^3 + 214/17*a^2 - 456/17*a - 88/17)*q^28 + (155/136*a^10 + 13/8*a^9 - 1289/68*a^8 - 3083/136*a^7 + 873/8*a^6 + 13727/136*a^5 - 17189/68*a^4 - 21293/136*a^3 + 3429/17*a^2 + 857/17*a - 415/17)*q^29 + (-91/68*a^10 - 9/4*a^9 + 739/34*a^8 + 2143/68*a^7 - 481/4*a^6 - 9595/68*a^5 + 8795/34*a^4 + 15021/68*a^3 - 3030/17*a^2 - 1232/17*a + 280/17)*q^30 + (31/68*a^10 + 1/2*a^9 - 519/68*a^8 - 433/68*a^7 + 89/2*a^6 + 405/17*a^5 - 7219/68*a^4 - 1627/68*a^3 + 6197/68*a^2 - 161/34*a - 166/17)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (5/34*a^10 + 1/2*a^9 - 35/17*a^8 - 253/34*a^7 + 17/2*a^6 + 1227/34*a^5 - 124/17*a^4 - 2139/34*a^3 - 152/17*a^2 + 478/17*a - 70/17)*q^33 + (-33/68*a^10 - 3/4*a^9 + 265/34*a^8 + 711/68*a^7 - 169/4*a^6 - 3107/68*a^5 + 2991/34*a^4 + 4475/68*a^3 - 1965/34*a^2 - 265/17*a + 78/17)*q^34 + (-5/34*a^10 + 87/34*a^8 - 19/34*a^7 - 16*a^6 + 109/17*a^5 + 1489/34*a^4 - 717/34*a^3 - 1651/34*a^2 + 355/17*a + 138/17)*q^35 + (1/17*a^10 + 1/2*a^9 - 14/17*a^8 - 261/34*a^7 + 3*a^6 + 1317/34*a^5 + 47/34*a^4 - 2457/34*a^3 - 465/34*a^2 + 623/17*a + 6/17)*q^36 + (13/17*a^10 + 3/2*a^9 - 415/34*a^8 - 362/17*a^7 + 133/2*a^6 + 3317/34*a^5 - 4829/34*a^4 - 2702/17*a^3 + 3305/34*a^2 + 1010/17*a - 126/17)*q^37 + O(q^38)
*]> ;  // time = 2.28 seconds




J[181] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 181, 181 ], new_dimensions := [ 5, 9 ], dimensions := [ 5, 9 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -5, -5, -2, -20, -2, -5, -6, -6, -17, 5, 2 ],
[ 3, 3, 1, 2, 24, -8, -1, 4, 14, 13, -7, -20 ]
], hecke_fields := [
x^5 + 3*x^4 - x^3 - 7*x^2 - 2*x + 1,
x^9 - 3*x^8 - 9*x^7 + 29*x^6 + 23*x^5 - 84*x^4 - 23*x^3 + 89*x^2 + 8*x - 27
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 15 ]
], tamagawa_numbers := [
[ 1 ],
[ 15 ]
], torsion_upper_bounds := [ 1, 15 ], torsion_lower_bounds := [ 1, 15 ], l_ratios := [ 0, 1/15 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^4 - 2*a^3 + 2*a^2 + 3*a - 1,
2*a^4 + 5*a^3 - 4*a^2 - 11*a - 1,
-2*a^3 - 2*a^2 + 5*a + 1,
-a^4 - 3*a^3 + a^2 + 6*a - 3,
-2*a^4 - 3*a^3 + 8*a^2 + 8*a - 5,
2*a^4 + 4*a^3 - 5*a^2 - 8*a,
-3*a^4 - 5*a^3 + 8*a^2 + 10*a - 2,
2*a^4 + 3*a^3 - 6*a^2 - 3*a + 2,
-a^4 - a^3 + 3*a^2 - a - 5,
-2*a^4 - 4*a^3 + 2*a^2 + 7*a + 6,
a^4 + 6*a^3 + 3*a^2 - 17*a - 7
],
[
a,
1/2*a^8 - 2*a^7 - 5/2*a^6 + 16*a^5 - 7/2*a^4 - 59/2*a^3 + 12*a^2 + 25/2*a - 7/2,
1/4*a^7 - 1/4*a^6 - 5/2*a^5 + 2*a^4 + 25/4*a^3 - 9/2*a^2 - 5/2*a + 15/4,
1/4*a^8 - 3/4*a^7 - a^6 + 5*a^5 - 19/4*a^4 - 5*a^3 + 29/2*a^2 - 1/4*a - 11/2,
-1/2*a^8 + 1/2*a^7 + 6*a^6 - 4*a^5 - 47/2*a^4 + 8*a^3 + 35*a^2 - 9/2*a - 12,
-1/2*a^8 + 7/4*a^7 + 11/4*a^6 - 29/2*a^5 + 7/2*a^4 + 121/4*a^3 - 41/2*a^2 - 18*a + 47/4,
3/2*a^8 - 9/2*a^7 - 10*a^6 + 35*a^5 + 13/2*a^4 - 61*a^3 + 17*a^2 + 45/2*a - 12,
-3/4*a^8 + 11/4*a^7 + 7/2*a^6 - 21*a^5 + 33/4*a^4 + 67/2*a^3 - 53/2*a^2 - 33/4*a + 11,
-5/4*a^8 + 19/4*a^7 + 6*a^6 - 38*a^5 + 51/4*a^4 + 72*a^3 - 91/2*a^2 - 147/4*a + 45/2,
3/4*a^7 - 11/4*a^6 - 9/2*a^5 + 22*a^4 + 7/4*a^3 - 79/2*a^2 + 5/2*a + 57/4,
3/4*a^8 - 11/4*a^7 - 9/2*a^6 + 23*a^5 + 3/4*a^4 - 97/2*a^3 + 15/2*a^2 + 113/4*a - 4,
1/2*a^8 - 5/4*a^7 - 13/4*a^6 + 17/2*a^5 + 1/2*a^4 - 31/4*a^3 + 23/2*a^2 - 6*a - 37/4
]
*], q_expansions := [*
q + a*q^2 + (-a^4 - 2*a^3 + 2*a^2 + 3*a - 1)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + 5*a^3 - 4*a^2 - 11*a - 1)*q^5 + (a^4 + a^3 - 4*a^2 - 3*a + 1)*q^6 + (-2*a^3 - 2*a^2 + 5*a + 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + 3*a^3 - 4*a - 2)*q^9 + (-a^4 - 2*a^3 + 3*a^2 + 3*a - 2)*q^10 + (-a^4 - 3*a^3 + a^2 + 6*a - 3)*q^11 + (a^3 - 3*a + 1)*q^12 + (-2*a^4 - 3*a^3 + 8*a^2 + 8*a - 5)*q^13 + (-2*a^4 - 2*a^3 + 5*a^2 + a)*q^14 + (-a^4 - 3*a^3 + 3*a^2 + 9*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + 4*a^3 - 5*a^2 - 8*a)*q^17 + (a^3 + 3*a^2 - 1)*q^18 + (-3*a^4 - 5*a^3 + 8*a^2 + 10*a - 2)*q^19 + (-3*a^4 - 8*a^3 + 4*a^2 + 18*a + 3)*q^20 + (2*a^4 + 5*a^3 - 4*a^2 - 8*a + 2)*q^21 + (-a^2 - 5*a + 1)*q^22 + (2*a^4 + 3*a^3 - 6*a^2 - 3*a + 2)*q^23 + (-a^4 - 2*a^3 + 5*a^2 + 7*a - 2)*q^24 + (-2*a^3 - 6*a^2 + 3*a + 11)*q^25 + (3*a^4 + 6*a^3 - 6*a^2 - 9*a + 2)*q^26 + (3*a^4 + 4*a^3 - 11*a^2 - 10*a + 4)*q^27 + (4*a^4 + 7*a^3 - 9*a^2 - 14*a)*q^28 + (-a^4 - a^3 + 3*a^2 - a - 5)*q^29 + (2*a^3 + 2*a^2 - 4*a + 1)*q^30 + (-2*a^4 - 4*a^3 + 2*a^2 + 7*a + 6)*q^31 + (-3*a^4 - 7*a^3 + 7*a^2 + 14*a - 1)*q^32 + (5*a^4 + 11*a^3 - 9*a^2 - 17*a + 5)*q^33 + (-2*a^4 - 3*a^3 + 6*a^2 + 4*a - 2)*q^34 + (-3*a^4 - 3*a^3 + 13*a^2 + 6*a - 11)*q^35 + (-a^4 - 3*a^3 + 7*a + 4)*q^36 + (a^4 + 6*a^3 + 3*a^2 - 17*a - 7)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^8 - 2*a^7 - 5/2*a^6 + 16*a^5 - 7/2*a^4 - 59/2*a^3 + 12*a^2 + 25/2*a - 7/2)*q^3 + (a^2 - 2)*q^4 + (1/4*a^7 - 1/4*a^6 - 5/2*a^5 + 2*a^4 + 25/4*a^3 - 9/2*a^2 - 5/2*a + 15/4)*q^5 + (-1/2*a^8 + 2*a^7 + 3/2*a^6 - 15*a^5 + 25/2*a^4 + 47/2*a^3 - 32*a^2 - 15/2*a + 27/2)*q^6 + (1/4*a^8 - 3/4*a^7 - a^6 + 5*a^5 - 19/4*a^4 - 5*a^3 + 29/2*a^2 - 1/4*a - 11/2)*q^7 + (a^3 - 4*a)*q^8 + (-a^7 + 2*a^6 + 9*a^5 - 16*a^4 - 21*a^3 + 30*a^2 + 13*a - 11)*q^9 + (1/4*a^8 - 1/4*a^7 - 5/2*a^6 + 2*a^5 + 25/4*a^4 - 9/2*a^3 - 5/2*a^2 + 15/4*a)*q^10 + (-1/2*a^8 + 1/2*a^7 + 6*a^6 - 4*a^5 - 47/2*a^4 + 8*a^3 + 35*a^2 - 9/2*a - 12)*q^11 + (-1/2*a^8 + a^7 + 9/2*a^6 - 8*a^5 - 23/2*a^4 + 31/2*a^3 + 13*a^2 - 15/2*a - 13/2)*q^12 + (-1/2*a^8 + 7/4*a^7 + 11/4*a^6 - 29/2*a^5 + 7/2*a^4 + 121/4*a^3 - 41/2*a^2 - 18*a + 47/4)*q^13 + (5/4*a^7 - 9/4*a^6 - 21/2*a^5 + 16*a^4 + 81/4*a^3 - 45/2*a^2 - 15/2*a + 27/4)*q^14 + (5/2*a^7 - 13/2*a^6 - 19*a^5 + 51*a^4 + 59/2*a^3 - 92*a^2 - 10*a + 75/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (3/2*a^8 - 9/2*a^7 - 10*a^6 + 35*a^5 + 13/2*a^4 - 61*a^3 + 17*a^2 + 45/2*a - 12)*q^17 + (-a^8 + 2*a^7 + 9*a^6 - 16*a^5 - 21*a^4 + 30*a^3 + 13*a^2 - 11*a)*q^18 + (-3/4*a^8 + 11/4*a^7 + 7/2*a^6 - 21*a^5 + 33/4*a^4 + 67/2*a^3 - 53/2*a^2 - 33/4*a + 11)*q^19 + (1/2*a^8 - 3/4*a^7 - 19/4*a^6 + 11/2*a^5 + 25/2*a^4 - 37/4*a^3 - 19/2*a^2 + 3*a - 3/4)*q^20 + (a^8 - 3/2*a^7 - 21/2*a^6 + 12*a^5 + 34*a^4 - 45/2*a^3 - 41*a^2 + 5*a + 25/2)*q^21 + (-a^8 + 3/2*a^7 + 21/2*a^6 - 12*a^5 - 34*a^4 + 47/2*a^3 + 40*a^2 - 8*a - 27/2)*q^22 + (-5/4*a^8 + 19/4*a^7 + 6*a^6 - 38*a^5 + 51/4*a^4 + 72*a^3 - 91/2*a^2 - 147/4*a + 45/2)*q^23 + (1/2*a^8 - 4*a^7 + 7/2*a^6 + 30*a^5 - 103/2*a^4 - 91/2*a^3 + 101*a^2 + 25/2*a - 81/2)*q^24 + (-a^8 + 5/4*a^7 + 43/4*a^6 - 19/2*a^5 - 36*a^4 + 65/4*a^3 + 91/2*a^2 - 9/2*a - 65/4)*q^25 + (1/4*a^8 - 7/4*a^7 + 15*a^5 - 47/4*a^4 - 32*a^3 + 53/2*a^2 + 63/4*a - 27/2)*q^26 + (a^8 - 5*a^7 - 2*a^6 + 40*a^5 - 32*a^4 - 74*a^3 + 75*a^2 + 33*a - 32)*q^27 + (3/4*a^8 - 3/4*a^7 - 17/2*a^6 + 6*a^5 + 119/4*a^4 - 25/2*a^3 - 73/2*a^2 + 29/4*a + 11)*q^28 + (3/4*a^7 - 11/4*a^6 - 9/2*a^5 + 22*a^4 + 7/4*a^3 - 79/2*a^2 + 5/2*a + 57/4)*q^29 + (5/2*a^8 - 13/2*a^7 - 19*a^6 + 51*a^5 + 59/2*a^4 - 92*a^3 - 10*a^2 + 75/2*a)*q^30 + (3/4*a^8 - 11/4*a^7 - 9/2*a^6 + 23*a^5 + 3/4*a^4 - 97/2*a^3 + 15/2*a^2 + 113/4*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^8 - 9*a^7 - 7*a^6 + 71*a^5 - 38*a^4 - 125*a^3 + 94*a^2 + 45*a - 39)*q^33 + (7/2*a^7 - 17/2*a^6 - 28*a^5 + 65*a^4 + 103/2*a^3 - 111*a^2 - 24*a + 81/2)*q^34 + (-2*a^8 + 9/2*a^7 + 35/2*a^6 - 36*a^5 - 42*a^4 + 137/2*a^3 + 41*a^2 - 29*a - 21/2)*q^35 + (-a^8 + 2*a^7 + 9*a^6 - 16*a^5 - 22*a^4 + 32*a^3 + 18*a^2 - 18*a - 5)*q^36 + (1/2*a^8 - 5/4*a^7 - 13/4*a^6 + 17/2*a^5 + 1/2*a^4 - 31/4*a^3 + 23/2*a^2 - 6*a - 37/4)*q^37 + O(q^38)
*]> ;  // time = 1.919 seconds




J[182] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 182, 182, 182, 182, 182, 91, 91, 91, 91, 26, 26, 14 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 4, 6, 2, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 11, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 1, 1, 5, 1, 1, 0, 3, 1, 5, 1, 1, 1, 1, 3, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 3, 1, 3, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 11, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 3, 1, 1, 3, 3, 1, 1, 1, 7, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 3, 1, 1, 3, 1, 0 ], ap_traces := [
[ -1, 1, 4, -1, -1, 1, 4, 2, -7, -8, 3, 7 ],
[ -1, 3, 0, 1, -5, -1, -4, 2, 5, 4, 1, 7 ],
[ 1, 0, 2, -1, 4, -1, -6, 0, 8, -10, -8, 6 ],
[ 1, 3, -4, -1, 1, -1, 0, -6, -7, -4, 7, 9 ],
[ 1, 1, 0, 1, -3, 1, 0, 2, -3, 0, 5, -7 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 11, 7, 1 ],
[ 7, 1, 5 ],
[ 5, 3, 1 ],
[ 1, 3, 1 ],
[ 9, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 9, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 5, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1/9 ], eigenvalues := [*
[ -1, 1, 4, -1, -1, 1, 4, 2, -7, -8, 3, 7 ],
[ -1, 3, 0, 1, -5, -1, -4, 2, 5, 4, 1, 7 ],
[ 1, 0, 2, -1, 4, -1, -6, 0, 8, -10, -8, 6 ],
[ 1, 3, -4, -1, 1, -1, 0, -6, -7, -4, 7, 9 ],
[ 1, 1, 0, 1, -3, 1, 0, 2, -3, 0, 5, -7 ]
*], q_expansions := [*
q - q^2 + q^3 + q^4 + 4*q^5 - q^6 - q^7 - q^8 - 2*q^9 - 4*q^10 - q^11 + q^12 + q^13 + q^14 + 4*q^15 + q^16 + 4*q^17 + 2*q^18 + 2*q^19 + 4*q^20 - q^21 + q^22 - 7*q^23 - q^24 + 11*q^25 - q^26 - 5*q^27 - q^28 - 8*q^29 - 4*q^30 + 3*q^31 - q^32 - q^33 - 4*q^34 - 4*q^35 - 2*q^36 + 7*q^37 + O(q^38),
q - q^2 + 3*q^3 + q^4 - 3*q^6 + q^7 - q^8 + 6*q^9 - 5*q^11 + 3*q^12 - q^13 - q^14 + q^16 - 4*q^17 - 6*q^18 + 2*q^19 + 3*q^21 + 5*q^22 + 5*q^23 - 3*q^24 - 5*q^25 + q^26 + 9*q^27 + q^28 + 4*q^29 + q^31 - q^32 - 15*q^33 + 4*q^34 + 6*q^36 + 7*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 - q^7 + q^8 - 3*q^9 + 2*q^10 + 4*q^11 - q^13 - q^14 + q^16 - 6*q^17 - 3*q^18 + 2*q^20 + 4*q^22 + 8*q^23 - q^25 - q^26 - q^28 - 10*q^29 - 8*q^31 + q^32 - 6*q^34 - 2*q^35 - 3*q^36 + 6*q^37 + O(q^38),
q + q^2 + 3*q^3 + q^4 - 4*q^5 + 3*q^6 - q^7 + q^8 + 6*q^9 - 4*q^10 + q^11 + 3*q^12 - q^13 - q^14 - 12*q^15 + q^16 + 6*q^18 - 6*q^19 - 4*q^20 - 3*q^21 + q^22 - 7*q^23 + 3*q^24 + 11*q^25 - q^26 + 9*q^27 - q^28 - 4*q^29 - 12*q^30 + 7*q^31 + q^32 + 3*q^33 + 4*q^35 + 6*q^36 + 9*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 + q^7 + q^8 - 2*q^9 - 3*q^11 + q^12 + q^13 + q^14 + q^16 - 2*q^18 + 2*q^19 + q^21 - 3*q^22 - 3*q^23 + q^24 - 5*q^25 + q^26 - 5*q^27 + q^28 + 5*q^31 + q^32 - 3*q^33 - 2*q^36 - 7*q^37 + O(q^38)
*]> ;  // time = 53.88 seconds




J[183] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 183, 183, 183, 61, 61 ], new_dimensions := [ 2, 3, 6, 1, 3 ], dimensions := [ 2, 3, 6, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 19, 1, 1, 0, 3, 1, 1, 1, 3, 0, 1, 1, 19, 1, 1, 0 ], ap_traces := [
[ -2, -2, -2, -2, -2, -6, -12, 4, -2, 0, 4, -4 ],
[ 1, -3, 6, 0, 2, 6, 12, -8, 2, 4, -8, -6 ],
[ 0, 6, 2, 2, -8, 6, 10, 8, 0, -10, 0, -4 ]
], hecke_fields := [
x^2 + 2*x - 1,
x^3 - x^2 - 3*x + 1,
x^6 - 11*x^4 + 2*x^3 + 31*x^2 - 10*x - 17
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 19, 1 ],
[ 93, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 93, 1 ]
], torsion_upper_bounds := [ 1, 1, 31 ], torsion_lower_bounds := [ 1, 1, 31 ], l_ratios := [ 0, 1, 3/31 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[
a,
-1,
-1,
-a - 2,
-a - 2,
-3,
-6,
4*a + 6,
3*a + 2,
-4*a - 4,
4*a + 6,
2*a
],
[
a,
-1,
2,
-2*a^2 + 2*a + 4,
-a^2 + 3,
2*a^2 - 2*a - 2,
-a^2 - 2*a + 7,
-2*a - 2,
3*a^2 - 4*a - 5,
-a^2 + 2*a + 3,
2*a^2 + 2*a - 8,
4*a^2 - 4*a - 10
],
[
a,
1,
1/2*a^5 + a^4 - 5*a^3 - 8*a^2 + 21/2*a + 10,
-a^5 - 3/2*a^4 + 9*a^3 + 11*a^2 - 17*a - 23/2,
-1/2*a^4 + 3*a^2 - a - 5/2,
-1/2*a^5 + 5*a^3 - 21/2*a + 1,
a^5 + a^4 - 9*a^3 - 6*a^2 + 16*a + 5,
a^5 + a^4 - 8*a^3 - 8*a^2 + 11*a + 13,
-1/2*a^4 + 5*a^2 - a - 17/2,
a^4 + a^3 - 8*a^2 - 5*a + 9,
-2*a^5 - 3*a^4 + 18*a^3 + 24*a^2 - 32*a - 31,
-a^5 - a^4 + 8*a^3 + 6*a^2 - 9*a - 5
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-2*a - 1)*q^4 - q^5 - a*q^6 + (-a - 2)*q^7 + (a - 2)*q^8 + q^9 - a*q^10 + (-a - 2)*q^11 + (2*a + 1)*q^12 - 3*q^13 - q^14 + q^15 + 3*q^16 - 6*q^17 + a*q^18 + (4*a + 6)*q^19 + (2*a + 1)*q^20 + (a + 2)*q^21 - q^22 + (3*a + 2)*q^23 + (-a + 2)*q^24 - 4*q^25 - 3*a*q^26 - q^27 + (a + 4)*q^28 + (-4*a - 4)*q^29 + a*q^30 + (4*a + 6)*q^31 + (a + 4)*q^32 + (a + 2)*q^33 - 6*a*q^34 + (a + 2)*q^35 + (-2*a - 1)*q^36 + 2*a*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + 2*q^5 - a*q^6 + (-2*a^2 + 2*a + 4)*q^7 + (a^2 - a - 1)*q^8 + q^9 + 2*a*q^10 + (-a^2 + 3)*q^11 + (-a^2 + 2)*q^12 + (2*a^2 - 2*a - 2)*q^13 + (-2*a + 2)*q^14 - 2*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-a^2 - 2*a + 7)*q^17 + a*q^18 + (-2*a - 2)*q^19 + (2*a^2 - 4)*q^20 + (2*a^2 - 2*a - 4)*q^21 + (-a^2 + 1)*q^22 + (3*a^2 - 4*a - 5)*q^23 + (-a^2 + a + 1)*q^24 - q^25 + (4*a - 2)*q^26 - q^27 + (2*a^2 - 2*a - 8)*q^28 + (-a^2 + 2*a + 3)*q^29 - 2*a*q^30 + (2*a^2 + 2*a - 8)*q^31 + (-2*a^2 - a + 4)*q^32 + (a^2 - 3)*q^33 + (-3*a^2 + 4*a + 1)*q^34 + (-4*a^2 + 4*a + 8)*q^35 + (a^2 - 2)*q^36 + (4*a^2 - 4*a - 10)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (1/2*a^5 + a^4 - 5*a^3 - 8*a^2 + 21/2*a + 10)*q^5 + a*q^6 + (-a^5 - 3/2*a^4 + 9*a^3 + 11*a^2 - 17*a - 23/2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^5 + 1/2*a^4 - 9*a^3 - 5*a^2 + 15*a + 17/2)*q^10 + (-1/2*a^4 + 3*a^2 - a - 5/2)*q^11 + (a^2 - 2)*q^12 + (-1/2*a^5 + 5*a^3 - 21/2*a + 1)*q^13 + (-3/2*a^5 - 2*a^4 + 13*a^3 + 14*a^2 - 43/2*a - 17)*q^14 + (1/2*a^5 + a^4 - 5*a^3 - 8*a^2 + 21/2*a + 10)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 + a^4 - 9*a^3 - 6*a^2 + 16*a + 5)*q^17 + a*q^18 + (a^5 + a^4 - 8*a^3 - 8*a^2 + 11*a + 13)*q^19 + (-1/2*a^5 + 3*a^3 - 5/2*a - 3)*q^20 + (-a^5 - 3/2*a^4 + 9*a^3 + 11*a^2 - 17*a - 23/2)*q^21 + (-1/2*a^5 + 3*a^3 - a^2 - 5/2*a)*q^22 + (-1/2*a^4 + 5*a^2 - a - 17/2)*q^23 + (a^3 - 4*a)*q^24 + (5/2*a^5 + 3*a^4 - 23*a^3 - 22*a^2 + 85/2*a + 27)*q^25 + (-1/2*a^4 + a^3 + 5*a^2 - 4*a - 17/2)*q^26 + q^27 + (-1/2*a^4 - a^3 + 3*a^2 + 2*a - 5/2)*q^28 + (a^4 + a^3 - 8*a^2 - 5*a + 9)*q^29 + (a^5 + 1/2*a^4 - 9*a^3 - 5*a^2 + 15*a + 17/2)*q^30 + (-2*a^5 - 3*a^4 + 18*a^3 + 24*a^2 - 32*a - 31)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-1/2*a^4 + 3*a^2 - a - 5/2)*q^33 + (a^5 + 2*a^4 - 8*a^3 - 15*a^2 + 15*a + 17)*q^34 + (-2*a^5 - 3/2*a^4 + 19*a^3 + 13*a^2 - 36*a - 43/2)*q^35 + (a^2 - 2)*q^36 + (-a^5 - a^4 + 8*a^3 + 6*a^2 - 9*a - 5)*q^37 + O(q^38)
*]> ;  // time = 19.031 seconds




J[185] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 185, 185, 185, 185, 185, 37, 37 ], new_dimensions := [ 1, 1, 1, 5, 5, 1, 1 ], dimensions := [ 1, 1, 1, 5, 5, 2, 2 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 0 ], ap_traces := [
[ 1, -2, -1, -2, 0, -2, 2, 2, -8, 2, -6, -1 ],
[ -2, 1, -1, -5, 3, -2, -4, -4, -2, 2, 0, -1 ],
[ 0, -1, 1, -3, -5, 4, -4, -8, 4, 4, 2, 1 ],
[ 2, 3, -5, 11, -5, 4, 0, -4, 4, -4, 8, 5 ],
[ 0, -1, 5, 7, 7, 2, -8, 14, 2, 2, 8, -5 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 11*x - 12,
x^5 - 8*x^3 + 2*x^2 + 11*x - 2
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 9, 3 ],
[ 19, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 19, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 19 ], torsion_lower_bounds := [ 1, 1, 1, 3, 19 ], l_ratios := [ 0, 0, 0, 1/3, 1/19 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -2, -1, -2, 0, -2, 2, 2, -8, 2, -6, -1 ],
[ -2, 1, -1, -5, 3, -2, -4, -4, -2, 2, 0, -1 ],
[ 0, -1, 1, -3, -5, 4, -4, -8, 4, 4, 2, 1 ],
[
a,
-1/2*a^3 + 5/2*a + 1,
-1,
1/2*a^4 - 7/2*a^2 - a + 5,
-a^2 + 3,
-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 5/2*a + 2,
-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 9/2*a - 6,
-a^4 + 1/2*a^3 + 8*a^2 - 5/2*a - 10,
-a^4 + 9*a^2 - 12,
-a^3 + 5*a,
-1/2*a^4 + a^3 + 5/2*a^2 - 4*a + 2,
1
],
[
a,
-1/2*a^4 + 7/2*a^2 - a - 3,
1,
-1/2*a^3 - a^2 + 5/2*a + 4,
a^4 + a^3 - 6*a^2 - 3*a + 5,
-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 1/2*a - 3,
-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 5/2*a - 5,
-1/2*a^4 - a^3 + 5/2*a^2 + 2*a + 2,
a^4 - 7*a^2 + 6,
a^4 + 2*a^3 - 5*a^2 - 8*a + 2,
a^4 + 3/2*a^3 - 7*a^2 - 11/2*a + 9,
-1
]
*], q_expansions := [*
q + q^2 - 2*q^3 - q^4 - q^5 - 2*q^6 - 2*q^7 - 3*q^8 + q^9 - q^10 + 2*q^12 - 2*q^13 - 2*q^14 + 2*q^15 - q^16 + 2*q^17 + q^18 + 2*q^19 + q^20 + 4*q^21 - 8*q^23 + 6*q^24 + q^25 - 2*q^26 + 4*q^27 + 2*q^28 + 2*q^29 + 2*q^30 - 6*q^31 + 5*q^32 + 2*q^34 + 2*q^35 - q^36 - q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - q^5 - 2*q^6 - 5*q^7 - 2*q^9 + 2*q^10 + 3*q^11 + 2*q^12 - 2*q^13 + 10*q^14 - q^15 - 4*q^16 - 4*q^17 + 4*q^18 - 4*q^19 - 2*q^20 - 5*q^21 - 6*q^22 - 2*q^23 + q^25 + 4*q^26 - 5*q^27 - 10*q^28 + 2*q^29 + 2*q^30 + 8*q^32 + 3*q^33 + 8*q^34 + 5*q^35 - 4*q^36 - q^37 + O(q^38),
q - q^3 - 2*q^4 + q^5 - 3*q^7 - 2*q^9 - 5*q^11 + 2*q^12 + 4*q^13 - q^15 + 4*q^16 - 4*q^17 - 8*q^19 - 2*q^20 + 3*q^21 + 4*q^23 + q^25 + 5*q^27 + 6*q^28 + 4*q^29 + 2*q^31 + 5*q^33 - 3*q^35 + 4*q^36 + q^37 + O(q^38),
q + a*q^2 + (-1/2*a^3 + 5/2*a + 1)*q^3 + (a^2 - 2)*q^4 - q^5 + (-1/2*a^4 + 5/2*a^2 + a)*q^6 + (1/2*a^4 - 7/2*a^2 - a + 5)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 4)*q^9 - a*q^10 + (-a^2 + 3)*q^11 + (-a^4 - 1/2*a^3 + 8*a^2 + 1/2*a - 8)*q^12 + (-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 5/2*a + 2)*q^13 + (a^4 + 1/2*a^3 - 8*a^2 - 1/2*a + 6)*q^14 + (1/2*a^3 - 5/2*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 9/2*a - 6)*q^17 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 3/2*a + 6)*q^18 + (-a^4 + 1/2*a^3 + 8*a^2 - 5/2*a - 10)*q^19 + (-a^2 + 2)*q^20 + (1/2*a^4 - 3/2*a^3 - 7/2*a^2 + 11/2*a + 5)*q^21 + (-a^3 + 3*a)*q^22 + (-a^4 + 9*a^2 - 12)*q^23 + (-3/2*a^4 + 19/2*a^2 + a - 12)*q^24 + q^25 + (-1/2*a^4 - 3/2*a^3 + 9/2*a^2 + 15/2*a - 6)*q^26 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 7/2*a + 7)*q^27 + (3/2*a^4 - 15/2*a^2 - 3*a + 2)*q^28 + (-a^3 + 5*a)*q^29 + (1/2*a^4 - 5/2*a^2 - a)*q^30 + (-1/2*a^4 + a^3 + 5/2*a^2 - 4*a + 2)*q^31 + (2*a^4 - 14*a^2 + a + 12)*q^32 + (a^4 - 8*a^2 + 2*a + 9)*q^33 + (-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 1/2*a - 6)*q^34 + (-1/2*a^4 + 7/2*a^2 + a - 5)*q^35 + (1/2*a^4 + 1/2*a^3 - 3/2*a^2 - 9/2*a - 2)*q^36 + q^37 + O(q^38),
q + a*q^2 + (-1/2*a^4 + 7/2*a^2 - a - 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-1/2*a^3 + 5/2*a - 1)*q^6 + (-1/2*a^3 - a^2 + 5/2*a + 4)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 5/2*a + 7)*q^9 + a*q^10 + (a^4 + a^3 - 6*a^2 - 3*a + 5)*q^11 + (1/2*a^4 - 9/2*a^2 + a + 6)*q^12 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 1/2*a - 3)*q^13 + (-1/2*a^4 - a^3 + 5/2*a^2 + 4*a)*q^14 + (-1/2*a^4 + 7/2*a^2 - a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 5/2*a - 5)*q^17 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 3/2*a + 1)*q^18 + (-1/2*a^4 - a^3 + 5/2*a^2 + 2*a + 2)*q^19 + (a^2 - 2)*q^20 + (-3/2*a^4 - 1/2*a^3 + 23/2*a^2 + 1/2*a - 14)*q^21 + (a^4 + 2*a^3 - 5*a^2 - 6*a + 2)*q^22 + (a^4 - 7*a^2 + 6)*q^23 + (1/2*a^3 - 9/2*a + 3)*q^24 + q^25 + (-1/2*a^4 - 1/2*a^3 + 3/2*a^2 + 5/2*a - 1)*q^26 + (-1/2*a^4 + 1/2*a^3 + 11/2*a^2 - 7/2*a - 10)*q^27 + (-a^4 - 1/2*a^3 + 7*a^2 + 1/2*a - 9)*q^28 + (a^4 + 2*a^3 - 5*a^2 - 8*a + 2)*q^29 + (-1/2*a^3 + 5/2*a - 1)*q^30 + (a^4 + 3/2*a^3 - 7*a^2 - 11/2*a + 9)*q^31 + (-2*a^2 + a + 2)*q^32 + (-a^4 + 8*a^2 - 2*a - 13)*q^33 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 1/2*a - 1)*q^34 + (-1/2*a^3 - a^2 + 5/2*a + 4)*q^35 + (-3/2*a^4 - 1/2*a^3 + 19/2*a^2 + 1/2*a - 13)*q^36 - q^37 + O(q^38)
*]> ;  // time = 18.759 seconds




J[186] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 186, 186, 186, 186, 93, 93, 62, 62, 31 ], new_dimensions := [ 1, 1, 1, 2, 2, 3, 1, 2, 2 ], dimensions := [ 1, 1, 1, 2, 4, 6, 2, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 0, 19, 1, 1, 1, 1, 1, 1, 1, 19, 0, 1, 1, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 1, 1, 1, 0, 121, 1, 1, 5, 1, 1, 1, 1, 121, 0 ], ap_traces := [
[ -1, -1, -1, 2, 3, 3, 1, 7, 0, 4, 1, -10 ],
[ -1, 1, 3, -2, 5, -7, -1, 7, 4, -8, -1, -6 ],
[ 1, 1, 1, -2, -3, -1, 3, -5, 4, 0, 1, -2 ],
[ 2, -2, 3, 2, -1, 3, -1, -1, -16, -6, -2, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 3*x - 2
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 11, 1 ],
[ 7, 1, 1 ],
[ 5, 5, 1 ],
[ 19, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ],
[ 19, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 1, 1, 1, 19 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/25, 1 ], eigenvalues := [*
[ -1, -1, -1, 2, 3, 3, 1, 7, 0, 4, 1, -10 ],
[ -1, 1, 3, -2, 5, -7, -1, 7, 4, -8, -1, -6 ],
[ 1, 1, 1, -2, -3, -1, 3, -5, 4, 0, 1, -2 ],
[
1,
-1,
a,
-2*a + 4,
a - 2,
a,
-3*a + 4,
a - 2,
-8,
2*a - 6,
-1,
-4*a + 6
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 + 2*q^7 - q^8 + q^9 + q^10 + 3*q^11 - q^12 + 3*q^13 - 2*q^14 + q^15 + q^16 + q^17 - q^18 + 7*q^19 - q^20 - 2*q^21 - 3*q^22 + q^24 - 4*q^25 - 3*q^26 - q^27 + 2*q^28 + 4*q^29 - q^30 + q^31 - q^32 - 3*q^33 - q^34 - 2*q^35 + q^36 - 10*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 3*q^5 - q^6 - 2*q^7 - q^8 + q^9 - 3*q^10 + 5*q^11 + q^12 - 7*q^13 + 2*q^14 + 3*q^15 + q^16 - q^17 - q^18 + 7*q^19 + 3*q^20 - 2*q^21 - 5*q^22 + 4*q^23 - q^24 + 4*q^25 + 7*q^26 + q^27 - 2*q^28 - 8*q^29 - 3*q^30 - q^31 - q^32 + 5*q^33 + q^34 - 6*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 - 2*q^7 + q^8 + q^9 + q^10 - 3*q^11 + q^12 - q^13 - 2*q^14 + q^15 + q^16 + 3*q^17 + q^18 - 5*q^19 + q^20 - 2*q^21 - 3*q^22 + 4*q^23 + q^24 - 4*q^25 - q^26 + q^27 - 2*q^28 + q^30 + q^31 + q^32 - 3*q^33 + 3*q^34 - 2*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + a*q^5 - q^6 + (-2*a + 4)*q^7 + q^8 + q^9 + a*q^10 + (a - 2)*q^11 - q^12 + a*q^13 + (-2*a + 4)*q^14 - a*q^15 + q^16 + (-3*a + 4)*q^17 + q^18 + (a - 2)*q^19 + a*q^20 + (2*a - 4)*q^21 + (a - 2)*q^22 - 8*q^23 - q^24 + (3*a - 3)*q^25 + a*q^26 - q^27 + (-2*a + 4)*q^28 + (2*a - 6)*q^29 - a*q^30 - q^31 + q^32 + (-a + 2)*q^33 + (-3*a + 4)*q^34 + (-2*a - 4)*q^35 + q^36 + (-4*a + 6)*q^37 + O(q^38)
*]> ;  // time = 87.76 seconds




J[187] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 187, 187, 187, 187, 187, 187, 17, 11 ], new_dimensions := [ 1, 1, 2, 2, 3, 4, 1, 1 ], dimensions := [ 1, 1, 2, 2, 3, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 5, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 2, 0, 4, -5, -1, 4, 1, 2, -2, -3, 4, -2 ],
[ 0, 1, 3, 2, 1, 2, -1, 2, -3, -6, -7, -7 ],
[ 4, -1, 1, 3, 2, 0, -2, -6, 1, 15, -1, 5 ],
[ -2, 0, -4, -4, 2, -10, 2, -2, -4, -6, 8, -4 ],
[ -2, -3, -7, 0, -3, 0, -3, 6, -15, -14, -9, -11 ],
[ 1, 1, 3, 0, -4, -2, 4, -2, 5, 12, -17, 19 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2*x - 16,
x^2 + 2*x - 2,
x^3 + 2*x^2 - 2*x - 2,
x^4 - x^3 - 6*x^2 + 2*x + 2
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 1, 1, 1 ], l_ratios := [ 1, 1/3, 1, 0, 0, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 0, 1 ], eigenvalues := [*
[ 2, 0, 4, -5, -1, 4, 1, 2, -2, -3, 4, -2 ],
[ 0, 1, 3, 2, 1, 2, -1, 2, -3, -6, -7, -7 ],
[
2,
1/2*a - 1,
-1/2*a + 1,
-1/2*a + 2,
1,
0,
-1,
a - 4,
3/2*a - 1,
-1/2*a + 8,
1/2*a - 1,
-1/2*a + 3
],
[
a,
-a - 1,
a - 1,
-2,
1,
-a - 6,
1,
3*a + 2,
a - 1,
-a - 4,
a + 5,
a - 1
],
[
a,
-a^2 - a + 1,
-a - 3,
2*a^2 + 2*a - 4,
-1,
3*a + 2,
-1,
-2*a^2 - 5*a + 4,
-a^2 - a - 3,
-a^2 - 3*a - 4,
2*a^2 + 5*a - 5,
-5*a^2 - 7*a + 5
],
[
a,
-a^3 + a^2 + 5*a - 1,
-a + 1,
0,
-1,
a^3 - 2*a^2 - 5*a + 4,
1,
a^3 - 7*a - 2,
a^3 - a^2 - 7*a + 3,
a^2 - a,
-2*a^3 + 13*a - 1,
-a^3 + a^2 + 7*a + 3
]
*], q_expansions := [*
q + 2*q^2 + 2*q^4 + 4*q^5 - 5*q^7 - 3*q^9 + 8*q^10 - q^11 + 4*q^13 - 10*q^14 - 4*q^16 + q^17 - 6*q^18 + 2*q^19 + 8*q^20 - 2*q^22 - 2*q^23 + 11*q^25 + 8*q^26 - 10*q^28 - 3*q^29 + 4*q^31 - 8*q^32 + 2*q^34 - 20*q^35 - 6*q^36 - 2*q^37 + O(q^38),
q + q^3 - 2*q^4 + 3*q^5 + 2*q^7 - 2*q^9 + q^11 - 2*q^12 + 2*q^13 + 3*q^15 + 4*q^16 - q^17 + 2*q^19 - 6*q^20 + 2*q^21 - 3*q^23 + 4*q^25 - 5*q^27 - 4*q^28 - 6*q^29 - 7*q^31 + q^33 + 6*q^35 + 4*q^36 - 7*q^37 + O(q^38),
q + 2*q^2 + (1/2*a - 1)*q^3 + 2*q^4 + (-1/2*a + 1)*q^5 + (a - 2)*q^6 + (-1/2*a + 2)*q^7 + (-1/2*a + 2)*q^9 + (-a + 2)*q^10 + q^11 + (a - 2)*q^12 + (-a + 4)*q^14 + (1/2*a - 5)*q^15 - 4*q^16 - q^17 + (-a + 4)*q^18 + (a - 4)*q^19 + (-a + 2)*q^20 + (a - 6)*q^21 + 2*q^22 + (3/2*a - 1)*q^23 - 1/2*a*q^25 + (-1/2*a - 3)*q^27 + (-a + 4)*q^28 + (-1/2*a + 8)*q^29 + (a - 10)*q^30 + (1/2*a - 1)*q^31 - 8*q^32 + (1/2*a - 1)*q^33 - 2*q^34 + (-a + 6)*q^35 + (-a + 4)*q^36 + (-1/2*a + 3)*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 - 2*a*q^4 + (a - 1)*q^5 + (a - 2)*q^6 - 2*q^7 + (2*a - 4)*q^8 + (-3*a + 2)*q^10 + q^11 + (-2*a + 4)*q^12 + (-a - 6)*q^13 - 2*a*q^14 + (2*a - 1)*q^15 + (-4*a + 4)*q^16 + q^17 + (3*a + 2)*q^19 + (6*a - 4)*q^20 + (2*a + 2)*q^21 + a*q^22 + (a - 1)*q^23 + 6*a*q^24 + (-4*a - 2)*q^25 + (-4*a - 2)*q^26 + (3*a + 3)*q^27 + 4*a*q^28 + (-a - 4)*q^29 + (-5*a + 4)*q^30 + (a + 5)*q^31 + 8*a*q^32 + (-a - 1)*q^33 + a*q^34 + (-2*a + 2)*q^35 + (a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (-a - 3)*q^5 + (a^2 - a - 2)*q^6 + (2*a^2 + 2*a - 4)*q^7 + (-2*a^2 - 2*a + 2)*q^8 + (a^2 - 2)*q^9 + (-a^2 - 3*a)*q^10 - q^11 + (-a^2 + 2*a)*q^12 + (3*a + 2)*q^13 + (-2*a^2 + 4)*q^14 + (2*a^2 + 4*a - 1)*q^15 - 2*a*q^16 - q^17 + (-2*a^2 + 2)*q^18 + (-2*a^2 - 5*a + 4)*q^19 + (-a^2 + 4)*q^20 + (2*a - 4)*q^21 - a*q^22 + (-a^2 - a - 3)*q^23 + (2*a^2 + 2)*q^24 + (a^2 + 6*a + 4)*q^25 + (3*a^2 + 2*a)*q^26 + (2*a^2 + 5*a - 3)*q^27 + (-4*a + 4)*q^28 + (-a^2 - 3*a - 4)*q^29 + (3*a + 4)*q^30 + (2*a^2 + 5*a - 5)*q^31 + (2*a^2 + 4*a - 4)*q^32 + (a^2 + a - 1)*q^33 - a*q^34 + (-4*a^2 - 6*a + 8)*q^35 + (2*a^2 - 2*a)*q^36 + (-5*a^2 - 7*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + a^2 + 5*a - 1)*q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + (-a^2 + a + 2)*q^6 + (a^3 - 4*a)*q^8 + (-a^2 + 6)*q^9 + (-a^2 + a)*q^10 - q^11 + (a^3 - a^2 - 8*a + 2)*q^12 + (a^3 - 2*a^2 - 5*a + 4)*q^13 + (-a^3 + 2*a^2 + 4*a - 3)*q^15 + (a^3 - 2*a + 2)*q^16 + q^17 + (-a^3 + 6*a)*q^18 + (a^3 - 7*a - 2)*q^19 + (-a^3 + a^2 + 2*a - 2)*q^20 - a*q^22 + (a^3 - a^2 - 7*a + 3)*q^23 + (-2*a - 6)*q^24 + (a^2 - 2*a - 4)*q^25 + (-a^3 + a^2 + 2*a - 2)*q^26 + (-2*a^3 + 2*a^2 + 13*a - 3)*q^27 + (a^2 - a)*q^29 + (a^3 - 2*a^2 - a + 2)*q^30 + (-2*a^3 + 13*a - 1)*q^31 + (-a^3 + 4*a^2 + 8*a - 2)*q^32 + (a^3 - a^2 - 5*a + 1)*q^33 + a*q^34 + (-a^3 + 2*a^2 + 2*a - 10)*q^36 + (-a^3 + a^2 + 7*a + 3)*q^37 + O(q^38)
*]> ;  // time = 21.429 seconds




J[190] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 190, 190, 190, 190, 95, 95, 38, 38, 19 ], new_dimensions := [ 1, 1, 1, 2, 3, 4, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2, 6, 8, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 13, 1, 1, 1, 1, 1, 1, 1, 13, 0, 1, 1, 5, 1, 1, 11, 1, 1, 1, 0, 3, 1, 81, 1, 1, 1, 1, 1, 3, 0, 1, 9, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 3, 1, 1, 81, 9, 1, 0 ], ap_traces := [
[ -1, -1, -1, -1, 0, -3, -7, -1, -5, -5, 10, 2 ],
[ 1, -3, -1, -5, -4, -1, -3, 1, 7, -3, -2, -2 ],
[ 1, 1, 1, -1, 0, -1, -3, 1, 3, -3, 2, -10 ],
[ -2, -1, 2, -1, 8, -1, 11, -2, 3, 1, -2, -12 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 11, 1, 1 ],
[ 3, 3, 1 ],
[ 13, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 11, 1, 1 ],
[ 3, 3, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 0, 0, 1, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1/9, 1 ], eigenvalues := [*
[ -1, -1, -1, -1, 0, -3, -7, -1, -5, -5, 10, 2 ],
[ 1, -3, -1, -5, -4, -1, -3, 1, 7, -3, -2, -2 ],
[ 1, 1, 1, -1, 0, -1, -3, 1, 3, -3, 2, -10 ],
[
-1,
a,
1,
a,
4,
-3*a - 2,
a + 6,
-1,
-3*a,
3*a + 2,
2*a,
-6
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - q^7 - q^8 - 2*q^9 + q^10 - q^12 - 3*q^13 + q^14 + q^15 + q^16 - 7*q^17 + 2*q^18 - q^19 - q^20 + q^21 - 5*q^23 + q^24 + q^25 + 3*q^26 + 5*q^27 - q^28 - 5*q^29 - q^30 + 10*q^31 - q^32 + 7*q^34 + q^35 - 2*q^36 + 2*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - q^5 - 3*q^6 - 5*q^7 + q^8 + 6*q^9 - q^10 - 4*q^11 - 3*q^12 - q^13 - 5*q^14 + 3*q^15 + q^16 - 3*q^17 + 6*q^18 + q^19 - q^20 + 15*q^21 - 4*q^22 + 7*q^23 - 3*q^24 + q^25 - q^26 - 9*q^27 - 5*q^28 - 3*q^29 + 3*q^30 - 2*q^31 + q^32 + 12*q^33 - 3*q^34 + 5*q^35 + 6*q^36 - 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 - q^7 + q^8 - 2*q^9 + q^10 + q^12 - q^13 - q^14 + q^15 + q^16 - 3*q^17 - 2*q^18 + q^19 + q^20 - q^21 + 3*q^23 + q^24 + q^25 - q^26 - 5*q^27 - q^28 - 3*q^29 + q^30 + 2*q^31 + q^32 - 3*q^34 - q^35 - 2*q^36 - 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 + a*q^7 - q^8 + (-a + 1)*q^9 - q^10 + 4*q^11 + a*q^12 + (-3*a - 2)*q^13 - a*q^14 + a*q^15 + q^16 + (a + 6)*q^17 + (a - 1)*q^18 - q^19 + q^20 + (-a + 4)*q^21 - 4*q^22 - 3*a*q^23 - a*q^24 + q^25 + (3*a + 2)*q^26 + (-a - 4)*q^27 + a*q^28 + (3*a + 2)*q^29 - a*q^30 + 2*a*q^31 - q^32 + 4*a*q^33 + (-a - 6)*q^34 + a*q^35 + (-a + 1)*q^36 - 6*q^37 + O(q^38)
*]> ;  // time = 59.75 seconds




J[191] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 191, 191 ], new_dimensions := [ 2, 14 ], dimensions := [ 2, 14 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -2, -1, -1, -1, -7, 0, -6, -1, 0, -5, 2 ],
[ 0, 2, 1, 3, -3, 19, 14, 20, -13, 6, 15, -8 ]
], hecke_fields := [
x^2 + x - 1,
x^14 - 23*x^12 + x^11 + 205*x^10 - 13*x^9 - 895*x^8 + 35*x^7 + 1993*x^6 + 103*x^5 - 2135*x^4 - 465*x^3 + 853*x^2 + 374*x + 41
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 95 ]
], tamagawa_numbers := [
[ 1 ],
[ 95 ]
], torsion_upper_bounds := [ 1, 95 ], torsion_lower_bounds := [ 1, 95 ], l_ratios := [ 0, 1/95 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-1,
-a - 1,
-a - 1,
a,
3*a - 2,
0,
-3,
a,
-2*a - 1,
5*a,
-4*a - 1
],
[
a,
-145153/114035*a^13 + 32777/114035*a^12 + 3364061/114035*a^11 - 874037/114035*a^10 - 30238352/114035*a^9 + 8179107/114035*a^8 + 133274007/114035*a^7 - 31876833/114035*a^6 - 300314067/114035*a^5 + 43961084/114035*a^4 + 328052329/114035*a^3 + 4557079/114035*a^2 - 27781803/22807*a - 29013772/114035,
-44318/114035*a^13 - 468/114035*a^12 + 996676/114035*a^11 - 67192/114035*a^10 - 8645332/114035*a^9 + 1110732/114035*a^8 + 36541877/114035*a^7 - 5434583/114035*a^6 - 78444822/114035*a^5 + 7801444/114035*a^4 + 81404284/114035*a^3 + 2785164/114035*a^2 - 6622972/22807*a - 6986182/114035,
148787/114035*a^13 - 73368/114035*a^12 - 3418414/114035*a^11 + 1764598/114035*a^10 + 30273378/114035*a^9 - 15485288/114035*a^8 - 130230738/114035*a^7 + 59339692/114035*a^6 + 282975218/114035*a^5 - 90112966/114035*a^4 - 296004726/114035*a^3 + 24031844/114035*a^2 + 24591132/22807*a + 24473743/114035,
-317749/114035*a^13 + 87501/114035*a^12 + 7255723/114035*a^11 - 2329051/114035*a^10 - 63902811/114035*a^9 + 21925031/114035*a^8 + 273703901/114035*a^7 - 87350029/114035*a^6 - 592597121/114035*a^5 + 131174117/114035*a^4 + 615896407/114035*a^3 - 20228013/114035*a^2 - 50237157/22807*a - 50606546/114035,
169418/114035*a^13 - 44707/114035*a^12 - 3873501/114035*a^11 + 1208972/114035*a^10 + 34207957/114035*a^9 - 11502337/114035*a^8 - 147297467/114035*a^7 + 46178043/114035*a^6 + 321976277/114035*a^5 - 69816889/114035*a^4 - 339639974/114035*a^3 + 10698151/114035*a^2 + 28096743/22807*a + 28321417/114035,
303228/114035*a^13 - 86692/114035*a^12 - 6907461/114035*a^11 + 2286332/114035*a^10 + 60603762/114035*a^9 - 21383092/114035*a^8 - 257968172/114035*a^7 + 84810468/114035*a^6 + 552823792/114035*a^5 - 127305184/114035*a^4 - 565213084/114035*a^3 + 21919331/114035*a^2 + 45132248/22807*a + 45171892/114035,
-24374/114035*a^13 + 60751/114035*a^12 + 524093/114035*a^11 - 1347011/114035*a^10 - 4102891/114035*a^9 + 11125891/114035*a^8 + 13791251/114035*a^7 - 41743519/114035*a^6 - 16672401/114035*a^5 + 68606947/114035*a^4 - 1099913/114035*a^3 - 38565303/114035*a^2 + 1095165/22807*a + 3360679/114035,
39921/22807*a^13 - 4913/22807*a^12 - 908173/22807*a^11 + 165777/22807*a^10 + 7973795/22807*a^9 - 1768332/22807*a^8 - 34094825/22807*a^7 + 7468373/22807*a^6 + 73831676/22807*a^5 - 10996563/22807*a^4 - 76780679/22807*a^3 - 206151/22807*a^2 + 31072819/22807*a + 6279936/22807,
29682/22807*a^13 + 685/22807*a^12 - 686101/22807*a^11 + 22129/22807*a^10 + 6157277/22807*a^9 - 428091/22807*a^8 - 27138725/22807*a^7 + 1952471/22807*a^6 + 61244391/22807*a^5 - 1415669/22807*a^4 - 66926471/22807*a^3 - 5457861/22807*a^2 + 28139201/22807*a + 6245485/22807,
141063/114035*a^13 - 75647/114035*a^12 - 3159481/114035*a^11 + 1847727/114035*a^10 + 27001997/114035*a^9 - 16450667/114035*a^8 - 110256147/114035*a^7 + 64132173/114035*a^6 + 221254747/114035*a^5 - 101220029/114035*a^4 - 206018409/114035*a^3 + 37764231/114035*a^2 + 15179661/22807*a + 14145902/114035,
167816/114035*a^13 - 78339/114035*a^12 - 3890397/114035*a^11 + 1890079/114035*a^10 + 34906349/114035*a^9 - 16634679/114035*a^8 - 153103989/114035*a^7 + 63896051/114035*a^6 + 342297969/114035*a^5 - 96779723/114035*a^4 - 371525683/114035*a^3 + 22562677/114035*a^2 + 31806965/22807*a + 31900929/114035
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-a - 1)*q^4 + (-a - 1)*q^5 - a*q^6 + (-a - 1)*q^7 + (-2*a - 1)*q^8 - 2*q^9 - q^10 + a*q^11 + (a + 1)*q^12 + (3*a - 2)*q^13 - q^14 + (a + 1)*q^15 + 3*a*q^16 - 2*a*q^18 - 3*q^19 + (a + 2)*q^20 + (a + 1)*q^21 + (-a + 1)*q^22 + a*q^23 + (2*a + 1)*q^24 + (a - 3)*q^25 + (-5*a + 3)*q^26 + 5*q^27 + (a + 2)*q^28 + (-2*a - 1)*q^29 + q^30 + 5*a*q^31 + (a + 5)*q^32 - a*q^33 + (a + 2)*q^35 + (2*a + 2)*q^36 + (-4*a - 1)*q^37 + O(q^38),
q + a*q^2 + (-145153/114035*a^13 + 32777/114035*a^12 + 3364061/114035*a^11 - 874037/114035*a^10 - 30238352/114035*a^9 + 8179107/114035*a^8 + 133274007/114035*a^7 - 31876833/114035*a^6 - 300314067/114035*a^5 + 43961084/114035*a^4 + 328052329/114035*a^3 + 4557079/114035*a^2 - 27781803/22807*a - 29013772/114035)*q^3 + (a^2 - 2)*q^4 + (-44318/114035*a^13 - 468/114035*a^12 + 996676/114035*a^11 - 67192/114035*a^10 - 8645332/114035*a^9 + 1110732/114035*a^8 + 36541877/114035*a^7 - 5434583/114035*a^6 - 78444822/114035*a^5 + 7801444/114035*a^4 + 81404284/114035*a^3 + 2785164/114035*a^2 - 6622972/22807*a - 6986182/114035)*q^5 + (32777/114035*a^13 + 25542/114035*a^12 - 728884/114035*a^11 - 481987/114035*a^10 + 6292118/114035*a^9 + 3362072/114035*a^8 - 26796478/114035*a^7 - 11024138/114035*a^6 + 58911843/114035*a^5 + 18150674/114035*a^4 - 62939066/114035*a^3 - 15093506/114035*a^2 + 5054690/22807*a + 5951273/114035)*q^6 + (148787/114035*a^13 - 73368/114035*a^12 - 3418414/114035*a^11 + 1764598/114035*a^10 + 30273378/114035*a^9 - 15485288/114035*a^8 - 130230738/114035*a^7 + 59339692/114035*a^6 + 282975218/114035*a^5 - 90112966/114035*a^4 - 296004726/114035*a^3 + 24031844/114035*a^2 + 24591132/22807*a + 24473743/114035)*q^7 + (a^3 - 4*a)*q^8 + (34542/114035*a^13 + 21737/114035*a^12 - 802949/114035*a^11 - 412297/114035*a^10 + 7331993/114035*a^9 + 2916102/114035*a^8 - 33454383/114035*a^7 - 9948713/114035*a^6 + 79726068/114035*a^5 + 18237999/114035*a^4 - 92932081/114035*a^3 - 19074881/114035*a^2 + 8100797/22807*a + 10072718/114035)*q^9 + (-468/114035*a^13 - 22638/114035*a^12 - 22874/114035*a^11 + 439858/114035*a^10 + 534598/114035*a^9 - 3122733/114035*a^8 - 3883453/114035*a^7 + 9880952/114035*a^6 + 12366198/114035*a^5 - 13214646/114035*a^4 - 17822706/114035*a^3 + 4688394/114035*a^2 + 1917750/22807*a + 1817038/114035)*q^10 + (-317749/114035*a^13 + 87501/114035*a^12 + 7255723/114035*a^11 - 2329051/114035*a^10 - 63902811/114035*a^9 + 21925031/114035*a^8 + 273703901/114035*a^7 - 87350029/114035*a^6 - 592597121/114035*a^5 + 131174117/114035*a^4 + 615896407/114035*a^3 - 20228013/114035*a^2 - 50237157/22807*a - 50606546/114035)*q^11 + (315848/114035*a^13 - 40567/114035*a^12 - 7242886/114035*a^11 + 1320907/114035*a^10 + 64264877/114035*a^9 - 13819277/114035*a^8 - 278719347/114035*a^7 + 57340948/114035*a^6 + 615402777/114035*a^5 - 80882339/114035*a^4 - 655956859/114035*a^3 - 11799489/114035*a^2 + 54302141/22807*a + 56683687/114035)*q^12 + (169418/114035*a^13 - 44707/114035*a^12 - 3873501/114035*a^11 + 1208972/114035*a^10 + 34207957/114035*a^9 - 11502337/114035*a^8 - 147297467/114035*a^7 + 46178043/114035*a^6 + 321976277/114035*a^5 - 69816889/114035*a^4 - 339639974/114035*a^3 + 10698151/114035*a^2 + 28096743/22807*a + 28321417/114035)*q^13 + (-73368/114035*a^13 + 3687/114035*a^12 + 1615811/114035*a^11 - 227957/114035*a^10 - 13551057/114035*a^9 + 2933627/114035*a^8 + 54132147/114035*a^7 - 13557273/114035*a^6 - 105438027/114035*a^5 + 21655519/114035*a^4 + 93217799/114035*a^3 - 3959651/114035*a^2 - 6234519/22807*a - 6100267/114035)*q^14 + (101858/114035*a^13 - 58322/114035*a^12 - 2292531/114035*a^11 + 1387757/114035*a^10 + 19694912/114035*a^9 - 12095462/114035*a^8 - 80836142/114035*a^7 + 46393178/114035*a^6 + 162965222/114035*a^5 - 72409694/114035*a^4 - 152342989/114035*a^3 + 26703391/114035*a^2 + 11332620/22807*a + 10449012/114035)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (303228/114035*a^13 - 86692/114035*a^12 - 6907461/114035*a^11 + 2286332/114035*a^10 + 60603762/114035*a^9 - 21383092/114035*a^8 - 257968172/114035*a^7 + 84810468/114035*a^6 + 552823792/114035*a^5 - 127305184/114035*a^4 - 565213084/114035*a^3 + 21919331/114035*a^2 + 45132248/22807*a + 45171892/114035)*q^17 + (21737/114035*a^13 - 8483/114035*a^12 - 446839/114035*a^11 + 250883/114035*a^10 + 3365148/114035*a^9 - 2539293/114035*a^8 - 11157683/114035*a^7 + 10883862/114035*a^6 + 14680173/114035*a^5 - 19184911/114035*a^4 - 3012851/114035*a^3 + 11039659/114035*a^2 - 569198/22807*a - 1416222/114035)*q^18 + (-24374/114035*a^13 + 60751/114035*a^12 + 524093/114035*a^11 - 1347011/114035*a^10 - 4102891/114035*a^9 + 11125891/114035*a^8 + 13791251/114035*a^7 - 41743519/114035*a^6 - 16672401/114035*a^5 + 68606947/114035*a^4 - 1099913/114035*a^3 - 38565303/114035*a^2 + 1095165/22807*a + 3360679/114035)*q^19 + (65998/114035*a^13 - 32702/114035*a^12 - 1553026/114035*a^11 + 764922/114035*a^10 + 14161847/114035*a^9 - 6523777/114035*a^8 - 63186422/114035*a^7 + 24168088/114035*a^6 + 143723202/114035*a^5 - 34424774/114035*a^4 - 158337794/114035*a^3 + 4417626/114035*a^2 + 13644358/22807*a + 13991552/114035)*q^20 + (-504737/114035*a^13 + 144888/114035*a^12 + 11503414/114035*a^11 - 3823758/114035*a^10 - 101029758/114035*a^9 + 35742508/114035*a^8 + 430936308/114035*a^7 - 141443112/114035*a^6 - 927320908/114035*a^5 + 210797716/114035*a^4 + 955568936/114035*a^3 - 32381654/114035*a^2 - 77251470/22807*a - 78729853/114035)*q^21 + (87501/114035*a^13 - 52504/114035*a^12 - 2011302/114035*a^11 + 1235734/114035*a^10 + 17794294/114035*a^9 - 10681454/114035*a^8 - 76228814/114035*a^7 + 40676636/114035*a^6 + 163902264/114035*a^5 - 62497708/114035*a^4 - 167981298/114035*a^3 + 19854112/114035*a^2 + 13646316/22807*a + 13027709/114035)*q^22 + (39921/22807*a^13 - 4913/22807*a^12 - 908173/22807*a^11 + 165777/22807*a^10 + 7973795/22807*a^9 - 1768332/22807*a^8 - 34094825/22807*a^7 + 7468373/22807*a^6 + 73831676/22807*a^5 - 10996563/22807*a^4 - 76780679/22807*a^3 - 206151/22807*a^2 + 31072819/22807*a + 6279936/22807)*q^23 + (-106121/114035*a^13 - 29466/114035*a^12 + 2462827/114035*a^11 + 480011/114035*a^10 - 22297489/114035*a^9 - 2759531/114035*a^8 + 99879224/114035*a^7 + 7965989/114035*a^6 - 231238369/114035*a^5 - 17922727/114035*a^4 + 260947963/114035*a^3 + 32279373/114035*a^2 - 22398073/22807*a - 24852314/114035)*q^24 + (35334/114035*a^13 - 1356/114035*a^12 - 781783/114035*a^11 + 88941/114035*a^10 + 6620271/114035*a^9 - 1141371/114035*a^8 - 26952561/114035*a^7 + 5136669/114035*a^6 + 54351291/114035*a^5 - 7626787/114035*a^4 - 50630237/114035*a^3 + 447033/114035*a^2 + 3478182/22807*a + 2962646/114035)*q^25 + (-44707/114035*a^13 + 23113/114035*a^12 + 1039554/114035*a^11 - 522733/114035*a^10 - 9299903/114035*a^9 + 4331643/114035*a^8 + 40248413/114035*a^7 - 15673797/114035*a^6 - 87266943/114035*a^5 + 22067456/114035*a^4 + 89477521/114035*a^3 - 4029839/114035*a^2 - 7008183/22807*a - 6946138/114035)*q^26 + (-557464/114035*a^13 + 145556/114035*a^12 + 12789383/114035*a^11 - 3857481/114035*a^10 - 113360386/114035*a^9 + 36119091/114035*a^8 + 489914611/114035*a^7 - 142576889/114035*a^6 - 1074302751/114035*a^5 + 208584342/114035*a^4 + 1134739817/114035*a^3 - 17430173/114035*a^2 - 93655848/22807*a - 96218141/114035)*q^27 + (-293887/114035*a^13 + 75083/114035*a^12 + 6682239/114035*a^11 - 2039813/114035*a^10 - 58566913/114035*a^9 + 19438363/114035*a^8 + 249472083/114035*a^7 - 77894987/114035*a^6 - 536738013/114035*a^5 + 116803051/114035*a^4 + 553933681/114035*a^3 - 16653379/114035*a^2 - 44914391/22807*a - 45939398/114035)*q^28 + (29682/22807*a^13 + 685/22807*a^12 - 686101/22807*a^11 + 22129/22807*a^10 + 6157277/22807*a^9 - 428091/22807*a^8 - 27138725/22807*a^7 + 1952471/22807*a^6 + 61244391/22807*a^5 - 1415669/22807*a^4 - 66926471/22807*a^3 - 5457861/22807*a^2 + 28139201/22807*a + 6245485/22807)*q^29 + (-58322/114035*a^13 + 50203/114035*a^12 + 1285899/114035*a^11 - 1185978/114035*a^10 - 10771308/114035*a^9 + 10326768/114035*a^8 + 42828148/114035*a^7 - 40037772/114035*a^6 - 82901068/114035*a^5 + 65123841/114035*a^4 + 74067361/114035*a^3 - 30221774/114035*a^2 - 5529176/22807*a - 4176178/114035)*q^30 + (141063/114035*a^13 - 75647/114035*a^12 - 3159481/114035*a^11 + 1847727/114035*a^10 + 27001997/114035*a^9 - 16450667/114035*a^8 - 110256147/114035*a^7 + 64132173/114035*a^6 + 221254747/114035*a^5 - 101220029/114035*a^4 - 206018409/114035*a^3 + 37764231/114035*a^2 + 15179661/22807*a + 14145902/114035)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-98063/114035*a^13 + 9437/114035*a^12 + 2327431/114035*a^11 - 306897/114035*a^10 - 21575277/114035*a^9 + 3187387/114035*a^8 + 98962207/114035*a^7 - 12871453/114035*a^6 - 234448567/114035*a^5 + 15650379/114035*a^4 + 270634419/114035*a^3 + 12054799/114035*a^2 - 23802029/22807*a - 23649702/114035)*q^33 + (-86692/114035*a^13 + 66783/114035*a^12 + 1983104/114035*a^11 - 1557978/114035*a^10 - 17441128/114035*a^9 + 13420888/114035*a^8 + 74197488/114035*a^7 - 51509612/114035*a^6 - 158537668/114035*a^5 + 82178696/114035*a^4 + 162920351/114035*a^3 - 32992244/114035*a^2 - 13647076/22807*a - 12432348/114035)*q^34 + (-58851/114035*a^13 - 52871/114035*a^12 + 1399907/114035*a^11 + 1088501/114035*a^10 - 13111959/114035*a^9 - 8471251/114035*a^8 + 61447029/114035*a^7 + 31363979/114035*a^6 - 150287009/114035*a^5 - 56984197/114035*a^4 + 178560403/114035*a^3 + 48184383/114035*a^2 - 15433091/22807*a - 18678334/114035)*q^35 + (-77567/114035*a^13 + 9638/114035*a^12 + 1835044/114035*a^11 - 266343/114035*a^10 - 16920698/114035*a^9 + 2464728/114035*a^8 + 77031833/114035*a^7 - 8744242/114035*a^6 - 180875958/114035*a^5 + 6919646/114035*a^4 + 207011526/114035*a^3 + 16762111/114035*a^2 - 18110766/22807*a - 21036653/114035)*q^36 + (167816/114035*a^13 - 78339/114035*a^12 - 3890397/114035*a^11 + 1890079/114035*a^10 + 34906349/114035*a^9 - 16634679/114035*a^8 - 153103989/114035*a^7 + 63896051/114035*a^6 + 342297969/114035*a^5 - 96779723/114035*a^4 - 371525683/114035*a^3 + 22562677/114035*a^2 + 31806965/22807*a + 31900929/114035)*q^37 + O(q^38)
*]> ;  // time = 2.459 seconds




J[193] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 193, 193, 193 ], new_dimensions := [ 2, 5, 8 ], dimensions := [ 2, 5, 8 ], intersection_graph := [ 0, 11, 1, 11, 0, 1, 1, 1, 0 ], ap_traces := [
[ -3, -2, 0, -1, 3, -6, -6, -14, -9, 9, 1, 1 ],
[ -2, -5, -8, -10, -10, 2, -9, 14, -20, -3, -6, -6 ],
[ 2, 5, 8, 5, 9, -4, 7, 0, 23, -2, 7, -13 ]
], hecke_fields := [
x^2 + 3*x + 1,
x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1,
x^8 - 2*x^7 - 9*x^6 + 18*x^5 + 21*x^4 - 44*x^3 - 11*x^2 + 27*x + 1
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1 ], l_ratios := [ 0, 0, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[
a,
-1,
2*a + 3,
-3*a - 5,
-3*a - 3,
-3,
2*a,
-7,
3*a,
a + 6,
3*a + 5,
3*a + 5
],
[
a,
a^4 - 5*a^2 + a + 1,
-a^4 + 5*a^2 - 2*a - 4,
-a^4 - a^3 + 3*a^2 + a - 1,
a^4 + 3*a^3 - 3*a^2 - 8*a + 1,
-a^4 - 4*a^3 + 3*a^2 + 13*a - 4,
2*a^4 + 2*a^3 - 7*a^2 - 2*a - 1,
2*a^3 - 9*a + 6,
-a^4 - 2*a^3 + 2*a^2 + 5*a - 2,
-4*a^3 + 18*a - 7,
a^4 - 4*a^2 + a - 2,
-2*a^4 + 2*a^3 + 10*a^2 - 11*a - 2
],
[
a,
-1/7*a^7 + 4/7*a^6 + 8/7*a^5 - 34/7*a^4 - 16/7*a^3 + 69/7*a^2 + 6/7*a - 18/7,
-8/7*a^7 + 4/7*a^6 + 78/7*a^5 - 27/7*a^4 - 212/7*a^3 + 41/7*a^2 + 160/7*a + 10/7,
15/7*a^7 - 11/7*a^6 - 148/7*a^5 + 83/7*a^4 + 408/7*a^3 - 146/7*a^2 - 307/7*a + 18/7,
3/7*a^7 - 5/7*a^6 - 31/7*a^5 + 39/7*a^4 + 97/7*a^3 - 67/7*a^2 - 95/7*a + 19/7,
-4/7*a^7 + 2/7*a^6 + 39/7*a^5 - 17/7*a^4 - 99/7*a^3 + 38/7*a^2 + 52/7*a - 9/7,
23/7*a^7 - 15/7*a^6 - 219/7*a^5 + 110/7*a^4 + 564/7*a^3 - 187/7*a^2 - 383/7*a + 15/7,
-26/7*a^7 + 13/7*a^6 + 264/7*a^5 - 93/7*a^4 - 759/7*a^3 + 149/7*a^2 + 604/7*a + 22/7,
-19/7*a^7 + 13/7*a^6 + 187/7*a^5 - 93/7*a^4 - 514/7*a^3 + 142/7*a^2 + 380/7*a + 36/7,
26/7*a^7 - 13/7*a^6 - 250/7*a^5 + 79/7*a^4 + 661/7*a^3 - 79/7*a^2 - 485/7*a - 57/7,
-13/7*a^7 + 10/7*a^6 + 132/7*a^5 - 64/7*a^4 - 390/7*a^3 + 50/7*a^2 + 344/7*a + 81/7,
-3*a^7 + 2*a^6 + 29*a^5 - 15*a^4 - 77*a^3 + 25*a^2 + 57*a
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-3*a - 3)*q^4 + (2*a + 3)*q^5 - a*q^6 + (-3*a - 5)*q^7 + (4*a + 3)*q^8 - 2*q^9 + (-3*a - 2)*q^10 + (-3*a - 3)*q^11 + (3*a + 3)*q^12 - 3*q^13 + (4*a + 3)*q^14 + (-2*a - 3)*q^15 + (-3*a + 2)*q^16 + 2*a*q^17 - 2*a*q^18 - 7*q^19 + (3*a - 3)*q^20 + (3*a + 5)*q^21 + (6*a + 3)*q^22 + 3*a*q^23 + (-4*a - 3)*q^24 - 3*a*q^26 + 5*q^27 + (-3*a + 6)*q^28 + (a + 6)*q^29 + (3*a + 2)*q^30 + (3*a + 5)*q^31 + (3*a - 3)*q^32 + (3*a + 3)*q^33 + (-6*a - 2)*q^34 + (-a - 9)*q^35 + (6*a + 6)*q^36 + (3*a + 5)*q^37 + O(q^38),
q + a*q^2 + (a^4 - 5*a^2 + a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^4 + 5*a^2 - 2*a - 4)*q^5 + (-2*a^4 + 8*a^2 - 6*a - 1)*q^6 + (-a^4 - a^3 + 3*a^2 + a - 1)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 + a^3 + 7*a^2 - 4*a - 3)*q^9 + (2*a^4 - 9*a^2 + 3*a + 1)*q^10 + (a^4 + 3*a^3 - 3*a^2 - 8*a + 1)*q^11 + (2*a^4 - 2*a^3 - 10*a^2 + 11*a)*q^12 + (-a^4 - 4*a^3 + 3*a^2 + 13*a - 4)*q^13 + (a^4 - 2*a^3 - 6*a^2 + 6*a + 1)*q^14 + (-a^3 + 7*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + 2*a^3 - 7*a^2 - 2*a - 1)*q^17 + (3*a^4 + 2*a^3 - 11*a^2 + 4*a + 1)*q^18 + (2*a^3 - 9*a + 6)*q^19 + (-2*a^4 + a^3 + 7*a^2 - 9*a + 6)*q^20 + (-a^4 + 3*a^3 + 8*a^2 - 8*a - 2)*q^21 + (a^4 + 2*a^3 - a^2 - 6*a - 1)*q^22 + (-a^4 - 2*a^3 + 2*a^2 + 5*a - 2)*q^23 + (-2*a^4 + 9*a^2 - 2*a)*q^24 + (a^4 + a^3 - 6*a^2 - 4*a + 8)*q^25 + (-2*a^4 - 2*a^3 + 6*a^2 + 3*a + 1)*q^26 + (-5*a^3 - 5*a^2 + 17*a - 2)*q^27 + (-2*a^4 + a^3 + 7*a^2 - 8*a + 1)*q^28 + (-4*a^3 + 18*a - 7)*q^29 + (-a^4 + 7*a^2 - 2*a)*q^30 + (a^4 - 4*a^2 + a - 2)*q^31 + (-2*a^4 - 3*a^3 + 7*a^2 + 5*a - 1)*q^32 + (-5*a^4 - 3*a^3 + 18*a^2 - 2*a + 1)*q^33 + (-2*a^4 + 3*a^3 + 12*a^2 - 15*a - 2)*q^34 + (3*a^4 + 2*a^3 - 11*a^2 - a + 4)*q^35 + (-2*a^4 + 2*a^3 + 11*a^2 - 12*a + 3)*q^36 + (-2*a^4 + 2*a^3 + 10*a^2 - 11*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-1/7*a^7 + 4/7*a^6 + 8/7*a^5 - 34/7*a^4 - 16/7*a^3 + 69/7*a^2 + 6/7*a - 18/7)*q^3 + (a^2 - 2)*q^4 + (-8/7*a^7 + 4/7*a^6 + 78/7*a^5 - 27/7*a^4 - 212/7*a^3 + 41/7*a^2 + 160/7*a + 10/7)*q^5 + (2/7*a^7 - 1/7*a^6 - 16/7*a^5 + 5/7*a^4 + 25/7*a^3 - 5/7*a^2 + 9/7*a + 1/7)*q^6 + (15/7*a^7 - 11/7*a^6 - 148/7*a^5 + 83/7*a^4 + 408/7*a^3 - 146/7*a^2 - 307/7*a + 18/7)*q^7 + (a^3 - 4*a)*q^8 + (-5/7*a^7 + 6/7*a^6 + 47/7*a^5 - 44/7*a^4 - 122/7*a^3 + 58/7*a^2 + 86/7*a + 29/7)*q^9 + (-12/7*a^7 + 6/7*a^6 + 117/7*a^5 - 44/7*a^4 - 311/7*a^3 + 72/7*a^2 + 226/7*a + 8/7)*q^10 + (3/7*a^7 - 5/7*a^6 - 31/7*a^5 + 39/7*a^4 + 97/7*a^3 - 67/7*a^2 - 95/7*a + 19/7)*q^11 + (5/7*a^7 - 6/7*a^6 - 47/7*a^5 + 51/7*a^4 + 115/7*a^3 - 107/7*a^2 - 65/7*a + 34/7)*q^12 + (-4/7*a^7 + 2/7*a^6 + 39/7*a^5 - 17/7*a^4 - 99/7*a^3 + 38/7*a^2 + 52/7*a - 9/7)*q^13 + (19/7*a^7 - 13/7*a^6 - 187/7*a^5 + 93/7*a^4 + 514/7*a^3 - 142/7*a^2 - 387/7*a - 15/7)*q^14 + (-11/7*a^7 + 9/7*a^6 + 109/7*a^5 - 66/7*a^4 - 309/7*a^3 + 108/7*a^2 + 248/7*a - 2/7)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (23/7*a^7 - 15/7*a^6 - 219/7*a^5 + 110/7*a^4 + 564/7*a^3 - 187/7*a^2 - 383/7*a + 15/7)*q^17 + (-4/7*a^7 + 2/7*a^6 + 46/7*a^5 - 17/7*a^4 - 162/7*a^3 + 31/7*a^2 + 164/7*a + 5/7)*q^18 + (-26/7*a^7 + 13/7*a^6 + 264/7*a^5 - 93/7*a^4 - 759/7*a^3 + 149/7*a^2 + 604/7*a + 22/7)*q^19 + (-2/7*a^7 + 1/7*a^6 + 16/7*a^5 - 5/7*a^4 - 32/7*a^3 + 12/7*a^2 + 12/7*a - 8/7)*q^20 + (4*a^7 - 2*a^6 - 40*a^5 + 13*a^4 + 113*a^3 - 14*a^2 - 90*a - 14)*q^21 + (1/7*a^7 - 4/7*a^6 - 15/7*a^5 + 34/7*a^4 + 65/7*a^3 - 62/7*a^2 - 62/7*a - 3/7)*q^22 + (-19/7*a^7 + 13/7*a^6 + 187/7*a^5 - 93/7*a^4 - 514/7*a^3 + 142/7*a^2 + 380/7*a + 36/7)*q^23 + (-a^5 + 9*a^3 - 17*a - 1)*q^24 + (-10/7*a^7 + 5/7*a^6 + 94/7*a^5 - 32/7*a^4 - 244/7*a^3 + 53/7*a^2 + 179/7*a - 26/7)*q^25 + (-6/7*a^7 + 3/7*a^6 + 55/7*a^5 - 15/7*a^4 - 138/7*a^3 + 8/7*a^2 + 99/7*a + 4/7)*q^26 + (-3*a^7 + 2*a^6 + 29*a^5 - 15*a^4 - 76*a^3 + 26*a^2 + 51*a)*q^27 + (-5/7*a^7 + 6/7*a^6 + 47/7*a^5 - 51/7*a^4 - 122/7*a^3 + 114/7*a^2 + 86/7*a - 55/7)*q^28 + (26/7*a^7 - 13/7*a^6 - 250/7*a^5 + 79/7*a^4 + 661/7*a^3 - 79/7*a^2 - 485/7*a - 57/7)*q^29 + (-13/7*a^7 + 10/7*a^6 + 132/7*a^5 - 78/7*a^4 - 376/7*a^3 + 127/7*a^2 + 295/7*a + 11/7)*q^30 + (-13/7*a^7 + 10/7*a^6 + 132/7*a^5 - 64/7*a^4 - 390/7*a^3 + 50/7*a^2 + 344/7*a + 81/7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (15/7*a^7 - 4/7*a^6 - 155/7*a^5 + 20/7*a^4 + 464/7*a^3 + 1/7*a^2 - 412/7*a - 73/7)*q^33 + (31/7*a^7 - 12/7*a^6 - 304/7*a^5 + 81/7*a^4 + 825/7*a^3 - 130/7*a^2 - 606/7*a - 23/7)*q^34 + (-1/7*a^7 - 3/7*a^6 + 8/7*a^5 + 29/7*a^4 - 9/7*a^3 - 64/7*a^2 - 15/7*a + 17/7)*q^35 + (4/7*a^7 - 2/7*a^6 - 39/7*a^5 + 10/7*a^4 + 99/7*a^3 + 4/7*a^2 - 59/7*a - 54/7)*q^36 + (-3*a^7 + 2*a^6 + 29*a^5 - 15*a^4 - 77*a^3 + 25*a^2 + 57*a)*q^37 + O(q^38)
*]> ;  // time = 2.459 seconds




J[194] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 194, 194, 194, 97, 97 ], new_dimensions := [ 1, 4, 4, 3, 4 ], dimensions := [ 1, 4, 4, 6, 8 ], intersection_graph := [ 0, 1, 7, 1, 1, 1, 0, 1, 1, 67, 7, 1, 0, 71, 1, 1, 1, 71, 0, 1, 1, 67, 1, 1, 0 ], ap_traces := [
[ 1, 0, 4, -4, 4, -4, 6, -6, -4, 0, 0, -8 ],
[ -4, 2, -2, 6, 2, 4, -8, 8, 10, -6, 8, -2 ],
[ 4, 2, -2, 2, -2, 4, -8, 0, -10, 6, 8, 14 ]
], hecke_fields := [
x - 1,
x^4 - 2*x^3 - 9*x^2 + 18*x + 1,
x^4 - 2*x^3 - 9*x^2 + 18*x - 7
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 201, 3 ],
[ 3479, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 3479, 1 ]
], torsion_upper_bounds := [ 1, 3, 49 ], torsion_lower_bounds := [ 1, 3, 49 ], l_ratios := [ 1, 1/3, 71/49 ], analytic_sha_upper_bounds := [ 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1 ], eigenvalues := [*
[ 1, 0, 4, -4, 4, -4, 6, -6, -4, 0, 0, -8 ],
[
-1,
a,
-1/2*a^3 - 1/2*a^2 + 9/2*a + 1,
1/2*a^3 - 4*a + 5/2,
-a + 1,
a^3 - 8*a + 3,
a^3 - a^2 - 9*a + 6,
-a^3 - a^2 + 7*a + 6,
-1/2*a^3 + 3/2*a^2 + 9/2*a - 7,
1/2*a^3 - 2*a - 3/2,
-a^2 - 3*a + 9,
-3/2*a^3 + a^2 + 11*a - 17/2
],
[
1,
a,
1/2*a^3 - 1/2*a^2 - 11/2*a + 4,
-1/2*a^3 + 4*a - 1/2,
-2*a^3 + 2*a^2 + 19*a - 17,
a^3 - a^2 - 11*a + 10,
a^3 - a^2 - 9*a + 6,
a^3 - a^2 - 9*a + 8,
3/2*a^3 - 3/2*a^2 - 29/2*a + 10,
-1/2*a^3 + 2*a^2 + 4*a - 21/2,
-2*a^3 + 3*a^2 + 21*a - 21,
1/2*a^3 - a^2 - 3*a + 19/2
]
*], q_expansions := [*
q + q^2 + q^4 + 4*q^5 - 4*q^7 + q^8 - 3*q^9 + 4*q^10 + 4*q^11 - 4*q^13 - 4*q^14 + q^16 + 6*q^17 - 3*q^18 - 6*q^19 + 4*q^20 + 4*q^22 - 4*q^23 + 11*q^25 - 4*q^26 - 4*q^28 + q^32 + 6*q^34 - 16*q^35 - 3*q^36 - 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a^3 - 1/2*a^2 + 9/2*a + 1)*q^5 - a*q^6 + (1/2*a^3 - 4*a + 5/2)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^3 + 1/2*a^2 - 9/2*a - 1)*q^10 + (-a + 1)*q^11 + a*q^12 + (a^3 - 8*a + 3)*q^13 + (-1/2*a^3 + 4*a - 5/2)*q^14 + (-3/2*a^3 + 10*a + 1/2)*q^15 + q^16 + (a^3 - a^2 - 9*a + 6)*q^17 + (-a^2 + 3)*q^18 + (-a^3 - a^2 + 7*a + 6)*q^19 + (-1/2*a^3 - 1/2*a^2 + 9/2*a + 1)*q^20 + (a^3 + 1/2*a^2 - 13/2*a - 1/2)*q^21 + (a - 1)*q^22 + (-1/2*a^3 + 3/2*a^2 + 9/2*a - 7)*q^23 - a*q^24 + (-a^3 + a^2 + 8*a - 4)*q^25 + (-a^3 + 8*a - 3)*q^26 + (a^3 - 6*a)*q^27 + (1/2*a^3 - 4*a + 5/2)*q^28 + (1/2*a^3 - 2*a - 3/2)*q^29 + (3/2*a^3 - 10*a - 1/2)*q^30 + (-a^2 - 3*a + 9)*q^31 - q^32 + (-a^2 + a)*q^33 + (-a^3 + a^2 + 9*a - 6)*q^34 + (-a^2 - a + 2)*q^35 + (a^2 - 3)*q^36 + (-3/2*a^3 + a^2 + 11*a - 17/2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/2*a^3 - 1/2*a^2 - 11/2*a + 4)*q^5 + a*q^6 + (-1/2*a^3 + 4*a - 1/2)*q^7 + q^8 + (a^2 - 3)*q^9 + (1/2*a^3 - 1/2*a^2 - 11/2*a + 4)*q^10 + (-2*a^3 + 2*a^2 + 19*a - 17)*q^11 + a*q^12 + (a^3 - a^2 - 11*a + 10)*q^13 + (-1/2*a^3 + 4*a - 1/2)*q^14 + (1/2*a^3 - a^2 - 5*a + 7/2)*q^15 + q^16 + (a^3 - a^2 - 9*a + 6)*q^17 + (a^2 - 3)*q^18 + (a^3 - a^2 - 9*a + 8)*q^19 + (1/2*a^3 - 1/2*a^2 - 11/2*a + 4)*q^20 + (-a^3 - 1/2*a^2 + 17/2*a - 7/2)*q^21 + (-2*a^3 + 2*a^2 + 19*a - 17)*q^22 + (3/2*a^3 - 3/2*a^2 - 29/2*a + 10)*q^23 + a*q^24 + (-a^3 + a^2 + 10*a - 10)*q^25 + (a^3 - a^2 - 11*a + 10)*q^26 + (a^3 - 6*a)*q^27 + (-1/2*a^3 + 4*a - 1/2)*q^28 + (-1/2*a^3 + 2*a^2 + 4*a - 21/2)*q^29 + (1/2*a^3 - a^2 - 5*a + 7/2)*q^30 + (-2*a^3 + 3*a^2 + 21*a - 21)*q^31 + q^32 + (-2*a^3 + a^2 + 19*a - 14)*q^33 + (a^3 - a^2 - 9*a + 6)*q^34 + (2*a^3 - a^2 - 19*a + 12)*q^35 + (a^2 - 3)*q^36 + (1/2*a^3 - a^2 - 3*a + 19/2)*q^37 + O(q^38)
*]> ;  // time = 33.49 seconds




J[195] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 195, 195, 195, 195, 195, 65, 65, 65, 39, 39, 15 ], new_dimensions := [ 1, 1, 1, 1, 3, 1, 2, 2, 1, 2, 1 ], dimensions := [ 1, 1, 1, 1, 3, 2, 4, 4, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 7, 1, 1, 3, 1, 0, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 11, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 2, -1, 1, 3, -1, -1, -1, -2, -3, -2, -6, 11 ],
[ 2, 1, -1, -1, 5, -1, -7, -6, 3, 2, 2, 7 ],
[ -1, 1, 1, 0, 4, 1, 2, -4, 8, -2, -8, 6 ],
[ 2, 1, 1, -3, -5, 1, 5, 2, -1, 10, -2, -3 ],
[ 0, -3, -3, 1, 1, 3, -1, 6, -7, 18, 6, 13 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^3 - 7*x - 2
], atkin_lehners := [
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ]
], component_group_orders := [
[ 7, 1, 3 ],
[ 3, 7, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 11, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 3, 1, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1 ], eigenvalues := [*
[ 2, -1, 1, 3, -1, -1, -1, -2, -3, -2, -6, 11 ],
[ 2, 1, -1, -1, 5, -1, -7, -6, 3, 2, 2, 7 ],
[ -1, 1, 1, 0, 4, 1, 2, -4, 8, -2, -8, 6 ],
[ 2, 1, 1, -3, -5, 1, 5, 2, -1, 10, -2, -3 ],
[
a,
-1,
-1,
-a^2 + 5,
-a^2 + 5,
1,
a^2 - 2*a - 5,
-2*a + 2,
a^2 - 2*a - 7,
6,
2*a + 2,
-a^2 - 2*a + 9
]
*], q_expansions := [*
q + 2*q^2 - q^3 + 2*q^4 + q^5 - 2*q^6 + 3*q^7 + q^9 + 2*q^10 - q^11 - 2*q^12 - q^13 + 6*q^14 - q^15 - 4*q^16 - q^17 + 2*q^18 - 2*q^19 + 2*q^20 - 3*q^21 - 2*q^22 - 3*q^23 + q^25 - 2*q^26 - q^27 + 6*q^28 - 2*q^29 - 2*q^30 - 6*q^31 - 8*q^32 + q^33 - 2*q^34 + 3*q^35 + 2*q^36 + 11*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 - q^5 + 2*q^6 - q^7 + q^9 - 2*q^10 + 5*q^11 + 2*q^12 - q^13 - 2*q^14 - q^15 - 4*q^16 - 7*q^17 + 2*q^18 - 6*q^19 - 2*q^20 - q^21 + 10*q^22 + 3*q^23 + q^25 - 2*q^26 + q^27 - 2*q^28 + 2*q^29 - 2*q^30 + 2*q^31 - 8*q^32 + 5*q^33 - 14*q^34 + q^35 + 2*q^36 + 7*q^37 + O(q^38),
q - q^2 + q^3 - q^4 + q^5 - q^6 + 3*q^8 + q^9 - q^10 + 4*q^11 - q^12 + q^13 + q^15 - q^16 + 2*q^17 - q^18 - 4*q^19 - q^20 - 4*q^22 + 8*q^23 + 3*q^24 + q^25 - q^26 + q^27 - 2*q^29 - q^30 - 8*q^31 - 5*q^32 + 4*q^33 - 2*q^34 - q^36 + 6*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 + q^5 + 2*q^6 - 3*q^7 + q^9 + 2*q^10 - 5*q^11 + 2*q^12 + q^13 - 6*q^14 + q^15 - 4*q^16 + 5*q^17 + 2*q^18 + 2*q^19 + 2*q^20 - 3*q^21 - 10*q^22 - q^23 + q^25 + 2*q^26 + q^27 - 6*q^28 + 10*q^29 + 2*q^30 - 2*q^31 - 8*q^32 - 5*q^33 + 10*q^34 - 3*q^35 + 2*q^36 - 3*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 - q^5 - a*q^6 + (-a^2 + 5)*q^7 + (3*a + 2)*q^8 + q^9 - a*q^10 + (-a^2 + 5)*q^11 + (-a^2 + 2)*q^12 + q^13 + (-2*a - 2)*q^14 + q^15 + (a^2 + 2*a + 4)*q^16 + (a^2 - 2*a - 5)*q^17 + a*q^18 + (-2*a + 2)*q^19 + (-a^2 + 2)*q^20 + (a^2 - 5)*q^21 + (-2*a - 2)*q^22 + (a^2 - 2*a - 7)*q^23 + (-3*a - 2)*q^24 + q^25 + a*q^26 - q^27 + (-2*a - 10)*q^28 + 6*q^29 + a*q^30 + (2*a + 2)*q^31 + (2*a^2 + 5*a - 2)*q^32 + (a^2 - 5)*q^33 + (-2*a^2 + 2*a + 2)*q^34 + (a^2 - 5)*q^35 + (a^2 - 2)*q^36 + (-a^2 - 2*a + 9)*q^37 + O(q^38)
*]> ;  // time = 47.569 seconds




J[197] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 197, 197, 197 ], new_dimensions := [ 1, 5, 10 ], dimensions := [ 1, 5, 10 ], intersection_graph := [ 0, 5, 1, 5, 0, 1, 1, 1, 0 ], ap_traces := [
[ -2, 0, 0, -3, 4, -2, -8, -3, -3, 7, -10, 7 ],
[ 0, -8, -4, -10, -8, -8, 9, -16, -1, 2, 2, -17 ],
[ 0, 10, 2, 11, 2, 8, -3, 17, -4, -9, 20, 12 ]
], hecke_fields := [
x - 1,
x^5 - 5*x^3 + x^2 + 3*x - 1,
x^10 - 15*x^8 + x^7 + 78*x^6 - 7*x^5 - 165*x^4 + 15*x^3 + 123*x^2 - 9*x - 26
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 49 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 49 ]
], torsion_upper_bounds := [ 1, 1, 49 ], torsion_lower_bounds := [ 1, 1, 49 ], l_ratios := [ 0, 0, 1/49 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ -2, 0, 0, -3, 4, -2, -8, -3, -3, 7, -10, 7 ],
[
a,
-a^4 + 4*a^2 - a - 2,
3*a^4 + a^3 - 14*a^2 - 3*a + 5,
-2*a^4 - 2*a^3 + 9*a^2 + 6*a - 6,
-3*a^4 - 2*a^3 + 15*a^2 + 7*a - 10,
2*a^4 + 3*a^3 - 9*a^2 - 9*a + 3,
-3*a^4 - a^3 + 14*a^2 - 4,
4*a^4 + a^3 - 19*a^2 - a + 5,
-3*a^4 - a^3 + 13*a^2 + 3*a - 4,
-4*a^4 - 3*a^3 + 17*a^2 + 8*a - 5,
a^3 - 6*a + 1,
9*a^4 + 3*a^3 - 43*a^2 - 4*a + 16
],
[
a,
1/4*a^8 + 1/2*a^7 - 5/2*a^6 - 17/4*a^5 + 15/2*a^4 + 9*a^3 - 27/4*a^2 - 7/4*a + 5/2,
-1/2*a^8 + 5*a^6 - 3/2*a^5 - 13*a^4 + 7*a^3 + 11/2*a^2 - 9/2*a + 1,
-a^7 - a^6 + 10*a^5 + 8*a^4 - 27*a^3 - 18*a^2 + 14*a + 9,
-1/2*a^9 + 1/4*a^8 + 13/2*a^7 - 3*a^6 - 109/4*a^5 + 15/2*a^4 + 85/2*a^3 + 3/4*a^2 - 75/4*a - 3/2,
1/2*a^9 + 1/2*a^8 - 7*a^7 - 11/2*a^6 + 67/2*a^5 + 20*a^4 - 121/2*a^3 - 27*a^2 + 53/2*a + 11,
-1/2*a^9 + 1/2*a^8 + 7*a^7 - 11/2*a^6 - 63/2*a^5 + 16*a^4 + 105/2*a^3 - 11*a^2 - 49/2*a + 1,
a^3 + a^2 - 5*a - 1,
a^9 + 1/2*a^8 - 12*a^7 - 4*a^6 + 91/2*a^5 + 11*a^4 - 60*a^3 - 23/2*a^2 + 41/2*a + 2,
1/4*a^9 + a^8 - 7/2*a^7 - 45/4*a^6 + 18*a^5 + 38*a^4 - 143/4*a^3 - 157/4*a^2 + 17*a + 8,
-3/4*a^8 + 1/2*a^7 + 19/2*a^6 - 25/4*a^5 - 75/2*a^4 + 19*a^3 + 205/4*a^2 - 43/4*a - 31/2,
-1/4*a^9 + 9/2*a^7 + 9/4*a^6 - 25*a^5 - 19*a^4 + 195/4*a^3 + 165/4*a^2 - 22*a - 16
]
*], q_expansions := [*
q - 2*q^2 + 2*q^4 - 3*q^7 - 3*q^9 + 4*q^11 - 2*q^13 + 6*q^14 - 4*q^16 - 8*q^17 + 6*q^18 - 3*q^19 - 8*q^22 - 3*q^23 - 5*q^25 + 4*q^26 - 6*q^28 + 7*q^29 - 10*q^31 + 8*q^32 + 16*q^34 - 6*q^36 + 7*q^37 + O(q^38),
q + a*q^2 + (-a^4 + 4*a^2 - a - 2)*q^3 + (a^2 - 2)*q^4 + (3*a^4 + a^3 - 14*a^2 - 3*a + 5)*q^5 + (-a^3 + a - 1)*q^6 + (-2*a^4 - 2*a^3 + 9*a^2 + 6*a - 6)*q^7 + (a^3 - 4*a)*q^8 + (2*a^4 + a^3 - 7*a^2 - 2*a + 2)*q^9 + (a^4 + a^3 - 6*a^2 - 4*a + 3)*q^10 + (-3*a^4 - 2*a^3 + 15*a^2 + 7*a - 10)*q^11 + (a^4 - 7*a^2 + a + 4)*q^12 + (2*a^4 + 3*a^3 - 9*a^2 - 9*a + 3)*q^13 + (-2*a^4 - a^3 + 8*a^2 - 2)*q^14 + (-3*a^4 - a^3 + 15*a^2 + 6*a - 8)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^4 - a^3 + 14*a^2 - 4)*q^17 + (a^4 + 3*a^3 - 4*a^2 - 4*a + 2)*q^18 + (4*a^4 + a^3 - 19*a^2 - a + 5)*q^19 + (-5*a^4 - 3*a^3 + 23*a^2 + 6*a - 9)*q^20 + (5*a^4 + 2*a^3 - 21*a^2 - a + 8)*q^21 + (-2*a^4 + 10*a^2 - a - 3)*q^22 + (-3*a^4 - a^3 + 13*a^2 + 3*a - 4)*q^23 + (-a + 3)*q^24 + (-3*a^4 - 2*a^3 + 14*a^2 + 7*a - 5)*q^25 + (3*a^4 + a^3 - 11*a^2 - 3*a + 2)*q^26 + (-2*a^3 - 5*a^2 + 7*a + 3)*q^27 + (3*a^4 + 2*a^3 - 16*a^2 - 8*a + 10)*q^28 + (-4*a^4 - 3*a^3 + 17*a^2 + 8*a - 5)*q^29 + (-a^4 + 9*a^2 + a - 3)*q^30 + (a^3 - 6*a + 1)*q^31 + (-3*a^3 - a^2 + 9*a + 1)*q^32 + (7*a^4 + a^3 - 34*a^2 - a + 15)*q^33 + (-a^4 - a^3 + 3*a^2 + 5*a - 3)*q^34 + (-a^4 + 3*a^3 + 7*a^2 - 10*a - 3)*q^35 + (-a^4 - a^3 + 9*a^2 + 3*a - 3)*q^36 + (9*a^4 + 3*a^3 - 43*a^2 - 4*a + 16)*q^37 + O(q^38),
q + a*q^2 + (1/4*a^8 + 1/2*a^7 - 5/2*a^6 - 17/4*a^5 + 15/2*a^4 + 9*a^3 - 27/4*a^2 - 7/4*a + 5/2)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^8 + 5*a^6 - 3/2*a^5 - 13*a^4 + 7*a^3 + 11/2*a^2 - 9/2*a + 1)*q^5 + (1/4*a^9 + 1/2*a^8 - 5/2*a^7 - 17/4*a^6 + 15/2*a^5 + 9*a^4 - 27/4*a^3 - 7/4*a^2 + 5/2*a)*q^6 + (-a^7 - a^6 + 10*a^5 + 8*a^4 - 27*a^3 - 18*a^2 + 14*a + 9)*q^7 + (a^3 - 4*a)*q^8 + (-1/4*a^9 - 1/2*a^8 + 7/2*a^7 + 25/4*a^6 - 33/2*a^5 - 26*a^4 + 111/4*a^3 + 159/4*a^2 - 19/2*a - 13)*q^9 + (-1/2*a^9 + 5*a^7 - 3/2*a^6 - 13*a^5 + 7*a^4 + 11/2*a^3 - 9/2*a^2 + a)*q^10 + (-1/2*a^9 + 1/4*a^8 + 13/2*a^7 - 3*a^6 - 109/4*a^5 + 15/2*a^4 + 85/2*a^3 + 3/4*a^2 - 75/4*a - 3/2)*q^11 + (1/2*a^9 + 3/4*a^8 - 11/2*a^7 - 7*a^6 + 77/4*a^5 + 39/2*a^4 - 47/2*a^3 - 59/4*a^2 + 23/4*a + 3/2)*q^12 + (1/2*a^9 + 1/2*a^8 - 7*a^7 - 11/2*a^6 + 67/2*a^5 + 20*a^4 - 121/2*a^3 - 27*a^2 + 53/2*a + 11)*q^13 + (-a^8 - a^7 + 10*a^6 + 8*a^5 - 27*a^4 - 18*a^3 + 14*a^2 + 9*a)*q^14 + (1/2*a^9 - a^8 - 6*a^7 + 23/2*a^6 + 20*a^5 - 36*a^4 - 35/2*a^3 + 57/2*a^2 + a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^9 + 1/2*a^8 + 7*a^7 - 11/2*a^6 - 63/2*a^5 + 16*a^4 + 105/2*a^3 - 11*a^2 - 49/2*a + 1)*q^17 + (-1/2*a^9 - 1/4*a^8 + 13/2*a^7 + 3*a^6 - 111/4*a^5 - 27/2*a^4 + 87/2*a^3 + 85/4*a^2 - 61/4*a - 13/2)*q^18 + (a^3 + a^2 - 5*a - 1)*q^19 + (-3/2*a^8 - a^7 + 16*a^6 + 13/2*a^5 - 51*a^4 - 11*a^3 + 103/2*a^2 + 9/2*a - 15)*q^20 + (1/2*a^9 + 3/2*a^8 - 7*a^7 - 35/2*a^6 + 71/2*a^5 + 65*a^4 - 141/2*a^3 - 85*a^2 + 69/2*a + 29)*q^21 + (1/4*a^9 - a^8 - 5/2*a^7 + 47/4*a^6 + 4*a^5 - 40*a^4 + 33/4*a^3 + 171/4*a^2 - 6*a - 13)*q^22 + (a^9 + 1/2*a^8 - 12*a^7 - 4*a^6 + 91/2*a^5 + 11*a^4 - 60*a^3 - 23/2*a^2 + 41/2*a + 2)*q^23 + (1/4*a^9 + a^8 - 5/2*a^7 - 45/4*a^6 + 8*a^5 + 41*a^4 - 35/4*a^3 - 209/4*a^2 + a + 13)*q^24 + (a^8 + a^7 - 11*a^6 - 8*a^5 + 37*a^4 + 18*a^3 - 39*a^2 - 11*a + 9)*q^25 + (1/2*a^9 + 1/2*a^8 - 6*a^7 - 11/2*a^6 + 47/2*a^5 + 22*a^4 - 69/2*a^3 - 35*a^2 + 31/2*a + 13)*q^26 + (-a^9 - 2*a^8 + 13*a^7 + 23*a^6 - 58*a^5 - 87*a^4 + 97*a^3 + 120*a^2 - 38*a - 40)*q^27 + (-a^9 - a^8 + 12*a^7 + 10*a^6 - 47*a^5 - 34*a^4 + 68*a^3 + 45*a^2 - 28*a - 18)*q^28 + (1/4*a^9 + a^8 - 7/2*a^7 - 45/4*a^6 + 18*a^5 + 38*a^4 - 143/4*a^3 - 157/4*a^2 + 17*a + 8)*q^29 + (-a^9 + 3/2*a^8 + 11*a^7 - 19*a^6 - 65/2*a^5 + 65*a^4 + 21*a^3 - 121/2*a^2 + 1/2*a + 13)*q^30 + (-3/4*a^8 + 1/2*a^7 + 19/2*a^6 - 25/4*a^5 - 75/2*a^4 + 19*a^3 + 205/4*a^2 - 43/4*a - 31/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3/2*a^9 + 1/2*a^8 + 19*a^7 - 13/2*a^6 - 153/2*a^5 + 16*a^4 + 221/2*a^3 + 5*a^2 - 81/2*a - 7)*q^33 + (1/2*a^9 - 1/2*a^8 - 5*a^7 + 15/2*a^6 + 25/2*a^5 - 30*a^4 - 7/2*a^3 + 37*a^2 - 7/2*a - 13)*q^34 + (-a^8 + 11*a^6 - 2*a^5 - 34*a^4 + 9*a^3 + 26*a^2 - 5*a - 4)*q^35 + (1/4*a^9 - 7/2*a^7 - 5/4*a^6 + 16*a^5 + 13*a^4 - 107/4*a^3 - 133/4*a^2 + 8*a + 13)*q^36 + (-1/4*a^9 + 9/2*a^7 + 9/4*a^6 - 25*a^5 - 19*a^4 + 195/4*a^3 + 165/4*a^2 - 22*a - 16)*q^37 + O(q^38)
*]> ;  // time = 2.719 seconds




J[199] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 199, 199, 199 ], new_dimensions := [ 2, 4, 10 ], dimensions := [ 2, 4, 10 ], intersection_graph := [ 0, 1, 71, 1, 0, 1, 71, 1, 0 ], ap_traces := [
[ -1, 4, 6, 0, -6, 2, 2, 2, 0, 8, -4, -6 ],
[ -3, -2, -5, -3, -7, 0, -13, 0, -4, -19, -2, 11 ],
[ 5, -4, -1, -3, 17, 0, 13, -8, 4, 31, -10, -1 ]
], hecke_fields := [
x^2 + x - 1,
x^4 + 3*x^3 - 4*x - 1,
x^10 - 5*x^9 - 4*x^8 + 51*x^7 - 32*x^6 - 154*x^5 + 151*x^4 + 168*x^3 - 168*x^2 - 54*x + 27
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 33 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 33 ]
], torsion_upper_bounds := [ 1, 1, 33 ], torsion_lower_bounds := [ 1, 1, 33 ], l_ratios := [ 1, 0, 1/33 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[
a,
2,
3,
0,
2*a - 2,
-4*a - 1,
-2*a,
6*a + 4,
-6*a - 3,
-4*a + 2,
-2*a - 3,
6*a
],
[
a,
-a^3 - 2*a^2 + a + 1,
a^3 + a^2 - 3*a - 2,
2*a^3 + 5*a^2 - 2*a - 6,
-2*a^3 - 4*a^2 + 3*a + 2,
-2*a^3 - 3*a^2 + 5*a + 3,
-2*a^3 - 3*a^2 + 4*a - 1,
3*a^3 + 5*a^2 - 4*a - 3,
-4*a^2 - 4*a + 5,
3*a^2 + 6*a - 7,
-a^3 - 4*a^2 - a + 4,
-2*a^3 - 4*a^2 + a + 5
],
[
a,
-2/9*a^9 + 7/9*a^8 + 23/9*a^7 - 9*a^6 - 89/9*a^5 + 287/9*a^4 + 151/9*a^3 - 107/3*a^2 - 35/3*a + 3,
4/9*a^9 - 14/9*a^8 - 37/9*a^7 + 16*a^6 + 97/9*a^5 - 430/9*a^4 - 122/9*a^3 + 136/3*a^2 + 37/3*a - 4,
7/9*a^9 - 29/9*a^8 - 58/9*a^7 + 34*a^6 + 109/9*a^5 - 964/9*a^4 - 74/9*a^3 + 337/3*a^2 + 40/3*a - 14,
11/9*a^9 - 34/9*a^8 - 104/9*a^7 + 39*a^6 + 278/9*a^5 - 1070/9*a^4 - 313/9*a^3 + 362/3*a^2 + 68/3*a - 14,
-1/3*a^9 + 4/3*a^8 + 3*a^7 - 44/3*a^6 - 22/3*a^5 + 50*a^4 + 8*a^3 - 181/3*a^2 - 6*a + 13,
-17/9*a^9 + 55/9*a^8 + 164/9*a^7 - 64*a^6 - 473/9*a^5 + 1796/9*a^4 + 658/9*a^3 - 623/3*a^2 - 182/3*a + 29,
1/3*a^8 + 1/3*a^7 - 16/3*a^6 - 3*a^5 + 79/3*a^4 + 20/3*a^3 - 119/3*a^2 - 7*a + 6,
19/9*a^9 - 68/9*a^8 - 175/9*a^7 + 239/3*a^6 + 454/9*a^5 - 2260/9*a^4 - 569/9*a^3 + 797/3*a^2 + 178/3*a - 36,
-17/9*a^9 + 58/9*a^8 + 158/9*a^7 - 202/3*a^6 - 410/9*a^5 + 1880/9*a^4 + 466/9*a^3 - 646/3*a^2 - 128/3*a + 30,
10/9*a^9 - 23/9*a^8 - 112/9*a^7 + 83/3*a^6 + 400/9*a^5 - 820/9*a^4 - 569/9*a^3 + 296/3*a^2 + 103/3*a - 13,
-5/3*a^9 + 17/3*a^8 + 16*a^7 - 181/3*a^6 - 137/3*a^5 + 194*a^4 + 63*a^3 - 635/3*a^2 - 54*a + 30
]
*], q_expansions := [*
q + a*q^2 + 2*q^3 + (-a - 1)*q^4 + 3*q^5 + 2*a*q^6 + (-2*a - 1)*q^8 + q^9 + 3*a*q^10 + (2*a - 2)*q^11 + (-2*a - 2)*q^12 + (-4*a - 1)*q^13 + 6*q^15 + 3*a*q^16 - 2*a*q^17 + a*q^18 + (6*a + 4)*q^19 + (-3*a - 3)*q^20 + (-4*a + 2)*q^22 + (-6*a - 3)*q^23 + (-4*a - 2)*q^24 + 4*q^25 + (3*a - 4)*q^26 - 4*q^27 + (-4*a + 2)*q^29 + 6*a*q^30 + (-2*a - 3)*q^31 + (a + 5)*q^32 + (4*a - 4)*q^33 + (2*a - 2)*q^34 + (-a - 1)*q^36 + 6*a*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + a + 1)*q^3 + (a^2 - 2)*q^4 + (a^3 + a^2 - 3*a - 2)*q^5 + (a^3 + a^2 - 3*a - 1)*q^6 + (2*a^3 + 5*a^2 - 2*a - 6)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + 2*a^2 - a - 3)*q^9 + (-2*a^3 - 3*a^2 + 2*a + 1)*q^10 + (-2*a^3 - 4*a^2 + 3*a + 2)*q^11 + (a^2 + a - 1)*q^12 + (-2*a^3 - 3*a^2 + 5*a + 3)*q^13 + (-a^3 - 2*a^2 + 2*a + 2)*q^14 + (a^2 + 3*a)*q^15 + (-3*a^3 - 6*a^2 + 4*a + 5)*q^16 + (-2*a^3 - 3*a^2 + 4*a - 1)*q^17 + (-a^3 - a^2 + a + 1)*q^18 + (3*a^3 + 5*a^2 - 4*a - 3)*q^19 + (a^3 - a + 2)*q^20 + (a^2 + a - 3)*q^21 + (2*a^3 + 3*a^2 - 6*a - 2)*q^22 + (-4*a^2 - 4*a + 5)*q^23 + (-a^3 - a^2 + 5*a + 2)*q^24 + (2*a^2 + 3*a - 3)*q^25 + (3*a^3 + 5*a^2 - 5*a - 2)*q^26 + (4*a^3 + 8*a^2 - 4*a - 5)*q^27 + (-3*a^3 - 8*a^2 + 2*a + 11)*q^28 + (3*a^2 + 6*a - 7)*q^29 + (a^3 + 3*a^2)*q^30 + (-a^3 - 4*a^2 - a + 4)*q^31 + (a^3 + 4*a^2 + a - 3)*q^32 + (3*a^3 + 5*a^2 - 5*a - 1)*q^33 + (3*a^3 + 4*a^2 - 9*a - 2)*q^34 + (-a^3 - 4*a^2 - a + 6)*q^35 + (-3*a^2 - a + 5)*q^36 + (-2*a^3 - 4*a^2 + a + 5)*q^37 + O(q^38),
q + a*q^2 + (-2/9*a^9 + 7/9*a^8 + 23/9*a^7 - 9*a^6 - 89/9*a^5 + 287/9*a^4 + 151/9*a^3 - 107/3*a^2 - 35/3*a + 3)*q^3 + (a^2 - 2)*q^4 + (4/9*a^9 - 14/9*a^8 - 37/9*a^7 + 16*a^6 + 97/9*a^5 - 430/9*a^4 - 122/9*a^3 + 136/3*a^2 + 37/3*a - 4)*q^5 + (-1/3*a^9 + 5/3*a^8 + 7/3*a^7 - 17*a^6 - 7/3*a^5 + 151/3*a^4 + 5/3*a^3 - 49*a^2 - 9*a + 6)*q^6 + (7/9*a^9 - 29/9*a^8 - 58/9*a^7 + 34*a^6 + 109/9*a^5 - 964/9*a^4 - 74/9*a^3 + 337/3*a^2 + 40/3*a - 14)*q^7 + (a^3 - 4*a)*q^8 + (-8/3*a^9 + 26/3*a^8 + 25*a^7 - 271/3*a^6 - 194/3*a^5 + 279*a^4 + 65*a^3 - 860/3*a^2 - 41*a + 44)*q^9 + (2/3*a^9 - 7/3*a^8 - 20/3*a^7 + 25*a^6 + 62/3*a^5 - 242/3*a^4 - 88/3*a^3 + 87*a^2 + 20*a - 12)*q^10 + (11/9*a^9 - 34/9*a^8 - 104/9*a^7 + 39*a^6 + 278/9*a^5 - 1070/9*a^4 - 313/9*a^3 + 362/3*a^2 + 68/3*a - 14)*q^11 + (4/9*a^9 - 5/9*a^8 - 46/9*a^7 + 5*a^6 + 169/9*a^5 - 106/9*a^4 - 239/9*a^3 + 19/3*a^2 + 34/3*a + 3)*q^12 + (-1/3*a^9 + 4/3*a^8 + 3*a^7 - 44/3*a^6 - 22/3*a^5 + 50*a^4 + 8*a^3 - 181/3*a^2 - 6*a + 13)*q^13 + (2/3*a^9 - 10/3*a^8 - 17/3*a^7 + 37*a^6 + 38/3*a^5 - 377/3*a^4 - 55/3*a^3 + 144*a^2 + 28*a - 21)*q^14 + (14/9*a^9 - 46/9*a^8 - 140/9*a^7 + 167/3*a^6 + 416/9*a^5 - 1664/9*a^4 - 493/9*a^3 + 208*a^2 + 86/3*a - 37)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-17/9*a^9 + 55/9*a^8 + 164/9*a^7 - 64*a^6 - 473/9*a^5 + 1796/9*a^4 + 658/9*a^3 - 623/3*a^2 - 182/3*a + 29)*q^17 + (-14/3*a^9 + 43/3*a^8 + 137/3*a^7 - 150*a^6 - 395/3*a^5 + 1403/3*a^4 + 484/3*a^3 - 489*a^2 - 100*a + 72)*q^18 + (1/3*a^8 + 1/3*a^7 - 16/3*a^6 - 3*a^5 + 79/3*a^4 + 20/3*a^3 - 119/3*a^2 - 7*a + 6)*q^19 + (1/9*a^9 - 8/9*a^8 - 7/9*a^7 + 10*a^6 + 4/9*a^5 - 310/9*a^4 + 19/9*a^3 + 124/3*a^2 - 2/3*a - 10)*q^20 + (34/9*a^9 - 107/9*a^8 - 334/9*a^7 + 377/3*a^6 + 973/9*a^5 - 3580/9*a^4 - 1229/9*a^3 + 1265/3*a^2 + 274/3*a - 61)*q^21 + (7/3*a^9 - 20/3*a^8 - 70/3*a^7 + 70*a^6 + 208/3*a^5 - 658/3*a^4 - 254/3*a^3 + 228*a^2 + 52*a - 33)*q^22 + (19/9*a^9 - 68/9*a^8 - 175/9*a^7 + 239/3*a^6 + 454/9*a^5 - 2260/9*a^4 - 569/9*a^3 + 797/3*a^2 + 178/3*a - 36)*q^23 + (7/3*a^9 - 20/3*a^8 - 67/3*a^7 + 67*a^6 + 184/3*a^5 - 583/3*a^4 - 215/3*a^3 + 184*a^2 + 45*a - 24)*q^24 + (-5/9*a^9 + 25/9*a^8 + 29/9*a^7 - 85/3*a^6 + 34/9*a^5 + 761/9*a^4 - 197/9*a^3 - 256/3*a^2 + 16/3*a + 13)*q^25 + (-1/3*a^9 + 5/3*a^8 + 7/3*a^7 - 18*a^6 - 4/3*a^5 + 175/3*a^4 - 13/3*a^3 - 62*a^2 - 5*a + 9)*q^26 + (-34/9*a^9 + 113/9*a^8 + 340/9*a^7 - 406/3*a^6 - 1045/9*a^5 + 3964/9*a^4 + 1484/9*a^3 - 475*a^2 - 376/3*a + 60)*q^27 + (-14/9*a^9 + 31/9*a^8 + 143/9*a^7 - 34*a^6 - 425/9*a^5 + 857/9*a^4 + 436/9*a^3 - 254/3*a^2 - 35/3*a + 10)*q^28 + (-17/9*a^9 + 58/9*a^8 + 158/9*a^7 - 202/3*a^6 - 410/9*a^5 + 1880/9*a^4 + 466/9*a^3 - 646/3*a^2 - 128/3*a + 30)*q^29 + (8/3*a^9 - 28/3*a^8 - 71/3*a^7 + 96*a^6 + 164/3*a^5 - 869/3*a^4 - 160/3*a^3 + 290*a^2 + 47*a - 42)*q^30 + (10/9*a^9 - 23/9*a^8 - 112/9*a^7 + 83/3*a^6 + 400/9*a^5 - 820/9*a^4 - 569/9*a^3 + 296/3*a^2 + 103/3*a - 13)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (13/9*a^9 - 53/9*a^8 - 103/9*a^7 + 181/3*a^6 + 169/9*a^5 - 1639/9*a^4 - 101/9*a^3 + 189*a^2 + 67/3*a - 32)*q^33 + (-10/3*a^9 + 32/3*a^8 + 97/3*a^7 - 113*a^6 - 274/3*a^5 + 1075/3*a^4 + 329/3*a^3 - 378*a^2 - 73*a + 51)*q^34 + (-7/3*a^9 + 8*a^8 + 65/3*a^7 - 250/3*a^6 - 169/3*a^5 + 770/3*a^4 + 196/3*a^3 - 788/3*a^2 - 53*a + 37)*q^35 + (-11/3*a^9 + 29/3*a^8 + 38*a^7 - 301/3*a^6 - 365/3*a^5 + 308*a^4 + 165*a^3 - 932/3*a^2 - 98*a + 38)*q^36 + (-5/3*a^9 + 17/3*a^8 + 16*a^7 - 181/3*a^6 - 137/3*a^5 + 194*a^4 + 63*a^3 - 635/3*a^2 - 54*a + 30)*q^37 + O(q^38)
*]> ;  // time = 2.789 seconds




J[201] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 201, 201, 201, 201, 201, 67, 67, 67 ], new_dimensions := [ 1, 1, 1, 3, 5, 1, 2, 2 ], dimensions := [ 1, 1, 1, 3, 5, 2, 4, 4 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 5, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 19, 1, 1, 1, 1, 0, 1, 29, 1, 1, 1, 3, 1, 1, 0, 1, 25, 5, 1, 1, 1, 29, 1, 0, 1, 1, 1, 1, 19, 1, 25, 1, 0 ], ap_traces := [
[ 1, -1, -3, -3, 0, 4, 2, -2, -7, -8, -1, -3 ],
[ -2, -1, 0, 0, -6, 4, -7, -5, -1, 1, -4, 3 ],
[ -1, 1, -1, -5, -4, -4, 6, -2, -3, 4, -7, 5 ],
[ 3, -3, 1, 1, 10, -8, 0, -2, 3, 4, 11, -9 ],
[ 0, 5, -3, 7, 0, 10, -5, 5, -2, 3, 9, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^3 - 3*x^2 - x + 5,
x^5 - 8*x^3 + 13*x + 2
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 19, 1 ],
[ 493, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 493, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 17 ], torsion_lower_bounds := [ 1, 1, 1, 1, 17 ], l_ratios := [ 0, 0, 0, 1, 29/17 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -1, -3, -3, 0, 4, 2, -2, -7, -8, -1, -3 ],
[ -2, -1, 0, 0, -6, 4, -7, -5, -1, 1, -4, 3 ],
[ -1, 1, -1, -5, -4, -4, 6, -2, -3, 4, -7, 5 ],
[
a,
-1,
-a^2 + a + 3,
-a^2 + 2*a + 2,
-a^2 + 7,
-a^2 + 1,
3*a^2 - 4*a - 7,
-a^2 - 2*a + 5,
3*a^2 - 5*a - 5,
-4*a^2 + 4*a + 12,
4*a^2 - 6*a - 5,
3*a^2 - 2*a - 12
],
[
a,
1,
1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3,
-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 3/2*a + 1,
a^3 - 5*a,
a^3 - 5*a + 2,
-a^4 - a^3 + 6*a^2 + 3*a - 5,
a^4 - a^3 - 6*a^2 + 5*a + 5,
1/2*a^4 + 1/2*a^3 - 5/2*a^2 - 5/2*a,
a^3 + 3*a^2 - 5*a - 9,
-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 7/2*a - 5,
-1/2*a^4 + 1/2*a^3 + 7/2*a^2 + 1/2*a - 2
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - 3*q^5 - q^6 - 3*q^7 - 3*q^8 + q^9 - 3*q^10 + q^12 + 4*q^13 - 3*q^14 + 3*q^15 - q^16 + 2*q^17 + q^18 - 2*q^19 + 3*q^20 + 3*q^21 - 7*q^23 + 3*q^24 + 4*q^25 + 4*q^26 - q^27 + 3*q^28 - 8*q^29 + 3*q^30 - q^31 + 5*q^32 + 2*q^34 + 9*q^35 - q^36 - 3*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 + 2*q^6 + q^9 - 6*q^11 - 2*q^12 + 4*q^13 - 4*q^16 - 7*q^17 - 2*q^18 - 5*q^19 + 12*q^22 - q^23 - 5*q^25 - 8*q^26 - q^27 + q^29 - 4*q^31 + 8*q^32 + 6*q^33 + 14*q^34 + 2*q^36 + 3*q^37 + O(q^38),
q - q^2 + q^3 - q^4 - q^5 - q^6 - 5*q^7 + 3*q^8 + q^9 + q^10 - 4*q^11 - q^12 - 4*q^13 + 5*q^14 - q^15 - q^16 + 6*q^17 - q^18 - 2*q^19 + q^20 - 5*q^21 + 4*q^22 - 3*q^23 + 3*q^24 - 4*q^25 + 4*q^26 + q^27 + 5*q^28 + 4*q^29 + q^30 - 7*q^31 - 5*q^32 - 4*q^33 - 6*q^34 + 5*q^35 - q^36 + 5*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 3)*q^5 - a*q^6 + (-a^2 + 2*a + 2)*q^7 + (3*a^2 - 3*a - 5)*q^8 + q^9 + (-2*a^2 + 2*a + 5)*q^10 + (-a^2 + 7)*q^11 + (-a^2 + 2)*q^12 + (-a^2 + 1)*q^13 + (-a^2 + a + 5)*q^14 + (a^2 - a - 3)*q^15 + (4*a^2 - 2*a - 11)*q^16 + (3*a^2 - 4*a - 7)*q^17 + a*q^18 + (-a^2 - 2*a + 5)*q^19 + (-2*a^2 + a + 4)*q^20 + (a^2 - 2*a - 2)*q^21 + (-3*a^2 + 6*a + 5)*q^22 + (3*a^2 - 5*a - 5)*q^23 + (-3*a^2 + 3*a + 5)*q^24 + (-a^2 + 2*a - 1)*q^25 + (-3*a^2 + 5)*q^26 - q^27 + q^28 + (-4*a^2 + 4*a + 12)*q^29 + (2*a^2 - 2*a - 5)*q^30 + (4*a^2 - 6*a - 5)*q^31 + (4*a^2 - a - 10)*q^32 + (a^2 - 7)*q^33 + (5*a^2 - 4*a - 15)*q^34 + (-2*a^2 + 3*a + 6)*q^35 + (a^2 - 2)*q^36 + (3*a^2 - 2*a - 12)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3)*q^5 + a*q^6 + (-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 3/2*a + 1)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 7/2*a - 1)*q^10 + (a^3 - 5*a)*q^11 + (a^2 - 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (-1/2*a^4 - 3/2*a^3 + 3/2*a^2 + 15/2*a + 1)*q^14 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - a^3 + 6*a^2 + 3*a - 5)*q^17 + a*q^18 + (a^4 - a^3 - 6*a^2 + 5*a + 5)*q^19 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 1/2*a - 5)*q^20 + (-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 3/2*a + 1)*q^21 + (a^4 - 5*a^2)*q^22 + (1/2*a^4 + 1/2*a^3 - 5/2*a^2 - 5/2*a)*q^23 + (a^3 - 4*a)*q^24 + (-1/2*a^4 + 3/2*a^3 + 5/2*a^2 - 17/2*a)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 + q^27 + (-1/2*a^4 - 3/2*a^3 + 5/2*a^2 + 9/2*a - 1)*q^28 + (a^3 + 3*a^2 - 5*a - 9)*q^29 + (-1/2*a^4 + 1/2*a^3 + 5/2*a^2 - 7/2*a - 1)*q^30 + (-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 7/2*a - 5)*q^31 + (-a - 2)*q^32 + (a^3 - 5*a)*q^33 + (-a^4 - 2*a^3 + 3*a^2 + 8*a + 2)*q^34 + (3/2*a^4 - 1/2*a^3 - 17/2*a^2 + 9/2*a + 3)*q^35 + (a^2 - 2)*q^36 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 + 1/2*a - 2)*q^37 + O(q^38)
*]> ;  // time = 24.319 seconds




J[202] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 202, 202, 202, 101, 101 ], new_dimensions := [ 1, 3, 4, 1, 7 ], dimensions := [ 1, 3, 4, 2, 14 ], intersection_graph := [ 0, 1, 1, 1, 17, 1, 0, 1, 3, 1, 1, 1, 0, 3, 1, 1, 3, 3, 0, 1, 17, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, 2, 1, 4, 0, 5, 1, 6, -5, 0, -8 ],
[ -3, -3, -3, -3, -9, -3, -9, -6, -12, 0, 12, 3 ],
[ 4, -1, 3, 2, 1, 1, 4, -13, 2, 9, -8, -1 ]
], hecke_fields := [
x - 1,
x^3 + 3*x^2 - 1,
x^4 + x^3 - 8*x^2 + x + 8
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 17, 1 ],
[ 3, 1 ],
[ 51, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 51, 1 ]
], torsion_upper_bounds := [ 1, 1, 17 ], torsion_lower_bounds := [ 1, 1, 17 ], l_ratios := [ 1, 0, 3/17 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ -1, 0, 2, 1, 4, 0, 5, 1, 6, -5, 0, -8 ],
[
-1,
a,
a^2 + a - 3,
-3*a^2 - 8*a,
a^2 + 3*a - 3,
3*a^2 + 10*a,
-2*a^2 - 5*a - 2,
-2,
2*a^2 + 6*a - 4,
-4*a^2 - 6*a + 6,
4*a^2 + 8*a,
4*a^2 + 7*a - 4
],
[
1,
a,
a^3 + 2*a^2 - 5*a - 2,
-a^3 - 2*a^2 + 4*a + 3,
-3*a^3 - 8*a^2 + 11*a + 16,
-a^2 - 2*a + 4,
3*a^3 + 9*a^2 - 11*a - 19,
3*a^3 + 7*a^2 - 12*a - 15,
-2*a^3 - 4*a^2 + 10*a + 6,
-a^3 - a^2 + 6*a + 1,
4*a^3 + 12*a^2 - 12*a - 28,
a
]
*], q_expansions := [*
q - q^2 + q^4 + 2*q^5 + q^7 - q^8 - 3*q^9 - 2*q^10 + 4*q^11 - q^14 + q^16 + 5*q^17 + 3*q^18 + q^19 + 2*q^20 - 4*q^22 + 6*q^23 - q^25 + q^28 - 5*q^29 - q^32 - 5*q^34 + 2*q^35 - 3*q^36 - 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a^2 + a - 3)*q^5 - a*q^6 + (-3*a^2 - 8*a)*q^7 - q^8 + (a^2 - 3)*q^9 + (-a^2 - a + 3)*q^10 + (a^2 + 3*a - 3)*q^11 + a*q^12 + (3*a^2 + 10*a)*q^13 + (3*a^2 + 8*a)*q^14 + (-2*a^2 - 3*a + 1)*q^15 + q^16 + (-2*a^2 - 5*a - 2)*q^17 + (-a^2 + 3)*q^18 - 2*q^19 + (a^2 + a - 3)*q^20 + (a^2 - 3)*q^21 + (-a^2 - 3*a + 3)*q^22 + (2*a^2 + 6*a - 4)*q^23 - a*q^24 + (-2*a^2 - 5*a + 3)*q^25 + (-3*a^2 - 10*a)*q^26 + (-3*a^2 - 6*a + 1)*q^27 + (-3*a^2 - 8*a)*q^28 + (-4*a^2 - 6*a + 6)*q^29 + (2*a^2 + 3*a - 1)*q^30 + (4*a^2 + 8*a)*q^31 - q^32 + (-3*a + 1)*q^33 + (2*a^2 + 5*a + 2)*q^34 + (7*a^2 + 21*a - 2)*q^35 + (a^2 - 3)*q^36 + (4*a^2 + 7*a - 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a^3 + 2*a^2 - 5*a - 2)*q^5 + a*q^6 + (-a^3 - 2*a^2 + 4*a + 3)*q^7 + q^8 + (a^2 - 3)*q^9 + (a^3 + 2*a^2 - 5*a - 2)*q^10 + (-3*a^3 - 8*a^2 + 11*a + 16)*q^11 + a*q^12 + (-a^2 - 2*a + 4)*q^13 + (-a^3 - 2*a^2 + 4*a + 3)*q^14 + (a^3 + 3*a^2 - 3*a - 8)*q^15 + q^16 + (3*a^3 + 9*a^2 - 11*a - 19)*q^17 + (a^2 - 3)*q^18 + (3*a^3 + 7*a^2 - 12*a - 15)*q^19 + (a^3 + 2*a^2 - 5*a - 2)*q^20 + (-a^3 - 4*a^2 + 4*a + 8)*q^21 + (-3*a^3 - 8*a^2 + 11*a + 16)*q^22 + (-2*a^3 - 4*a^2 + 10*a + 6)*q^23 + a*q^24 + (-2*a^2 - 3*a + 7)*q^25 + (-a^2 - 2*a + 4)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 - 2*a^2 + 4*a + 3)*q^28 + (-a^3 - a^2 + 6*a + 1)*q^29 + (a^3 + 3*a^2 - 3*a - 8)*q^30 + (4*a^3 + 12*a^2 - 12*a - 28)*q^31 + q^32 + (-5*a^3 - 13*a^2 + 19*a + 24)*q^33 + (3*a^3 + 9*a^2 - 11*a - 19)*q^34 + (a^2 + a - 6)*q^35 + (a^2 - 3)*q^36 + a*q^37 + O(q^38)
*]> ;  // time = 31.339 seconds




J[203] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 203, 203, 203, 203, 203, 203, 203, 29 ], new_dimensions := [ 1, 1, 1, 2, 2, 3, 5, 2 ], dimensions := [ 1, 1, 1, 2, 2, 3, 5, 4 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 9, 0, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 1, 0 ], ap_traces := [
[ 1, 2, 2, 1, -4, -2, 4, 2, 0, -1, -2, 2 ],
[ -2, -1, -4, 1, 2, 4, -2, 5, 9, -1, -8, 8 ],
[ -1, -1, 1, 1, -5, -5, -4, -4, 6, 1, 7, -10 ],
[ -2, -1, 3, -2, -1, 5, 6, 8, -2, 2, -5, 12 ],
[ 4, 2, 0, -2, -4, 8, 0, 2, -2, 2, 4, 0 ],
[ -1, -3, -5, -3, 5, -15, 2, -6, 2, -3, -5, -12 ],
[ 2, -2, 5, 5, 3, 15, -4, -15, -5, -5, 9, 14 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 17,
x^2 - 6*x + 7,
x^3 + x^2 - 3*x - 1,
x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 9*x - 6
], atkin_lehners := [
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 5, 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 5, 1, 1, 1, 1, 3 ], l_ratios := [ 1, 1/5, 0, 1, 1, 0, 1/3 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 1, 0, 1 ], eigenvalues := [*
[ 1, 2, 2, 1, -4, -2, 4, 2, 0, -1, -2, 2 ],
[ -2, -1, -4, 1, 2, 4, -2, 5, 9, -1, -8, 8 ],
[ -1, -1, 1, 1, -5, -5, -4, -4, 6, 1, 7, -10 ],
[
-1,
-1/2*a - 1/2,
-1/2*a + 3/2,
-1,
-1/2*a - 1/2,
1/2*a + 5/2,
a + 3,
4,
-a - 1,
1,
3/2*a - 5/2,
6
],
[
2,
a - 2,
-2*a + 6,
-1,
-2*a + 4,
2*a - 2,
-2*a + 6,
3*a - 8,
2*a - 7,
1,
2,
6*a - 18
],
[
a,
-a^2 - a + 1,
a^2 - 4,
-1,
a^2 - a - 1,
-5,
-3*a^2 - 2*a + 7,
a^2 + 4*a - 3,
4*a + 2,
-1,
2*a^2 + a - 6,
a^2 - 2*a - 7
],
[
a,
-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 7/2*a - 2,
1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3,
1,
-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 7/2*a + 3,
1/2*a^4 + 1/2*a^3 - 7/2*a^2 - 9/2*a + 5,
-a^3 + 5*a,
a^2 - 7,
-a^3 - a^2 + 7*a + 3,
-1,
-3/2*a^4 + 3/2*a^3 + 23/2*a^2 - 21/2*a - 7,
-a^3 + 9*a + 2
]
*], q_expansions := [*
q + q^2 + 2*q^3 - q^4 + 2*q^5 + 2*q^6 + q^7 - 3*q^8 + q^9 + 2*q^10 - 4*q^11 - 2*q^12 - 2*q^13 + q^14 + 4*q^15 - q^16 + 4*q^17 + q^18 + 2*q^19 - 2*q^20 + 2*q^21 - 4*q^22 - 6*q^24 - q^25 - 2*q^26 - 4*q^27 - q^28 - q^29 + 4*q^30 - 2*q^31 + 5*q^32 - 8*q^33 + 4*q^34 + 2*q^35 - q^36 + 2*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 - 4*q^5 + 2*q^6 + q^7 - 2*q^9 + 8*q^10 + 2*q^11 - 2*q^12 + 4*q^13 - 2*q^14 + 4*q^15 - 4*q^16 - 2*q^17 + 4*q^18 + 5*q^19 - 8*q^20 - q^21 - 4*q^22 + 9*q^23 + 11*q^25 - 8*q^26 + 5*q^27 + 2*q^28 - q^29 - 8*q^30 - 8*q^31 + 8*q^32 - 2*q^33 + 4*q^34 - 4*q^35 - 4*q^36 + 8*q^37 + O(q^38),
q - q^2 - q^3 - q^4 + q^5 + q^6 + q^7 + 3*q^8 - 2*q^9 - q^10 - 5*q^11 + q^12 - 5*q^13 - q^14 - q^15 - q^16 - 4*q^17 + 2*q^18 - 4*q^19 - q^20 - q^21 + 5*q^22 + 6*q^23 - 3*q^24 - 4*q^25 + 5*q^26 + 5*q^27 - q^28 + q^29 + q^30 + 7*q^31 - 5*q^32 + 5*q^33 + 4*q^34 + q^35 + 2*q^36 - 10*q^37 + O(q^38),
q - q^2 + (-1/2*a - 1/2)*q^3 - q^4 + (-1/2*a + 3/2)*q^5 + (1/2*a + 1/2)*q^6 - q^7 + 3*q^8 + (1/2*a + 3/2)*q^9 + (1/2*a - 3/2)*q^10 + (-1/2*a - 1/2)*q^11 + (1/2*a + 1/2)*q^12 + (1/2*a + 5/2)*q^13 + q^14 + (-1/2*a + 7/2)*q^15 - q^16 + (a + 3)*q^17 + (-1/2*a - 3/2)*q^18 + 4*q^19 + (1/2*a - 3/2)*q^20 + (1/2*a + 1/2)*q^21 + (1/2*a + 1/2)*q^22 + (-a - 1)*q^23 + (-3/2*a - 3/2)*q^24 + (-3/2*a + 3/2)*q^25 + (-1/2*a - 5/2)*q^26 + (1/2*a - 7/2)*q^27 + q^28 + q^29 + (1/2*a - 7/2)*q^30 + (3/2*a - 5/2)*q^31 - 5*q^32 + (1/2*a + 9/2)*q^33 + (-a - 3)*q^34 + (1/2*a - 3/2)*q^35 + (-1/2*a - 3/2)*q^36 + 6*q^37 + O(q^38),
q + 2*q^2 + (a - 2)*q^3 + 2*q^4 + (-2*a + 6)*q^5 + (2*a - 4)*q^6 - q^7 + (2*a - 6)*q^9 + (-4*a + 12)*q^10 + (-2*a + 4)*q^11 + (2*a - 4)*q^12 + (2*a - 2)*q^13 - 2*q^14 + (-2*a + 2)*q^15 - 4*q^16 + (-2*a + 6)*q^17 + (4*a - 12)*q^18 + (3*a - 8)*q^19 + (-4*a + 12)*q^20 + (-a + 2)*q^21 + (-4*a + 8)*q^22 + (2*a - 7)*q^23 + 3*q^25 + (4*a - 4)*q^26 + (-a + 4)*q^27 - 2*q^28 + q^29 + (-4*a + 4)*q^30 + 2*q^31 - 8*q^32 + (-4*a + 6)*q^33 + (-4*a + 12)*q^34 + (2*a - 6)*q^35 + (4*a - 12)*q^36 + (6*a - 18)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 - 4)*q^5 + (-2*a - 1)*q^6 - q^7 + (-a^2 - a + 1)*q^8 + (a^2 + 2*a - 1)*q^9 + (-a^2 - a + 1)*q^10 + (a^2 - a - 1)*q^11 + (a - 2)*q^12 - 5*q^13 - a*q^14 + (2*a^2 + 3*a - 4)*q^15 + (-2*a^2 - 2*a + 3)*q^16 + (-3*a^2 - 2*a + 7)*q^17 + (a^2 + 2*a + 1)*q^18 + (a^2 + 4*a - 3)*q^19 + (-2*a^2 - 2*a + 7)*q^20 + (a^2 + a - 1)*q^21 + (-2*a^2 + 2*a + 1)*q^22 + (4*a + 2)*q^23 + (a^2 + 2*a + 2)*q^24 + (-4*a^2 - 2*a + 10)*q^25 - 5*a*q^26 + (2*a^2 - a - 6)*q^27 + (-a^2 + 2)*q^28 - q^29 + (a^2 + 2*a + 2)*q^30 + (2*a^2 + a - 6)*q^31 + (2*a^2 - a - 4)*q^32 + (-a^2 + 2*a)*q^33 + (a^2 - 2*a - 3)*q^34 + (-a^2 + 4)*q^35 + (-a^2 + 3)*q^36 + (a^2 - 2*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 7/2*a - 2)*q^3 + (a^2 - 2)*q^4 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3)*q^5 + (-1/2*a^4 - 1/2*a^3 + 7/2*a^2 + 5/2*a - 3)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 5/2*a + 7)*q^9 + (1/2*a^4 + 1/2*a^3 - 9/2*a^2 - 3/2*a + 3)*q^10 + (-1/2*a^4 - 1/2*a^3 + 5/2*a^2 + 7/2*a + 3)*q^11 + (-1/2*a^4 - 3/2*a^3 + 5/2*a^2 + 17/2*a + 1)*q^12 + (1/2*a^4 + 1/2*a^3 - 7/2*a^2 - 9/2*a + 5)*q^13 + a*q^14 + (-1/2*a^4 + 1/2*a^3 + 9/2*a^2 - 7/2*a - 9)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^3 + 5*a)*q^17 + (3/2*a^4 - 1/2*a^3 - 19/2*a^2 + 5/2*a + 3)*q^18 + (a^2 - 7)*q^19 + (1/2*a^4 + 1/2*a^3 - 3/2*a^2 - 13/2*a - 3)*q^20 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 7/2*a - 2)*q^21 + (-3/2*a^4 - 3/2*a^3 + 21/2*a^2 + 15/2*a - 3)*q^22 + (-a^3 - a^2 + 7*a + 3)*q^23 + (-3/2*a^4 - 1/2*a^3 + 17/2*a^2 + 1/2*a + 3)*q^24 + (1/2*a^4 - 3/2*a^3 - 7/2*a^2 + 15/2*a + 4)*q^25 + (3/2*a^4 + 1/2*a^3 - 23/2*a^2 + 1/2*a + 3)*q^26 + (-1/2*a^4 + 3/2*a^3 + 7/2*a^2 - 21/2*a - 2)*q^27 + (a^2 - 2)*q^28 - q^29 + (-1/2*a^4 + 1/2*a^3 + 7/2*a^2 - 9/2*a - 3)*q^30 + (-3/2*a^4 + 3/2*a^3 + 23/2*a^2 - 21/2*a - 7)*q^31 + (2*a^4 - 14*a^2 + 3*a + 6)*q^32 + (-1/2*a^4 + 5/2*a^3 + 11/2*a^2 - 29/2*a - 9)*q^33 + (-a^4 + 5*a^2)*q^34 + (1/2*a^4 - 1/2*a^3 - 7/2*a^2 + 5/2*a + 3)*q^35 + (3/2*a^4 + 3/2*a^3 - 19/2*a^2 - 11/2*a - 5)*q^36 + (-a^3 + 9*a + 2)*q^37 + O(q^38)
*]> ;  // time = 24.459 seconds




J[205] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 205, 205, 205, 205, 205, 205, 205, 41 ], new_dimensions := [ 1, 1, 1, 2, 2, 3, 3, 3 ], dimensions := [ 1, 1, 1, 2, 2, 3, 3, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 13, 1, 1, 1, 1, 1, 0, 1, 31, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 13, 31, 1, 0 ], ap_traces := [
[ -1, 2, -1, 2, 6, 2, 2, -6, -4, 10, 0, -6 ],
[ 1, 2, 1, 2, 0, -4, 4, 0, -8, 2, 0, -6 ],
[ -1, 0, 1, -4, 0, -2, -6, 0, -8, 6, 0, 6 ],
[ -1, -2, -2, 3, -8, -3, 0, -5, -6, -3, -7, 1 ],
[ -1, -6, 2, -3, -6, -1, -4, -3, 4, -5, -3, -3 ],
[ 2, 2, -3, -9, 4, -3, 4, 15, 6, 1, 1, -17 ],
[ 0, 2, 3, 1, 4, 1, -2, -5, 20, -13, -11, 11 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + x - 1,
x^2 + x - 3,
x^3 - 2*x^2 - 4*x + 7,
x^3 - 4*x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 13, 1 ],
[ 31, 1 ],
[ 7, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 13, 1 ],
[ 1, 1 ],
[ 7, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 7 ], l_ratios := [ 1, 1, 0, 0, 0, 1, 1/7 ], analytic_sha_upper_bounds := [ 1, 1, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 2, -1, 2, 6, 2, 2, -6, -4, 10, 0, -6 ],
[ 1, 2, 1, 2, 0, -4, 4, 0, -8, 2, 0, -6 ],
[ -1, 0, 1, -4, 0, -2, -6, 0, -8, 6, 0, 6 ],
[
a,
-1,
-1,
-3*a,
2*a - 3,
3*a,
2*a + 1,
-3*a - 4,
-3,
-a - 2,
5*a - 1,
-a
],
[
a,
-3,
1,
-a - 2,
-3,
-3*a - 2,
2*a - 1,
3*a,
2*a + 3,
a - 2,
-3*a - 3,
3*a
],
[
a,
-a^2 + a + 4,
-1,
a^2 - 7,
-a^2 - a + 6,
-a^2 + 3,
3*a^2 - a - 10,
a^2 + 1,
a^2 - 3*a,
a^2 + 2*a - 5,
-2*a^2 - a + 9,
-a^2 + 2*a - 3
],
[
a,
a^2 - a - 2,
1,
-a^2 + 3,
-a^2 + a + 4,
-a^2 + 2*a + 3,
-a^2 - a + 2,
-a^2 + 1,
a^2 - a + 4,
a^2 - 7,
2*a^2 + 3*a - 9,
a^2 + 1
]
*], q_expansions := [*
q - q^2 + 2*q^3 - q^4 - q^5 - 2*q^6 + 2*q^7 + 3*q^8 + q^9 + q^10 + 6*q^11 - 2*q^12 + 2*q^13 - 2*q^14 - 2*q^15 - q^16 + 2*q^17 - q^18 - 6*q^19 + q^20 + 4*q^21 - 6*q^22 - 4*q^23 + 6*q^24 + q^25 - 2*q^26 - 4*q^27 - 2*q^28 + 10*q^29 + 2*q^30 - 5*q^32 + 12*q^33 - 2*q^34 - 2*q^35 - q^36 - 6*q^37 + O(q^38),
q + q^2 + 2*q^3 - q^4 + q^5 + 2*q^6 + 2*q^7 - 3*q^8 + q^9 + q^10 - 2*q^12 - 4*q^13 + 2*q^14 + 2*q^15 - q^16 + 4*q^17 + q^18 - q^20 + 4*q^21 - 8*q^23 - 6*q^24 + q^25 - 4*q^26 - 4*q^27 - 2*q^28 + 2*q^29 + 2*q^30 + 5*q^32 + 4*q^34 + 2*q^35 - q^36 - 6*q^37 + O(q^38),
q - q^2 - q^4 + q^5 - 4*q^7 + 3*q^8 - 3*q^9 - q^10 - 2*q^13 + 4*q^14 - q^16 - 6*q^17 + 3*q^18 - q^20 - 8*q^23 + q^25 + 2*q^26 + 4*q^28 + 6*q^29 - 5*q^32 + 6*q^34 - 4*q^35 + 3*q^36 + 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^4 - q^5 - a*q^6 - 3*a*q^7 + (-2*a - 1)*q^8 - 2*q^9 - a*q^10 + (2*a - 3)*q^11 + (a + 1)*q^12 + 3*a*q^13 + (3*a - 3)*q^14 + q^15 + 3*a*q^16 + (2*a + 1)*q^17 - 2*a*q^18 + (-3*a - 4)*q^19 + (a + 1)*q^20 + 3*a*q^21 + (-5*a + 2)*q^22 - 3*q^23 + (2*a + 1)*q^24 + q^25 + (-3*a + 3)*q^26 + 5*q^27 + 3*q^28 + (-a - 2)*q^29 + a*q^30 + (5*a - 1)*q^31 + (a + 5)*q^32 + (-2*a + 3)*q^33 + (-a + 2)*q^34 + 3*a*q^35 + (2*a + 2)*q^36 - a*q^37 + O(q^38),
q + a*q^2 - 3*q^3 + (-a + 1)*q^4 + q^5 - 3*a*q^6 + (-a - 2)*q^7 - 3*q^8 + 6*q^9 + a*q^10 - 3*q^11 + (3*a - 3)*q^12 + (-3*a - 2)*q^13 + (-a - 3)*q^14 - 3*q^15 + (-a - 2)*q^16 + (2*a - 1)*q^17 + 6*a*q^18 + 3*a*q^19 + (-a + 1)*q^20 + (3*a + 6)*q^21 - 3*a*q^22 + (2*a + 3)*q^23 + 9*q^24 + q^25 + (a - 9)*q^26 - 9*q^27 + q^28 + (a - 2)*q^29 - 3*a*q^30 + (-3*a - 3)*q^31 + (-a + 3)*q^32 + 9*q^33 + (-3*a + 6)*q^34 + (-a - 2)*q^35 + (-6*a + 6)*q^36 + 3*a*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 4)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a^2 + 7)*q^6 + (a^2 - 7)*q^7 + (2*a^2 - 7)*q^8 + (-3*a^2 + a + 13)*q^9 - a*q^10 + (-a^2 - a + 6)*q^11 + (a - 1)*q^12 + (-a^2 + 3)*q^13 + (2*a^2 - 3*a - 7)*q^14 + (a^2 - a - 4)*q^15 + (2*a^2 + a - 10)*q^16 + (3*a^2 - a - 10)*q^17 + (-5*a^2 + a + 21)*q^18 + (a^2 + 1)*q^19 + (-a^2 + 2)*q^20 + (5*a^2 - 4*a - 21)*q^21 + (-3*a^2 + 2*a + 7)*q^22 + (a^2 - 3*a)*q^23 + (3*a^2 - a - 14)*q^24 + q^25 + (-2*a^2 - a + 7)*q^26 + (-5*a^2 + a + 26)*q^27 + (-a^2 + a)*q^28 + (a^2 + 2*a - 5)*q^29 + (a^2 - 7)*q^30 + (-2*a^2 - a + 9)*q^31 + (a^2 - 2*a)*q^32 + (-3*a^2 + 3*a + 10)*q^33 + (5*a^2 + 2*a - 21)*q^34 + (-a^2 + 7)*q^35 + (-3*a^2 - a + 9)*q^36 + (-a^2 + 2*a - 3)*q^37 + O(q^38),
q + a*q^2 + (a^2 - a - 2)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^2 + 2*a + 1)*q^6 + (-a^2 + 3)*q^7 + q^8 + (a^2 - 3*a - 1)*q^9 + a*q^10 + (-a^2 + a + 4)*q^11 + (-a + 3)*q^12 + (-a^2 + 2*a + 3)*q^13 + (-a - 1)*q^14 + (a^2 - a - 2)*q^15 + (-2*a^2 + a + 4)*q^16 + (-a^2 - a + 2)*q^17 + (-3*a^2 + 3*a + 1)*q^18 + (-a^2 + 1)*q^19 + (a^2 - 2)*q^20 + (a^2 - 5)*q^21 + (a^2 - 1)*q^22 + (a^2 - a + 4)*q^23 + (a^2 - a - 2)*q^24 + q^25 + (2*a^2 - a - 1)*q^26 + (a^2 - 5*a + 4)*q^27 + (a^2 - a - 6)*q^28 + (a^2 - 7)*q^29 + (-a^2 + 2*a + 1)*q^30 + (2*a^2 + 3*a - 9)*q^31 + (a^2 - 4*a - 4)*q^32 + (a^2 + a - 6)*q^33 + (-a^2 - 2*a - 1)*q^34 + (-a^2 + 3)*q^35 + (a^2 - 5*a - 1)*q^36 + (a^2 + 1)*q^37 + O(q^38)
*]> ;  // time = 23.091 seconds




J[206] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 206, 206, 206, 206, 103, 103 ], new_dimensions := [ 1, 2, 2, 4, 2, 6 ], dimensions := [ 1, 2, 2, 4, 4, 12 ], intersection_graph := [ 0, 5, 3, 1, 1, 1, 5, 0, 1, 1, 1, 67, 3, 1, 0, 1, 1, 17, 1, 1, 1, 0, 19, 1, 1, 1, 1, 19, 0, 1, 1, 67, 17, 1, 1, 0 ], ap_traces := [
[ -1, 2, 4, 0, -6, -2, 2, -4, 0, -6, 8, 8 ],
[ -2, 1, 1, -3, 8, 2, -3, 12, -7, -12, 16, -7 ],
[ -2, -3, -5, 5, 0, 6, 5, 4, -3, 12, -8, 1 ],
[ 4, 2, 0, 2, 4, 0, -14, 0, 2, 0, 8, 10 ]
], hecke_fields := [
x - 1,
x^2 - x - 7,
x^2 + 3*x - 1,
x^4 - 2*x^3 - 5*x^2 + 12*x - 5
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 67, 1 ],
[ 51, 3 ],
[ 247, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 247, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 13 ], torsion_lower_bounds := [ 1, 1, 3, 13 ], l_ratios := [ 1, 1, 1/3, 19/13 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1 ], eigenvalues := [*
[ -1, 2, 4, 0, -6, -2, 2, -4, 0, -6, 8, 8 ],
[
-1,
a,
-a + 1,
a - 2,
4,
-2*a + 2,
-a - 1,
6,
-a - 3,
-6,
8,
a - 4
],
[
-1,
a,
a - 1,
a + 4,
0,
2*a + 6,
-a + 1,
2,
3*a + 3,
6,
-4,
-3*a - 4
],
[
1,
a,
-a^3 + 5*a - 2,
2*a^3 - a^2 - 12*a + 9,
-2*a^3 + 2*a^2 + 10*a - 10,
2*a^3 - 10*a + 4,
2*a^3 - 3*a^2 - 12*a + 12,
-2*a^2 - 2*a + 8,
-4*a^3 + 3*a^2 + 24*a - 20,
-4*a^3 + 2*a^2 + 22*a - 16,
-4*a^3 + 2*a^2 + 22*a - 14,
2*a^3 + 2*a^2 - 11*a
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 + 4*q^5 - 2*q^6 - q^8 + q^9 - 4*q^10 - 6*q^11 + 2*q^12 - 2*q^13 + 8*q^15 + q^16 + 2*q^17 - q^18 - 4*q^19 + 4*q^20 + 6*q^22 - 2*q^24 + 11*q^25 + 2*q^26 - 4*q^27 - 6*q^29 - 8*q^30 + 8*q^31 - q^32 - 12*q^33 - 2*q^34 + q^36 + 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a + 1)*q^5 - a*q^6 + (a - 2)*q^7 - q^8 + (a + 4)*q^9 + (a - 1)*q^10 + 4*q^11 + a*q^12 + (-2*a + 2)*q^13 + (-a + 2)*q^14 - 7*q^15 + q^16 + (-a - 1)*q^17 + (-a - 4)*q^18 + 6*q^19 + (-a + 1)*q^20 + (-a + 7)*q^21 - 4*q^22 + (-a - 3)*q^23 - a*q^24 + (-a + 3)*q^25 + (2*a - 2)*q^26 + (2*a + 7)*q^27 + (a - 2)*q^28 - 6*q^29 + 7*q^30 + 8*q^31 - q^32 + 4*a*q^33 + (a + 1)*q^34 + (2*a - 9)*q^35 + (a + 4)*q^36 + (a - 4)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a - 1)*q^5 - a*q^6 + (a + 4)*q^7 - q^8 + (-3*a - 2)*q^9 + (-a + 1)*q^10 + a*q^12 + (2*a + 6)*q^13 + (-a - 4)*q^14 + (-4*a + 1)*q^15 + q^16 + (-a + 1)*q^17 + (3*a + 2)*q^18 + 2*q^19 + (a - 1)*q^20 + (a + 1)*q^21 + (3*a + 3)*q^23 - a*q^24 + (-5*a - 3)*q^25 + (-2*a - 6)*q^26 + (4*a - 3)*q^27 + (a + 4)*q^28 + 6*q^29 + (4*a - 1)*q^30 - 4*q^31 - q^32 + (a - 1)*q^34 - 3*q^35 + (-3*a - 2)*q^36 + (-3*a - 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^3 + 5*a - 2)*q^5 + a*q^6 + (2*a^3 - a^2 - 12*a + 9)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^3 + 5*a - 2)*q^10 + (-2*a^3 + 2*a^2 + 10*a - 10)*q^11 + a*q^12 + (2*a^3 - 10*a + 4)*q^13 + (2*a^3 - a^2 - 12*a + 9)*q^14 + (-2*a^3 + 10*a - 5)*q^15 + q^16 + (2*a^3 - 3*a^2 - 12*a + 12)*q^17 + (a^2 - 3)*q^18 + (-2*a^2 - 2*a + 8)*q^19 + (-a^3 + 5*a - 2)*q^20 + (3*a^3 - 2*a^2 - 15*a + 10)*q^21 + (-2*a^3 + 2*a^2 + 10*a - 10)*q^22 + (-4*a^3 + 3*a^2 + 24*a - 20)*q^23 + a*q^24 + (a^2 + 2*a - 6)*q^25 + (2*a^3 - 10*a + 4)*q^26 + (a^3 - 6*a)*q^27 + (2*a^3 - a^2 - 12*a + 9)*q^28 + (-4*a^3 + 2*a^2 + 22*a - 16)*q^29 + (-2*a^3 + 10*a - 5)*q^30 + (-4*a^3 + 2*a^2 + 22*a - 14)*q^31 + q^32 + (-2*a^3 + 14*a - 10)*q^33 + (2*a^3 - 3*a^2 - 12*a + 12)*q^34 + (3*a^3 - 2*a^2 - 18*a + 12)*q^35 + (a^2 - 3)*q^36 + (2*a^3 + 2*a^2 - 11*a)*q^37 + O(q^38)
*]> ;  // time = 34.639 seconds




J[209] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 209, 209, 209, 209, 19, 11 ], new_dimensions := [ 1, 2, 5, 7, 1, 1 ], dimensions := [ 1, 2, 5, 7, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 0, 15, 1, 3, 1, 1, 15, 0, 1, 1, 1, 5, 1, 1, 0 ], ap_traces := [
[ 0, 1, -3, -4, 1, 2, 0, 1, 3, -6, -7, -7 ],
[ 0, -2, -2, -4, -2, -4, 4, -2, -6, -4, -10, 6 ],
[ 2, 1, -5, 6, 5, 4, -4, -5, 3, 10, 11, 1 ],
[ -1, 2, 2, 10, -7, -4, 2, 7, 10, -18, 24, 0 ]
], hecke_fields := [
x - 1,
x^2 - 2,
x^5 - 2*x^4 - 6*x^3 + 10*x^2 + 5*x - 4,
x^7 + x^6 - 14*x^5 - 10*x^4 + 59*x^3 + 27*x^2 - 66*x - 30
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ],
[ 5, 5 ],
[ 45, 3 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ],
[ 5, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 3, 1, 5, 3 ], torsion_lower_bounds := [ 1, 1, 5, 3 ], l_ratios := [ 0, 0, 1/5, 1/3 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ 0, 1, -3, -4, 1, 2, 0, 1, 3, -6, -7, -7 ],
[
a,
-a - 1,
-1,
-a - 2,
-1,
3*a - 2,
a + 2,
-1,
-3,
-3*a - 2,
-a - 5,
5*a + 3
],
[
a,
1/2*a^4 - a^3 - 5/2*a^2 + 4*a + 1,
-1/2*a^3 + 7/2*a - 1,
-1/2*a^3 + 3/2*a + 2,
1,
-1/2*a^4 + 7/2*a^2 - 2,
a^4 - a^3 - 5*a^2 + 3*a,
-1,
-a^4 + a^3 + 8*a^2 - 5*a - 9,
3/2*a^4 - a^3 - 17/2*a^2 + 2*a + 6,
-1/2*a^4 + 2*a^3 + 5/2*a^2 - 10*a + 1,
a^4 - 8*a^2 + 9
],
[
a,
-1/2*a^4 + 7/2*a^2 - a - 2,
1/2*a^5 - 9/2*a^3 + 7*a + 3,
-1/4*a^6 + 3*a^4 - 37/4*a^2 + 13/2,
-1,
-1/4*a^6 - 1/2*a^5 + 5/2*a^4 + 9/2*a^3 - 27/4*a^2 - 9*a + 7/2,
a^4 - a^3 - 9*a^2 + 7*a + 12,
1,
1/2*a^6 - 5*a^4 + 21/2*a^2 + 2*a,
-1/2*a^4 + 9/2*a^2 - a - 9,
1/4*a^6 + 1/2*a^5 - 5/2*a^4 - 9/2*a^3 + 23/4*a^2 + 9*a + 7/2,
-a^5 - a^4 + 10*a^3 + 8*a^2 - 21*a - 13
]
*], q_expansions := [*
q + q^3 - 2*q^4 - 3*q^5 - 4*q^7 - 2*q^9 + q^11 - 2*q^12 + 2*q^13 - 3*q^15 + 4*q^16 + q^19 + 6*q^20 - 4*q^21 + 3*q^23 + 4*q^25 - 5*q^27 + 8*q^28 - 6*q^29 - 7*q^31 + q^33 + 12*q^35 + 4*q^36 - 7*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 - q^5 + (-a - 2)*q^6 + (-a - 2)*q^7 - 2*a*q^8 + 2*a*q^9 - a*q^10 - q^11 + (3*a - 2)*q^13 + (-2*a - 2)*q^14 + (a + 1)*q^15 - 4*q^16 + (a + 2)*q^17 + 4*q^18 - q^19 + (3*a + 4)*q^21 - a*q^22 - 3*q^23 + (2*a + 4)*q^24 - 4*q^25 + (-2*a + 6)*q^26 + (a - 1)*q^27 + (-3*a - 2)*q^29 + (a + 2)*q^30 + (-a - 5)*q^31 + (a + 1)*q^33 + (2*a + 2)*q^34 + (a + 2)*q^35 + (5*a + 3)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^4 - a^3 - 5/2*a^2 + 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (-1/2*a^3 + 7/2*a - 1)*q^5 + (1/2*a^3 - a^2 - 3/2*a + 2)*q^6 + (-1/2*a^3 + 3/2*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^3 - a^2 - 7/2*a + 4)*q^9 + (-1/2*a^4 + 7/2*a^2 - a)*q^10 + q^11 + (-1/2*a^4 + a^3 + 7/2*a^2 - 6*a - 2)*q^12 + (-1/2*a^4 + 7/2*a^2 - 2)*q^13 + (-1/2*a^4 + 3/2*a^2 + 2*a)*q^14 + (-1/2*a^4 + 2*a^3 + 1/2*a^2 - 8*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - a^3 - 5*a^2 + 3*a)*q^17 + (1/2*a^4 - a^3 - 7/2*a^2 + 4*a)*q^18 - q^19 + (-a^4 + 3/2*a^3 + 4*a^2 - 9/2*a)*q^20 + (a^4 - 2*a^3 - 5*a^2 + 7*a + 4)*q^21 + a*q^22 + (-a^4 + a^3 + 8*a^2 - 5*a - 9)*q^23 + (-1/2*a^3 + a^2 + 7/2*a - 6)*q^24 + (-a^4 + 3/2*a^3 + 6*a^2 - 17/2*a - 2)*q^25 + (-a^4 + 1/2*a^3 + 5*a^2 + 1/2*a - 2)*q^26 + (-a^3 + a^2 + 6*a - 5)*q^27 + (-a^4 - 1/2*a^3 + 7*a^2 - 1/2*a - 6)*q^28 + (3/2*a^4 - a^3 - 17/2*a^2 + 2*a + 6)*q^29 + (a^4 - 5/2*a^3 - 3*a^2 + 15/2*a - 2)*q^30 + (-1/2*a^4 + 2*a^3 + 5/2*a^2 - 10*a + 1)*q^31 + (2*a^4 - 2*a^3 - 10*a^2 + 7*a + 4)*q^32 + (1/2*a^4 - a^3 - 5/2*a^2 + 4*a + 1)*q^33 + (a^4 + a^3 - 7*a^2 - 5*a + 4)*q^34 + (-a^2 + 4*a)*q^35 + (-3/2*a^3 + a^2 + 9/2*a - 6)*q^36 + (a^4 - 8*a^2 + 9)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^4 + 7/2*a^2 - a - 2)*q^3 + (a^2 - 2)*q^4 + (1/2*a^5 - 9/2*a^3 + 7*a + 3)*q^5 + (-1/2*a^5 + 7/2*a^3 - a^2 - 2*a)*q^6 + (-1/4*a^6 + 3*a^4 - 37/4*a^2 + 13/2)*q^7 + (a^3 - 4*a)*q^8 + (1/4*a^6 - 3*a^4 + a^3 + 41/4*a^2 - 5*a - 13/2)*q^9 + (1/2*a^6 - 9/2*a^4 + 7*a^2 + 3*a)*q^10 - q^11 + (-1/2*a^6 + 9/2*a^4 - a^3 - 9*a^2 + 2*a + 4)*q^12 + (-1/4*a^6 - 1/2*a^5 + 5/2*a^4 + 9/2*a^3 - 27/4*a^2 - 9*a + 7/2)*q^13 + (1/4*a^6 - 1/2*a^5 - 5/2*a^4 + 11/2*a^3 + 27/4*a^2 - 10*a - 15/2)*q^14 + (1/4*a^6 + 1/2*a^5 - 5/2*a^4 - 9/2*a^3 + 23/4*a^2 + 7*a + 3/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - a^3 - 9*a^2 + 7*a + 12)*q^17 + (-1/4*a^6 + 1/2*a^5 + 7/2*a^4 - 9/2*a^3 - 47/4*a^2 + 10*a + 15/2)*q^18 + q^19 + (-1/2*a^6 + 3/2*a^5 + 5*a^4 - 27/2*a^3 - 21/2*a^2 + 19*a + 9)*q^20 + (-1/4*a^6 - 1/2*a^5 + 2*a^4 + 7/2*a^3 - 9/4*a^2 - 5*a - 11/2)*q^21 - a*q^22 + (1/2*a^6 - 5*a^4 + 21/2*a^2 + 2*a)*q^23 + (1/2*a^6 - 3/2*a^5 - 6*a^4 + 27/2*a^3 + 35/2*a^2 - 25*a - 15)*q^24 + (-1/4*a^6 + 2*a^4 - a^3 - 5/4*a^2 + 3*a - 7/2)*q^25 + (-1/4*a^6 - a^5 + 2*a^4 + 8*a^3 - 9/4*a^2 - 13*a - 15/2)*q^26 + (1/4*a^6 - 1/2*a^5 - 3*a^4 + 11/2*a^3 + 33/4*a^2 - 15*a - 7/2)*q^27 + (-1/4*a^6 + a^5 + 2*a^4 - 8*a^3 + 7/4*a^2 + 9*a - 11/2)*q^28 + (-1/2*a^4 + 9/2*a^2 - a - 9)*q^29 + (1/4*a^6 + a^5 - 2*a^4 - 9*a^3 + 1/4*a^2 + 18*a + 15/2)*q^30 + (1/4*a^6 + 1/2*a^5 - 5/2*a^4 - 9/2*a^3 + 23/4*a^2 + 9*a + 7/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^4 - 7/2*a^2 + a + 2)*q^33 + (a^5 - a^4 - 9*a^3 + 7*a^2 + 12*a)*q^34 + (-1/4*a^6 + 1/2*a^5 + 3*a^4 - 9/2*a^3 - 33/4*a^2 + 5*a + 9/2)*q^35 + (1/4*a^6 - a^4 + a^3 - 15/4*a^2 + a + 11/2)*q^36 + (-a^5 - a^4 + 10*a^3 + 8*a^2 - 21*a - 13)*q^37 + O(q^38)
*]> ;  // time = 22.899 seconds




J[210] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 210, 210, 210, 210, 210, 105, 105, 70, 42, 35, 35, 30, 21, 15, 14 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 4, 2, 2, 4, 8, 2, 4, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 25, 1, 1, 0, 1, 3, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 9, 1, 3, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, -1, -4, -2, -6, 0, -8, 10, -8, 2 ],
[ -1, 1, 1, 1, 0, 2, -6, 8, 0, 6, -4, -10 ],
[ 1, -1, 1, 1, 4, -2, 2, -4, -8, 6, -8, -2 ],
[ 1, 1, -1, 1, 0, 2, -6, -4, 0, -6, -4, 2 ],
[ 1, 1, 1, -1, -4, -2, 2, 4, -8, -2, 0, 6 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1, 1 ],
[ 1, -1, -1, -1 ],
[ -1, 1, -1, -1 ],
[ -1, -1, 1, -1 ],
[ -1, -1, -1, 1 ]
], component_group_orders := [
[ 1, 1, 1, 1 ],
[ 1, 3, 3, 1 ],
[ 1, 1, 1, 1 ],
[ 3, 3, 1, 1 ],
[ 1, 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1, 1 ],
[ 1, 3, 3, 1 ],
[ 1, 1, 1, 1 ],
[ 3, 3, 1, 1 ],
[ 1, 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 3, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1/9, 1, 1/9, 1 ], eigenvalues := [*
[ -1, -1, -1, -1, -4, -2, -6, 0, -8, 10, -8, 2 ],
[ -1, 1, 1, 1, 0, 2, -6, 8, 0, 6, -4, -10 ],
[ 1, -1, 1, 1, 4, -2, 2, -4, -8, 6, -8, -2 ],
[ 1, 1, -1, 1, 0, 2, -6, -4, 0, -6, -4, 2 ],
[ 1, 1, 1, -1, -4, -2, 2, 4, -8, -2, 0, 6 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - q^7 - q^8 + q^9 + q^10 - 4*q^11 - q^12 - 2*q^13 + q^14 + q^15 + q^16 - 6*q^17 - q^18 - q^20 + q^21 + 4*q^22 - 8*q^23 + q^24 + q^25 + 2*q^26 - q^27 - q^28 + 10*q^29 - q^30 - 8*q^31 - q^32 + 4*q^33 + 6*q^34 + q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + q^5 - q^6 + q^7 - q^8 + q^9 - q^10 + q^12 + 2*q^13 - q^14 + q^15 + q^16 - 6*q^17 - q^18 + 8*q^19 + q^20 + q^21 - q^24 + q^25 - 2*q^26 + q^27 + q^28 + 6*q^29 - q^30 - 4*q^31 - q^32 + 6*q^34 + q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + q^7 + q^8 + q^9 + q^10 + 4*q^11 - q^12 - 2*q^13 + q^14 - q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 + q^20 - q^21 + 4*q^22 - 8*q^23 - q^24 + q^25 - 2*q^26 - q^27 + q^28 + 6*q^29 - q^30 - 8*q^31 + q^32 - 4*q^33 + 2*q^34 + q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + q^7 + q^8 + q^9 - q^10 + q^12 + 2*q^13 + q^14 - q^15 + q^16 - 6*q^17 + q^18 - 4*q^19 - q^20 + q^21 + q^24 + q^25 + 2*q^26 + q^27 + q^28 - 6*q^29 - q^30 - 4*q^31 + q^32 - 6*q^34 - q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 - q^7 + q^8 + q^9 + q^10 - 4*q^11 + q^12 - 2*q^13 - q^14 + q^15 + q^16 + 2*q^17 + q^18 + 4*q^19 + q^20 - q^21 - 4*q^22 - 8*q^23 + q^24 + q^25 - 2*q^26 + q^27 - q^28 - 2*q^29 + q^30 + q^32 - 4*q^33 + 2*q^34 - q^35 + q^36 + 6*q^37 + O(q^38)
*]> ;  // time = 502.771 seconds




J[211] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 211, 211, 211, 211 ], new_dimensions := [ 2, 3, 3, 9 ], dimensions := [ 2, 3, 3, 9 ], intersection_graph := [ 0, 1, 1, 41, 1, 0, 7, 1, 1, 7, 0, 1, 41, 1, 1, 0 ], ap_traces := [
[ 1, 3, 2, 1, -6, 8, 11, -5, 8, 0, -11, -4 ],
[ 0, -3, -5, -3, -9, 1, -17, 2, 16, -20, 3, 5 ],
[ -2, -1, -8, 2, -2, -3, 6, -7, -19, -6, -5, -2 ],
[ -1, -1, 15, -2, 13, -4, 4, -2, -3, 26, 5, 5 ]
], hecke_fields := [
x^2 - x - 1,
x^3 - 4*x + 1,
x^3 + 2*x^2 - x - 1,
x^9 + x^8 - 14*x^7 - 11*x^6 + 66*x^5 + 36*x^4 - 123*x^3 - 38*x^2 + 72*x + 8
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 5 ],
[ 1 ],
[ 1 ],
[ 7 ]
], tamagawa_numbers := [
[ 5 ],
[ 1 ],
[ 1 ],
[ 7 ]
], torsion_upper_bounds := [ 5, 1, 1, 7 ], torsion_lower_bounds := [ 5, 1, 1, 7 ], l_ratios := [ 1/5, 0, 0, 1/7 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1 ], eigenvalues := [*
[
a,
a + 1,
-2*a + 2,
-a + 1,
-3,
-2*a + 5,
-a + 6,
-3*a - 1,
2*a + 3,
2*a - 1,
5*a - 8,
8*a - 6
],
[
a,
-a - 1,
-a^2 - a + 1,
a - 1,
-3,
2*a^2 - 5,
-a^2 - 3,
a^2 - 2,
-a^2 + a + 8,
-a^2 + a - 4,
-3*a^2 + 9,
a^2 - a - 1
],
[
a,
-a^2 - a + 1,
a^2 + a - 4,
-a^2 - 4*a,
3*a^2 + 7*a - 2,
2*a^2 + 3*a - 3,
a^2 + 3*a + 2,
-2*a^2 - a + 1,
-a - 7,
-7*a^2 - 12*a + 4,
-a^2 - 5*a - 3,
-2*a^2 + a + 4
],
[
a,
9/58*a^8 + 15/58*a^7 - 2*a^6 - 157/58*a^5 + 235/29*a^4 + 222/29*a^3 - 637/58*a^2 - 161/29*a + 62/29,
7/116*a^8 + 31/116*a^7 - 1/2*a^6 - 309/116*a^5 + 41/58*a^4 + 183/29*a^3 + 91/116*a^2 - 93/58*a + 8/29,
-13/58*a^8 - 41/58*a^7 + 2*a^6 + 433/58*a^5 - 101/29*a^4 - 630/29*a^3 - 111/58*a^2 + 500/29*a + 78/29,
3/29*a^8 - 19/58*a^7 - 3/2*a^6 + 112/29*a^5 + 381/58*a^4 - 374/29*a^3 - 280/29*a^2 + 665/58*a + 167/29,
3/116*a^8 + 5/116*a^7 - 33/116*a^5 - 43/29*a^4 + 8/29*a^3 + 271/116*a^2 + 7/29*a + 49/29,
-5/29*a^8 - 18/29*a^7 + 2*a^6 + 200/29*a^5 - 216/29*a^4 - 614/29*a^3 + 341/29*a^2 + 456/29*a - 172/29,
33/116*a^8 + 55/116*a^7 - 3*a^6 - 595/116*a^5 + 223/29*a^4 + 465/29*a^3 - 151/116*a^2 - 416/29*a - 99/29,
7/29*a^8 + 2/29*a^7 - 3*a^6 - 19/29*a^5 + 314/29*a^4 + 65/29*a^3 - 286/29*a^2 - 128/29*a - 84/29,
-4/29*a^8 + 3/29*a^7 + 2*a^6 - 43/29*a^5 - 283/29*a^4 + 170/29*a^3 + 499/29*a^2 - 192/29*a - 68/29,
17/58*a^8 + 9/58*a^7 - 3*a^6 - 13/58*a^5 + 228/29*a^4 - 180/29*a^3 - 301/58*a^2 + 350/29*a + 72/29,
25/58*a^8 + 16/29*a^7 - 9/2*a^6 - 275/58*a^5 + 703/58*a^4 + 259/29*a^3 - 313/58*a^2 - 105/58*a - 121/29
]
*], q_expansions := [*
q + a*q^2 + (a + 1)*q^3 + (a - 1)*q^4 + (-2*a + 2)*q^5 + (2*a + 1)*q^6 + (-a + 1)*q^7 + (-2*a + 1)*q^8 + (3*a - 1)*q^9 - 2*q^10 - 3*q^11 + a*q^12 + (-2*a + 5)*q^13 - q^14 - 2*a*q^15 - 3*a*q^16 + (-a + 6)*q^17 + (2*a + 3)*q^18 + (-3*a - 1)*q^19 + (2*a - 4)*q^20 - a*q^21 - 3*a*q^22 + (2*a + 3)*q^23 + (-3*a - 1)*q^24 + (-4*a + 3)*q^25 + (3*a - 2)*q^26 + (2*a - 1)*q^27 + (a - 2)*q^28 + (2*a - 1)*q^29 + (-2*a - 2)*q^30 + (5*a - 8)*q^31 + (a - 5)*q^32 + (-3*a - 3)*q^33 + (5*a - 1)*q^34 + (-2*a + 4)*q^35 + (-a + 4)*q^36 + (8*a - 6)*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 1)*q^5 + (-a^2 - a)*q^6 + (a - 1)*q^7 - q^8 + (a^2 + 2*a - 2)*q^9 + (-a^2 - 3*a + 1)*q^10 - 3*q^11 + (-a^2 - 2*a + 3)*q^12 + (2*a^2 - 5)*q^13 + (a^2 - a)*q^14 + (2*a^2 + 4*a - 2)*q^15 + (-2*a^2 - a + 4)*q^16 + (-a^2 - 3)*q^17 + (2*a^2 + 2*a - 1)*q^18 + (a^2 - 2)*q^19 + (-a^2 - a - 1)*q^20 + (-a^2 + 1)*q^21 - 3*a*q^22 + (-a^2 + a + 8)*q^23 + (a + 1)*q^24 + (3*a^2 + 5*a - 6)*q^25 + (3*a - 2)*q^26 + (-3*a^2 - a + 6)*q^27 + (-a^2 + 2*a + 1)*q^28 + (-a^2 + a - 4)*q^29 + (4*a^2 + 6*a - 2)*q^30 + (-3*a^2 + 9)*q^31 + (-a^2 - 4*a + 4)*q^32 + (3*a + 3)*q^33 + (-7*a + 1)*q^34 - 2*a*q^35 + (3*a + 2)*q^36 + (a^2 - a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 4)*q^5 + (a^2 - 1)*q^6 + (-a^2 - 4*a)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (-a - 2)*q^9 + (-a^2 - 3*a + 1)*q^10 + (3*a^2 + 7*a - 2)*q^11 + (2*a - 1)*q^12 + (2*a^2 + 3*a - 3)*q^13 + (-2*a^2 - a - 1)*q^14 + (3*a^2 + 4*a - 4)*q^15 + (-a^2 - a + 2)*q^16 + (a^2 + 3*a + 2)*q^17 + (-a^2 - 2*a)*q^18 + (-2*a^2 - a + 1)*q^19 + (-3*a^2 - 2*a + 7)*q^20 + (-2*a^2 + 3)*q^21 + (a^2 + a + 3)*q^22 + (-a - 7)*q^23 + (-a + 2)*q^24 + (-6*a^2 - 7*a + 11)*q^25 + (-a^2 - a + 2)*q^26 + (4*a^2 + 5*a - 4)*q^27 + (5*a^2 + 5*a - 2)*q^28 + (-7*a^2 - 12*a + 4)*q^29 + (-2*a^2 - a + 3)*q^30 + (-a^2 - 5*a - 3)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (3*a^2 + 2*a - 6)*q^33 + (a^2 + 3*a + 1)*q^34 + (5*a^2 + 12*a - 3)*q^35 + (a + 3)*q^36 + (-2*a^2 + a + 4)*q^37 + O(q^38),
q + a*q^2 + (9/58*a^8 + 15/58*a^7 - 2*a^6 - 157/58*a^5 + 235/29*a^4 + 222/29*a^3 - 637/58*a^2 - 161/29*a + 62/29)*q^3 + (a^2 - 2)*q^4 + (7/116*a^8 + 31/116*a^7 - 1/2*a^6 - 309/116*a^5 + 41/58*a^4 + 183/29*a^3 + 91/116*a^2 - 93/58*a + 8/29)*q^5 + (3/29*a^8 + 5/29*a^7 - a^6 - 62/29*a^5 + 60/29*a^4 + 235/29*a^3 + 10/29*a^2 - 262/29*a - 36/29)*q^6 + (-13/58*a^8 - 41/58*a^7 + 2*a^6 + 433/58*a^5 - 101/29*a^4 - 630/29*a^3 - 111/58*a^2 + 500/29*a + 78/29)*q^7 + (a^3 - 4*a)*q^8 + (-7/29*a^8 - 2/29*a^7 + 3*a^6 + 19/29*a^5 - 314/29*a^4 - 65/29*a^3 + 286/29*a^2 + 70/29*a + 113/29)*q^9 + (6/29*a^8 + 10/29*a^7 - 2*a^6 - 95/29*a^5 + 120/29*a^4 + 238/29*a^3 + 20/29*a^2 - 118/29*a - 14/29)*q^10 + (3/29*a^8 - 19/58*a^7 - 3/2*a^6 + 112/29*a^5 + 381/58*a^4 - 374/29*a^3 - 280/29*a^2 + 665/58*a + 167/29)*q^11 + (-7/29*a^8 - 2/29*a^7 + 3*a^6 + 19/29*a^5 - 343/29*a^4 - 65/29*a^3 + 489/29*a^2 + 70/29*a - 148/29)*q^12 + (3/116*a^8 + 5/116*a^7 - 33/116*a^5 - 43/29*a^4 + 8/29*a^3 + 271/116*a^2 + 7/29*a + 49/29)*q^13 + (-14/29*a^8 - 33/29*a^7 + 5*a^6 + 328/29*a^5 - 396/29*a^4 - 855/29*a^3 + 253/29*a^2 + 546/29*a + 52/29)*q^14 + (11/58*a^8 + 57/58*a^7 - 2*a^6 - 643/58*a^5 + 168/29*a^4 + 1035/29*a^3 - 205/58*a^2 - 954/29*a - 66/29)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5/29*a^8 - 18/29*a^7 + 2*a^6 + 200/29*a^5 - 216/29*a^4 - 614/29*a^3 + 341/29*a^2 + 456/29*a - 172/29)*q^17 + (5/29*a^8 - 11/29*a^7 - 2*a^6 + 148/29*a^5 + 187/29*a^4 - 575/29*a^3 - 196/29*a^2 + 617/29*a + 56/29)*q^18 + (33/116*a^8 + 55/116*a^7 - 3*a^6 - 595/116*a^5 + 223/29*a^4 + 465/29*a^3 - 151/116*a^2 - 416/29*a - 99/29)*q^19 + (1/58*a^8 + 21/58*a^7 - 243/58*a^5 - 19/29*a^4 + 392/29*a^3 + 129/58*a^2 - 353/29*a - 64/29)*q^20 + (-3/29*a^8 - 5/29*a^7 + a^6 + 33/29*a^5 - 60/29*a^4 + 26/29*a^3 - 10/29*a^2 - 260/29*a + 36/29)*q^21 + (-25/58*a^8 - 3/58*a^7 + 5*a^6 - 15/58*a^5 - 482/29*a^4 + 89/29*a^3 + 893/58*a^2 - 49/29*a - 24/29)*q^22 + (7/29*a^8 + 2/29*a^7 - 3*a^6 - 19/29*a^5 + 314/29*a^4 + 65/29*a^3 - 286/29*a^2 - 128/29*a - 84/29)*q^23 + (-1/29*a^8 - 21/29*a^7 + 243/29*a^5 + 67/29*a^4 - 842/29*a^3 - 216/29*a^2 + 880/29*a + 128/29)*q^24 + (13/58*a^8 + 35/29*a^7 - 3/2*a^6 - 723/58*a^5 - 59/58*a^4 + 949/29*a^3 + 691/58*a^2 - 971/58*a - 194/29)*q^25 + (1/58*a^8 + 21/58*a^7 - 185/58*a^5 - 19/29*a^4 + 160/29*a^3 + 71/58*a^2 - 5/29*a - 6/29)*q^26 + (-1/29*a^8 + 8/29*a^7 - 105/29*a^5 + 96/29*a^4 + 405/29*a^3 - 303/29*a^2 - 454/29*a + 12/29)*q^27 + (-6/29*a^8 - 10/29*a^7 + 2*a^6 + 95/29*a^5 - 149/29*a^4 - 209/29*a^3 + 125/29*a^2 + 60/29*a - 44/29)*q^28 + (-4/29*a^8 + 3/29*a^7 + 2*a^6 - 43/29*a^5 - 283/29*a^4 + 170/29*a^3 + 499/29*a^2 - 192/29*a - 68/29)*q^29 + (23/29*a^8 + 19/29*a^7 - 9*a^6 - 195/29*a^5 + 837/29*a^4 + 574/29*a^3 - 745/29*a^2 - 462/29*a - 44/29)*q^30 + (17/58*a^8 + 9/58*a^7 - 3*a^6 - 13/58*a^5 + 228/29*a^4 - 180/29*a^3 - 301/58*a^2 + 350/29*a + 72/29)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (37/58*a^8 + 23/58*a^7 - 8*a^6 - 233/58*a^5 + 892/29*a^4 + 381/29*a^3 - 2303/58*a^2 - 446/29*a + 300/29)*q^33 + (-13/29*a^8 - 12/29*a^7 + 5*a^6 + 114/29*a^5 - 434/29*a^4 - 274/29*a^3 + 266/29*a^2 + 188/29*a + 40/29)*q^34 + (-49/58*a^8 - 101/58*a^7 + 9*a^6 + 1061/58*a^5 - 751/29*a^4 - 1518/29*a^3 + 987/58*a^2 + 1086/29*a + 120/29)*q^35 + (-2/29*a^8 + 16/29*a^7 + a^6 - 181/29*a^5 - 127/29*a^4 + 549/29*a^3 + 235/29*a^2 - 444/29*a - 266/29)*q^36 + (25/58*a^8 + 16/29*a^7 - 9/2*a^6 - 275/58*a^5 + 703/58*a^4 + 259/29*a^3 - 313/58*a^2 - 105/58*a - 121/29)*q^37 + O(q^38)
*]> ;  // time = 2.99 seconds




J[213] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 213, 213, 213, 213, 213, 71, 71 ], new_dimensions := [ 1, 2, 2, 2, 4, 3, 3 ], dimensions := [ 1, 2, 2, 2, 4, 6, 6 ], intersection_graph := [ 0, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 9, 5, 1, 1, 1, 1, 0, 19, 61, 1, 1, 1, 9, 19, 0, 81, 1, 1, 1, 5, 61, 81, 0 ], ap_traces := [
[ 1, 1, 2, 2, 0, -2, 0, 0, 0, -2, -10, -6 ],
[ -1, -2, 1, -6, -4, -5, 0, -8, -3, 3, -4, 3 ],
[ 1, 2, -1, -2, 6, -3, 6, -4, 3, 7, 4, -1 ],
[ -3, 2, -5, -4, -8, -1, -4, -8, -3, 3, 8, -1 ],
[ 3, -4, -3, 6, 2, 5, -8, 8, -1, -5, 2, 19 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^2 - x - 3,
x^2 + 3*x + 1,
x^4 - 3*x^3 - 2*x^2 + 7*x + 1
], atkin_lehners := [
[ -1, 1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 45, 1 ],
[ 1159, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 45, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1 ], l_ratios := [ 1, 0, 1/3, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 0, 1 ], eigenvalues := [*
[ 1, 1, 2, 2, 0, -2, 0, 0, 0, -2, -10, -6 ],
[
a,
-1,
-a,
-3,
-2*a - 3,
3*a - 1,
2*a + 1,
-2*a - 5,
5*a + 1,
3*a + 3,
-2,
-9*a - 3
],
[
a,
1,
-a,
-1,
3,
-a - 1,
3,
-2*a - 1,
-3*a + 3,
a + 3,
2,
a - 1
],
[
a,
1,
-a - 4,
2*a + 1,
-2*a - 7,
-3*a - 5,
2*a + 1,
2*a - 1,
3*a + 3,
-7*a - 9,
4*a + 10,
5*a + 7
],
[
a,
-1,
-a^2 + 2*a + 1,
-a^2 + a + 4,
-a^3 + a^2 + 3*a + 1,
-a^3 + 2*a^2 + a,
2*a^3 - 5*a^2 - 5*a + 6,
3*a^3 - 5*a^2 - 9*a + 7,
-a^3 + 4*a^2 + a - 8,
-a^3 + 4*a^2 - 3*a - 6,
-a^3 - 2*a^2 + 8*a + 7,
-a^3 + 2*a^2 + 3*a + 2
]
*], q_expansions := [*
q + q^2 + q^3 - q^4 + 2*q^5 + q^6 + 2*q^7 - 3*q^8 + q^9 + 2*q^10 - q^12 - 2*q^13 + 2*q^14 + 2*q^15 - q^16 + q^18 - 2*q^20 + 2*q^21 - 3*q^24 - q^25 - 2*q^26 + q^27 - 2*q^28 - 2*q^29 + 2*q^30 - 10*q^31 + 5*q^32 + 4*q^35 - q^36 - 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^4 - a*q^5 - a*q^6 - 3*q^7 + (-2*a - 1)*q^8 + q^9 + (a - 1)*q^10 + (-2*a - 3)*q^11 + (a + 1)*q^12 + (3*a - 1)*q^13 - 3*a*q^14 + a*q^15 + 3*a*q^16 + (2*a + 1)*q^17 + a*q^18 + (-2*a - 5)*q^19 + q^20 + 3*q^21 + (-a - 2)*q^22 + (5*a + 1)*q^23 + (2*a + 1)*q^24 + (-a - 4)*q^25 + (-4*a + 3)*q^26 - q^27 + (3*a + 3)*q^28 + (3*a + 3)*q^29 + (-a + 1)*q^30 - 2*q^31 + (a + 5)*q^32 + (2*a + 3)*q^33 + (-a + 2)*q^34 + 3*a*q^35 + (-a - 1)*q^36 + (-9*a - 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a + 1)*q^4 - a*q^5 + a*q^6 - q^7 + 3*q^8 + q^9 + (-a - 3)*q^10 + 3*q^11 + (a + 1)*q^12 + (-a - 1)*q^13 - a*q^14 - a*q^15 + (a - 2)*q^16 + 3*q^17 + a*q^18 + (-2*a - 1)*q^19 + (-2*a - 3)*q^20 - q^21 + 3*a*q^22 + (-3*a + 3)*q^23 + 3*q^24 + (a - 2)*q^25 + (-2*a - 3)*q^26 + q^27 + (-a - 1)*q^28 + (a + 3)*q^29 + (-a - 3)*q^30 + 2*q^31 + (-a - 3)*q^32 + 3*q^33 + 3*a*q^34 + a*q^35 + (a + 1)*q^36 + (a - 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (-3*a - 3)*q^4 + (-a - 4)*q^5 + a*q^6 + (2*a + 1)*q^7 + (4*a + 3)*q^8 + q^9 + (-a + 1)*q^10 + (-2*a - 7)*q^11 + (-3*a - 3)*q^12 + (-3*a - 5)*q^13 + (-5*a - 2)*q^14 + (-a - 4)*q^15 + (-3*a + 2)*q^16 + (2*a + 1)*q^17 + a*q^18 + (2*a - 1)*q^19 + (6*a + 9)*q^20 + (2*a + 1)*q^21 + (-a + 2)*q^22 + (3*a + 3)*q^23 + (4*a + 3)*q^24 + (5*a + 10)*q^25 + (4*a + 3)*q^26 + q^27 + (9*a + 3)*q^28 + (-7*a - 9)*q^29 + (-a + 1)*q^30 + (4*a + 10)*q^31 + (3*a - 3)*q^32 + (-2*a - 7)*q^33 + (-5*a - 2)*q^34 + (-3*a - 2)*q^35 + (-3*a - 3)*q^36 + (5*a + 7)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + 2*a + 1)*q^5 - a*q^6 + (-a^2 + a + 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^3 + 2*a^2 + a)*q^10 + (-a^3 + a^2 + 3*a + 1)*q^11 + (-a^2 + 2)*q^12 + (-a^3 + 2*a^2 + a)*q^13 + (-a^3 + a^2 + 4*a)*q^14 + (a^2 - 2*a - 1)*q^15 + (3*a^3 - 4*a^2 - 7*a + 3)*q^16 + (2*a^3 - 5*a^2 - 5*a + 6)*q^17 + a*q^18 + (3*a^3 - 5*a^2 - 9*a + 7)*q^19 + (-a^3 + a^2 + 3*a - 1)*q^20 + (a^2 - a - 4)*q^21 + (-2*a^3 + a^2 + 8*a + 1)*q^22 + (-a^3 + 4*a^2 + a - 8)*q^23 + (-a^3 + 4*a)*q^24 + (-a^3 + 4*a^2 - 3*a - 5)*q^25 + (-a^3 - a^2 + 7*a + 1)*q^26 - q^27 + (-2*a^3 + 4*a^2 + 5*a - 7)*q^28 + (-a^3 + 4*a^2 - 3*a - 6)*q^29 + (a^3 - 2*a^2 - a)*q^30 + (-a^3 - 2*a^2 + 8*a + 7)*q^31 + (3*a^3 - a^2 - 10*a - 3)*q^32 + (a^3 - a^2 - 3*a - 1)*q^33 + (a^3 - a^2 - 8*a - 2)*q^34 + (-a^2 + 2*a + 3)*q^35 + (a^2 - 2)*q^36 + (-a^3 + 2*a^2 + 3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 24.339 seconds




J[214] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 214, 214, 214, 214, 214, 214, 107, 107 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 2, 7 ], dimensions := [ 1, 1, 1, 1, 2, 2, 4, 14 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 5, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 109, 1, 1, 3, 1, 1, 0, 11, 1, 5, 1, 1, 1, 1, 11, 0, 1, 1, 1, 1, 7, 109, 1, 1, 0 ], ap_traces := [
[ -1, 1, -4, -2, -3, -1, 6, 1, -7, -6, 4, -9 ],
[ -1, -2, -1, 4, -6, -4, -6, -2, 5, 0, -2, 0 ],
[ 1, 1, 0, 2, -3, -1, 6, -7, 9, -6, -4, -1 ],
[ 1, -2, -3, -4, -2, 4, -2, -2, 1, -4, -10, 12 ],
[ -2, -2, 4, -2, 2, 2, 10, 4, 0, 10, -4, -8 ],
[ 2, 2, 0, -2, 6, -2, -6, 4, -12, 6, 4, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 2,
x^2 - 2*x - 2
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 7, 1 ],
[ 109, 1 ],
[ 33, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 33, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1, 3 ], l_ratios := [ 0, 0, 1/3, 0, 1, 11/3 ], analytic_sha_upper_bounds := [ 0, 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 1, -4, -2, -3, -1, 6, 1, -7, -6, 4, -9 ],
[ -1, -2, -1, 4, -6, -4, -6, -2, 5, 0, -2, 0 ],
[ 1, 1, 0, 2, -3, -1, 6, -7, 9, -6, -4, -1 ],
[ 1, -2, -3, -4, -2, 4, -2, -2, 1, -4, -10, 12 ],
[
-1,
a,
a + 3,
a,
-a,
-a,
-a + 4,
2,
-a - 1,
-a + 4,
-4*a - 6,
-4
],
[
1,
a,
-a + 1,
-a,
-a + 4,
-a,
a - 4,
2,
-a - 5,
3*a,
2,
4*a - 8
]
*], q_expansions := [*
q - q^2 + q^3 + q^4 - 4*q^5 - q^6 - 2*q^7 - q^8 - 2*q^9 + 4*q^10 - 3*q^11 + q^12 - q^13 + 2*q^14 - 4*q^15 + q^16 + 6*q^17 + 2*q^18 + q^19 - 4*q^20 - 2*q^21 + 3*q^22 - 7*q^23 - q^24 + 11*q^25 + q^26 - 5*q^27 - 2*q^28 - 6*q^29 + 4*q^30 + 4*q^31 - q^32 - 3*q^33 - 6*q^34 + 8*q^35 - 2*q^36 - 9*q^37 + O(q^38),
q - q^2 - 2*q^3 + q^4 - q^5 + 2*q^6 + 4*q^7 - q^8 + q^9 + q^10 - 6*q^11 - 2*q^12 - 4*q^13 - 4*q^14 + 2*q^15 + q^16 - 6*q^17 - q^18 - 2*q^19 - q^20 - 8*q^21 + 6*q^22 + 5*q^23 + 2*q^24 - 4*q^25 + 4*q^26 + 4*q^27 + 4*q^28 - 2*q^30 - 2*q^31 - q^32 + 12*q^33 + 6*q^34 - 4*q^35 + q^36 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 + 2*q^7 + q^8 - 2*q^9 - 3*q^11 + q^12 - q^13 + 2*q^14 + q^16 + 6*q^17 - 2*q^18 - 7*q^19 + 2*q^21 - 3*q^22 + 9*q^23 + q^24 - 5*q^25 - q^26 - 5*q^27 + 2*q^28 - 6*q^29 - 4*q^31 + q^32 - 3*q^33 + 6*q^34 - 2*q^36 - q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 3*q^5 - 2*q^6 - 4*q^7 + q^8 + q^9 - 3*q^10 - 2*q^11 - 2*q^12 + 4*q^13 - 4*q^14 + 6*q^15 + q^16 - 2*q^17 + q^18 - 2*q^19 - 3*q^20 + 8*q^21 - 2*q^22 + q^23 - 2*q^24 + 4*q^25 + 4*q^26 + 4*q^27 - 4*q^28 - 4*q^29 + 6*q^30 - 10*q^31 + q^32 + 4*q^33 - 2*q^34 + 12*q^35 + q^36 + 12*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (a + 3)*q^5 - a*q^6 + a*q^7 - q^8 + (-2*a - 1)*q^9 + (-a - 3)*q^10 - a*q^11 + a*q^12 - a*q^13 - a*q^14 + (a + 2)*q^15 + q^16 + (-a + 4)*q^17 + (2*a + 1)*q^18 + 2*q^19 + (a + 3)*q^20 + (-2*a + 2)*q^21 + a*q^22 + (-a - 1)*q^23 - a*q^24 + (4*a + 6)*q^25 + a*q^26 - 4*q^27 + a*q^28 + (-a + 4)*q^29 + (-a - 2)*q^30 + (-4*a - 6)*q^31 - q^32 + (2*a - 2)*q^33 + (a - 4)*q^34 + (a + 2)*q^35 + (-2*a - 1)*q^36 - 4*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 1)*q^5 + a*q^6 - a*q^7 + q^8 + (2*a - 1)*q^9 + (-a + 1)*q^10 + (-a + 4)*q^11 + a*q^12 - a*q^13 - a*q^14 + (-a - 2)*q^15 + q^16 + (a - 4)*q^17 + (2*a - 1)*q^18 + 2*q^19 + (-a + 1)*q^20 + (-2*a - 2)*q^21 + (-a + 4)*q^22 + (-a - 5)*q^23 + a*q^24 - 2*q^25 - a*q^26 + 4*q^27 - a*q^28 + 3*a*q^29 + (-a - 2)*q^30 + 2*q^31 + q^32 + (2*a - 2)*q^33 + (a - 4)*q^34 + (a + 2)*q^35 + (2*a - 1)*q^36 + (4*a - 8)*q^37 + O(q^38)
*]> ;  // time = 36.25 seconds




J[215] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 215, 215, 215, 215, 43, 43 ], new_dimensions := [ 1, 3, 5, 6, 1, 2 ], dimensions := [ 1, 3, 5, 6, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 0, 49, 1, 1, 1, 1, 49, 0, 1, 5, 1, 1, 1, 1, 0, 1, 31, 1, 1, 5, 1, 0, 1, 1, 1, 1, 31, 1, 0 ], ap_traces := [
[ 0, 0, -1, -2, -1, -1, -3, -2, -1, 4, 3, -8 ],
[ -2, 1, 3, -3, 9, -2, 10, 6, -6, 2, 13, 9 ],
[ 2, -1, 5, 5, -6, 5, -17, -6, 1, 6, 6, 5 ],
[ 3, 4, -6, 8, 0, 6, 6, 6, 0, -10, 0, 28 ]
], hecke_fields := [
x - 1,
x^3 + 2*x^2 - 3*x - 3,
x^5 - 2*x^4 - 7*x^3 + 13*x^2 + 5*x - 4,
x^6 - 3*x^5 - 5*x^4 + 17*x^3 + 3*x^2 - 17*x - 3
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ],
[ 5, 1 ],
[ 93, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 11, 1 ],
[ 5, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 11, 1, 3 ], torsion_lower_bounds := [ 1, 11, 1, 3 ], l_ratios := [ 0, 1/11, 5, 1/3 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1 ], eigenvalues := [*
[ 0, 0, -1, -2, -1, -1, -3, -2, -1, 4, 3, -8 ],
[
a,
a + 1,
1,
-a^2 - 2*a + 1,
-a^2 + a + 7,
-2*a - 2,
-2*a + 2,
-2*a^2 - 4*a + 6,
2*a^2 + 4*a - 6,
2*a + 2,
a^2 + 1,
a^2 - a - 1
],
[
a,
-a^3 + 5*a,
1,
a^4 - a^3 - 6*a^2 + 6*a + 2,
a^3 - 6*a - 1,
-a^4 + 5*a^2 + a + 3,
a^4 - 7*a^2 + a + 1,
-2*a^4 + 14*a^2 - 2*a - 10,
-a^4 + 5*a^2 - a + 3,
-2*a^4 + 2*a^3 + 14*a^2 - 12*a - 8,
2*a^4 + a^3 - 13*a^2 - 5*a + 7,
-a^4 + a^3 + 7*a^2 - 5*a - 4
],
[
a,
a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 6*a - 2,
-1,
-2*a^5 + 3*a^4 + 13*a^3 - 12*a^2 - 16*a + 2,
-3*a^5 + 3*a^4 + 23*a^3 - 9*a^2 - 38*a - 9,
-2*a + 2,
4*a^5 - 4*a^4 - 30*a^3 + 12*a^2 + 48*a + 12,
2*a^5 - 2*a^4 - 16*a^3 + 6*a^2 + 28*a + 8,
-2*a^5 + 4*a^4 + 12*a^3 - 16*a^2 - 14*a,
2*a^5 - 2*a^4 - 16*a^3 + 8*a^2 + 26*a,
2*a^5 - 3*a^4 - 15*a^3 + 14*a^2 + 24*a - 4,
-a^5 + a^4 + 9*a^3 - 5*a^2 - 16*a + 5
]
*], q_expansions := [*
q - 2*q^4 - q^5 - 2*q^7 - 3*q^9 - q^11 - q^13 + 4*q^16 - 3*q^17 - 2*q^19 + 2*q^20 - q^23 + q^25 + 4*q^28 + 4*q^29 + 3*q^31 + 2*q^35 + 6*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (a^2 - 2)*q^4 + q^5 + (a^2 + a)*q^6 + (-a^2 - 2*a + 1)*q^7 + (-2*a^2 - a + 3)*q^8 + (a^2 + 2*a - 2)*q^9 + a*q^10 + (-a^2 + a + 7)*q^11 + (-a^2 + a + 1)*q^12 + (-2*a - 2)*q^13 + (-2*a - 3)*q^14 + (a + 1)*q^15 + (a^2 - 3*a - 2)*q^16 + (-2*a + 2)*q^17 + (a + 3)*q^18 + (-2*a^2 - 4*a + 6)*q^19 + (a^2 - 2)*q^20 + (-a^2 - 4*a - 2)*q^21 + (3*a^2 + 4*a - 3)*q^22 + (2*a^2 + 4*a - 6)*q^23 + (a^2 - 4*a - 3)*q^24 + q^25 + (-2*a^2 - 2*a)*q^26 + (a^2 - 2)*q^27 + (a - 2)*q^28 + (2*a + 2)*q^29 + (a^2 + a)*q^30 + (a^2 + 1)*q^31 + (-a^2 + 3*a - 3)*q^32 + (2*a^2 + 5*a + 4)*q^33 + (-2*a^2 + 2*a)*q^34 + (-a^2 - 2*a + 1)*q^35 + (-a^2 - a + 4)*q^36 + (a^2 - a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 5*a)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^4 + 5*a^2)*q^6 + (a^4 - a^3 - 6*a^2 + 6*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + a^3 - 6*a^2 - 6*a + 5)*q^9 + a*q^10 + (a^3 - 6*a - 1)*q^11 + (-2*a^4 + 13*a^2 - 5*a - 4)*q^12 + (-a^4 + 5*a^2 + a + 3)*q^13 + (a^4 + a^3 - 7*a^2 - 3*a + 4)*q^14 + (-a^3 + 5*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 - 7*a^2 + a + 1)*q^17 + (3*a^4 + a^3 - 19*a^2 + 4)*q^18 + (-2*a^4 + 14*a^2 - 2*a - 10)*q^19 + (a^2 - 2)*q^20 + (-a^4 + 5*a^2 - 4*a + 8)*q^21 + (a^4 - 6*a^2 - a)*q^22 + (-a^4 + 5*a^2 - a + 3)*q^23 + (-2*a^4 - a^3 + 11*a^2 + 6*a - 8)*q^24 + q^25 + (-2*a^4 - 2*a^3 + 14*a^2 + 8*a - 4)*q^26 + (-a^4 - 2*a^3 + 7*a^2 + 8*a - 8)*q^27 + (a^4 + 2*a^3 - 4*a^2 - 13*a)*q^28 + (-2*a^4 + 2*a^3 + 14*a^2 - 12*a - 8)*q^29 + (-a^4 + 5*a^2)*q^30 + (2*a^4 + a^3 - 13*a^2 - 5*a + 7)*q^31 + (2*a^4 - a^3 - 13*a^2 + 7*a + 4)*q^32 + (a^2 + a - 8)*q^33 + (2*a^4 - 12*a^2 - 4*a + 4)*q^34 + (a^4 - a^3 - 6*a^2 + 6*a + 2)*q^35 + (5*a^4 - 27*a^2 + a + 2)*q^36 + (-a^4 + a^3 + 7*a^2 - 5*a - 4)*q^37 + O(q^38),
q + a*q^2 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 6*a - 2)*q^3 + (a^2 - 2)*q^4 - q^5 + (a^5 - a^4 - 8*a^3 + 3*a^2 + 15*a + 3)*q^6 + (-2*a^5 + 3*a^4 + 13*a^3 - 12*a^2 - 16*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (2*a^5 - 3*a^4 - 13*a^3 + 10*a^2 + 16*a + 7)*q^9 - a*q^10 + (-3*a^5 + 3*a^4 + 23*a^3 - 9*a^2 - 38*a - 9)*q^11 + (a^4 - 2*a^3 - 6*a^2 + 8*a + 7)*q^12 + (-2*a + 2)*q^13 + (-3*a^5 + 3*a^4 + 22*a^3 - 10*a^2 - 32*a - 6)*q^14 + (-a^5 + 2*a^4 + 6*a^3 - 9*a^2 - 6*a + 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (4*a^5 - 4*a^4 - 30*a^3 + 12*a^2 + 48*a + 12)*q^17 + (3*a^5 - 3*a^4 - 24*a^3 + 10*a^2 + 41*a + 6)*q^18 + (2*a^5 - 2*a^4 - 16*a^3 + 6*a^2 + 28*a + 8)*q^19 + (-a^2 + 2)*q^20 + (-a^4 + a^3 + 8*a^2 - 4*a - 13)*q^21 + (-6*a^5 + 8*a^4 + 42*a^3 - 29*a^2 - 60*a - 9)*q^22 + (-2*a^5 + 4*a^4 + 12*a^3 - 16*a^2 - 14*a)*q^23 + (-a^5 + 10*a^3 + 2*a^2 - 23*a - 6)*q^24 + q^25 + (-2*a^2 + 2*a)*q^26 + (2*a^5 - 5*a^4 - 9*a^3 + 22*a^2 - 5)*q^27 + (-2*a^5 + a^4 + 15*a^3 + a^2 - 25*a - 13)*q^28 + (2*a^5 - 2*a^4 - 16*a^3 + 8*a^2 + 26*a)*q^29 + (-a^5 + a^4 + 8*a^3 - 3*a^2 - 15*a - 3)*q^30 + (2*a^5 - 3*a^4 - 15*a^3 + 14*a^2 + 24*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-5*a^5 + 6*a^4 + 38*a^3 - 23*a^2 - 64*a - 3)*q^33 + (8*a^5 - 10*a^4 - 56*a^3 + 36*a^2 + 80*a + 12)*q^34 + (2*a^5 - 3*a^4 - 13*a^3 + 12*a^2 + 16*a - 2)*q^35 + (2*a^5 - 3*a^4 - 15*a^3 + 12*a^2 + 25*a - 5)*q^36 + (-a^5 + a^4 + 9*a^3 - 5*a^2 - 16*a + 5)*q^37 + O(q^38)
*]> ;  // time = 24.949 seconds




J[217] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 217, 217, 217, 217, 31 ], new_dimensions := [ 3, 3, 4, 5, 2 ], dimensions := [ 3, 3, 4, 5, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 19, 1, 1, 0, 1, 1, 1, 1, 1, 0, 31, 1, 19, 1, 31, 0 ], ap_traces := [
[ -3, -3, 0, -3, -6, -3, -6, 3, -18, -15, -3, 0 ],
[ -3, -3, -6, 3, 0, -3, -12, -3, -12, 9, 3, 6 ],
[ 0, 3, 4, 4, 2, -1, 8, 5, 20, -7, -4, 0 ],
[ 3, 3, 0, -5, 4, -3, -4, -9, 18, -1, 5, -12 ]
], hecke_fields := [
x^3 + 3*x^2 - 3,
x^3 + 3*x^2 - 3,
x^4 - 5*x^2 + x + 1,
x^5 - 3*x^4 - 5*x^3 + 16*x^2 + 6*x - 19
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 31, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 0, 0, 1, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
a^2 + a - 3,
-2*a^2 - 3*a + 3,
-1,
a^2 - 5,
2*a^2 + 5*a - 2,
a - 1,
-a,
a^2 + 3*a - 6,
-a^2 + a - 1,
-1,
-a^2 + a + 4
],
[
a,
-a^2 - a + 1,
-a - 3,
1,
3*a^2 + 6*a - 3,
-3*a - 4,
a - 3,
3*a + 2,
-3*a^2 - 5*a,
3*a^2 + 3*a - 3,
1,
-a^2 - 3*a + 2
],
[
a,
-a^3 + 5*a,
-a + 1,
1,
-a^2 - 2*a + 3,
a^3 - a^2 - 5*a + 3,
2*a^2 + a - 3,
3*a^3 + a^2 - 13*a + 1,
2*a^3 + a^2 - 9*a + 4,
a^3 + 2*a^2 - 3*a - 6,
-1,
-6*a^3 - a^2 + 25*a - 2
],
[
a,
-a^3 + 2*a^2 + 3*a - 4,
a^4 - 2*a^3 - 5*a^2 + 6*a + 6,
-1,
-a^4 + 2*a^3 + 4*a^2 - 5*a - 2,
-a^4 + a^3 + 6*a^2 - 2*a - 8,
2*a^3 - 4*a^2 - 7*a + 9,
2*a^4 - 3*a^3 - 11*a^2 + 9*a + 11,
-a^2 - a + 8,
-2*a^4 + a^3 + 16*a^2 - 3*a - 26,
1,
-a^4 + 4*a^3 + 2*a^2 - 12*a - 3
]
*], q_expansions := [*
q + a*q^2 + (a^2 + a - 3)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 - 3*a + 3)*q^5 + (-2*a^2 - 3*a + 3)*q^6 - q^7 + (-3*a^2 - 4*a + 3)*q^8 + (-2*a^2 - 3*a + 3)*q^9 + (3*a^2 + 3*a - 6)*q^10 + (a^2 - 5)*q^11 + (a^2 + a)*q^12 + (2*a^2 + 5*a - 2)*q^13 - a*q^14 + (3*a^2 + 6*a - 6)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (a - 1)*q^17 + (3*a^2 + 3*a - 6)*q^18 - a*q^19 + (-2*a^2 + 3)*q^20 + (-a^2 - a + 3)*q^21 + (-3*a^2 - 5*a + 3)*q^22 + (a^2 + 3*a - 6)*q^23 + (2*a^2 + 6*a - 3)*q^24 + (-3*a^2 - 6*a + 4)*q^25 + (-a^2 - 2*a + 6)*q^26 + (3*a + 3)*q^27 + (-a^2 + 2)*q^28 + (-a^2 + a - 1)*q^29 + (-3*a^2 - 6*a + 9)*q^30 - q^31 + (3*a + 3)*q^32 + (-2*a^2 - 2*a + 9)*q^33 + (a^2 - a)*q^34 + (2*a^2 + 3*a - 3)*q^35 + (-2*a^2 + 3)*q^36 + (-a^2 + a + 4)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (-a - 3)*q^5 + (2*a^2 + a - 3)*q^6 + q^7 + (-3*a^2 - 4*a + 3)*q^8 + (2*a^2 + a - 5)*q^9 + (-a^2 - 3*a)*q^10 + (3*a^2 + 6*a - 3)*q^11 + (-3*a^2 - a + 4)*q^12 + (-3*a - 4)*q^13 + a*q^14 + (a^2 + 2*a)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (a - 3)*q^17 + (-5*a^2 - 5*a + 6)*q^18 + (3*a + 2)*q^19 + (2*a + 3)*q^20 + (-a^2 - a + 1)*q^21 + (-3*a^2 - 3*a + 9)*q^22 + (-3*a^2 - 5*a)*q^23 + (4*a^2 + 2*a - 3)*q^24 + (a^2 + 6*a + 4)*q^25 + (-3*a^2 - 4*a)*q^26 + (3*a + 1)*q^27 + (a^2 - 2)*q^28 + (3*a^2 + 3*a - 3)*q^29 + (-a^2 + 3)*q^30 + q^31 + (3*a + 3)*q^32 - 3*q^33 + (a^2 - 3*a)*q^34 + (-a - 3)*q^35 + (6*a^2 + 4*a - 5)*q^36 + (-a^2 - 3*a + 2)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 5*a)*q^3 + (a^2 - 2)*q^4 + (-a + 1)*q^5 + (a + 1)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-a^3 - a^2 + 5*a + 2)*q^9 + (-a^2 + a)*q^10 + (-a^2 - 2*a + 3)*q^11 + (2*a^3 + a^2 - 9*a)*q^12 + (a^3 - a^2 - 5*a + 3)*q^13 + a*q^14 + (-a^3 + 4*a - 1)*q^15 + (-a^2 - a + 3)*q^16 + (2*a^2 + a - 3)*q^17 + (-a^3 + 3*a + 1)*q^18 + (3*a^3 + a^2 - 13*a + 1)*q^19 + (-a^3 + a^2 + 2*a - 2)*q^20 + (-a^3 + 5*a)*q^21 + (-a^3 - 2*a^2 + 3*a)*q^22 + (2*a^3 + a^2 - 9*a + 4)*q^23 + (a^3 + a^2 - 4*a - 4)*q^24 + (a^2 - 2*a - 4)*q^25 + (-a^3 + 2*a - 1)*q^26 + (-2*a^2 - a + 5)*q^27 + (a^2 - 2)*q^28 + (a^3 + 2*a^2 - 3*a - 6)*q^29 + (-a^2 + 1)*q^30 - q^31 + (-3*a^3 - a^2 + 11*a)*q^32 + (-3*a^3 - a^2 + 12*a - 2)*q^33 + (2*a^3 + a^2 - 3*a)*q^34 + (-a + 1)*q^35 + (2*a^3 - 8*a - 3)*q^36 + (-6*a^3 - a^2 + 25*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 2*a^2 + 3*a - 4)*q^3 + (a^2 - 2)*q^4 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 6)*q^5 + (-a^4 + 2*a^3 + 3*a^2 - 4*a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^3 + 3*a^2 + a - 6)*q^9 + (a^4 - 10*a^2 + 19)*q^10 + (-a^4 + 2*a^3 + 4*a^2 - 5*a - 2)*q^11 + (-a^4 + 8*a^2 - 11)*q^12 + (-a^4 + a^3 + 6*a^2 - 2*a - 8)*q^13 - a*q^14 + (a^4 - a^3 - 7*a^2 + a + 14)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^3 - 4*a^2 - 7*a + 9)*q^17 + (-a^4 + 3*a^3 + a^2 - 6*a)*q^18 + (2*a^4 - 3*a^3 - 11*a^2 + 9*a + 11)*q^19 + (a^4 - a^3 - 6*a^2 + a + 7)*q^20 + (a^3 - 2*a^2 - 3*a + 4)*q^21 + (-a^4 - a^3 + 11*a^2 + 4*a - 19)*q^22 + (-a^2 - a + 8)*q^23 + (-a^4 - a^3 + 10*a^2 + 3*a - 19)*q^24 + (-3*a^2 + 2*a + 12)*q^25 + (-2*a^4 + a^3 + 14*a^2 - 2*a - 19)*q^26 + (a^4 - 2*a^3 - a^2 - 2)*q^27 + (-a^2 + 2)*q^28 + (-2*a^4 + a^3 + 16*a^2 - 3*a - 26)*q^29 + (2*a^4 - 2*a^3 - 15*a^2 + 8*a + 19)*q^30 + q^31 + (3*a^4 - 3*a^3 - 16*a^2 + 6*a + 19)*q^32 + (-a^4 + a^3 + 6*a^2 + a - 11)*q^33 + (2*a^4 - 4*a^3 - 7*a^2 + 9*a)*q^34 + (-a^4 + 2*a^3 + 5*a^2 - 6*a - 6)*q^35 + (-2*a^3 + 4*a^2 + 4*a - 7)*q^36 + (-a^4 + 4*a^3 + 2*a^2 - 12*a - 3)*q^37 + O(q^38)
*]> ;  // time = 23.439 seconds




J[218] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 218, 218, 218, 218, 218, 109, 109, 109 ], new_dimensions := [ 1, 2, 2, 2, 3, 1, 3, 4 ], dimensions := [ 1, 2, 2, 2, 3, 2, 6, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 0, 11, 1, 1, 1, 1, 1, 1, 11, 0, 1, 1, 41, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 41, 1, 1, 0, 1, 3, 1, 1, 1, 3, 1, 1, 0 ], ap_traces := [
[ 1, -2, -3, -4, 3, -4, -6, 5, 3, -3, -4, -4 ],
[ -2, -4, 2, -4, -2, -8, -4, -10, -2, 6, -4, -4 ],
[ 2, -2, 0, 6, 2, 4, 2, -2, -8, -16, 6, 2 ],
[ 2, 3, 2, -4, -6, 3, -4, 0, 3, 10, -6, 1 ],
[ -3, 3, -3, 6, 3, 9, 0, 3, 0, -3, 0, -3 ]
], hecke_fields := [
x - 1,
x^2 + 4*x + 2,
x^2 + 2*x - 2,
x^2 - 3*x + 1,
x^3 - 3*x^2 - 3*x + 8
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 7, 1 ],
[ 11, 1 ],
[ 205, 1 ],
[ 9, 3 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 205, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 3, 1, 11, 5, 3 ], torsion_lower_bounds := [ 1, 1, 11, 5, 3 ], l_ratios := [ 0, 0, 1/11, 41/5, 1/3 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 1 ], eigenvalues := [*
[ 1, -2, -3, -4, 3, -4, -6, 5, 3, -3, -4, -4 ],
[
-1,
a,
-a - 1,
-a - 4,
2*a + 3,
2*a,
a,
-2*a - 9,
-5*a - 11,
3*a + 9,
3*a + 4,
3*a + 4
],
[
1,
a,
-a - 1,
a + 4,
1,
-2*a,
-a,
2*a + 1,
-a - 5,
a - 7,
-3*a,
3*a + 4
],
[
1,
a,
-2*a + 4,
-2,
-2*a,
3*a - 3,
-4*a + 4,
0,
3*a - 3,
-2*a + 8,
6*a - 12,
-a + 2
],
[
-1,
a,
-a^2 + a + 3,
2,
a^2 - a - 3,
a^2 - 2*a,
0,
-a^2 - a + 7,
-3*a + 3,
-a^2 + a + 3,
-2*a^2 + 4*a + 6,
-3*a + 2
]
*], q_expansions := [*
q + q^2 - 2*q^3 + q^4 - 3*q^5 - 2*q^6 - 4*q^7 + q^8 + q^9 - 3*q^10 + 3*q^11 - 2*q^12 - 4*q^13 - 4*q^14 + 6*q^15 + q^16 - 6*q^17 + q^18 + 5*q^19 - 3*q^20 + 8*q^21 + 3*q^22 + 3*q^23 - 2*q^24 + 4*q^25 - 4*q^26 + 4*q^27 - 4*q^28 - 3*q^29 + 6*q^30 - 4*q^31 + q^32 - 6*q^33 - 6*q^34 + 12*q^35 + q^36 - 4*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 1)*q^5 - a*q^6 + (-a - 4)*q^7 - q^8 + (-4*a - 5)*q^9 + (a + 1)*q^10 + (2*a + 3)*q^11 + a*q^12 + 2*a*q^13 + (a + 4)*q^14 + (3*a + 2)*q^15 + q^16 + a*q^17 + (4*a + 5)*q^18 + (-2*a - 9)*q^19 + (-a - 1)*q^20 + 2*q^21 + (-2*a - 3)*q^22 + (-5*a - 11)*q^23 - a*q^24 + (-2*a - 6)*q^25 - 2*a*q^26 + (8*a + 8)*q^27 + (-a - 4)*q^28 + (3*a + 9)*q^29 + (-3*a - 2)*q^30 + (3*a + 4)*q^31 - q^32 + (-5*a - 4)*q^33 - a*q^34 + (a + 2)*q^35 + (-4*a - 5)*q^36 + (3*a + 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a - 1)*q^5 + a*q^6 + (a + 4)*q^7 + q^8 + (-2*a - 1)*q^9 + (-a - 1)*q^10 + q^11 + a*q^12 - 2*a*q^13 + (a + 4)*q^14 + (a - 2)*q^15 + q^16 - a*q^17 + (-2*a - 1)*q^18 + (2*a + 1)*q^19 + (-a - 1)*q^20 + (2*a + 2)*q^21 + q^22 + (-a - 5)*q^23 + a*q^24 - 2*q^25 - 2*a*q^26 - 4*q^27 + (a + 4)*q^28 + (a - 7)*q^29 + (a - 2)*q^30 - 3*a*q^31 + q^32 + a*q^33 - a*q^34 + (-3*a - 6)*q^35 + (-2*a - 1)*q^36 + (3*a + 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-2*a + 4)*q^5 + a*q^6 - 2*q^7 + q^8 + (3*a - 4)*q^9 + (-2*a + 4)*q^10 - 2*a*q^11 + a*q^12 + (3*a - 3)*q^13 - 2*q^14 + (-2*a + 2)*q^15 + q^16 + (-4*a + 4)*q^17 + (3*a - 4)*q^18 + (-2*a + 4)*q^20 - 2*a*q^21 - 2*a*q^22 + (3*a - 3)*q^23 + a*q^24 + (-4*a + 7)*q^25 + (3*a - 3)*q^26 + (2*a - 3)*q^27 - 2*q^28 + (-2*a + 8)*q^29 + (-2*a + 2)*q^30 + (6*a - 12)*q^31 + q^32 + (-6*a + 2)*q^33 + (-4*a + 4)*q^34 + (4*a - 8)*q^35 + (3*a - 4)*q^36 + (-a + 2)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 + a + 3)*q^5 - a*q^6 + 2*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 - a - 3)*q^10 + (a^2 - a - 3)*q^11 + a*q^12 + (a^2 - 2*a)*q^13 - 2*q^14 + (-2*a^2 + 8)*q^15 + q^16 + (-a^2 + 3)*q^18 + (-a^2 - a + 7)*q^19 + (-a^2 + a + 3)*q^20 + 2*a*q^21 + (-a^2 + a + 3)*q^22 + (-3*a + 3)*q^23 - a*q^24 + (a^2 + a - 4)*q^25 + (-a^2 + 2*a)*q^26 + (3*a^2 - 3*a - 8)*q^27 + 2*q^28 + (-a^2 + a + 3)*q^29 + (2*a^2 - 8)*q^30 + (-2*a^2 + 4*a + 6)*q^31 - q^32 + (2*a^2 - 8)*q^33 + (-2*a^2 + 2*a + 6)*q^35 + (a^2 - 3)*q^36 + (-3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 39.05 seconds




J[219] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 219, 219, 219, 219, 219, 73, 73, 73 ], new_dimensions := [ 1, 1, 1, 4, 6, 1, 2, 2 ], dimensions := [ 1, 1, 1, 4, 6, 2, 4, 4 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 5, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 17, 1, 1, 1, 1, 0, 1, 29, 1, 1, 1, 1, 1, 1, 0, 1, 9, 5, 1, 1, 1, 29, 1, 0, 1, 1, 1, 3, 17, 1, 9, 1, 0 ], ap_traces := [
[ 1, -1, -4, 2, -4, -2, 0, -4, 0, 8, 6, -2 ],
[ -2, -1, -1, 2, -4, -2, -3, -1, 0, -10, -6, 1 ],
[ 0, 1, -3, -4, 0, -4, 3, -1, 6, -6, -10, -7 ],
[ 1, -4, 9, -4, 2, 6, 9, 1, 4, 10, -10, -11 ],
[ -1, 6, 5, 8, -2, 4, -3, 5, -6, -4, 4, 13 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^4 - x^3 - 6*x^2 + 4*x + 4,
x^6 + x^5 - 9*x^4 - 5*x^3 + 20*x^2 + 4*x - 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 17, 1 ],
[ 1073, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1073, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 37 ], torsion_lower_bounds := [ 1, 1, 1, 1, 37 ], l_ratios := [ 0, 0, 0, 1, 29/37 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -1, -4, 2, -4, -2, 0, -4, 0, 8, 6, -2 ],
[ -2, -1, -1, 2, -4, -2, -3, -1, 0, -10, -6, 1 ],
[ 0, 1, -3, -4, 0, -4, 3, -1, 6, -6, -10, -7 ],
[
a,
-1,
-1/2*a^3 + 1/2*a^2 + 2*a + 1,
-a^2 + a + 2,
-a^2 - a + 4,
-a^3 + 5*a + 2,
3/2*a^3 - 1/2*a^2 - 7*a + 3,
a^3 + a^2 - 7*a - 3,
-a^3 + 3*a + 2,
a^3 - 5*a + 2,
a^3 + a^2 - 6*a - 6,
2*a^3 - 2*a^2 - 11*a + 3
],
[
a,
1,
-1/2*a^5 - 1/2*a^4 + 7/2*a^3 + 3/2*a^2 - 5*a + 1,
1/2*a^5 + a^4 - 7/2*a^3 - 5*a^2 + 5*a + 4,
1/2*a^5 - 11/2*a^3 + 13*a,
a^3 - 5*a + 2,
-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + 3/2*a^2 - 10*a + 1,
a^3 + a^2 - 5*a - 1,
a^3 + 2*a^2 - 5*a - 6,
-a^4 - a^3 + 7*a^2 + 3*a - 8,
1/2*a^5 - a^4 - 13/2*a^3 + 5*a^2 + 16*a,
-a^5 - a^4 + 8*a^3 + 4*a^2 - 13*a + 1
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - 4*q^5 - q^6 + 2*q^7 - 3*q^8 + q^9 - 4*q^10 - 4*q^11 + q^12 - 2*q^13 + 2*q^14 + 4*q^15 - q^16 + q^18 - 4*q^19 + 4*q^20 - 2*q^21 - 4*q^22 + 3*q^24 + 11*q^25 - 2*q^26 - q^27 - 2*q^28 + 8*q^29 + 4*q^30 + 6*q^31 + 5*q^32 + 4*q^33 - 8*q^35 - q^36 - 2*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 - q^5 + 2*q^6 + 2*q^7 + q^9 + 2*q^10 - 4*q^11 - 2*q^12 - 2*q^13 - 4*q^14 + q^15 - 4*q^16 - 3*q^17 - 2*q^18 - q^19 - 2*q^20 - 2*q^21 + 8*q^22 - 4*q^25 + 4*q^26 - q^27 + 4*q^28 - 10*q^29 - 2*q^30 - 6*q^31 + 8*q^32 + 4*q^33 + 6*q^34 - 2*q^35 + 2*q^36 + q^37 + O(q^38),
q + q^3 - 2*q^4 - 3*q^5 - 4*q^7 + q^9 - 2*q^12 - 4*q^13 - 3*q^15 + 4*q^16 + 3*q^17 - q^19 + 6*q^20 - 4*q^21 + 6*q^23 + 4*q^25 + q^27 + 8*q^28 - 6*q^29 - 10*q^31 + 12*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-1/2*a^3 + 1/2*a^2 + 2*a + 1)*q^5 - a*q^6 + (-a^2 + a + 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^2 + 3*a + 2)*q^10 + (-a^2 - a + 4)*q^11 + (-a^2 + 2)*q^12 + (-a^3 + 5*a + 2)*q^13 + (-a^3 + a^2 + 2*a)*q^14 + (1/2*a^3 - 1/2*a^2 - 2*a - 1)*q^15 + (a^3 - 4*a)*q^16 + (3/2*a^3 - 1/2*a^2 - 7*a + 3)*q^17 + a*q^18 + (a^3 + a^2 - 7*a - 3)*q^19 + (2*a^2 - 2*a - 2)*q^20 + (a^2 - a - 2)*q^21 + (-a^3 - a^2 + 4*a)*q^22 + (-a^3 + 3*a + 2)*q^23 + (-a^3 + 4*a)*q^24 + (-2*a^3 + 2*a^2 + 7*a - 2)*q^25 + (-a^3 - a^2 + 6*a + 4)*q^26 - q^27 + (-2*a^2 + 2*a)*q^28 + (a^3 - 5*a + 2)*q^29 + (a^2 - 3*a - 2)*q^30 + (a^3 + a^2 - 6*a - 6)*q^31 + (-a^3 + 2*a^2 + 4*a - 4)*q^32 + (a^2 + a - 4)*q^33 + (a^3 + 2*a^2 - 3*a - 6)*q^34 + (-3*a^2 + 5*a + 4)*q^35 + (a^2 - 2)*q^36 + (2*a^3 - 2*a^2 - 11*a + 3)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-1/2*a^5 - 1/2*a^4 + 7/2*a^3 + 3/2*a^2 - 5*a + 1)*q^5 + a*q^6 + (1/2*a^5 + a^4 - 7/2*a^3 - 5*a^2 + 5*a + 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 - a^3 + 5*a^2 + 3*a - 2)*q^10 + (1/2*a^5 - 11/2*a^3 + 13*a)*q^11 + (a^2 - 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (1/2*a^5 + a^4 - 5/2*a^3 - 5*a^2 + 2*a + 2)*q^14 + (-1/2*a^5 - 1/2*a^4 + 7/2*a^3 + 3/2*a^2 - 5*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + 3/2*a^2 - 10*a + 1)*q^17 + a*q^18 + (a^3 + a^2 - 5*a - 1)*q^19 + (-2*a^3 + 8*a - 2)*q^20 + (1/2*a^5 + a^4 - 7/2*a^3 - 5*a^2 + 5*a + 4)*q^21 + (-1/2*a^5 - a^4 + 5/2*a^3 + 3*a^2 - 2*a + 2)*q^22 + (a^3 + 2*a^2 - 5*a - 6)*q^23 + (a^3 - 4*a)*q^24 + (-a^5 - a^4 + 8*a^3 + 4*a^2 - 15*a)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 + q^27 + (-1/2*a^5 + 9/2*a^3 + 2*a^2 - 10*a - 6)*q^28 + (-a^4 - a^3 + 7*a^2 + 3*a - 8)*q^29 + (-a^4 - a^3 + 5*a^2 + 3*a - 2)*q^30 + (1/2*a^5 - a^4 - 13/2*a^3 + 5*a^2 + 16*a)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^5 - 11/2*a^3 + 13*a)*q^33 + (-a^3 + 3*a - 2)*q^34 + (a^4 + a^3 - 5*a^2 - 5*a)*q^35 + (a^2 - 2)*q^36 + (-a^5 - a^4 + 8*a^3 + 4*a^2 - 13*a + 1)*q^37 + O(q^38)
*]> ;  // time = 28.249 seconds




J[221] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 221, 221, 221, 221, 221, 221, 221, 17 ], new_dimensions := [ 1, 1, 2, 2, 2, 3, 6, 1 ], dimensions := [ 1, 1, 2, 2, 2, 3, 6, 2 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 5, 1, 1, 1, 3, 5, 1, 5, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, 2, 2, 2, -6, -1, 1, 4, 6, -6, -2, 2 ],
[ -1, 0, 4, -2, 6, -1, 1, 8, 4, -6, -2, -8 ],
[ -1, -3, 0, -1, -3, -2, -2, -7, 6, -8, -14, 10 ],
[ 0, 2, -2, 4, 4, -2, 2, 4, -6, -12, 0, 10 ],
[ -1, 1, -2, -5, 3, -2, 2, 5, 6, 18, 8, -8 ],
[ 0, -3, -2, -9, -7, 3, 3, -17, 2, 4, -6, -4 ],
[ 1, 1, -2, 7, -1, 6, -6, 23, -10, -4, 16, 4 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + x - 1,
x^2 - 5,
x^2 + x - 5,
x^3 - 4*x + 1,
x^6 - x^5 - 9*x^4 + 6*x^3 + 19*x^2 - 5*x - 3
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 7 ],
[ 1, 1 ],
[ 9, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 7 ],
[ 1, 1 ],
[ 9, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 7, 1, 9 ], torsion_lower_bounds := [ 1, 1, 1, 1, 7, 1, 9 ], l_ratios := [ 1, 1, 0, 1, 1/7, 0, 1/9 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 1, 0, 1 ], eigenvalues := [*
[ 1, 2, 2, 2, -6, -1, 1, 4, 6, -6, -2, 2 ],
[ -1, 0, 4, -2, 6, -1, 1, 8, 4, -6, -2, -8 ],
[
a,
a - 1,
-2*a - 1,
-a - 1,
3*a,
-1,
-1,
3*a - 2,
-2*a + 2,
2*a - 3,
-7,
4*a + 7
],
[
a,
-a + 1,
a - 1,
2,
2,
-1,
1,
-2*a + 2,
-a - 3,
-6,
2*a,
-a + 5
],
[
a,
a + 1,
-1,
-a - 3,
a + 2,
-1,
1,
-a + 2,
-2*a + 2,
9,
2*a + 5,
-2*a - 5
],
[
a,
-a - 1,
-a^2 - a + 2,
a - 3,
a^2 - 5,
1,
1,
-a^2 - 3,
4*a^2 + 2*a - 10,
-a^2 + a + 4,
-3*a^2 - a + 6,
a^2 - 5*a - 4
],
[
a,
-1/2*a^5 + 1/2*a^4 + 4*a^3 - 5/2*a^2 - 13/2*a + 1,
1/2*a^4 - 1/2*a^3 - 3*a^2 + 3/2*a + 3/2,
-a^3 + 5*a + 2,
-a^2 + 3,
1,
-1,
a^5 - a^4 - 8*a^3 + 6*a^2 + 13*a - 1,
1/2*a^5 + 1/2*a^4 - 4*a^3 - 7/2*a^2 + 13/2*a,
-a^3 + a^2 + 5*a - 3,
a^3 + a^2 - 7*a - 1,
-a^5 + 1/2*a^4 + 17/2*a^3 - 2*a^2 - 29/2*a + 1/2
]
*], q_expansions := [*
q + q^2 + 2*q^3 - q^4 + 2*q^5 + 2*q^6 + 2*q^7 - 3*q^8 + q^9 + 2*q^10 - 6*q^11 - 2*q^12 - q^13 + 2*q^14 + 4*q^15 - q^16 + q^17 + q^18 + 4*q^19 - 2*q^20 + 4*q^21 - 6*q^22 + 6*q^23 - 6*q^24 - q^25 - q^26 - 4*q^27 - 2*q^28 - 6*q^29 + 4*q^30 - 2*q^31 + 5*q^32 - 12*q^33 + q^34 + 4*q^35 - q^36 + 2*q^37 + O(q^38),
q - q^2 - q^4 + 4*q^5 - 2*q^7 + 3*q^8 - 3*q^9 - 4*q^10 + 6*q^11 - q^13 + 2*q^14 - q^16 + q^17 + 3*q^18 + 8*q^19 - 4*q^20 - 6*q^22 + 4*q^23 + 11*q^25 + q^26 + 2*q^28 - 6*q^29 - 2*q^31 - 5*q^32 - q^34 - 8*q^35 + 3*q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (a - 1)*q^3 + (-a - 1)*q^4 + (-2*a - 1)*q^5 + (-2*a + 1)*q^6 + (-a - 1)*q^7 + (-2*a - 1)*q^8 + (-3*a - 1)*q^9 + (a - 2)*q^10 + 3*a*q^11 + a*q^12 - q^13 - q^14 + (3*a - 1)*q^15 + 3*a*q^16 - q^17 + (2*a - 3)*q^18 + (3*a - 2)*q^19 + (a + 3)*q^20 + a*q^21 + (-3*a + 3)*q^22 + (-2*a + 2)*q^23 + (3*a - 1)*q^24 - a*q^26 + (2*a + 1)*q^27 + (a + 2)*q^28 + (2*a - 3)*q^29 + (-4*a + 3)*q^30 - 7*q^31 + (a + 5)*q^32 + (-6*a + 3)*q^33 - a*q^34 + (a + 3)*q^35 + (a + 4)*q^36 + (4*a + 7)*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + 3*q^4 + (a - 1)*q^5 + (a - 5)*q^6 + 2*q^7 + a*q^8 + (-2*a + 3)*q^9 + (-a + 5)*q^10 + 2*q^11 + (-3*a + 3)*q^12 - q^13 + 2*a*q^14 + (2*a - 6)*q^15 - q^16 + q^17 + (3*a - 10)*q^18 + (-2*a + 2)*q^19 + (3*a - 3)*q^20 + (-2*a + 2)*q^21 + 2*a*q^22 + (-a - 3)*q^23 + (a - 5)*q^24 + (-2*a + 1)*q^25 - a*q^26 + (-2*a + 10)*q^27 + 6*q^28 - 6*q^29 + (-6*a + 10)*q^30 + 2*a*q^31 - 3*a*q^32 + (-2*a + 2)*q^33 + a*q^34 + (2*a - 2)*q^35 + (-6*a + 9)*q^36 + (-a + 5)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-a + 3)*q^4 - q^5 + 5*q^6 + (-a - 3)*q^7 + (2*a - 5)*q^8 + (a + 3)*q^9 - a*q^10 + (a + 2)*q^11 + (3*a - 2)*q^12 - q^13 + (-2*a - 5)*q^14 + (-a - 1)*q^15 + (-5*a + 4)*q^16 + q^17 + (2*a + 5)*q^18 + (-a + 2)*q^19 + (a - 3)*q^20 + (-3*a - 8)*q^21 + (a + 5)*q^22 + (-2*a + 2)*q^23 + (-5*a + 5)*q^24 - 4*q^25 - a*q^26 + 5*q^27 + (-a - 4)*q^28 + 9*q^29 - 5*q^30 + (2*a + 5)*q^31 + (5*a - 15)*q^32 + (2*a + 7)*q^33 + a*q^34 + (a + 3)*q^35 + (a + 4)*q^36 + (-2*a - 5)*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 2)*q^5 + (-a^2 - a)*q^6 + (a - 3)*q^7 - q^8 + (a^2 + 2*a - 2)*q^9 + (-a^2 - 2*a + 1)*q^10 + (a^2 - 5)*q^11 + (-a^2 - 2*a + 3)*q^12 + q^13 + (a^2 - 3*a)*q^14 + (2*a^2 + 3*a - 3)*q^15 + (-2*a^2 - a + 4)*q^16 + q^17 + (2*a^2 + 2*a - 1)*q^18 + (-a^2 - 3)*q^19 + (-a - 3)*q^20 + (-a^2 + 2*a + 3)*q^21 + (-a - 1)*q^22 + (4*a^2 + 2*a - 10)*q^23 + (a + 1)*q^24 + (a^2 + 3*a - 3)*q^25 + a*q^26 + (-3*a^2 - a + 6)*q^27 + (-3*a^2 + 2*a + 5)*q^28 + (-a^2 + a + 4)*q^29 + (3*a^2 + 5*a - 2)*q^30 + (-3*a^2 - a + 6)*q^31 + (-a^2 - 4*a + 4)*q^32 + (-a^2 + a + 6)*q^33 + a*q^34 + (2*a^2 + a - 5)*q^35 + (3*a + 2)*q^36 + (a^2 - 5*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^5 + 1/2*a^4 + 4*a^3 - 5/2*a^2 - 13/2*a + 1)*q^3 + (a^2 - 2)*q^4 + (1/2*a^4 - 1/2*a^3 - 3*a^2 + 3/2*a + 3/2)*q^5 + (-1/2*a^4 + 1/2*a^3 + 3*a^2 - 3/2*a - 3/2)*q^6 + (-a^3 + 5*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (-a^2 + 4)*q^9 + (1/2*a^5 - 1/2*a^4 - 3*a^3 + 3/2*a^2 + 3/2*a)*q^10 + (-a^2 + 3)*q^11 + (1/2*a^5 - 1/2*a^4 - 5*a^3 + 7/2*a^2 + 23/2*a - 2)*q^12 + q^13 + (-a^4 + 5*a^2 + 2*a)*q^14 + (a^3 - 7*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - q^17 + (-a^3 + 4*a)*q^18 + (a^5 - a^4 - 8*a^3 + 6*a^2 + 13*a - 1)*q^19 + (1/2*a^4 - 1/2*a^3 - 2*a^2 - 1/2*a - 3/2)*q^20 + (-a^5 + 9*a^3 + 2*a^2 - 18*a - 4)*q^21 + (-a^3 + 3*a)*q^22 + (1/2*a^5 + 1/2*a^4 - 4*a^3 - 7/2*a^2 + 13/2*a)*q^23 + (1/2*a^4 - 1/2*a^3 - 4*a^2 + 7/2*a + 9/2)*q^24 + (-a^4 + 7*a^2 - 5)*q^25 + a*q^26 + (a^3 - a^2 - 5*a + 1)*q^27 + (-a^5 + 7*a^3 + 2*a^2 - 10*a - 4)*q^28 + (-a^3 + a^2 + 5*a - 3)*q^29 + (a^4 - 7*a^2)*q^30 + (a^3 + a^2 - 7*a - 1)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 + a^4 + 9*a^3 - 6*a^2 - 18*a + 3)*q^33 - a*q^34 + (a^5 - 8*a^3 - a^2 + 9*a + 3)*q^35 + (-a^4 + 6*a^2 - 8)*q^36 + (-a^5 + 1/2*a^4 + 17/2*a^3 - 2*a^2 - 29/2*a + 1/2)*q^37 + O(q^38)
*]> ;  // time = 26.56 seconds




J[222] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 222, 222, 222, 222, 222, 111, 111, 74, 74, 37, 37 ], new_dimensions := [ 1, 1, 1, 1, 1, 3, 4, 2, 2, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 6, 8, 4, 4, 4, 4 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 0, 1, 1, 1, 23, 1, 9, 1, 1, 1, 1, 1, 0, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 23, 1, 1, 1, 0, 1, 1, 1, 1, 25, 1, 1, 13, 1, 1, 1, 0, 1, 19, 49, 1, 3, 9, 1, 1, 1, 1, 1, 0, 1, 1, 9, 1, 1, 1, 11, 1, 1, 19, 1, 0, 25, 1, 1, 1, 1, 1, 1, 1, 49, 1, 25, 0, 1, 1, 1, 1, 1, 3, 25, 1, 9, 1, 1, 0 ], ap_traces := [
[ -1, -1, 2, 0, -4, 6, 6, 8, 0, -6, 4, 1 ],
[ -1, -1, -4, 3, 5, 3, 3, -7, 9, 0, -2, 1 ],
[ -1, 1, 4, -1, -1, -3, 3, -5, 5, 4, -10, -1 ],
[ 1, -1, 0, 3, 1, 1, -3, 3, -1, -4, -6, -1 ],
[ 1, 1, 0, -1, 3, -1, -3, -7, 3, 0, 2, 1 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 23, 9, 1 ],
[ 13, 1, 1 ],
[ 1, 11, 1 ],
[ 3, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 1, 1, 1 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1/9 ], eigenvalues := [*
[ -1, -1, 2, 0, -4, 6, 6, 8, 0, -6, 4, 1 ],
[ -1, -1, -4, 3, 5, 3, 3, -7, 9, 0, -2, 1 ],
[ -1, 1, 4, -1, -1, -3, 3, -5, 5, 4, -10, -1 ],
[ 1, -1, 0, 3, 1, 1, -3, 3, -1, -4, -6, -1 ],
[ 1, 1, 0, -1, 3, -1, -3, -7, 3, 0, 2, 1 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + 2*q^5 + q^6 - q^8 + q^9 - 2*q^10 - 4*q^11 - q^12 + 6*q^13 - 2*q^15 + q^16 + 6*q^17 - q^18 + 8*q^19 + 2*q^20 + 4*q^22 + q^24 - q^25 - 6*q^26 - q^27 - 6*q^29 + 2*q^30 + 4*q^31 - q^32 + 4*q^33 - 6*q^34 + q^36 + q^37 + O(q^38),
q - q^2 - q^3 + q^4 - 4*q^5 + q^6 + 3*q^7 - q^8 + q^9 + 4*q^10 + 5*q^11 - q^12 + 3*q^13 - 3*q^14 + 4*q^15 + q^16 + 3*q^17 - q^18 - 7*q^19 - 4*q^20 - 3*q^21 - 5*q^22 + 9*q^23 + q^24 + 11*q^25 - 3*q^26 - q^27 + 3*q^28 - 4*q^30 - 2*q^31 - q^32 - 5*q^33 - 3*q^34 - 12*q^35 + q^36 + q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 4*q^5 - q^6 - q^7 - q^8 + q^9 - 4*q^10 - q^11 + q^12 - 3*q^13 + q^14 + 4*q^15 + q^16 + 3*q^17 - q^18 - 5*q^19 + 4*q^20 - q^21 + q^22 + 5*q^23 - q^24 + 11*q^25 + 3*q^26 + q^27 - q^28 + 4*q^29 - 4*q^30 - 10*q^31 - q^32 - q^33 - 3*q^34 - 4*q^35 + q^36 - q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^6 + 3*q^7 + q^8 + q^9 + q^11 - q^12 + q^13 + 3*q^14 + q^16 - 3*q^17 + q^18 + 3*q^19 - 3*q^21 + q^22 - q^23 - q^24 - 5*q^25 + q^26 - q^27 + 3*q^28 - 4*q^29 - 6*q^31 + q^32 - q^33 - 3*q^34 + q^36 - q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^6 - q^7 + q^8 + q^9 + 3*q^11 + q^12 - q^13 - q^14 + q^16 - 3*q^17 + q^18 - 7*q^19 - q^21 + 3*q^22 + 3*q^23 + q^24 - 5*q^25 - q^26 + q^27 - q^28 + 2*q^31 + q^32 + 3*q^33 - 3*q^34 + q^36 + q^37 + O(q^38)
*]> ;  // time = 108.04 seconds




J[223] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 223, 223, 223 ], new_dimensions := [ 2, 4, 12 ], dimensions := [ 2, 4, 12 ], intersection_graph := [ 0, 7, 1, 7, 0, 1, 1, 1, 0 ], ap_traces := [
[ -2, -2, -4, 0, 2, 4, -6, -4, -6, -14, 8, 2 ],
[ -4, 0, -3, -6, -10, -9, -17, 7, -2, 7, 0, -2 ],
[ 7, 0, 7, 2, 6, 1, 27, -5, 12, 3, -12, 2 ]
], hecke_fields := [
x^2 + 2*x - 1,
x^4 + 4*x^3 + 2*x^2 - 5*x - 3,
x^12 - 7*x^11 + 6*x^10 + 57*x^9 - 122*x^8 - 105*x^7 + 430*x^6 - 73*x^5 - 499*x^4 + 242*x^3 + 143*x^2 - 52*x - 19
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 37 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 37 ]
], torsion_upper_bounds := [ 1, 1, 37 ], torsion_lower_bounds := [ 1, 1, 37 ], l_ratios := [ 0, 0, 1/37 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[
a,
a,
-a - 3,
-a - 1,
-a,
a + 3,
2*a - 1,
-a - 3,
3*a,
-7,
-2*a + 2,
2*a + 3
],
[
a,
-a - 1,
-a^3 - 3*a^2 + a + 3,
2*a^3 + 5*a^2 - 2*a - 6,
-2*a^3 - 6*a^2 + a + 4,
a^3 + 4*a^2 - 8,
a^3 + a^2 - 4*a - 5,
a^3 + 4*a^2 + 3*a - 1,
-2*a^3 - 2*a^2 + 8*a + 1,
a^3 + 4*a^2 + a - 3,
-4*a^3 - 12*a^2 + 3*a + 14,
-2*a^3 - 7*a^2 - 2*a + 6
],
[
a,
2*a^11 - 11*a^10 - 2*a^9 + 98*a^8 - 103*a^7 - 245*a^6 + 397*a^5 + 123*a^4 - 412*a^3 + 129*a^2 + 41*a - 18,
4*a^11 - 21*a^10 - 10*a^9 + 196*a^8 - 152*a^7 - 550*a^6 + 654*a^5 + 468*a^4 - 731*a^3 + 20*a^2 + 114*a + 4,
-9*a^11 + 45*a^10 + 34*a^9 - 435*a^8 + 235*a^7 + 1320*a^6 - 1172*a^5 - 1412*a^4 + 1388*a^3 + 350*a^2 - 263*a - 61,
-12*a^11 + 60*a^10 + 45*a^9 - 578*a^8 + 315*a^7 + 1739*a^6 - 1559*a^5 - 1813*a^4 + 1827*a^3 + 390*a^2 - 327*a - 68,
a^11 - 7*a^10 + 6*a^9 + 56*a^8 - 119*a^7 - 96*a^6 + 400*a^5 - 95*a^4 - 403*a^3 + 248*a^2 + 36*a - 31,
14*a^11 - 66*a^10 - 73*a^9 + 663*a^8 - 176*a^7 - 2169*a^6 + 1282*a^5 + 2737*a^4 - 1683*a^3 - 1153*a^2 + 418*a + 185,
10*a^11 - 50*a^10 - 37*a^9 + 481*a^8 - 268*a^7 - 1444*a^6 + 1319*a^5 + 1500*a^4 - 1550*a^3 - 318*a^2 + 285*a + 56,
a^11 - 4*a^10 - 8*a^9 + 42*a^8 + 15*a^7 - 147*a^6 + 5*a^5 + 204*a^4 - 23*a^3 - 97*a^2 + a + 10,
3*a^11 - 14*a^10 - 17*a^9 + 144*a^8 - 26*a^7 - 492*a^6 + 245*a^5 + 674*a^4 - 335*a^3 - 336*a^2 + 86*a + 53,
13*a^11 - 63*a^10 - 59*a^9 + 620*a^8 - 244*a^7 - 1951*a^6 + 1410*a^5 + 2273*a^4 - 1739*a^3 - 773*a^2 + 371*a + 120,
-2*a^11 + 12*a^10 - 3*a^9 - 101*a^8 + 150*a^7 + 211*a^6 - 533*a^5 + 32*a^4 + 544*a^3 - 306*a^2 - 56*a + 43
]
*], q_expansions := [*
q + a*q^2 + a*q^3 + (-2*a - 1)*q^4 + (-a - 3)*q^5 + (-2*a + 1)*q^6 + (-a - 1)*q^7 + (a - 2)*q^8 + (-2*a - 2)*q^9 + (-a - 1)*q^10 - a*q^11 + (3*a - 2)*q^12 + (a + 3)*q^13 + (a - 1)*q^14 + (-a - 1)*q^15 + 3*q^16 + (2*a - 1)*q^17 + (2*a - 2)*q^18 + (-a - 3)*q^19 + (3*a + 5)*q^20 + (a - 1)*q^21 + (2*a - 1)*q^22 + 3*a*q^23 + (-4*a + 1)*q^24 + (4*a + 5)*q^25 + (a + 1)*q^26 + (-a - 2)*q^27 + (-a + 3)*q^28 - 7*q^29 + (a - 1)*q^30 + (-2*a + 2)*q^31 + (a + 4)*q^32 + (2*a - 1)*q^33 + (-5*a + 2)*q^34 + (2*a + 4)*q^35 + (-2*a + 6)*q^36 + (2*a + 3)*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^3 - 3*a^2 + a + 3)*q^5 + (-a^2 - a)*q^6 + (2*a^3 + 5*a^2 - 2*a - 6)*q^7 + (a^3 - 4*a)*q^8 + (a^2 + 2*a - 2)*q^9 + (a^3 + 3*a^2 - 2*a - 3)*q^10 + (-2*a^3 - 6*a^2 + a + 4)*q^11 + (-a^3 - a^2 + 2*a + 2)*q^12 + (a^3 + 4*a^2 - 8)*q^13 + (-3*a^3 - 6*a^2 + 4*a + 6)*q^14 + a*q^15 + (-4*a^3 - 8*a^2 + 5*a + 7)*q^16 + (a^3 + a^2 - 4*a - 5)*q^17 + (a^3 + 2*a^2 - 2*a)*q^18 + (a^3 + 4*a^2 + 3*a - 1)*q^19 + (a^3 + 2*a^2 - 3)*q^20 + (a^3 + a^2 - 2*a)*q^21 + (2*a^3 + 5*a^2 - 6*a - 6)*q^22 + (-2*a^3 - 2*a^2 + 8*a + 1)*q^23 + (3*a^3 + 6*a^2 - a - 3)*q^24 + (a^3 + 2*a^2 - 3*a - 5)*q^25 + (-2*a^2 - 3*a + 3)*q^26 + (-a^3 - 3*a^2 + 3*a + 5)*q^27 + (2*a^3 - 5*a + 3)*q^28 + (a^3 + 4*a^2 + a - 3)*q^29 + a^2*q^30 + (-4*a^3 - 12*a^2 + 3*a + 14)*q^31 + (6*a^3 + 13*a^2 - 5*a - 12)*q^32 + (a^2 + 5*a + 2)*q^33 + (-3*a^3 - 6*a^2 + 3)*q^34 + (-a^3 + 4*a - 3)*q^35 + (-2*a^3 - 6*a^2 + a + 7)*q^36 + (-2*a^3 - 7*a^2 - 2*a + 6)*q^37 + O(q^38),
q + a*q^2 + (2*a^11 - 11*a^10 - 2*a^9 + 98*a^8 - 103*a^7 - 245*a^6 + 397*a^5 + 123*a^4 - 412*a^3 + 129*a^2 + 41*a - 18)*q^3 + (a^2 - 2)*q^4 + (4*a^11 - 21*a^10 - 10*a^9 + 196*a^8 - 152*a^7 - 550*a^6 + 654*a^5 + 468*a^4 - 731*a^3 + 20*a^2 + 114*a + 4)*q^5 + (3*a^11 - 14*a^10 - 16*a^9 + 141*a^8 - 35*a^7 - 463*a^6 + 269*a^5 + 586*a^4 - 355*a^3 - 245*a^2 + 86*a + 38)*q^6 + (-9*a^11 + 45*a^10 + 34*a^9 - 435*a^8 + 235*a^7 + 1320*a^6 - 1172*a^5 - 1412*a^4 + 1388*a^3 + 350*a^2 - 263*a - 61)*q^7 + (a^3 - 4*a)*q^8 + (-a^9 + 3*a^8 + 9*a^7 - 29*a^6 - 23*a^5 + 87*a^4 + 13*a^3 - 88*a^2 + 10*a + 17)*q^9 + (7*a^11 - 34*a^10 - 32*a^9 + 336*a^8 - 130*a^7 - 1066*a^6 + 760*a^5 + 1265*a^4 - 948*a^3 - 458*a^2 + 212*a + 76)*q^10 + (-12*a^11 + 60*a^10 + 45*a^9 - 578*a^8 + 315*a^7 + 1739*a^6 - 1559*a^5 - 1813*a^4 + 1827*a^3 + 390*a^2 - 327*a - 68)*q^11 + (3*a^11 - 12*a^10 - 26*a^9 + 135*a^8 + 58*a^7 - 531*a^6 + 11*a^5 + 896*a^4 - 147*a^3 - 601*a^2 + 112*a + 93)*q^12 + (a^11 - 7*a^10 + 6*a^9 + 56*a^8 - 119*a^7 - 96*a^6 + 400*a^5 - 95*a^4 - 403*a^3 + 248*a^2 + 36*a - 31)*q^13 + (-18*a^11 + 88*a^10 + 78*a^9 - 863*a^8 + 375*a^7 + 2698*a^6 - 2069*a^5 - 3103*a^4 + 2528*a^3 + 1024*a^2 - 529*a - 171)*q^14 + (2*a^11 - 9*a^10 - 12*a^9 + 91*a^8 - 9*a^7 - 300*a^6 + 128*a^5 + 380*a^4 - 165*a^3 - 158*a^2 + 25*a + 23)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (14*a^11 - 66*a^10 - 73*a^9 + 663*a^8 - 176*a^7 - 2169*a^6 + 1282*a^5 + 2737*a^4 - 1683*a^3 - 1153*a^2 + 418*a + 185)*q^17 + (-a^10 + 3*a^9 + 9*a^8 - 29*a^7 - 23*a^6 + 87*a^5 + 13*a^4 - 88*a^3 + 10*a^2 + 17*a)*q^18 + (10*a^11 - 50*a^10 - 37*a^9 + 481*a^8 - 268*a^7 - 1444*a^6 + 1319*a^5 + 1500*a^4 - 1550*a^3 - 318*a^2 + 285*a + 56)*q^19 + (7*a^11 - 32*a^10 - 43*a^9 + 332*a^8 - 27*a^7 - 1150*a^6 + 468*a^5 + 1609*a^4 - 690*a^3 - 829*a^2 + 212*a + 125)*q^20 + (-a^11 + 3*a^10 + 15*a^9 - 46*a^8 - 78*a^7 + 250*a^6 + 158*a^5 - 573*a^4 - 79*a^3 + 503*a^2 - 60*a - 80)*q^21 + (-24*a^11 + 117*a^10 + 106*a^9 - 1149*a^8 + 479*a^7 + 3601*a^6 - 2689*a^5 - 4161*a^4 + 3294*a^3 + 1389*a^2 - 692*a - 228)*q^22 + (a^11 - 4*a^10 - 8*a^9 + 42*a^8 + 15*a^7 - 147*a^6 + 5*a^5 + 204*a^4 - 23*a^3 - 97*a^2 + a + 10)*q^23 + (3*a^11 - 16*a^10 - 4*a^9 + 142*a^8 - 146*a^7 - 353*a^6 + 577*a^5 + 178*a^4 - 617*a^3 + 173*a^2 + 77*a - 19)*q^24 + (13*a^11 - 64*a^10 - 54*a^9 + 625*a^8 - 294*a^7 - 1938*a^6 + 1568*a^5 + 2191*a^4 - 1912*a^3 - 692*a^2 + 407*a + 125)*q^25 + (-a^9 + 3*a^8 + 9*a^7 - 30*a^6 - 22*a^5 + 96*a^4 + 6*a^3 - 107*a^2 + 21*a + 19)*q^26 + (-6*a^11 + 28*a^10 + 33*a^9 - 283*a^8 + 58*a^7 + 935*a^6 - 493*a^5 - 1199*a^4 + 657*a^3 + 522*a^2 - 164*a - 81)*q^27 + (-20*a^11 + 96*a^10 + 95*a^9 - 951*a^8 + 338*a^7 + 3031*a^6 - 2073*a^5 - 3630*a^4 + 2604*a^3 + 1345*a^2 - 581*a - 220)*q^28 + (3*a^11 - 14*a^10 - 17*a^9 + 144*a^8 - 26*a^7 - 492*a^6 + 245*a^5 + 674*a^4 - 335*a^3 - 336*a^2 + 86*a + 53)*q^29 + (5*a^11 - 24*a^10 - 23*a^9 + 235*a^8 - 90*a^7 - 732*a^6 + 526*a^5 + 833*a^4 - 642*a^3 - 261*a^2 + 127*a + 38)*q^30 + (13*a^11 - 63*a^10 - 59*a^9 + 620*a^8 - 244*a^7 - 1951*a^6 + 1410*a^5 + 2273*a^4 - 1739*a^3 - 773*a^2 + 371*a + 120)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^11 + 4*a^10 + 8*a^9 - 43*a^8 - 13*a^7 + 157*a^6 - 21*a^5 - 238*a^4 + 59*a^3 + 147*a^2 - 30*a - 30)*q^33 + (32*a^11 - 157*a^10 - 135*a^9 + 1532*a^8 - 699*a^7 - 4738*a^6 + 3759*a^5 + 5303*a^4 - 4541*a^3 - 1584*a^2 + 913*a + 266)*q^34 + (-16*a^11 + 76*a^10 + 81*a^9 - 761*a^8 + 224*a^7 + 2476*a^6 - 1530*a^5 - 3096*a^4 + 1978*a^3 + 1283*a^2 - 473*a - 206)*q^35 + (-a^11 + 3*a^10 + 11*a^9 - 35*a^8 - 41*a^7 + 145*a^6 + 59*a^5 - 262*a^4 - 16*a^3 + 193*a^2 - 20*a - 34)*q^36 + (-2*a^11 + 12*a^10 - 3*a^9 - 101*a^8 + 150*a^7 + 211*a^6 - 533*a^5 + 32*a^4 + 544*a^3 - 306*a^2 - 56*a + 43)*q^37 + O(q^38)
*]> ;  // time = 3.179 seconds




J[226] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 226, 226, 226, 226, 113, 113, 113, 113 ], new_dimensions := [ 1, 2, 2, 4, 1, 2, 3, 3 ], dimensions := [ 1, 2, 2, 4, 2, 4, 6, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 41, 1, 1, 1, 1, 1, 0, 1, 1, 9, 1, 1, 1, 1, 1, 0, 1, 121, 1, 7, 1, 41, 1, 1, 0, 1, 3, 1, 3, 1, 9, 121, 1, 0 ], ap_traces := [
[ 1, -2, -4, 0, -4, -2, -2, -2, 4, -4, 8, -8 ],
[ -2, 0, -4, -4, -8, 4, -4, 0, 0, -4, -12, 12 ],
[ -2, 2, 4, 0, 4, -4, -4, 2, 14, 4, 4, -4 ],
[ 4, 2, 4, -4, 0, 4, 0, -6, -6, 0, 0, -8 ]
], hecke_fields := [
x - 1,
x^2 - 2,
x^2 - 2*x - 2,
x^4 - 2*x^3 - 6*x^2 + 12*x - 4
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 7, 1 ],
[ 3, 1 ],
[ 779, 1 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 779, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 19 ], torsion_lower_bounds := [ 1, 1, 1, 19 ], l_ratios := [ 0, 0, 1, 41/19 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -2, -4, 0, -4, -2, -2, -2, 4, -4, 8, -8 ],
[
-1,
a,
-a - 2,
-2*a - 2,
-4,
2,
2*a - 2,
5*a,
4*a,
-5*a - 2,
-2*a - 6,
-3*a + 6
],
[
-1,
a,
2,
0,
-2*a + 4,
-2*a,
-2,
-3*a + 4,
-a + 8,
2,
2*a,
4*a - 6
],
[
1,
a,
1/2*a^3 - a^2 - 4*a + 6,
-a^3 + a^2 + 6*a - 6,
a^2 - 4,
2*a^3 - 2*a^2 - 14*a + 12,
-2*a^3 + 2*a^2 + 12*a - 10,
-2*a^3 + 2*a^2 + 13*a - 12,
3/2*a^3 - 3*a^2 - 9*a + 12,
-3/2*a^3 + a^2 + 10*a - 6,
2*a^3 - a^2 - 12*a + 6,
-1/2*a^3 - a^2 + 2*a + 2
]
*], q_expansions := [*
q + q^2 - 2*q^3 + q^4 - 4*q^5 - 2*q^6 + q^8 + q^9 - 4*q^10 - 4*q^11 - 2*q^12 - 2*q^13 + 8*q^15 + q^16 - 2*q^17 + q^18 - 2*q^19 - 4*q^20 - 4*q^22 + 4*q^23 - 2*q^24 + 11*q^25 - 2*q^26 + 4*q^27 - 4*q^29 + 8*q^30 + 8*q^31 + q^32 + 8*q^33 - 2*q^34 + q^36 - 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 2)*q^5 - a*q^6 + (-2*a - 2)*q^7 - q^8 - q^9 + (a + 2)*q^10 - 4*q^11 + a*q^12 + 2*q^13 + (2*a + 2)*q^14 + (-2*a - 2)*q^15 + q^16 + (2*a - 2)*q^17 + q^18 + 5*a*q^19 + (-a - 2)*q^20 + (-2*a - 4)*q^21 + 4*q^22 + 4*a*q^23 - a*q^24 + (4*a + 1)*q^25 - 2*q^26 - 4*a*q^27 + (-2*a - 2)*q^28 + (-5*a - 2)*q^29 + (2*a + 2)*q^30 + (-2*a - 6)*q^31 - q^32 - 4*a*q^33 + (-2*a + 2)*q^34 + (6*a + 8)*q^35 - q^36 + (-3*a + 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + 2*q^5 - a*q^6 - q^8 + (2*a - 1)*q^9 - 2*q^10 + (-2*a + 4)*q^11 + a*q^12 - 2*a*q^13 + 2*a*q^15 + q^16 - 2*q^17 + (-2*a + 1)*q^18 + (-3*a + 4)*q^19 + 2*q^20 + (2*a - 4)*q^22 + (-a + 8)*q^23 - a*q^24 - q^25 + 2*a*q^26 + 4*q^27 + 2*q^29 - 2*a*q^30 + 2*a*q^31 - q^32 - 4*q^33 + 2*q^34 + (2*a - 1)*q^36 + (4*a - 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/2*a^3 - a^2 - 4*a + 6)*q^5 + a*q^6 + (-a^3 + a^2 + 6*a - 6)*q^7 + q^8 + (a^2 - 3)*q^9 + (1/2*a^3 - a^2 - 4*a + 6)*q^10 + (a^2 - 4)*q^11 + a*q^12 + (2*a^3 - 2*a^2 - 14*a + 12)*q^13 + (-a^3 + a^2 + 6*a - 6)*q^14 + (-a^2 + 2)*q^15 + q^16 + (-2*a^3 + 2*a^2 + 12*a - 10)*q^17 + (a^2 - 3)*q^18 + (-2*a^3 + 2*a^2 + 13*a - 12)*q^19 + (1/2*a^3 - a^2 - 4*a + 6)*q^20 + (-a^3 + 6*a - 4)*q^21 + (a^2 - 4)*q^22 + (3/2*a^3 - 3*a^2 - 9*a + 12)*q^23 + a*q^24 + (3*a^3 - 4*a^2 - 20*a + 21)*q^25 + (2*a^3 - 2*a^2 - 14*a + 12)*q^26 + (a^3 - 6*a)*q^27 + (-a^3 + a^2 + 6*a - 6)*q^28 + (-3/2*a^3 + a^2 + 10*a - 6)*q^29 + (-a^2 + 2)*q^30 + (2*a^3 - a^2 - 12*a + 6)*q^31 + q^32 + (a^3 - 4*a)*q^33 + (-2*a^3 + 2*a^2 + 12*a - 10)*q^34 + (-2*a^3 + 4*a^2 + 14*a - 20)*q^35 + (a^2 - 3)*q^36 + (-1/2*a^3 - a^2 + 2*a + 2)*q^37 + O(q^38)
*]> ;  // time = 41.27 seconds




J[227] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 227, 227, 227, 227, 227 ], new_dimensions := [ 2, 2, 2, 3, 10 ], dimensions := [ 2, 2, 2, 3, 10 ], intersection_graph := [ 0, 1, 1, 7, 1, 1, 0, 1, 1, 31, 1, 1, 0, 1, 65, 7, 1, 1, 0, 1, 1, 31, 65, 1, 0 ], ap_traces := [
[ 0, -4, 0, -2, 2, -8, -8, 10, -6, -6, -4, -20 ],
[ 0, 3, -4, 7, 1, -2, -8, 13, 11, -3, 0, 8 ],
[ 2, -1, 4, 3, 5, 2, -8, 1, 7, 5, -12, 16 ],
[ -2, 1, -5, -6, -1, -9, 7, -10, 2, -1, 2, -14 ],
[ 0, 1, 7, 0, -3, 23, 17, -16, -16, -3, 14, 38 ]
], hecke_fields := [
x^2 - 2,
x^2 - 5,
x^2 - x - 7,
x^3 + 2*x^2 - x - 1,
x^10 - 17*x^8 - 3*x^7 + 98*x^6 + 40*x^5 - 218*x^4 - 148*x^3 + 136*x^2 + 144*x + 32
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 113 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 113 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 113 ], torsion_lower_bounds := [ 1, 1, 1, 1, 113 ], l_ratios := [ 0, 1, 1, 0, 1/113 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1 ], eigenvalues := [*
[
a,
-2,
-a,
-2*a - 1,
2*a + 1,
2*a - 4,
a - 4,
2*a + 5,
-2*a - 3,
-4*a - 3,
3*a - 2,
-a - 10
],
[
a,
-1/2*a + 3/2,
-2,
1/2*a + 7/2,
-1/2*a + 1/2,
-a - 1,
-4,
1/2*a + 13/2,
-1/2*a + 11/2,
-3/2*a - 3/2,
-2*a,
4
],
[
1,
a - 1,
2,
-a + 2,
a + 2,
-2*a + 2,
-4,
-a + 1,
a + 3,
-a + 3,
-6,
8
],
[
a,
-a^2 - 2*a + 1,
a^2 + a - 3,
a^2 + 3*a - 2,
a^2 - a - 3,
-3,
a + 3,
-4*a^2 - 7*a,
-2*a^2 + 2*a + 6,
2*a^2 + 2*a - 3,
4*a^2 + 8*a - 2,
a^2 + 4*a - 4
],
[
a,
1/16*a^9 - 21/16*a^7 - 3/16*a^6 + 75/8*a^5 + 9/4*a^4 - 209/8*a^3 - 33/4*a^2 + 23*a + 10,
-3/4*a^9 + 3/4*a^8 + 49/4*a^7 - 19/2*a^6 - 269/4*a^5 + 31*a^4 + 289/2*a^3 - 21/2*a^2 - 101*a - 30,
13/16*a^9 - 1/2*a^8 - 213/16*a^7 + 97/16*a^6 + 589/8*a^5 - 16*a^4 - 1281/8*a^3 - 53/4*a^2 + 227/2*a + 42,
1/8*a^9 - 1/4*a^8 - 15/8*a^7 + 27/8*a^6 + 35/4*a^5 - 51/4*a^4 - 53/4*a^3 + 11*a^2 + 7/2*a + 1,
-1/4*a^8 + 13/4*a^6 - 1/4*a^5 - 25/2*a^4 + a^3 + 29/2*a^2 + a,
-9/8*a^9 + a^8 + 149/8*a^7 - 101/8*a^6 - 415/4*a^5 + 81/2*a^4 + 901/4*a^3 - 19/2*a^2 - 157*a - 46,
3/8*a^9 - 1/8*a^8 - 49/8*a^7 + a^6 + 271/8*a^5 + 2*a^4 - 297/4*a^3 - 85/4*a^2 + 53*a + 23,
-15/16*a^9 + 3/8*a^8 + 247/16*a^7 - 73/16*a^6 - 173/2*a^5 + 43/4*a^4 + 1539/8*a^3 + 20*a^2 - 140*a - 51,
3/4*a^9 - 3/8*a^8 - 25/2*a^7 + 33/8*a^6 + 563/8*a^5 - 15/2*a^4 - 154*a^3 - 85/4*a^2 + 105*a + 37,
1/8*a^9 - 1/4*a^8 - 21/8*a^7 + 23/8*a^6 + 37/2*a^5 - 8*a^4 - 201/4*a^3 - 2*a^2 + 42*a + 18,
-3/8*a^9 + 51/8*a^7 + 9/8*a^6 - 147/4*a^5 - 14*a^4 + 335/4*a^3 + 95/2*a^2 - 66*a - 38
]
*], q_expansions := [*
q + a*q^2 - 2*q^3 - a*q^5 - 2*a*q^6 + (-2*a - 1)*q^7 - 2*a*q^8 + q^9 - 2*q^10 + (2*a + 1)*q^11 + (2*a - 4)*q^13 + (-a - 4)*q^14 + 2*a*q^15 - 4*q^16 + (a - 4)*q^17 + a*q^18 + (2*a + 5)*q^19 + (4*a + 2)*q^21 + (a + 4)*q^22 + (-2*a - 3)*q^23 + 4*a*q^24 - 3*q^25 + (-4*a + 4)*q^26 + 4*q^27 + (-4*a - 3)*q^29 + 4*q^30 + (3*a - 2)*q^31 + (-4*a - 2)*q^33 + (-4*a + 2)*q^34 + (a + 4)*q^35 + (-a - 10)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a + 3/2)*q^3 + 3*q^4 - 2*q^5 + (3/2*a - 5/2)*q^6 + (1/2*a + 7/2)*q^7 + a*q^8 + (-3/2*a + 1/2)*q^9 - 2*a*q^10 + (-1/2*a + 1/2)*q^11 + (-3/2*a + 9/2)*q^12 + (-a - 1)*q^13 + (7/2*a + 5/2)*q^14 + (a - 3)*q^15 - q^16 - 4*q^17 + (1/2*a - 15/2)*q^18 + (1/2*a + 13/2)*q^19 - 6*q^20 + (-a + 4)*q^21 + (1/2*a - 5/2)*q^22 + (-1/2*a + 11/2)*q^23 + (3/2*a - 5/2)*q^24 - q^25 + (-a - 5)*q^26 - a*q^27 + (3/2*a + 21/2)*q^28 + (-3/2*a - 3/2)*q^29 + (-3*a + 5)*q^30 - 2*a*q^31 - 3*a*q^32 + (-a + 2)*q^33 - 4*a*q^34 + (-a - 7)*q^35 + (-9/2*a + 3/2)*q^36 + 4*q^37 + O(q^38),
q + q^2 + (a - 1)*q^3 - q^4 + 2*q^5 + (a - 1)*q^6 + (-a + 2)*q^7 - 3*q^8 + (-a + 5)*q^9 + 2*q^10 + (a + 2)*q^11 + (-a + 1)*q^12 + (-2*a + 2)*q^13 + (-a + 2)*q^14 + (2*a - 2)*q^15 - q^16 - 4*q^17 + (-a + 5)*q^18 + (-a + 1)*q^19 - 2*q^20 + (2*a - 9)*q^21 + (a + 2)*q^22 + (a + 3)*q^23 + (-3*a + 3)*q^24 - q^25 + (-2*a + 2)*q^26 + (2*a - 9)*q^27 + (a - 2)*q^28 + (-a + 3)*q^29 + (2*a - 2)*q^30 - 6*q^31 + 5*q^32 + (2*a + 5)*q^33 - 4*q^34 + (-2*a + 4)*q^35 + (a - 5)*q^36 + 8*q^37 + O(q^38),
q + a*q^2 + (-a^2 - 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 + a - 3)*q^5 - q^6 + (a^2 + 3*a - 2)*q^7 + (-2*a^2 - 3*a + 1)*q^8 + (-a^2 - a)*q^9 + (-a^2 - 2*a + 1)*q^10 + (a^2 - a - 3)*q^11 + (2*a^2 + 3*a - 2)*q^12 - 3*q^13 + (a^2 - a + 1)*q^14 + (3*a^2 + 5*a - 4)*q^15 + (-a^2 - a + 2)*q^16 + (a + 3)*q^17 + (a^2 - a - 1)*q^18 + (-4*a^2 - 7*a)*q^19 + (-2*a^2 - 2*a + 5)*q^20 + (2*a^2 + 3*a - 5)*q^21 + (-3*a^2 - 2*a + 1)*q^22 + (-2*a^2 + 2*a + 6)*q^23 + (-a^2 + 4)*q^24 + (-4*a^2 - 5*a + 4)*q^25 - 3*a*q^26 + (3*a^2 + 7*a - 2)*q^27 + (-5*a^2 - 4*a + 5)*q^28 + (2*a^2 + 2*a - 3)*q^29 + (-a^2 - a + 3)*q^30 + (4*a^2 + 8*a - 2)*q^31 + (5*a^2 + 7*a - 3)*q^32 + (3*a^2 + 5*a - 2)*q^33 + (a^2 + 3*a)*q^34 + (-5*a^2 - 8*a + 8)*q^35 + (-a^2 + 2*a + 1)*q^36 + (a^2 + 4*a - 4)*q^37 + O(q^38),
q + a*q^2 + (1/16*a^9 - 21/16*a^7 - 3/16*a^6 + 75/8*a^5 + 9/4*a^4 - 209/8*a^3 - 33/4*a^2 + 23*a + 10)*q^3 + (a^2 - 2)*q^4 + (-3/4*a^9 + 3/4*a^8 + 49/4*a^7 - 19/2*a^6 - 269/4*a^5 + 31*a^4 + 289/2*a^3 - 21/2*a^2 - 101*a - 30)*q^5 + (-1/4*a^8 + 13/4*a^6 - 1/4*a^5 - 25/2*a^4 + a^3 + 29/2*a^2 + a - 2)*q^6 + (13/16*a^9 - 1/2*a^8 - 213/16*a^7 + 97/16*a^6 + 589/8*a^5 - 16*a^4 - 1281/8*a^3 - 53/4*a^2 + 227/2*a + 42)*q^7 + (a^3 - 4*a)*q^8 + (-5/16*a^9 + 1/4*a^8 + 81/16*a^7 - 45/16*a^6 - 217/8*a^5 + 25/4*a^4 + 441/8*a^3 + 31/4*a^2 - 35*a - 14)*q^9 + (3/4*a^9 - 1/2*a^8 - 47/4*a^7 + 25/4*a^6 + 61*a^5 - 19*a^4 - 243/2*a^3 + a^2 + 78*a + 24)*q^10 + (1/8*a^9 - 1/4*a^8 - 15/8*a^7 + 27/8*a^6 + 35/4*a^5 - 51/4*a^4 - 53/4*a^3 + 11*a^2 + 7/2*a + 1)*q^11 + (-3/8*a^9 + 47/8*a^7 + 1/8*a^6 - 125/4*a^5 - 7/2*a^4 + 267/4*a^3 + 35/2*a^2 - 48*a - 20)*q^12 + (-1/4*a^8 + 13/4*a^6 - 1/4*a^5 - 25/2*a^4 + a^3 + 29/2*a^2 + a)*q^13 + (-1/2*a^9 + 1/2*a^8 + 17/2*a^7 - 6*a^6 - 97/2*a^5 + 17*a^4 + 107*a^3 + 3*a^2 - 75*a - 26)*q^14 + (5/4*a^9 - 3/4*a^8 - 83/4*a^7 + 9*a^6 + 465/4*a^5 - 24*a^4 - 507/2*a^3 - 31/2*a^2 + 172*a + 58)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-9/8*a^9 + a^8 + 149/8*a^7 - 101/8*a^6 - 415/4*a^5 + 81/2*a^4 + 901/4*a^3 - 19/2*a^2 - 157*a - 46)*q^17 + (1/4*a^9 - 1/4*a^8 - 15/4*a^7 + 7/2*a^6 + 75/4*a^5 - 13*a^4 - 77/2*a^3 + 15/2*a^2 + 31*a + 10)*q^18 + (3/8*a^9 - 1/8*a^8 - 49/8*a^7 + a^6 + 271/8*a^5 + 2*a^4 - 297/4*a^3 - 85/4*a^2 + 53*a + 23)*q^19 + (a^9 - 1/2*a^8 - 16*a^7 + 13/2*a^6 + 171/2*a^5 - 20*a^4 - 177*a^3 - 3*a^2 + 118*a + 36)*q^20 + (-13/16*a^9 + 5/8*a^8 + 217/16*a^7 - 123/16*a^6 - 305/4*a^5 + 23*a^4 + 1329/8*a^3 - 225/2*a - 32)*q^21 + (-1/4*a^9 + 1/4*a^8 + 15/4*a^7 - 7/2*a^6 - 71/4*a^5 + 14*a^4 + 59/2*a^3 - 27/2*a^2 - 17*a - 4)*q^22 + (-15/16*a^9 + 3/8*a^8 + 247/16*a^7 - 73/16*a^6 - 173/2*a^5 + 43/4*a^4 + 1539/8*a^3 + 20*a^2 - 140*a - 51)*q^23 + (-a^7 - a^6 + 12*a^5 + 10*a^4 - 40*a^3 - 26*a^2 + 32*a + 16)*q^24 + (-1/4*a^9 + 17/4*a^7 + 3/4*a^6 - 51/2*a^5 - 10*a^4 + 129/2*a^3 + 36*a^2 - 58*a - 29)*q^25 + (-1/4*a^9 + 13/4*a^7 - 1/4*a^6 - 25/2*a^5 + a^4 + 29/2*a^3 + a^2)*q^26 + (-1/2*a^9 + 1/4*a^8 + 17/2*a^7 - 9/4*a^6 - 195/4*a^5 - a^4 + 217/2*a^3 + 67/2*a^2 - 77*a - 35)*q^27 + (-9/8*a^9 + a^8 + 153/8*a^7 - 93/8*a^6 - 441/4*a^5 + 30*a^4 + 997/4*a^3 + 39/2*a^2 - 181*a - 68)*q^28 + (3/4*a^9 - 3/8*a^8 - 25/2*a^7 + 33/8*a^6 + 563/8*a^5 - 15/2*a^4 - 154*a^3 - 85/4*a^2 + 105*a + 37)*q^29 + (-3/4*a^9 + 1/2*a^8 + 51/4*a^7 - 25/4*a^6 - 74*a^5 + 19*a^4 + 339/2*a^3 + 2*a^2 - 122*a - 40)*q^30 + (1/8*a^9 - 1/4*a^8 - 21/8*a^7 + 23/8*a^6 + 37/2*a^5 - 8*a^4 - 201/4*a^3 - 2*a^2 + 42*a + 18)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (9/16*a^9 - 3/8*a^8 - 149/16*a^7 + 59/16*a^6 + 52*a^5 - 3*a^4 - 913/8*a^3 - 63/2*a^2 + 163/2*a + 33)*q^33 + (a^9 - 1/2*a^8 - 16*a^7 + 13/2*a^6 + 171/2*a^5 - 20*a^4 - 176*a^3 - 4*a^2 + 116*a + 36)*q^34 + (9/8*a^9 - 3/4*a^8 - 153/8*a^7 + 67/8*a^6 + 221/2*a^5 - 33/2*a^4 - 1009/4*a^3 - 39*a^2 + 187*a + 70)*q^35 + (3/8*a^9 - 47/8*a^7 - 1/8*a^6 + 125/4*a^5 + 7/2*a^4 - 263/4*a^3 - 37/2*a^2 + 44*a + 20)*q^36 + (-3/8*a^9 + 51/8*a^7 + 9/8*a^6 - 147/4*a^5 - 14*a^4 + 335/4*a^3 + 95/2*a^2 - 66*a - 38)*q^37 + O(q^38)
*]> ;  // time = 3.87 seconds




J[229] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 229, 229, 229 ], new_dimensions := [ 1, 6, 11 ], dimensions := [ 1, 6, 11 ], intersection_graph := [ 0, 1, 1, 1, 0, 1, 1, 1, 0 ], ap_traces := [
[ -1, 1, -3, 2, -3, -6, -7, 3, 4, -6, 4, 2 ],
[ -4, -6, -3, -5, -22, 1, 6, -19, -10, -7, -3, 2 ],
[ 5, 3, 0, 1, 27, -7, 1, 8, -2, 17, -3, -14 ]
], hecke_fields := [
x - 1,
x^6 + 4*x^5 - 12*x^3 - 3*x^2 + 9*x - 1,
x^11 - 5*x^10 - 4*x^9 + 50*x^8 - 26*x^7 - 165*x^6 + 152*x^5 + 193*x^4 - 207*x^3 - 50*x^2 + 52*x + 1
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 19 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 19 ]
], torsion_upper_bounds := [ 1, 1, 19 ], torsion_lower_bounds := [ 1, 1, 19 ], l_ratios := [ 0, 0, 1/19 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ -1, 1, -3, 2, -3, -6, -7, 3, 4, -6, 4, 2 ],
[
a,
a^4 + 2*a^3 - 3*a^2 - 4*a + 1,
-a^5 - 4*a^4 - a^3 + 8*a^2 + 3*a - 2,
a^5 + 2*a^4 - 3*a^3 - 2*a^2 + 4*a - 4,
a^4 + 3*a^3 - 2*a^2 - 6*a - 1,
a^5 + 5*a^4 + 4*a^3 - 11*a^2 - 12*a + 5,
-a^4 - 4*a^3 + a^2 + 10*a - 1,
a^5 + 4*a^4 + a^3 - 8*a^2 - 2*a - 1,
-3*a^4 - 9*a^3 + 4*a^2 + 17*a - 5,
3*a^5 + 9*a^4 - 6*a^3 - 25*a^2 + 3*a + 10,
-a^5 - a^4 + 7*a^3 + 5*a^2 - 8*a - 2,
-4*a^5 - 10*a^4 + 13*a^3 + 28*a^2 - 14*a - 9
],
[
a,
1/4*a^9 - 1/4*a^8 - 13/4*a^7 + 11/4*a^6 + 55/4*a^5 - 10*a^4 - 83/4*a^3 + 53/4*a^2 + 8*a - 11/4,
-1/4*a^9 + 1/4*a^8 + 11/4*a^7 - 5/4*a^6 - 43/4*a^5 + 65/4*a^3 + 15/4*a^2 - 6*a - 3/4,
-1/4*a^10 + 3/4*a^9 + 9/4*a^8 - 31/4*a^7 - 21/4*a^6 + 53/2*a^5 - 3/4*a^4 - 131/4*a^3 + 13/2*a^2 + 41/4*a + 3/2,
1/2*a^10 - 7/4*a^9 - 17/4*a^8 + 71/4*a^7 + 39/4*a^6 - 235/4*a^5 - 1/2*a^4 + 265/4*a^3 - 49/4*a^2 - 27/2*a + 23/4,
1/2*a^10 - 3/2*a^9 - 9/2*a^8 + 29/2*a^7 + 25/2*a^6 - 46*a^5 - 19/2*a^4 + 105/2*a^3 - 3*a^2 - 31/2*a + 2,
-1/2*a^10 + 5/2*a^9 + 5/2*a^8 - 25*a^7 + 6*a^6 + 82*a^5 - 89/2*a^4 - 93*a^3 + 54*a^2 + 39/2*a - 15/2,
-1/2*a^10 + 5/4*a^9 + 19/4*a^8 - 45/4*a^7 - 57/4*a^6 + 121/4*a^5 + 23/2*a^4 - 75/4*a^3 + 27/4*a^2 - 23/2*a - 13/4,
1/2*a^8 - 1/2*a^7 - 6*a^6 + 3*a^5 + 49/2*a^4 - 2*a^3 - 34*a^2 - 11/2*a + 7,
-1/2*a^9 + 3/2*a^8 + 9/2*a^7 - 29/2*a^6 - 25/2*a^5 + 46*a^4 + 17/2*a^3 - 99/2*a^2 + 4*a + 17/2,
1/2*a^10 - 2*a^9 - 7/2*a^8 + 41/2*a^7 + 2*a^6 - 141/2*a^5 + 26*a^4 + 88*a^3 - 85/2*a^2 - 23*a + 15/2,
3/4*a^9 - 3/4*a^8 - 33/4*a^7 + 15/4*a^6 + 125/4*a^5 + 2*a^4 - 179/4*a^3 - 77/4*a^2 + 19*a + 21/4
]
*], q_expansions := [*
q - q^2 + q^3 - q^4 - 3*q^5 - q^6 + 2*q^7 + 3*q^8 - 2*q^9 + 3*q^10 - 3*q^11 - q^12 - 6*q^13 - 2*q^14 - 3*q^15 - q^16 - 7*q^17 + 2*q^18 + 3*q^19 + 3*q^20 + 2*q^21 + 3*q^22 + 4*q^23 + 3*q^24 + 4*q^25 + 6*q^26 - 5*q^27 - 2*q^28 - 6*q^29 + 3*q^30 + 4*q^31 - 5*q^32 - 3*q^33 + 7*q^34 - 6*q^35 + 2*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (a^4 + 2*a^3 - 3*a^2 - 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 4*a^4 - a^3 + 8*a^2 + 3*a - 2)*q^5 + (a^5 + 2*a^4 - 3*a^3 - 4*a^2 + a)*q^6 + (a^5 + 2*a^4 - 3*a^3 - 2*a^2 + 4*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^4 - 5*a^3 + 5*a^2 + 10*a - 4)*q^9 + (-a^4 - 4*a^3 + 7*a - 1)*q^10 + (a^4 + 3*a^3 - 2*a^2 - 6*a - 1)*q^11 + (-2*a^5 - 5*a^4 + 4*a^3 + 10*a^2 - a - 1)*q^12 + (a^5 + 5*a^4 + 4*a^3 - 11*a^2 - 12*a + 5)*q^13 + (-2*a^5 - 3*a^4 + 10*a^3 + 7*a^2 - 13*a + 1)*q^14 + (2*a^5 + 7*a^4 + a^3 - 12*a^2 - 5*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - 4*a^3 + a^2 + 10*a - 1)*q^17 + (-2*a^5 - 5*a^4 + 5*a^3 + 10*a^2 - 4*a)*q^18 + (a^5 + 4*a^4 + a^3 - 8*a^2 - 2*a - 1)*q^19 + (a^5 + 4*a^4 + 2*a^3 - 9*a^2 - 7*a + 4)*q^20 + (-3*a^5 - 9*a^4 + 4*a^3 + 18*a^2 - 2)*q^21 + (a^5 + 3*a^4 - 2*a^3 - 6*a^2 - a)*q^22 + (-3*a^4 - 9*a^3 + 4*a^2 + 17*a - 5)*q^23 + (a^5 - 8*a^3 + a^2 + 15*a - 2)*q^24 + (-a^5 - 3*a^4 + 2*a^3 + 9*a^2 + 2*a - 3)*q^25 + (a^5 + 4*a^4 + a^3 - 9*a^2 - 4*a + 1)*q^26 + (-a^5 - 2*a^4 + 6*a^3 + 8*a^2 - 8*a - 2)*q^27 + (3*a^5 + 6*a^4 - 11*a^3 - 15*a^2 + 11*a + 6)*q^28 + (3*a^5 + 9*a^4 - 6*a^3 - 25*a^2 + 3*a + 10)*q^29 + (-a^5 + a^4 + 12*a^3 + a^2 - 18*a + 2)*q^30 + (-a^5 - a^4 + 7*a^3 + 5*a^2 - 8*a - 2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^5 - 3*a^4 - 15*a^3 + 8*a^2 + 26*a - 4)*q^33 + (-a^5 - 4*a^4 + a^3 + 10*a^2 - a)*q^34 + (a^5 + 6*a^4 + 4*a^3 - 17*a^2 - 11*a + 7)*q^35 + (3*a^5 + 9*a^4 - 4*a^3 - 20*a^2 - 2*a + 6)*q^36 + (-4*a^5 - 10*a^4 + 13*a^3 + 28*a^2 - 14*a - 9)*q^37 + O(q^38),
q + a*q^2 + (1/4*a^9 - 1/4*a^8 - 13/4*a^7 + 11/4*a^6 + 55/4*a^5 - 10*a^4 - 83/4*a^3 + 53/4*a^2 + 8*a - 11/4)*q^3 + (a^2 - 2)*q^4 + (-1/4*a^9 + 1/4*a^8 + 11/4*a^7 - 5/4*a^6 - 43/4*a^5 + 65/4*a^3 + 15/4*a^2 - 6*a - 3/4)*q^5 + (1/4*a^10 - 1/4*a^9 - 13/4*a^8 + 11/4*a^7 + 55/4*a^6 - 10*a^5 - 83/4*a^4 + 53/4*a^3 + 8*a^2 - 11/4*a)*q^6 + (-1/4*a^10 + 3/4*a^9 + 9/4*a^8 - 31/4*a^7 - 21/4*a^6 + 53/2*a^5 - 3/4*a^4 - 131/4*a^3 + 13/2*a^2 + 41/4*a + 3/2)*q^7 + (a^3 - 4*a)*q^8 + (-1/2*a^10 + 5/4*a^9 + 23/4*a^8 - 53/4*a^7 - 97/4*a^6 + 189/4*a^5 + 89/2*a^4 - 247/4*a^3 - 125/4*a^2 + 37/2*a + 23/4)*q^9 + (-1/4*a^10 + 1/4*a^9 + 11/4*a^8 - 5/4*a^7 - 43/4*a^6 + 65/4*a^4 + 15/4*a^3 - 6*a^2 - 3/4*a)*q^10 + (1/2*a^10 - 7/4*a^9 - 17/4*a^8 + 71/4*a^7 + 39/4*a^6 - 235/4*a^5 - 1/2*a^4 + 265/4*a^3 - 49/4*a^2 - 27/2*a + 23/4)*q^11 + (a^10 - 11/4*a^9 - 37/4*a^8 + 107/4*a^7 + 103/4*a^6 - 345/4*a^5 - 15*a^4 + 405/4*a^3 - 67/4*a^2 - 29*a + 21/4)*q^12 + (1/2*a^10 - 3/2*a^9 - 9/2*a^8 + 29/2*a^7 + 25/2*a^6 - 46*a^5 - 19/2*a^4 + 105/2*a^3 - 3*a^2 - 31/2*a + 2)*q^13 + (-1/2*a^10 + 5/4*a^9 + 19/4*a^8 - 47/4*a^7 - 59/4*a^6 + 149/4*a^5 + 31/2*a^4 - 181/4*a^3 - 9/4*a^2 + 29/2*a + 1/4)*q^14 + (-1/4*a^9 + 1/4*a^8 + 13/4*a^7 - 11/4*a^6 - 55/4*a^5 + 10*a^4 + 79/4*a^3 - 49/4*a^2 - 5*a + 7/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^10 + 5/2*a^9 + 5/2*a^8 - 25*a^7 + 6*a^6 + 82*a^5 - 89/2*a^4 - 93*a^3 + 54*a^2 + 39/2*a - 15/2)*q^17 + (-5/4*a^10 + 15/4*a^9 + 47/4*a^8 - 149/4*a^7 - 141/4*a^6 + 241/2*a^5 + 139/4*a^4 - 539/4*a^3 - 13/2*a^2 + 127/4*a + 1/2)*q^18 + (-1/2*a^10 + 5/4*a^9 + 19/4*a^8 - 45/4*a^7 - 57/4*a^6 + 121/4*a^5 + 23/2*a^4 - 75/4*a^3 + 27/4*a^2 - 23/2*a - 13/4)*q^19 + (-a^10 + 9/4*a^9 + 43/4*a^8 - 91/4*a^7 - 155/4*a^6 + 303/4*a^5 + 52*a^4 - 361/4*a^3 - 83/4*a^2 + 25*a + 7/4)*q^20 + (1/2*a^9 - 3/2*a^8 - 9/2*a^7 + 27/2*a^6 + 29/2*a^5 - 38*a^4 - 45/2*a^3 + 67/2*a^2 + 16*a - 7/2)*q^21 + (3/4*a^10 - 9/4*a^9 - 29/4*a^8 + 91/4*a^7 + 95/4*a^6 - 153/2*a^5 - 121/4*a^4 + 365/4*a^3 + 23/2*a^2 - 81/4*a - 1/2)*q^22 + (1/2*a^8 - 1/2*a^7 - 6*a^6 + 3*a^5 + 49/2*a^4 - 2*a^3 - 34*a^2 - 11/2*a + 7)*q^23 + (7/4*a^10 - 19/4*a^9 - 67/4*a^8 + 185/4*a^7 + 205/4*a^6 - 147*a^5 - 201/4*a^4 + 655/4*a^3 + 5*a^2 - 165/4*a - 1)*q^24 + (3/2*a^10 - 9/2*a^9 - 29/2*a^8 + 46*a^7 + 46*a^6 - 156*a^5 - 105/2*a^4 + 188*a^3 + 18*a^2 - 95/2*a - 11/2)*q^25 + (a^10 - 5/2*a^9 - 21/2*a^8 + 51/2*a^7 + 73/2*a^6 - 171/2*a^5 - 44*a^4 + 201/2*a^3 + 19/2*a^2 - 24*a - 1/2)*q^26 + (-1/2*a^10 + 7/4*a^9 + 17/4*a^8 - 71/4*a^7 - 39/4*a^6 + 239/4*a^5 - 5/2*a^4 - 277/4*a^3 + 97/4*a^2 + 19/2*a - 27/4)*q^27 + (-3/4*a^10 + 5/4*a^9 + 35/4*a^8 - 49/4*a^7 - 139/4*a^6 + 77/2*a^5 + 211/4*a^4 - 161/4*a^3 - 47/2*a^2 + 23/4*a - 5/2)*q^28 + (-1/2*a^9 + 3/2*a^8 + 9/2*a^7 - 29/2*a^6 - 25/2*a^5 + 46*a^4 + 17/2*a^3 - 99/2*a^2 + 4*a + 17/2)*q^29 + (-1/4*a^10 + 1/4*a^9 + 13/4*a^8 - 11/4*a^7 - 55/4*a^6 + 10*a^5 + 79/4*a^4 - 49/4*a^3 - 5*a^2 + 7/4*a)*q^30 + (1/2*a^10 - 2*a^9 - 7/2*a^8 + 41/2*a^7 + 2*a^6 - 141/2*a^5 + 26*a^4 + 88*a^3 - 85/2*a^2 - 23*a + 15/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^10 - 3/4*a^9 - 25/4*a^8 + 23/4*a^7 + 127/4*a^6 - 43/4*a^5 - 159/2*a^4 - 11/4*a^3 + 343/4*a^2 + 17/2*a - 69/4)*q^33 + (1/2*a^9 - 7*a^7 - 1/2*a^6 + 63/2*a^5 + 7/2*a^4 - 99/2*a^3 - 11/2*a^2 + 37/2*a + 1/2)*q^34 + (1/4*a^10 - 1/4*a^9 - 13/4*a^8 + 11/4*a^7 + 55/4*a^6 - 10*a^5 - 83/4*a^4 + 57/4*a^3 + 9*a^2 - 35/4*a - 1)*q^35 + (-3/2*a^10 + 17/4*a^9 + 55/4*a^8 - 165/4*a^7 - 149/4*a^6 + 521/4*a^5 + 35/2*a^4 - 567/4*a^3 + 127/4*a^2 + 57/2*a - 41/4)*q^36 + (3/4*a^9 - 3/4*a^8 - 33/4*a^7 + 15/4*a^6 + 125/4*a^5 + 2*a^4 - 179/4*a^3 - 77/4*a^2 + 19*a + 21/4)*q^37 + O(q^38)
*]> ;  // time = 3.08 seconds




J[230] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 230, 230, 230, 230, 115, 115, 115, 46, 23 ], new_dimensions := [ 2, 2, 2, 3, 1, 2, 4, 1, 2 ], dimensions := [ 2, 2, 2, 3, 2, 4, 8, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 5, 1, 1, 5, 5, 1, 0, 1, 1, 1, 1, 43, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 11, 1, 1, 1, 0, 1, 19, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 5, 25, 1, 1, 1, 19, 1, 0, 1, 1, 1, 1, 43, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 5, 1, 1, 0, 25, 5, 1, 11, 1, 25, 1, 1, 25, 0 ], ap_traces := [
[ -2, -1, -2, 1, 3, 7, -3, 7, 2, 6, 7, -8 ],
[ -2, 3, 2, 3, -7, 3, 3, 1, -2, 2, -5, 16 ],
[ 2, 1, 2, 1, 1, -3, 1, -3, 2, -14, 7, 4 ],
[ 3, 1, -3, 3, 3, -1, -7, 3, -3, -4, -5, -2 ]
], hecke_fields := [
x^2 + x - 5,
x^2 - 3*x - 1,
x^2 - x - 1,
x^3 - x^2 - 9*x + 12
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 5, 5, 3 ],
[ 43, 3, 1 ],
[ 11, 11, 1 ],
[ 57, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 3 ],
[ 1, 3, 1 ],
[ 11, 11, 1 ],
[ 57, 1, 1 ]
], torsion_upper_bounds := [ 3, 3, 11, 3 ], torsion_lower_bounds := [ 3, 3, 1, 3 ], l_ratios := [ 1/3, 1/3, 1, 19/3 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/121, 1 ], eigenvalues := [*
[
-1,
a,
-1,
a + 1,
a + 2,
-a + 3,
-a - 2,
-a + 3,
1,
-2*a + 2,
3*a + 5,
-4
],
[
-1,
a,
1,
-a + 3,
-a - 2,
-a + 3,
-3*a + 6,
-3*a + 5,
-1,
2*a - 2,
3*a - 7,
8
],
[
1,
a,
1,
-a + 1,
-3*a + 2,
-5*a + 1,
5*a - 2,
3*a - 3,
1,
-2*a - 6,
5*a + 1,
4*a
],
[
1,
a,
-1,
-a^2 - 2*a + 8,
2*a^2 + a - 12,
-a^2 + 6,
-a - 2,
-a^2 - 2*a + 8,
-1,
2*a - 2,
a^2 - 8,
2*a^2 + 2*a - 14
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (a + 1)*q^7 - q^8 + (-a + 2)*q^9 + q^10 + (a + 2)*q^11 + a*q^12 + (-a + 3)*q^13 + (-a - 1)*q^14 - a*q^15 + q^16 + (-a - 2)*q^17 + (a - 2)*q^18 + (-a + 3)*q^19 - q^20 + 5*q^21 + (-a - 2)*q^22 + q^23 - a*q^24 + q^25 + (a - 3)*q^26 - 5*q^27 + (a + 1)*q^28 + (-2*a + 2)*q^29 + a*q^30 + (3*a + 5)*q^31 - q^32 + (a + 5)*q^33 + (a + 2)*q^34 + (-a - 1)*q^35 + (-a + 2)*q^36 - 4*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 + (-a + 3)*q^7 - q^8 + (3*a - 2)*q^9 - q^10 + (-a - 2)*q^11 + a*q^12 + (-a + 3)*q^13 + (a - 3)*q^14 + a*q^15 + q^16 + (-3*a + 6)*q^17 + (-3*a + 2)*q^18 + (-3*a + 5)*q^19 + q^20 - q^21 + (a + 2)*q^22 - q^23 - a*q^24 + q^25 + (a - 3)*q^26 + (4*a + 3)*q^27 + (-a + 3)*q^28 + (2*a - 2)*q^29 - a*q^30 + (3*a - 7)*q^31 - q^32 + (-5*a - 1)*q^33 + (3*a - 6)*q^34 + (-a + 3)*q^35 + (3*a - 2)*q^36 + 8*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 + (-a + 1)*q^7 + q^8 + (a - 2)*q^9 + q^10 + (-3*a + 2)*q^11 + a*q^12 + (-5*a + 1)*q^13 + (-a + 1)*q^14 + a*q^15 + q^16 + (5*a - 2)*q^17 + (a - 2)*q^18 + (3*a - 3)*q^19 + q^20 - q^21 + (-3*a + 2)*q^22 + q^23 + a*q^24 + q^25 + (-5*a + 1)*q^26 + (-4*a + 1)*q^27 + (-a + 1)*q^28 + (-2*a - 6)*q^29 + a*q^30 + (5*a + 1)*q^31 + q^32 + (-a - 3)*q^33 + (5*a - 2)*q^34 + (-a + 1)*q^35 + (a - 2)*q^36 + 4*a*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + (-a^2 - 2*a + 8)*q^7 + q^8 + (a^2 - 3)*q^9 - q^10 + (2*a^2 + a - 12)*q^11 + a*q^12 + (-a^2 + 6)*q^13 + (-a^2 - 2*a + 8)*q^14 - a*q^15 + q^16 + (-a - 2)*q^17 + (a^2 - 3)*q^18 + (-a^2 - 2*a + 8)*q^19 - q^20 + (-3*a^2 - a + 12)*q^21 + (2*a^2 + a - 12)*q^22 - q^23 + a*q^24 + q^25 + (-a^2 + 6)*q^26 + (a^2 + 3*a - 12)*q^27 + (-a^2 - 2*a + 8)*q^28 + (2*a - 2)*q^29 - a*q^30 + (a^2 - 8)*q^31 + q^32 + (3*a^2 + 6*a - 24)*q^33 + (-a - 2)*q^34 + (a^2 + 2*a - 8)*q^35 + (a^2 - 3)*q^36 + (2*a^2 + 2*a - 14)*q^37 + O(q^38)
*]> ;  // time = 83.25 seconds




J[231] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 231, 231, 231, 231, 231, 77, 77, 77, 77, 33, 21, 11 ], new_dimensions := [ 1, 2, 2, 3, 3, 1, 1, 1, 2, 1, 1, 1 ], dimensions := [ 1, 2, 2, 3, 3, 2, 2, 2, 4, 2, 2, 4 ], intersection_graph := [ 0, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 3, 1, 1, 3, 1, 3, 1, 1, 1, 1, 0, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 3, 1, 9, 1, 5, 1, 1, 1, 1, 1, 0, 25, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 25, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 0, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 3, 1, 1, 9, 1, 1, 9, 1, 0 ], ap_traces := [
[ -1, -1, -2, 1, -1, 6, 2, 4, 0, -2, 8, 6 ],
[ -1, -2, 6, 2, -2, 2, 6, -4, -2, 2, -2, 2 ],
[ 1, 2, 2, 2, 2, -2, 6, 0, -2, 10, -6, -14 ],
[ 0, -3, 0, -3, 3, 0, 0, 12, -6, 12, -6, 0 ],
[ 2, 3, 4, -3, -3, -4, 8, -8, 10, -4, -2, 0 ]
], hecke_fields := [
x - 1,
x^2 + x - 5,
x^2 - x - 1,
x^3 - 6*x - 1,
x^3 - 2*x^2 - 4*x + 7
], atkin_lehners := [
[ 1, -1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 25, 1, 1 ],
[ 5, 5, 1 ],
[ 3, 3, 1 ],
[ 7, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 5, 1 ],
[ 1, 1, 1 ],
[ 7, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 1, 1, 7 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/25, 1, 1 ], eigenvalues := [*
[ -1, -1, -2, 1, -1, 6, 2, 4, 0, -2, 8, 6 ],
[
a,
-1,
3,
1,
-1,
1,
2*a + 4,
-2*a - 3,
-2*a - 2,
-4*a - 1,
2*a,
1
],
[
a,
1,
1,
1,
1,
-4*a + 1,
-2*a + 4,
6*a - 3,
-6*a + 2,
5,
2*a - 4,
-7
],
[
a,
-1,
-a^2 + a + 4,
-1,
1,
-a^2 + a + 4,
-2*a,
-a^2 - a + 8,
-2*a - 2,
a^2 - a,
2*a^2 - 10,
a^2 + 3*a - 4
],
[
a,
1,
-a^2 - a + 6,
-1,
-1,
-3*a^2 + a + 10,
4*a^2 - 2*a - 12,
a^2 - a - 6,
2*a + 2,
-3*a^2 + a + 10,
2*a^2 - 4*a - 6,
-a^2 + 3*a + 2
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - 2*q^5 + q^6 + q^7 + 3*q^8 + q^9 + 2*q^10 - q^11 + q^12 + 6*q^13 - q^14 + 2*q^15 - q^16 + 2*q^17 - q^18 + 4*q^19 + 2*q^20 - q^21 + q^22 - 3*q^24 - q^25 - 6*q^26 - q^27 - q^28 - 2*q^29 - 2*q^30 + 8*q^31 - 5*q^32 + q^33 - 2*q^34 - 2*q^35 - q^36 + 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a + 3)*q^4 + 3*q^5 - a*q^6 + q^7 + (2*a - 5)*q^8 + q^9 + 3*a*q^10 - q^11 + (a - 3)*q^12 + q^13 + a*q^14 - 3*q^15 + (-5*a + 4)*q^16 + (2*a + 4)*q^17 + a*q^18 + (-2*a - 3)*q^19 + (-3*a + 9)*q^20 - q^21 - a*q^22 + (-2*a - 2)*q^23 + (-2*a + 5)*q^24 + 4*q^25 + a*q^26 - q^27 + (-a + 3)*q^28 + (-4*a - 1)*q^29 - 3*a*q^30 + 2*a*q^31 + (5*a - 15)*q^32 + q^33 + (2*a + 10)*q^34 + 3*q^35 + (-a + 3)*q^36 + q^37 + O(q^38),
q + a*q^2 + q^3 + (a - 1)*q^4 + q^5 + a*q^6 + q^7 + (-2*a + 1)*q^8 + q^9 + a*q^10 + q^11 + (a - 1)*q^12 + (-4*a + 1)*q^13 + a*q^14 + q^15 - 3*a*q^16 + (-2*a + 4)*q^17 + a*q^18 + (6*a - 3)*q^19 + (a - 1)*q^20 + q^21 + a*q^22 + (-6*a + 2)*q^23 + (-2*a + 1)*q^24 - 4*q^25 + (-3*a - 4)*q^26 + q^27 + (a - 1)*q^28 + 5*q^29 + a*q^30 + (2*a - 4)*q^31 + (a - 5)*q^32 + q^33 + (2*a - 2)*q^34 + q^35 + (a - 1)*q^36 - 7*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 4)*q^5 - a*q^6 - q^7 + (2*a + 1)*q^8 + q^9 + (a^2 - 2*a - 1)*q^10 + q^11 + (-a^2 + 2)*q^12 + (-a^2 + a + 4)*q^13 - a*q^14 + (a^2 - a - 4)*q^15 + (a + 4)*q^16 - 2*a*q^17 + a*q^18 + (-a^2 - a + 8)*q^19 + (3*a - 7)*q^20 + q^21 + a*q^22 + (-2*a - 2)*q^23 + (-2*a - 1)*q^24 + (-a^2 - 3*a + 9)*q^25 + (a^2 - 2*a - 1)*q^26 - q^27 + (-a^2 + 2)*q^28 + (a^2 - a)*q^29 + (-a^2 + 2*a + 1)*q^30 + (2*a^2 - 10)*q^31 + (a^2 - 2)*q^32 - q^33 - 2*a^2*q^34 + (a^2 - a - 4)*q^35 + (a^2 - 2)*q^36 + (a^2 + 3*a - 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 - a + 6)*q^5 + a*q^6 - q^7 + (2*a^2 - 7)*q^8 + q^9 + (-3*a^2 + 2*a + 7)*q^10 - q^11 + (a^2 - 2)*q^12 + (-3*a^2 + a + 10)*q^13 - a*q^14 + (-a^2 - a + 6)*q^15 + (2*a^2 + a - 10)*q^16 + (4*a^2 - 2*a - 12)*q^17 + a*q^18 + (a^2 - a - 6)*q^19 + (-2*a^2 - 3*a + 9)*q^20 - q^21 - a*q^22 + (2*a + 2)*q^23 + (2*a^2 - 7)*q^24 + (a^2 - 3*a + 3)*q^25 + (-5*a^2 - 2*a + 21)*q^26 + q^27 + (-a^2 + 2)*q^28 + (-3*a^2 + a + 10)*q^29 + (-3*a^2 + 2*a + 7)*q^30 + (2*a^2 - 4*a - 6)*q^31 + (a^2 - 2*a)*q^32 - q^33 + (6*a^2 + 4*a - 28)*q^34 + (a^2 + a - 6)*q^35 + (a^2 - 2)*q^36 + (-a^2 + 3*a + 2)*q^37 + O(q^38)
*]> ;  // time = 56.311 seconds




J[233] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 233, 233, 233 ], new_dimensions := [ 1, 7, 11 ], dimensions := [ 1, 7, 11 ], intersection_graph := [ 0, 1, 27, 1, 0, 1, 27, 1, 0 ], ap_traces := [
[ 1, -2, 2, 4, 6, 6, -6, -4, 0, -2, 4, -6 ],
[ -2, -8, -3, -17, 1, -12, -5, -8, -16, 3, -24, -10 ],
[ -2, 10, -1, 15, -5, 4, 7, 8, 8, -9, 24, 14 ]
], hecke_fields := [
x - 1,
x^7 + 2*x^6 - 6*x^5 - 10*x^4 + 10*x^3 + 8*x^2 - 7*x + 1,
x^11 + 2*x^10 - 16*x^9 - 30*x^8 + 91*x^7 + 158*x^6 - 213*x^5 - 349*x^4 + 152*x^3 + 290*x^2 + 41*x - 19
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 29 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 29 ]
], torsion_upper_bounds := [ 1, 1, 29 ], torsion_lower_bounds := [ 1, 1, 29 ], l_ratios := [ 1, 0, 1/29 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[ 1, -2, 2, 4, 6, 6, -6, -4, 0, -2, 4, -6 ],
[
a,
a^5 + a^4 - 5*a^3 - 4*a^2 + 3*a,
-a^5 - 2*a^4 + 4*a^3 + 8*a^2 - a - 3,
-a^6 - 3*a^5 + 5*a^4 + 16*a^3 - 6*a^2 - 16*a + 3,
-a^6 - 2*a^5 + 7*a^4 + 11*a^3 - 13*a^2 - 11*a + 5,
6*a^6 + 14*a^5 - 29*a^4 - 68*a^3 + 25*a^2 + 52*a - 16,
5*a^6 + 13*a^5 - 24*a^4 - 65*a^3 + 22*a^2 + 53*a - 17,
-5*a^6 - 10*a^5 + 24*a^4 + 46*a^3 - 18*a^2 - 28*a + 6,
-3*a^6 - 7*a^5 + 17*a^4 + 35*a^3 - 26*a^2 - 29*a + 14,
-4*a^6 - 11*a^5 + 19*a^4 + 57*a^3 - 16*a^2 - 51*a + 13,
a^6 + a^5 - 7*a^4 - 5*a^3 + 11*a^2 + 4*a - 4,
3*a^6 + 7*a^5 - 13*a^4 - 34*a^3 + 6*a^2 + 24*a - 8
],
[
a,
7/4*a^10 - 1/2*a^9 - 107/4*a^8 + 8*a^7 + 139*a^6 - 65/2*a^5 - 1147/4*a^4 + 31/4*a^3 + 883/4*a^2 + 203/4*a - 16,
27/2*a^10 - 9/2*a^9 - 409/2*a^8 + 145/2*a^7 + 1046*a^6 - 310*a^5 - 4193/2*a^4 + 183*a^3 + 1550*a^2 + 294*a - 219/2,
a^10 - 1/2*a^9 - 15*a^8 + 15/2*a^7 + 75*a^6 - 31*a^5 - 143*a^4 + 43/2*a^3 + 195/2*a^2 + 41/2*a - 5/2,
9/4*a^10 - 3/4*a^9 - 135/4*a^8 + 49/4*a^7 + 170*a^6 - 107/2*a^5 - 1331/4*a^4 + 75/2*a^3 + 242*a^2 + 37*a - 81/4,
-a^10 + 15*a^8 - a^7 - 76*a^6 + 6*a^5 + 150*a^4 + 3*a^3 - 104*a^2 - 20*a + 7,
-21/2*a^10 + 4*a^9 + 319/2*a^8 - 63*a^7 - 819*a^6 + 268*a^5 + 3305/2*a^4 - 349/2*a^3 - 2477/2*a^2 - 455/2*a + 92,
33/2*a^10 - 13/2*a^9 - 499/2*a^8 + 205/2*a^7 + 1271*a^6 - 439*a^5 - 5055/2*a^4 + 306*a^3 + 1855*a^2 + 332*a - 249/2,
-9/2*a^10 + 2*a^9 + 135/2*a^8 - 31*a^7 - 339*a^6 + 132*a^5 + 1315/2*a^4 - 197/2*a^3 - 941/2*a^2 - 163/2*a + 31,
-33*a^10 + 12*a^9 + 500*a^8 - 191*a^7 - 2556*a^6 + 819*a^5 + 5112*a^4 - 544*a^3 - 3768*a^2 - 670*a + 264,
14*a^10 - 5*a^9 - 212*a^8 + 80*a^7 + 1083*a^6 - 345*a^5 - 2165*a^4 + 236*a^3 + 1600*a^2 + 268*a - 118,
29*a^10 - 23/2*a^9 - 438*a^8 + 363/2*a^7 + 2227*a^6 - 781*a^5 - 4415*a^4 + 1137/2*a^3 + 6467/2*a^2 + 1091/2*a - 455/2
]
*], q_expansions := [*
q + q^2 - 2*q^3 - q^4 + 2*q^5 - 2*q^6 + 4*q^7 - 3*q^8 + q^9 + 2*q^10 + 6*q^11 + 2*q^12 + 6*q^13 + 4*q^14 - 4*q^15 - q^16 - 6*q^17 + q^18 - 4*q^19 - 2*q^20 - 8*q^21 + 6*q^22 + 6*q^24 - q^25 + 6*q^26 + 4*q^27 - 4*q^28 - 2*q^29 - 4*q^30 + 4*q^31 + 5*q^32 - 12*q^33 - 6*q^34 + 8*q^35 - q^36 - 6*q^37 + O(q^38),
q + a*q^2 + (a^5 + a^4 - 5*a^3 - 4*a^2 + 3*a)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 2*a^4 + 4*a^3 + 8*a^2 - a - 3)*q^5 + (a^6 + a^5 - 5*a^4 - 4*a^3 + 3*a^2)*q^6 + (-a^6 - 3*a^5 + 5*a^4 + 16*a^3 - 6*a^2 - 16*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 - 4*a^5 + 3*a^4 + 19*a^3 + 4*a^2 - 11*a - 1)*q^9 + (-a^6 - 2*a^5 + 4*a^4 + 8*a^3 - a^2 - 3*a)*q^10 + (-a^6 - 2*a^5 + 7*a^4 + 11*a^3 - 13*a^2 - 11*a + 5)*q^11 + (-a^6 - a^5 + 4*a^4 + 3*a^3 + a - 1)*q^12 + (6*a^6 + 14*a^5 - 29*a^4 - 68*a^3 + 25*a^2 + 52*a - 16)*q^13 + (-a^6 - a^5 + 6*a^4 + 4*a^3 - 8*a^2 - 4*a + 1)*q^14 + (2*a^6 + 6*a^5 - 7*a^4 - 27*a^3 - a^2 + 16*a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (5*a^6 + 13*a^5 - 24*a^4 - 65*a^3 + 22*a^2 + 53*a - 17)*q^17 + (-2*a^6 - 3*a^5 + 9*a^4 + 14*a^3 - 3*a^2 - 8*a + 1)*q^18 + (-5*a^6 - 10*a^5 + 24*a^4 + 46*a^3 - 18*a^2 - 28*a + 6)*q^19 + (2*a^4 + a^3 - 11*a^2 - 5*a + 7)*q^20 + (-a^6 - 5*a^5 + 2*a^4 + 24*a^3 + 7*a^2 - 13*a + 2)*q^21 + (a^5 + a^4 - 3*a^3 - 3*a^2 - 2*a + 1)*q^22 + (-3*a^6 - 7*a^5 + 17*a^4 + 35*a^3 - 26*a^2 - 29*a + 14)*q^23 + (-a^6 - 4*a^5 + 3*a^4 + 18*a^3 + 3*a^2 - 8*a + 1)*q^24 + (-4*a^6 - 10*a^5 + 19*a^4 + 49*a^3 - 15*a^2 - 34*a + 10)*q^25 + (2*a^6 + 7*a^5 - 8*a^4 - 35*a^3 + 4*a^2 + 26*a - 6)*q^26 + (2*a^6 + 5*a^5 - 10*a^4 - 23*a^3 + 9*a^2 + 13*a - 5)*q^27 + (3*a^6 + 6*a^5 - 16*a^4 - 30*a^3 + 16*a^2 + 26*a - 5)*q^28 + (-4*a^6 - 11*a^5 + 19*a^4 + 57*a^3 - 16*a^2 - 51*a + 13)*q^29 + (2*a^6 + 5*a^5 - 7*a^4 - 21*a^3 + 10*a - 2)*q^30 + (a^6 + a^5 - 7*a^4 - 5*a^3 + 11*a^2 + 4*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3*a^6 - 7*a^5 + 11*a^4 + 31*a^3 + a^2 - 17*a + 4)*q^33 + (3*a^6 + 6*a^5 - 15*a^4 - 28*a^3 + 13*a^2 + 18*a - 5)*q^34 + (4*a^6 + 12*a^5 - 15*a^4 - 56*a^3 + a^2 + 36*a - 6)*q^35 + (3*a^6 + 5*a^5 - 12*a^4 - 21*a^3 + 9*a + 4)*q^36 + (3*a^6 + 7*a^5 - 13*a^4 - 34*a^3 + 6*a^2 + 24*a - 8)*q^37 + O(q^38),
q + a*q^2 + (7/4*a^10 - 1/2*a^9 - 107/4*a^8 + 8*a^7 + 139*a^6 - 65/2*a^5 - 1147/4*a^4 + 31/4*a^3 + 883/4*a^2 + 203/4*a - 16)*q^3 + (a^2 - 2)*q^4 + (27/2*a^10 - 9/2*a^9 - 409/2*a^8 + 145/2*a^7 + 1046*a^6 - 310*a^5 - 4193/2*a^4 + 183*a^3 + 1550*a^2 + 294*a - 219/2)*q^5 + (-4*a^10 + 5/4*a^9 + 121/2*a^8 - 81/4*a^7 - 309*a^6 + 86*a^5 + 1237/2*a^4 - 181/4*a^3 - 1827/4*a^2 - 351/4*a + 133/4)*q^6 + (a^10 - 1/2*a^9 - 15*a^8 + 15/2*a^7 + 75*a^6 - 31*a^5 - 143*a^4 + 43/2*a^3 + 195/2*a^2 + 41/2*a - 5/2)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^10 + 1/2*a^9 + 30*a^8 - 17/2*a^7 - 151*a^6 + 36*a^5 + 294*a^4 - 23/2*a^3 - 417/2*a^2 - 95/2*a + 31/2)*q^9 + (-63/2*a^10 + 23/2*a^9 + 955/2*a^8 - 365/2*a^7 - 2443*a^6 + 779*a^5 + 9789/2*a^4 - 502*a^3 - 3621*a^2 - 663*a + 513/2)*q^10 + (9/4*a^10 - 3/4*a^9 - 135/4*a^8 + 49/4*a^7 + 170*a^6 - 107/2*a^5 - 1331/4*a^4 + 75/2*a^3 + 242*a^2 + 37*a - 81/4)*q^11 + (23/4*a^10 - 5/2*a^9 - 347/4*a^8 + 39*a^7 + 440*a^6 - 337/2*a^5 - 3471/4*a^4 + 543/4*a^3 + 2523/4*a^2 + 383/4*a - 44)*q^12 + (-a^10 + 15*a^8 - a^7 - 76*a^6 + 6*a^5 + 150*a^4 + 3*a^3 - 104*a^2 - 20*a + 7)*q^13 + (-5/2*a^10 + a^9 + 75/2*a^8 - 16*a^7 - 189*a^6 + 70*a^5 + 741/2*a^4 - 109/2*a^3 - 539/2*a^2 - 87/2*a + 19)*q^14 + (-17/2*a^10 + 7/2*a^9 + 257/2*a^8 - 109/2*a^7 - 654*a^6 + 231*a^5 + 2597/2*a^4 - 158*a^3 - 956*a^2 - 175*a + 141/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-21/2*a^10 + 4*a^9 + 319/2*a^8 - 63*a^7 - 819*a^6 + 268*a^5 + 3305/2*a^4 - 349/2*a^3 - 2477/2*a^2 - 455/2*a + 92)*q^17 + (9/2*a^10 - 2*a^9 - 137/2*a^8 + 31*a^7 + 352*a^6 - 132*a^5 - 1419/2*a^4 + 191/2*a^3 + 1065/2*a^2 + 195/2*a - 38)*q^18 + (33/2*a^10 - 13/2*a^9 - 499/2*a^8 + 205/2*a^7 + 1271*a^6 - 439*a^5 - 5055/2*a^4 + 306*a^3 + 1855*a^2 + 332*a - 249/2)*q^19 + (95/2*a^10 - 35/2*a^9 - 1437/2*a^8 + 557/2*a^7 + 3664*a^6 - 1195*a^5 - 14605/2*a^4 + 801*a^3 + 5372*a^2 + 960*a - 759/2)*q^20 + (3/2*a^10 - 1/2*a^9 - 45/2*a^8 + 15/2*a^7 + 113*a^6 - 28*a^5 - 437/2*a^4 - a^3 + 153*a^2 + 49*a - 15/2)*q^21 + (-21/4*a^10 + 9/4*a^9 + 319/4*a^8 - 139/4*a^7 - 409*a^6 + 293/2*a^5 + 3291/4*a^4 - 100*a^3 - 1231/2*a^2 - 225/2*a + 171/4)*q^22 + (-9/2*a^10 + 2*a^9 + 135/2*a^8 - 31*a^7 - 339*a^6 + 132*a^5 + 1315/2*a^4 - 197/2*a^3 - 941/2*a^2 - 163/2*a + 31)*q^23 + (-6*a^10 + 11/4*a^9 + 181/2*a^8 - 171/4*a^7 - 459*a^6 + 185*a^5 + 1811/2*a^4 - 611/4*a^3 - 2633/4*a^2 - 417/4*a + 171/4)*q^24 + (-10*a^10 + 4*a^9 + 151*a^8 - 63*a^7 - 768*a^6 + 270*a^5 + 1525*a^4 - 191*a^3 - 1120*a^2 - 200*a + 77)*q^25 + (2*a^10 - a^9 - 31*a^8 + 15*a^7 + 164*a^6 - 63*a^5 - 346*a^4 + 48*a^3 + 270*a^2 + 48*a - 19)*q^26 + (-15/2*a^10 + 11/4*a^9 + 113*a^8 - 175/4*a^7 - 572*a^6 + 187*a^5 + 1124*a^4 - 489/4*a^3 - 3239/4*a^2 - 595/4*a + 207/4)*q^27 + (4*a^10 - 3/2*a^9 - 61*a^8 + 47/2*a^7 + 315*a^6 - 100*a^5 - 641*a^4 + 135/2*a^3 + 973/2*a^2 + 161/2*a - 85/2)*q^28 + (-33*a^10 + 12*a^9 + 500*a^8 - 191*a^7 - 2556*a^6 + 819*a^5 + 5112*a^4 - 544*a^3 - 3768*a^2 - 670*a + 264)*q^29 + (41/2*a^10 - 15/2*a^9 - 619/2*a^8 + 239/2*a^7 + 1574*a^6 - 512*a^5 - 6249/2*a^4 + 336*a^3 + 2290*a^2 + 419*a - 323/2)*q^30 + (14*a^10 - 5*a^9 - 212*a^8 + 80*a^7 + 1083*a^6 - 345*a^5 - 2165*a^4 + 236*a^3 + 1600*a^2 + 268*a - 118)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-4*a^10 + 3/2*a^9 + 61*a^8 - 47/2*a^7 - 315*a^6 + 99*a^5 + 640*a^4 - 117/2*a^3 - 955/2*a^2 - 199/2*a + 59/2)*q^33 + (25*a^10 - 17/2*a^9 - 378*a^8 + 273/2*a^7 + 1927*a^6 - 584*a^5 - 3839*a^4 + 715/2*a^3 + 5635/2*a^2 + 1045/2*a - 399/2)*q^34 + (17*a^10 - 6*a^9 - 257*a^8 + 96*a^7 + 1310*a^6 - 410*a^5 - 2610*a^4 + 251*a^3 + 1916*a^2 + 371*a - 130)*q^35 + (-7*a^10 + 5/2*a^9 + 106*a^8 - 81/2*a^7 - 541*a^6 + 177*a^5 + 1078*a^4 - 257/2*a^3 - 1581/2*a^2 - 255/2*a + 109/2)*q^36 + (29*a^10 - 23/2*a^9 - 438*a^8 + 363/2*a^7 + 2227*a^6 - 781*a^5 - 4415*a^4 + 1137/2*a^3 + 6467/2*a^2 + 1091/2*a - 455/2)*q^37 + O(q^38)
*]> ;  // time = 3.2 seconds




J[235] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 235, 235, 235, 235, 235, 47 ], new_dimensions := [ 1, 1, 1, 5, 7, 4 ], dimensions := [ 1, 1, 1, 5, 7, 8 ], intersection_graph := [ 0, 3, 1, 1, 1, 9, 3, 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 9, 3, 3, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, 1, 3, 3, 6, -1, 4, 2, -3, 0 ],
[ 2, 2, -1, -2, 0, 3, 0, -4, 1, 8, 6, -6 ],
[ -1, -1, 1, 1, -3, -3, -6, -7, 4, -10, 3, 12 ],
[ -4, -5, -5, -5, -1, -11, -14, 5, -6, -16, 3, -16 ],
[ 1, 1, 7, -3, 1, 2, 12, 3, 1, 26, -5, 0 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^5 + 4*x^4 - 12*x^2 - 4*x + 7,
x^7 - x^6 - 10*x^5 + 8*x^4 + 28*x^3 - 17*x^2 - 19*x + 2
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 1 ],
[ 3, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 1, 0, 0, 1 ], analytic_sha_upper_bounds := [ 1, 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 0, 1 ], eigenvalues := [*
[ -1, -1, -1, 1, 3, 3, 6, -1, 4, 2, -3, 0 ],
[ 2, 2, -1, -2, 0, 3, 0, -4, 1, 8, 6, -6 ],
[ -1, -1, 1, 1, -3, -3, -6, -7, 4, -10, 3, 12 ],
[
a,
a^4 + 2*a^3 - 4*a^2 - 5*a + 3,
-1,
-2*a^4 - 5*a^3 + 5*a^2 + 10*a - 5,
a^4 + 3*a^3 + a^2 - 3*a - 5,
a^4 + a^3 - 5*a^2 - 3*a + 1,
a^3 + a^2 - 2*a - 2,
-a^4 - a^3 + 3*a^2 - a + 1,
-2*a^4 - 2*a^3 + 12*a^2 + 6*a - 14,
-4*a^3 - 8*a^2 + 10*a + 8,
a^4 + a^3 - 9*a^2 - 5*a + 15,
2*a^4 + 5*a^3 - 3*a^2 - 8*a - 4
],
[
a,
1/2*a^6 - 5*a^4 + 12*a^2 - 3/2*a - 3,
1,
-1/2*a^6 + 4*a^4 + a^3 - 7*a^2 - 3/2*a + 1,
-3/2*a^6 + 13*a^4 + 3*a^3 - 25*a^2 - 15/2*a + 3,
-1/2*a^6 - a^5 + 5*a^4 + 9*a^3 - 11*a^2 - 33/2*a + 2,
a^6 - 8*a^4 - 3*a^3 + 13*a^2 + 9*a + 2,
1/2*a^6 + 2*a^5 - 5*a^4 - 17*a^3 + 9*a^2 + 57/2*a + 3,
a^6 + a^5 - 10*a^4 - 10*a^3 + 24*a^2 + 17*a - 7,
-2*a + 4,
-1/2*a^6 + 5*a^4 + a^3 - 11*a^2 - 5/2*a - 1,
2*a^6 + 2*a^5 - 18*a^4 - 19*a^3 + 33*a^2 + 34*a + 2
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 - q^5 + q^6 + q^7 + 3*q^8 - 2*q^9 + q^10 + 3*q^11 + q^12 + 3*q^13 - q^14 + q^15 - q^16 + 6*q^17 + 2*q^18 - q^19 + q^20 - q^21 - 3*q^22 + 4*q^23 - 3*q^24 + q^25 - 3*q^26 + 5*q^27 - q^28 + 2*q^29 - q^30 - 3*q^31 - 5*q^32 - 3*q^33 - 6*q^34 - q^35 + 2*q^36 + O(q^38),
q + 2*q^2 + 2*q^3 + 2*q^4 - q^5 + 4*q^6 - 2*q^7 + q^9 - 2*q^10 + 4*q^12 + 3*q^13 - 4*q^14 - 2*q^15 - 4*q^16 + 2*q^18 - 4*q^19 - 2*q^20 - 4*q^21 + q^23 + q^25 + 6*q^26 - 4*q^27 - 4*q^28 + 8*q^29 - 4*q^30 + 6*q^31 - 8*q^32 + 2*q^35 + 2*q^36 - 6*q^37 + O(q^38),
q - q^2 - q^3 - q^4 + q^5 + q^6 + q^7 + 3*q^8 - 2*q^9 - q^10 - 3*q^11 + q^12 - 3*q^13 - q^14 - q^15 - q^16 - 6*q^17 + 2*q^18 - 7*q^19 - q^20 - q^21 + 3*q^22 + 4*q^23 - 3*q^24 + q^25 + 3*q^26 + 5*q^27 - q^28 - 10*q^29 + q^30 + 3*q^31 - 5*q^32 + 3*q^33 + 6*q^34 + q^35 + 2*q^36 + 12*q^37 + O(q^38),
q + a*q^2 + (a^4 + 2*a^3 - 4*a^2 - 5*a + 3)*q^3 + (a^2 - 2)*q^4 - q^5 + (-2*a^4 - 4*a^3 + 7*a^2 + 7*a - 7)*q^6 + (-2*a^4 - 5*a^3 + 5*a^2 + 10*a - 5)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^4 - 3*a^3 + 9*a^2 + 6*a - 8)*q^9 - a*q^10 + (a^4 + 3*a^3 + a^2 - 3*a - 5)*q^11 + (2*a^4 + 3*a^3 - 9*a^2 - 5*a + 8)*q^12 + (a^4 + a^3 - 5*a^2 - 3*a + 1)*q^13 + (3*a^4 + 5*a^3 - 14*a^2 - 13*a + 14)*q^14 + (-a^4 - 2*a^3 + 4*a^2 + 5*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^3 + a^2 - 2*a - 2)*q^17 + (5*a^4 + 9*a^3 - 18*a^2 - 16*a + 14)*q^18 + (-a^4 - a^3 + 3*a^2 - a + 1)*q^19 + (-a^2 + 2)*q^20 + (2*a^4 + 4*a^3 - 4*a^2 - 2*a - 1)*q^21 + (-a^4 + a^3 + 9*a^2 - a - 7)*q^22 + (-2*a^4 - 2*a^3 + 12*a^2 + 6*a - 14)*q^23 + (-a^4 - a^3 + 5*a^2 + 2*a)*q^24 + q^25 + (-3*a^4 - 5*a^3 + 9*a^2 + 5*a - 7)*q^26 + (2*a^4 + 2*a^3 - 10*a^2 + 9)*q^27 + (-3*a^4 - 4*a^3 + 13*a^2 + 6*a - 11)*q^28 + (-4*a^3 - 8*a^2 + 10*a + 8)*q^29 + (2*a^4 + 4*a^3 - 7*a^2 - 7*a + 7)*q^30 + (a^4 + a^3 - 9*a^2 - 5*a + 15)*q^31 + (-4*a^4 - 8*a^3 + 12*a^2 + 16*a - 7)*q^32 + (-3*a^4 - 9*a^3 + 3*a^2 + 15*a - 1)*q^33 + (a^4 + a^3 - 2*a^2 - 2*a)*q^34 + (2*a^4 + 5*a^3 - 5*a^2 - 10*a + 5)*q^35 + (-7*a^4 - 12*a^3 + 26*a^2 + 22*a - 19)*q^36 + (2*a^4 + 5*a^3 - 3*a^2 - 8*a - 4)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^6 - 5*a^4 + 12*a^2 - 3/2*a - 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (1/2*a^6 - 4*a^4 - 2*a^3 + 7*a^2 + 13/2*a - 1)*q^6 + (-1/2*a^6 + 4*a^4 + a^3 - 7*a^2 - 3/2*a + 1)*q^7 + (a^3 - 4*a)*q^8 + (1/2*a^6 - 4*a^4 - a^3 + 5*a^2 + 3/2*a + 6)*q^9 + a*q^10 + (-3/2*a^6 + 13*a^4 + 3*a^3 - 25*a^2 - 15/2*a + 3)*q^11 + (-1/2*a^6 + a^5 + 4*a^4 - 7*a^3 - 9*a^2 + 23/2*a + 5)*q^12 + (-1/2*a^6 - a^5 + 5*a^4 + 9*a^3 - 11*a^2 - 33/2*a + 2)*q^13 + (-1/2*a^6 - a^5 + 5*a^4 + 7*a^3 - 10*a^2 - 17/2*a + 1)*q^14 + (1/2*a^6 - 5*a^4 + 12*a^2 - 3/2*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - 8*a^4 - 3*a^3 + 13*a^2 + 9*a + 2)*q^17 + (1/2*a^6 + a^5 - 5*a^4 - 9*a^3 + 10*a^2 + 31/2*a - 1)*q^18 + (1/2*a^6 + 2*a^5 - 5*a^4 - 17*a^3 + 9*a^2 + 57/2*a + 3)*q^19 + (a^2 - 2)*q^20 + (1/2*a^6 - 4*a^4 - 2*a^3 + 8*a^2 + 11/2*a - 3)*q^21 + (-3/2*a^6 - 2*a^5 + 15*a^4 + 17*a^3 - 33*a^2 - 51/2*a + 3)*q^22 + (a^6 + a^5 - 10*a^4 - 10*a^3 + 24*a^2 + 17*a - 7)*q^23 + (-1/2*a^6 - a^5 + 5*a^4 + 9*a^3 - 11*a^2 - 35/2*a + 3)*q^24 + q^25 + (-3/2*a^6 + 13*a^4 + 3*a^3 - 25*a^2 - 15/2*a + 1)*q^26 + (1/2*a^6 - 2*a^5 - 4*a^4 + 16*a^3 + 10*a^2 - 57/2*a - 7)*q^27 + (-1/2*a^6 + 3*a^4 + 2*a^3 - 3*a^2 - 11/2*a - 1)*q^28 + (-2*a + 4)*q^29 + (1/2*a^6 - 4*a^4 - 2*a^3 + 7*a^2 + 13/2*a - 1)*q^30 + (-1/2*a^6 + 5*a^4 + a^3 - 11*a^2 - 5/2*a - 1)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3/2*a^6 + 13*a^4 + 3*a^3 - 23*a^2 - 19/2*a - 5)*q^33 + (a^6 + 2*a^5 - 11*a^4 - 15*a^3 + 26*a^2 + 21*a - 2)*q^34 + (-1/2*a^6 + 4*a^4 + a^3 - 7*a^2 - 3/2*a + 1)*q^35 + (1/2*a^6 - 5*a^4 - 2*a^3 + 14*a^2 + 11/2*a - 13)*q^36 + (2*a^6 + 2*a^5 - 18*a^4 - 19*a^3 + 33*a^2 + 34*a + 2)*q^37 + O(q^38)
*]> ;  // time = 26.59 seconds




J[237] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 237, 237, 237, 79, 79 ], new_dimensions := [ 2, 4, 7, 1, 5 ], dimensions := [ 2, 4, 7, 2, 10 ], intersection_graph := [ 0, 1, 1, 1, 31, 1, 0, 1, 3, 1, 1, 1, 0, 5, 1, 1, 3, 5, 0, 1, 31, 1, 1, 1, 0 ], ap_traces := [
[ 2, -2, 0, 2, 6, -2, 2, -4, 6, 6, -4, 0 ],
[ -3, -4, -4, -2, -8, -6, -8, -4, -18, -2, 0, 4 ],
[ 2, 7, -2, 4, 2, 6, -8, 4, 8, -10, 4, 10 ]
], hecke_fields := [
x^2 - 2*x - 1,
x^4 + 3*x^3 - x^2 - 5*x + 1,
x^7 - 2*x^6 - 11*x^5 + 22*x^4 + 30*x^3 - 65*x^2 - 2*x + 23
], atkin_lehners := [
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 31, 1 ],
[ 3, 1 ],
[ 25, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 25, 1 ]
], torsion_upper_bounds := [ 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 5 ], l_ratios := [ 1, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[
a,
-1,
0,
1,
-a + 4,
-2*a + 1,
-a + 2,
-2,
-3*a + 6,
-a + 4,
-2*a,
6*a - 6
],
[
a,
-1,
-a^3 - 3*a^2 + 2,
2*a^3 + 4*a^2 - 4*a - 4,
-a^3 - a^2 + 2*a - 3,
-a^3 + a^2 + 6*a - 5,
2*a^3 + 4*a^2 - 2*a - 4,
-a^3 - 5*a^2 - 2*a + 6,
a^3 + 5*a^2 + 4*a - 10,
-2*a^3 - 8*a^2 - 4*a + 8,
3*a^3 + 5*a^2 - 4*a - 1,
-2*a^3 - 4*a^2 + 6*a + 6
],
[
a,
1,
-a^6 + 12*a^4 - a^3 - 37*a^2 + 9*a + 16,
3/2*a^6 - 1/2*a^5 - 17*a^4 + 4*a^3 + 49*a^2 - 25/2*a - 37/2,
1/2*a^6 + 1/2*a^5 - 6*a^4 - 4*a^3 + 17*a^2 + 7/2*a - 7/2,
5/2*a^6 - 1/2*a^5 - 28*a^4 + 4*a^3 + 79*a^2 - 33/2*a - 57/2,
-5/2*a^6 + 1/2*a^5 + 27*a^4 - 2*a^3 - 73*a^2 + 11/2*a + 53/2,
-3*a^6 + 34*a^4 + a^3 - 97*a^2 + 7*a + 38,
-3/2*a^6 + 1/2*a^5 + 17*a^4 - 5*a^3 - 48*a^2 + 33/2*a + 33/2,
5/2*a^6 - 1/2*a^5 - 29*a^4 + 4*a^3 + 87*a^2 - 35/2*a - 81/2,
-3*a^6 + 35*a^4 - 104*a^2 + 12*a + 44,
-a^6 + a^5 + 10*a^4 - 6*a^3 - 26*a^2 + 5*a + 15
]
*], q_expansions := [*
q + a*q^2 - q^3 + (2*a - 1)*q^4 - a*q^6 + q^7 + (a + 2)*q^8 + q^9 + (-a + 4)*q^11 + (-2*a + 1)*q^12 + (-2*a + 1)*q^13 + a*q^14 + 3*q^16 + (-a + 2)*q^17 + a*q^18 - 2*q^19 - q^21 + (2*a - 1)*q^22 + (-3*a + 6)*q^23 + (-a - 2)*q^24 - 5*q^25 + (-3*a - 2)*q^26 - q^27 + (2*a - 1)*q^28 + (-a + 4)*q^29 - 2*a*q^31 + (a - 4)*q^32 + (a - 4)*q^33 - q^34 + (2*a - 1)*q^36 + (6*a - 6)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^3 - 3*a^2 + 2)*q^5 - a*q^6 + (2*a^3 + 4*a^2 - 4*a - 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^2 - 3*a + 1)*q^10 + (-a^3 - a^2 + 2*a - 3)*q^11 + (-a^2 + 2)*q^12 + (-a^3 + a^2 + 6*a - 5)*q^13 + (-2*a^3 - 2*a^2 + 6*a - 2)*q^14 + (a^3 + 3*a^2 - 2)*q^15 + (-3*a^3 - 5*a^2 + 5*a + 3)*q^16 + (2*a^3 + 4*a^2 - 2*a - 4)*q^17 + a*q^18 + (-a^3 - 5*a^2 - 2*a + 6)*q^19 + (a^3 + 3*a^2 + a - 4)*q^20 + (-2*a^3 - 4*a^2 + 4*a + 4)*q^21 + (2*a^3 + a^2 - 8*a + 1)*q^22 + (a^3 + 5*a^2 + 4*a - 10)*q^23 + (-a^3 + 4*a)*q^24 + (a^3 + 3*a^2 + 2*a - 2)*q^25 + (4*a^3 + 5*a^2 - 10*a + 1)*q^26 - q^27 + (-4*a^2 - 4*a + 10)*q^28 + (-2*a^3 - 8*a^2 - 4*a + 8)*q^29 + (a^2 + 3*a - 1)*q^30 + (3*a^3 + 5*a^2 - 4*a - 1)*q^31 + (2*a^3 + 2*a^2 - 4*a + 3)*q^32 + (a^3 + a^2 - 2*a + 3)*q^33 + (-2*a^3 + 6*a - 2)*q^34 + (4*a^2 + 6*a - 10)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 - 4*a^2 + 6*a + 6)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^6 + 12*a^4 - a^3 - 37*a^2 + 9*a + 16)*q^5 + a*q^6 + (3/2*a^6 - 1/2*a^5 - 17*a^4 + 4*a^3 + 49*a^2 - 25/2*a - 37/2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2*a^6 + a^5 + 21*a^4 - 7*a^3 - 56*a^2 + 14*a + 23)*q^10 + (1/2*a^6 + 1/2*a^5 - 6*a^4 - 4*a^3 + 17*a^2 + 7/2*a - 7/2)*q^11 + (a^2 - 2)*q^12 + (5/2*a^6 - 1/2*a^5 - 28*a^4 + 4*a^3 + 79*a^2 - 33/2*a - 57/2)*q^13 + (5/2*a^6 - 1/2*a^5 - 29*a^4 + 4*a^3 + 85*a^2 - 31/2*a - 69/2)*q^14 + (-a^6 + 12*a^4 - a^3 - 37*a^2 + 9*a + 16)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5/2*a^6 + 1/2*a^5 + 27*a^4 - 2*a^3 - 73*a^2 + 11/2*a + 53/2)*q^17 + a*q^18 + (-3*a^6 + 34*a^4 + a^3 - 97*a^2 + 7*a + 38)*q^19 + (-a^6 - a^5 + 13*a^4 + 6*a^3 - 42*a^2 + a + 14)*q^20 + (3/2*a^6 - 1/2*a^5 - 17*a^4 + 4*a^3 + 49*a^2 - 25/2*a - 37/2)*q^21 + (3/2*a^6 - 1/2*a^5 - 15*a^4 + 2*a^3 + 36*a^2 - 5/2*a - 23/2)*q^22 + (-3/2*a^6 + 1/2*a^5 + 17*a^4 - 5*a^3 - 48*a^2 + 33/2*a + 33/2)*q^23 + (a^3 - 4*a)*q^24 + (a^5 - a^4 - 8*a^3 + 6*a^2 + 11*a - 2)*q^25 + (9/2*a^6 - 1/2*a^5 - 51*a^4 + 4*a^3 + 146*a^2 - 47/2*a - 115/2)*q^26 + q^27 + (3/2*a^6 - 1/2*a^5 - 17*a^4 + 2*a^3 + 49*a^2 - 9/2*a - 41/2)*q^28 + (5/2*a^6 - 1/2*a^5 - 29*a^4 + 4*a^3 + 87*a^2 - 35/2*a - 81/2)*q^29 + (-2*a^6 + a^5 + 21*a^4 - 7*a^3 - 56*a^2 + 14*a + 23)*q^30 + (-3*a^6 + 35*a^4 - 104*a^2 + 12*a + 44)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^6 + 1/2*a^5 - 6*a^4 - 4*a^3 + 17*a^2 + 7/2*a - 7/2)*q^33 + (-9/2*a^6 - 1/2*a^5 + 53*a^4 + 2*a^3 - 157*a^2 + 43/2*a + 115/2)*q^34 + (-2*a^6 + 24*a^4 - 72*a^2 + 8*a + 26)*q^35 + (a^2 - 2)*q^36 + (-a^6 + a^5 + 10*a^4 - 6*a^3 - 26*a^2 + 5*a + 15)*q^37 + O(q^38)
*]> ;  // time = 29.42 seconds




J[238] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 238, 238, 238, 238, 238, 238, 119, 119, 34, 17, 14 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 4, 5, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 2, 8, 10, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 61, 1, 1, 1, 1, 5, 1, 7, 1, 1, 0, 1, 3, 1, 3, 1, 1, 1, 1, 1, 61, 1, 0, 1, 9, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -2, -1, -2, 0, -1, -2, -8, 0, 8, -4 ],
[ -1, 2, 4, 1, -4, -4, -1, -6, 0, 6, 4, -10 ],
[ 1, 2, 0, -1, -2, -2, -1, 0, 4, 4, 0, 8 ],
[ 1, -2, -4, 1, -6, -2, -1, 0, -4, 8, 0, 4 ],
[ 1, 0, 2, 1, 0, -2, 1, 4, 0, -6, 0, -6 ],
[ -2, 2, 2, -2, 6, 4, 2, -8, 16, 2, -12, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 2*x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, 1 ],
[ -1, -1, -1 ],
[ 1, 1, -1 ]
], component_group_orders := [
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 1, 1 ],
[ 1, 1, 1 ],
[ 61, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 0, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, -2, -1, -2, 0, -1, -2, -8, 0, 8, -4 ],
[ -1, 2, 4, 1, -4, -4, -1, -6, 0, 6, 4, -10 ],
[ 1, 2, 0, -1, -2, -2, -1, 0, 4, 4, 0, 8 ],
[ 1, -2, -4, 1, -6, -2, -1, 0, -4, 8, 0, 4 ],
[ 1, 0, 2, 1, 0, -2, 1, 4, 0, -6, 0, -6 ],
[
-1,
a,
-a + 2,
-1,
a + 2,
-2*a + 4,
1,
-2*a - 2,
8,
-3*a + 4,
2*a - 8,
-a
]
*], q_expansions := [*
q - q^2 + q^4 - 2*q^5 - q^7 - q^8 - 3*q^9 + 2*q^10 - 2*q^11 + q^14 + q^16 - q^17 + 3*q^18 - 2*q^19 - 2*q^20 + 2*q^22 - 8*q^23 - q^25 - q^28 + 8*q^31 - q^32 + q^34 + 2*q^35 - 3*q^36 - 4*q^37 + O(q^38),
q - q^2 + 2*q^3 + q^4 + 4*q^5 - 2*q^6 + q^7 - q^8 + q^9 - 4*q^10 - 4*q^11 + 2*q^12 - 4*q^13 - q^14 + 8*q^15 + q^16 - q^17 - q^18 - 6*q^19 + 4*q^20 + 2*q^21 + 4*q^22 - 2*q^24 + 11*q^25 + 4*q^26 - 4*q^27 + q^28 + 6*q^29 - 8*q^30 + 4*q^31 - q^32 - 8*q^33 + q^34 + 4*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + 2*q^6 - q^7 + q^8 + q^9 - 2*q^11 + 2*q^12 - 2*q^13 - q^14 + q^16 - q^17 + q^18 - 2*q^21 - 2*q^22 + 4*q^23 + 2*q^24 - 5*q^25 - 2*q^26 - 4*q^27 - q^28 + 4*q^29 + q^32 - 4*q^33 - q^34 + q^36 + 8*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 4*q^5 - 2*q^6 + q^7 + q^8 + q^9 - 4*q^10 - 6*q^11 - 2*q^12 - 2*q^13 + q^14 + 8*q^15 + q^16 - q^17 + q^18 - 4*q^20 - 2*q^21 - 6*q^22 - 4*q^23 - 2*q^24 + 11*q^25 - 2*q^26 + 4*q^27 + q^28 + 8*q^29 + 8*q^30 + q^32 + 12*q^33 - q^34 - 4*q^35 + q^36 + 4*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 + q^7 + q^8 - 3*q^9 + 2*q^10 - 2*q^13 + q^14 + q^16 + q^17 - 3*q^18 + 4*q^19 + 2*q^20 - q^25 - 2*q^26 + q^28 - 6*q^29 + q^32 + q^34 + 2*q^35 - 3*q^36 - 6*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a + 2)*q^5 - a*q^6 - q^7 - q^8 + (2*a + 1)*q^9 + (a - 2)*q^10 + (a + 2)*q^11 + a*q^12 + (-2*a + 4)*q^13 + q^14 - 4*q^15 + q^16 + q^17 + (-2*a - 1)*q^18 + (-2*a - 2)*q^19 + (-a + 2)*q^20 - a*q^21 + (-a - 2)*q^22 + 8*q^23 - a*q^24 + (-2*a + 3)*q^25 + (2*a - 4)*q^26 + (2*a + 8)*q^27 - q^28 + (-3*a + 4)*q^29 + 4*q^30 + (2*a - 8)*q^31 - q^32 + (4*a + 4)*q^33 - q^34 + (a - 2)*q^35 + (2*a + 1)*q^36 - a*q^37 + O(q^38)
*]> ;  // time = 81.379 seconds




J[239] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 239, 239 ], new_dimensions := [ 3, 17 ], dimensions := [ 3, 17 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -1, -4, -3, -1, -7, -2, -10, 3, 4, -8, -3 ],
[ 0, 3, 6, 5, -1, 15, 4, 24, -9, -2, 28, 11 ]
], hecke_fields := [
x^3 + x^2 - 2*x - 1,
x^17 - 28*x^15 + x^14 + 319*x^13 - 17*x^12 - 1903*x^11 + 91*x^10 + 6377*x^9 - 125*x^8 - 11967*x^7 - 233*x^6 + 11733*x^5 + 503*x^4 - 5015*x^3 - 94*x^2 + 609*x + 49
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 119 ]
], tamagawa_numbers := [
[ 1 ],
[ 119 ]
], torsion_upper_bounds := [ 1, 119 ], torsion_lower_bounds := [ 1, 119 ], l_ratios := [ 0, 1/119 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^2 - a + 1,
a^2 - 3,
-1,
a^2 - 2,
a^2 - 4,
-a^2 + 1,
a^2 + 3*a - 4,
-a^2 + a + 3,
-6*a^2 - a + 11,
-2*a^2 - 2*a,
3*a
],
[
a,
16771351/11107271*a^16 - 2866545/1586753*a^15 - 63196242/1586753*a^14 + 548454202/11107271*a^13 + 4613893796/11107271*a^12 - 5855599700/11107271*a^11 - 24126751696/11107271*a^10 + 4398458577/1586753*a^9 + 9469941088/1586753*a^8 - 82906055202/11107271*a^7 - 91822850183/11107271*a^6 + 108744026520/11107271*a^5 + 54627655140/11107271*a^4 - 59185678764/11107271*a^3 - 7102994828/11107271*a^2 + 7384450585/11107271*a + 86905773/1586753,
22511799/11107271*a^16 - 4122295/1586753*a^15 - 85029894/1586753*a^14 + 783888478/11107271*a^13 + 6223382488/11107271*a^12 - 8326382581/11107271*a^11 - 32632212856/11107271*a^10 + 6229020626/1586753*a^9 + 12852845780/1586753*a^8 - 117052738164/11107271*a^7 - 125297104388/11107271*a^6 + 153180936380/11107271*a^5 + 75340597103/11107271*a^4 - 83236570496/11107271*a^3 - 10250253852/11107271*a^2 + 10451957825/11107271*a + 132668371/1586753,
25677032/11107271*a^16 - 4808908/1586753*a^15 - 96911585/1586753*a^14 + 913041769/11107271*a^13 + 7082868525/11107271*a^12 - 9683160111/11107271*a^11 - 37044681867/11107271*a^10 + 7231854089/1586753*a^9 + 2075098395/226679*a^8 - 135617406635/11107271*a^7 - 140464578889/11107271*a^6 + 176959976663/11107271*a^5 + 83052116143/11107271*a^4 - 95724702685/11107271*a^3 - 10472865097/11107271*a^2 + 11880604573/11107271*a + 142368927/1586753,
11795867/11107271*a^16 - 1932394/1586753*a^15 - 44322451/1586753*a^14 + 372521827/11107271*a^13 + 3225743447/11107271*a^12 - 4005866463/11107271*a^11 - 16804920021/11107271*a^10 + 3031135855/1586753*a^9 + 6564330462/1586753*a^8 - 57627409134/11107271*a^7 - 63241803565/11107271*a^6 + 76509429271/11107271*a^5 + 37396414775/11107271*a^4 - 42451276279/11107271*a^3 - 5056555641/11107271*a^2 + 5464612926/11107271*a + 75908807/1586753,
12932667/11107271*a^16 - 2279337/1586753*a^15 - 48752987/1586753*a^14 + 433764071/11107271*a^13 + 3560780261/11107271*a^12 - 4604482467/11107271*a^11 - 18627365653/11107271*a^10 + 3435101051/1586753*a^9 + 7316629361/1586753*a^8 - 64145365971/11107271*a^7 - 71086180147/11107271*a^6 + 82910826763/11107271*a^5 + 42558283977/11107271*a^4 - 44016310883/11107271*a^3 - 5687517959/11107271*a^2 + 5215960508/11107271*a + 67672208/1586753,
21279582/11107271*a^16 - 576557/226679*a^15 - 11490920/226679*a^14 + 764328658/11107271*a^13 + 5888803376/11107271*a^12 - 8085603784/11107271*a^11 - 30866495077/11107271*a^10 + 6022752188/1586753*a^9 + 12144661700/1586753*a^8 - 112598812800/11107271*a^7 - 118266415576/11107271*a^6 + 146376439975/11107271*a^5 + 71289580280/11107271*a^4 - 78898734658/11107271*a^3 - 10026490116/11107271*a^2 + 9892317506/11107271*a + 131645167/1586753,
17310495/11107271*a^16 - 3414606/1586753*a^15 - 65437688/1586753*a^14 + 645668596/11107271*a^13 + 4788816728/11107271*a^12 - 6824305772/11107271*a^11 - 25069140146/11107271*a^10 + 5083421254/1586753*a^9 + 9834005994/1586753*a^8 - 95167008616/11107271*a^7 - 95086769046/11107271*a^6 + 124129226300/11107271*a^5 + 56185475128/11107271*a^4 - 67333009400/11107271*a^3 - 7048228324/11107271*a^2 + 8503642143/11107271*a + 97915806/1586753,
31722361/11107271*a^16 - 5850154/1586753*a^15 - 119732695/1586753*a^14 + 1112154343/11107271*a^13 + 8752755413/11107271*a^12 - 11810292925/11107271*a^11 - 45803042055/11107271*a^10 + 8833142877/1586753*a^9 + 17978970083/1586753*a^8 - 165930762117/11107271*a^7 - 174209659179/11107271*a^6 + 216989136849/11107271*a^5 + 103470227181/11107271*a^4 - 117637416119/11107271*a^3 - 13353180733/11107271*a^2 + 14550510082/11107271*a + 176544419/1586753,
37599616/11107271*a^16 - 6005504/1586753*a^15 - 141443329/1586753*a^14 + 1156074400/11107271*a^13 + 10313257723/11107271*a^12 - 12402758789/11107271*a^11 - 53893343681/11107271*a^10 + 9348637439/1586753*a^9 + 21162527937/1586753*a^8 - 176565199519/11107271*a^7 - 205761663785/11107271*a^6 + 231733252097/11107271*a^5 + 123644621259/11107271*a^4 - 126013913667/11107271*a^3 - 17196071544/11107271*a^2 + 15589598961/11107271*a + 203454605/1586753,
-24153904/11107271*a^16 + 4321005/1586753*a^15 + 91255413/1586753*a^14 - 822194252/11107271*a^13 - 6682216498/11107271*a^12 + 8733648358/11107271*a^11 + 35066854706/11107271*a^10 - 6528082826/1586753*a^9 - 1975726498/226679*a^8 + 122383812294/11107271*a^7 + 135081794294/11107271*a^6 - 159364496414/11107271*a^5 - 81358052074/11107271*a^4 + 85759333630/11107271*a^3 + 10925236722/11107271*a^2 - 10535502669/11107271*a - 128905963/1586753,
58834648/11107271*a^16 - 10469071/1586753*a^15 - 221869889/1586753*a^14 + 1994193703/11107271*a^13 + 16206951361/11107271*a^12 - 21201818723/11107271*a^11 - 84762261663/11107271*a^10 + 15858972953/1586753*a^9 + 33262149523/1586753*a^8 - 297518575153/11107271*a^7 - 322391208789/11107271*a^6 + 387851937953/11107271*a^5 + 191863930809/11107271*a^4 - 209242126735/11107271*a^3 - 25038696915/11107271*a^2 + 25744954717/11107271*a + 307195088/1586753
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 + (-a - 1)*q^6 - q^7 + (-a^2 - 2*a + 1)*q^8 + (a - 1)*q^9 + (-a^2 - a + 1)*q^10 + (a^2 - 2)*q^11 + (a^2 + a - 2)*q^12 + (a^2 - 4)*q^13 - a*q^14 + (2*a^2 + 2*a - 3)*q^15 + (-3*a^2 - a + 3)*q^16 + (-a^2 + 1)*q^17 + (a^2 - a)*q^18 + (a^2 + 3*a - 4)*q^19 + (-2*a^2 - a + 5)*q^20 + (a^2 + a - 1)*q^21 + (-a^2 + 1)*q^22 + (-a^2 + a + 3)*q^23 + (2*a + 3)*q^24 + (-3*a^2 - a + 3)*q^25 + (-a^2 - 2*a + 1)*q^26 + (4*a^2 + 3*a - 5)*q^27 + (-a^2 + 2)*q^28 + (-6*a^2 - a + 11)*q^29 + (a + 2)*q^30 + (-2*a^2 - 2*a)*q^31 + (4*a^2 + a - 5)*q^32 + (a^2 + a - 2)*q^33 + (a^2 - a - 1)*q^34 + (-a^2 + 3)*q^35 + (-2*a^2 + 3)*q^36 + 3*a*q^37 + O(q^38),
q + a*q^2 + (16771351/11107271*a^16 - 2866545/1586753*a^15 - 63196242/1586753*a^14 + 548454202/11107271*a^13 + 4613893796/11107271*a^12 - 5855599700/11107271*a^11 - 24126751696/11107271*a^10 + 4398458577/1586753*a^9 + 9469941088/1586753*a^8 - 82906055202/11107271*a^7 - 91822850183/11107271*a^6 + 108744026520/11107271*a^5 + 54627655140/11107271*a^4 - 59185678764/11107271*a^3 - 7102994828/11107271*a^2 + 7384450585/11107271*a + 86905773/1586753)*q^3 + (a^2 - 2)*q^4 + (22511799/11107271*a^16 - 4122295/1586753*a^15 - 85029894/1586753*a^14 + 783888478/11107271*a^13 + 6223382488/11107271*a^12 - 8326382581/11107271*a^11 - 32632212856/11107271*a^10 + 6229020626/1586753*a^9 + 12852845780/1586753*a^8 - 117052738164/11107271*a^7 - 125297104388/11107271*a^6 + 153180936380/11107271*a^5 + 75340597103/11107271*a^4 - 83236570496/11107271*a^3 - 10250253852/11107271*a^2 + 10451957825/11107271*a + 132668371/1586753)*q^5 + (-2866545/1586753*a^16 + 3889162/1586753*a^15 + 75954693/1586753*a^14 - 105166739/1586753*a^13 - 795783819/1586753*a^12 + 1112732751/1586753*a^11 + 4180431014/1586753*a^10 - 5808759673/1586753*a^9 - 11544233761/1586753*a^8 + 15554272462/1586753*a^7 + 16093107329/1586753*a^6 - 20307229449/1586753*a^5 - 9660238331/1586753*a^4 + 11000761491/1586753*a^3 + 1280136797/1586753*a^2 - 1372201764/1586753*a - 16771351/226679)*q^6 + (25677032/11107271*a^16 - 4808908/1586753*a^15 - 96911585/1586753*a^14 + 913041769/11107271*a^13 + 7082868525/11107271*a^12 - 9683160111/11107271*a^11 - 37044681867/11107271*a^10 + 7231854089/1586753*a^9 + 2075098395/226679*a^8 - 135617406635/11107271*a^7 - 140464578889/11107271*a^6 + 176959976663/11107271*a^5 + 83052116143/11107271*a^4 - 95724702685/11107271*a^3 - 10472865097/11107271*a^2 + 11880604573/11107271*a + 142368927/1586753)*q^7 + (a^3 - 4*a)*q^8 + (-40326507/11107271*a^16 + 7012377/1586753*a^15 + 151773551/1586753*a^14 - 1340855037/11107271*a^13 - 11062061824/11107271*a^12 + 14306805063/11107271*a^11 + 57702618949/11107271*a^10 - 10739526779/1586753*a^9 - 3223836327/226679*a^8 + 202279847143/11107271*a^7 + 217699265401/11107271*a^6 - 265111857765/11107271*a^5 - 128705356679/11107271*a^4 + 144216800690/11107271*a^3 + 16680675317/11107271*a^2 - 17999251300/11107271*a - 216160587/1586753)*q^9 + (-4122295/1586753*a^16 + 5017302/1586753*a^15 + 108768097/1586753*a^14 - 136840199/1586753*a^13 - 1134811714/1586753*a^12 + 1458248663/1586753*a^11 + 5936367239/1586753*a^10 - 7655403109/1586753*a^9 - 16319823327/1586753*a^8 + 20585942035/1586753*a^7 + 22632312221/1586753*a^6 - 26970048652/1586753*a^5 - 13508572199/1586753*a^4 + 14663774019/1586753*a^3 + 1795438133/1586753*a^2 - 1825858142/1586753*a - 22511799/226679)*q^10 + (11795867/11107271*a^16 - 1932394/1586753*a^15 - 44322451/1586753*a^14 + 372521827/11107271*a^13 + 3225743447/11107271*a^12 - 4005866463/11107271*a^11 - 16804920021/11107271*a^10 + 3031135855/1586753*a^9 + 6564330462/1586753*a^8 - 57627409134/11107271*a^7 - 63241803565/11107271*a^6 + 76509429271/11107271*a^5 + 37396414775/11107271*a^4 - 42451276279/11107271*a^3 - 5056555641/11107271*a^2 + 5464612926/11107271*a + 75908807/1586753)*q^11 + (-6318568/11107271*a^16 + 1424523/1586753*a^15 + 24092290/1586753*a^14 - 266400152/11107271*a^13 - 1779777190/11107271*a^12 + 2788970553/11107271*a^11 + 9418174846/11107271*a^10 - 2061193450/1586753*a^9 - 3743927839/1586753*a^8 + 38336253602/11107271*a^7 + 36819759328/11107271*a^6 - 49677513962/11107271*a^5 - 22156874898/11107271*a^4 + 26702252882/11107271*a^3 + 2714390698/11107271*a^2 - 3370616034/11107271*a - 33350841/1586753)*q^12 + (12932667/11107271*a^16 - 2279337/1586753*a^15 - 48752987/1586753*a^14 + 433764071/11107271*a^13 + 3560780261/11107271*a^12 - 4604482467/11107271*a^11 - 18627365653/11107271*a^10 + 3435101051/1586753*a^9 + 7316629361/1586753*a^8 - 64145365971/11107271*a^7 - 71086180147/11107271*a^6 + 82910826763/11107271*a^5 + 42558283977/11107271*a^4 - 44016310883/11107271*a^3 - 5687517959/11107271*a^2 + 5215960508/11107271*a + 67672208/1586753)*q^13 + (-4808908/1586753*a^16 + 5796543/1586753*a^15 + 126766391/1586753*a^14 - 158300669/1586753*a^13 - 1320950081/1586753*a^12 + 1688387147/1586753*a^11 + 6898052673/1586753*a^10 - 8866087387/1586753*a^9 - 18915396805/1586753*a^8 + 23830351865/1586753*a^7 + 26134675017/1586753*a^6 - 31173785759/1586753*a^5 - 15520035683/1586753*a^4 + 16899635769/1586753*a^3 + 2042035083/1586753*a^2 - 2091532857/1586753*a - 25677032/226679)*q^14 + (-36280233/11107271*a^16 + 6756275/1586753*a^15 + 137081748/1586753*a^14 - 1281596277/11107271*a^13 - 10034246150/11107271*a^12 + 13578645544/11107271*a^11 + 52603913191/11107271*a^10 - 10129810610/1586753*a^9 - 20707252022/1586753*a^8 + 189684933246/11107271*a^7 + 201718786246/11107271*a^6 - 247013229219/11107271*a^5 - 121377536570/11107271*a^4 + 133344739412/11107271*a^3 + 16781354739/11107271*a^2 - 16683671513/11107271*a - 215351389/1586753)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (21279582/11107271*a^16 - 576557/226679*a^15 - 11490920/226679*a^14 + 764328658/11107271*a^13 + 5888803376/11107271*a^12 - 8085603784/11107271*a^11 - 30866495077/11107271*a^10 + 6022752188/1586753*a^9 + 12144661700/1586753*a^8 - 112598812800/11107271*a^7 - 118266415576/11107271*a^6 + 146376439975/11107271*a^5 + 71289580280/11107271*a^4 - 78898734658/11107271*a^3 - 10026490116/11107271*a^2 + 9892317506/11107271*a + 131645167/1586753)*q^17 + (7012377/1586753*a^16 - 9532477/1586753*a^15 - 185789790/1586753*a^14 + 257441987/1586753*a^13 + 1945893492/1586753*a^12 - 2719817696/1586753*a^11 - 10215282188/1586753*a^10 + 14170593588/1586753*a^9 + 28177004824/1586753*a^8 - 37841149124/1586753*a^7 - 39215419128/1586753*a^6 + 49206507136/1586753*a^5 + 23500147673/1586753*a^4 - 26508108184/1586753*a^3 - 3112848994/1586753*a^2 + 3292245522/1586753*a + 40326507/226679)*q^18 + (17310495/11107271*a^16 - 3414606/1586753*a^15 - 65437688/1586753*a^14 + 645668596/11107271*a^13 + 4788816728/11107271*a^12 - 6824305772/11107271*a^11 - 25069140146/11107271*a^10 + 5083421254/1586753*a^9 + 9834005994/1586753*a^8 - 95167008616/11107271*a^7 - 95086769046/11107271*a^6 + 124129226300/11107271*a^5 + 56185475128/11107271*a^4 - 67333009400/11107271*a^3 - 7048228324/11107271*a^2 + 8503642143/11107271*a + 97915806/1586753)*q^19 + (-9902484/11107271*a^16 + 1588427/1586753*a^15 + 37341884/1586753*a^14 - 306374219/11107271*a^13 - 2729577440/11107271*a^12 + 3294244140/11107271*a^11 + 14302505864/11107271*a^10 - 2489989364/1586753*a^9 - 805005200/226679*a^8 + 47211132020/11107271*a^7 + 55080405067/11107271*a^6 - 62353667508/11107271*a^5 - 33520175378/11107271*a^4 + 34328041948/11107271*a^3 + 5007030600/11107271*a^2 - 4433650216/11107271*a - 63344287/1586753)*q^20 + (-60389393/11107271*a^16 + 11166166/1586753*a^15 + 228189755/1586753*a^14 - 2121785233/11107271*a^13 - 16704515587/11107271*a^12 + 22522996135/11107271*a^11 + 87572121447/11107271*a^10 - 16839940973/1586753*a^9 - 34457385811/1586753*a^8 + 316253630139/11107271*a^7 + 334942204895/11107271*a^6 - 413450505207/11107271*a^5 - 199657525257/11107271*a^4 + 224025771901/11107271*a^3 + 25793598659/11107271*a^2 - 27640305732/11107271*a - 332347363/1586753)*q^21 + (-1932394/1586753*a^16 + 2861017/1586753*a^15 + 51532280/1586753*a^14 - 76734018/1586753*a^13 - 543619532/1586753*a^12 + 806087840/1586753*a^11 + 2877789584/1586753*a^10 - 4181704375/1586753*a^9 - 8021846537/1586753*a^8 + 11131333832/1586753*a^7 + 11322552326/1586753*a^6 - 14429213248/1586753*a^5 - 6912085340/1586753*a^4 + 7728531052/1586753*a^3 + 939060632/1586753*a^2 - 950331622/1586753*a - 11795867/226679)*q^22 + (31722361/11107271*a^16 - 5850154/1586753*a^15 - 119732695/1586753*a^14 + 1112154343/11107271*a^13 + 8752755413/11107271*a^12 - 11810292925/11107271*a^11 - 45803042055/11107271*a^10 + 8833142877/1586753*a^9 + 17978970083/1586753*a^8 - 165930762117/11107271*a^7 - 174209659179/11107271*a^6 + 216989136849/11107271*a^5 + 103470227181/11107271*a^4 - 117637416119/11107271*a^3 - 13353180733/11107271*a^2 + 14550510082/11107271*a + 176544419/1586753)*q^23 + (7157613/1586753*a^16 - 8960306/1586753*a^15 - 189063898/1586753*a^14 + 244025764/1586753*a^13 + 1974646909/1586753*a^12 - 2597759796/1586753*a^11 - 10339914094/1586753*a^10 + 13629806955/1586753*a^9 + 28452243608/1586753*a^8 - 36650622628/1586753*a^7 - 39493320416/1586753*a^6 + 48040013676/1586753*a^5 + 23589118460/1586753*a^4 - 26140555528/1586753*a^3 - 3126639512/1586753*a^2 + 3260768103/1586753*a + 39861270/226679)*q^24 + (-25462033/11107271*a^16 + 4395613/1586753*a^15 + 95804186/1586753*a^14 - 839651038/11107271*a^13 - 6980479892/11107271*a^12 + 8946254792/11107271*a^11 + 36397594000/11107271*a^10 - 957366636/226679*a^9 - 14228060939/1586753*a^8 + 125828529167/11107271*a^7 + 137208083944/11107271*a^6 - 164162253174/11107271*a^5 - 81202433244/11107271*a^4 + 88842208296/11107271*a^3 + 10692881072/11107271*a^2 - 11137228887/11107271*a - 134495476/1586753)*q^25 + (-2279337/1586753*a^16 + 425383/226679*a^15 + 8588396/226679*a^14 - 80677216/1586753*a^13 - 626375304/1586753*a^12 + 854785664/1586753*a^11 + 3266976380/1586753*a^10 - 637861468/226679*a^9 - 1276097604/226679*a^8 + 11954149406/1586753*a^7 + 12274876882/1586753*a^6 - 15597242562/1586753*a^5 - 7217348912/1586753*a^4 + 8452829578/1586753*a^3 + 918804458/1586753*a^2 - 1057469821/1586753*a - 12932667/226679)*q^26 + (42256325/11107271*a^16 - 6785852/1586753*a^15 - 159054515/1586753*a^14 + 1305111919/11107271*a^13 + 11603698718/11107271*a^12 - 13991580215/11107271*a^11 - 60661871593/11107271*a^10 + 10540136738/1586753*a^9 + 23820822709/1586753*a^8 - 198956641101/11107271*a^7 - 231309666626/11107271*a^6 + 260869534865/11107271*a^5 + 138106652683/11107271*a^4 - 141473618446/11107271*a^3 - 18317061865/11107271*a^2 + 17298885530/11107271*a + 214943577/1586753)*q^27 + (-10778263/11107271*a^16 + 1734783/1586753*a^15 + 40331409/1586753*a^14 - 334442541/11107271*a^13 - 2919287073/11107271*a^12 + 3593225465/11107271*a^11 + 15090026421/11107271*a^10 - 387528381/226679*a^9 - 5822139165/1586753*a^8 + 51340124137/11107271*a^7 + 54869328517/11107271*a^6 - 67599780159/11107271*a^5 - 30874616835/11107271*a^4 + 36926935611/11107271*a^3 + 3140738731/11107271*a^2 - 4519008910/11107271*a - 49101362/1586753)*q^28 + (37599616/11107271*a^16 - 6005504/1586753*a^15 - 141443329/1586753*a^14 + 1156074400/11107271*a^13 + 10313257723/11107271*a^12 - 12402758789/11107271*a^11 - 53893343681/11107271*a^10 + 9348637439/1586753*a^9 + 21162527937/1586753*a^8 - 176565199519/11107271*a^7 - 205761663785/11107271*a^6 + 231733252097/11107271*a^5 + 123644621259/11107271*a^4 - 126013913667/11107271*a^3 - 17196071544/11107271*a^2 + 15589598961/11107271*a + 203454605/1586753)*q^29 + (6756275/1586753*a^16 - 8039184/1586753*a^15 - 177902292/1586753*a^14 + 219878311/1586753*a^13 + 1851697369/1586753*a^12 - 2348195744/1586753*a^11 - 9658167581/1586753*a^10 + 12344040241/1586753*a^9 + 26449986303/1586753*a^8 - 33206680295/1586753*a^7 - 36495217644/1586753*a^6 + 43471205317/1586753*a^5 + 21656242373/1586753*a^4 - 23594859108/1586753*a^3 - 2870573345/1586753*a^2 + 2941028882/1586753*a + 36280233/226679)*q^30 + (-24153904/11107271*a^16 + 4321005/1586753*a^15 + 91255413/1586753*a^14 - 822194252/11107271*a^13 - 6682216498/11107271*a^12 + 8733648358/11107271*a^11 + 35066854706/11107271*a^10 - 6528082826/1586753*a^9 - 1975726498/226679*a^8 + 122383812294/11107271*a^7 + 135081794294/11107271*a^6 - 159364496414/11107271*a^5 - 81358052074/11107271*a^4 + 85759333630/11107271*a^3 + 10925236722/11107271*a^2 - 10535502669/11107271*a - 128905963/1586753)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-67423899/11107271*a^16 + 1675760/226679*a^15 + 36336930/226679*a^14 - 2238101394/11107271*a^13 - 18596294425/11107271*a^12 + 23828089507/11107271*a^11 + 97422150367/11107271*a^10 - 17843348701/1586753*a^9 - 38348772811/1586753*a^8 + 335017240785/11107271*a^7 + 373830398447/11107271*a^6 - 436921975895/11107271*a^5 - 225166281001/11107271*a^4 + 235699120185/11107271*a^3 + 31079452962/11107271*a^2 - 29079193803/11107271*a - 381202163/1586753)*q^33 + (-576557/226679*a^16 + 4681888/1586753*a^15 + 106149868/1586753*a^14 - 128483326/1586753*a^13 - 157629610/226679*a^12 + 1375507067/1586753*a^11 + 820873946/226679*a^10 - 7241037502/1586753*a^9 - 15705552150/1586753*a^8 + 19483763174/1586753*a^7 + 3088460869/226679*a^6 - 25483393618/1586753*a^5 - 12800337772/1586753*a^4 + 13812944802/1586753*a^3 + 242706086/226679*a^2 - 1719678467/1586753*a - 21279582/226679)*q^34 + (-53415365/11107271*a^16 + 9336701/1586753*a^15 + 201488144/1586753*a^14 - 1783241386/11107271*a^13 - 14727403738/11107271*a^12 + 19012774104/11107271*a^11 + 77112264086/11107271*a^10 - 14267804958/1586753*a^9 - 30314587188/1586753*a^8 + 268767500488/11107271*a^7 + 294505713500/11107271*a^6 - 352301417140/11107271*a^5 - 175561828396/11107271*a^4 + 191294580606/11107271*a^3 + 22872039584/11107271*a^2 - 23488614189/11107271*a - 295067627/1586753)*q^35 + (13925675/11107271*a^16 - 3467988/1586753*a^15 - 53117492/1586753*a^14 + 644326677/11107271*a^13 + 3919872639/11107271*a^12 - 6708711425/11107271*a^11 - 20677966931/11107271*a^10 + 705447179/226679*a^9 + 8169106579/1586753*a^8 - 91647819269/11107271*a^7 - 79515793963/11107271*a^6 + 118791213854/11107271*a^5 + 47163376653/11107271*a^4 - 64054049753/11107271*a^3 - 5701487914/11107271*a^2 + 8080738292/11107271*a + 88714701/1586753)*q^36 + (58834648/11107271*a^16 - 10469071/1586753*a^15 - 221869889/1586753*a^14 + 1994193703/11107271*a^13 + 16206951361/11107271*a^12 - 21201818723/11107271*a^11 - 84762261663/11107271*a^10 + 15858972953/1586753*a^9 + 33262149523/1586753*a^8 - 297518575153/11107271*a^7 - 322391208789/11107271*a^6 + 387851937953/11107271*a^5 + 191863930809/11107271*a^4 - 209242126735/11107271*a^3 - 25038696915/11107271*a^2 + 25744954717/11107271*a + 307195088/1586753)*q^37 + O(q^38)
*]> ;  // time = 3.649 seconds




J[241] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 241, 241 ], new_dimensions := [ 7, 12 ], dimensions := [ 7, 12 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -4, -3, -8, -7, -18, -1, -2, -6, -22, -16, -18, 8 ],
[ 3, 1, 6, 3, 22, -5, -4, -6, 32, 6, 8, -8 ]
], hecke_fields := [
x^7 + 4*x^6 - 14*x^4 - 10*x^3 + 6*x^2 + 3*x - 1,
x^12 - 3*x^11 - 14*x^10 + 44*x^9 + 65*x^8 - 219*x^7 - 123*x^6 + 444*x^5 + 105*x^4 - 328*x^3 - 45*x^2 + 18*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 5 ]
], tamagawa_numbers := [
[ 1 ],
[ 5 ]
], torsion_upper_bounds := [ 1, 5 ], torsion_lower_bounds := [ 1, 5 ], l_ratios := [ 0, 1/5 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^6 - 3*a^5 + 3*a^4 + 11*a^3 - a^2 - 6*a + 1,
a^6 + 2*a^5 - 6*a^4 - 9*a^3 + 10*a^2 + 8*a - 4,
2*a^6 + 9*a^5 + 3*a^4 - 29*a^3 - 28*a^2 + 4*a + 3,
-2*a^6 - 8*a^5 - 2*a^4 + 23*a^3 + 26*a^2 + 3*a - 8,
2*a^6 + 7*a^5 - a^4 - 21*a^3 - 15*a^2 + 2*a + 1,
-5*a^6 - 21*a^5 - 4*a^4 + 68*a^3 + 60*a^2 - 12*a - 10,
-2*a^6 - 4*a^5 + 11*a^4 + 17*a^3 - 16*a^2 - 14*a + 4,
a^6 + 4*a^5 + a^4 - 13*a^3 - 15*a^2 + 3*a + 2,
5*a^6 + 20*a^5 + 3*a^4 - 63*a^3 - 60*a^2 + 8*a + 12,
3*a^6 + 13*a^5 + 5*a^4 - 39*a^3 - 46*a^2 - a + 8,
a^5 + a^4 - 6*a^3 - 5*a^2 + 6*a + 6
],
[
a,
11/8*a^11 - 15/4*a^10 - 79/4*a^9 + 54*a^8 + 773/8*a^7 - 1043/4*a^6 - 1631/8*a^5 + 4025/8*a^4 + 827/4*a^3 - 1375/4*a^2 - 741/8*a + 93/8,
11/8*a^11 - 17/4*a^10 - 75/4*a^9 + 123/2*a^8 + 669/8*a^7 - 1199/4*a^6 - 1223/8*a^5 + 4717/8*a^4 + 589/4*a^3 - 1677/4*a^2 - 737/8*a + 117/8,
-15/16*a^11 + 7/4*a^10 + 61/4*a^9 - 205/8*a^8 - 1415/16*a^7 + 1011/8*a^6 + 3567/16*a^5 - 3951/16*a^4 - 1809/8*a^3 + 1283/8*a^2 + 813/16*a - 71/16,
-5/4*a^11 + 31/8*a^10 + 135/8*a^9 - 445/8*a^8 - 589/8*a^7 + 535/2*a^6 + 255/2*a^5 - 4119/8*a^4 - 443/4*a^3 + 711/2*a^2 + 65*a - 85/8,
7/8*a^11 - 5/2*a^10 - 25/2*a^9 + 145/4*a^8 + 487/8*a^7 - 707/4*a^6 - 1039/8*a^5 + 2759/8*a^4 + 569/4*a^3 - 947/4*a^2 - 613/8*a + 47/8,
-13/8*a^11 + 7/2*a^10 + 53/2*a^9 - 215/4*a^8 - 1237/8*a^7 + 1141/4*a^6 + 3173/8*a^5 - 4981/8*a^4 - 1715/4*a^3 + 1909/4*a^2 + 1127/8*a - 133/8,
5/16*a^11 - 7/8*a^10 - 27/8*a^9 + 41/4*a^8 + 111/16*a^7 - 249/8*a^6 + 287/16*a^5 + 99/16*a^4 - 423/8*a^3 + 311/8*a^2 + 501/16*a + 15/16,
9/16*a^11 - 15/8*a^10 - 59/8*a^9 + 107/4*a^8 + 483/16*a^7 - 1013/8*a^6 - 709/16*a^5 + 3751/16*a^4 + 205/8*a^3 - 1189/8*a^2 - 167/16*a + 99/16,
-11/4*a^11 + 17/2*a^10 + 38*a^9 - 124*a^8 - 695/4*a^7 + 1223/2*a^6 + 1323/4*a^5 - 4881/4*a^4 - 321*a^3 + 876*a^2 + 727/4*a - 115/4,
1/2*a^11 + 1/8*a^10 - 71/8*a^9 - 39/8*a^8 + 447/8*a^7 + 49*a^6 - 575/4*a^5 - 1439/8*a^4 + 425/4*a^3 + 219*a^2 + 233/4*a - 73/8,
-a^11 + 13/4*a^10 + 57/4*a^9 - 199/4*a^8 - 273/4*a^7 + 264*a^6 + 275/2*a^5 - 2335/4*a^4 - 277/2*a^3 + 471*a^2 + 181/2*a - 81/4
]
*], q_expansions := [*
q + a*q^2 + (-a^6 - 3*a^5 + 3*a^4 + 11*a^3 - a^2 - 6*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^6 + 2*a^5 - 6*a^4 - 9*a^3 + 10*a^2 + 8*a - 4)*q^5 + (a^6 + 3*a^5 - 3*a^4 - 11*a^3 + 4*a - 1)*q^6 + (2*a^6 + 9*a^5 + 3*a^4 - 29*a^3 - 28*a^2 + 4*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 - 2*a^4 + 5*a^3 + 7*a^2 - 5*a - 2)*q^9 + (-2*a^6 - 6*a^5 + 5*a^4 + 20*a^3 + 2*a^2 - 7*a + 1)*q^10 + (-2*a^6 - 8*a^5 - 2*a^4 + 23*a^3 + 26*a^2 + 3*a - 8)*q^11 + (a^6 + 3*a^5 - 3*a^4 - 12*a^3 + 8*a - 1)*q^12 + (2*a^6 + 7*a^5 - a^4 - 21*a^3 - 15*a^2 + 2*a + 1)*q^13 + (a^6 + 3*a^5 - a^4 - 8*a^3 - 8*a^2 - 3*a + 2)*q^14 + (a^6 + 5*a^5 + 2*a^4 - 18*a^3 - 14*a^2 + 11*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5*a^6 - 21*a^5 - 4*a^4 + 68*a^3 + 60*a^2 - 12*a - 10)*q^17 + (-a^6 - 2*a^5 + 5*a^4 + 7*a^3 - 5*a^2 - 2*a)*q^18 + (-2*a^6 - 4*a^5 + 11*a^4 + 17*a^3 - 16*a^2 - 14*a + 4)*q^19 + (a^5 + 4*a^4 - 15*a^2 - 9*a + 6)*q^20 + (a^6 + 2*a^5 - 7*a^4 - 11*a^3 + 15*a^2 + 16*a - 6)*q^21 + (-2*a^5 - 5*a^4 + 6*a^3 + 15*a^2 - 2*a - 2)*q^22 + (a^6 + 4*a^5 + a^4 - 13*a^3 - 15*a^2 + 3*a + 2)*q^23 + (-3*a^6 - 9*a^5 + 8*a^4 + 32*a^3 + 2*a^2 - 12*a + 3)*q^24 + (-2*a^6 - 7*a^5 + 4*a^4 + 28*a^3 + 6*a^2 - 20*a + 1)*q^25 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 10*a^2 - 5*a + 2)*q^26 + (-a^4 - 2*a^3 + 3*a^2 + 6*a + 1)*q^27 + (-5*a^6 - 19*a^5 + 60*a^3 + 47*a^2 - 9*a - 5)*q^28 + (5*a^6 + 20*a^5 + 3*a^4 - 63*a^3 - 60*a^2 + 8*a + 12)*q^29 + (a^6 + 2*a^5 - 4*a^4 - 4*a^3 + 5*a^2 - 4*a + 1)*q^30 + (3*a^6 + 13*a^5 + 5*a^4 - 39*a^3 - 46*a^2 - a + 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (6*a^6 + 20*a^5 - 11*a^4 - 69*a^3 - 18*a^2 + 26*a - 2)*q^33 + (-a^6 - 4*a^5 - 2*a^4 + 10*a^3 + 18*a^2 + 5*a - 5)*q^34 + (-2*a^6 - 7*a^5 + 6*a^4 + 31*a^3 - 2*a^2 - 26*a + 5)*q^35 + (2*a^6 + 7*a^5 - 3*a^4 - 25*a^3 - 10*a^2 + 13*a + 3)*q^36 + (a^5 + a^4 - 6*a^3 - 5*a^2 + 6*a + 6)*q^37 + O(q^38),
q + a*q^2 + (11/8*a^11 - 15/4*a^10 - 79/4*a^9 + 54*a^8 + 773/8*a^7 - 1043/4*a^6 - 1631/8*a^5 + 4025/8*a^4 + 827/4*a^3 - 1375/4*a^2 - 741/8*a + 93/8)*q^3 + (a^2 - 2)*q^4 + (11/8*a^11 - 17/4*a^10 - 75/4*a^9 + 123/2*a^8 + 669/8*a^7 - 1199/4*a^6 - 1223/8*a^5 + 4717/8*a^4 + 589/4*a^3 - 1677/4*a^2 - 737/8*a + 117/8)*q^5 + (3/8*a^11 - 1/2*a^10 - 13/2*a^9 + 29/4*a^8 + 323/8*a^7 - 139/4*a^6 - 859/8*a^5 + 499/8*a^4 + 429/4*a^3 - 123/4*a^2 - 105/8*a + 11/8)*q^6 + (-15/16*a^11 + 7/4*a^10 + 61/4*a^9 - 205/8*a^8 - 1415/16*a^7 + 1011/8*a^6 + 3567/16*a^5 - 3951/16*a^4 - 1809/8*a^3 + 1283/8*a^2 + 813/16*a - 71/16)*q^7 + (a^3 - 4*a)*q^8 + (-3/2*a^11 + 5*a^10 + 20*a^9 - 73*a^8 - 171/2*a^7 + 361*a^6 + 293/2*a^5 - 1453/2*a^4 - 149*a^3 + 532*a^2 + 251/2*a - 27/2)*q^9 + (-1/8*a^11 + 1/2*a^10 + a^9 - 23/4*a^8 + 11/8*a^7 + 65/4*a^6 - 167/8*a^5 + 23/8*a^4 + 127/4*a^3 - 121/4*a^2 - 81/8*a + 11/8)*q^10 + (-5/4*a^11 + 31/8*a^10 + 135/8*a^9 - 445/8*a^8 - 589/8*a^7 + 535/2*a^6 + 255/2*a^5 - 4119/8*a^4 - 443/4*a^3 + 711/2*a^2 + 65*a - 85/8)*q^11 + (-17/8*a^11 + 25/4*a^10 + 121/4*a^9 - 92*a^8 - 1167/8*a^7 + 1841/4*a^6 + 2429/8*a^5 - 7507/8*a^4 - 1285/4*a^3 + 2765/4*a^2 + 1439/8*a - 183/8)*q^12 + (7/8*a^11 - 5/2*a^10 - 25/2*a^9 + 145/4*a^8 + 487/8*a^7 - 707/4*a^6 - 1039/8*a^5 + 2759/8*a^4 + 569/4*a^3 - 947/4*a^2 - 613/8*a + 47/8)*q^13 + (-17/16*a^11 + 17/8*a^10 + 125/8*a^9 - 55/2*a^8 - 1263/16*a^7 + 861/8*a^6 + 2709/16*a^5 - 2043/16*a^4 - 1177/8*a^3 + 69/8*a^2 + 199/16*a - 15/16)*q^14 + (7/8*a^11 - 2*a^10 - 14*a^9 + 123/4*a^8 + 635/8*a^7 - 655/4*a^6 - 1559/8*a^5 + 2883/8*a^4 + 785/4*a^3 - 1127/4*a^2 - 461/8*a + 115/8)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-13/8*a^11 + 7/2*a^10 + 53/2*a^9 - 215/4*a^8 - 1237/8*a^7 + 1141/4*a^6 + 3173/8*a^5 - 4981/8*a^4 - 1715/4*a^3 + 1909/4*a^2 + 1127/8*a - 133/8)*q^17 + (1/2*a^11 - a^10 - 7*a^9 + 12*a^8 + 65/2*a^7 - 38*a^6 - 121/2*a^5 + 17/2*a^4 + 40*a^3 + 58*a^2 + 27/2*a - 3/2)*q^18 + (5/16*a^11 - 7/8*a^10 - 27/8*a^9 + 41/4*a^8 + 111/16*a^7 - 249/8*a^6 + 287/16*a^5 + 99/16*a^4 - 423/8*a^3 + 311/8*a^2 + 501/16*a + 15/16)*q^19 + (-21/8*a^11 + 31/4*a^10 + 149/4*a^9 - 227/2*a^8 - 1427/8*a^7 + 2253/4*a^6 + 2913/8*a^5 - 9075/8*a^4 - 1463/4*a^3 + 3291/4*a^2 + 1503/8*a - 235/8)*q^20 + (2*a^11 - 23/4*a^10 - 119/4*a^9 + 349/4*a^8 + 615/4*a^7 - 457*a^6 - 701/2*a^5 + 3969/4*a^4 + 779/2*a^3 - 780*a^2 - 425/2*a + 95/4)*q^21 + (1/8*a^11 - 5/8*a^10 - 5/8*a^9 + 61/8*a^8 - 25/4*a^7 - 105/4*a^6 + 321/8*a^5 + 41/2*a^4 - 109/2*a^3 + 35/4*a^2 + 95/8*a - 5/4)*q^22 + (9/16*a^11 - 15/8*a^10 - 59/8*a^9 + 107/4*a^8 + 483/16*a^7 - 1013/8*a^6 - 709/16*a^5 + 3751/16*a^4 + 205/8*a^3 - 1189/8*a^2 - 167/16*a + 99/16)*q^23 + (-7/8*a^11 + 3/2*a^10 + 29/2*a^9 - 89/4*a^8 - 687/8*a^7 + 447/4*a^6 + 1759/8*a^5 - 1783/8*a^4 - 881/4*a^3 + 583/4*a^2 + 333/8*a - 39/8)*q^24 + (7/2*a^11 - 10*a^10 - 103/2*a^9 + 150*a^8 + 261*a^7 - 772*a^6 - 1147/2*a^5 + 3271/2*a^4 + 1187/2*a^3 - 2503/2*a^2 - 283*a + 45)*q^25 + (1/8*a^11 - 1/4*a^10 - 9/4*a^9 + 4*a^8 + 119/8*a^7 - 89/4*a^6 - 349/8*a^5 + 403/8*a^4 + 201/4*a^3 - 149/4*a^2 - 79/8*a + 7/8)*q^26 + (9/4*a^11 - 13/2*a^10 - 65/2*a^9 + 96*a^8 + 643/4*a^7 - 965/2*a^6 - 1389/4*a^5 + 3951/4*a^4 + 745/2*a^3 - 1443/2*a^2 - 779/4*a + 63/4)*q^27 + (13/16*a^11 - 11/4*a^10 - 45/4*a^9 + 331/8*a^8 + 829/16*a^7 - 1713/8*a^6 - 1629/16*a^5 + 7333/16*a^4 + 899/8*a^3 - 2849/8*a^2 - 1335/16*a + 125/16)*q^28 + (-11/4*a^11 + 17/2*a^10 + 38*a^9 - 124*a^8 - 695/4*a^7 + 1223/2*a^6 + 1323/4*a^5 - 4881/4*a^4 - 321*a^3 + 876*a^2 + 727/4*a - 115/4)*q^29 + (5/8*a^11 - 7/4*a^10 - 31/4*a^9 + 45/2*a^8 + 223/8*a^7 - 349/4*a^6 - 225/8*a^5 + 835/8*a^4 + 21/4*a^3 - 73/4*a^2 - 11/8*a + 7/8)*q^30 + (1/2*a^11 + 1/8*a^10 - 71/8*a^9 - 39/8*a^8 + 447/8*a^7 + 49*a^6 - 575/4*a^5 - 1439/8*a^4 + 425/4*a^3 + 219*a^2 + 233/4*a - 73/8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^9 - 3*a^8 - 12*a^7 + 38*a^6 + 40*a^5 - 143*a^4 - 30*a^3 + 156*a^2 - 5*a - 6)*q^33 + (-11/8*a^11 + 15/4*a^10 + 71/4*a^9 - 49*a^8 - 565/8*a^7 + 787/4*a^6 + 791/8*a^5 - 2065/8*a^4 - 223/4*a^3 + 271/4*a^2 + 101/8*a - 13/8)*q^34 + (11/16*a^11 - 19/8*a^10 - 87/8*a^9 + 79/2*a^8 + 981/16*a^7 - 1863/8*a^6 - 2487/16*a^5 + 9241/16*a^4 + 1531/8*a^3 - 4071/8*a^2 - 1949/16*a + 261/16)*q^35 + (7/2*a^11 - 10*a^10 - 50*a^9 + 146*a^8 + 485/2*a^7 - 721*a^6 - 1013/2*a^5 + 2881/2*a^4 + 520*a^3 - 1028*a^2 - 523/2*a + 55/2)*q^36 + (-a^11 + 13/4*a^10 + 57/4*a^9 - 199/4*a^8 - 273/4*a^7 + 264*a^6 + 275/2*a^5 - 2335/4*a^4 - 277/2*a^3 + 471*a^2 + 181/2*a - 81/4)*q^37 + O(q^38)
*]> ;  // time = 3.16 seconds




J[246] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 246, 246, 246, 246, 246, 246, 246, 123, 123, 123, 123, 82, 82, 41 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 3 ], dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 6, 2, 4, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 0, 5, 1, 1, 1, 1, 1, 7, 1, 3, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 0, 3, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 25, 1, 1, 7, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 529, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 25, 1, 529, 1, 1, 0 ], ap_traces := [
[ -1, -1, -2, 2, -4, -4, -2, -8, 4, -8, 4, 2 ],
[ -1, -1, 3, -2, 2, 1, 5, -1, 6, 8, 3, -6 ],
[ -1, 1, -2, 2, 4, 4, -2, 0, 4, 0, 4, 2 ],
[ -1, 1, 3, 2, -6, -1, 3, 5, -6, 0, -1, 2 ],
[ 1, -1, 1, 2, 2, -7, 7, 7, -2, -8, -5, -10 ],
[ 1, 1, 1, -2, 2, -1, -7, 5, -6, 0, 7, -2 ],
[ 1, 1, -2, 4, -4, 2, 2, -4, 0, -6, -8, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 11, 1, 1 ],
[ 7, 3, 1 ],
[ 1, 3, 1 ],
[ 3, 7, 1 ],
[ 25, 5, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 3, 1 ],
[ 3, 1, 1 ],
[ 25, 5, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1, 1, 1 ], l_ratios := [ 0, 1, 3, 1/3, 3, 5, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 1, 1/25, 1 ], eigenvalues := [*
[ -1, -1, -2, 2, -4, -4, -2, -8, 4, -8, 4, 2 ],
[ -1, -1, 3, -2, 2, 1, 5, -1, 6, 8, 3, -6 ],
[ -1, 1, -2, 2, 4, 4, -2, 0, 4, 0, 4, 2 ],
[ -1, 1, 3, 2, -6, -1, 3, 5, -6, 0, -1, 2 ],
[ 1, -1, 1, 2, 2, -7, 7, 7, -2, -8, -5, -10 ],
[ 1, 1, 1, -2, 2, -1, -7, 5, -6, 0, 7, -2 ],
[ 1, 1, -2, 4, -4, 2, 2, -4, 0, -6, -8, -2 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 + 2*q^7 - q^8 + q^9 + 2*q^10 - 4*q^11 - q^12 - 4*q^13 - 2*q^14 + 2*q^15 + q^16 - 2*q^17 - q^18 - 8*q^19 - 2*q^20 - 2*q^21 + 4*q^22 + 4*q^23 + q^24 - q^25 + 4*q^26 - q^27 + 2*q^28 - 8*q^29 - 2*q^30 + 4*q^31 - q^32 + 4*q^33 + 2*q^34 - 4*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + 3*q^5 + q^6 - 2*q^7 - q^8 + q^9 - 3*q^10 + 2*q^11 - q^12 + q^13 + 2*q^14 - 3*q^15 + q^16 + 5*q^17 - q^18 - q^19 + 3*q^20 + 2*q^21 - 2*q^22 + 6*q^23 + q^24 + 4*q^25 - q^26 - q^27 - 2*q^28 + 8*q^29 + 3*q^30 + 3*q^31 - q^32 - 2*q^33 - 5*q^34 - 6*q^35 + q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 2*q^5 - q^6 + 2*q^7 - q^8 + q^9 + 2*q^10 + 4*q^11 + q^12 + 4*q^13 - 2*q^14 - 2*q^15 + q^16 - 2*q^17 - q^18 - 2*q^20 + 2*q^21 - 4*q^22 + 4*q^23 - q^24 - q^25 - 4*q^26 + q^27 + 2*q^28 + 2*q^30 + 4*q^31 - q^32 + 4*q^33 + 2*q^34 - 4*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + 3*q^5 - q^6 + 2*q^7 - q^8 + q^9 - 3*q^10 - 6*q^11 + q^12 - q^13 - 2*q^14 + 3*q^15 + q^16 + 3*q^17 - q^18 + 5*q^19 + 3*q^20 + 2*q^21 + 6*q^22 - 6*q^23 - q^24 + 4*q^25 + q^26 + q^27 + 2*q^28 - 3*q^30 - q^31 - q^32 - 6*q^33 - 3*q^34 + 6*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 2*q^7 + q^8 + q^9 + q^10 + 2*q^11 - q^12 - 7*q^13 + 2*q^14 - q^15 + q^16 + 7*q^17 + q^18 + 7*q^19 + q^20 - 2*q^21 + 2*q^22 - 2*q^23 - q^24 - 4*q^25 - 7*q^26 - q^27 + 2*q^28 - 8*q^29 - q^30 - 5*q^31 + q^32 - 2*q^33 + 7*q^34 + 2*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 - 2*q^7 + q^8 + q^9 + q^10 + 2*q^11 + q^12 - q^13 - 2*q^14 + q^15 + q^16 - 7*q^17 + q^18 + 5*q^19 + q^20 - 2*q^21 + 2*q^22 - 6*q^23 + q^24 - 4*q^25 - q^26 + q^27 - 2*q^28 + q^30 + 7*q^31 + q^32 + 2*q^33 - 7*q^34 - 2*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - 2*q^5 + q^6 + 4*q^7 + q^8 + q^9 - 2*q^10 - 4*q^11 + q^12 + 2*q^13 + 4*q^14 - 2*q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 - 2*q^20 + 4*q^21 - 4*q^22 + q^24 - q^25 + 2*q^26 + q^27 + 4*q^28 - 6*q^29 - 2*q^30 - 8*q^31 + q^32 - 4*q^33 + 2*q^34 - 8*q^35 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 140.95 seconds




J[247] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 247, 247, 247, 247, 247, 19 ], new_dimensions := [ 2, 3, 4, 5, 5, 1 ], dimensions := [ 2, 3, 4, 5, 5, 2 ], intersection_graph := [ 0, 1, 1, 1, 31, 1, 1, 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 5, 31, 1, 1, 1, 0, 1, 1, 3, 1, 5, 1, 0 ], ap_traces := [
[ 1, -2, 2, -4, -6, 2, 6, -2, 8, 0, 4, 6 ],
[ -3, -3, -3, -3, 0, 3, -12, 3, -6, -15, -3, 6 ],
[ -3, -1, -8, -2, -5, -4, -15, -4, -2, 1, 7, 2 ],
[ 4, 3, 3, -1, -2, -5, 14, 5, -6, -9, -3, 6 ],
[ 0, 3, 2, 4, 7, 5, 23, -5, -2, 5, -9, -18 ]
], hecke_fields := [
x^2 - x - 1,
x^3 + 3*x^2 - 3,
x^4 + 3*x^3 - 2*x^2 - 9*x - 4,
x^5 - 4*x^4 + 12*x^2 - 5*x - 5,
x^5 - 9*x^3 - x^2 + 19*x + 4
], atkin_lehners := [
[ -1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 5, 7 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 5, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 1, 7 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 5, 3, 1, 7, 1 ], torsion_lower_bounds := [ 5, 1, 1, 7, 1 ], l_ratios := [ 1/5, 0, 0, 1/7, 1 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[
a,
2*a - 2,
2*a,
-2,
2*a - 4,
1,
-4*a + 5,
-1,
-2*a + 5,
4*a - 2,
2*a + 1,
4*a + 1
],
[
a,
-a^2 - a + 1,
-a^2 - 2*a,
2*a^2 + 3*a - 4,
a^2 - 3,
1,
a^2 + 4*a - 3,
1,
-a^2 - 4*a - 3,
2*a^2 + 5*a - 6,
-4*a^2 - 3*a + 8,
5*a^2 + 6*a - 7
],
[
a,
-a^3 - 2*a^2 + 3*a + 4,
a^3 + 2*a^2 - 4*a - 7,
a^3 + a^2 - 5*a - 3,
a^2 + 2*a - 3,
-1,
a^2 - 7,
-1,
-3*a^3 - 6*a^2 + 14*a + 16,
2*a^3 + 2*a^2 - 9*a - 4,
2*a^3 + 6*a^2 - 7*a - 14,
-5*a^3 - 10*a^2 + 18*a + 24
],
[
a,
-a^2 + a + 3,
a^3 - 2*a^2 - 2*a + 3,
-a^4 + 2*a^3 + 3*a^2 - 4*a - 1,
a^4 - 4*a^3 + 9*a - 2,
-1,
a^3 - 6*a + 2,
1,
-2*a^4 + 3*a^3 + 10*a^2 - 8*a - 10,
-3*a^4 + 6*a^3 + 11*a^2 - 14*a - 9,
a^3 - a^2 - 5*a + 1,
2*a^4 - 5*a^3 - 4*a^2 + 8*a + 2
],
[
a,
a^3 - 5*a,
-a^3 + 4*a + 1,
-a^3 - a^2 + 5*a + 5,
-a^2 + 5,
1,
a^2 + 1,
-1,
a^4 - 6*a^2 - a + 4,
-a^4 + a^3 + 6*a^2 - 6*a - 4,
a^4 + a^3 - 6*a^2 - 4*a + 2,
-a^4 + 6*a^2 - a - 8
]
*], q_expansions := [*
q + a*q^2 + (2*a - 2)*q^3 + (a - 1)*q^4 + 2*a*q^5 + 2*q^6 - 2*q^7 + (-2*a + 1)*q^8 + (-4*a + 5)*q^9 + (2*a + 2)*q^10 + (2*a - 4)*q^11 + (-2*a + 4)*q^12 + q^13 - 2*a*q^14 + 4*q^15 - 3*a*q^16 + (-4*a + 5)*q^17 + (a - 4)*q^18 - q^19 + 2*q^20 + (-4*a + 4)*q^21 + (-2*a + 2)*q^22 + (-2*a + 5)*q^23 + (2*a - 6)*q^24 + (4*a - 1)*q^25 + a*q^26 + (4*a - 12)*q^27 + (-2*a + 2)*q^28 + (4*a - 2)*q^29 + 4*a*q^30 + (2*a + 1)*q^31 + (a - 5)*q^32 + (-8*a + 12)*q^33 + (a - 4)*q^34 - 4*a*q^35 + (5*a - 9)*q^36 + (4*a + 1)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a)*q^5 + (2*a^2 + a - 3)*q^6 + (2*a^2 + 3*a - 4)*q^7 + (-3*a^2 - 4*a + 3)*q^8 + (2*a^2 + a - 5)*q^9 + (a^2 - 3)*q^10 + (a^2 - 3)*q^11 + (-3*a^2 - a + 4)*q^12 + q^13 + (-3*a^2 - 4*a + 6)*q^14 + (a^2 + a)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (a^2 + 4*a - 3)*q^17 + (-5*a^2 - 5*a + 6)*q^18 + q^19 + (-a^2 + a + 3)*q^20 + (a - 1)*q^21 + (-3*a^2 - 3*a + 3)*q^22 + (-a^2 - 4*a - 3)*q^23 + (4*a^2 + 2*a - 3)*q^24 + (a^2 + 3*a - 2)*q^25 + a*q^26 + (3*a + 1)*q^27 + (a^2 - 1)*q^28 + (2*a^2 + 5*a - 6)*q^29 + (-2*a^2 + 3)*q^30 + (-4*a^2 - 3*a + 8)*q^31 + (3*a + 3)*q^32 + (-2*a^2 + 3)*q^33 + (a^2 - 3*a + 3)*q^34 + (a^2 + 2*a - 3)*q^35 + (6*a^2 + 4*a - 5)*q^36 + (5*a^2 + 6*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + 3*a + 4)*q^3 + (a^2 - 2)*q^4 + (a^3 + 2*a^2 - 4*a - 7)*q^5 + (a^3 + a^2 - 5*a - 4)*q^6 + (a^3 + a^2 - 5*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (a + 1)*q^9 + (-a^3 - 2*a^2 + 2*a + 4)*q^10 + (a^2 + 2*a - 3)*q^11 + (a^2 - a - 4)*q^12 - q^13 + (-2*a^3 - 3*a^2 + 6*a + 4)*q^14 + (2*a^3 + 5*a^2 - 5*a - 12)*q^15 + (-3*a^3 - 4*a^2 + 9*a + 8)*q^16 + (a^2 - 7)*q^17 + (a^2 + a)*q^18 - q^19 + (-a^3 - 4*a^2 + 3*a + 10)*q^20 + (-a^3 - a^2 + 7*a + 4)*q^21 + (a^3 + 2*a^2 - 3*a)*q^22 + (-3*a^3 - 6*a^2 + 14*a + 16)*q^23 + (-a^3 - 3*a^2 + 6*a + 8)*q^24 + (-4*a^3 - 9*a^2 + 15*a + 24)*q^25 - a*q^26 + (3*a^3 + 5*a^2 - 11*a - 12)*q^27 + (a^3 - 4*a - 2)*q^28 + (2*a^3 + 2*a^2 - 9*a - 4)*q^29 + (-a^3 - a^2 + 6*a + 8)*q^30 + (2*a^3 + 6*a^2 - 7*a - 14)*q^31 + (3*a^3 + 3*a^2 - 11*a - 12)*q^32 + (3*a^3 + 5*a^2 - 14*a - 16)*q^33 + (a^3 - 7*a)*q^34 + (a^2 + 2*a + 1)*q^35 + (a^3 + a^2 - 2*a - 2)*q^36 + (-5*a^3 - 10*a^2 + 18*a + 24)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + a + 3)*q^3 + (a^2 - 2)*q^4 + (a^3 - 2*a^2 - 2*a + 3)*q^5 + (-a^3 + a^2 + 3*a)*q^6 + (-a^4 + 2*a^3 + 3*a^2 - 4*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 6)*q^9 + (a^4 - 2*a^3 - 2*a^2 + 3*a)*q^10 + (a^4 - 4*a^3 + 9*a - 2)*q^11 + (-a^4 + a^3 + 5*a^2 - 2*a - 6)*q^12 - q^13 + (-2*a^4 + 3*a^3 + 8*a^2 - 6*a - 5)*q^14 + (-a^4 + 3*a^3 + a^2 - 8*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^3 - 6*a + 2)*q^17 + (2*a^4 - 5*a^3 - 6*a^2 + 11*a + 5)*q^18 + q^19 + (2*a^4 - 4*a^3 - 5*a^2 + 9*a - 1)*q^20 + (a^3 - a^2 - 3*a + 2)*q^21 + (-3*a^2 + 3*a + 5)*q^22 + (-2*a^4 + 3*a^3 + 10*a^2 - 8*a - 10)*q^23 + (-3*a^4 + 7*a^3 + 8*a^2 - 17*a - 5)*q^24 + (2*a^3 - 3*a^2 - 7*a + 4)*q^25 - a*q^26 + (2*a^4 - 5*a^3 - 5*a^2 + 11*a + 4)*q^27 + (-3*a^4 + 4*a^3 + 12*a^2 - 7*a - 8)*q^28 + (-3*a^4 + 6*a^3 + 11*a^2 - 14*a - 9)*q^29 + (-a^4 + a^3 + 4*a^2 - a - 5)*q^30 + (a^3 - a^2 - 5*a + 1)*q^31 + (4*a^4 - 8*a^3 - 12*a^2 + 17*a + 5)*q^32 + (3*a^4 - 9*a^3 - 6*a^2 + 25*a - 1)*q^33 + (a^4 - 6*a^2 + 2*a)*q^34 + (-a^4 + 2*a^3 + 2*a^2 - 5*a + 2)*q^35 + (a^4 - 2*a^3 - 3*a^2 + 3*a - 2)*q^36 + (2*a^4 - 5*a^3 - 4*a^2 + 8*a + 2)*q^37 + O(q^38),
q + a*q^2 + (a^3 - 5*a)*q^3 + (a^2 - 2)*q^4 + (-a^3 + 4*a + 1)*q^5 + (a^4 - 5*a^2)*q^6 + (-a^3 - a^2 + 5*a + 5)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 + a^3 + 6*a^2 - 4*a - 3)*q^9 + (-a^4 + 4*a^2 + a)*q^10 + (-a^2 + 5)*q^11 + (2*a^3 + a^2 - 9*a - 4)*q^12 + q^13 + (-a^4 - a^3 + 5*a^2 + 5*a)*q^14 + (-a^2 - a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^2 + 1)*q^17 + (a^4 - 3*a^3 - 5*a^2 + 16*a + 4)*q^18 - q^19 + (-3*a^3 + 11*a + 2)*q^20 + (a^4 - 7*a^2 - 2*a + 4)*q^21 + (-a^3 + 5*a)*q^22 + (a^4 - 6*a^2 - a + 4)*q^23 + (a^3 + a^2 - 4*a)*q^24 + (a^4 - a^3 - 3*a^2 + 4*a - 4)*q^25 + a*q^26 + (-a^4 + 2*a^3 + 7*a^2 - 12*a - 8)*q^27 + (-a^4 - 2*a^3 + 6*a^2 + 9*a - 6)*q^28 + (-a^4 + a^3 + 6*a^2 - 6*a - 4)*q^29 + (-a^3 - a^2)*q^30 + (a^4 + a^3 - 6*a^2 - 4*a + 2)*q^31 + (a^3 + a^2 - 7*a - 4)*q^32 + (a^3 - a^2 - 6*a + 4)*q^33 + (a^3 + a)*q^34 + (a^2 + 2*a + 1)*q^35 + (-a^4 + 2*a^3 + 5*a^2 - 7*a + 2)*q^36 + (-a^4 + 6*a^2 - a - 8)*q^37 + O(q^38)
*]> ;  // time = 29.739 seconds




J[249] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 249, 249, 249, 249, 249, 83, 83 ], new_dimensions := [ 1, 1, 2, 4, 5, 1, 6 ], dimensions := [ 1, 1, 2, 4, 5, 2, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 31, 1, 1, 1, 0, 1, 5, 1, 1, 1, 1, 1, 0, 1, 2711, 1, 3, 1, 5, 1, 0, 1, 1, 1, 31, 1, 2711, 1, 0 ], ap_traces := [
[ 1, -1, -1, -4, -3, 2, 4, -1, -3, 4, -6, -9 ],
[ -1, -1, 1, 0, -3, -6, -4, -7, 5, 8, -10, 7 ],
[ -2, 2, -6, -4, -6, 0, 0, -2, -2, -12, -16, -2 ],
[ 2, 4, 6, 0, 4, -6, 0, -2, 8, 0, 8, -16 ],
[ -3, -5, -2, 8, 4, 4, 2, 12, 8, -2, 24, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 1,
x^4 - 2*x^3 - 4*x^2 + 8*x - 1,
x^5 + 3*x^4 - 4*x^3 - 14*x^2 - 3*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 3, 1 ],
[ 31, 1 ],
[ 35, 1 ],
[ 2711, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 31, 1 ],
[ 35, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 7, 1 ], torsion_lower_bounds := [ 1, 1, 1, 7, 1 ], l_ratios := [ 0, 0, 0, 5/7, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, -1, -1, -4, -3, 2, 4, -1, -3, 4, -6, -9 ],
[ -1, -1, 1, 0, -3, -6, -4, -7, 5, 8, -10, 7 ],
[
a,
1,
-a - 4,
-2,
2*a - 1,
0,
-4*a - 4,
a,
4*a + 3,
-6,
-8,
-1
],
[
a,
1,
-a + 2,
-a^2 + 3,
-2*a^3 + a^2 + 8*a - 2,
-a^3 + 5*a - 2,
2*a^3 - 2*a^2 - 8*a + 6,
2*a^3 - 9*a,
4*a^3 - 2*a^2 - 18*a + 9,
-2*a^3 + 3*a^2 + 8*a - 9,
-2*a^3 + 3*a^2 + 8*a - 7,
2*a^3 - 6*a - 5
],
[
a,
-1,
-1/2*a^4 - 2*a^3 + 2*a^2 + 10*a + 1/2,
a^4 + 2*a^3 - 5*a^2 - 8*a + 2,
-1/2*a^4 - 2*a^3 + a^2 + 9*a + 9/2,
a^3 - 5*a + 2,
2*a^4 + 4*a^3 - 10*a^2 - 18*a,
-5/2*a^4 - 6*a^3 + 12*a^2 + 26*a + 5/2,
-1/2*a^4 + 4*a^2 - a - 5/2,
-a^4 - 2*a^3 + 5*a^2 + 6*a - 2,
a^4 + 2*a^3 - 5*a^2 - 10*a + 4,
1/2*a^4 - 4*a^2 - a + 5/2
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - q^5 - q^6 - 4*q^7 - 3*q^8 + q^9 - q^10 - 3*q^11 + q^12 + 2*q^13 - 4*q^14 + q^15 - q^16 + 4*q^17 + q^18 - q^19 + q^20 + 4*q^21 - 3*q^22 - 3*q^23 + 3*q^24 - 4*q^25 + 2*q^26 - q^27 + 4*q^28 + 4*q^29 + q^30 - 6*q^31 + 5*q^32 + 3*q^33 + 4*q^34 + 4*q^35 - q^36 - 9*q^37 + O(q^38),
q - q^2 - q^3 - q^4 + q^5 + q^6 + 3*q^8 + q^9 - q^10 - 3*q^11 + q^12 - 6*q^13 - q^15 - q^16 - 4*q^17 - q^18 - 7*q^19 - q^20 + 3*q^22 + 5*q^23 - 3*q^24 - 4*q^25 + 6*q^26 - q^27 + 8*q^29 + q^30 - 10*q^31 - 5*q^32 + 3*q^33 + 4*q^34 - q^36 + 7*q^37 + O(q^38),
q + a*q^2 + q^3 + (-2*a - 1)*q^4 + (-a - 4)*q^5 + a*q^6 - 2*q^7 + (a - 2)*q^8 + q^9 + (-2*a - 1)*q^10 + (2*a - 1)*q^11 + (-2*a - 1)*q^12 - 2*a*q^14 + (-a - 4)*q^15 + 3*q^16 + (-4*a - 4)*q^17 + a*q^18 + a*q^19 + (5*a + 6)*q^20 - 2*q^21 + (-5*a + 2)*q^22 + (4*a + 3)*q^23 + (a - 2)*q^24 + (6*a + 12)*q^25 + q^27 + (4*a + 2)*q^28 - 6*q^29 + (-2*a - 1)*q^30 - 8*q^31 + (a + 4)*q^32 + (2*a - 1)*q^33 + (4*a - 4)*q^34 + (2*a + 8)*q^35 + (-2*a - 1)*q^36 - q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a + 2)*q^5 + a*q^6 + (-a^2 + 3)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^2 + 2*a)*q^10 + (-2*a^3 + a^2 + 8*a - 2)*q^11 + (a^2 - 2)*q^12 + (-a^3 + 5*a - 2)*q^13 + (-a^3 + 3*a)*q^14 + (-a + 2)*q^15 + (2*a^3 - 2*a^2 - 8*a + 5)*q^16 + (2*a^3 - 2*a^2 - 8*a + 6)*q^17 + a*q^18 + (2*a^3 - 9*a)*q^19 + (-a^3 + 2*a^2 + 2*a - 4)*q^20 + (-a^2 + 3)*q^21 + (-3*a^3 + 14*a - 2)*q^22 + (4*a^3 - 2*a^2 - 18*a + 9)*q^23 + (a^3 - 4*a)*q^24 + (a^2 - 4*a - 1)*q^25 + (-2*a^3 + a^2 + 6*a - 1)*q^26 + q^27 + (-2*a^3 + a^2 + 8*a - 7)*q^28 + (-2*a^3 + 3*a^2 + 8*a - 9)*q^29 + (-a^2 + 2*a)*q^30 + (-2*a^3 + 3*a^2 + 8*a - 7)*q^31 + (-3*a + 2)*q^32 + (-2*a^3 + a^2 + 8*a - 2)*q^33 + (2*a^3 - 10*a + 2)*q^34 + (a^3 - 2*a^2 - 3*a + 6)*q^35 + (a^2 - 2)*q^36 + (2*a^3 - 6*a - 5)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-1/2*a^4 - 2*a^3 + 2*a^2 + 10*a + 1/2)*q^5 - a*q^6 + (a^4 + 2*a^3 - 5*a^2 - 8*a + 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-1/2*a^4 + 3*a^2 - a + 1/2)*q^10 + (-1/2*a^4 - 2*a^3 + a^2 + 9*a + 9/2)*q^11 + (-a^2 + 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (-a^4 - a^3 + 6*a^2 + 5*a - 1)*q^14 + (1/2*a^4 + 2*a^3 - 2*a^2 - 10*a - 1/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^4 + 4*a^3 - 10*a^2 - 18*a)*q^17 + a*q^18 + (-5/2*a^4 - 6*a^3 + 12*a^2 + 26*a + 5/2)*q^19 + (5/2*a^4 + 5*a^3 - 12*a^2 - 21*a - 1/2)*q^20 + (-a^4 - 2*a^3 + 5*a^2 + 8*a - 2)*q^21 + (-1/2*a^4 - a^3 + 2*a^2 + 3*a + 1/2)*q^22 + (-1/2*a^4 + 4*a^2 - a - 5/2)*q^23 + (-a^3 + 4*a)*q^24 + (1/2*a^4 + 2*a^3 - 3*a^2 - 11*a + 5/2)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 - q^27 + (-2*a^3 + a^2 + 12*a - 3)*q^28 + (-a^4 - 2*a^3 + 5*a^2 + 6*a - 2)*q^29 + (1/2*a^4 - 3*a^2 + a - 1/2)*q^30 + (a^4 + 2*a^3 - 5*a^2 - 10*a + 4)*q^31 + (-3*a^4 - 4*a^3 + 14*a^2 + 15*a - 1)*q^32 + (1/2*a^4 + 2*a^3 - a^2 - 9*a - 9/2)*q^33 + (-2*a^4 - 2*a^3 + 10*a^2 + 6*a - 2)*q^34 + (-3*a^4 - 7*a^3 + 16*a^2 + 31*a - 5)*q^35 + (a^2 - 2)*q^36 + (1/2*a^4 - 4*a^2 - a + 5/2)*q^37 + O(q^38)
*]> ;  // time = 32.129 seconds




J[251] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 251, 251 ], new_dimensions := [ 4, 17 ], dimensions := [ 4, 17 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -2, -3, -3, -3, -12, 1, -9, 4, -12, -2, -13 ],
[ 2, 0, 3, 3, -1, 22, -1, 13, -2, 28, 12, 27 ]
], hecke_fields := [
x^4 + 6*x^3 - 3*x^2 - 16*x + 11,
x^17 - 2*x^16 - 28*x^15 + 54*x^14 + 317*x^13 - 582*x^12 - 1867*x^11 + 3178*x^10 + 6186*x^9 - 9216*x^8 - 11921*x^7 + 13680*x^6 + 13752*x^5 - 9400*x^4 - 8800*x^3 + 1920*x^2 + 2240*x + 256
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 125 ]
], tamagawa_numbers := [
[ 1 ],
[ 125 ]
], torsion_upper_bounds := [ 1, 125 ], torsion_lower_bounds := [ 1, 125 ], l_ratios := [ 0, 1/125 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
2/7*a^3 + 13/7*a^2 + 4/7*a - 23/7,
-1/7*a^3 - 13/14*a^2 + 3/14*a + 23/14,
-3/14*a^3 - 23/14*a^2 - 27/14*a + 12/7,
3/14*a^3 + 23/14*a^2 + 13/14*a - 33/7,
5/14*a^3 + 18/7*a^2 + 12/7*a - 75/14,
1/7*a^3 + 13/14*a^2 + 11/14*a - 51/14,
5/14*a^3 + 43/14*a^2 + 59/14*a - 41/7,
-9/14*a^3 - 69/14*a^2 - 53/14*a + 57/7,
-1/7*a^3 - 10/7*a^2 - 23/7*a + 22/7,
-1/7*a^3 - 3/7*a^2 + 26/7*a - 6/7,
6/7*a^3 + 85/14*a^2 + 31/14*a - 187/14,
1/14*a^3 - 2/7*a^2 - 27/7*a - 29/14
],
[
a,
69/1216*a^16 - 53/304*a^15 - 219/152*a^14 + 2819/608*a^13 + 903/64*a^12 - 1857/38*a^11 - 79979/1216*a^10 + 9809/38*a^9 + 87207/608*a^8 - 216513/304*a^7 - 7719/64*a^6 + 31535/32*a^5 + 6777/152*a^4 - 97473/152*a^3 - 3451/76*a^2 + 5735/38*a + 434/19,
-21/304*a^16 - 37/608*a^15 + 653/304*a^14 + 287/152*a^13 - 109/4*a^12 - 14297/608*a^11 + 27443/152*a^10 + 91723/608*a^9 - 200943/304*a^8 - 161767/304*a^7 + 20607/16*a^6 + 32619/32*a^5 - 21707/19*a^4 - 146925/152*a^3 + 5341/19*a^2 + 5948/19*a + 743/19,
7/19*a^16 - 85/304*a^15 - 801/76*a^14 + 1009/152*a^13 + 973/8*a^12 - 17893/304*a^11 - 13748/19*a^10 + 68557/304*a^9 + 89407/38*a^8 - 18169/76*a^7 - 4087*a^6 - 9741/16*a^5 + 518077/152*a^4 + 205791/152*a^3 - 68487/76*a^2 - 10829/19*a - 1119/19,
-4/19*a^16 - 11/152*a^15 + 967/152*a^14 + 203/76*a^13 - 313/4*a^12 - 5829/152*a^11 + 76243/152*a^10 + 42431/152*a^9 - 269993/152*a^8 - 42051/38*a^7 + 13471/4*a^6 + 18769/8*a^5 - 451977/152*a^4 - 89797/38*a^3 + 29179/38*a^2 + 14852/19*a + 1622/19,
-277/1216*a^16 + 47/304*a^15 + 2007/304*a^14 - 2231/608*a^13 - 4951/64*a^12 + 616/19*a^11 + 569887/1216*a^10 - 9297/76*a^9 - 946677/608*a^8 + 34695/304*a^7 + 177391/64*a^6 + 12773/32*a^5 - 720659/304*a^4 - 127435/152*a^3 + 25057/38*a^2 + 6630/19*a + 606/19,
17/64*a^16 - 11/32*a^15 - 59/8*a^14 + 275/32*a^13 + 5253/64*a^12 - 2657/32*a^11 - 29879/64*a^10 + 12219/32*a^9 + 45967/32*a^8 - 6455/8*a^7 - 150313/64*a^6 + 8557/16*a^5 + 30275/16*a^4 + 857/4*a^3 - 1051/2*a^2 - 379/2*a - 11,
167/304*a^16 - 113/304*a^15 - 1203/76*a^14 + 1315/152*a^13 + 2947/16*a^12 - 22429/304*a^11 - 336329/304*a^10 + 77359/304*a^9 + 552825/152*a^8 - 13795/152*a^7 - 102241/16*a^6 - 22063/16*a^5 + 815887/152*a^4 + 184777/76*a^3 - 26577/19*a^2 - 18561/19*a - 2086/19,
-301/1216*a^16 + 59/608*a^15 + 2199/304*a^14 - 1219/608*a^13 - 5483/64*a^12 + 8133/608*a^11 + 639823/1216*a^10 - 7751/608*a^9 - 1080393/608*a^8 - 8365/38*a^7 + 205535/64*a^6 + 14891/16*a^5 - 208521/76*a^4 - 47879/38*a^3 + 27539/38*a^2 + 17769/38*a + 973/19,
-455/608*a^16 + 127/152*a^15 + 3203/152*a^14 - 6385/304*a^13 - 7629/32*a^12 + 15531/76*a^11 + 840781/608*a^10 - 36001/38*a^9 - 1323811/304*a^8 + 306159/152*a^7 + 233493/32*a^6 - 20781/16*a^5 - 906415/152*a^4 - 26099/38*a^3 + 31473/19*a^2 + 10806/19*a + 902/19,
443/608*a^16 - 505/608*a^15 - 6233/304*a^14 + 6321/304*a^13 + 7423/32*a^12 - 122337/608*a^11 - 818923/608*a^10 + 562955/608*a^9 + 646365/152*a^8 - 591193/304*a^7 - 229025/32*a^6 + 38505/32*a^5 + 892785/152*a^4 + 110843/152*a^3 - 123189/76*a^2 - 10727/19*a - 991/19,
-71/304*a^16 + 2/19*a^15 + 511/76*a^14 - 309/152*a^13 - 1253/16*a^12 + 821/76*a^11 + 143605/304*a^10 + 1771/76*a^9 - 238323/152*a^8 - 31575/76*a^7 + 44837/16*a^6 + 11253/8*a^5 - 182785/76*a^4 - 65537/38*a^3 + 23569/38*a^2 + 11673/19*a + 1306/19
]
*], q_expansions := [*
q + (2/7*a^3 + 13/7*a^2 + 4/7*a - 23/7)*q^2 + (-1/7*a^3 - 13/14*a^2 + 3/14*a + 23/14)*q^3 + (-2/7*a^3 - 13/7*a^2 - 4/7*a + 16/7)*q^4 + (-3/14*a^3 - 23/14*a^2 - 27/14*a + 12/7)*q^5 + (3/14*a^3 + 23/14*a^2 + 13/14*a - 26/7)*q^6 + (3/14*a^3 + 23/14*a^2 + 13/14*a - 33/7)*q^7 + (-4/7*a^3 - 26/7*a^2 - 8/7*a + 39/7)*q^8 + (-1/7*a^3 - 13/14*a^2 - 11/14*a - 5/14)*q^9 + (-5/14*a^3 - 18/7*a^2 - 12/7*a + 61/14)*q^10 + (5/14*a^3 + 18/7*a^2 + 12/7*a - 75/14)*q^11 + (-1/14*a^3 - 5/7*a^2 - 8/7*a + 29/14)*q^12 + (1/7*a^3 + 13/14*a^2 + 11/14*a - 51/14)*q^13 + (-9/14*a^3 - 31/7*a^2 - 9/7*a + 121/14)*q^14 - q^15 + (6/7*a^3 + 39/7*a^2 + 12/7*a - 69/7)*q^16 + (5/14*a^3 + 43/14*a^2 + 59/14*a - 41/7)*q^17 + (-1/2*a^3 - 7/2*a^2 - 3/2*a + 6)*q^18 + (-9/14*a^3 - 69/14*a^2 - 53/14*a + 57/7)*q^19 + (4/7*a^3 + 59/14*a^2 + 51/14*a - 85/14)*q^20 + (1/2*a^3 + 3*a^2 - 11/2)*q^21 + (-3/7*a^3 - 39/14*a^2 - 5/14*a + 83/14)*q^22 + (-1/7*a^3 - 10/7*a^2 - 23/7*a + 22/7)*q^23 + (-2/7*a^3 - 33/14*a^2 - 29/14*a + 81/14)*q^24 + (15/14*a^3 + 54/7*a^2 + 43/7*a - 197/14)*q^25 + (-9/14*a^3 - 55/14*a^2 - 11/14*a + 50/7)*q^26 + (9/14*a^3 + 55/14*a^2 - 17/14*a - 50/7)*q^27 + (3/7*a^3 + 39/14*a^2 + 5/14*a - 55/14)*q^28 + (-1/7*a^3 - 3/7*a^2 + 26/7*a - 6/7)*q^29 + (-2/7*a^3 - 13/7*a^2 - 4/7*a + 23/7)*q^30 + (6/7*a^3 + 85/14*a^2 + 31/14*a - 187/14)*q^31 + (2/7*a^3 + 13/7*a^2 + 4/7*a + 12/7)*q^32 + (3/7*a^3 + 39/14*a^2 + 5/14*a - 69/14)*q^33 + (1/14*a^3 + 5/7*a^2 + 15/7*a - 15/14)*q^34 + (-1/14*a^3 - 3/14*a^2 + 19/14*a + 11/7)*q^35 + (9/14*a^3 + 31/7*a^2 + 16/7*a - 79/14)*q^36 + (1/14*a^3 - 2/7*a^2 - 27/7*a - 29/14)*q^37 + O(q^38),
q + a*q^2 + (69/1216*a^16 - 53/304*a^15 - 219/152*a^14 + 2819/608*a^13 + 903/64*a^12 - 1857/38*a^11 - 79979/1216*a^10 + 9809/38*a^9 + 87207/608*a^8 - 216513/304*a^7 - 7719/64*a^6 + 31535/32*a^5 + 6777/152*a^4 - 97473/152*a^3 - 3451/76*a^2 + 5735/38*a + 434/19)*q^3 + (a^2 - 2)*q^4 + (-21/304*a^16 - 37/608*a^15 + 653/304*a^14 + 287/152*a^13 - 109/4*a^12 - 14297/608*a^11 + 27443/152*a^10 + 91723/608*a^9 - 200943/304*a^8 - 161767/304*a^7 + 20607/16*a^6 + 32619/32*a^5 - 21707/19*a^4 - 146925/152*a^3 + 5341/19*a^2 + 5948/19*a + 743/19)*q^5 + (-37/608*a^16 + 45/304*a^15 + 239/152*a^14 - 1179/304*a^13 - 507/32*a^12 + 12211/304*a^11 + 47303/608*a^10 - 63105/304*a^9 - 57537/304*a^8 + 42243/76*a^7 + 6695/32*a^6 - 2943/4*a^5 - 8199/76*a^4 + 34499/76*a^3 + 1595/38*a^2 - 1981/19*a - 276/19)*q^6 + (7/19*a^16 - 85/304*a^15 - 801/76*a^14 + 1009/152*a^13 + 973/8*a^12 - 17893/304*a^11 - 13748/19*a^10 + 68557/304*a^9 + 89407/38*a^8 - 18169/76*a^7 - 4087*a^6 - 9741/16*a^5 + 518077/152*a^4 + 205791/152*a^3 - 68487/76*a^2 - 10829/19*a - 1119/19)*q^7 + (a^3 - 4*a)*q^8 + (-85/1216*a^16 + 89/608*a^15 + 283/152*a^14 - 2347/608*a^13 - 1243/64*a^12 + 24279/608*a^11 + 120979/1216*a^10 - 123313/608*a^9 - 156211/608*a^8 + 78283/152*a^7 + 20239/64*a^6 - 4757/8*a^5 - 58625/304*a^4 + 41921/152*a^3 + 4151/76*a^2 - 1323/38*a - 31/19)*q^9 + (-121/608*a^16 + 65/304*a^15 + 427/76*a^14 - 1627/304*a^13 - 2039/32*a^12 + 15679/304*a^11 + 225199/608*a^10 - 71037/304*a^9 - 355303/304*a^8 + 17649/38*a^7 + 62859/32*a^6 - 385/2*a^5 - 245625/152*a^4 - 6209/19*a^3 + 8468/19*a^2 + 3683/19*a + 336/19)*q^10 + (-4/19*a^16 - 11/152*a^15 + 967/152*a^14 + 203/76*a^13 - 313/4*a^12 - 5829/152*a^11 + 76243/152*a^10 + 42431/152*a^9 - 269993/152*a^8 - 42051/38*a^7 + 13471/4*a^6 + 18769/8*a^5 - 451977/152*a^4 - 89797/38*a^3 + 29179/38*a^2 + 14852/19*a + 1622/19)*q^11 + (-53/608*a^16 + 33/152*a^15 + 87/38*a^14 - 1771/304*a^13 - 751/32*a^12 + 2353/38*a^11 + 71355/608*a^10 - 12505/38*a^9 - 88731/304*a^8 + 138045/152*a^7 + 10815/32*a^6 - 19871/16*a^5 - 15753/76*a^4 + 59963/76*a^3 + 3929/38*a^2 - 3421/19*a - 572/19)*q^12 + (-277/1216*a^16 + 47/304*a^15 + 2007/304*a^14 - 2231/608*a^13 - 4951/64*a^12 + 616/19*a^11 + 569887/1216*a^10 - 9297/76*a^9 - 946677/608*a^8 + 34695/304*a^7 + 177391/64*a^6 + 12773/32*a^5 - 720659/304*a^4 - 127435/152*a^3 + 25057/38*a^2 + 6630/19*a + 606/19)*q^13 + (139/304*a^16 - 17/76*a^15 - 2015/152*a^14 + 735/152*a^13 + 2489/16*a^12 - 679/19*a^11 - 287379/304*a^10 + 2803/38*a^9 + 239879/76*a^8 + 5794/19*a^7 - 90381/16*a^6 - 13265/8*a^5 + 732191/152*a^4 + 177913/76*a^3 - 24269/19*a^2 - 16799/19*a - 1792/19)*q^14 + (-259/608*a^16 + 91/152*a^15 + 1787/152*a^14 - 4605/304*a^13 - 4153/32*a^12 + 11323/76*a^11 + 443753/608*a^10 - 13419/19*a^9 - 671799/304*a^8 + 242391/152*a^7 + 113153/32*a^6 - 21817/16*a^5 - 423745/152*a^4 + 1231/19*a^3 + 28721/38*a^2 + 7169/38*a + 386/19)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (17/64*a^16 - 11/32*a^15 - 59/8*a^14 + 275/32*a^13 + 5253/64*a^12 - 2657/32*a^11 - 29879/64*a^10 + 12219/32*a^9 + 45967/32*a^8 - 6455/8*a^7 - 150313/64*a^6 + 8557/16*a^5 + 30275/16*a^4 + 857/4*a^3 - 1051/2*a^2 - 379/2*a - 11)*q^17 + (1/152*a^16 - 29/304*a^15 - 13/152*a^14 + 52/19*a^13 - 3/4*a^12 - 9429/304*a^11 + 1469/76*a^10 + 53347/304*a^9 - 19637/152*a^8 - 78593/152*a^7 + 2893/8*a^6 + 12295/16*a^5 - 28977/76*a^4 - 42599/76*a^3 + 3777/38*a^2 + 2944/19*a + 340/19)*q^18 + (167/304*a^16 - 113/304*a^15 - 1203/76*a^14 + 1315/152*a^13 + 2947/16*a^12 - 22429/304*a^11 - 336329/304*a^10 + 77359/304*a^9 + 552825/152*a^8 - 13795/152*a^7 - 102241/16*a^6 - 22063/16*a^5 + 815887/152*a^4 + 184777/76*a^3 - 26577/19*a^2 - 18561/19*a - 2086/19)*q^19 + (-7/152*a^16 + 51/304*a^15 + 167/152*a^14 - 335/76*a^13 - 39/4*a^12 + 13943/304*a^11 + 2865/76*a^10 - 72773/304*a^9 - 7245/152*a^8 + 99737/152*a^7 - 367/8*a^6 - 14685/16*a^5 + 6645/76*a^4 + 47697/76*a^3 + 261/19*a^2 - 3090/19*a - 518/19)*q^20 + (939/1216*a^16 - 105/304*a^15 - 6847/304*a^14 + 4457/608*a^13 + 17033/64*a^12 - 3939/76*a^11 - 1982345/1216*a^10 + 6169/76*a^9 + 3338887/608*a^8 + 191863/304*a^7 - 634721/64*a^6 - 94955/32*a^5 + 2589711/304*a^4 + 623103/152*a^3 - 173497/76*a^2 - 29432/19*a - 3080/19)*q^21 + (-75/152*a^16 + 71/152*a^15 + 1067/76*a^14 - 875/76*a^13 - 1287/8*a^12 + 16499/152*a^11 + 144127/152*a^10 - 72041/152*a^9 - 115779/38*a^8 + 65213/76*a^7 + 41809/8*a^6 - 627/8*a^5 - 164997/38*a^4 - 41221/38*a^3 + 22532/19*a^2 + 10582/19*a + 1024/19)*q^22 + (-301/1216*a^16 + 59/608*a^15 + 2199/304*a^14 - 1219/608*a^13 - 5483/64*a^12 + 8133/608*a^11 + 639823/1216*a^10 - 7751/608*a^9 - 1080393/608*a^8 - 8365/38*a^7 + 205535/64*a^6 + 14891/16*a^5 - 208521/76*a^4 - 47879/38*a^3 + 27539/38*a^2 + 17769/38*a + 973/19)*q^23 + (25/152*a^16 - 17/38*a^15 - 81/19*a^14 + 453/38*a^13 + 343/8*a^12 - 9555/76*a^11 - 31563/152*a^10 + 12588/19*a^9 + 36735/76*a^8 - 137777/76*a^7 - 3743/8*a^6 + 2463*a^5 + 7043/38*a^4 - 29860/19*a^3 - 1836/19*a^2 + 7100/19*a + 976/19)*q^24 + (-97/1216*a^16 + 157/608*a^15 + 605/304*a^14 - 4159/608*a^13 - 1215/64*a^12 + 43655/608*a^11 + 102595/1216*a^10 - 229565/608*a^9 - 98961/608*a^8 + 157517/152*a^7 + 4443/64*a^6 - 11381/8*a^5 + 5387/76*a^4 + 69241/76*a^3 - 180/19*a^2 - 8103/38*a - 446/19)*q^25 + (-183/608*a^16 + 17/76*a^15 + 164/19*a^14 - 1565/304*a^13 - 3205/32*a^12 + 6591/152*a^11 + 365777/608*a^10 - 22479/152*a^9 - 603513/304*a^8 + 8539/152*a^7 + 112493/32*a^6 + 12193/16*a^5 - 226455/76*a^4 - 25559/19*a^3 + 14940/19*a^2 + 10301/19*a + 1108/19)*q^26 + (-3/304*a^16 - 23/304*a^15 + 153/304*a^14 + 36/19*a^13 - 139/16*a^12 - 5645/304*a^11 + 10793/152*a^10 + 27339/304*a^9 - 91037/304*a^8 - 4284/19*a^7 + 10131/16*a^6 + 4663/16*a^5 - 174807/304*a^4 - 15531/76*a^3 + 11545/76*a^2 + 1941/38*a + 98/19)*q^27 + (-7/152*a^16 + 2/19*a^15 + 93/76*a^14 - 101/38*a^13 - 103/8*a^12 + 495/19*a^11 + 10309/152*a^10 - 9363/76*a^9 - 3549/19*a^8 + 21283/76*a^7 + 2087/8*a^6 - 1013/4*a^5 - 6757/38*a^4 + 2933/76*a^3 + 1529/38*a^2 + 406/19*a + 14/19)*q^28 + (-455/608*a^16 + 127/152*a^15 + 3203/152*a^14 - 6385/304*a^13 - 7629/32*a^12 + 15531/76*a^11 + 840781/608*a^10 - 36001/38*a^9 - 1323811/304*a^8 + 306159/152*a^7 + 233493/32*a^6 - 20781/16*a^5 - 906415/152*a^4 - 26099/38*a^3 + 31473/19*a^2 + 10806/19*a + 902/19)*q^29 + (-77/304*a^16 - 13/76*a^15 + 597/76*a^14 + 799/152*a^13 - 1583/16*a^12 - 4975/76*a^11 + 196847/304*a^10 + 16161/38*a^9 - 354345/152*a^8 - 29301/19*a^7 + 71423/16*a^6 + 24563/8*a^5 - 299401/76*a^4 - 113729/38*a^3 + 38249/38*a^2 + 18516/19*a + 2072/19)*q^30 + (443/608*a^16 - 505/608*a^15 - 6233/304*a^14 + 6321/304*a^13 + 7423/32*a^12 - 122337/608*a^11 - 818923/608*a^10 + 562955/608*a^9 + 646365/152*a^8 - 591193/304*a^7 - 229025/32*a^6 + 38505/32*a^5 + 892785/152*a^4 + 110843/152*a^3 - 123189/76*a^2 - 10727/19*a - 991/19)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-365/608*a^16 + 29/304*a^15 + 673/38*a^14 - 243/304*a^13 - 6787/32*a^12 - 4669/304*a^11 + 802531/608*a^10 + 79083/304*a^9 - 1376815/304*a^8 - 114347/76*a^7 + 266727/32*a^6 + 3982*a^5 - 1100343/152*a^4 - 343253/76*a^3 + 36216/19*a^2 + 29660/19*a + 3080/19)*q^33 + (3/16*a^16 + 1/16*a^15 - 23/4*a^14 - 17/8*a^13 + 1145/16*a^12 + 465/16*a^11 - 7397/16*a^10 - 3307/16*a^9 + 13129/8*a^8 + 6543/8*a^7 - 49583/16*a^6 - 28171/16*a^5 + 21689/8*a^4 + 1812*a^3 - 1399/2*a^2 - 606*a - 68)*q^34 + (-245/1216*a^16 + 159/304*a^15 + 1561/304*a^14 - 8267/608*a^13 - 3239/64*a^12 + 10553/76*a^11 + 290743/1216*a^10 - 106327/152*a^9 - 327817/608*a^8 + 542797/304*a^7 + 32143/64*a^6 - 68883/32*a^5 - 60821/304*a^4 + 21692/19*a^3 + 2735/38*a^2 - 8047/38*a - 485/19)*q^35 + (35/608*a^16 - 59/304*a^15 - 51/38*a^14 + 1485/304*a^13 + 373/32*a^12 - 14669/304*a^11 - 26997/608*a^10 + 71667/304*a^9 + 17457/304*a^8 - 44839/76*a^7 + 1471/32*a^6 + 1435/2*a^5 - 17173/152*a^4 - 29967/76*a^3 + 1257/38*a^2 + 1383/19*a + 30/19)*q^36 + (-71/304*a^16 + 2/19*a^15 + 511/76*a^14 - 309/152*a^13 - 1253/16*a^12 + 821/76*a^11 + 143605/304*a^10 + 1771/76*a^9 - 238323/152*a^8 - 31575/76*a^7 + 44837/16*a^6 + 11253/8*a^5 - 182785/76*a^4 - 65537/38*a^3 + 23569/38*a^2 + 11673/19*a + 1306/19)*q^37 + O(q^38)
*]> ;  // time = 3.881 seconds




J[253] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 253, 253, 253, 253, 23, 11 ], new_dimensions := [ 3, 3, 5, 6, 2, 1 ], dimensions := [ 3, 3, 5, 6, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 19, 1, 1, 0, 1, 1, 5, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 23, 19, 5, 1, 1, 0, 1, 1, 5, 1, 23, 1, 0 ], ap_traces := [
[ 3, 3, 3, 3, -3, -3, 3, 9, 3, 0, 0, -18 ],
[ -1, -5, -5, -3, 3, -1, -9, -5, 3, 12, -4, -14 ],
[ -4, -5, -3, -3, -5, -15, -9, -5, -5, -8, -4, 8 ],
[ 3, 7, 3, -1, 6, -3, 5, 1, -6, 6, -8, 2 ]
], hecke_fields := [
x^3 - 3*x^2 + 3,
x^3 + x^2 - 4*x + 1,
x^5 + 4*x^4 - 14*x^2 - 13*x - 1,
x^6 - 3*x^5 - 4*x^4 + 16*x^3 - 3*x^2 - 10*x + 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 19, 1 ],
[ 5, 5 ],
[ 1, 1 ],
[ 1, 23 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 5, 5 ],
[ 1, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 1, 0, 0, 1 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1 ], eigenvalues := [*
[
a,
-a^2 + a + 3,
a^2 - 2*a,
-a^2 + a + 3,
-1,
a^2 - 3*a - 1,
-a^2 + 2*a + 2,
2*a^2 - 4*a + 1,
1,
-a^2 - 3*a + 6,
3*a^2 - 4*a - 5,
-3*a^2 + 6*a - 3
],
[
a,
-a^2 - a + 1,
a^2 + 2*a - 4,
-a^2 - 3*a + 1,
1,
a^2 + a - 3,
a^2 - 6,
2*a - 1,
1,
a^2 + 3*a + 2,
-5*a^2 - 8*a + 11,
a^2 + 2*a - 7
],
[
a,
-a^4 - 3*a^3 + 3*a^2 + 10*a + 1,
2*a^4 + 5*a^3 - 8*a^2 - 18*a - 1,
-2*a^4 - 4*a^3 + 9*a^2 + 13*a - 3,
-1,
-a^4 - 3*a^3 + 3*a^2 + 10*a - 1,
-a^3 - 2*a^2 + 6*a + 5,
a^4 + 3*a^3 - 2*a^2 - 11*a - 7,
-1,
2*a^4 + 4*a^3 - 7*a^2 - 11*a - 4,
-2*a^4 - 5*a^3 + 6*a^2 + 18*a + 6,
-a^4 - 4*a^3 + 2*a^2 + 17*a + 8
],
[
a,
a^4 - a^3 - 5*a^2 + 4*a + 3,
-a^3 + 4*a + 1,
-a^5 + 6*a^3 + a^2 - 6*a - 2,
1,
-2*a^5 + 3*a^4 + 11*a^3 - 15*a^2 - 6*a + 5,
2*a^5 - 4*a^4 - 9*a^3 + 20*a^2 - 2*a - 7,
4*a^5 - 5*a^4 - 21*a^3 + 22*a^2 + 11*a - 3,
-1,
-2*a^5 + 14*a^3 + 3*a^2 - 21*a - 6,
a^5 - 7*a^3 + 2*a^2 + 9*a - 7,
4*a^5 - 5*a^4 - 22*a^3 + 24*a^2 + 15*a - 8
]
*], q_expansions := [*
q + a*q^2 + (-a^2 + a + 3)*q^3 + (a^2 - 2)*q^4 + (a^2 - 2*a)*q^5 + (-2*a^2 + 3*a + 3)*q^6 + (-a^2 + a + 3)*q^7 + (3*a^2 - 4*a - 3)*q^8 + (-2*a^2 + 3*a + 3)*q^9 + (a^2 - 3)*q^10 - q^11 + (-a^2 + a)*q^12 + (a^2 - 3*a - 1)*q^13 + (-2*a^2 + 3*a + 3)*q^14 + (a^2 - 3*a)*q^15 + (3*a^2 - 3*a - 5)*q^16 + (-a^2 + 2*a + 2)*q^17 + (-3*a^2 + 3*a + 6)*q^18 + (2*a^2 - 4*a + 1)*q^19 + (a^2 + a - 3)*q^20 + (-2*a^2 + 3*a + 6)*q^21 - a*q^22 + q^23 + (2*a^2 - 6*a - 3)*q^24 + (a^2 - 3*a - 2)*q^25 + (-a - 3)*q^26 + (3*a - 3)*q^27 + (-a^2 + a)*q^28 + (-a^2 - 3*a + 6)*q^29 - 3*q^30 + (3*a^2 - 4*a - 5)*q^31 + (3*a - 3)*q^32 + (a^2 - a - 3)*q^33 + (-a^2 + 2*a + 3)*q^34 + (a^2 - 3*a)*q^35 + (-2*a^2 + 3)*q^36 + (-3*a^2 + 6*a - 3)*q^37 + O(q^38),
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 + 2*a - 4)*q^5 + (-3*a + 1)*q^6 + (-a^2 - 3*a + 1)*q^7 + (-a^2 - 1)*q^8 + (2*a^2 + a - 3)*q^9 + (a^2 - 1)*q^10 + q^11 + (-a^2 + 3*a - 2)*q^12 + (a^2 + a - 3)*q^13 + (-2*a^2 - 3*a + 1)*q^14 + (a^2 - a - 2)*q^15 + (-a^2 - 5*a + 5)*q^16 + (a^2 - 6)*q^17 + (-a^2 + 5*a - 2)*q^18 + (2*a - 1)*q^19 + (-3*a^2 - a + 7)*q^20 + (2*a^2 + 7*a - 2)*q^21 + a*q^22 + q^23 + (4*a^2 - 1)*q^24 + (-3*a^2 - 5*a + 8)*q^25 + (a - 1)*q^26 + (5*a - 5)*q^27 + (a^2 - a)*q^28 + (a^2 + 3*a + 2)*q^29 + (-2*a^2 + 2*a - 1)*q^30 + (-5*a^2 - 8*a + 11)*q^31 + (-2*a^2 + a + 3)*q^32 + (-a^2 - a + 1)*q^33 + (-a^2 - 2*a - 1)*q^34 + (-a^2 - a)*q^35 + (2*a^2 - 8*a + 7)*q^36 + (a^2 + 2*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-a^4 - 3*a^3 + 3*a^2 + 10*a + 1)*q^3 + (a^2 - 2)*q^4 + (2*a^4 + 5*a^3 - 8*a^2 - 18*a - 1)*q^5 + (a^4 + 3*a^3 - 4*a^2 - 12*a - 1)*q^6 + (-2*a^4 - 4*a^3 + 9*a^2 + 13*a - 3)*q^7 + (a^3 - 4*a)*q^8 + (4*a^4 + 11*a^3 - 13*a^2 - 37*a - 6)*q^9 + (-3*a^4 - 8*a^3 + 10*a^2 + 25*a + 2)*q^10 - q^11 + (a^4 + 2*a^3 - 4*a^2 - 8*a - 1)*q^12 + (-a^4 - 3*a^3 + 3*a^2 + 10*a - 1)*q^13 + (4*a^4 + 9*a^3 - 15*a^2 - 29*a - 2)*q^14 + (-5*a^4 - 13*a^3 + 19*a^2 + 48*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^3 - 2*a^2 + 6*a + 5)*q^17 + (-5*a^4 - 13*a^3 + 19*a^2 + 46*a + 4)*q^18 + (a^4 + 3*a^3 - 2*a^2 - 11*a - 7)*q^19 + (-a^2 - a - 1)*q^20 + (3*a^4 + 8*a^3 - 11*a^2 - 28*a - 3)*q^21 - a*q^22 - q^23 + (-4*a^4 - 10*a^3 + 14*a^2 + 36*a + 3)*q^24 + (4*a^4 + 12*a^3 - 11*a^2 - 39*a - 8)*q^25 + (a^4 + 3*a^3 - 4*a^2 - 14*a - 1)*q^26 + (-7*a^4 - 18*a^3 + 25*a^2 + 62*a + 4)*q^27 + (-3*a^4 - 7*a^3 + 9*a^2 + 24*a + 10)*q^28 + (2*a^4 + 4*a^3 - 7*a^2 - 11*a - 4)*q^29 + (7*a^4 + 19*a^3 - 22*a^2 - 61*a - 5)*q^30 + (-2*a^4 - 5*a^3 + 6*a^2 + 18*a + 6)*q^31 + (-4*a^4 - 8*a^3 + 14*a^2 + 25*a + 1)*q^32 + (a^4 + 3*a^3 - 3*a^2 - 10*a - 1)*q^33 + (-a^4 - 2*a^3 + 6*a^2 + 5*a)*q^34 + (a^4 + a^3 - 5*a^2 - 2*a - 2)*q^35 + (-a^4 - 3*a^3 + 2*a^2 + 13*a + 7)*q^36 + (-a^4 - 4*a^3 + 2*a^2 + 17*a + 8)*q^37 + O(q^38),
q + a*q^2 + (a^4 - a^3 - 5*a^2 + 4*a + 3)*q^3 + (a^2 - 2)*q^4 + (-a^3 + 4*a + 1)*q^5 + (a^5 - a^4 - 5*a^3 + 4*a^2 + 3*a)*q^6 + (-a^5 + 6*a^3 + a^2 - 6*a - 2)*q^7 + (a^3 - 4*a)*q^8 + (2*a^4 - a^3 - 11*a^2 + 3*a + 8)*q^9 + (-a^4 + 4*a^2 + a)*q^10 + q^11 + (2*a^5 - 3*a^4 - 10*a^3 + 16*a^2 + 2*a - 7)*q^12 + (-2*a^5 + 3*a^4 + 11*a^3 - 15*a^2 - 6*a + 5)*q^13 + (-3*a^5 + 2*a^4 + 17*a^3 - 9*a^2 - 12*a + 1)*q^14 + (-a^5 + a^4 + 5*a^3 - 5*a^2 - 3*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^5 - 4*a^4 - 9*a^3 + 20*a^2 - 2*a - 7)*q^17 + (2*a^5 - a^4 - 11*a^3 + 3*a^2 + 8*a)*q^18 + (4*a^5 - 5*a^4 - 21*a^3 + 22*a^2 + 11*a - 3)*q^19 + (-a^5 + 6*a^3 + a^2 - 8*a - 2)*q^20 + (-a^5 - a^4 + 6*a^3 + 7*a^2 - 7*a - 8)*q^21 + a*q^22 - q^23 + (a^5 - 6*a^3 + 7*a - 2)*q^24 + (3*a^5 - 4*a^4 - 18*a^3 + 19*a^2 + 18*a - 5)*q^25 + (-3*a^5 + 3*a^4 + 17*a^3 - 12*a^2 - 15*a + 2)*q^26 + (-2*a^5 + 5*a^4 + 10*a^3 - 27*a^2 - 4*a + 18)*q^27 + (-5*a^5 + 5*a^4 + 27*a^3 - 23*a^2 - 17*a + 7)*q^28 + (-2*a^5 + 14*a^3 + 3*a^2 - 21*a - 6)*q^29 + (-2*a^5 + a^4 + 11*a^3 - 6*a^2 - 5*a + 1)*q^30 + (a^5 - 7*a^3 + 2*a^2 + 9*a - 7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - a^3 - 5*a^2 + 4*a + 3)*q^33 + (2*a^5 - a^4 - 12*a^3 + 4*a^2 + 13*a - 2)*q^34 + (3*a^5 - 3*a^4 - 17*a^3 + 15*a^2 + 13*a - 5)*q^35 + (5*a^5 - 7*a^4 - 27*a^3 + 36*a^2 + 14*a - 18)*q^36 + (4*a^5 - 5*a^4 - 22*a^3 + 24*a^2 + 15*a - 8)*q^37 + O(q^38)
*]> ;  // time = 29.17 seconds




J[254] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 254, 254, 254, 254, 254, 254, 127, 127 ], new_dimensions := [ 1, 1, 1, 1, 2, 5, 3, 7 ], dimensions := [ 1, 1, 1, 1, 2, 5, 6, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 1, 0, 1, 17, 1, 1, 1, 1, 1, 1, 0, 1, 1149, 3, 3, 1, 1, 17, 1, 0, 1, 1, 1, 1, 9, 1, 1149, 1, 0 ], ap_traces := [
[ -1, 0, -1, -3, 1, -2, -1, -7, 9, -6, -10, 4 ],
[ 1, 0, 2, 0, 4, -2, 2, -4, 0, -6, 8, -2 ],
[ 1, -2, 0, 4, 0, 6, -6, 8, 4, -8, -8, -6 ],
[ 1, -2, -3, -1, -3, -4, 3, -7, 3, 6, -4, 2 ],
[ 2, 4, -1, 1, -7, -2, -3, 5, -3, 6, 0, 4 ],
[ -5, -2, -1, 3, 1, 10, 7, 17, -1, 0, 14, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - 6*x - 8,
x^5 + 2*x^4 - 10*x^3 - 16*x^2 + 10*x + 16
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 3, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 9, 1 ],
[ 17, 1 ],
[ 3447, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 9, 1 ],
[ 17, 1 ],
[ 1, 3 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 3 ], l_ratios := [ 0, 3, 1, 0, 17, 1/3 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, -1, -3, 1, -2, -1, -7, 9, -6, -10, 4 ],
[ 1, 0, 2, 0, 4, -2, 2, -4, 0, -6, 8, -2 ],
[ 1, -2, 0, 4, 0, 6, -6, 8, 4, -8, -8, -6 ],
[ 1, -2, -3, -1, -3, -4, 3, -7, 3, 6, -4, 2 ],
[
1,
2,
-1/2*a + 1,
1/2*a - 1,
1/2*a - 5,
a - 4,
1/2*a - 3,
-3/2*a + 7,
-3/2*a + 3,
-a + 6,
0,
2
],
[
-1,
a,
-5/2*a^4 - 2*a^3 + 27*a^2 + 7*a - 31,
3/2*a^4 + a^3 - 17*a^2 - 2*a + 23,
1/2*a^4 + a^3 - 5*a^2 - 6*a + 5,
2,
3/2*a^4 + a^3 - 17*a^2 - 4*a + 23,
-3/2*a^4 - a^3 + 17*a^2 + 2*a - 19,
-1/2*a^4 - a^3 + 5*a^2 + 6*a - 5,
-2*a^4 - a^3 + 22*a^2 + a - 26,
3*a^4 + 2*a^3 - 33*a^2 - 6*a + 42,
-5*a^4 - 4*a^3 + 54*a^2 + 14*a - 60
]
*], q_expansions := [*
q - q^2 + q^4 - q^5 - 3*q^7 - q^8 - 3*q^9 + q^10 + q^11 - 2*q^13 + 3*q^14 + q^16 - q^17 + 3*q^18 - 7*q^19 - q^20 - q^22 + 9*q^23 - 4*q^25 + 2*q^26 - 3*q^28 - 6*q^29 - 10*q^31 - q^32 + q^34 + 3*q^35 - 3*q^36 + 4*q^37 + O(q^38),
q + q^2 + q^4 + 2*q^5 + q^8 - 3*q^9 + 2*q^10 + 4*q^11 - 2*q^13 + q^16 + 2*q^17 - 3*q^18 - 4*q^19 + 2*q^20 + 4*q^22 - q^25 - 2*q^26 - 6*q^29 + 8*q^31 + q^32 + 2*q^34 - 3*q^36 - 2*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^6 + 4*q^7 + q^8 + q^9 - 2*q^12 + 6*q^13 + 4*q^14 + q^16 - 6*q^17 + q^18 + 8*q^19 - 8*q^21 + 4*q^23 - 2*q^24 - 5*q^25 + 6*q^26 + 4*q^27 + 4*q^28 - 8*q^29 - 8*q^31 + q^32 - 6*q^34 + q^36 - 6*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 3*q^5 - 2*q^6 - q^7 + q^8 + q^9 - 3*q^10 - 3*q^11 - 2*q^12 - 4*q^13 - q^14 + 6*q^15 + q^16 + 3*q^17 + q^18 - 7*q^19 - 3*q^20 + 2*q^21 - 3*q^22 + 3*q^23 - 2*q^24 + 4*q^25 - 4*q^26 + 4*q^27 - q^28 + 6*q^29 + 6*q^30 - 4*q^31 + q^32 + 6*q^33 + 3*q^34 + 3*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + (-1/2*a + 1)*q^5 + 2*q^6 + (1/2*a - 1)*q^7 + q^8 + q^9 + (-1/2*a + 1)*q^10 + (1/2*a - 5)*q^11 + 2*q^12 + (a - 4)*q^13 + (1/2*a - 1)*q^14 + (-a + 2)*q^15 + q^16 + (1/2*a - 3)*q^17 + q^18 + (-3/2*a + 7)*q^19 + (-1/2*a + 1)*q^20 + (a - 2)*q^21 + (1/2*a - 5)*q^22 + (-3/2*a + 3)*q^23 + 2*q^24 + (1/2*a - 2)*q^25 + (a - 4)*q^26 - 4*q^27 + (1/2*a - 1)*q^28 + (-a + 6)*q^29 + (-a + 2)*q^30 + q^32 + (a - 10)*q^33 + (1/2*a - 3)*q^34 + (-1/2*a - 3)*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-5/2*a^4 - 2*a^3 + 27*a^2 + 7*a - 31)*q^5 - a*q^6 + (3/2*a^4 + a^3 - 17*a^2 - 2*a + 23)*q^7 - q^8 + (a^2 - 3)*q^9 + (5/2*a^4 + 2*a^3 - 27*a^2 - 7*a + 31)*q^10 + (1/2*a^4 + a^3 - 5*a^2 - 6*a + 5)*q^11 + a*q^12 + 2*q^13 + (-3/2*a^4 - a^3 + 17*a^2 + 2*a - 23)*q^14 + (3*a^4 + 2*a^3 - 33*a^2 - 6*a + 40)*q^15 + q^16 + (3/2*a^4 + a^3 - 17*a^2 - 4*a + 23)*q^17 + (-a^2 + 3)*q^18 + (-3/2*a^4 - a^3 + 17*a^2 + 2*a - 19)*q^19 + (-5/2*a^4 - 2*a^3 + 27*a^2 + 7*a - 31)*q^20 + (-2*a^4 - 2*a^3 + 22*a^2 + 8*a - 24)*q^21 + (-1/2*a^4 - a^3 + 5*a^2 + 6*a - 5)*q^22 + (-1/2*a^4 - a^3 + 5*a^2 + 6*a - 5)*q^23 - a*q^24 + (1/2*a^4 + a^3 - 6*a^2 - 8*a + 12)*q^25 - 2*q^26 + (a^3 - 6*a)*q^27 + (3/2*a^4 + a^3 - 17*a^2 - 2*a + 23)*q^28 + (-2*a^4 - a^3 + 22*a^2 + a - 26)*q^29 + (-3*a^4 - 2*a^3 + 33*a^2 + 6*a - 40)*q^30 + (3*a^4 + 2*a^3 - 33*a^2 - 6*a + 42)*q^31 - q^32 + (2*a^2 - 8)*q^33 + (-3/2*a^4 - a^3 + 17*a^2 + 4*a - 23)*q^34 + (-5/2*a^4 - 3*a^3 + 27*a^2 + 16*a - 33)*q^35 + (a^2 - 3)*q^36 + (-5*a^4 - 4*a^3 + 54*a^2 + 14*a - 60)*q^37 + O(q^38)
*]> ;  // time = 47.83 seconds




J[255] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 255, 255, 255, 255, 85, 85, 85, 51, 51, 17, 15 ], new_dimensions := [ 2, 2, 3, 4, 1, 2, 2, 1, 2, 1, 1 ], dimensions := [ 2, 2, 3, 4, 2, 4, 4, 2, 4, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 1, 13, 1, 1, 1, 0, 1, 1, 1, 1, 11, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 17, 1, 9, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 0, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 9, 1, 1, 3, 0, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, -2, -2, 0, 10, -6, 2, -4, 2, 8, -6, 2 ],
[ 3, -2, 2, 0, 2, 6, -2, -12, 10, -4, -10, 10 ],
[ 0, 3, 3, 4, -2, 4, 3, 0, -6, -6, 2, 16 ],
[ 1, 4, -4, 4, 2, -2, -4, 12, 2, 4, 6, -2 ]
], hecke_fields := [
x^2 - x - 3,
x^2 - 3*x + 1,
x^3 - 4*x + 1,
x^4 - x^3 - 8*x^2 + 7*x + 9
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 3, 13, 1 ],
[ 11, 1, 5 ],
[ 1, 1, 1 ],
[ 51, 9, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 51, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 3 ], l_ratios := [ 1, 1, 1, 17/3 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1 ], eigenvalues := [*
[
a,
-1,
-1,
2*a - 1,
5,
-2*a - 2,
1,
-2*a - 1,
-2*a + 2,
-2*a + 5,
-2*a - 2,
-4*a + 3
],
[
a,
-1,
1,
-2*a + 3,
-4*a + 7,
-2*a + 6,
-1,
2*a - 9,
2*a + 2,
-6*a + 7,
-2*a - 2,
4*a - 1
],
[
a,
1,
1,
-a^2 - a + 4,
-a^2 + a + 2,
2*a^2 - 4,
1,
-3*a^2 - 3*a + 8,
-2*a - 2,
3*a^2 - a - 10,
4*a^2 + 2*a - 10,
-a^2 - 3*a + 8
],
[
a,
1,
-1,
-a^3 - a^2 + 5*a + 5,
a^3 + a^2 - 7*a - 3,
-2*a^2 + 8,
-1,
a^3 + a^2 - 5*a - 1,
-2*a^3 + 10*a,
a^3 + a^2 - 5*a - 3,
-2*a + 2,
a^3 + 3*a^2 - 5*a - 13
]
*], q_expansions := [*
q + a*q^2 - q^3 + (a + 1)*q^4 - q^5 - a*q^6 + (2*a - 1)*q^7 + 3*q^8 + q^9 - a*q^10 + 5*q^11 + (-a - 1)*q^12 + (-2*a - 2)*q^13 + (a + 6)*q^14 + q^15 + (a - 2)*q^16 + q^17 + a*q^18 + (-2*a - 1)*q^19 + (-a - 1)*q^20 + (-2*a + 1)*q^21 + 5*a*q^22 + (-2*a + 2)*q^23 - 3*q^24 + q^25 + (-4*a - 6)*q^26 - q^27 + (3*a + 5)*q^28 + (-2*a + 5)*q^29 + a*q^30 + (-2*a - 2)*q^31 + (-a - 3)*q^32 - 5*q^33 + a*q^34 + (-2*a + 1)*q^35 + (a + 1)*q^36 + (-4*a + 3)*q^37 + O(q^38),
q + a*q^2 - q^3 + (3*a - 3)*q^4 + q^5 - a*q^6 + (-2*a + 3)*q^7 + (4*a - 3)*q^8 + q^9 + a*q^10 + (-4*a + 7)*q^11 + (-3*a + 3)*q^12 + (-2*a + 6)*q^13 + (-3*a + 2)*q^14 - q^15 + (3*a + 2)*q^16 - q^17 + a*q^18 + (2*a - 9)*q^19 + (3*a - 3)*q^20 + (2*a - 3)*q^21 + (-5*a + 4)*q^22 + (2*a + 2)*q^23 + (-4*a + 3)*q^24 + q^25 + 2*q^26 - q^27 + (-3*a - 3)*q^28 + (-6*a + 7)*q^29 - a*q^30 + (-2*a - 2)*q^31 + (3*a + 3)*q^32 + (4*a - 7)*q^33 - a*q^34 + (-2*a + 3)*q^35 + (3*a - 3)*q^36 + (4*a - 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + q^5 + a*q^6 + (-a^2 - a + 4)*q^7 - q^8 + q^9 + a*q^10 + (-a^2 + a + 2)*q^11 + (a^2 - 2)*q^12 + (2*a^2 - 4)*q^13 + (-a^2 + 1)*q^14 + q^15 + (-2*a^2 - a + 4)*q^16 + q^17 + a*q^18 + (-3*a^2 - 3*a + 8)*q^19 + (a^2 - 2)*q^20 + (-a^2 - a + 4)*q^21 + (a^2 - 2*a + 1)*q^22 + (-2*a - 2)*q^23 - q^24 + q^25 + (4*a - 2)*q^26 + q^27 + (2*a^2 - a - 7)*q^28 + (3*a^2 - a - 10)*q^29 + a*q^30 + (4*a^2 + 2*a - 10)*q^31 + (-a^2 - 4*a + 4)*q^32 + (-a^2 + a + 2)*q^33 + a*q^34 + (-a^2 - a + 4)*q^35 + (a^2 - 2)*q^36 + (-a^2 - 3*a + 8)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 - q^5 + a*q^6 + (-a^3 - a^2 + 5*a + 5)*q^7 + (a^3 - 4*a)*q^8 + q^9 - a*q^10 + (a^3 + a^2 - 7*a - 3)*q^11 + (a^2 - 2)*q^12 + (-2*a^2 + 8)*q^13 + (-2*a^3 - 3*a^2 + 12*a + 9)*q^14 - q^15 + (a^3 + 2*a^2 - 7*a - 5)*q^16 - q^17 + a*q^18 + (a^3 + a^2 - 5*a - 1)*q^19 + (-a^2 + 2)*q^20 + (-a^3 - a^2 + 5*a + 5)*q^21 + (2*a^3 + a^2 - 10*a - 9)*q^22 + (-2*a^3 + 10*a)*q^23 + (a^3 - 4*a)*q^24 + q^25 + (-2*a^3 + 8*a)*q^26 + q^27 + (-3*a^3 - 2*a^2 + 13*a + 8)*q^28 + (a^3 + a^2 - 5*a - 3)*q^29 - a*q^30 + (-2*a + 2)*q^31 + (a^3 + a^2 - 4*a - 9)*q^32 + (a^3 + a^2 - 7*a - 3)*q^33 - a*q^34 + (a^3 + a^2 - 5*a - 5)*q^35 + (a^2 - 2)*q^36 + (a^3 + 3*a^2 - 5*a - 13)*q^37 + O(q^38)
*]> ;  // time = 68.171 seconds




J[257] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 257, 257 ], new_dimensions := [ 7, 14 ], dimensions := [ 7, 14 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -5, -1, -18, -2, -10, -10, -7, -12, 7, -9, -11 ],
[ 2, 3, -1, 24, 2, 12, -4, 9, 20, -3, 3, 5 ]
], hecke_fields := [
x^7 + 3*x^6 - 3*x^5 - 11*x^4 + 3*x^3 + 10*x^2 - x - 1,
x^14 - 2*x^13 - 21*x^12 + 42*x^11 + 163*x^10 - 327*x^9 - 568*x^8 + 1153*x^7 + 830*x^6 - 1755*x^5 - 318*x^4 + 825*x^3 + 10*x^2 - 96*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 1 ], torsion_lower_bounds := [ 1, 1 ], l_ratios := [ 0, 1 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
a^4 + 2*a^3 - 3*a^2 - 4*a + 1,
-a^5 - 4*a^4 - a^3 + 9*a^2 + 4*a - 3,
a^6 + 4*a^5 - 12*a^3 - 4*a^2 + 8*a - 1,
-a^6 - 2*a^5 + 6*a^4 + 9*a^3 - 9*a^2 - 7*a,
a^6 + 2*a^5 - 5*a^4 - 5*a^3 + 11*a^2 - 6,
2*a^6 + 8*a^5 + a^4 - 22*a^3 - 9*a^2 + 14*a,
-3*a^6 - 8*a^5 + 11*a^4 + 28*a^3 - 15*a^2 - 20*a + 4,
-a^6 - 5*a^5 - 2*a^4 + 16*a^3 + 9*a^2 - 12*a - 4,
a^5 + a^4 - 7*a^3 - 8*a^2 + 6*a + 9,
-a^6 - 5*a^5 - 6*a^4 + 4*a^3 + 12*a^2 + 9*a - 1,
3*a^6 + 7*a^5 - 13*a^4 - 27*a^3 + 17*a^2 + 25*a - 6
],
[
a,
1755/144512*a^13 - 14949/144512*a^12 - 15147/72256*a^11 + 77379/36128*a^10 + 155093/144512*a^9 - 1184607/72256*a^8 - 21849/72256*a^7 + 8189141/144512*a^6 - 1591687/144512*a^5 - 6092391/72256*a^4 + 826663/36128*a^3 + 5567751/144512*a^2 - 838701/144512*a - 479015/144512,
6245/72256*a^13 - 7803/72256*a^12 - 66405/36128*a^11 + 40205/18064*a^10 + 1060043/72256*a^9 - 610385/36128*a^8 - 1969527/36128*a^7 + 4165227/72256*a^6 + 6795559/72256*a^5 - 3048569/36128*a^4 - 1165231/18064*a^3 + 2740441/72256*a^2 + 1042445/72256*a - 214841/72256,
3085/144512*a^13 - 803/144512*a^12 - 29405/72256*a^11 + 2701/36128*a^10 + 376483/144512*a^9 - 13089/72256*a^8 - 389111/72256*a^7 - 168493/144512*a^6 - 729569/144512*a^5 + 434759/72256*a^4 + 866533/36128*a^3 - 1185999/144512*a^2 - 1265867/144512*a + 477775/144512,
7307/36128*a^13 - 11013/36128*a^12 - 78211/18064*a^11 + 57571/9032*a^10 + 1255701/36128*a^9 - 887991/18064*a^8 - 2333329/18064*a^7 + 6124677/36128*a^6 + 7879545/36128*a^5 - 4385815/18064*a^4 - 1210133/9032*a^3 + 3144647/36128*a^2 + 698611/36128*a - 95719/36128,
215/36128*a^13 - 905/36128*a^12 - 2203/18064*a^11 + 4481/9032*a^10 + 29473/36128*a^9 - 63719/18064*a^8 - 22053/18064*a^7 + 383777/36128*a^6 - 252067/36128*a^5 - 201971/18064*a^4 + 208273/9032*a^3 - 46029/36128*a^2 - 424425/36128*a + 76437/36128,
255/4516*a^13 - 261/2258*a^12 - 5357/4516*a^11 + 5667/2258*a^10 + 10321/1129*a^9 - 91783/4516*a^8 - 140295/4516*a^7 + 338339/4516*a^6 + 47119/1129*a^5 - 135015/1129*a^4 - 35287/4516*a^3 + 66268/1129*a^2 - 7256/1129*a - 6788/1129,
-24769/144512*a^13 + 44607/144512*a^12 + 263521/72256*a^11 - 233793/36128*a^10 - 4182639/144512*a^9 + 3614269/72256*a^8 + 7602267/72256*a^7 - 24927727/144512*a^6 - 24546683/144512*a^5 + 17660933/72256*a^4 + 3435315/36128*a^3 - 11568517/144512*a^2 - 2663753/144512*a + 320581/144512,
-4017/36128*a^13 + 8927/36128*a^12 + 40089/18064*a^11 - 46449/9032*a^10 - 567343/36128*a^9 + 711749/18064*a^8 + 804483/18064*a^7 - 4870079/36128*a^6 - 1036987/36128*a^5 + 3480933/18064*a^4 - 481241/9032*a^3 - 2725669/36128*a^2 + 1005655/36128*a + 299589/36128,
1823/36128*a^13 - 5153/36128*a^12 - 21431/18064*a^11 + 25749/9032*a^10 + 391601/36128*a^9 - 373879/18064*a^8 - 873757/18064*a^7 + 2364609/36128*a^6 + 3881085/36128*a^5 - 1449695/18064*a^4 - 944983/9032*a^3 + 540475/36128*a^2 + 999399/36128*a - 27731/36128,
-8595/72256*a^13 + 9293/72256*a^12 + 93635/36128*a^11 - 46859/18064*a^10 - 1541405/72256*a^9 + 694983/36128*a^8 + 2976401/36128*a^7 - 4612349/72256*a^6 - 10800545/72256*a^5 + 3178799/36128*a^4 + 2019817/18064*a^3 - 1991999/72256*a^2 - 2301067/72256*a - 59809/72256,
-12759/72256*a^13 + 10857/72256*a^12 + 143191/36128*a^11 - 54583/18064*a^10 - 2452665/72256*a^9 + 799931/36128*a^8 + 5001293/36128*a^7 - 5150393/72256*a^6 - 19579405/72256*a^5 + 3307859/36128*a^4 + 4006917/18064*a^3 - 1552051/72256*a^2 - 3973391/72256*a - 162125/72256
]
*], q_expansions := [*
q + a*q^2 + (a^4 + 2*a^3 - 3*a^2 - 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^5 - 4*a^4 - a^3 + 9*a^2 + 4*a - 3)*q^5 + (a^5 + 2*a^4 - 3*a^3 - 4*a^2 + a)*q^6 + (a^6 + 4*a^5 - 12*a^3 - 4*a^2 + 8*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^6 - 6*a^5 + 3*a^4 + 15*a^3 + a^2 - 6*a - 1)*q^9 + (-a^6 - 4*a^5 - a^4 + 9*a^3 + 4*a^2 - 3*a)*q^10 + (-a^6 - 2*a^5 + 6*a^4 + 9*a^3 - 9*a^2 - 7*a)*q^11 + (a^6 + 2*a^5 - 5*a^4 - 8*a^3 + 7*a^2 + 8*a - 2)*q^12 + (a^6 + 2*a^5 - 5*a^4 - 5*a^3 + 11*a^2 - 6)*q^13 + (a^6 + 3*a^5 - a^4 - 7*a^3 - 2*a^2 + 1)*q^14 + (3*a^6 + 10*a^5 - 3*a^4 - 26*a^3 - 2*a^2 + 13*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^6 + 8*a^5 + a^4 - 22*a^3 - 9*a^2 + 14*a)*q^17 + (-3*a^5 - 7*a^4 + 7*a^3 + 14*a^2 - 3*a - 2)*q^18 + (-3*a^6 - 8*a^5 + 11*a^4 + 28*a^3 - 15*a^2 - 20*a + 4)*q^19 + (-a^6 - 2*a^5 + 6*a^4 + 9*a^3 - 11*a^2 - 9*a + 5)*q^20 + (-a^6 - 5*a^5 - 6*a^4 + 7*a^3 + 19*a^2 + 6*a - 6)*q^21 + (a^6 + 3*a^5 - 2*a^4 - 6*a^3 + 3*a^2 - a - 1)*q^22 + (-a^6 - 5*a^5 - 2*a^4 + 16*a^3 + 9*a^2 - 12*a - 4)*q^23 + (-a^6 - 4*a^5 - a^4 + 10*a^3 + 6*a^2 - 3*a + 1)*q^24 + (-3*a^6 - 9*a^5 + 8*a^4 + 30*a^3 - 7*a^2 - 20*a + 2)*q^25 + (-a^6 - 2*a^5 + 6*a^4 + 8*a^3 - 10*a^2 - 5*a + 1)*q^26 + (3*a^6 + 10*a^5 - 3*a^4 - 27*a^3 - 4*a^2 + 17*a)*q^27 + (-2*a^6 - 6*a^5 + 4*a^4 + 19*a^3 - 2*a^2 - 14*a + 3)*q^28 + (a^5 + a^4 - 7*a^3 - 8*a^2 + 6*a + 9)*q^29 + (a^6 + 6*a^5 + 7*a^4 - 11*a^3 - 17*a^2 + 3)*q^30 + (-a^6 - 5*a^5 - 6*a^4 + 4*a^3 + 12*a^2 + 9*a - 1)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 - 4*a^5 - a^4 + 8*a^3 + 3*a^2 + 2)*q^33 + (2*a^6 + 7*a^5 - 15*a^3 - 6*a^2 + 2*a + 2)*q^34 + (4*a^5 + 15*a^4 + 2*a^3 - 34*a^2 - 15*a + 10)*q^35 + (a^6 + 5*a^5 + a^4 - 16*a^3 - 5*a^2 + 10*a + 2)*q^36 + (3*a^6 + 7*a^5 - 13*a^4 - 27*a^3 + 17*a^2 + 25*a - 6)*q^37 + O(q^38),
q + a*q^2 + (1755/144512*a^13 - 14949/144512*a^12 - 15147/72256*a^11 + 77379/36128*a^10 + 155093/144512*a^9 - 1184607/72256*a^8 - 21849/72256*a^7 + 8189141/144512*a^6 - 1591687/144512*a^5 - 6092391/72256*a^4 + 826663/36128*a^3 + 5567751/144512*a^2 - 838701/144512*a - 479015/144512)*q^3 + (a^2 - 2)*q^4 + (6245/72256*a^13 - 7803/72256*a^12 - 66405/36128*a^11 + 40205/18064*a^10 + 1060043/72256*a^9 - 610385/36128*a^8 - 1969527/36128*a^7 + 4165227/72256*a^6 + 6795559/72256*a^5 - 3048569/36128*a^4 - 1165231/18064*a^3 + 2740441/72256*a^2 + 1042445/72256*a - 214841/72256)*q^5 + (-11439/144512*a^13 + 6561/144512*a^12 + 117903/72256*a^11 - 32743/36128*a^10 - 1795329/144512*a^9 + 476571/72256*a^8 + 3082813/72256*a^7 - 3048337/144512*a^6 - 9104757/144512*a^5 + 1932371/72256*a^4 + 1029969/36128*a^3 - 856251/144512*a^2 - 310535/144512*a + 1755/144512)*q^6 + (3085/144512*a^13 - 803/144512*a^12 - 29405/72256*a^11 + 2701/36128*a^10 + 376483/144512*a^9 - 13089/72256*a^8 - 389111/72256*a^7 - 168493/144512*a^6 - 729569/144512*a^5 + 434759/72256*a^4 + 866533/36128*a^3 - 1185999/144512*a^2 - 1265867/144512*a + 477775/144512)*q^7 + (a^3 - 4*a)*q^8 + (-2903/18064*a^13 + 4973/18064*a^12 + 31447/9032*a^11 - 12931/2258*a^10 - 510665/18064*a^9 + 396635/9032*a^8 + 955811/9032*a^7 - 2725157/18064*a^6 - 3211105/18064*a^5 + 1967487/9032*a^4 + 472569/4516*a^3 - 1557671/18064*a^2 - 246359/18064*a + 134227/18064)*q^9 + (4687/72256*a^13 - 1665/72256*a^12 - 50735/36128*a^11 + 10527/18064*a^10 + 821345/72256*a^9 - 195947/36128*a^8 - 1517629/36128*a^7 + 1612209/72256*a^6 + 4862837/72256*a^5 - 1337507/36128*a^4 - 602921/18064*a^3 + 979995/72256*a^2 + 384679/72256*a + 6245/72256)*q^10 + (7307/36128*a^13 - 11013/36128*a^12 - 78211/18064*a^11 + 57571/9032*a^10 + 1255701/36128*a^9 - 887991/18064*a^8 - 2333329/18064*a^7 + 6124677/36128*a^6 + 7879545/36128*a^5 - 4385815/18064*a^4 - 1210133/9032*a^3 + 3144647/36128*a^2 + 698611/36128*a - 95719/36128)*q^11 + (-19827/144512*a^13 + 25485/144512*a^12 + 205027/72256*a^11 - 137451/36128*a^10 - 3097597/144512*a^9 + 2203351/72256*a^8 + 5114113/72256*a^7 - 15988669/144512*a^6 - 13027329/144512*a^5 + 12425919/72256*a^4 + 491905/36128*a^3 - 11331647/144512*a^2 + 581013/144512*a + 946591/144512)*q^12 + (215/36128*a^13 - 905/36128*a^12 - 2203/18064*a^11 + 4481/9032*a^10 + 29473/36128*a^9 - 63719/18064*a^8 - 22053/18064*a^7 + 383777/36128*a^6 - 252067/36128*a^5 - 201971/18064*a^4 + 208273/9032*a^3 - 46029/36128*a^2 - 424425/36128*a + 76437/36128)*q^13 + (5367/144512*a^13 + 5975/144512*a^12 - 59383/72256*a^11 - 31593/36128*a^10 + 982617/144512*a^9 + 487029/72256*a^8 - 1862749/72256*a^7 - 3290119/144512*a^6 + 6283693/144512*a^5 + 2223581/72256*a^4 - 932781/36128*a^3 - 1296717/144512*a^2 + 773935/144512*a + 3085/144512)*q^14 + (-6555/72256*a^13 + 14149/72256*a^12 + 67691/36128*a^11 - 73867/18064*a^10 - 1021461/72256*a^9 + 1145247/36128*a^8 + 1679113/36128*a^7 - 8065461/72256*a^6 - 4117401/72256*a^5 + 6157767/36128*a^4 - 21991/18064*a^3 - 5841575/72256*a^2 + 998253/72256*a + 743591/72256)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (255/4516*a^13 - 261/2258*a^12 - 5357/4516*a^11 + 5667/2258*a^10 + 10321/1129*a^9 - 91783/4516*a^8 - 140295/4516*a^7 + 338339/4516*a^6 + 47119/1129*a^5 - 135015/1129*a^4 - 35287/4516*a^3 + 66268/1129*a^2 - 7256/1129*a - 6788/1129)*q^17 + (-833/18064*a^13 + 1931/18064*a^12 + 9239/9032*a^11 - 9369/4516*a^10 - 156011/18064*a^9 + 131359/9032*a^8 + 311001/9032*a^7 - 801615/18064*a^6 - 1159791/18064*a^5 + 483561/9032*a^4 + 104663/2258*a^3 - 217329/18064*a^2 - 144461/18064*a - 2903/18064)*q^18 + (-24769/144512*a^13 + 44607/144512*a^12 + 263521/72256*a^11 - 233793/36128*a^10 - 4182639/144512*a^9 + 3614269/72256*a^8 + 7602267/72256*a^7 - 24927727/144512*a^6 - 24546683/144512*a^5 + 17660933/72256*a^4 + 3435315/36128*a^3 - 11568517/144512*a^2 - 2663753/144512*a + 320581/144512)*q^19 + (-4781/72256*a^13 + 12563/72256*a^12 + 55437/36128*a^11 - 66069/18064*a^10 - 979331/72256*a^9 + 1034249/36128*a^8 + 2043103/36128*a^7 - 7357827/72256*a^6 - 8040447/72256*a^5 + 5636529/36128*a^4 + 1608767/18064*a^3 - 5143073/72256*a^2 - 1628693/72256*a + 434369/72256)*q^20 + (3189/36128*a^13 - 11323/36128*a^12 - 32109/18064*a^11 + 58819/9032*a^10 + 459803/36128*a^9 - 905501/18064*a^8 - 663975/18064*a^7 + 6317115/36128*a^6 + 919151/36128*a^5 - 4772341/18064*a^4 + 368867/9032*a^3 + 4469209/36128*a^2 - 770035/36128*a - 407313/36128)*q^21 + (3601/36128*a^13 - 2975/36128*a^12 - 38305/18064*a^11 + 16165/9032*a^10 + 613407/36128*a^9 - 258141/18064*a^8 - 1150147/18064*a^7 + 1814735/36128*a^6 + 4052155/36128*a^5 - 1258453/18064*a^4 - 720907/9032*a^3 + 625541/36128*a^2 + 605753/36128*a + 7307/36128)*q^22 + (-4017/36128*a^13 + 8927/36128*a^12 + 40089/18064*a^11 - 46449/9032*a^10 - 567343/36128*a^9 + 711749/18064*a^8 + 804483/18064*a^7 - 4870079/36128*a^6 - 1036987/36128*a^5 + 3480933/18064*a^4 - 481241/9032*a^3 - 2725669/36128*a^2 + 1005655/36128*a + 299589/36128)*q^23 + (8709/144512*a^13 - 19435/144512*a^12 - 94341/72256*a^11 + 99037/36128*a^10 + 1513931/144512*a^9 - 1469897/72256*a^8 - 2729695/72256*a^7 + 9525755/144512*a^6 + 8264967/144512*a^5 - 6033425/72256*a^4 - 803531/36128*a^3 + 2491785/144512*a^2 - 335731/144512*a - 23337/144512)*q^24 + (2075/18064*a^13 - 2853/18064*a^12 - 23467/9032*a^11 + 14523/4516*a^10 + 403125/18064*a^9 - 215559/9032*a^8 - 817561/9032*a^7 + 1394853/18064*a^6 + 3151977/18064*a^5 - 865415/9032*a^4 - 636877/4516*a^3 + 243879/18064*a^2 + 653587/18064*a + 92233/18064)*q^25 + (-475/36128*a^13 + 109/36128*a^12 + 4447/18064*a^11 - 1393/9032*a^10 - 57133/36128*a^9 + 39007/18064*a^8 + 67941/18064*a^7 - 430517/36128*a^6 - 26617/36128*a^5 + 450731/18064*a^4 - 55851/9032*a^3 - 426575/36128*a^2 + 97077/36128*a + 215/36128)*q^26 + (-5133/72256*a^13 + 6483/72256*a^12 + 55557/36128*a^11 - 31249/18064*a^10 - 912563/72256*a^9 + 418993/36128*a^8 + 1783967/36128*a^7 - 2136691/72256*a^6 - 6789759/72256*a^5 + 345681/36128*a^4 + 1391939/18064*a^3 + 3390271/72256*a^2 - 1207301/72256*a - 1084559/72256)*q^27 + (10539/144512*a^13 - 4453/144512*a^12 - 117083/72256*a^11 + 21547/36128*a^10 + 1976101/144512*a^9 - 312343/72256*a^8 - 3960913/72256*a^7 + 2166069/144512*a^6 + 15325385/144512*a^5 - 1881727/72256*a^4 - 3164189/36128*a^3 + 3092263/144512*a^2 + 3050051/144512*a - 950183/144512)*q^28 + (1823/36128*a^13 - 5153/36128*a^12 - 21431/18064*a^11 + 25749/9032*a^10 + 391601/36128*a^9 - 373879/18064*a^8 - 873757/18064*a^7 + 2364609/36128*a^6 + 3881085/36128*a^5 - 1449695/18064*a^4 - 944983/9032*a^3 + 540475/36128*a^2 + 999399/36128*a - 27731/36128)*q^29 + (1039/72256*a^13 - 2273/72256*a^12 - 10079/36128*a^11 + 11751/18064*a^10 + 147009/72256*a^9 - 182507/36128*a^8 - 253773/36128*a^7 + 1323249/72256*a^6 + 811509/72256*a^5 - 1086227/36128*a^4 - 108425/18064*a^3 + 1063803/72256*a^2 + 114311/72256*a - 6555/72256)*q^30 + (-8595/72256*a^13 + 9293/72256*a^12 + 93635/36128*a^11 - 46859/18064*a^10 - 1541405/72256*a^9 + 694983/36128*a^8 + 2976401/36128*a^7 - 4612349/72256*a^6 - 10800545/72256*a^5 + 3178799/36128*a^4 + 2019817/18064*a^3 - 1991999/72256*a^2 - 2301067/72256*a - 59809/72256)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (6729/36128*a^13 - 12991/36128*a^12 - 74473/18064*a^11 + 66277/9032*a^10 + 1250487/36128*a^9 - 984857/18064*a^8 - 2471255/18064*a^7 + 6372671/36128*a^6 + 9135747/36128*a^5 - 3952129/18064*a^4 - 1639893/9032*a^3 + 1086805/36128*a^2 + 1106561/36128*a + 345019/36128)*q^33 + (-3/1129*a^13 - 1/2258*a^12 + 156/1129*a^11 - 281/4516*a^10 - 4199/2258*a^9 + 4545/4516*a^8 + 11081/1129*a^7 - 11587/2258*a^6 - 92535/4516*a^5 + 45803/4516*a^4 + 54697/4516*a^3 - 15787/2258*a^2 - 668/1129*a + 255/4516)*q^34 + (8695/72256*a^13 - 5513/72256*a^12 - 91719/36128*a^11 + 30039/18064*a^10 + 1445049/72256*a^9 - 486427/36128*a^8 - 2619917/36128*a^7 + 3594425/72256*a^6 + 8571917/72256*a^5 - 2983715/36128*a^4 - 1295957/18064*a^3 + 3762707/72256*a^2 + 1141647/72256*a - 754067/72256)*q^35 + (6071/18064*a^13 - 8961/18064*a^12 - 64139/9032*a^11 + 23333/2258*a^10 + 1011657/18064*a^9 - 718841/9032*a^8 - 1832205/9032*a^7 + 4981913/18064*a^6 + 5927417/18064*a^5 - 3648769/9032*a^4 - 206916/1129*a^3 + 2979211/18064*a^2 + 409847/18064*a - 269287/18064)*q^36 + (-12759/72256*a^13 + 10857/72256*a^12 + 143191/36128*a^11 - 54583/18064*a^10 - 2452665/72256*a^9 + 799931/36128*a^8 + 5001293/36128*a^7 - 5150393/72256*a^6 - 19579405/72256*a^5 + 3307859/36128*a^4 + 4006917/18064*a^3 - 1552051/72256*a^2 - 3973391/72256*a - 162125/72256)*q^37 + O(q^38)
*]> ;  // time = 3.641 seconds




J[258] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 258, 258, 258, 258, 258, 258, 258, 129, 129, 129, 129, 86, 86, 43, 43 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 1, 2 ], dimensions := [ 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 6, 4, 4, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 5, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 25, 1, 1, 9, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 0, 1, 11, 1, 1, 1, 7, 5, 1, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 49, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 11, 1, 0, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 25, 0, 1, 1, 7, 1, 1, 1, 7, 1, 1, 1, 49, 1, 49, 1, 1, 0 ], ap_traces := [
[ -1, -1, 1, -5, 1, -3, 0, -7, -4, -3, -2, 2 ],
[ -1, -1, -2, 2, 0, 2, 6, 4, 6, -2, 4, 4 ],
[ -1, 1, -3, -3, -5, -3, 0, 7, -4, 1, -6, -6 ],
[ 1, -1, -2, 4, 4, 6, -6, -4, -4, 6, -8, 2 ],
[ 1, -1, 3, -1, -1, 1, 4, 1, -4, -9, 2, 2 ],
[ 1, 1, -1, 1, 5, -7, 4, -1, -4, -5, -10, 10 ],
[ 1, 1, 2, -2, -4, 2, -2, -4, 2, 10, -4, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 7, 7, 1 ],
[ 1, 5, 1 ],
[ 3, 1, 1 ],
[ 1, 19, 1 ],
[ 7, 7, 1 ],
[ 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 5, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 7, 7, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 7, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 0, 3, 1, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1, 1/49, 1 ], eigenvalues := [*
[ -1, -1, 1, -5, 1, -3, 0, -7, -4, -3, -2, 2 ],
[ -1, -1, -2, 2, 0, 2, 6, 4, 6, -2, 4, 4 ],
[ -1, 1, -3, -3, -5, -3, 0, 7, -4, 1, -6, -6 ],
[ 1, -1, -2, 4, 4, 6, -6, -4, -4, 6, -8, 2 ],
[ 1, -1, 3, -1, -1, 1, 4, 1, -4, -9, 2, 2 ],
[ 1, 1, -1, 1, 5, -7, 4, -1, -4, -5, -10, 10 ],
[ 1, 1, 2, -2, -4, 2, -2, -4, 2, 10, -4, -8 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 + q^5 + q^6 - 5*q^7 - q^8 + q^9 - q^10 + q^11 - q^12 - 3*q^13 + 5*q^14 - q^15 + q^16 - q^18 - 7*q^19 + q^20 + 5*q^21 - q^22 - 4*q^23 + q^24 - 4*q^25 + 3*q^26 - q^27 - 5*q^28 - 3*q^29 + q^30 - 2*q^31 - q^32 - q^33 - 5*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 - q^3 + q^4 - 2*q^5 + q^6 + 2*q^7 - q^8 + q^9 + 2*q^10 - q^12 + 2*q^13 - 2*q^14 + 2*q^15 + q^16 + 6*q^17 - q^18 + 4*q^19 - 2*q^20 - 2*q^21 + 6*q^23 + q^24 - q^25 - 2*q^26 - q^27 + 2*q^28 - 2*q^29 - 2*q^30 + 4*q^31 - q^32 - 6*q^34 - 4*q^35 + q^36 + 4*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - 3*q^5 - q^6 - 3*q^7 - q^8 + q^9 + 3*q^10 - 5*q^11 + q^12 - 3*q^13 + 3*q^14 - 3*q^15 + q^16 - q^18 + 7*q^19 - 3*q^20 - 3*q^21 + 5*q^22 - 4*q^23 - q^24 + 4*q^25 + 3*q^26 + q^27 - 3*q^28 + q^29 + 3*q^30 - 6*q^31 - q^32 - 5*q^33 + 9*q^35 + q^36 - 6*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 2*q^5 - q^6 + 4*q^7 + q^8 + q^9 - 2*q^10 + 4*q^11 - q^12 + 6*q^13 + 4*q^14 + 2*q^15 + q^16 - 6*q^17 + q^18 - 4*q^19 - 2*q^20 - 4*q^21 + 4*q^22 - 4*q^23 - q^24 - q^25 + 6*q^26 - q^27 + 4*q^28 + 6*q^29 + 2*q^30 - 8*q^31 + q^32 - 4*q^33 - 6*q^34 - 8*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + 3*q^5 - q^6 - q^7 + q^8 + q^9 + 3*q^10 - q^11 - q^12 + q^13 - q^14 - 3*q^15 + q^16 + 4*q^17 + q^18 + q^19 + 3*q^20 + q^21 - q^22 - 4*q^23 - q^24 + 4*q^25 + q^26 - q^27 - q^28 - 9*q^29 - 3*q^30 + 2*q^31 + q^32 + q^33 + 4*q^34 - 3*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 + q^3 + q^4 - q^5 + q^6 + q^7 + q^8 + q^9 - q^10 + 5*q^11 + q^12 - 7*q^13 + q^14 - q^15 + q^16 + 4*q^17 + q^18 - q^19 - q^20 + q^21 + 5*q^22 - 4*q^23 + q^24 - 4*q^25 - 7*q^26 + q^27 + q^28 - 5*q^29 - q^30 - 10*q^31 + q^32 + 5*q^33 + 4*q^34 - q^35 + q^36 + 10*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + 2*q^5 + q^6 - 2*q^7 + q^8 + q^9 + 2*q^10 - 4*q^11 + q^12 + 2*q^13 - 2*q^14 + 2*q^15 + q^16 - 2*q^17 + q^18 - 4*q^19 + 2*q^20 - 2*q^21 - 4*q^22 + 2*q^23 + q^24 - q^25 + 2*q^26 + q^27 - 2*q^28 + 10*q^29 + 2*q^30 - 4*q^31 + q^32 - 4*q^33 - 2*q^34 - 4*q^35 + q^36 - 8*q^37 + O(q^38)
*]> ;  // time = 140.949 seconds




J[259] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 259, 259, 259, 259, 259, 259, 259, 37, 37 ], new_dimensions := [ 1, 2, 2, 3, 3, 4, 4, 1, 1 ], dimensions := [ 1, 2, 2, 3, 3, 4, 4, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 3, 3, 1, 1, 0, 1, 1, 1, 17, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 17, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 3, 1, 3, 1, 1, 7, 1, 1, 3, 0, 1, 1, 7, 1, 1, 3, 1, 1, 1, 0 ], ap_traces := [
[ 1, 0, 4, 1, 4, 4, 0, -6, -4, -6, 2, -1 ],
[ 0, 0, 6, -2, -6, 2, 0, 4, 0, 0, 2, 2 ],
[ 1, 0, 1, 2, -1, 1, 2, 6, 8, 6, -5, -2 ],
[ 1, -2, -6, -3, -1, 1, -7, -7, -1, -10, 2, -3 ],
[ -3, 0, -6, 3, -9, -3, -3, -3, -9, -18, 6, 3 ],
[ 0, 2, 6, -4, 3, 5, 13, -7, -5, 20, 10, 4 ],
[ 1, 0, 1, 4, 10, -8, -3, -3, -1, 18, -13, -4 ]
], hecke_fields := [
x - 1,
x^2 - 32,
x^2 - x - 4,
x^3 - x^2 - 2*x + 1,
x^3 + 3*x^2 - 3,
x^4 - 9*x^2 + x + 17,
x^4 - x^3 - 6*x^2 + 5*x + 4
], atkin_lehners := [
[ -1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 57, 1 ]
], tamagawa_numbers := [
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 57, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3, 1, 19 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 19 ], l_ratios := [ 3, 1, 1, 0, 0, 1, 3/19 ], analytic_sha_upper_bounds := [ 1, 1, 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 1, 0, 4, 1, 4, 4, 0, -6, -4, -6, 2, -1 ],
[
0,
-1/2*a,
-1/4*a + 3,
-1,
1/2*a - 3,
3/4*a + 1,
1/2*a,
2,
1/2*a,
-1/2*a,
3/4*a + 1,
1
],
[
a,
0,
-a + 1,
1,
a - 1,
-a + 1,
-2*a + 2,
-2*a + 4,
4,
-2*a + 4,
a - 3,
-1
],
[
a,
-a^2 + 1,
a^2 - 2*a - 3,
-1,
a^2 - 2,
-3*a^2 + a + 5,
3*a^2 + 2*a - 8,
-2*a^2 + 1,
-2*a^2 + 3*a + 2,
-4*a^2 + a + 3,
6*a^2 - a - 9,
-1
],
[
a,
-a^2 - 2*a + 1,
a^2 + 2*a - 3,
1,
a^2 - 6,
3*a^2 + 3*a - 7,
-a^2 - 2*a,
-2*a^2 + 5,
2*a^2 + 3*a - 6,
3*a - 3,
-4*a^2 - 3*a + 11,
1
],
[
a,
-a^2 + 5,
a^2 - 3,
-1,
-a^3 - 2*a^2 + 4*a + 9,
a^3 - 5*a + 2,
a^3 + 2*a^2 - 6*a - 5,
-a^3 - a^2 + 6*a + 2,
a^3 + a^2 - 5*a - 5,
-a + 5,
-2*a^3 - 4*a^2 + 9*a + 19,
1
],
[
a,
-a^3 + 4*a,
a^2 - 3,
1,
a^3 - 6*a + 3,
-a^2 + a + 1,
-a^2 + 2*a + 2,
a^3 + a^2 - 4*a - 4,
-2*a^3 + 7*a,
a^3 - a^2 - 5*a + 8,
-a - 3,
-1
]
*], q_expansions := [*
q + q^2 - q^4 + 4*q^5 + q^7 - 3*q^8 - 3*q^9 + 4*q^10 + 4*q^11 + 4*q^13 + q^14 - q^16 - 3*q^18 - 6*q^19 - 4*q^20 + 4*q^22 - 4*q^23 + 11*q^25 + 4*q^26 - q^28 - 6*q^29 + 2*q^31 + 5*q^32 + 4*q^35 + 3*q^36 - q^37 + O(q^38),
q - 1/2*a*q^3 - 2*q^4 + (-1/4*a + 3)*q^5 - q^7 + 5*q^9 + (1/2*a - 3)*q^11 + a*q^12 + (3/4*a + 1)*q^13 + (-3/2*a + 4)*q^15 + 4*q^16 + 1/2*a*q^17 + 2*q^19 + (1/2*a - 6)*q^20 + 1/2*a*q^21 + 1/2*a*q^23 + (-3/2*a + 6)*q^25 - a*q^27 + 2*q^28 - 1/2*a*q^29 + (3/4*a + 1)*q^31 + (3/2*a - 8)*q^33 + (1/4*a - 3)*q^35 - 10*q^36 + q^37 + O(q^38),
q + a*q^2 + (a + 2)*q^4 + (-a + 1)*q^5 + q^7 + (a + 4)*q^8 - 3*q^9 - 4*q^10 + (a - 1)*q^11 + (-a + 1)*q^13 + a*q^14 + 3*a*q^16 + (-2*a + 2)*q^17 - 3*a*q^18 + (-2*a + 4)*q^19 + (-2*a - 2)*q^20 + 4*q^22 + 4*q^23 - a*q^25 - 4*q^26 + (a + 2)*q^28 + (-2*a + 4)*q^29 + (a - 3)*q^31 + (a + 4)*q^32 - 8*q^34 + (-a + 1)*q^35 + (-3*a - 6)*q^36 - q^37 + O(q^38),
q + a*q^2 + (-a^2 + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 - 2*a - 3)*q^5 + (-a^2 - a + 1)*q^6 - q^7 + (a^2 - 2*a - 1)*q^8 + (a^2 + a - 3)*q^9 + (-a^2 - a - 1)*q^10 + (a^2 - 2)*q^11 + (-a - 1)*q^12 + (-3*a^2 + a + 5)*q^13 - a*q^14 + (3*a^2 + a - 4)*q^15 + (-3*a^2 + a + 3)*q^16 + (3*a^2 + 2*a - 8)*q^17 + (2*a^2 - a - 1)*q^18 + (-2*a^2 + 1)*q^19 + (-4*a^2 + a + 7)*q^20 + (a^2 - 1)*q^21 + (a^2 - 1)*q^22 + (-2*a^2 + 3*a + 2)*q^23 + (a^2 + a - 2)*q^24 + (-3*a^2 + 5*a + 7)*q^25 + (-2*a^2 - a + 3)*q^26 + (3*a^2 - 2*a - 4)*q^27 + (-a^2 + 2)*q^28 + (-4*a^2 + a + 3)*q^29 + (4*a^2 + 2*a - 3)*q^30 + (6*a^2 - a - 9)*q^31 + (-4*a^2 + a + 5)*q^32 + (-a - 1)*q^33 + (5*a^2 - 2*a - 3)*q^34 + (-a^2 + 2*a + 3)*q^35 + (-a^2 + a + 4)*q^36 - q^37 + O(q^38),
q + a*q^2 + (-a^2 - 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^2 + 2*a - 3)*q^5 + (a^2 + a - 3)*q^6 + q^7 + (-3*a^2 - 4*a + 3)*q^8 + (-a^2 - a + 1)*q^9 + (-a^2 - 3*a + 3)*q^10 + (a^2 - 6)*q^11 + (a + 1)*q^12 + (3*a^2 + 3*a - 7)*q^13 + a*q^14 + (3*a^2 + 5*a - 6)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (-a^2 - 2*a)*q^17 + (2*a^2 + a - 3)*q^18 + (-2*a^2 + 5)*q^19 + (-2*a^2 - a + 3)*q^20 + (-a^2 - 2*a + 1)*q^21 + (-3*a^2 - 6*a + 3)*q^22 + (2*a^2 + 3*a - 6)*q^23 + (-a^2 - a + 6)*q^24 + (-5*a^2 - 9*a + 7)*q^25 + (-6*a^2 - 7*a + 9)*q^26 + (3*a^2 + 6*a - 2)*q^27 + (a^2 - 2)*q^28 + (3*a - 3)*q^29 + (-4*a^2 - 6*a + 9)*q^30 + (-4*a^2 - 3*a + 11)*q^31 + (3*a + 3)*q^32 + (4*a^2 + 9*a - 3)*q^33 + (a^2 - 3)*q^34 + (a^2 + 2*a - 3)*q^35 + (-3*a^2 - a + 4)*q^36 + q^37 + O(q^38),
q + a*q^2 + (-a^2 + 5)*q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 + (-a^3 + 5*a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^2 - a + 5)*q^9 + (a^3 - 3*a)*q^10 + (-a^3 - 2*a^2 + 4*a + 9)*q^11 + (-2*a^2 + a + 7)*q^12 + (a^3 - 5*a + 2)*q^13 - a*q^14 + (-a^2 + a + 2)*q^15 + (3*a^2 - a - 13)*q^16 + (a^3 + 2*a^2 - 6*a - 5)*q^17 + (-a^3 - a^2 + 5*a)*q^18 + (-a^3 - a^2 + 6*a + 2)*q^19 + (4*a^2 - a - 11)*q^20 + (a^2 - 5)*q^21 + (-2*a^3 - 5*a^2 + 10*a + 17)*q^22 + (a^3 + a^2 - 5*a - 5)*q^23 + (a^2 - 3*a)*q^24 + (3*a^2 - a - 13)*q^25 + (4*a^2 + a - 17)*q^26 + (a^3 + 2*a^2 - 6*a - 7)*q^27 + (-a^2 + 2)*q^28 + (-a + 5)*q^29 + (-a^3 + a^2 + 2*a)*q^30 + (-2*a^3 - 4*a^2 + 9*a + 19)*q^31 + (a^3 - a^2 - 5*a)*q^32 + (-2*a^2 + a + 11)*q^33 + (2*a^3 + 3*a^2 - 6*a - 17)*q^34 + (-a^2 + 3)*q^35 + (-a^3 - 2*a^2 + 3*a + 7)*q^36 + q^37 + O(q^38),
q + a*q^2 + (-a^3 + 4*a)*q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 + (-a^3 - 2*a^2 + 5*a + 4)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (a^2 + a + 1)*q^9 + (a^3 - 3*a)*q^10 + (a^3 - 6*a + 3)*q^11 + (-a^3 - a^2 + a + 4)*q^12 + (-a^2 + a + 1)*q^13 + a*q^14 + (-a^2 - 3*a + 4)*q^15 + (a^3 - 5*a)*q^16 + (-a^2 + 2*a + 2)*q^17 + (a^3 + a^2 + a)*q^18 + (a^3 + a^2 - 4*a - 4)*q^19 + (a^3 + a^2 - 5*a + 2)*q^20 + (-a^3 + 4*a)*q^21 + (a^3 - 2*a - 4)*q^22 + (-2*a^3 + 7*a)*q^23 + (-a^2 - a - 4)*q^24 + (a^3 - 5*a)*q^25 + (-a^3 + a^2 + a)*q^26 + (-2*a^3 - 3*a^2 + 6*a + 8)*q^27 + (a^2 - 2)*q^28 + (a^3 - a^2 - 5*a + 8)*q^29 + (-a^3 - 3*a^2 + 4*a)*q^30 + (-a - 3)*q^31 + (-a^3 + a^2 + 3*a - 4)*q^32 + (-a^3 + 3*a^2 + a - 12)*q^33 + (-a^3 + 2*a^2 + 2*a)*q^34 + (a^2 - 3)*q^35 + (2*a^3 + 5*a^2 - 7*a - 6)*q^36 - q^37 + O(q^38)
*]> ;  // time = 32.27 seconds




J[262] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 262, 262, 262, 262, 262, 262, 131, 131 ], new_dimensions := [ 1, 1, 2, 2, 2, 2, 1, 10 ], dimensions := [ 1, 1, 2, 2, 2, 2, 2, 20 ], intersection_graph := [ 0, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 11, 3, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 313, 1, 1, 1, 1, 0, 11, 3, 1, 1, 1, 1, 1, 11, 0, 1, 1, 1, 1, 3, 1, 3, 1, 0, 1, 1, 11, 1, 313, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, 0, -5, 2, -2, -6, 7, -6, -3, 2, -1 ],
[ 1, -2, -2, -3, -6, 4, -4, 3, -4, 3, -4, -3 ],
[ -2, -1, -5, 3, -7, -5, -2, -4, -2, -12, 6, -6 ],
[ -2, 0, 4, 2, 4, 0, 8, -2, 12, 6, -4, 6 ],
[ 2, -2, 2, 4, 0, -6, 2, 8, 14, -6, -10, -10 ],
[ 2, 3, -1, -1, 5, 3, -2, -8, -6, 0, 2, -6 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + x - 3,
x^2 - 2,
x^2 + 2*x - 2,
x^2 - 3*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ],
[ 3, 1 ],
[ 313, 1 ],
[ 33, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 11, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 33, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 11, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 11, 1 ], l_ratios := [ 0, 0, 0, 1, 3/11, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1, 1 ], eigenvalues := [*
[ -1, 0, 0, -5, 2, -2, -6, 7, -6, -3, 2, -1 ],
[ 1, -2, -2, -3, -6, 4, -4, 3, -4, 3, -4, -3 ],
[
-1,
a,
-a - 3,
-a + 1,
-a - 4,
a - 2,
2*a,
-2,
2*a,
-6,
-2*a + 2,
-2*a - 4
],
[
-1,
a,
-a + 2,
a + 1,
2*a + 2,
-3*a,
-a + 4,
-a - 1,
a + 6,
2*a + 3,
-3*a - 2,
6*a + 3
],
[
1,
a,
a + 2,
-a + 1,
-2*a - 2,
-a - 4,
-a,
a + 5,
-a + 6,
-3,
3*a - 2,
2*a - 3
],
[
1,
a,
-a + 1,
-a + 1,
-a + 4,
-3*a + 6,
2*a - 4,
4*a - 10,
-2*a,
-4*a + 6,
-6*a + 10,
6*a - 12
]
*], q_expansions := [*
q - q^2 + q^4 - 5*q^7 - q^8 - 3*q^9 + 2*q^11 - 2*q^13 + 5*q^14 + q^16 - 6*q^17 + 3*q^18 + 7*q^19 - 2*q^22 - 6*q^23 - 5*q^25 + 2*q^26 - 5*q^28 - 3*q^29 + 2*q^31 - q^32 + 6*q^34 - 3*q^36 - q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^5 - 2*q^6 - 3*q^7 + q^8 + q^9 - 2*q^10 - 6*q^11 - 2*q^12 + 4*q^13 - 3*q^14 + 4*q^15 + q^16 - 4*q^17 + q^18 + 3*q^19 - 2*q^20 + 6*q^21 - 6*q^22 - 4*q^23 - 2*q^24 - q^25 + 4*q^26 + 4*q^27 - 3*q^28 + 3*q^29 + 4*q^30 - 4*q^31 + q^32 + 12*q^33 - 4*q^34 + 6*q^35 + q^36 - 3*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 3)*q^5 - a*q^6 + (-a + 1)*q^7 - q^8 - a*q^9 + (a + 3)*q^10 + (-a - 4)*q^11 + a*q^12 + (a - 2)*q^13 + (a - 1)*q^14 + (-2*a - 3)*q^15 + q^16 + 2*a*q^17 + a*q^18 - 2*q^19 + (-a - 3)*q^20 + (2*a - 3)*q^21 + (a + 4)*q^22 + 2*a*q^23 - a*q^24 + (5*a + 7)*q^25 + (-a + 2)*q^26 + (-2*a - 3)*q^27 + (-a + 1)*q^28 - 6*q^29 + (2*a + 3)*q^30 + (-2*a + 2)*q^31 - q^32 + (-3*a - 3)*q^33 - 2*a*q^34 + a*q^35 - a*q^36 + (-2*a - 4)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a + 2)*q^5 - a*q^6 + (a + 1)*q^7 - q^8 - q^9 + (a - 2)*q^10 + (2*a + 2)*q^11 + a*q^12 - 3*a*q^13 + (-a - 1)*q^14 + (2*a - 2)*q^15 + q^16 + (-a + 4)*q^17 + q^18 + (-a - 1)*q^19 + (-a + 2)*q^20 + (a + 2)*q^21 + (-2*a - 2)*q^22 + (a + 6)*q^23 - a*q^24 + (-4*a + 1)*q^25 + 3*a*q^26 - 4*a*q^27 + (a + 1)*q^28 + (2*a + 3)*q^29 + (-2*a + 2)*q^30 + (-3*a - 2)*q^31 - q^32 + (2*a + 4)*q^33 + (a - 4)*q^34 + a*q^35 - q^36 + (6*a + 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a + 2)*q^5 + a*q^6 + (-a + 1)*q^7 + q^8 + (-2*a - 1)*q^9 + (a + 2)*q^10 + (-2*a - 2)*q^11 + a*q^12 + (-a - 4)*q^13 + (-a + 1)*q^14 + 2*q^15 + q^16 - a*q^17 + (-2*a - 1)*q^18 + (a + 5)*q^19 + (a + 2)*q^20 + (3*a - 2)*q^21 + (-2*a - 2)*q^22 + (-a + 6)*q^23 + a*q^24 + (2*a + 1)*q^25 + (-a - 4)*q^26 - 4*q^27 + (-a + 1)*q^28 - 3*q^29 + 2*q^30 + (3*a - 2)*q^31 + q^32 + (2*a - 4)*q^33 - a*q^34 + a*q^35 + (-2*a - 1)*q^36 + (2*a - 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 1)*q^5 + a*q^6 + (-a + 1)*q^7 + q^8 + (3*a - 4)*q^9 + (-a + 1)*q^10 + (-a + 4)*q^11 + a*q^12 + (-3*a + 6)*q^13 + (-a + 1)*q^14 + (-2*a + 1)*q^15 + q^16 + (2*a - 4)*q^17 + (3*a - 4)*q^18 + (4*a - 10)*q^19 + (-a + 1)*q^20 + (-2*a + 1)*q^21 + (-a + 4)*q^22 - 2*a*q^23 + a*q^24 + (a - 5)*q^25 + (-3*a + 6)*q^26 + (2*a - 3)*q^27 + (-a + 1)*q^28 + (-4*a + 6)*q^29 + (-2*a + 1)*q^30 + (-6*a + 10)*q^31 + q^32 + (a + 1)*q^33 + (2*a - 4)*q^34 + a*q^35 + (3*a - 4)*q^36 + (6*a - 12)*q^37 + O(q^38)
*]> ;  // time = 48.29 seconds




J[263] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 263, 263 ], new_dimensions := [ 5, 17 ], dimensions := [ 5, 17 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -5, -3, -5, 2, -15, -10, -5, 0, -2, -5, -9 ],
[ 1, 7, 3, 7, -2, 27, 16, 5, -4, -12, 11, 17 ]
], hecke_fields := [
x^5 + 2*x^4 - 3*x^3 - 6*x^2 + 1,
x^17 - x^16 - 26*x^15 + 24*x^14 + 274*x^13 - 225*x^12 - 1505*x^11 + 1041*x^10 + 4613*x^9 - 2467*x^8 - 7815*x^7 + 2761*x^6 + 6709*x^5 - 974*x^4 - 2284*x^3 - 239*x^2 + 135*x + 19
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 131 ]
], tamagawa_numbers := [
[ 1 ],
[ 131 ]
], torsion_upper_bounds := [ 1, 131 ], torsion_lower_bounds := [ 1, 131 ], l_ratios := [ 0, 1/131 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^4 - a^3 + 3*a^2 + 2*a - 1,
a^4 + a^3 - 4*a^2 - 3*a + 1,
a^4 + 2*a^3 - 3*a^2 - 6*a - 1,
-a^3 + a^2 + 3*a - 2,
-a^3 - a^2 + 4*a - 1,
-4*a^4 - 5*a^3 + 14*a^2 + 12*a - 6,
-a^4 - 3*a^3 + 3*a^2 + 10*a - 1,
3*a^4 + 4*a^3 - 10*a^2 - 10*a + 2,
-a^4 + 2*a^3 + 6*a^2 - 4*a - 4,
-2*a^4 - 4*a^3 + 5*a^2 + 12*a + 1,
-a^4 + 2*a^3 + 5*a^2 - 8*a - 5
],
[
a,
85010/668441*a^16 - 176339/668441*a^15 - 2241538/668441*a^14 + 4190472/668441*a^13 + 23933223/668441*a^12 - 39391493/668441*a^11 - 132842471/668441*a^10 + 186205893/668441*a^9 + 408643734/668441*a^8 - 465256935/668441*a^7 - 683138027/668441*a^6 + 586757546/668441*a^5 + 555506577/668441*a^4 - 303194375/668441*a^3 - 158959094/668441*a^2 + 17326687/668441*a + 6750715/668441,
143848/668441*a^16 - 199927/668441*a^15 - 3606981/668441*a^14 + 4857661/668441*a^13 + 36214213/668441*a^12 - 46276983/668441*a^11 - 186415557/668441*a^10 + 219401931/668441*a^9 + 523834133/668441*a^8 - 543663031/668441*a^7 - 789092227/668441*a^6 + 674003695/668441*a^5 + 572350237/668441*a^4 - 346151879/668441*a^3 - 145298876/668441*a^2 + 28757148/668441*a + 6281260/668441,
-43514/668441*a^16 + 387440/668441*a^15 + 1361549/668441*a^14 - 9030537/668441*a^13 - 16703058/668441*a^12 + 83027396/668441*a^11 + 103963774/668441*a^10 - 382002286/668441*a^9 - 350947554/668441*a^8 + 922397046/668441*a^7 + 629731852/668441*a^6 - 1116987852/668441*a^5 - 539197064/668441*a^4 + 560122572/668441*a^3 + 159965080/668441*a^2 - 45325035/668441*a - 6004853/668441,
-47976/668441*a^16 - 59269/668441*a^15 + 1131843/668441*a^14 + 1309592/668441*a^13 - 10511458/668441*a^12 - 11592732/668441*a^11 + 48829796/668441*a^10 + 52587277/668441*a^9 - 120312720/668441*a^8 - 129264310/668441*a^7 + 158327476/668441*a^6 + 165877480/668441*a^5 - 115340775/668441*a^4 - 92636576/668441*a^3 + 50139863/668441*a^2 + 9500135/668441*a - 3596410/668441,
81195/668441*a^16 - 58067/668441*a^15 - 2131430/668441*a^14 + 1449193/668441*a^13 + 22632202/668441*a^12 - 14341944/668441*a^11 - 124620842/668441*a^10 + 71906730/668441*a^9 + 378754518/668441*a^8 - 193643585/668441*a^7 - 622117679/668441*a^6 + 271133268/668441*a^5 + 494039702/668441*a^4 - 164894323/668441*a^3 - 139152381/668441*a^2 + 15752546/668441*a + 8602445/668441,
-163352/668441*a^16 - 181517/668441*a^15 + 3926005/668441*a^14 + 3879384/668441*a^13 - 37768822/668441*a^12 - 31928283/668441*a^11 + 185718644/668441*a^10 + 125556894/668441*a^9 - 494068580/668441*a^8 - 234706784/668441*a^7 + 687597052/668441*a^6 + 170902912/668441*a^5 - 422743240/668441*a^4 - 10753004/668441*a^3 + 54574006/668441*a^2 + 56457/668441*a + 1613950/668441,
-305545/668441*a^16 + 396376/668441*a^15 + 7729643/668441*a^14 - 9663251/668441*a^13 - 78677679/668441*a^12 + 92893507/668441*a^11 + 412897535/668441*a^10 - 447731635/668441*a^9 - 1189364747/668441*a^8 + 1138378461/668441*a^7 + 1843017565/668441*a^6 - 1462656613/668441*a^5 - 1374163219/668441*a^4 + 784387360/668441*a^3 + 357763439/668441*a^2 - 64709348/668441*a - 17273024/668441,
190268/668441*a^16 + 65799/668441*a^15 - 4573543/668441*a^14 - 1121760/668441*a^13 + 43799157/668441*a^12 + 6118939/668441*a^11 - 212988923/668441*a^10 - 5212643/668441*a^9 + 555260801/668441*a^8 - 59217770/668441*a^7 - 748409934/668441*a^6 + 192621427/668441*a^5 + 440494369/668441*a^4 - 187017515/668441*a^3 - 54965704/668441*a^2 + 29420594/668441*a + 739471/668441,
-27439/668441*a^16 - 331684/668441*a^15 + 234410/668441*a^14 + 7633817/668441*a^13 + 2530626/668441*a^12 - 68791754/668441*a^11 - 41010444/668441*a^10 + 306568660/668441*a^9 + 205630004/668441*a^8 - 704262848/668441*a^7 - 470330618/668441*a^6 + 790737304/668441*a^5 + 490154914/668441*a^4 - 351151409/668441*a^3 - 185873264/668441*a^2 + 19154680/668441*a + 8867071/668441,
28575/668441*a^16 + 481667/668441*a^15 - 172932/668441*a^14 - 11146025/668441*a^13 - 4279251/668441*a^12 + 101607191/668441*a^11 + 57300348/668441*a^10 - 462224165/668441*a^9 - 275732201/668441*a^8 + 1097405047/668441*a^7 + 612026151/668441*a^6 - 1291804681/668441*a^5 - 600172325/668441*a^4 + 610391623/668441*a^3 + 189762478/668441*a^2 - 35697637/668441*a - 5682028/668441,
-31476/668441*a^16 - 25008/668441*a^15 + 626712/668441*a^14 + 749181/668441*a^13 - 4650589/668441*a^12 - 8830599/668441*a^11 + 15488313/668441*a^10 + 52716960/668441*a^9 - 21329231/668441*a^8 - 170031529/668441*a^7 + 10613449/668441*a^6 + 287525021/668441*a^5 - 23987414/668441*a^4 - 215749803/668441*a^3 + 42275405/668441*a^2 + 38387049/668441*a - 1957926/668441
]
*], q_expansions := [*
q + a*q^2 + (-a^4 - a^3 + 3*a^2 + 2*a - 1)*q^3 + (a^2 - 2)*q^4 + (a^4 + a^3 - 4*a^2 - 3*a + 1)*q^5 + (a^4 - 4*a^2 - a + 1)*q^6 + (a^4 + 2*a^3 - 3*a^2 - 6*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + a^3 - 2*a^2 - 2*a - 2)*q^9 + (-a^4 - a^3 + 3*a^2 + a - 1)*q^10 + (-a^3 + a^2 + 3*a - 2)*q^11 + (a^3 - a^2 - 3*a + 1)*q^12 + (-a^3 - a^2 + 4*a - 1)*q^13 + (-a - 1)*q^14 + (a^2 + 2*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-4*a^4 - 5*a^3 + 14*a^2 + 12*a - 6)*q^17 + (-a^4 + a^3 + 4*a^2 - 2*a - 1)*q^18 + (-a^4 - 3*a^3 + 3*a^2 + 10*a - 1)*q^19 + (-a^4 - 2*a^3 + 3*a^2 + 5*a - 1)*q^20 + (a^2 + a - 1)*q^21 + (-a^4 + a^3 + 3*a^2 - 2*a)*q^22 + (3*a^4 + 4*a^3 - 10*a^2 - 10*a + 2)*q^23 + (-a^4 - a^3 + 5*a^2 + 3*a - 2)*q^24 + (a^3 + a^2 - 2*a - 4)*q^25 + (-a^4 - a^3 + 4*a^2 - a)*q^26 + (3*a^4 + 4*a^3 - 11*a^2 - 9*a + 4)*q^27 + (-2*a^4 - 4*a^3 + 5*a^2 + 11*a + 2)*q^28 + (-a^4 + 2*a^3 + 6*a^2 - 4*a - 4)*q^29 + (a^3 + 2*a^2 - a)*q^30 + (-2*a^4 - 4*a^3 + 5*a^2 + 12*a + 1)*q^31 + (-2*a^4 - 5*a^3 + 6*a^2 + 12*a - 1)*q^32 + (2*a^3 - 2*a^2 - 5*a + 2)*q^33 + (3*a^4 + 2*a^3 - 12*a^2 - 6*a + 4)*q^34 + (a + 2)*q^35 + (a^4 - a^3 - 4*a^2 + 3*a + 5)*q^36 + (-a^4 + 2*a^3 + 5*a^2 - 8*a - 5)*q^37 + O(q^38),
q + a*q^2 + (85010/668441*a^16 - 176339/668441*a^15 - 2241538/668441*a^14 + 4190472/668441*a^13 + 23933223/668441*a^12 - 39391493/668441*a^11 - 132842471/668441*a^10 + 186205893/668441*a^9 + 408643734/668441*a^8 - 465256935/668441*a^7 - 683138027/668441*a^6 + 586757546/668441*a^5 + 555506577/668441*a^4 - 303194375/668441*a^3 - 158959094/668441*a^2 + 17326687/668441*a + 6750715/668441)*q^3 + (a^2 - 2)*q^4 + (143848/668441*a^16 - 199927/668441*a^15 - 3606981/668441*a^14 + 4857661/668441*a^13 + 36214213/668441*a^12 - 46276983/668441*a^11 - 186415557/668441*a^10 + 219401931/668441*a^9 + 523834133/668441*a^8 - 543663031/668441*a^7 - 789092227/668441*a^6 + 674003695/668441*a^5 + 572350237/668441*a^4 - 346151879/668441*a^3 - 145298876/668441*a^2 + 28757148/668441*a + 6281260/668441)*q^5 + (-91329/668441*a^16 - 31278/668441*a^15 + 2150232/668441*a^14 + 640483/668441*a^13 - 20264243/668441*a^12 - 4902421/668441*a^11 + 97710483/668441*a^10 + 16492604/668441*a^9 - 255537265/668441*a^8 - 18784877/668441*a^7 + 352044936/668441*a^6 - 14825513/668441*a^5 - 220394635/668441*a^4 + 35203746/668441*a^3 + 37644077/668441*a^2 - 4725635/668441*a - 1615190/668441)*q^6 + (-43514/668441*a^16 + 387440/668441*a^15 + 1361549/668441*a^14 - 9030537/668441*a^13 - 16703058/668441*a^12 + 83027396/668441*a^11 + 103963774/668441*a^10 - 382002286/668441*a^9 - 350947554/668441*a^8 + 922397046/668441*a^7 + 629731852/668441*a^6 - 1116987852/668441*a^5 - 539197064/668441*a^4 + 560122572/668441*a^3 + 159965080/668441*a^2 - 45325035/668441*a - 6004853/668441)*q^7 + (a^3 - 4*a)*q^8 + (42054/668441*a^16 - 262455/668441*a^15 - 1209902/668441*a^14 + 6116298/668441*a^13 + 14043018/668441*a^12 - 56453950/668441*a^11 - 84463769/668441*a^10 + 262318806/668441*a^9 + 280220078/668441*a^8 - 644775138/668441*a^7 - 501512106/668441*a^6 + 801919566/668441*a^5 + 434439282/668441*a^4 - 416801437/668441*a^3 - 135528601/668441*a^2 + 35976810/668441*a + 9629069/668441)*q^9 + (-56079/668441*a^16 + 133067/668441*a^15 + 1405309/668441*a^14 - 3200139/668441*a^13 - 13911183/668441*a^12 + 30075683/668441*a^11 + 69656163/668441*a^10 - 139736691/668441*a^9 - 188790015/668441*a^8 + 335079893/668441*a^7 + 276839367/668441*a^6 - 392725995/668441*a^5 - 206043927/668441*a^4 + 183249956/668441*a^3 + 63136820/668441*a^2 - 13138220/668441*a - 2733112/668441)*q^10 + (-47976/668441*a^16 - 59269/668441*a^15 + 1131843/668441*a^14 + 1309592/668441*a^13 - 10511458/668441*a^12 - 11592732/668441*a^11 + 48829796/668441*a^10 + 52587277/668441*a^9 - 120312720/668441*a^8 - 129264310/668441*a^7 + 158327476/668441*a^6 + 165877480/668441*a^5 - 115340775/668441*a^4 - 92636576/668441*a^3 + 50139863/668441*a^2 + 9500135/668441*a - 3596410/668441)*q^11 + (-292627/668441*a^16 + 128356/668441*a^15 + 7315455/668441*a^14 - 3621041/668441*a^13 - 73317892/668441*a^12 + 39043324/668441*a^11 + 377251035/668441*a^10 - 206648374/668441*a^9 - 1061380988/668441*a^8 + 568822671/668441*a^7 + 1603609910/668441*a^6 - 781183466/668441*a^5 - 1164763854/668441*a^4 + 435437391/668441*a^3 + 291364922/668441*a^2 - 23939149/668441*a - 11766179/668441)*q^12 + (81195/668441*a^16 - 58067/668441*a^15 - 2131430/668441*a^14 + 1449193/668441*a^13 + 22632202/668441*a^12 - 14341944/668441*a^11 - 124620842/668441*a^10 + 71906730/668441*a^9 + 378754518/668441*a^8 - 193643585/668441*a^7 - 622117679/668441*a^6 + 271133268/668441*a^5 + 494039702/668441*a^4 - 164894323/668441*a^3 - 139152381/668441*a^2 + 15752546/668441*a + 8602445/668441)*q^13 + (343926/668441*a^16 + 230185/668441*a^15 - 7986201/668441*a^14 - 4780222/668441*a^13 + 73236746/668441*a^12 + 38475204/668441*a^11 - 336704212/668441*a^10 - 150217472/668441*a^9 + 815048008/668441*a^8 + 289669942/668441*a^7 - 996845698/668441*a^6 - 247261638/668441*a^5 + 517739936/668441*a^4 + 60579104/668441*a^3 - 55724881/668441*a^2 - 130463/668441*a + 826766/668441)*q^14 + (33901/668441*a^16 + 195128/668441*a^15 - 734373/668441*a^14 - 4348962/668441*a^13 + 5964676/668441*a^12 + 38079778/668441*a^11 - 21329382/668441*a^10 - 165695826/668441*a^9 + 24034258/668441*a^8 + 373508124/668441*a^7 + 41245074/668441*a^6 - 413682388/668441*a^5 - 118411148/668441*a^4 + 187871331/668441*a^3 + 74098916/668441*a^2 - 21479655/668441*a - 4189942/668441)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-163352/668441*a^16 - 181517/668441*a^15 + 3926005/668441*a^14 + 3879384/668441*a^13 - 37768822/668441*a^12 - 31928283/668441*a^11 + 185718644/668441*a^10 + 125556894/668441*a^9 - 494068580/668441*a^8 - 234706784/668441*a^7 + 687597052/668441*a^6 + 170902912/668441*a^5 - 422743240/668441*a^4 - 10753004/668441*a^3 + 54574006/668441*a^2 + 56457/668441*a + 1613950/668441)*q^17 + (-220401/668441*a^16 - 116498/668441*a^15 + 5107002/668441*a^14 + 2520222/668441*a^13 - 46991800/668441*a^12 - 21172499/668441*a^11 + 218540592/668441*a^10 + 86224976/668441*a^9 - 541027920/668441*a^8 - 172860096/668441*a^7 + 685808472/668441*a^6 + 152298996/668441*a^5 - 375840841/668441*a^4 - 39477265/668441*a^3 + 46027716/668441*a^2 + 3951779/668441*a - 799026/668441)*q^18 + (-305545/668441*a^16 + 396376/668441*a^15 + 7729643/668441*a^14 - 9663251/668441*a^13 - 78677679/668441*a^12 + 92893507/668441*a^11 + 412897535/668441*a^10 - 447731635/668441*a^9 - 1189364747/668441*a^8 + 1138378461/668441*a^7 + 1843017565/668441*a^6 - 1462656613/668441*a^5 - 1374163219/668441*a^4 + 784387360/668441*a^3 + 357763439/668441*a^2 - 64709348/668441*a - 17273024/668441)*q^19 + (-210708/668441*a^16 + 347109/668441*a^15 + 5359719/668441*a^14 - 8260859/668441*a^13 - 54970518/668441*a^12 + 77811234/668441*a^11 + 291472662/668441*a^10 - 368901450/668441*a^9 - 850935266/668441*a^8 + 925908044/668441*a^7 + 1340292578/668441*a^6 - 1177817306/668441*a^5 - 1016071464/668441*a^4 + 627356142/668441*a^3 + 264056651/668441*a^2 - 52676743/668441*a - 11497019/668441)*q^20 + (230655/668441*a^16 + 104003/668441*a^15 - 5477067/668441*a^14 - 2081190/668441*a^13 + 51975564/668441*a^12 + 15945274/668441*a^11 - 252394580/668441*a^10 - 57891692/668441*a^9 + 669784150/668441*a^8 + 98335400/668441*a^7 - 965614658/668441*a^6 - 62142906/668441*a^5 + 701195070/668441*a^4 - 2680705/668441*a^3 - 205873841/668441*a^2 + 3745997/668441*a + 11268782/668441)*q^21 + (-107245/668441*a^16 - 115533/668441*a^15 + 2461016/668441*a^14 + 2633966/668441*a^13 - 22387332/668441*a^12 - 23374084/668441*a^11 + 102530293/668441*a^10 + 101000568/668441*a^9 - 247621102/668441*a^8 - 216604964/668441*a^7 + 298339216/668441*a^6 + 206530209/668441*a^5 - 139365200/668441*a^4 - 59437321/668441*a^3 - 1966129/668441*a^2 + 2880350/668441*a + 911544/668441)*q^22 + (190268/668441*a^16 + 65799/668441*a^15 - 4573543/668441*a^14 - 1121760/668441*a^13 + 43799157/668441*a^12 + 6118939/668441*a^11 - 212988923/668441*a^10 - 5212643/668441*a^9 + 555260801/668441*a^8 - 59217770/668441*a^7 - 748409934/668441*a^6 + 192621427/668441*a^5 + 440494369/668441*a^4 - 187017515/668441*a^3 - 54965704/668441*a^2 + 29420594/668441*a + 739471/668441)*q^23 + (18387/668441*a^16 - 230291/668441*a^15 - 898457/668441*a^14 + 5580940/668441*a^13 + 13730735/668441*a^12 - 53347758/668441*a^11 - 97444633/668441*a^10 + 255522155/668441*a^9 + 357986392/668441*a^8 - 645700341/668441*a^7 - 677330191/668441*a^6 + 828121715/668441*a^5 + 591207963/668441*a^4 - 447402638/668441*a^3 - 169165156/668441*a^2 + 37189736/668441*a + 8790293/668441)*q^24 + (-182820/668441*a^16 + 74928/668441*a^15 + 4741247/668441*a^14 - 2266478/668441*a^13 - 49751449/668441*a^12 + 26239789/668441*a^11 + 271136067/668441*a^10 - 150472493/668441*a^9 - 818451701/668441*a^8 + 455230155/668441*a^7 + 1341380923/668441*a^6 - 699413509/668441*a^5 - 1060536893/668441*a^4 + 448490811/668441*a^3 + 286306875/668441*a^2 - 41781650/668441*a - 14197232/668441)*q^25 + (23128/668441*a^16 - 20360/668441*a^15 - 499487/668441*a^14 + 384772/668441*a^13 + 3926931/668441*a^12 - 2422367/668441*a^11 - 12617265/668441*a^10 + 4201983/668441*a^9 + 6664480/668441*a^8 + 12421246/668441*a^7 + 46953873/668441*a^6 - 50697553/668441*a^5 - 85810393/668441*a^4 + 46296999/668441*a^3 + 35158151/668441*a^2 - 2358880/668441*a - 1542705/668441)*q^26 + (128760/668441*a^16 - 318437/668441*a^15 - 3246680/668441*a^14 + 7454516/668441*a^13 + 32880147/668441*a^12 - 68497690/668441*a^11 - 171530087/668441*a^10 + 312449599/668441*a^9 + 491846360/668441*a^8 - 736724891/668441*a^7 - 763948559/668441*a^6 + 842473872/668441*a^5 + 582381989/668441*a^4 - 362325457/668441*a^3 - 161338545/668441*a^2 + 2263337/668441*a + 4329747/668441)*q^27 + (661139/668441*a^16 + 180995/668441*a^15 - 15757544/668441*a^14 - 2937904/668441*a^13 + 149264670/668441*a^12 + 14849626/668441*a^11 - 716171986/668441*a^10 - 7478058/668441*a^9 + 1840030492/668441*a^8 - 153858100/668441*a^7 - 2456305028/668441*a^6 + 444316106/668441*a^5 + 1473957156/668441*a^4 - 390443041/668441*a^3 - 237862309/668441*a^2 + 45046826/668441*a + 5475112/668441)*q^28 + (-27439/668441*a^16 - 331684/668441*a^15 + 234410/668441*a^14 + 7633817/668441*a^13 + 2530626/668441*a^12 - 68791754/668441*a^11 - 41010444/668441*a^10 + 306568660/668441*a^9 + 205630004/668441*a^8 - 704262848/668441*a^7 - 470330618/668441*a^6 + 790737304/668441*a^5 + 490154914/668441*a^4 - 351151409/668441*a^3 - 185873264/668441*a^2 + 19154680/668441*a + 8867071/668441)*q^29 + (229029/668441*a^16 + 147053/668441*a^15 - 5162586/668441*a^14 - 3324198/668441*a^13 + 45707503/668441*a^12 + 29691623/668441*a^11 - 200986767/668441*a^10 - 132351055/668441*a^9 + 457141891/668441*a^8 + 306181389/668441*a^7 - 507283049/668441*a^6 - 345852957/668441*a^5 + 220890905/668441*a^4 + 151528800/668441*a^3 - 13377316/668441*a^2 - 8766577/668441*a - 644119/668441)*q^30 + (28575/668441*a^16 + 481667/668441*a^15 - 172932/668441*a^14 - 11146025/668441*a^13 - 4279251/668441*a^12 + 101607191/668441*a^11 + 57300348/668441*a^10 - 462224165/668441*a^9 - 275732201/668441*a^8 + 1097405047/668441*a^7 + 612026151/668441*a^6 - 1291804681/668441*a^5 - 600172325/668441*a^4 + 610391623/668441*a^3 + 189762478/668441*a^2 - 35697637/668441*a - 5682028/668441)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (205441/668441*a^16 - 333455/668441*a^15 - 5210507/668441*a^14 + 8210575/668441*a^13 + 53148393/668441*a^12 - 80180890/668441*a^11 - 279076356/668441*a^10 + 395460805/668441*a^9 + 800405168/668441*a^8 - 1037595482/668441*a^7 - 1215830164/668441*a^6 + 1386834420/668441*a^5 + 840048083/668441*a^4 - 778443043/668441*a^3 - 148601811/668441*a^2 + 65640558/668441*a + 712737/668441)*q^33 + (-344869/668441*a^16 - 321147/668441*a^15 + 7799832/668441*a^14 + 6989626/668441*a^13 - 68682483/668441*a^12 - 60126116/668441*a^11 + 295606326/668441*a^10 + 259474196/668441*a^9 - 637696168/668441*a^8 - 588998828/668441*a^7 + 621917784/668441*a^6 + 673185328/668441*a^5 - 169857852/668441*a^4 - 318521962/668441*a^3 - 38984671/668441*a^2 + 23666470/668441*a + 3103688/668441)*q^34 + (-89862/668441*a^16 - 607831/668441*a^15 + 1315224/668441*a^14 + 13973940/668441*a^13 - 2363814/668441*a^12 - 127097854/668441*a^11 - 54181682/668441*a^10 + 580558106/668441*a^9 + 377224866/668441*a^8 - 1397435006/668441*a^7 - 973215626/668441*a^6 + 1694572898/668441*a^5 + 1056590290/668441*a^4 - 854379516/668441*a^3 - 381027413/668441*a^2 + 71394762/668441*a + 16294488/668441)*q^35 + (-421007/668441*a^16 - 98514/668441*a^15 + 10229650/668441*a^14 + 1165478/668441*a^13 - 98848760/668441*a^12 - 255013/668441*a^11 + 484589955/668441*a^10 - 48955719/668441*a^9 - 1277029519/668441*a^8 + 252924933/668441*a^7 + 1763850369/668441*a^6 - 501009664/668441*a^5 - 1123026403/668441*a^4 + 376234706/668441*a^3 + 222333142/668441*a^2 - 42998511/668441*a - 15070519/668441)*q^36 + (-31476/668441*a^16 - 25008/668441*a^15 + 626712/668441*a^14 + 749181/668441*a^13 - 4650589/668441*a^12 - 8830599/668441*a^11 + 15488313/668441*a^10 + 52716960/668441*a^9 - 21329231/668441*a^8 - 170031529/668441*a^7 + 10613449/668441*a^6 + 287525021/668441*a^5 - 23987414/668441*a^4 - 215749803/668441*a^3 + 42275405/668441*a^2 + 38387049/668441*a - 1957926/668441)*q^37 + O(q^38)
*]> ;  // time = 4.281 seconds




J[265] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 265, 265, 265, 265, 265, 265, 265, 265, 53, 53 ], new_dimensions := [ 1, 2, 2, 2, 2, 2, 2, 4, 1, 3 ], dimensions := [ 1, 2, 2, 2, 2, 2, 2, 4, 2, 6 ], intersection_graph := [ 0, 5, 1, 1, 1, 1, 1, 1, 3, 1, 5, 0, 7, 1, 1, 1, 1, 1, 1, 1, 1, 7, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 11, 1, 1, 1, 1, 1, 1, 1, 1, 11, 0, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 0, 1, 17, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 17, 1, 0, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 31, 1, 5, 1, 1, 0 ], ap_traces := [
[ -1, 0, -1, 2, 0, -6, -6, -2, -8, 2, 10, 2 ],
[ -1, -1, -2, -6, -10, 0, -3, 6, -7, 6, 2, 0 ],
[ -2, -2, -2, -4, 4, 2, 2, -2, -10, -10, -12, -10 ],
[ 0, 4, -2, 2, 4, 0, 4, -2, 8, 12, -6, 4 ],
[ 3, -3, -2, 4, 6, 2, 3, -14, 1, 2, -2, -4 ],
[ -1, 1, 2, -2, 6, -4, 3, 0, 1, 2, 6, 4 ],
[ -1, -1, 2, -4, -10, 2, 1, -8, -11, -2, -6, 8 ],
[ 4, -2, 4, 4, 4, -2, -2, 14, 14, -2, 0, -14 ]
], hecke_fields := [
x - 1,
x^2 + x - 5,
x^2 + 2*x - 1,
x^2 - 3,
x^2 - 3*x + 1,
x^2 + x - 3,
x^2 + x - 1,
x^4 - 10*x^3 - 37*x^2 + 220*x - 92
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 31, 1 ],
[ 27, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 27, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 9, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 9, 1, 1 ], l_ratios := [ 0, 0, 0, 1, 1, 1/3, 0, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1, 1, 0, 1 ], eigenvalues := [*
[ -1, 0, -1, 2, 0, -6, -6, -2, -8, 2, 10, 2 ],
[
a,
-a - 1,
-1,
-3,
-5,
2*a + 1,
-a - 2,
3,
-a - 4,
2*a + 4,
2*a + 2,
-4*a - 2
],
[
a,
a,
-1,
-2*a - 4,
2,
-2*a - 1,
2*a + 3,
a,
3*a - 2,
2*a - 3,
-6,
-4*a - 9
],
[
a,
2,
-1,
a + 1,
-2*a + 2,
-2*a,
2,
a - 1,
-2*a + 4,
2*a + 6,
-a - 3,
-4*a + 2
],
[
a,
a - 3,
-1,
-2*a + 5,
3,
1,
-3*a + 6,
-7,
-5*a + 8,
-2*a + 4,
-2*a + 2,
8*a - 14
],
[
a,
a + 1,
1,
-1,
3,
2*a - 1,
-3*a,
-2*a - 1,
-a,
-2*a,
-2*a + 2,
2
],
[
a,
-a - 1,
1,
2*a - 1,
-5,
-4*a - 1,
-a,
2*a - 3,
3*a - 4,
2*a,
-6*a - 6,
4*a + 6
],
[
5/286*a^3 - 21/143*a^2 - 15/22*a + 394/143,
5/858*a^3 - 7/143*a^2 - 37/66*a + 394/429,
1,
-2/143*a^3 + 79/429*a^2 + 7/33*a - 1060/429,
-20/429*a^3 + 56/143*a^2 + 82/33*a - 2294/429,
-19/429*a^3 + 131/429*a^2 + 79/33*a - 531/143,
3/143*a^3 - 47/429*a^2 - 71/33*a + 875/429,
7/858*a^3 - 58/429*a^2 + 23/66*a + 794/143,
35/858*a^3 - 49/143*a^2 - 127/66*a + 3616/429,
-7/429*a^3 - 9/143*a^2 + 65/33*a + 1385/429,
1/39*a^3 - 11/39*a^2 - 4/3*a + 82/13,
4/429*a^3 - 5/429*a^2 - 34/33*a - 543/143
]
*], q_expansions := [*
q - q^2 - q^4 - q^5 + 2*q^7 + 3*q^8 - 3*q^9 + q^10 - 6*q^13 - 2*q^14 - q^16 - 6*q^17 + 3*q^18 - 2*q^19 + q^20 - 8*q^23 + q^25 + 6*q^26 - 2*q^28 + 2*q^29 + 10*q^31 - 5*q^32 + 6*q^34 - 2*q^35 + 3*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (-a + 3)*q^4 - q^5 - 5*q^6 - 3*q^7 + (2*a - 5)*q^8 + (a + 3)*q^9 - a*q^10 - 5*q^11 + (-3*a + 2)*q^12 + (2*a + 1)*q^13 - 3*a*q^14 + (a + 1)*q^15 + (-5*a + 4)*q^16 + (-a - 2)*q^17 + (2*a + 5)*q^18 + 3*q^19 + (a - 3)*q^20 + (3*a + 3)*q^21 - 5*a*q^22 + (-a - 4)*q^23 + (5*a - 5)*q^24 + q^25 + (-a + 10)*q^26 - 5*q^27 + (3*a - 9)*q^28 + (2*a + 4)*q^29 + 5*q^30 + (2*a + 2)*q^31 + (5*a - 15)*q^32 + (5*a + 5)*q^33 + (-a - 5)*q^34 + 3*q^35 + (a + 4)*q^36 + (-4*a - 2)*q^37 + O(q^38),
q + a*q^2 + a*q^3 + (-2*a - 1)*q^4 - q^5 + (-2*a + 1)*q^6 + (-2*a - 4)*q^7 + (a - 2)*q^8 + (-2*a - 2)*q^9 - a*q^10 + 2*q^11 + (3*a - 2)*q^12 + (-2*a - 1)*q^13 - 2*q^14 - a*q^15 + 3*q^16 + (2*a + 3)*q^17 + (2*a - 2)*q^18 + a*q^19 + (2*a + 1)*q^20 - 2*q^21 + 2*a*q^22 + (3*a - 2)*q^23 + (-4*a + 1)*q^24 + q^25 + (3*a - 2)*q^26 + (-a - 2)*q^27 + (2*a + 8)*q^28 + (2*a - 3)*q^29 + (2*a - 1)*q^30 - 6*q^31 + (a + 4)*q^32 + 2*a*q^33 + (-a + 2)*q^34 + (2*a + 4)*q^35 + (-2*a + 6)*q^36 + (-4*a - 9)*q^37 + O(q^38),
q + a*q^2 + 2*q^3 + q^4 - q^5 + 2*a*q^6 + (a + 1)*q^7 - a*q^8 + q^9 - a*q^10 + (-2*a + 2)*q^11 + 2*q^12 - 2*a*q^13 + (a + 3)*q^14 - 2*q^15 - 5*q^16 + 2*q^17 + a*q^18 + (a - 1)*q^19 - q^20 + (2*a + 2)*q^21 + (2*a - 6)*q^22 + (-2*a + 4)*q^23 - 2*a*q^24 + q^25 - 6*q^26 - 4*q^27 + (a + 1)*q^28 + (2*a + 6)*q^29 - 2*a*q^30 + (-a - 3)*q^31 - 3*a*q^32 + (-4*a + 4)*q^33 + 2*a*q^34 + (-a - 1)*q^35 + q^36 + (-4*a + 2)*q^37 + O(q^38),
q + a*q^2 + (a - 3)*q^3 + (3*a - 3)*q^4 - q^5 - q^6 + (-2*a + 5)*q^7 + (4*a - 3)*q^8 + (-3*a + 5)*q^9 - a*q^10 + 3*q^11 + (-3*a + 6)*q^12 + q^13 + (-a + 2)*q^14 + (-a + 3)*q^15 + (3*a + 2)*q^16 + (-3*a + 6)*q^17 + (-4*a + 3)*q^18 - 7*q^19 + (-3*a + 3)*q^20 + (5*a - 13)*q^21 + 3*a*q^22 + (-5*a + 8)*q^23 + (-3*a + 5)*q^24 + q^25 + a*q^26 + (2*a - 3)*q^27 + (3*a - 9)*q^28 + (-2*a + 4)*q^29 + q^30 + (-2*a + 2)*q^31 + (3*a + 3)*q^32 + (3*a - 9)*q^33 + (-3*a + 3)*q^34 + (2*a - 5)*q^35 + (-3*a - 6)*q^36 + (8*a - 14)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-a + 1)*q^4 + q^5 + 3*q^6 - q^7 - 3*q^8 + (a + 1)*q^9 + a*q^10 + 3*q^11 + (a - 2)*q^12 + (2*a - 1)*q^13 - a*q^14 + (a + 1)*q^15 + (-a - 2)*q^16 - 3*a*q^17 + 3*q^18 + (-2*a - 1)*q^19 + (-a + 1)*q^20 + (-a - 1)*q^21 + 3*a*q^22 - a*q^23 + (-3*a - 3)*q^24 + q^25 + (-3*a + 6)*q^26 + (-2*a + 1)*q^27 + (a - 1)*q^28 - 2*a*q^29 + 3*q^30 + (-2*a + 2)*q^31 + (-a + 3)*q^32 + (3*a + 3)*q^33 + (3*a - 9)*q^34 - q^35 + (a - 2)*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (-a - 1)*q^4 + q^5 - q^6 + (2*a - 1)*q^7 + (-2*a - 1)*q^8 + (a - 1)*q^9 + a*q^10 - 5*q^11 + (a + 2)*q^12 + (-4*a - 1)*q^13 + (-3*a + 2)*q^14 + (-a - 1)*q^15 + 3*a*q^16 - a*q^17 + (-2*a + 1)*q^18 + (2*a - 3)*q^19 + (-a - 1)*q^20 + (a - 1)*q^21 - 5*a*q^22 + (3*a - 4)*q^23 + (a + 3)*q^24 + q^25 + (3*a - 4)*q^26 + (4*a + 3)*q^27 + (a - 1)*q^28 + 2*a*q^29 - q^30 + (-6*a - 6)*q^31 + (a + 5)*q^32 + (5*a + 5)*q^33 + (a - 1)*q^34 + (2*a - 1)*q^35 + a*q^36 + (4*a + 6)*q^37 + O(q^38),
q + (5/286*a^3 - 21/143*a^2 - 15/22*a + 394/143)*q^2 + (5/858*a^3 - 7/143*a^2 - 37/66*a + 394/429)*q^3 + (5/143*a^3 - 42/143*a^2 - 15/11*a + 645/143)*q^4 + q^5 + (1/429*a^3 - 37/429*a^2 - 1/11*a + 701/429)*q^6 + (-2/143*a^3 + 79/429*a^2 + 7/33*a - 1060/429)*q^7 + (5/286*a^3 - 21/143*a^2 - 15/22*a + 680/143)*q^8 + (-1/429*a^3 + 37/429*a^2 + 1/11*a - 1130/429)*q^9 + (5/286*a^3 - 21/143*a^2 - 15/22*a + 394/143)*q^10 + (-20/429*a^3 + 56/143*a^2 + 82/33*a - 2294/429)*q^11 + (-1/858*a^3 - 53/429*a^2 + 25/66*a + 336/143)*q^12 + (-19/429*a^3 + 131/429*a^2 + 79/33*a - 531/143)*q^13 + (-1/39*a^3 + 11/39*a^2 + 4/3*a - 82/13)*q^14 + (5/858*a^3 - 7/143*a^2 - 37/66*a + 394/429)*q^15 + 3*q^16 + (3/143*a^3 - 47/429*a^2 - 71/33*a + 875/429)*q^17 + (-4/143*a^3 + 158/429*a^2 + 47/33*a - 2978/429)*q^18 + (7/858*a^3 - 58/429*a^2 + 23/66*a + 794/143)*q^19 + (5/143*a^3 - 42/143*a^2 - 15/11*a + 645/143)*q^20 + (-10/429*a^3 + 28/143*a^2 + 8/33*a - 718/429)*q^21 + (-17/429*a^3 + 200/429*a^2 + 17/11*a - 4624/429)*q^22 + (35/858*a^3 - 49/143*a^2 - 127/66*a + 3616/429)*q^23 + (2/143*a^3 - 79/429*a^2 - 40/33*a + 1489/429)*q^24 + q^25 + (-25/858*a^3 + 35/143*a^2 + 53/66*a - 2828/429)*q^26 + (-41/858*a^3 + 115/429*a^2 + 63/22*a - 2144/429)*q^27 + (-16/429*a^3 + 163/429*a^2 + 27/11*a - 4352/429)*q^28 + (-7/429*a^3 - 9/143*a^2 + 65/33*a + 1385/429)*q^29 + (1/429*a^3 - 37/429*a^2 - 1/11*a + 701/429)*q^30 + (1/39*a^3 - 11/39*a^2 - 4/3*a + 82/13)*q^31 + (5/286*a^3 - 21/143*a^2 - 15/22*a - 178/143)*q^32 + (5/429*a^3 - 14/143*a^2 - 37/33*a - 928/429)*q^33 + (-1/858*a^3 - 53/429*a^2 + 25/66*a + 336/143)*q^34 + (-2/143*a^3 + 79/429*a^2 + 7/33*a - 1060/429)*q^35 + (-23/429*a^3 + 93/143*a^2 + 91/33*a - 4826/429)*q^36 + (4/429*a^3 - 5/429*a^2 - 34/33*a - 543/143)*q^37 + O(q^38)
*]> ;  // time = 32.659 seconds




J[266] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 266, 266, 266, 266, 133, 133, 133, 133, 38, 38, 19, 14 ], new_dimensions := [ 2, 2, 2, 3, 2, 2, 2, 3, 1, 1, 1, 1 ], dimensions := [ 2, 2, 2, 3, 4, 4, 4, 6, 2, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 13, 7, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 1, 11, 1, 1, 0, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 1, 0, 19, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 19, 0, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 9, 1, 1, 1, 0, 1, 3, 1, 9, 3, 13, 1, 1, 1, 1, 1, 1, 0, 1, 1, 49, 1, 7, 1, 1, 1, 1, 1, 3, 1, 0, 1, 9, 3, 1, 1, 1, 11, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 9, 49, 9, 1, 0, 3, 1, 11, 1, 1, 1, 1, 3, 1, 3, 1, 3, 0 ], ap_traces := [
[ -2, 1, -1, -2, 3, -2, -8, 2, -6, 5, 20, 3 ],
[ -2, 3, 1, 2, 7, 6, -4, -2, 2, -11, 8, 3 ],
[ 2, 1, 1, 2, -5, 6, 0, 2, -2, -9, 0, 1 ],
[ 3, -1, 5, -3, 3, -4, 6, -3, -2, 5, 4, 7 ]
], hecke_fields := [
x^2 - x - 7,
x^2 - 3*x + 1,
x^2 - x - 3,
x^3 + x^2 - 7*x + 4
], atkin_lehners := [
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 13, 7, 1 ],
[ 11, 1, 11 ],
[ 81, 3, 1 ],
[ 19, 11, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 81, 3, 1 ],
[ 19, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 9, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1 ], l_ratios := [ 1, 1, 3, 19 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 1/81, 1 ], eigenvalues := [*
[
-1,
a,
a - 1,
-1,
-a + 2,
-2*a,
-4,
1,
-2*a - 2,
-a + 3,
10,
a + 1
],
[
-1,
a,
-3*a + 5,
1,
a + 2,
2*a,
4*a - 8,
-1,
-6*a + 10,
-3*a - 1,
-4*a + 10,
3*a - 3
],
[
1,
a,
-a + 1,
1,
-a - 2,
-2*a + 4,
0,
1,
2*a - 2,
-3*a - 3,
4*a - 2,
3*a - 1
],
[
1,
a,
-a^2 - 2*a + 6,
-1,
2*a^2 + 3*a - 8,
2*a^2 + 4*a - 10,
-2*a^2 - 6*a + 10,
-1,
-2*a^2 - 4*a + 8,
a^2 + 4*a - 2,
2*a^2 + 2*a - 8,
-a^2 - 4*a + 6
]
*], q_expansions := [*
q - q^2 + a*q^3 + q^4 + (a - 1)*q^5 - a*q^6 - q^7 - q^8 + (a + 4)*q^9 + (-a + 1)*q^10 + (-a + 2)*q^11 + a*q^12 - 2*a*q^13 + q^14 + 7*q^15 + q^16 - 4*q^17 + (-a - 4)*q^18 + q^19 + (a - 1)*q^20 - a*q^21 + (a - 2)*q^22 + (-2*a - 2)*q^23 - a*q^24 + (-a + 3)*q^25 + 2*a*q^26 + (2*a + 7)*q^27 - q^28 + (-a + 3)*q^29 - 7*q^30 + 10*q^31 - q^32 + (a - 7)*q^33 + 4*q^34 + (-a + 1)*q^35 + (a + 4)*q^36 + (a + 1)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-3*a + 5)*q^5 - a*q^6 + q^7 - q^8 + (3*a - 4)*q^9 + (3*a - 5)*q^10 + (a + 2)*q^11 + a*q^12 + 2*a*q^13 - q^14 + (-4*a + 3)*q^15 + q^16 + (4*a - 8)*q^17 + (-3*a + 4)*q^18 - q^19 + (-3*a + 5)*q^20 + a*q^21 + (-a - 2)*q^22 + (-6*a + 10)*q^23 - a*q^24 + (-3*a + 11)*q^25 - 2*a*q^26 + (2*a - 3)*q^27 + q^28 + (-3*a - 1)*q^29 + (4*a - 3)*q^30 + (-4*a + 10)*q^31 - q^32 + (5*a - 1)*q^33 + (-4*a + 8)*q^34 + (-3*a + 5)*q^35 + (3*a - 4)*q^36 + (3*a - 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 1)*q^5 + a*q^6 + q^7 + q^8 + a*q^9 + (-a + 1)*q^10 + (-a - 2)*q^11 + a*q^12 + (-2*a + 4)*q^13 + q^14 - 3*q^15 + q^16 + a*q^18 + q^19 + (-a + 1)*q^20 + a*q^21 + (-a - 2)*q^22 + (2*a - 2)*q^23 + a*q^24 + (-a - 1)*q^25 + (-2*a + 4)*q^26 + (-2*a + 3)*q^27 + q^28 + (-3*a - 3)*q^29 - 3*q^30 + (4*a - 2)*q^31 + q^32 + (-3*a - 3)*q^33 + (-a + 1)*q^35 + a*q^36 + (3*a - 1)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 - 2*a + 6)*q^5 + a*q^6 - q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 - 2*a + 6)*q^10 + (2*a^2 + 3*a - 8)*q^11 + a*q^12 + (2*a^2 + 4*a - 10)*q^13 - q^14 + (-a^2 - a + 4)*q^15 + q^16 + (-2*a^2 - 6*a + 10)*q^17 + (a^2 - 3)*q^18 - q^19 + (-a^2 - 2*a + 6)*q^20 - a*q^21 + (2*a^2 + 3*a - 8)*q^22 + (-2*a^2 - 4*a + 8)*q^23 + a*q^24 + (-4*a^2 - 7*a + 19)*q^25 + (2*a^2 + 4*a - 10)*q^26 + (-a^2 + a - 4)*q^27 - q^28 + (a^2 + 4*a - 2)*q^29 + (-a^2 - a + 4)*q^30 + (2*a^2 + 2*a - 8)*q^31 + q^32 + (a^2 + 6*a - 8)*q^33 + (-2*a^2 - 6*a + 10)*q^34 + (a^2 + 2*a - 6)*q^35 + (a^2 - 3)*q^36 + (-a^2 - 4*a + 6)*q^37 + O(q^38)
*]> ;  // time = 102.28 seconds




J[267] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 267, 267, 267, 267, 267, 267, 89, 89, 89 ], new_dimensions := [ 1, 1, 3, 3, 3, 4, 1, 1, 5 ], dimensions := [ 1, 1, 3, 3, 3, 4, 2, 2, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 7, 1, 1, 17, 1, 0, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 5, 1, 0, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 113, 7, 1, 1, 1, 1, 0, 1, 3, 13, 1, 1, 3, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 25, 17, 1, 1, 1, 113, 13, 1, 25, 0 ], ap_traces := [
[ 0, -1, 4, -2, 2, 6, 4, -4, -3, 3, 8, -8 ],
[ 0, 1, 0, 2, 6, 2, 0, -4, 3, -3, -4, -4 ],
[ 0, -3, -3, -6, 6, -15, -6, -6, 3, -6, -9, -9 ],
[ 2, 3, 5, -4, -4, 3, 6, -4, -1, 12, -1, 7 ],
[ -4, 3, -7, -4, -8, -11, -4, 0, -7, -6, -3, -11 ],
[ 1, -4, 3, 6, -6, 9, 2, 10, 1, -2, -11, 23 ]
], hecke_fields := [
x - 1,
x - 1,
x^3 - 3*x + 1,
x^3 - 2*x^2 - 3*x + 5,
x^3 + 4*x^2 + 3*x - 1,
x^4 - x^3 - 7*x^2 + 6*x + 7
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ 1, -1 ]
], component_group_orders := [
[ 17, 1 ],
[ 3, 1 ],
[ 3, 1 ],
[ 25, 1 ],
[ 113, 1 ],
[ 39, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 3, 1 ],
[ 1, 1 ],
[ 25, 1 ],
[ 113, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 5, 1, 1 ], l_ratios := [ 1, 1/3, 0, 1, 0, 1 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 0, 1 ], eigenvalues := [*
[ 0, -1, 4, -2, 2, 6, 4, -4, -3, 3, 8, -8 ],
[ 0, 1, 0, 2, 6, 2, 0, -4, 3, -3, -4, -4 ],
[
a,
-1,
-a^2 - 2*a + 1,
-a^2,
3*a^2 + a - 4,
a^2 + a - 7,
3*a^2 + 4*a - 8,
-3*a - 2,
-3*a^2 + 7,
-5*a^2 + 8,
-3*a^2 + 3,
-4*a^2 - 3*a + 5
],
[
a,
1,
-a^2 + 5,
-a^2 + 2,
a^2 - a - 4,
a^2 + a - 3,
a^2 - 2*a,
-2*a^2 - a + 6,
-a^2 + 3,
a^2 - 2*a + 2,
3*a^2 - 2*a - 9,
4*a^2 - 3*a - 9
],
[
a,
1,
a^2 + 2*a - 3,
-3*a^2 - 8*a - 2,
a^2 + 3*a - 2,
a^2 + 3*a - 3,
a^2 + 2*a - 2,
4*a^2 + 13*a + 4,
-a^2 - 6*a - 7,
-a^2 + 2*a + 4,
5*a^2 + 14*a + 1,
-6*a^2 - 13*a - 1
],
[
a,
-1,
a^2 - 3,
-a^3 - a^2 + 5*a + 5,
-a^2 + a + 2,
-a^3 - a^2 + 4*a + 6,
a^3 + a^2 - 5*a - 3,
a^3 - 6*a + 3,
a^2 - 2*a - 3,
-a^3 - a^2 + 5*a + 3,
-a^2 + 1,
2*a^3 + 2*a^2 - 11*a - 1
]
*], q_expansions := [*
q - q^3 - 2*q^4 + 4*q^5 - 2*q^7 + q^9 + 2*q^11 + 2*q^12 + 6*q^13 - 4*q^15 + 4*q^16 + 4*q^17 - 4*q^19 - 8*q^20 + 2*q^21 - 3*q^23 + 11*q^25 - q^27 + 4*q^28 + 3*q^29 + 8*q^31 - 2*q^33 - 8*q^35 - 2*q^36 - 8*q^37 + O(q^38),
q + q^3 - 2*q^4 + 2*q^7 + q^9 + 6*q^11 - 2*q^12 + 2*q^13 + 4*q^16 - 4*q^19 + 2*q^21 + 3*q^23 - 5*q^25 + q^27 - 4*q^28 - 3*q^29 - 4*q^31 + 6*q^33 - 2*q^36 - 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a + 1)*q^5 - a*q^6 - a^2*q^7 + (-a - 1)*q^8 + q^9 + (-2*a^2 - 2*a + 1)*q^10 + (3*a^2 + a - 4)*q^11 + (-a^2 + 2)*q^12 + (a^2 + a - 7)*q^13 + (-3*a + 1)*q^14 + (a^2 + 2*a - 1)*q^15 + (-3*a^2 - a + 4)*q^16 + (3*a^2 + 4*a - 8)*q^17 + a*q^18 + (-3*a - 2)*q^19 - a*q^20 + a^2*q^21 + (a^2 + 5*a - 3)*q^22 + (-3*a^2 + 7)*q^23 + (a + 1)*q^24 + (5*a^2 + 7*a - 8)*q^25 + (a^2 - 4*a - 1)*q^26 - q^27 + (-a^2 + a)*q^28 + (-5*a^2 + 8)*q^29 + (2*a^2 + 2*a - 1)*q^30 + (-3*a^2 + 3)*q^31 + (-a^2 - 3*a + 5)*q^32 + (-3*a^2 - a + 4)*q^33 + (4*a^2 + a - 3)*q^34 + (2*a^2 + 5*a - 2)*q^35 + (a^2 - 2)*q^36 + (-4*a^2 - 3*a + 5)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 + 5)*q^5 + a*q^6 + (-a^2 + 2)*q^7 + (2*a^2 - a - 5)*q^8 + q^9 + (-2*a^2 + 2*a + 5)*q^10 + (a^2 - a - 4)*q^11 + (a^2 - 2)*q^12 + (a^2 + a - 3)*q^13 + (-2*a^2 - a + 5)*q^14 + (-a^2 + 5)*q^15 + (a^2 + a - 6)*q^16 + (a^2 - 2*a)*q^17 + a*q^18 + (-2*a^2 - a + 6)*q^19 - a*q^20 + (-a^2 + 2)*q^21 + (a^2 - a - 5)*q^22 + (-a^2 + 3)*q^23 + (2*a^2 - a - 5)*q^24 + (-3*a^2 + a + 10)*q^25 + (3*a^2 - 5)*q^26 + q^27 + (-3*a^2 - a + 6)*q^28 + (a^2 - 2*a + 2)*q^29 + (-2*a^2 + 2*a + 5)*q^30 + (3*a^2 - 2*a - 9)*q^31 + (-a^2 - a + 5)*q^32 + (a^2 - a - 4)*q^33 + (3*a - 5)*q^34 + a*q^35 + (a^2 - 2)*q^36 + (4*a^2 - 3*a - 9)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (a^2 + 2*a - 3)*q^5 + a*q^6 + (-3*a^2 - 8*a - 2)*q^7 + (-4*a^2 - 7*a + 1)*q^8 + q^9 + (-2*a^2 - 6*a + 1)*q^10 + (a^2 + 3*a - 2)*q^11 + (a^2 - 2)*q^12 + (a^2 + 3*a - 3)*q^13 + (4*a^2 + 7*a - 3)*q^14 + (a^2 + 2*a - 3)*q^15 + (7*a^2 + 13*a)*q^16 + (a^2 + 2*a - 2)*q^17 + a*q^18 + (4*a^2 + 13*a + 4)*q^19 + (3*a + 4)*q^20 + (-3*a^2 - 8*a - 2)*q^21 + (-a^2 - 5*a + 1)*q^22 + (-a^2 - 6*a - 7)*q^23 + (-4*a^2 - 7*a + 1)*q^24 + (-5*a^2 - 11*a + 4)*q^25 + (-a^2 - 6*a + 1)*q^26 + q^27 + (-3*a^2 + a + 8)*q^28 + (-a^2 + 2*a + 4)*q^29 + (-2*a^2 - 6*a + 1)*q^30 + (5*a^2 + 14*a + 1)*q^31 + (-7*a^2 - 7*a + 5)*q^32 + (a^2 + 3*a - 2)*q^33 + (-2*a^2 - 5*a + 1)*q^34 + (8*a^2 + 23*a + 4)*q^35 + (a^2 - 2)*q^36 + (-6*a^2 - 13*a - 1)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^2 - 3)*q^5 - a*q^6 + (-a^3 - a^2 + 5*a + 5)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^3 - 3*a)*q^10 + (-a^2 + a + 2)*q^11 + (-a^2 + 2)*q^12 + (-a^3 - a^2 + 4*a + 6)*q^13 + (-2*a^3 - 2*a^2 + 11*a + 7)*q^14 + (-a^2 + 3)*q^15 + (a^3 + a^2 - 6*a - 3)*q^16 + (a^3 + a^2 - 5*a - 3)*q^17 + a*q^18 + (a^3 - 6*a + 3)*q^19 + (a^3 + 2*a^2 - 6*a - 1)*q^20 + (a^3 + a^2 - 5*a - 5)*q^21 + (-a^3 + a^2 + 2*a)*q^22 + (a^2 - 2*a - 3)*q^23 + (-a^3 + 4*a)*q^24 + (a^3 + a^2 - 6*a - 3)*q^25 + (-2*a^3 - 3*a^2 + 12*a + 7)*q^26 - q^27 + (-2*a^3 - a^2 + 9*a + 4)*q^28 + (-a^3 - a^2 + 5*a + 3)*q^29 + (-a^3 + 3*a)*q^30 + (-a^2 + 1)*q^31 + (a^2 - a - 7)*q^32 + (a^2 - a - 2)*q^33 + (2*a^3 + 2*a^2 - 9*a - 7)*q^34 + (-a^3 + 4*a - 1)*q^35 + (a^2 - 2)*q^36 + (2*a^3 + 2*a^2 - 11*a - 1)*q^37 + O(q^38)
*]> ;  // time = 41.039 seconds




J[269] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 269, 269, 269 ], new_dimensions := [ 1, 5, 16 ], dimensions := [ 1, 5, 16 ], intersection_graph := [ 0, 3, 1, 3, 0, 1, 1, 1, 0 ], ap_traces := [
[ 0, 0, 1, -4, -3, 2, -4, 2, -1, -2, -8, 7 ],
[ -1, -5, -4, -5, -9, -5, 6, -25, 2, -2, 1, -9 ],
[ 1, 5, -1, 11, 16, -1, -2, 35, 1, 2, 13, 4 ]
], hecke_fields := [
x - 1,
x^5 + x^4 - 5*x^3 - 4*x^2 + 5*x + 3,
x^16 - x^15 - 28*x^14 + 27*x^13 + 314*x^12 - 283*x^11 - 1803*x^10 + 1435*x^9 + 5637*x^8 - 3547*x^7 - 9470*x^6 + 3701*x^5 + 7860*x^4 - 1001*x^3 - 2363*x^2 - 43*x + 172
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 67 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 67 ]
], torsion_upper_bounds := [ 1, 1, 67 ], torsion_lower_bounds := [ 1, 1, 67 ], l_ratios := [ 0, 0, 1/67 ], analytic_sha_upper_bounds := [ 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1 ], eigenvalues := [*
[ 0, 0, 1, -4, -3, 2, -4, 2, -1, -2, -8, 7 ],
[
a,
a^4 - 5*a^2 + 3,
-a^4 + 5*a^2 - a - 5,
-a^4 - a^3 + 3*a^2 + 2*a - 1,
a^4 - 4*a^2,
2*a^3 + 3*a^2 - 5*a - 7,
-a^3 + a^2 + 4*a - 1,
-a^4 - a^3 + 4*a^2 + 3*a - 7,
2*a^4 + a^3 - 11*a^2 - 2*a + 11,
-2*a^4 - a^3 + 7*a^2 + 3*a - 2,
3*a^4 + a^3 - 15*a^2 + 13,
-a^3 + 3*a - 2
],
[
a,
18/683*a^15 - 991/10928*a^14 - 9143/10928*a^13 + 26463/10928*a^12 + 58569/5464*a^11 - 279911/10928*a^10 - 773187/10928*a^9 + 92792/683*a^8 + 693889/2732*a^7 - 4097871/10928*a^6 - 5203557/10928*a^5 + 5451909/10928*a^4 + 2147933/5464*a^3 - 2720323/10928*a^2 - 840769/10928*a + 79841/2732,
70/683*a^15 - 363/10928*a^14 - 30851/10928*a^13 + 11845/10928*a^12 + 84629/2732*a^11 - 148583/10928*a^10 - 1882165/10928*a^9 + 454851/5464*a^8 + 1392713/2732*a^7 - 2841689/10928*a^6 - 8410593/10928*a^5 + 4298529/10928*a^4 + 695081/1366*a^3 - 2654109/10928*a^2 - 976295/10928*a + 93147/2732,
2287/10928*a^15 - 333/1366*a^14 - 15109/2732*a^13 + 72055/10928*a^12 + 624789/10928*a^11 - 377619/5464*a^10 - 3183057/10928*a^9 + 478169/1366*a^8 + 8282669/10928*a^7 - 4746505/5464*a^6 - 5240293/5464*a^5 + 10399189/10928*a^4 + 5962023/10928*a^3 - 528717/1366*a^2 - 999017/10928*a + 117181/2732,
-581/2732*a^15 + 1717/5464*a^14 + 31231/5464*a^13 - 46055/5464*a^12 - 164865/2732*a^11 + 480091/5464*a^10 + 1727655/5464*a^9 - 1215601/2732*a^8 - 585729/683*a^7 + 6088951/5464*a^6 + 6340331/5464*a^5 - 6839219/5464*a^4 - 990813/1366*a^3 + 2851401/5464*a^2 + 722503/5464*a - 73529/1366,
3/2732*a^15 + 49/683*a^14 + 42/683*a^13 - 5167/2732*a^12 - 5311/2732*a^11 + 53695/2732*a^10 + 27423/1366*a^9 - 277997/2732*a^8 - 266457/2732*a^7 + 370859/1366*a^6 + 317525/1366*a^5 - 469565/1366*a^4 - 654743/2732*a^3 + 437761/2732*a^2 + 42097/683*a - 12622/683,
291/2732*a^15 - 2273/5464*a^14 - 15901/5464*a^13 + 59667/5464*a^12 + 42595/1366*a^11 - 610205/5464*a^10 - 905991/5464*a^9 + 380726/683*a^8 + 1259209/2732*a^7 - 7570837/5464*a^6 - 3661403/5464*a^5 + 8479841/5464*a^4 + 696685/1366*a^3 - 3408805/5464*a^2 - 632393/5464*a + 88677/1366,
91/2732*a^15 + 13/1366*a^14 - 2417/2732*a^13 - 553/2732*a^12 + 25131/2732*a^11 + 2401/1366*a^10 - 64265/1366*a^9 - 23935/2732*a^8 + 82837/683*a^7 + 77483/2732*a^6 - 391963/2732*a^5 - 34814/683*a^4 + 42337/683*a^3 + 81369/2732*a^2 - 6187/683*a - 1298/683,
117/1366*a^15 - 1525/5464*a^14 - 12723/5464*a^13 + 40185/5464*a^12 + 16985/683*a^11 - 413107/5464*a^10 - 721213/5464*a^9 + 1038961/2732*a^8 + 999273/2732*a^7 - 5235583/5464*a^6 - 2858339/5464*a^5 + 6047185/5464*a^4 + 1027237/2732*a^3 - 2636785/5464*a^2 - 427893/5464*a + 72455/1366,
1439/5464*a^15 - 575/2732*a^14 - 19129/2732*a^13 + 31815/5464*a^12 + 399863/5464*a^11 - 85489/1366*a^10 - 2075633/5464*a^9 + 892031/2732*a^8 + 5569797/5464*a^7 - 2303547/2732*a^6 - 921679/683*a^5 + 5392391/5464*a^4 + 4341637/5464*a^3 - 307307/683*a^2 - 774853/5464*a + 66921/1366,
-2125/5464*a^15 + 4369/5464*a^14 + 57897/5464*a^13 - 29201/1366*a^12 - 623357/5464*a^11 + 1218507/5464*a^10 + 1682807/2732*a^9 - 1554179/1366*a^8 - 9590531/5464*a^7 + 15858173/5464*a^6 + 14111367/5464*a^5 - 2303174/683*a^4 - 9912439/5464*a^3 + 7889031/5464*a^2 + 969499/2732*a - 105353/683,
-43/2732*a^15 - 247/683*a^14 + 845/1366*a^13 + 6278/683*a^12 - 26781/2732*a^11 - 61328/683*a^10 + 106893/1366*a^9 + 285096/683*a^8 - 879823/2732*a^7 - 2495623/2732*a^6 + 1688789/2732*a^5 + 1045595/1366*a^4 - 1082553/2732*a^3 - 288307/2732*a^2 + 110579/2732*a - 6682/683
]
*], q_expansions := [*
q - 2*q^4 + q^5 - 4*q^7 - 3*q^9 - 3*q^11 + 2*q^13 + 4*q^16 - 4*q^17 + 2*q^19 - 2*q^20 - q^23 - 4*q^25 + 8*q^28 - 2*q^29 - 8*q^31 - 4*q^35 + 6*q^36 + 7*q^37 + O(q^38),
q + a*q^2 + (a^4 - 5*a^2 + 3)*q^3 + (a^2 - 2)*q^4 + (-a^4 + 5*a^2 - a - 5)*q^5 + (-a^4 + 4*a^2 - 2*a - 3)*q^6 + (-a^4 - a^3 + 3*a^2 + 2*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 + a^3 + 5*a^2 - 3*a - 3)*q^9 + (a^4 - 5*a^2 + 3)*q^10 + (a^4 - 4*a^2)*q^11 + (-a^4 - a^3 + 4*a^2 + 2*a - 3)*q^12 + (2*a^3 + 3*a^2 - 5*a - 7)*q^13 + (-2*a^3 - 2*a^2 + 4*a + 3)*q^14 + (-a^3 + a^2 + 5*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^3 + a^2 + 4*a - 1)*q^17 + (2*a^4 - 7*a^2 + 2*a + 3)*q^18 + (-a^4 - a^3 + 4*a^2 + 3*a - 7)*q^19 + (a^4 - 6*a^2 + 7)*q^20 + (a^4 + 2*a^3 - a^2 - 3*a - 3)*q^21 + (-a^4 + a^3 + 4*a^2 - 5*a - 3)*q^22 + (2*a^4 + a^3 - 11*a^2 - 2*a + 11)*q^23 + (2*a^4 - a^3 - 10*a^2 + 6*a + 9)*q^24 + (a^4 + a^3 - 6*a^2 - 3*a + 5)*q^25 + (2*a^4 + 3*a^3 - 5*a^2 - 7*a)*q^26 + (-a^4 - 2*a^3 + 4*a^2 + 7*a - 3)*q^27 + (-2*a^2 - a + 2)*q^28 + (-2*a^4 - a^3 + 7*a^2 + 3*a - 2)*q^29 + (-a^4 + a^3 + 5*a^2 - 3*a)*q^30 + (3*a^4 + a^3 - 15*a^2 + 13)*q^31 + (-a^4 - 3*a^3 + 4*a^2 + 7*a - 3)*q^32 + (-3*a^4 + 14*a^2 - a - 6)*q^33 + (-a^4 + a^3 + 4*a^2 - a)*q^34 + (a^4 + 2*a^3 - 3*a^2 - 5*a + 2)*q^35 + (a^3 - a)*q^36 + (-a^3 + 3*a - 2)*q^37 + O(q^38),
q + a*q^2 + (18/683*a^15 - 991/10928*a^14 - 9143/10928*a^13 + 26463/10928*a^12 + 58569/5464*a^11 - 279911/10928*a^10 - 773187/10928*a^9 + 92792/683*a^8 + 693889/2732*a^7 - 4097871/10928*a^6 - 5203557/10928*a^5 + 5451909/10928*a^4 + 2147933/5464*a^3 - 2720323/10928*a^2 - 840769/10928*a + 79841/2732)*q^3 + (a^2 - 2)*q^4 + (70/683*a^15 - 363/10928*a^14 - 30851/10928*a^13 + 11845/10928*a^12 + 84629/2732*a^11 - 148583/10928*a^10 - 1882165/10928*a^9 + 454851/5464*a^8 + 1392713/2732*a^7 - 2841689/10928*a^6 - 8410593/10928*a^5 + 4298529/10928*a^4 + 695081/1366*a^3 - 2654109/10928*a^2 - 976295/10928*a + 93147/2732)*q^5 + (-703/10928*a^15 - 1079/10928*a^14 + 18687/10928*a^13 + 13353/5464*a^12 - 198407/10928*a^11 - 253923/10928*a^10 + 66962/683*a^9 + 288025/2732*a^8 - 3076335/10928*a^7 - 2476197/10928*a^6 + 4386021/10928*a^5 + 1016093/5464*a^4 - 2432035/10928*a^3 - 160225/10928*a^2 + 82937/2732*a - 3096/683)*q^6 + (2287/10928*a^15 - 333/1366*a^14 - 15109/2732*a^13 + 72055/10928*a^12 + 624789/10928*a^11 - 377619/5464*a^10 - 3183057/10928*a^9 + 478169/1366*a^8 + 8282669/10928*a^7 - 4746505/5464*a^6 - 5240293/5464*a^5 + 10399189/10928*a^4 + 5962023/10928*a^3 - 528717/1366*a^2 - 999017/10928*a + 117181/2732)*q^7 + (a^3 - 4*a)*q^8 + (-170/683*a^15 + 879/2732*a^14 + 8963/1366*a^13 - 5902/683*a^12 - 184257/2732*a^11 + 122809/1366*a^10 + 231930/683*a^9 - 1234197/2732*a^8 - 2359169/2732*a^7 + 3034549/2732*a^6 + 715749/683*a^5 - 3283869/2732*a^4 - 778493/1366*a^3 + 329537/683*a^2 + 135419/1366*a - 33795/683)*q^9 + (757/10928*a^15 + 509/10928*a^14 - 18395/10928*a^13 - 3291/2732*a^12 + 168377/10928*a^11 + 137195/10928*a^10 - 348749/5464*a^9 - 185647/2732*a^8 + 1130951/10928*a^7 + 2195807/10928*a^6 + 153409/10928*a^5 - 405319/1366*a^4 - 1532989/10928*a^3 + 1670265/10928*a^2 + 105187/2732*a - 12040/683)*q^10 + (-581/2732*a^15 + 1717/5464*a^14 + 31231/5464*a^13 - 46055/5464*a^12 - 164865/2732*a^11 + 480091/5464*a^10 + 1727655/5464*a^9 - 1215601/2732*a^8 - 585729/683*a^7 + 6088951/5464*a^6 + 6340331/5464*a^5 - 6839219/5464*a^4 - 990813/1366*a^3 + 2851401/5464*a^2 + 722503/5464*a - 73529/1366)*q^11 + (-1179/5464*a^15 + 985/10928*a^14 + 63973/10928*a^13 - 30591/10928*a^12 - 171787/2732*a^11 + 363705/10928*a^10 + 3707279/10928*a^9 - 520717/2732*a^8 - 5260425/5464*a^7 + 5924353/10928*a^6 + 15041103/10928*a^5 - 7810273/10928*a^4 - 2363915/2732*a^3 + 4111205/10928*a^2 + 1601773/10928*a - 129453/2732)*q^12 + (3/2732*a^15 + 49/683*a^14 + 42/683*a^13 - 5167/2732*a^12 - 5311/2732*a^11 + 53695/2732*a^10 + 27423/1366*a^9 - 277997/2732*a^8 - 266457/2732*a^7 + 370859/1366*a^6 + 317525/1366*a^5 - 469565/1366*a^4 - 654743/2732*a^3 + 437761/2732*a^2 + 42097/683*a - 12622/683)*q^13 + (-377/10928*a^15 + 225/683*a^14 + 5153/5464*a^13 - 93329/10928*a^12 - 108017/10928*a^11 + 235101/2732*a^10 + 543507/10928*a^9 - 2304575/5464*a^8 - 1381021/10928*a^7 + 1397163/1366*a^6 + 967501/5464*a^5 - 12013797/10928*a^4 - 1940449/10928*a^3 + 1101291/2732*a^2 + 567065/10928*a - 98341/2732)*q^14 + (439/5464*a^15 + 223/5464*a^14 - 11615/5464*a^13 - 629/683*a^12 + 120741/5464*a^11 + 43393/5464*a^10 - 155587/1366*a^9 - 22604/683*a^8 + 1646959/5464*a^7 + 375683/5464*a^6 - 2092481/5464*a^5 - 41043/683*a^4 + 1086029/5464*a^3 - 2731/5464*a^2 - 50097/1366*a + 2866/683)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (291/2732*a^15 - 2273/5464*a^14 - 15901/5464*a^13 + 59667/5464*a^12 + 42595/1366*a^11 - 610205/5464*a^10 - 905991/5464*a^9 + 380726/683*a^8 + 1259209/2732*a^7 - 7570837/5464*a^6 - 3661403/5464*a^5 + 8479841/5464*a^4 + 696685/1366*a^3 - 3408805/5464*a^2 - 632393/5464*a + 88677/1366)*q^17 + (199/2732*a^15 - 557/1366*a^14 - 1312/683*a^13 + 29263/2732*a^12 + 26589/1366*a^11 - 74580/683*a^10 - 258397/2732*a^9 + 1473991/2732*a^8 + 622589/2732*a^7 - 894151/683*a^6 - 767189/2732*a^5 + 1893907/1366*a^4 + 159367/683*a^3 - 668001/1366*a^2 - 41105/683*a + 29240/683)*q^18 + (91/2732*a^15 + 13/1366*a^14 - 2417/2732*a^13 - 553/2732*a^12 + 25131/2732*a^11 + 2401/1366*a^10 - 64265/1366*a^9 - 23935/2732*a^8 + 82837/683*a^7 + 77483/2732*a^6 - 391963/2732*a^5 - 34814/683*a^4 + 42337/683*a^3 + 81369/2732*a^2 - 6187/683*a - 1298/683)*q^19 + (-487/5464*a^15 + 3527/10928*a^14 + 28099/10928*a^13 - 93011/10928*a^12 - 162803/5464*a^11 + 964539/10928*a^10 + 1935447/10928*a^9 - 2477831/5464*a^8 - 3130409/5464*a^7 + 13005577/10928*a^6 + 10776977/10928*a^5 - 16080067/10928*a^4 - 4346637/5464*a^3 + 7517757/10928*a^2 + 1792501/10928*a - 218845/2732)*q^20 + (849/10928*a^15 - 269/5464*a^14 - 5189/2732*a^13 + 13019/10928*a^12 + 189461/10928*a^11 - 56197/5464*a^10 - 767449/10928*a^9 + 185561/5464*a^8 + 1143309/10928*a^7 - 22637/5464*a^6 + 24673/683*a^5 - 1808633/10928*a^4 - 1566635/10928*a^3 + 946159/5464*a^2 + 375861/10928*a - 62089/2732)*q^21 + (555/5464*a^15 - 1305/5464*a^14 - 14681/5464*a^13 + 17569/2732*a^12 + 151245/5464*a^11 - 367431/5464*a^10 - 190933/1366*a^9 + 932181/2732*a^8 + 1967337/5464*a^7 - 4663809/5464*a^6 - 2538657/5464*a^5 + 1292517/1366*a^4 + 1688239/5464*a^3 - 2023303/5464*a^2 - 172041/2732*a + 24983/683)*q^22 + (117/1366*a^15 - 1525/5464*a^14 - 12723/5464*a^13 + 40185/5464*a^12 + 16985/683*a^11 - 413107/5464*a^10 - 721213/5464*a^9 + 1038961/2732*a^8 + 999273/2732*a^7 - 5235583/5464*a^6 - 2858339/5464*a^5 + 6047185/5464*a^4 + 1027237/2732*a^3 - 2636785/5464*a^2 - 427893/5464*a + 72455/1366)*q^23 + (33/10928*a^15 + 107/10928*a^14 - 4299/10928*a^13 - 37/2732*a^12 + 93205/10928*a^11 - 36349/10928*a^10 - 420961/5464*a^9 + 116749/2732*a^8 + 3713197/10928*a^7 - 2336763/10928*a^6 - 7855357/10928*a^5 + 626731/1366*a^4 + 6614917/10928*a^3 - 3649731/10928*a^2 - 641351/5464*a + 63081/1366)*q^24 + (3283/10928*a^15 - 1473/2732*a^14 - 43993/5464*a^13 + 156999/10928*a^12 + 925563/10928*a^11 - 203459/1366*a^10 - 4827629/10928*a^9 + 4105865/5464*a^8 + 13036151/10928*a^7 - 5133891/2732*a^6 - 8839721/5464*a^5 + 23072643/10928*a^4 + 11420195/10928*a^3 - 597851/683*a^2 - 2243543/10928*a + 255531/2732)*q^25 + (199/2732*a^15 + 63/683*a^14 - 1312/683*a^13 - 6253/2732*a^12 + 13636/683*a^11 + 60255/2732*a^10 - 141151/1366*a^9 - 70842/683*a^8 + 752359/2732*a^7 + 165865/683*a^6 - 950233/2732*a^5 - 678323/2732*a^4 + 110191/683*a^3 + 175477/2732*a^2 - 50359/2732*a - 129/683)*q^26 + (-2373/10928*a^15 + 43/683*a^14 + 15271/2732*a^13 - 20465/10928*a^12 - 610051/10928*a^11 + 113183/5464*a^10 + 2956315/10928*a^9 - 142531/1366*a^8 - 7072631/10928*a^7 + 1265313/5464*a^6 + 3781135/5464*a^5 - 1942595/10928*a^4 - 3089321/10928*a^3 + 62037/1366*a^2 + 485267/10928*a - 11703/2732)*q^27 + (-1351/10928*a^15 + 2539/5464*a^14 + 18861/5464*a^13 - 133749/10928*a^12 - 415865/10928*a^11 + 343563/2732*a^10 + 2297959/10928*a^9 - 431661/683*a^8 - 6725253/10928*a^7 + 1084427/683*a^6 + 2585663/2732*a^5 - 19775607/10928*a^4 - 7896259/10928*a^3 + 4067843/5464*a^2 + 1588459/10928*a - 218151/2732)*q^28 + (1439/5464*a^15 - 575/2732*a^14 - 19129/2732*a^13 + 31815/5464*a^12 + 399863/5464*a^11 - 85489/1366*a^10 - 2075633/5464*a^9 + 892031/2732*a^8 + 5569797/5464*a^7 - 2303547/2732*a^6 - 921679/683*a^5 + 5392391/5464*a^4 + 4341637/5464*a^3 - 307307/683*a^2 - 774853/5464*a + 66921/1366)*q^29 + (331/2732*a^15 + 677/5464*a^14 - 16885/5464*a^13 - 17105/5464*a^12 + 83815/2732*a^11 + 169169/5464*a^10 - 810797/5464*a^9 - 206921/1366*a^8 + 241602/683*a^7 + 2064849/5464*a^6 - 1953083/5464*a^5 - 2364511/5464*a^4 + 109177/1366*a^3 + 836969/5464*a^2 + 41805/5464*a - 18877/1366)*q^30 + (-2125/5464*a^15 + 4369/5464*a^14 + 57897/5464*a^13 - 29201/1366*a^12 - 623357/5464*a^11 + 1218507/5464*a^10 + 1682807/2732*a^9 - 1554179/1366*a^8 - 9590531/5464*a^7 + 15858173/5464*a^6 + 14111367/5464*a^5 - 2303174/683*a^4 - 9912439/5464*a^3 + 7889031/5464*a^2 + 969499/2732*a - 105353/683)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (961/5464*a^15 - 1189/5464*a^14 - 27461/5464*a^13 + 16493/2732*a^12 + 315381/5464*a^11 - 362819/5464*a^10 - 464221/1366*a^9 + 499813/1366*a^8 + 5911499/5464*a^7 - 5721523/5464*a^6 - 9788297/5464*a^5 + 3952517/2732*a^4 + 7191167/5464*a^3 - 4191365/5464*a^2 - 658799/2732*a + 61071/683)*q^33 + (-1691/5464*a^15 + 395/5464*a^14 + 43953/5464*a^13 - 1546/683*a^12 - 445499/5464*a^11 + 143355/5464*a^10 + 1105319/2732*a^9 - 190579/1366*a^8 - 5506483/5464*a^7 + 1850137/5464*a^6 + 6325859/5464*a^5 - 446945/1366*a^4 - 2826223/5464*a^3 + 742873/5464*a^2 + 189867/2732*a - 12513/683)*q^34 + (-903/10928*a^15 + 425/10928*a^14 + 22513/10928*a^13 - 2713/2732*a^12 - 214071/10928*a^11 + 102767/10928*a^10 + 475783/5464*a^9 - 26336/683*a^8 - 1886213/10928*a^7 + 572227/10928*a^6 + 1057761/10928*a^5 + 111193/2732*a^4 + 553955/10928*a^3 - 921019/10928*a^2 - 17291/683*a + 11705/683)*q^35 + (445/2732*a^15 - 717/1366*a^14 - 5981/1366*a^13 + 9477/683*a^12 + 126511/2732*a^11 - 97709/683*a^10 - 333507/1366*a^9 + 492305/683*a^8 + 1847587/2732*a^7 - 4951757/2732*a^6 - 2674677/2732*a^5 + 2820533/1366*a^4 + 1977169/2732*a^3 - 2330479/2732*a^2 - 416159/2732*a + 59033/683)*q^36 + (-43/2732*a^15 - 247/683*a^14 + 845/1366*a^13 + 6278/683*a^12 - 26781/2732*a^11 - 61328/683*a^10 + 106893/1366*a^9 + 285096/683*a^8 - 879823/2732*a^7 - 2495623/2732*a^6 + 1688789/2732*a^5 + 1045595/1366*a^4 - 1082553/2732*a^3 - 288307/2732*a^2 + 110579/2732*a - 6682/683)*q^37 + O(q^38)
*]> ;  // time = 4.431 seconds




J[271] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 271, 271 ], new_dimensions := [ 6, 16 ], dimensions := [ 6, 16 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -4, -1, -8, -3, -11, -2, -10, -5, -3, -17, -6, 0 ],
[ 5, 1, 10, -3, 17, -4, 12, -3, 5, 21, -10, 2 ]
], hecke_fields := [
x^6 + 4*x^5 + x^4 - 9*x^3 - 4*x^2 + 5*x + 1,
x^16 - 5*x^15 - 12*x^14 + 91*x^13 + 11*x^12 - 620*x^11 + 381*x^10 + 1953*x^9 - 1863*x^8 - 2853*x^7 + 3137*x^6 + 1830*x^5 - 1758*x^4 - 831*x^3 + 308*x^2 + 204*x + 27
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 45 ]
], tamagawa_numbers := [
[ 1 ],
[ 45 ]
], torsion_upper_bounds := [ 1, 45 ], torsion_lower_bounds := [ 1, 45 ], l_ratios := [ 0, 1/45 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^5 - 3*a^4 + a^3 + 5*a^2 - a - 1,
a^5 + 4*a^4 + 2*a^3 - 6*a^2 - 4*a,
a^5 + 2*a^4 - 5*a^3 - 7*a^2 + 5*a + 2,
a^5 + 3*a^4 - a^3 - 4*a^2 + 3*a - 2,
-a^5 - 5*a^4 - 4*a^3 + 9*a^2 + 7*a - 4,
a^4 + 2*a^3 - 2*a^2 - 2*a - 1,
-2*a^5 - 7*a^4 + a^3 + 15*a^2 - 6,
-a^5 - a^4 + 9*a^3 + 10*a^2 - 9*a - 7,
-a^5 - 4*a^4 - 3*a^3 + a^2 + 2*a + 2,
a^5 + 6*a^4 + 8*a^3 - 10*a^2 - 14*a + 6,
-2*a^4 - 8*a^3 - 4*a^2 + 9*a + 4
],
[
a,
4966/763*a^15 - 26858/763*a^14 - 49243/763*a^13 + 474081/763*a^12 - 128875/763*a^11 - 3063997/763*a^10 + 3087453/763*a^9 + 8695891/763*a^8 - 1814217/109*a^7 - 9799739/763*a^6 + 19637291/763*a^5 + 2259965/763*a^4 - 1419203/109*a^3 - 760516/763*a^2 + 1897494/763*a + 406918/763,
-2931/763*a^15 + 15816/763*a^14 + 29560/763*a^13 - 280031/763*a^12 + 67017/763*a^11 + 1819457/763*a^10 - 1760793/763*a^9 - 5219351/763*a^8 + 1043544/109*a^7 + 6055573/763*a^6 - 11326071/763*a^5 - 1666627/763*a^4 + 817097/109*a^3 + 533915/763*a^2 - 1063246/763*a - 229968/763,
4747/763*a^15 - 25342/763*a^14 - 48836/763*a^13 + 449248/763*a^12 - 91214/763*a^11 - 2925197/763*a^10 + 2735429/763*a^9 + 8428341/763*a^8 - 1639143/109*a^7 - 9899208/763*a^6 + 17856212/763*a^5 + 2928854/763*a^4 - 1289523/109*a^3 - 966229/763*a^2 + 1684731/763*a + 377795/763,
7251/763*a^15 - 38561/763*a^14 - 74756/763*a^13 + 683219/763*a^12 - 136608/763*a^11 - 4444746/763*a^10 + 4161832/763*a^9 + 12784879/763*a^8 - 2498112/109*a^7 - 14949252/763*a^6 + 27259040/763*a^5 + 4317273/763*a^4 - 1977730/109*a^3 - 1421394/763*a^2 + 2608957/763*a + 583200/763,
-5580/763*a^15 + 29983/763*a^14 + 56725/763*a^13 - 531848/763*a^12 + 121076/763*a^11 + 3466885/763*a^10 - 3325823/763*a^9 - 10012231/763*a^8 + 1988907/109*a^7 + 11833721/763*a^6 - 21864055/763*a^5 - 3620923/763*a^4 + 1631536/109*a^3 + 1218208/763*a^2 - 2212377/763*a - 498223/763,
-5031/763*a^15 + 26862/763*a^14 + 51827/763*a^13 - 477424/763*a^12 + 97635/763*a^11 + 3122927/763*a^10 - 2930010/763*a^9 - 9083295/763*a^8 + 1770391/109*a^7 + 10944961/763*a^6 - 19647573/763*a^5 - 3696284/763*a^4 + 1497695/109*a^3 + 1294955/763*a^2 - 2085085/763*a - 491712/763,
-5161/763*a^15 + 27633/763*a^14 + 51654/763*a^13 - 486399/763*a^12 + 123663/763*a^11 + 3127863/763*a^10 - 3120993/763*a^9 - 8782273/763*a^8 + 1831851/109*a^7 + 9580635/763*a^6 - 19581155/763*a^5 - 1649098/763*a^4 + 1355256/109*a^3 + 456333/763*a^2 - 1725498/763*a - 336262/763,
4806/763*a^15 - 25733/763*a^14 - 49632/763*a^13 + 458046/763*a^12 - 91030/763*a^11 - 3003925/763*a^10 + 2783727/763*a^9 + 8782661/763*a^8 - 1684359/109*a^7 - 10728587/763*a^6 + 18698377/763*a^5 + 3857405/763*a^4 - 1423894/109*a^3 - 1364271/763*a^2 + 1967073/763*a + 474459/763,
-1888/109*a^15 + 10114/109*a^14 + 19041/109*a^13 - 178640/109*a^12 + 43162/109*a^11 + 1155815/109*a^10 - 1133843/109*a^9 - 3287391/109*a^8 + 4701383/109*a^7 + 3725665/109*a^6 - 7280339/109*a^5 - 887819/109*a^4 + 3667367/109*a^3 + 287364/109*a^2 - 692847/109*a - 147741/109,
-647/109*a^15 + 3449/109*a^14 + 6743/109*a^13 - 61391/109*a^12 + 11053/109*a^11 + 402563/109*a^10 - 365690/109*a^9 - 1176425/109*a^8 + 1554123/109*a^7 + 1433995/109*a^6 - 2456291/109*a^5 - 506978/109*a^4 + 1288760/109*a^3 + 171449/109*a^2 - 246702/109*a - 58720/109,
13014/763*a^15 - 68567/763*a^14 - 136420/763*a^13 + 1216931/763*a^12 - 206238/763*a^11 - 7940319/763*a^10 + 7225376/763*a^9 + 22976028/763*a^8 - 4390072/109*a^7 - 27292612/763*a^6 + 48299044/763*a^5 + 8542042/763*a^4 - 3555707/109*a^3 - 2811128/763*a^2 + 4741176/763*a + 1077998/763
]
*], q_expansions := [*
q + a*q^2 + (-a^5 - 3*a^4 + a^3 + 5*a^2 - a - 1)*q^3 + (a^2 - 2)*q^4 + (a^5 + 4*a^4 + 2*a^3 - 6*a^2 - 4*a)*q^5 + (a^5 + 2*a^4 - 4*a^3 - 5*a^2 + 4*a + 1)*q^6 + (a^5 + 2*a^4 - 5*a^3 - 7*a^2 + 5*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + 2*a^2 - 2*a - 3)*q^9 + (a^4 + 3*a^3 - 5*a - 1)*q^10 + (a^5 + 3*a^4 - a^3 - 4*a^2 + 3*a - 2)*q^11 + (a^4 + 2*a^3 - 2*a^2 - 2*a + 1)*q^12 + (-a^5 - 5*a^4 - 4*a^3 + 9*a^2 + 7*a - 4)*q^13 + (-2*a^5 - 6*a^4 + 2*a^3 + 9*a^2 - 3*a - 1)*q^14 + (a^5 + 3*a^4 - a^3 - 5*a^2 + a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + 2*a^3 - 2*a^2 - 2*a - 1)*q^17 + (a^4 + 2*a^3 - 2*a^2 - 3*a)*q^18 + (-2*a^5 - 7*a^4 + a^3 + 15*a^2 - 6)*q^19 + (-a^5 - 5*a^4 - 4*a^3 + 7*a^2 + 7*a)*q^20 + (a^5 + 4*a^4 + a^3 - 6*a^2 + 2*a)*q^21 + (-a^5 - 2*a^4 + 5*a^3 + 7*a^2 - 7*a - 1)*q^22 + (-a^5 - a^4 + 9*a^3 + 10*a^2 - 9*a - 7)*q^23 + (-a^5 - 2*a^4 + 6*a^3 + 8*a^2 - 7*a - 2)*q^24 + (-3*a^5 - 13*a^4 - 10*a^3 + 16*a^2 + 18*a - 2)*q^25 + (-a^5 - 3*a^4 + 3*a^2 + a + 1)*q^26 + (3*a^5 + 10*a^4 - 16*a^2 - a + 4)*q^27 + (a^3 + 3*a^2 - a - 2)*q^28 + (-a^5 - 4*a^4 - 3*a^3 + a^2 + 2*a + 2)*q^29 + (-a^5 - 2*a^4 + 4*a^3 + 5*a^2 - 5*a - 1)*q^30 + (a^5 + 6*a^4 + 8*a^3 - 10*a^2 - 14*a + 6)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3*a^5 + 8*a^4 - 8*a^3 - 19*a^2 + 9*a + 4)*q^33 + (a^5 + 2*a^4 - 2*a^3 - 2*a^2 - a)*q^34 + (-a^5 - 2*a^4 + 5*a^3 + 6*a^2 - 7*a - 1)*q^35 + (a^5 + 2*a^4 - 4*a^3 - 7*a^2 + 4*a + 6)*q^36 + (-2*a^4 - 8*a^3 - 4*a^2 + 9*a + 4)*q^37 + O(q^38),
q + a*q^2 + (4966/763*a^15 - 26858/763*a^14 - 49243/763*a^13 + 474081/763*a^12 - 128875/763*a^11 - 3063997/763*a^10 + 3087453/763*a^9 + 8695891/763*a^8 - 1814217/109*a^7 - 9799739/763*a^6 + 19637291/763*a^5 + 2259965/763*a^4 - 1419203/109*a^3 - 760516/763*a^2 + 1897494/763*a + 406918/763)*q^3 + (a^2 - 2)*q^4 + (-2931/763*a^15 + 15816/763*a^14 + 29560/763*a^13 - 280031/763*a^12 + 67017/763*a^11 + 1819457/763*a^10 - 1760793/763*a^9 - 5219351/763*a^8 + 1043544/109*a^7 + 6055573/763*a^6 - 11326071/763*a^5 - 1666627/763*a^4 + 817097/109*a^3 + 533915/763*a^2 - 1063246/763*a - 229968/763)*q^5 + (-2028/763*a^15 + 10349/763*a^14 + 22175/763*a^13 - 183501/763*a^12 + 14923/763*a^11 + 1195407/763*a^10 - 1002707/763*a^9 - 3447861/763*a^8 + 624037/109*a^7 + 4058949/763*a^6 - 6827815/763*a^5 - 1204193/763*a^4 + 480890/109*a^3 + 367966/763*a^2 - 606146/763*a - 134082/763)*q^6 + (4747/763*a^15 - 25342/763*a^14 - 48836/763*a^13 + 449248/763*a^12 - 91214/763*a^11 - 2925197/763*a^10 + 2735429/763*a^9 + 8428341/763*a^8 - 1639143/109*a^7 - 9899208/763*a^6 + 17856212/763*a^5 + 2928854/763*a^4 - 1289523/109*a^3 - 966229/763*a^2 + 1684731/763*a + 377795/763)*q^7 + (a^3 - 4*a)*q^8 + (-711/763*a^15 + 4117/763*a^14 + 6631/763*a^13 - 73473/763*a^12 + 26518/763*a^11 + 483904/763*a^10 - 502266/763*a^9 - 1426970/763*a^8 + 291298/109*a^7 + 1785758/763*a^6 - 3224758/763*a^5 - 727467/763*a^4 + 254767/109*a^3 + 299893/763*a^2 - 373803/763*a - 96515/763)*q^9 + (1161/763*a^15 - 5612/763*a^14 - 13310/763*a^13 + 99258/763*a^12 + 2237/763*a^11 - 644082/763*a^10 + 504892/763*a^9 + 1844355/763*a^8 - 329510/109*a^7 - 2131524/763*a^6 + 3697103/763*a^5 + 566981/763*a^4 - 271678/109*a^3 - 160498/763*a^2 + 367956/763*a + 79137/763)*q^10 + (7251/763*a^15 - 38561/763*a^14 - 74756/763*a^13 + 683219/763*a^12 - 136608/763*a^11 - 4444746/763*a^10 + 4161832/763*a^9 + 12784879/763*a^8 - 2498112/109*a^7 - 14949252/763*a^6 + 27259040/763*a^5 + 4317273/763*a^4 - 1977730/109*a^3 - 1421394/763*a^2 + 2608957/763*a + 583200/763)*q^11 + (-1389/109*a^15 + 7365/109*a^14 + 14219/109*a^13 - 130133/109*a^12 + 27971/109*a^11 + 842565/109*a^10 - 808869/109*a^9 - 2400241/109*a^8 + 3381729/109*a^7 + 2733357/109*a^6 - 5252505/109*a^5 - 674132/109*a^4 + 2650220/109*a^3 + 219930/109*a^2 - 502194/109*a - 108440/109)*q^12 + (-5580/763*a^15 + 29983/763*a^14 + 56725/763*a^13 - 531848/763*a^12 + 121076/763*a^11 + 3466885/763*a^10 - 3325823/763*a^9 - 10012231/763*a^8 + 1988907/109*a^7 + 11833721/763*a^6 - 21864055/763*a^5 - 3620923/763*a^4 + 1631536/109*a^3 + 1218208/763*a^2 - 2212377/763*a - 498223/763)*q^13 + (-1607/763*a^15 + 8128/763*a^14 + 17271/763*a^13 - 143431/763*a^12 + 17943/763*a^11 + 926822/763*a^10 - 842550/763*a^9 - 2630340/763*a^8 + 520569/109*a^7 + 2964873/763*a^6 - 5758156/763*a^5 - 681435/763*a^4 + 425504/109*a^3 + 222655/763*a^2 - 590593/763*a - 128169/763)*q^14 + (7319/763*a^15 - 39516/763*a^14 - 73656/763*a^13 + 700239/763*a^12 - 172244/763*a^11 - 4556343/763*a^10 + 4452023/763*a^9 + 13109473/763*a^8 - 2647603/109*a^7 - 15335651/763*a^6 + 29041283/763*a^5 + 4437222/763*a^4 - 2165241/109*a^3 - 1487261/763*a^2 + 2952512/763*a + 659007/763)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-5031/763*a^15 + 26862/763*a^14 + 51827/763*a^13 - 477424/763*a^12 + 97635/763*a^11 + 3122927/763*a^10 - 2930010/763*a^9 - 9083295/763*a^8 + 1770391/109*a^7 + 10944961/763*a^6 - 19647573/763*a^5 - 3696284/763*a^4 + 1497695/109*a^3 + 1294955/763*a^2 - 2085085/763*a - 491712/763)*q^17 + (562/763*a^15 - 1901/763*a^14 - 8772/763*a^13 + 34339/763*a^12 + 43084/763*a^11 - 231375/763*a^10 - 38387/763*a^9 + 714493/763*a^8 - 34675/109*a^7 - 994351/763*a^6 + 573663/763*a^5 + 533431/763*a^4 - 41564/109*a^3 - 154815/763*a^2 + 48529/763*a + 19197/763)*q^18 + (-5161/763*a^15 + 27633/763*a^14 + 51654/763*a^13 - 486399/763*a^12 + 123663/763*a^11 + 3127863/763*a^10 - 3120993/763*a^9 - 8782273/763*a^8 + 1831851/109*a^7 + 9580635/763*a^6 - 19581155/763*a^5 - 1649098/763*a^4 + 1355256/109*a^3 + 456333/763*a^2 - 1725498/763*a - 336262/763)*q^19 + (865/109*a^15 - 4430/109*a^14 - 9359/109*a^13 + 78504/109*a^12 - 8328/109*a^11 - 510909/109*a^10 + 442644/109*a^9 + 1470725/109*a^8 - 1918401/109*a^7 - 1722300/109*a^6 + 3013499/109*a^5 + 496078/109*a^4 - 1519295/109*a^3 - 151066/109*a^2 + 281255/109*a + 61227/109)*q^20 + (-2050/763*a^15 + 11219/763*a^14 + 20338/763*a^13 - 198343/763*a^12 + 52125/763*a^11 + 1285079/763*a^10 - 1258281/763*a^9 - 3663781/763*a^8 + 735221/109*a^7 + 4175545/763*a^6 - 7851743/763*a^5 - 1027273/763*a^4 + 545412/109*a^3 + 323815/763*a^2 - 696942/763*a - 146512/763)*q^21 + (-2306/763*a^15 + 12256/763*a^14 + 23378/763*a^13 - 216369/763*a^12 + 50874/763*a^11 + 1399201/763*a^10 - 1376324/763*a^9 - 3978171/763*a^8 + 819693/109*a^7 + 4512653/763*a^6 - 8952057/763*a^5 - 1096852/763*a^4 + 657741/109*a^3 + 375649/763*a^2 - 896004/763*a - 195777/763)*q^22 + (4806/763*a^15 - 25733/763*a^14 - 49632/763*a^13 + 458046/763*a^12 - 91030/763*a^11 - 3003925/763*a^10 + 2783727/763*a^9 + 8782661/763*a^8 - 1684359/109*a^7 - 10728587/763*a^6 + 18698377/763*a^5 + 3857405/763*a^4 - 1423894/109*a^3 - 1364271/763*a^2 + 1967073/763*a + 474459/763)*q^23 + (6996/763*a^15 - 37841/763*a^14 - 70488/763*a^13 + 669752/763*a^12 - 160151/763*a^11 - 4348434/763*a^10 + 4192746/763*a^9 + 12453876/763*a^8 - 2477534/109*a^7 - 14384382/763*a^6 + 26729796/763*a^5 + 3866892/763*a^4 - 1896109/109*a^3 - 1256606/763*a^2 + 2436704/763*a + 530685/763)*q^24 + (-10230/763*a^15 + 54333/763*a^14 + 105649/763*a^13 - 962338/763*a^12 + 188655/763*a^11 + 6256893/763*a^10 - 5834743/763*a^9 - 17975910/763*a^8 + 3500215/109*a^7 + 20951103/763*a^6 - 38052359/763*a^5 - 5938815/763*a^4 + 2725589/109*a^3 + 1931742/763*a^2 - 3529173/763*a - 780011/763)*q^25 + (2083/763*a^15 - 10235/763*a^14 - 24068/763*a^13 + 182456/763*a^12 + 7285/763*a^11 - 1199843/763*a^10 + 885509/763*a^9 + 3526809/763*a^8 - 583717/109*a^7 - 4359595/763*a^6 + 6590477/763*a^5 + 1611112/763*a^4 - 488396/109*a^3 - 493737/763*a^2 + 640097/763*a + 150660/763)*q^26 + (-5756/763*a^15 + 29313/763*a^14 + 64156/763*a^13 - 523926/763*a^12 + 24221/763*a^11 + 3460174/763*a^10 - 2766296/763*a^9 - 10254030/763*a^8 + 1769958/109*a^7 + 12933586/763*a^6 - 20054838/763*a^5 - 5194234/763*a^4 + 1542871/109*a^3 + 1693618/763*a^2 - 2092578/763*a - 512207/763)*q^27 + (-1343/109*a^15 + 6953/109*a^14 + 14354/109*a^13 - 123268/109*a^12 + 16130/109*a^11 + 802873/109*a^10 - 708961/109*a^9 - 2315220/109*a^8 + 3046872/109*a^7 + 2725917/109*a^6 - 4779007/109*a^5 - 814898/109*a^4 + 2420080/109*a^3 + 262403/109*a^2 - 452829/109*a - 101743/109)*q^28 + (-1888/109*a^15 + 10114/109*a^14 + 19041/109*a^13 - 178640/109*a^12 + 43162/109*a^11 + 1155815/109*a^10 - 1133843/109*a^9 - 3287391/109*a^8 + 4701383/109*a^7 + 3725665/109*a^6 - 7280339/109*a^5 - 887819/109*a^4 + 3667367/109*a^3 + 287364/109*a^2 - 692847/109*a - 147741/109)*q^29 + (-2921/763*a^15 + 14172/763*a^14 + 34210/763*a^13 - 252753/763*a^12 - 18563/763*a^11 + 1663484/763*a^10 - 1184534/763*a^9 - 4897924/763*a^8 + 792208/109*a^7 + 6081580/763*a^6 - 8956548/763*a^5 - 2289885/763*a^4 + 656404/109*a^3 + 698260/763*a^2 - 834069/763*a - 197613/763)*q^30 + (-647/109*a^15 + 3449/109*a^14 + 6743/109*a^13 - 61391/109*a^12 + 11053/109*a^11 + 402563/109*a^10 - 365690/109*a^9 - 1176425/109*a^8 + 1554123/109*a^7 + 1433995/109*a^6 - 2456291/109*a^5 - 506978/109*a^4 + 1288760/109*a^3 + 171449/109*a^2 - 246702/109*a - 58720/109)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2112/763*a^15 - 11798/763*a^14 - 19739/763*a^13 + 207847/763*a^12 - 76852/763*a^11 - 1338648/763*a^10 + 1465036/763*a^9 + 3771408/763*a^8 - 841428/109*a^7 - 4161408/763*a^6 + 9088654/763*a^5 + 822574/763*a^4 - 669338/109*a^3 - 303643/763*a^2 + 920845/763*a + 199854/763)*q^33 + (1707/763*a^15 - 8545/763*a^14 - 19603/763*a^13 + 152976/763*a^12 + 3707/763*a^11 - 1013199/763*a^10 + 742248/763*a^9 + 3019984/763*a^8 - 486926/109*a^7 - 3865326/763*a^6 + 5510446/763*a^5 + 1639367/763*a^4 - 412258/109*a^3 - 535537/763*a^2 + 534612/763*a + 135837/763)*q^34 + (9169/763*a^15 - 48375/763*a^14 - 96197/763*a^13 + 858891/763*a^12 - 143300/763*a^11 - 5607628/763*a^10 + 5071608/763*a^9 + 16244993/763*a^8 - 3080273/109*a^7 - 19351503/763*a^6 + 33813791/763*a^5 + 6129860/763*a^4 - 2469550/109*a^3 - 1988751/763*a^2 + 3232657/763*a + 732195/763)*q^35 + (333/109*a^15 - 1466/109*a^14 - 4295/109*a^13 + 26264/109*a^12 + 9147/109*a^11 - 174331/109*a^10 + 88777/109*a^9 + 522603/109*a^8 - 495591/109*a^7 - 680121/109*a^6 + 850641/109*a^5 + 307426/109*a^4 - 464933/109*a^3 - 103479/109*a^2 + 93165/109*a + 25408/109)*q^36 + (13014/763*a^15 - 68567/763*a^14 - 136420/763*a^13 + 1216931/763*a^12 - 206238/763*a^11 - 7940319/763*a^10 + 7225376/763*a^9 + 22976028/763*a^8 - 4390072/109*a^7 - 27292612/763*a^6 + 48299044/763*a^5 + 8542042/763*a^4 - 3555707/109*a^3 - 2811128/763*a^2 + 4741176/763*a + 1077998/763)*q^37 + O(q^38)
*]> ;  // time = 3.97 seconds




J[273] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 273, 273, 273, 273, 273, 91, 91, 91, 91, 39, 39, 21 ], new_dimensions := [ 1, 1, 2, 3, 4, 1, 1, 2, 3, 1, 2, 1 ], dimensions := [ 1, 1, 2, 3, 4, 2, 2, 4, 6, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 3, 1, 1, 0, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ -2, -1, -1, 1, -2, 1, -4, 3, -9, -1, -5, -8 ],
[ 2, 1, 1, -1, -2, -1, 0, 1, 3, -5, 9, 0 ],
[ 2, -2, 0, 2, 4, -2, 4, 0, 8, 4, -8, -4 ],
[ -2, -3, -3, -3, -2, -3, -8, -7, -9, -1, -7, 12 ],
[ 1, 4, -3, 4, -2, 4, -2, 7, 3, 1, 3, 10 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2*x - 1,
x^3 + 2*x^2 - 3*x - 2,
x^4 - x^3 - 7*x^2 + 5*x + 6
], atkin_lehners := [
[ 1, -1, -1 ],
[ -1, 1, 1 ],
[ 1, -1, 1 ],
[ 1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 1, 7, 3 ],
[ 7, 1, 1 ],
[ 1, 1, 1 ],
[ 9, 1, 1 ]
], tamagawa_numbers := [
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 9, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1, 0, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1/9 ], eigenvalues := [*
[ -2, -1, -1, 1, -2, 1, -4, 3, -9, -1, -5, -8 ],
[ 2, 1, 1, -1, -2, -1, 0, 1, 3, -5, 9, 0 ],
[
a,
-1,
0,
1,
2,
-1,
-2*a + 4,
-4*a + 4,
-2*a + 6,
-4*a + 6,
4*a - 8,
-4*a + 2
],
[
a,
-1,
-a^2 - 2*a + 1,
-1,
2*a^2 + 2*a - 6,
-1,
-2*a - 4,
a^2 + 4*a - 3,
a^2 + 2*a - 5,
a^2 + 4*a - 1,
-3*a^2 - 4*a + 5,
-2*a^2 - 4*a + 8
],
[
a,
1,
-a^2 + 3,
1,
-a^3 + 5*a,
1,
-2*a,
a^3 - a^2 - 5*a + 5,
a^3 + a^2 - 7*a - 3,
-a^3 + a^2 + 5*a - 3,
a^3 - a^2 - 9*a + 5,
-2*a^3 + 2*a^2 + 10*a - 4
]
*], q_expansions := [*
q - 2*q^2 - q^3 + 2*q^4 - q^5 + 2*q^6 + q^7 + q^9 + 2*q^10 - 2*q^11 - 2*q^12 + q^13 - 2*q^14 + q^15 - 4*q^16 - 4*q^17 - 2*q^18 + 3*q^19 - 2*q^20 - q^21 + 4*q^22 - 9*q^23 - 4*q^25 - 2*q^26 - q^27 + 2*q^28 - q^29 - 2*q^30 - 5*q^31 + 8*q^32 + 2*q^33 + 8*q^34 - q^35 + 2*q^36 - 8*q^37 + O(q^38),
q + 2*q^2 + q^3 + 2*q^4 + q^5 + 2*q^6 - q^7 + q^9 + 2*q^10 - 2*q^11 + 2*q^12 - q^13 - 2*q^14 + q^15 - 4*q^16 + 2*q^18 + q^19 + 2*q^20 - q^21 - 4*q^22 + 3*q^23 - 4*q^25 - 2*q^26 + q^27 - 2*q^28 - 5*q^29 + 2*q^30 + 9*q^31 - 8*q^32 - 2*q^33 - q^35 + 2*q^36 + O(q^38),
q + a*q^2 - q^3 + (2*a - 1)*q^4 - a*q^6 + q^7 + (a + 2)*q^8 + q^9 + 2*q^11 + (-2*a + 1)*q^12 - q^13 + a*q^14 + 3*q^16 + (-2*a + 4)*q^17 + a*q^18 + (-4*a + 4)*q^19 - q^21 + 2*a*q^22 + (-2*a + 6)*q^23 + (-a - 2)*q^24 - 5*q^25 - a*q^26 - q^27 + (2*a - 1)*q^28 + (-4*a + 6)*q^29 + (4*a - 8)*q^31 + (a - 4)*q^32 - 2*q^33 - 2*q^34 + (2*a - 1)*q^36 + (-4*a + 2)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a + 1)*q^5 - a*q^6 - q^7 + (-2*a^2 - a + 2)*q^8 + q^9 + (-2*a - 2)*q^10 + (2*a^2 + 2*a - 6)*q^11 + (-a^2 + 2)*q^12 - q^13 - a*q^14 + (a^2 + 2*a - 1)*q^15 + (a^2 - 4*a)*q^16 + (-2*a - 4)*q^17 + a*q^18 + (a^2 + 4*a - 3)*q^19 + (2*a - 2)*q^20 + q^21 + (-2*a^2 + 4)*q^22 + (a^2 + 2*a - 5)*q^23 + (2*a^2 + a - 2)*q^24 + (a^2 + 4*a)*q^25 - a*q^26 - q^27 + (-a^2 + 2)*q^28 + (a^2 + 4*a - 1)*q^29 + (2*a + 2)*q^30 + (-3*a^2 - 4*a + 5)*q^31 + (-2*a^2 + 5*a - 2)*q^32 + (-2*a^2 - 2*a + 6)*q^33 + (-2*a^2 - 4*a)*q^34 + (a^2 + 2*a - 1)*q^35 + (a^2 - 2)*q^36 + (-2*a^2 - 4*a + 8)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^2 + 3)*q^5 + a*q^6 + q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^3 + 3*a)*q^10 + (-a^3 + 5*a)*q^11 + (a^2 - 2)*q^12 + q^13 + a*q^14 + (-a^2 + 3)*q^15 + (a^3 + a^2 - 5*a - 2)*q^16 - 2*a*q^17 + a*q^18 + (a^3 - a^2 - 5*a + 5)*q^19 + (-a^3 - 2*a^2 + 5*a)*q^20 + q^21 + (-a^3 - 2*a^2 + 5*a + 6)*q^22 + (a^3 + a^2 - 7*a - 3)*q^23 + (a^3 - 4*a)*q^24 + (a^3 + a^2 - 5*a - 2)*q^25 + a*q^26 + q^27 + (a^2 - 2)*q^28 + (-a^3 + a^2 + 5*a - 3)*q^29 + (-a^3 + 3*a)*q^30 + (a^3 - a^2 - 9*a + 5)*q^31 + (2*a^2 + a - 6)*q^32 + (-a^3 + 5*a)*q^33 - 2*a^2*q^34 + (-a^2 + 3)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 + 2*a^2 + 10*a - 4)*q^37 + O(q^38)
*]> ;  // time = 74.71 seconds




J[274] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 274, 274, 274, 274, 274, 137, 137 ], new_dimensions := [ 1, 1, 1, 3, 5, 4, 7 ], dimensions := [ 1, 1, 1, 3, 5, 8, 14 ], intersection_graph := [ 0, 3, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 11, 1, 1, 1, 0, 1, 1, 1, 7, 1, 1, 1, 0, 1, 1, 109, 1, 1, 1, 1, 0, 149, 1, 1, 11, 1, 1, 149, 0, 1, 1, 1, 7, 109, 1, 1, 0 ], ap_traces := [
[ -1, 0, 0, -4, -4, 4, 2, -4, -6, -8, 10, -2 ],
[ -1, 0, -3, 2, -1, -2, -7, -1, 0, 1, -11, 4 ],
[ 1, -2, -3, 0, -3, -6, 1, -3, 0, -3, 7, 10 ],
[ -3, 2, 5, 2, 5, -8, 3, -3, 10, 11, 13, -12 ],
[ 5, 2, 5, -4, -1, 4, 7, -1, -8, -5, -11, 2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^3 - 2*x^2 - 4*x + 4,
x^5 - 2*x^4 - 10*x^3 + 20*x^2 - 8
], atkin_lehners := [
[ 1, 1 ],
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 11, 1 ],
[ 7, 1 ],
[ 109, 1 ],
[ 3427, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 1 ],
[ 1, 1 ],
[ 3427, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 23 ], torsion_lower_bounds := [ 1, 1, 1, 1, 23 ], l_ratios := [ 0, 0, 0, 1, 149/23 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, 0, -4, -4, 4, 2, -4, -6, -8, 10, -2 ],
[ -1, 0, -3, 2, -1, -2, -7, -1, 0, 1, -11, 4 ],
[ 1, -2, -3, 0, -3, -6, 1, -3, 0, -3, 7, 10 ],
[
-1,
a,
-1/2*a^2 + a + 3,
-a^2 + a + 4,
a^2 - 2*a - 1,
a^2 - a - 6,
-2*a^2 + 9,
a^2 - 3*a - 3,
-a + 4,
5/2*a^2 - 2*a - 5,
1/2*a^2 - a + 3,
a^2 - 3*a - 6
],
[
1,
a,
1/2*a^4 - 1/2*a^3 - 11/2*a^2 + 4*a + 5,
-1/2*a^4 + 1/2*a^3 + 5*a^2 - 5*a - 2,
-3/4*a^4 + 1/2*a^3 + 8*a^2 - 5*a - 5,
1/2*a^3 - 5*a + 2,
-1/4*a^4 + 1/2*a^3 + 3*a^2 - 5*a - 1,
1/4*a^4 - a^3 - 2*a^2 + 8*a - 3,
-1/2*a^4 + a^3 + 5*a^2 - 9*a - 2,
a^4 - a^3 - 23/2*a^2 + 9*a + 9,
1/2*a^4 - a^3 - 11/2*a^2 + 8*a + 1,
a^4 - 1/2*a^3 - 11*a^2 + 7*a + 8
]
*], q_expansions := [*
q - q^2 + q^4 - 4*q^7 - q^8 - 3*q^9 - 4*q^11 + 4*q^13 + 4*q^14 + q^16 + 2*q^17 + 3*q^18 - 4*q^19 + 4*q^22 - 6*q^23 - 5*q^25 - 4*q^26 - 4*q^28 - 8*q^29 + 10*q^31 - q^32 - 2*q^34 - 3*q^36 - 2*q^37 + O(q^38),
q - q^2 + q^4 - 3*q^5 + 2*q^7 - q^8 - 3*q^9 + 3*q^10 - q^11 - 2*q^13 - 2*q^14 + q^16 - 7*q^17 + 3*q^18 - q^19 - 3*q^20 + q^22 + 4*q^25 + 2*q^26 + 2*q^28 + q^29 - 11*q^31 - q^32 + 7*q^34 - 6*q^35 - 3*q^36 + 4*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 3*q^5 - 2*q^6 + q^8 + q^9 - 3*q^10 - 3*q^11 - 2*q^12 - 6*q^13 + 6*q^15 + q^16 + q^17 + q^18 - 3*q^19 - 3*q^20 - 3*q^22 - 2*q^24 + 4*q^25 - 6*q^26 + 4*q^27 - 3*q^29 + 6*q^30 + 7*q^31 + q^32 + 6*q^33 + q^34 + q^36 + 10*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a^2 + a + 3)*q^5 - a*q^6 + (-a^2 + a + 4)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^2 - a - 3)*q^10 + (a^2 - 2*a - 1)*q^11 + a*q^12 + (a^2 - a - 6)*q^13 + (a^2 - a - 4)*q^14 + (a + 2)*q^15 + q^16 + (-2*a^2 + 9)*q^17 + (-a^2 + 3)*q^18 + (a^2 - 3*a - 3)*q^19 + (-1/2*a^2 + a + 3)*q^20 + (-a^2 + 4)*q^21 + (-a^2 + 2*a + 1)*q^22 + (-a + 4)*q^23 - a*q^24 + (-2*a^2 + 3*a + 6)*q^25 + (-a^2 + a + 6)*q^26 + (2*a^2 - 2*a - 4)*q^27 + (-a^2 + a + 4)*q^28 + (5/2*a^2 - 2*a - 5)*q^29 + (-a - 2)*q^30 + (1/2*a^2 - a + 3)*q^31 - q^32 + (3*a - 4)*q^33 + (2*a^2 - 9)*q^34 + (-3*a^2 + 3*a + 14)*q^35 + (a^2 - 3)*q^36 + (a^2 - 3*a - 6)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/2*a^4 - 1/2*a^3 - 11/2*a^2 + 4*a + 5)*q^5 + a*q^6 + (-1/2*a^4 + 1/2*a^3 + 5*a^2 - 5*a - 2)*q^7 + q^8 + (a^2 - 3)*q^9 + (1/2*a^4 - 1/2*a^3 - 11/2*a^2 + 4*a + 5)*q^10 + (-3/4*a^4 + 1/2*a^3 + 8*a^2 - 5*a - 5)*q^11 + a*q^12 + (1/2*a^3 - 5*a + 2)*q^13 + (-1/2*a^4 + 1/2*a^3 + 5*a^2 - 5*a - 2)*q^14 + (1/2*a^4 - 1/2*a^3 - 6*a^2 + 5*a + 4)*q^15 + q^16 + (-1/4*a^4 + 1/2*a^3 + 3*a^2 - 5*a - 1)*q^17 + (a^2 - 3)*q^18 + (1/4*a^4 - a^3 - 2*a^2 + 8*a - 3)*q^19 + (1/2*a^4 - 1/2*a^3 - 11/2*a^2 + 4*a + 5)*q^20 + (-1/2*a^4 + 5*a^2 - 2*a - 4)*q^21 + (-3/4*a^4 + 1/2*a^3 + 8*a^2 - 5*a - 5)*q^22 + (-1/2*a^4 + a^3 + 5*a^2 - 9*a - 2)*q^23 + a*q^24 + (7/4*a^4 - 2*a^3 - 19*a^2 + 18*a + 12)*q^25 + (1/2*a^3 - 5*a + 2)*q^26 + (a^3 - 6*a)*q^27 + (-1/2*a^4 + 1/2*a^3 + 5*a^2 - 5*a - 2)*q^28 + (a^4 - a^3 - 23/2*a^2 + 9*a + 9)*q^29 + (1/2*a^4 - 1/2*a^3 - 6*a^2 + 5*a + 4)*q^30 + (1/2*a^4 - a^3 - 11/2*a^2 + 8*a + 1)*q^31 + q^32 + (-a^4 + 1/2*a^3 + 10*a^2 - 5*a - 6)*q^33 + (-1/4*a^4 + 1/2*a^3 + 3*a^2 - 5*a - 1)*q^34 + (-a^4 + 3/2*a^3 + 11*a^2 - 13*a - 8)*q^35 + (a^2 - 3)*q^36 + (a^4 - 1/2*a^3 - 11*a^2 + 7*a + 8)*q^37 + O(q^38)
*]> ;  // time = 62.839 seconds




J[277] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 277, 277, 277, 277 ], new_dimensions := [ 1, 3, 9, 9 ], dimensions := [ 1, 3, 9, 9 ], intersection_graph := [ 0, 1, 5, 1, 1, 0, 1, 137, 5, 1, 0, 1, 1, 137, 1, 0 ], ap_traces := [
[ 1, -2, 2, -4, 1, -5, 2, -6, 0, 5, -3, -4 ],
[ -1, 6, 4, 4, 11, 1, -4, -10, -8, 3, -11, 12 ],
[ -6, -10, -12, -2, -14, -2, -19, 1, -30, -8, 0, 1 ],
[ 4, 6, 4, -2, 2, -2, 15, 13, 26, -4, 12, -25 ]
], hecke_fields := [
x - 1,
x^3 + x^2 - 3*x - 1,
x^9 + 6*x^8 + 4*x^7 - 37*x^6 - 69*x^5 + 24*x^4 + 119*x^3 + 34*x^2 - 52*x - 25,
x^9 - 4*x^8 - 6*x^7 + 37*x^6 - 3*x^5 - 100*x^4 + 49*x^3 + 64*x^2 - 20*x - 1
], atkin_lehners := [
[ 1 ],
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 23 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 23 ]
], torsion_upper_bounds := [ 1, 1, 1, 23 ], torsion_lower_bounds := [ 1, 1, 1, 23 ], l_ratios := [ 0, 1, 0, 1/23 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1 ], eigenvalues := [*
[ 1, -2, 2, -4, 1, -5, 2, -6, 0, 5, -3, -4 ],
[
a,
2,
a^2 - 1,
-a^2 - 2*a + 3,
a + 4,
2*a + 1,
-3*a^2 - 2*a + 5,
-a^2 - 1,
-a^2 - 2*a - 1,
a^2 - 2*a - 2,
3*a^2 + 5*a - 9,
4
],
[
a,
-6*a^8 - 26*a^7 + 19*a^6 + 189*a^5 + 101*a^4 - 302*a^3 - 213*a^2 + 131*a + 95,
8*a^8 + 34*a^7 - 27*a^6 - 247*a^5 - 122*a^4 + 394*a^3 + 260*a^2 - 171*a - 117,
-6*a^8 - 24*a^7 + 25*a^6 + 175*a^5 + 55*a^4 - 281*a^3 - 129*a^2 + 118*a + 58,
5*a^8 + 20*a^7 - 22*a^6 - 149*a^5 - 40*a^4 + 253*a^3 + 111*a^2 - 113*a - 59,
8*a^8 + 34*a^7 - 26*a^6 - 244*a^5 - 127*a^4 + 375*a^3 + 258*a^2 - 152*a - 111,
-7*a^8 - 28*a^7 + 30*a^6 + 208*a^5 + 63*a^4 - 352*a^3 - 170*a^2 + 160*a + 83,
2*a^8 + 7*a^7 - 12*a^6 - 52*a^5 + 10*a^4 + 86*a^3 - 9*a^2 - 32*a + 4,
-7*a^8 - 31*a^7 + 19*a^6 + 222*a^5 + 139*a^4 - 340*a^3 - 273*a^2 + 142*a + 114,
6*a^8 + 25*a^7 - 23*a^6 - 184*a^5 - 70*a^4 + 305*a^3 + 156*a^2 - 139*a - 71,
-10*a^8 - 42*a^7 + 36*a^6 + 304*a^5 + 131*a^4 - 477*a^3 - 269*a^2 + 196*a + 113,
9*a^8 + 38*a^7 - 33*a^6 - 280*a^5 - 119*a^4 + 463*a^3 + 267*a^2 - 205*a - 119
],
[
a,
2*a^8 - 4*a^7 - 19*a^6 + 33*a^5 + 55*a^4 - 74*a^3 - 43*a^2 + 27*a + 1,
-2*a^8 + 4*a^7 + 19*a^6 - 33*a^5 - 54*a^4 + 72*a^3 + 38*a^2 - 19*a + 3,
-2*a^8 + 4*a^7 + 19*a^6 - 33*a^5 - 55*a^4 + 73*a^3 + 43*a^2 - 22*a,
-a^8 + 2*a^7 + 10*a^6 - 19*a^5 - 28*a^4 + 51*a^3 + 15*a^2 - 29*a + 1,
-2*a^8 + 4*a^7 + 20*a^6 - 36*a^5 - 59*a^4 + 89*a^3 + 42*a^2 - 38*a + 1,
a^8 - 2*a^7 - 10*a^6 + 18*a^5 + 29*a^4 - 44*a^3 - 18*a^2 + 16*a - 1,
2*a^8 - 3*a^7 - 22*a^6 + 26*a^5 + 76*a^4 - 58*a^3 - 79*a^2 + 10*a + 6,
a^8 - a^7 - 11*a^6 + 8*a^5 + 37*a^4 - 16*a^3 - 35*a^2 + 4,
2*a^8 - 3*a^7 - 21*a^6 + 26*a^5 + 64*a^4 - 57*a^3 - 44*a^2 + 7*a - 5,
2*a^5 - 3*a^4 - 11*a^3 + 11*a^2 + 10*a + 3,
3*a^8 - 6*a^7 - 29*a^6 + 52*a^5 + 83*a^4 - 123*a^3 - 57*a^2 + 45*a - 7
]
*], q_expansions := [*
q + q^2 - 2*q^3 - q^4 + 2*q^5 - 2*q^6 - 4*q^7 - 3*q^8 + q^9 + 2*q^10 + q^11 + 2*q^12 - 5*q^13 - 4*q^14 - 4*q^15 - q^16 + 2*q^17 + q^18 - 6*q^19 - 2*q^20 + 8*q^21 + q^22 + 6*q^24 - q^25 - 5*q^26 + 4*q^27 + 4*q^28 + 5*q^29 - 4*q^30 - 3*q^31 + 5*q^32 - 2*q^33 + 2*q^34 - 8*q^35 - q^36 - 4*q^37 + O(q^38),
q + a*q^2 + 2*q^3 + (a^2 - 2)*q^4 + (a^2 - 1)*q^5 + 2*a*q^6 + (-a^2 - 2*a + 3)*q^7 + (-a^2 - a + 1)*q^8 + q^9 + (-a^2 + 2*a + 1)*q^10 + (a + 4)*q^11 + (2*a^2 - 4)*q^12 + (2*a + 1)*q^13 + (-a^2 - 1)*q^14 + (2*a^2 - 2)*q^15 + (-2*a^2 - 2*a + 3)*q^16 + (-3*a^2 - 2*a + 5)*q^17 + a*q^18 + (-a^2 - 1)*q^19 + (a^2 - 2*a + 1)*q^20 + (-2*a^2 - 4*a + 6)*q^21 + (a^2 + 4*a)*q^22 + (-a^2 - 2*a - 1)*q^23 + (-2*a^2 - 2*a + 2)*q^24 + (2*a^2 - 2*a - 5)*q^25 + (2*a^2 + a)*q^26 - 4*q^27 + (3*a^2 - 7)*q^28 + (a^2 - 2*a - 2)*q^29 + (-2*a^2 + 4*a + 2)*q^30 + (3*a^2 + 5*a - 9)*q^31 + (2*a^2 - a - 4)*q^32 + (2*a + 8)*q^33 + (a^2 - 4*a - 3)*q^34 + (2*a^2 - 2*a - 4)*q^35 + (a^2 - 2)*q^36 + 4*q^37 + O(q^38),
q + a*q^2 + (-6*a^8 - 26*a^7 + 19*a^6 + 189*a^5 + 101*a^4 - 302*a^3 - 213*a^2 + 131*a + 95)*q^3 + (a^2 - 2)*q^4 + (8*a^8 + 34*a^7 - 27*a^6 - 247*a^5 - 122*a^4 + 394*a^3 + 260*a^2 - 171*a - 117)*q^5 + (10*a^8 + 43*a^7 - 33*a^6 - 313*a^5 - 158*a^4 + 501*a^3 + 335*a^2 - 217*a - 150)*q^6 + (-6*a^8 - 24*a^7 + 25*a^6 + 175*a^5 + 55*a^4 - 281*a^3 - 129*a^2 + 118*a + 58)*q^7 + (a^3 - 4*a)*q^8 + (10*a^8 + 43*a^7 - 33*a^6 - 313*a^5 - 158*a^4 + 502*a^3 + 337*a^2 - 219*a - 153)*q^9 + (-14*a^8 - 59*a^7 + 49*a^6 + 430*a^5 + 202*a^4 - 692*a^3 - 443*a^2 + 299*a + 200)*q^10 + (5*a^8 + 20*a^7 - 22*a^6 - 149*a^5 - 40*a^4 + 253*a^3 + 111*a^2 - 113*a - 59)*q^11 + (-5*a^8 - 21*a^7 + 19*a^6 + 154*a^5 + 59*a^4 - 251*a^3 - 131*a^2 + 108*a + 60)*q^12 + (8*a^8 + 34*a^7 - 26*a^6 - 244*a^5 - 127*a^4 + 375*a^3 + 258*a^2 - 152*a - 111)*q^13 + (12*a^8 + 49*a^7 - 47*a^6 - 359*a^5 - 137*a^4 + 585*a^3 + 322*a^2 - 254*a - 150)*q^14 + (-6*a^8 - 25*a^7 + 21*a^6 + 181*a^5 + 87*a^4 - 286*a^3 - 190*a^2 + 124*a + 85)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-7*a^8 - 28*a^7 + 30*a^6 + 208*a^5 + 63*a^4 - 352*a^3 - 170*a^2 + 160*a + 83)*q^17 + (-17*a^8 - 73*a^7 + 57*a^6 + 532*a^5 + 262*a^4 - 853*a^3 - 559*a^2 + 367*a + 250)*q^18 + (2*a^8 + 7*a^7 - 12*a^6 - 52*a^5 + 10*a^4 + 86*a^3 - 9*a^2 - 32*a + 4)*q^19 + (9*a^8 + 37*a^7 - 34*a^6 - 270*a^5 - 112*a^4 + 435*a^3 + 255*a^2 - 186*a - 116)*q^20 + (11*a^8 + 45*a^7 - 42*a^6 - 327*a^5 - 132*a^4 + 521*a^3 + 301*a^2 - 219*a - 140)*q^21 + (-10*a^8 - 42*a^7 + 36*a^6 + 305*a^5 + 133*a^4 - 484*a^3 - 283*a^2 + 201*a + 125)*q^22 + (-7*a^8 - 31*a^7 + 19*a^6 + 222*a^5 + 139*a^4 - 340*a^3 - 273*a^2 + 142*a + 114)*q^23 + (-11*a^8 - 47*a^7 + 35*a^6 + 340*a^5 + 185*a^4 - 538*a^3 - 392*a^2 + 234*a + 175)*q^24 + (-5*a^8 - 21*a^7 + 17*a^6 + 151*a^5 + 73*a^4 - 234*a^3 - 145*a^2 + 99*a + 59)*q^25 + (-14*a^8 - 58*a^7 + 52*a^6 + 425*a^5 + 183*a^4 - 694*a^3 - 424*a^2 + 305*a + 200)*q^26 + (-6*a^8 - 24*a^7 + 26*a^6 + 176*a^5 + 47*a^4 - 287*a^3 - 117*a^2 + 124*a + 55)*q^27 + (-11*a^8 - 47*a^7 + 35*a^6 + 341*a^5 + 187*a^4 - 544*a^3 - 404*a^2 + 238*a + 184)*q^28 + (6*a^8 + 25*a^7 - 23*a^6 - 184*a^5 - 70*a^4 + 305*a^3 + 156*a^2 - 139*a - 71)*q^29 + (11*a^8 + 45*a^7 - 41*a^6 - 327*a^5 - 142*a^4 + 524*a^3 + 328*a^2 - 227*a - 150)*q^30 + (-10*a^8 - 42*a^7 + 36*a^6 + 304*a^5 + 131*a^4 - 477*a^3 - 269*a^2 + 196*a + 113)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3*a^8 + 15*a^7 - 2*a^6 - 106*a^5 - 106*a^4 + 159*a^3 + 197*a^2 - 72*a - 80)*q^33 + (14*a^8 + 58*a^7 - 51*a^6 - 420*a^5 - 184*a^4 + 663*a^3 + 398*a^2 - 281*a - 175)*q^34 + (-3*a^8 - 12*a^7 + 14*a^6 + 91*a^5 + 20*a^4 - 160*a^3 - 69*a^2 + 72*a + 39)*q^35 + (9*a^8 + 39*a^7 - 31*a^6 - 285*a^5 - 129*a^4 + 460*a^3 + 271*a^2 - 196*a - 119)*q^36 + (9*a^8 + 38*a^7 - 33*a^6 - 280*a^5 - 119*a^4 + 463*a^3 + 267*a^2 - 205*a - 119)*q^37 + O(q^38),
q + a*q^2 + (2*a^8 - 4*a^7 - 19*a^6 + 33*a^5 + 55*a^4 - 74*a^3 - 43*a^2 + 27*a + 1)*q^3 + (a^2 - 2)*q^4 + (-2*a^8 + 4*a^7 + 19*a^6 - 33*a^5 - 54*a^4 + 72*a^3 + 38*a^2 - 19*a + 3)*q^5 + (4*a^8 - 7*a^7 - 41*a^6 + 61*a^5 + 126*a^4 - 141*a^3 - 101*a^2 + 41*a + 2)*q^6 + (-2*a^8 + 4*a^7 + 19*a^6 - 33*a^5 - 55*a^4 + 73*a^3 + 43*a^2 - 22*a)*q^7 + (a^3 - 4*a)*q^8 + (2*a^8 - 5*a^7 - 17*a^6 + 41*a^5 + 42*a^4 - 94*a^3 - 23*a^2 + 43*a - 1)*q^9 + (-4*a^8 + 7*a^7 + 41*a^6 - 60*a^5 - 128*a^4 + 136*a^3 + 109*a^2 - 37*a - 2)*q^10 + (-a^8 + 2*a^7 + 10*a^6 - 19*a^5 - 28*a^4 + 51*a^3 + 15*a^2 - 29*a + 1)*q^11 + (5*a^8 - 9*a^7 - 49*a^6 + 72*a^5 + 149*a^4 - 149*a^3 - 129*a^2 + 28*a + 2)*q^12 + (-2*a^8 + 4*a^7 + 20*a^6 - 36*a^5 - 59*a^4 + 89*a^3 + 42*a^2 - 38*a + 1)*q^13 + (-4*a^8 + 7*a^7 + 41*a^6 - 61*a^5 - 127*a^4 + 141*a^3 + 106*a^2 - 40*a - 2)*q^14 + (-2*a^8 + 3*a^7 + 21*a^6 - 23*a^5 - 71*a^4 + 42*a^3 + 74*a^2 + 4*a - 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^8 - 2*a^7 - 10*a^6 + 18*a^5 + 29*a^4 - 44*a^3 - 18*a^2 + 16*a - 1)*q^17 + (3*a^8 - 5*a^7 - 33*a^6 + 48*a^5 + 106*a^4 - 121*a^3 - 85*a^2 + 39*a + 2)*q^18 + (2*a^8 - 3*a^7 - 22*a^6 + 26*a^5 + 76*a^4 - 58*a^3 - 79*a^2 + 10*a + 6)*q^19 + (-5*a^8 + 9*a^7 + 50*a^6 - 74*a^5 - 156*a^4 + 161*a^3 + 143*a^2 - 44*a - 10)*q^20 + (a^8 - a^7 - 12*a^6 + 11*a^5 + 40*a^4 - 29*a^3 - 31*a^2 + 5*a)*q^21 + (-2*a^8 + 4*a^7 + 18*a^6 - 31*a^5 - 49*a^4 + 64*a^3 + 35*a^2 - 19*a - 1)*q^22 + (a^8 - a^7 - 11*a^6 + 8*a^5 + 37*a^4 - 16*a^3 - 35*a^2 + 4)*q^23 + (3*a^8 - 5*a^7 - 31*a^6 + 42*a^5 + 99*a^4 - 92*a^3 - 90*a^2 + 20*a + 1)*q^24 + (3*a^8 - 5*a^7 - 31*a^6 + 41*a^5 + 101*a^4 - 86*a^3 - 101*a^2 + 13*a + 11)*q^25 + (-4*a^8 + 8*a^7 + 38*a^6 - 65*a^5 - 111*a^4 + 140*a^3 + 90*a^2 - 39*a - 2)*q^26 + (-2*a^7 + 4*a^6 + 16*a^5 - 25*a^4 - 41*a^3 + 35*a^2 + 34*a + 3)*q^27 + (-5*a^8 + 9*a^7 + 49*a^6 - 73*a^5 - 149*a^4 + 156*a^3 + 130*a^2 - 38*a - 4)*q^28 + (2*a^8 - 3*a^7 - 21*a^6 + 26*a^5 + 64*a^4 - 57*a^3 - 44*a^2 + 7*a - 5)*q^29 + (-5*a^8 + 9*a^7 + 51*a^6 - 77*a^5 - 158*a^4 + 172*a^3 + 132*a^2 - 41*a - 2)*q^30 + (2*a^5 - 3*a^4 - 11*a^3 + 11*a^2 + 10*a + 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^8 - a^7 - 10*a^6 + 2*a^5 + 38*a^4 + 17*a^3 - 55*a^2 - 34*a - 2)*q^33 + (2*a^8 - 4*a^7 - 19*a^6 + 32*a^5 + 56*a^4 - 67*a^3 - 48*a^2 + 19*a + 1)*q^34 + (-a^8 + 2*a^7 + 10*a^6 - 19*a^5 - 28*a^4 + 50*a^3 + 15*a^2 - 24*a + 3)*q^35 + (3*a^8 - 5*a^7 - 29*a^6 + 33*a^5 + 95*a^4 - 44*a^3 - 107*a^2 - 24*a + 5)*q^36 + (3*a^8 - 6*a^7 - 29*a^6 + 52*a^5 + 83*a^4 - 123*a^3 - 57*a^2 + 45*a - 7)*q^37 + O(q^38)
*]> ;  // time = 3.71 seconds




J[278] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 278, 278, 278, 278, 278, 139, 139, 139 ], new_dimensions := [ 1, 1, 2, 3, 5, 1, 3, 7 ], dimensions := [ 1, 1, 2, 3, 5, 2, 6, 14 ], intersection_graph := [ 0, 1, 1, 17, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 1, 17, 1, 1, 0, 1, 1, 1, 271, 1, 1, 1, 1, 0, 1, 41, 1, 1, 1, 1, 1, 1, 0, 1, 9, 1, 1, 7, 1, 41, 1, 0, 1, 1, 1, 1, 271, 1, 9, 1, 0 ], ap_traces := [
[ -1, -2, 3, -1, -3, 5, 6, 2, 6, -3, 5, 2 ],
[ 1, -2, -1, -5, -3, 1, 2, -2, -6, 1, 9, -6 ],
[ -2, 0, -2, -6, 2, -10, 0, 0, 4, -6, -6, -8 ],
[ -3, 3, 0, 9, 0, 0, 0, 9, -6, 6, -3, 12 ],
[ 5, 1, -2, 7, 6, 2, 0, -1, -2, -20, 3, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2,
x^3 - 3*x^2 + 3,
x^5 - x^4 - 10*x^3 + 11*x^2 + 12*x - 2
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 3 ],
[ 1, 1 ],
[ 7, 1 ],
[ 271, 1 ],
[ 1435, 1 ]
], tamagawa_numbers := [
[ 1, 3 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1435, 1 ]
], torsion_upper_bounds := [ 3, 1, 1, 1, 35 ], torsion_lower_bounds := [ 3, 1, 1, 1, 35 ], l_ratios := [ 1/3, 0, 0, 1, 41/35 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, -2, 3, -1, -3, 5, 6, 2, 6, -3, 5, 2 ],
[ 1, -2, -1, -5, -3, 1, 2, -2, -6, 1, 9, -6 ],
[
-1,
a,
-a - 1,
-a - 3,
-2*a + 1,
-a - 5,
5*a,
a,
3*a + 2,
3*a - 3,
a - 3,
2*a - 4
],
[
-1,
a,
-2*a^2 + 4*a + 2,
-a^2 + a + 5,
2*a^2 - 4*a - 2,
4*a^2 - 6*a - 6,
-2*a + 2,
-a^2 + 6,
2*a^2 - 2*a - 6,
-4*a + 6,
5*a^2 - 6*a - 10,
-2*a^2 + 10
],
[
1,
a,
1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 11/5*a + 9/5,
-2/5*a^4 - 4/5*a^3 + 13/5*a^2 + 17/5*a + 7/5,
a^3 + a^2 - 8*a - 1,
3/5*a^4 - 4/5*a^3 - 27/5*a^2 + 37/5*a + 17/5,
-7/5*a^4 + 1/5*a^3 + 58/5*a^2 - 33/5*a - 28/5,
3/5*a^4 + 1/5*a^3 - 27/5*a^2 + 7/5*a + 22/5,
3/5*a^4 + 1/5*a^3 - 22/5*a^2 - 3/5*a + 2/5,
a^4 - 9*a^2 + 5*a + 3,
-3/5*a^4 - 6/5*a^3 + 22/5*a^2 + 23/5*a - 7/5,
2/5*a^4 + 4/5*a^3 - 8/5*a^2 - 22/5*a - 12/5
]
*], q_expansions := [*
q - q^2 - 2*q^3 + q^4 + 3*q^5 + 2*q^6 - q^7 - q^8 + q^9 - 3*q^10 - 3*q^11 - 2*q^12 + 5*q^13 + q^14 - 6*q^15 + q^16 + 6*q^17 - q^18 + 2*q^19 + 3*q^20 + 2*q^21 + 3*q^22 + 6*q^23 + 2*q^24 + 4*q^25 - 5*q^26 + 4*q^27 - q^28 - 3*q^29 + 6*q^30 + 5*q^31 - q^32 + 6*q^33 - 6*q^34 - 3*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - q^5 - 2*q^6 - 5*q^7 + q^8 + q^9 - q^10 - 3*q^11 - 2*q^12 + q^13 - 5*q^14 + 2*q^15 + q^16 + 2*q^17 + q^18 - 2*q^19 - q^20 + 10*q^21 - 3*q^22 - 6*q^23 - 2*q^24 - 4*q^25 + q^26 + 4*q^27 - 5*q^28 + q^29 + 2*q^30 + 9*q^31 + q^32 + 6*q^33 + 2*q^34 + 5*q^35 + q^36 - 6*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 1)*q^5 - a*q^6 + (-a - 3)*q^7 - q^8 - q^9 + (a + 1)*q^10 + (-2*a + 1)*q^11 + a*q^12 + (-a - 5)*q^13 + (a + 3)*q^14 + (-a - 2)*q^15 + q^16 + 5*a*q^17 + q^18 + a*q^19 + (-a - 1)*q^20 + (-3*a - 2)*q^21 + (2*a - 1)*q^22 + (3*a + 2)*q^23 - a*q^24 + (2*a - 2)*q^25 + (a + 5)*q^26 - 4*a*q^27 + (-a - 3)*q^28 + (3*a - 3)*q^29 + (a + 2)*q^30 + (a - 3)*q^31 - q^32 + (a - 4)*q^33 - 5*a*q^34 + (4*a + 5)*q^35 - q^36 + (2*a - 4)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-2*a^2 + 4*a + 2)*q^5 - a*q^6 + (-a^2 + a + 5)*q^7 - q^8 + (a^2 - 3)*q^9 + (2*a^2 - 4*a - 2)*q^10 + (2*a^2 - 4*a - 2)*q^11 + a*q^12 + (4*a^2 - 6*a - 6)*q^13 + (a^2 - a - 5)*q^14 + (-2*a^2 + 2*a + 6)*q^15 + q^16 + (-2*a + 2)*q^17 + (-a^2 + 3)*q^18 + (-a^2 + 6)*q^19 + (-2*a^2 + 4*a + 2)*q^20 + (-2*a^2 + 5*a + 3)*q^21 + (-2*a^2 + 4*a + 2)*q^22 + (2*a^2 - 2*a - 6)*q^23 - a*q^24 + (-4*a^2 + 4*a + 11)*q^25 + (-4*a^2 + 6*a + 6)*q^26 + (3*a^2 - 6*a - 3)*q^27 + (-a^2 + a + 5)*q^28 + (-4*a + 6)*q^29 + (2*a^2 - 2*a - 6)*q^30 + (5*a^2 - 6*a - 10)*q^31 - q^32 + (2*a^2 - 2*a - 6)*q^33 + (2*a - 2)*q^34 + (-8*a^2 + 16*a + 10)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 + 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 11/5*a + 9/5)*q^5 + a*q^6 + (-2/5*a^4 - 4/5*a^3 + 13/5*a^2 + 17/5*a + 7/5)*q^7 + q^8 + (a^2 - 3)*q^9 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 11/5*a + 9/5)*q^10 + (a^3 + a^2 - 8*a - 1)*q^11 + a*q^12 + (3/5*a^4 - 4/5*a^3 - 27/5*a^2 + 37/5*a + 17/5)*q^13 + (-2/5*a^4 - 4/5*a^3 + 13/5*a^2 + 17/5*a + 7/5)*q^14 + (3/5*a^4 + 1/5*a^3 - 22/5*a^2 - 3/5*a + 2/5)*q^15 + q^16 + (-7/5*a^4 + 1/5*a^3 + 58/5*a^2 - 33/5*a - 28/5)*q^17 + (a^2 - 3)*q^18 + (3/5*a^4 + 1/5*a^3 - 27/5*a^2 + 7/5*a + 22/5)*q^19 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 11/5*a + 9/5)*q^20 + (-6/5*a^4 - 7/5*a^3 + 39/5*a^2 + 31/5*a - 4/5)*q^21 + (a^3 + a^2 - 8*a - 1)*q^22 + (3/5*a^4 + 1/5*a^3 - 22/5*a^2 - 3/5*a + 2/5)*q^23 + a*q^24 + (-4/5*a^4 - 3/5*a^3 + 31/5*a^2 + 4/5*a - 16/5)*q^25 + (3/5*a^4 - 4/5*a^3 - 27/5*a^2 + 37/5*a + 17/5)*q^26 + (a^3 - 6*a)*q^27 + (-2/5*a^4 - 4/5*a^3 + 13/5*a^2 + 17/5*a + 7/5)*q^28 + (a^4 - 9*a^2 + 5*a + 3)*q^29 + (3/5*a^4 + 1/5*a^3 - 22/5*a^2 - 3/5*a + 2/5)*q^30 + (-3/5*a^4 - 6/5*a^3 + 22/5*a^2 + 23/5*a - 7/5)*q^31 + q^32 + (a^4 + a^3 - 8*a^2 - a)*q^33 + (-7/5*a^4 + 1/5*a^3 + 58/5*a^2 - 33/5*a - 28/5)*q^34 + (6/5*a^4 + 7/5*a^3 - 49/5*a^2 - 26/5*a + 19/5)*q^35 + (a^2 - 3)*q^36 + (2/5*a^4 + 4/5*a^3 - 8/5*a^2 - 22/5*a - 12/5)*q^37 + O(q^38)
*]> ;  // time = 56.26 seconds




J[281] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 281, 281 ], new_dimensions := [ 7, 16 ], dimensions := [ 7, 16 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -2, -4, -4, -12, -7, -7, -4, -20, 1, -2, -41, -2 ],
[ -1, 4, 2, 16, 1, 9, -6, 28, 7, -8, 59, 2 ]
], hecke_fields := [
x^7 + 2*x^6 - 5*x^5 - 9*x^4 + 7*x^3 + 10*x^2 - 2*x - 1,
x^16 + x^15 - 27*x^14 - 24*x^13 + 294*x^12 + 229*x^11 - 1650*x^10 - 1115*x^9 + 5054*x^8 + 2991*x^7 - 8223*x^6 - 4526*x^5 + 6338*x^4 + 3707*x^3 - 1604*x^2 - 1215*x - 167
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 35 ]
], tamagawa_numbers := [
[ 1 ],
[ 35 ]
], torsion_upper_bounds := [ 1, 35 ], torsion_lower_bounds := [ 1, 35 ], l_ratios := [ 0, 1/35 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
a^6 + a^5 - 6*a^4 - 4*a^3 + 9*a^2 + 3*a - 2,
-a^6 - a^5 + 7*a^4 + 5*a^3 - 13*a^2 - 6*a + 3,
-a^6 - a^5 + 5*a^4 + 3*a^3 - 6*a^2 - 2*a - 1,
-a^6 - 2*a^5 + 2*a^4 + 4*a^3 + 3*a^2 + 2*a - 4,
a^4 - 3*a^2 + 2*a - 1,
2*a^6 + 5*a^5 - 8*a^4 - 21*a^3 + 8*a^2 + 19*a - 2,
a^6 + a^5 - 6*a^4 - 4*a^3 + 8*a^2 + 4*a - 2,
a^6 - a^5 - 9*a^4 + 6*a^3 + 20*a^2 - 7*a - 7,
3*a^6 + 6*a^5 - 12*a^4 - 20*a^3 + 15*a^2 + 13*a - 7,
2*a^6 + 5*a^5 - 7*a^4 - 20*a^3 + 4*a^2 + 20*a - 4,
-a^6 + 2*a^5 + 10*a^4 - 7*a^3 - 19*a^2 + 4*a + 4
],
[
a,
-13665/151856*a^15 - 4453/75928*a^14 + 360823/151856*a^13 + 192549/151856*a^12 - 3808793/151856*a^11 - 393525/37964*a^10 + 10220589/75928*a^9 + 6015201/151856*a^8 - 58521373/151856*a^7 - 5496873/75928*a^6 + 85533697/151856*a^5 + 10360255/151856*a^4 - 55824393/151856*a^3 - 495365/9491*a^2 + 6299351/75928*a + 2953595/151856,
-5097/75928*a^15 - 73/9491*a^14 + 142687/75928*a^13 - 599/75928*a^12 - 1608837/75928*a^11 + 87021/37964*a^10 + 4649421/37964*a^9 - 1750371/75928*a^8 - 28958277/75928*a^7 + 3301675/37964*a^6 + 46755675/75928*a^5 - 9261139/75928*a^4 - 34843841/75928*a^3 + 249793/9491*a^2 + 1195511/9491*a + 1626197/75928,
599/18982*a^15 + 3543/37964*a^14 - 15197/18982*a^13 - 42087/18982*a^12 + 305459/37964*a^11 + 777481/37964*a^10 - 1529371/37964*a^9 - 3507895/37964*a^8 + 975791/9491*a^7 + 1985247/9491*a^6 - 2259949/18982*a^5 - 8255973/37964*a^4 + 1467147/37964*a^3 + 739551/9491*a^2 + 371647/37964*a + 33381/18982,
-12727/151856*a^15 + 204/9491*a^14 + 346247/151856*a^13 - 99493/151856*a^12 - 3793561/151856*a^11 + 144027/18982*a^10 + 10706791/75928*a^9 - 6451005/151856*a^8 - 66041481/151856*a^7 + 8902335/75928*a^6 + 108659163/151856*a^5 - 20422589/151856*a^4 - 86268599/151856*a^3 + 1062797/75928*a^2 + 1623433/9491*a + 5250719/151856,
1845/18982*a^15 + 1311/37964*a^14 - 101841/37964*a^13 - 8453/18982*a^12 + 1130421/37964*a^11 - 2887/9491*a^10 - 3205285/18982*a^9 + 515547/18982*a^8 + 19453149/37964*a^7 - 2577655/18982*a^6 - 7543373/9491*a^5 + 8568847/37964*a^4 + 5259886/9491*a^3 - 3199653/37964*a^2 - 5388413/37964*a - 668059/37964,
-12825/151856*a^15 - 137/75928*a^14 + 331621/151856*a^13 - 23651/151856*a^12 - 3407013/151856*a^11 + 270075/75928*a^10 + 1104410/9491*a^9 - 4198049/151856*a^8 - 48509991/151856*a^7 + 7224269/75928*a^6 + 67546421/151856*a^5 - 20784153/151856*a^4 - 42201483/151856*a^3 + 3879829/75928*a^2 + 4946355/75928*a + 1356261/151856,
7373/37964*a^15 + 5081/37964*a^14 - 48131/9491*a^13 - 55551/18982*a^12 + 1999655/37964*a^11 + 920249/37964*a^10 - 5237881/18982*a^9 - 1776419/18982*a^8 + 7219115/9491*a^7 + 6374821/37964*a^6 - 9890044/9491*a^5 - 5068599/37964*a^4 + 5685979/9491*a^3 + 2717221/37964*a^2 - 1985371/18982*a - 746545/37964,
-1471/151856*a^15 - 10767/75928*a^14 + 497/151856*a^13 + 534079/151856*a^12 + 470353/151856*a^11 - 327182/9491*a^10 - 2801443/75928*a^9 + 25536335/151856*a^8 + 27102325/151856*a^7 - 31740777/75928*a^6 - 61392841/151856*a^5 + 71502829/151856*a^4 + 61901993/151856*a^3 - 1415021/9491*a^2 - 11374473/75928*a - 3762107/151856,
4133/37964*a^15 + 5553/18982*a^14 - 105649/37964*a^13 - 65385/9491*a^12 + 1068203/37964*a^11 + 2386447/37964*a^10 - 5365733/37964*a^9 - 10595625/37964*a^8 + 13688985/37964*a^7 + 23574929/37964*a^6 - 15887983/37964*a^5 - 6124297/9491*a^4 + 5799147/37964*a^3 + 2425273/9491*a^2 + 228357/37964*a - 494225/37964,
-5857/37964*a^15 - 3745/18982*a^14 + 74385/18982*a^13 + 171509/37964*a^12 - 1490571/37964*a^11 - 1509711/37964*a^10 + 7426625/37964*a^9 + 1589060/9491*a^8 - 9479359/18982*a^7 - 3229211/9491*a^6 + 22656067/37964*a^5 + 11247503/37964*a^4 - 4702321/18982*a^3 - 2987479/37964*a^2 + 86059/18982*a - 48488/9491,
1299/75928*a^15 - 527/18982*a^14 - 30041/75928*a^13 + 56149/75928*a^12 + 251853/75928*a^11 - 293769/37964*a^10 - 208019/18982*a^9 + 3077775/75928*a^8 + 56775/75928*a^7 - 4253999/37964*a^6 + 5693565/75928*a^5 + 11955561/75928*a^4 - 10735111/75928*a^3 - 1814201/18982*a^2 + 619469/9491*a + 1419859/75928
]
*], q_expansions := [*
q + a*q^2 + (a^6 + a^5 - 6*a^4 - 4*a^3 + 9*a^2 + 3*a - 2)*q^3 + (a^2 - 2)*q^4 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 13*a^2 - 6*a + 3)*q^5 + (-a^6 - a^5 + 5*a^4 + 2*a^3 - 7*a^2 + 1)*q^6 + (-a^6 - a^5 + 5*a^4 + 3*a^3 - 6*a^2 - 2*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (a^4 + 3*a^3 - 2*a^2 - 7*a)*q^9 + (a^6 + 2*a^5 - 4*a^4 - 6*a^3 + 4*a^2 + a - 1)*q^10 + (-a^6 - 2*a^5 + 2*a^4 + 4*a^3 + 3*a^2 + 2*a - 4)*q^11 + (-a^6 - 2*a^5 + 5*a^4 + 8*a^3 - 8*a^2 - 7*a + 3)*q^12 + (a^4 - 3*a^2 + 2*a - 1)*q^13 + (a^6 - 6*a^4 + a^3 + 8*a^2 - 3*a - 1)*q^14 + (a^5 - 7*a^3 + 2*a^2 + 12*a - 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^6 + 5*a^5 - 8*a^4 - 21*a^3 + 8*a^2 + 19*a - 2)*q^17 + (a^5 + 3*a^4 - 2*a^3 - 7*a^2)*q^18 + (a^6 + a^5 - 6*a^4 - 4*a^3 + 8*a^2 + 4*a - 2)*q^19 + (2*a^6 + 3*a^5 - 11*a^4 - 13*a^3 + 17*a^2 + 13*a - 5)*q^20 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 12*a^2 - 3*a + 2)*q^21 + (-3*a^5 - 5*a^4 + 10*a^3 + 12*a^2 - 6*a - 1)*q^22 + (a^6 - a^5 - 9*a^4 + 6*a^3 + 20*a^2 - 7*a - 7)*q^23 + (2*a^6 + 2*a^5 - 11*a^4 - 5*a^3 + 17*a^2 + a - 3)*q^24 + (-2*a^6 - 7*a^5 + 4*a^4 + 27*a^3 + a^2 - 22*a + 3)*q^25 + (a^5 - 3*a^3 + 2*a^2 - a)*q^26 + (-2*a^6 - 3*a^5 + 9*a^4 + 10*a^3 - 10*a^2 - 7*a + 2)*q^27 + (a^5 - 5*a^3 - a^2 + 5*a + 3)*q^28 + (3*a^6 + 6*a^5 - 12*a^4 - 20*a^3 + 15*a^2 + 13*a - 7)*q^29 + (a^6 - 7*a^4 + 2*a^3 + 12*a^2 - 5*a)*q^30 + (2*a^6 + 5*a^5 - 7*a^4 - 20*a^3 + 4*a^2 + 20*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^6 - 2*a^5 + 15*a^4 + 12*a^3 - 28*a^2 - 13*a + 8)*q^33 + (a^6 + 2*a^5 - 3*a^4 - 6*a^3 - a^2 + 2*a + 2)*q^34 + (2*a^6 + 2*a^5 - 13*a^4 - 8*a^3 + 22*a^2 + 7*a - 3)*q^35 + (a^6 + 3*a^5 - 4*a^4 - 13*a^3 + 4*a^2 + 14*a)*q^36 + (-a^6 + 2*a^5 + 10*a^4 - 7*a^3 - 19*a^2 + 4*a + 4)*q^37 + O(q^38),
q + a*q^2 + (-13665/151856*a^15 - 4453/75928*a^14 + 360823/151856*a^13 + 192549/151856*a^12 - 3808793/151856*a^11 - 393525/37964*a^10 + 10220589/75928*a^9 + 6015201/151856*a^8 - 58521373/151856*a^7 - 5496873/75928*a^6 + 85533697/151856*a^5 + 10360255/151856*a^4 - 55824393/151856*a^3 - 495365/9491*a^2 + 6299351/75928*a + 2953595/151856)*q^3 + (a^2 - 2)*q^4 + (-5097/75928*a^15 - 73/9491*a^14 + 142687/75928*a^13 - 599/75928*a^12 - 1608837/75928*a^11 + 87021/37964*a^10 + 4649421/37964*a^9 - 1750371/75928*a^8 - 28958277/75928*a^7 + 3301675/37964*a^6 + 46755675/75928*a^5 - 9261139/75928*a^4 - 34843841/75928*a^3 + 249793/9491*a^2 + 1195511/9491*a + 1626197/75928)*q^5 + (4759/151856*a^15 - 2033/37964*a^14 - 135411/151856*a^13 + 208717/151856*a^12 + 1555185/151856*a^11 - 263259/18982*a^10 - 4610637/75928*a^9 + 10541537/151856*a^8 + 29878269/151856*a^7 - 13416799/75928*a^6 - 51487535/151856*a^5 + 30784377/151856*a^4 + 42730315/151856*a^3 - 4659979/75928*a^2 - 3412345/37964*a - 2282055/151856)*q^6 + (599/18982*a^15 + 3543/37964*a^14 - 15197/18982*a^13 - 42087/18982*a^12 + 305459/37964*a^11 + 777481/37964*a^10 - 1529371/37964*a^9 - 3507895/37964*a^8 + 975791/9491*a^7 + 1985247/9491*a^6 - 2259949/18982*a^5 - 8255973/37964*a^4 + 1467147/37964*a^3 + 739551/9491*a^2 + 371647/37964*a + 33381/18982)*q^7 + (a^3 - 4*a)*q^8 + (-4843/151856*a^15 - 9653/75928*a^14 + 117451/151856*a^13 + 458291/151856*a^12 - 1101831/151856*a^11 - 2104033/75928*a^10 + 610951/18982*a^9 + 18715513/151856*a^8 - 9503777/151856*a^7 - 20597367/75928*a^6 + 2873867/151856*a^5 + 40752581/151856*a^4 + 10907739/151856*a^3 - 6622291/75928*a^2 - 3428859/75928*a - 475745/151856)*q^9 + (4513/75928*a^15 + 1267/18982*a^14 - 122927/75928*a^13 - 110319/75928*a^12 + 1341255/75928*a^11 + 111099/9491*a^10 - 3716763/37964*a^9 - 3198039/75928*a^8 + 21848477/75928*a^7 + 1210761/18982*a^6 - 32330161/75928*a^5 - 2539055/75928*a^4 + 20892923/75928*a^3 + 347125/18982*a^2 - 2283329/37964*a - 851199/75928)*q^10 + (-12727/151856*a^15 + 204/9491*a^14 + 346247/151856*a^13 - 99493/151856*a^12 - 3793561/151856*a^11 + 144027/18982*a^10 + 10706791/75928*a^9 - 6451005/151856*a^8 - 66041481/151856*a^7 + 8902335/75928*a^6 + 108659163/151856*a^5 - 20422589/151856*a^4 - 86268599/151856*a^3 + 1062797/75928*a^2 + 1623433/9491*a + 5250719/151856)*q^11 + (14439/151856*a^15 + 5447/75928*a^14 - 398713/151856*a^13 - 229059/151856*a^12 + 4421703/151856*a^11 + 444819/37964*a^10 - 12517267/75928*a^9 - 6204119/151856*a^8 + 75974979/151856*a^7 + 4816607/75928*a^6 - 118743783/151856*a^5 - 8152737/151856*a^4 + 84687215/151856*a^3 + 1229467/18982*a^2 - 10848637/75928*a - 5112437/151856)*q^12 + (1845/18982*a^15 + 1311/37964*a^14 - 101841/37964*a^13 - 8453/18982*a^12 + 1130421/37964*a^11 - 2887/9491*a^10 - 3205285/18982*a^9 + 515547/18982*a^8 + 19453149/37964*a^7 - 2577655/18982*a^6 - 7543373/9491*a^5 + 8568847/37964*a^4 + 5259886/9491*a^3 - 3199653/37964*a^2 - 5388413/37964*a - 668059/37964)*q^13 + (2345/37964*a^15 + 488/9491*a^14 - 27711/18982*a^13 - 46753/37964*a^12 + 503139/37964*a^11 + 447329/37964*a^10 - 2172125/37964*a^9 - 537882/9491*a^8 + 2178885/18982*a^7 + 1332814/9491*a^6 - 2833825/37964*a^5 - 6125777/37964*a^4 - 741391/18982*a^3 + 2293239/37964*a^2 + 380583/9491*a + 100033/18982)*q^14 + (-3707/151856*a^15 - 3093/75928*a^14 + 109957/151856*a^13 + 120711/151856*a^12 - 1283403/151856*a^11 - 47861/9491*a^10 + 3671003/75928*a^9 + 1194587/151856*a^8 - 20653287/151856*a^7 + 2306125/75928*a^6 + 23719231/151856*a^5 - 15391871/151856*a^4 - 2615603/151856*a^3 + 695142/9491*a^2 - 2669661/75928*a - 2017859/151856)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-12825/151856*a^15 - 137/75928*a^14 + 331621/151856*a^13 - 23651/151856*a^12 - 3407013/151856*a^11 + 270075/75928*a^10 + 1104410/9491*a^9 - 4198049/151856*a^8 - 48509991/151856*a^7 + 7224269/75928*a^6 + 67546421/151856*a^5 - 20784153/151856*a^4 - 42201483/151856*a^3 + 3879829/75928*a^2 + 4946355/75928*a + 1356261/151856)*q^17 + (-14463/151856*a^15 - 6655/75928*a^14 + 342059/151856*a^13 + 322011/151856*a^12 - 3099019/151856*a^11 - 1551671/75928*a^10 + 832223/9491*a^9 + 14972745/151856*a^8 - 26709321/151856*a^7 - 18475061/75928*a^6 + 18833163/151856*a^5 + 41602673/151856*a^4 + 4708419/151856*a^3 - 7312945/75928*a^2 - 3179995/75928*a - 808781/151856)*q^18 + (7373/37964*a^15 + 5081/37964*a^14 - 48131/9491*a^13 - 55551/18982*a^12 + 1999655/37964*a^11 + 920249/37964*a^10 - 5237881/18982*a^9 - 1776419/18982*a^8 + 7219115/9491*a^7 + 6374821/37964*a^6 - 9890044/9491*a^5 - 5068599/37964*a^4 + 5685979/9491*a^3 + 2717221/37964*a^2 - 1985371/18982*a - 746545/37964)*q^19 + (10749/75928*a^15 + 23/18982*a^14 - 287381/75928*a^13 + 15631/75928*a^12 + 3072989/75928*a^11 - 41895/9491*a^10 - 2095466/9491*a^9 + 2540517/75928*a^8 + 49261215/75928*a^7 - 4213231/37964*a^6 - 75624567/75928*a^5 + 10811807/75928*a^4 + 54346491/75928*a^3 - 662247/37964*a^2 - 1812010/9491*a - 2498723/75928)*q^20 + (2407/37964*a^15 + 933/18982*a^14 - 14835/9491*a^13 - 40113/37964*a^12 + 563075/37964*a^11 + 316617/37964*a^10 - 2520841/37964*a^9 - 263937/9491*a^8 + 1246031/9491*a^7 + 484245/18982*a^6 - 1814107/37964*a^5 + 1758137/37964*a^4 - 2618509/18982*a^3 - 2999693/37964*a^2 + 850803/9491*a + 267161/9491)*q^21 + (15991/151856*a^15 + 1309/75928*a^14 - 404941/151856*a^13 - 51823/151856*a^12 + 4066699/151856*a^11 + 25877/9491*a^10 - 10320805/75928*a^9 - 1719223/151856*a^8 + 55871127/151856*a^7 + 2002521/75928*a^6 - 78024991/151856*a^5 - 5604873/151856*a^4 + 49304583/151856*a^3 + 1390205/37964*a^2 - 5106293/75928*a - 2125409/151856)*q^22 + (-1471/151856*a^15 - 10767/75928*a^14 + 497/151856*a^13 + 534079/151856*a^12 + 470353/151856*a^11 - 327182/9491*a^10 - 2801443/75928*a^9 + 25536335/151856*a^8 + 27102325/151856*a^7 - 31740777/75928*a^6 - 61392841/151856*a^5 + 71502829/151856*a^4 + 61901993/151856*a^3 - 1415021/9491*a^2 - 11374473/75928*a - 3762107/151856)*q^23 + (-13063/151856*a^15 + 1851/37964*a^14 + 388299/151856*a^13 - 240797/151856*a^12 - 4637625/151856*a^11 + 375245/18982*a^10 + 14168957/75928*a^9 - 18082801/151856*a^8 - 93310373/151856*a^7 + 26827655/75928*a^6 + 160173247/151856*a^5 - 68395921/151856*a^4 - 129150267/151856*a^3 + 10051399/75928*a^2 + 9932427/37964*a + 6975423/151856)*q^24 + (-18787/151856*a^15 + 9815/75928*a^14 + 514887/151856*a^13 - 546433/151856*a^12 - 5645395/151856*a^11 + 2983727/75928*a^10 + 7872913/37964*a^9 - 32258431/151856*a^8 - 93641125/151856*a^7 + 44336255/75928*a^6 + 141315311/151856*a^5 - 111563159/151856*a^4 - 93387109/151856*a^3 + 22080703/75928*a^2 + 10720555/75928*a + 1245711/151856)*q^25 + (-2379/37964*a^15 - 2211/37964*a^14 + 35827/18982*a^13 + 45561/37964*a^12 - 428279/18982*a^11 - 161035/18982*a^10 + 1286361/9491*a^9 + 803889/37964*a^8 - 4048025/9491*a^7 + 84689/18982*a^6 + 25269787/37964*a^5 - 586919/9491*a^4 - 16878483/37964*a^3 + 530347/37964*a^2 + 3815291/37964*a + 308115/18982)*q^26 + (9697/75928*a^15 - 14063/75928*a^14 - 135709/37964*a^13 + 369555/75928*a^12 + 382183/9491*a^11 - 950825/18982*a^10 - 2216470/9491*a^9 + 19296375/75928*a^8 + 7013062/9491*a^7 - 6174524/9491*a^6 - 94400127/75928*a^5 + 28322871/37964*a^4 + 76302919/75928*a^3 - 17391781/75928*a^2 - 23743103/75928*a - 483117/9491)*q^27 + (-2789/37964*a^15 + 807/37964*a^14 + 70315/37964*a^13 - 17943/37964*a^12 - 350297/18982*a^11 + 142163/37964*a^10 + 3521889/37964*a^9 - 239035/18982*a^8 - 9488967/37964*a^7 + 283567/18982*a^6 + 13527489/37964*a^5 + 83277/18982*a^4 - 4666985/18982*a^3 - 158174/9491*a^2 + 2305947/37964*a + 258091/37964)*q^28 + (4133/37964*a^15 + 5553/18982*a^14 - 105649/37964*a^13 - 65385/9491*a^12 + 1068203/37964*a^11 + 2386447/37964*a^10 - 5365733/37964*a^9 - 10595625/37964*a^8 + 13688985/37964*a^7 + 23574929/37964*a^6 - 15887983/37964*a^5 - 6124297/9491*a^4 + 5799147/37964*a^3 + 2425273/9491*a^2 + 228357/37964*a - 494225/37964)*q^29 + (-2479/151856*a^15 + 2467/37964*a^14 + 31743/151856*a^13 - 193545/151856*a^12 + 83127/151856*a^11 + 76591/9491*a^10 - 1469359/75928*a^9 - 1918109/151856*a^8 + 15699887/151856*a^7 - 3381715/75928*a^6 - 32169753/151856*a^5 + 20879363/151856*a^4 + 24864121/151856*a^3 - 5642675/75928*a^2 - 815233/18982*a - 619069/151856)*q^30 + (-5857/37964*a^15 - 3745/18982*a^14 + 74385/18982*a^13 + 171509/37964*a^12 - 1490571/37964*a^11 - 1509711/37964*a^10 + 7426625/37964*a^9 + 1589060/9491*a^8 - 9479359/18982*a^7 - 3229211/9491*a^6 + 22656067/37964*a^5 + 11247503/37964*a^4 - 4702321/18982*a^3 - 2987479/37964*a^2 + 86059/18982*a - 48488/9491)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-25091/151856*a^15 + 2553/75928*a^14 + 692823/151856*a^13 - 200217/151856*a^12 - 7666363/151856*a^11 + 1376685/75928*a^10 + 10799969/37964*a^9 - 17553207/151856*a^8 - 129821653/151856*a^7 + 26926159/75928*a^6 + 198180323/151856*a^5 - 69615435/151856*a^4 - 132831349/151856*a^3 + 10002703/75928*a^2 + 14910685/75928*a + 5436963/151856)*q^33 + (12551/151856*a^15 - 7327/75928*a^14 - 331451/151856*a^13 + 363537/151856*a^12 + 3477075/151856*a^11 - 1745345/75928*a^10 - 4624481/37964*a^9 + 16307559/151856*a^8 + 52808113/151856*a^7 - 18956777/75928*a^6 - 78830103/151856*a^5 + 39083367/151856*a^4 + 55301933/151856*a^3 - 5339295/75928*a^2 - 7113057/75928*a - 2141775/151856)*q^34 + (9111/75928*a^15 + 3019/37964*a^14 - 219997/75928*a^13 - 132239/75928*a^12 + 2052243/75928*a^11 + 277131/18982*a^10 - 4589521/37964*a^9 - 4350975/75928*a^8 + 19335935/75928*a^7 + 3818453/37964*a^6 - 13615819/75928*a^5 - 3963197/75928*a^4 - 7149809/75928*a^3 - 399003/18982*a^2 + 3882849/37964*a + 1562331/75928)*q^35 + (10839/151856*a^15 - 4915/75928*a^14 - 260003/151856*a^13 + 236521/151856*a^12 + 2412347/151856*a^11 - 1066125/75928*a^10 - 2732179/37964*a^9 + 8955655/151856*a^8 + 25316265/151856*a^7 - 8853309/75928*a^6 - 29604599/151856*a^5 + 14869751/151856*a^4 + 17172973/151856*a^3 - 1534739/75928*a^2 - 2332945/75928*a - 1463831/151856)*q^36 + (1299/75928*a^15 - 527/18982*a^14 - 30041/75928*a^13 + 56149/75928*a^12 + 251853/75928*a^11 - 293769/37964*a^10 - 208019/18982*a^9 + 3077775/75928*a^8 + 56775/75928*a^7 - 4253999/37964*a^6 + 5693565/75928*a^5 + 11955561/75928*a^4 - 10735111/75928*a^3 - 1814201/18982*a^2 + 619469/9491*a + 1419859/75928)*q^37 + O(q^38)
*]> ;  // time = 4.099 seconds




J[282] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 282, 282, 282, 282, 282, 141, 141, 141, 141, 141, 141, 94, 94, 47 ], new_dimensions := [ 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 2, 1, 2, 4 ], dimensions := [ 1, 1, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 4, 16 ], intersection_graph := [ 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 23, 3, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1849, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2209, 1, 1, 1, 1, 23, 1, 9, 1, 1, 49, 1849, 1, 2209, 0 ], ap_traces := [
[ 1, -1, 2, 0, 0, 2, 2, 0, 0, 2, -8, -2 ],
[ 1, -1, -4, -4, 0, -2, -6, 6, -4, 4, 2, -6 ],
[ -2, -2, -2, 0, -6, -2, -8, -6, -12, -2, -4, -4 ],
[ -2, 2, 0, 4, 0, 4, 0, 4, 0, 0, 4, 4 ],
[ 3, 3, 2, 0, -6, 0, -2, -4, -8, -6, 6, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 2,
x^2 - 6,
x^3 - 2*x^2 - 8*x - 4
], atkin_lehners := [
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 3, 1, 1 ],
[ 5, 3, 1 ],
[ 115, 23, 1 ]
], tamagawa_numbers := [
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 115, 23, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 23 ], torsion_lower_bounds := [ 1, 1, 1, 3, 1 ], l_ratios := [ 3, 0, 0, 1/3, 5 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1/529 ], eigenvalues := [*
[ 1, -1, 2, 0, 0, 2, 2, 0, 0, 2, -8, -2 ],
[ 1, -1, -4, -4, 0, -2, -6, 6, -4, 4, 2, -6 ],
[
-1,
-1,
a,
-2*a - 2,
-a - 4,
3*a + 2,
-4,
a - 2,
-2*a - 8,
-3*a - 4,
4*a + 2,
-4*a - 6
],
[
-1,
1,
a,
2,
-a,
-a + 2,
-2*a,
a + 2,
2*a,
-3*a,
2,
4*a + 2
],
[
1,
1,
a,
a^2 - 4*a - 4,
-2*a^2 + 5*a + 8,
-2*a^2 + 5*a + 10,
a^2 - 2*a - 6,
2*a^2 - 7*a - 10,
2*a^2 - 6*a - 12,
2*a^2 - 5*a - 12,
-2*a^2 + 8*a + 10,
-4*a^2 + 12*a + 18
]
*], q_expansions := [*
q + q^2 - q^3 + q^4 + 2*q^5 - q^6 + q^8 + q^9 + 2*q^10 - q^12 + 2*q^13 - 2*q^15 + q^16 + 2*q^17 + q^18 + 2*q^20 - q^24 - q^25 + 2*q^26 - q^27 + 2*q^29 - 2*q^30 - 8*q^31 + q^32 + 2*q^34 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 4*q^5 - q^6 - 4*q^7 + q^8 + q^9 - 4*q^10 - q^12 - 2*q^13 - 4*q^14 + 4*q^15 + q^16 - 6*q^17 + q^18 + 6*q^19 - 4*q^20 + 4*q^21 - 4*q^23 - q^24 + 11*q^25 - 2*q^26 - q^27 - 4*q^28 + 4*q^29 + 4*q^30 + 2*q^31 + q^32 - 6*q^34 + 16*q^35 + q^36 - 6*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + a*q^5 + q^6 + (-2*a - 2)*q^7 - q^8 + q^9 - a*q^10 + (-a - 4)*q^11 - q^12 + (3*a + 2)*q^13 + (2*a + 2)*q^14 - a*q^15 + q^16 - 4*q^17 - q^18 + (a - 2)*q^19 + a*q^20 + (2*a + 2)*q^21 + (a + 4)*q^22 + (-2*a - 8)*q^23 + q^24 + (-2*a - 3)*q^25 + (-3*a - 2)*q^26 - q^27 + (-2*a - 2)*q^28 + (-3*a - 4)*q^29 + a*q^30 + (4*a + 2)*q^31 - q^32 + (a + 4)*q^33 + 4*q^34 + (2*a - 4)*q^35 + q^36 + (-4*a - 6)*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + a*q^5 - q^6 + 2*q^7 - q^8 + q^9 - a*q^10 - a*q^11 + q^12 + (-a + 2)*q^13 - 2*q^14 + a*q^15 + q^16 - 2*a*q^17 - q^18 + (a + 2)*q^19 + a*q^20 + 2*q^21 + a*q^22 + 2*a*q^23 - q^24 + q^25 + (a - 2)*q^26 + q^27 + 2*q^28 - 3*a*q^29 - a*q^30 + 2*q^31 - q^32 - a*q^33 + 2*a*q^34 + 2*a*q^35 + q^36 + (4*a + 2)*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (a^2 - 4*a - 4)*q^7 + q^8 + q^9 + a*q^10 + (-2*a^2 + 5*a + 8)*q^11 + q^12 + (-2*a^2 + 5*a + 10)*q^13 + (a^2 - 4*a - 4)*q^14 + a*q^15 + q^16 + (a^2 - 2*a - 6)*q^17 + q^18 + (2*a^2 - 7*a - 10)*q^19 + a*q^20 + (a^2 - 4*a - 4)*q^21 + (-2*a^2 + 5*a + 8)*q^22 + (2*a^2 - 6*a - 12)*q^23 + q^24 + (a^2 - 5)*q^25 + (-2*a^2 + 5*a + 10)*q^26 + q^27 + (a^2 - 4*a - 4)*q^28 + (2*a^2 - 5*a - 12)*q^29 + a*q^30 + (-2*a^2 + 8*a + 10)*q^31 + q^32 + (-2*a^2 + 5*a + 8)*q^33 + (a^2 - 2*a - 6)*q^34 + (-2*a^2 + 4*a + 4)*q^35 + q^36 + (-4*a^2 + 12*a + 18)*q^37 + O(q^38)
*]> ;  // time = 160.61 seconds




J[283] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 283, 283 ], new_dimensions := [ 9, 14 ], dimensions := [ 9, 14 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -6, -6, -14, -2, -5, -9, -13, 3, -24, -33, -1, -24 ],
[ 6, 4, 14, 0, 5, 9, 13, -7, 22, 33, -13, 16 ]
], hecke_fields := [
x^9 + 6*x^8 + 5*x^7 - 29*x^6 - 50*x^5 + 27*x^4 + 83*x^3 + 19*x^2 - 13*x + 1,
x^14 - 6*x^13 - 4*x^12 + 83*x^11 - 77*x^10 - 394*x^9 + 617*x^8 + 724*x^7 - 1566*x^6 - 370*x^5 + 1489*x^4 - 153*x^3 - 410*x^2 + 120*x - 8
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 47 ]
], tamagawa_numbers := [
[ 1 ],
[ 47 ]
], torsion_upper_bounds := [ 1, 47 ], torsion_lower_bounds := [ 1, 47 ], l_ratios := [ 0, 1/47 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
1/5*a^8 + 2/5*a^7 - 13/5*a^6 - 22/5*a^5 + 53/5*a^4 + 13*a^3 - 77/5*a^2 - 53/5*a + 14/5,
a^7 + 4*a^6 - 3*a^5 - 23*a^4 - 4*a^3 + 34*a^2 + 12*a - 5,
3/5*a^8 + 16/5*a^7 + 11/5*a^6 - 66/5*a^5 - 111/5*a^4 + 6*a^3 + 169/5*a^2 + 76/5*a - 23/5,
-3/5*a^8 - 21/5*a^7 - 31/5*a^6 + 76/5*a^5 + 216/5*a^4 + 3*a^3 - 309/5*a^2 - 176/5*a + 28/5,
2/5*a^8 + 14/5*a^7 + 19/5*a^6 - 64/5*a^5 - 169/5*a^4 + 2*a^3 + 291/5*a^2 + 164/5*a - 42/5,
-2/5*a^8 - 19/5*a^7 - 39/5*a^6 + 79/5*a^5 + 284/5*a^4 + a^3 - 461/5*a^2 - 199/5*a + 42/5,
-2*a^8 - 9*a^7 + 2*a^6 + 49*a^5 + 30*a^4 - 66*a^3 - 54*a^2,
3/5*a^8 + 21/5*a^7 + 31/5*a^6 - 86/5*a^5 - 251/5*a^4 - a^3 + 409/5*a^2 + 216/5*a - 53/5,
-a^8 - 5*a^7 - a^6 + 26*a^5 + 26*a^4 - 33*a^3 - 45*a^2 - 2*a + 2,
-19/5*a^8 - 93/5*a^7 - 3/5*a^6 + 513/5*a^5 + 438/5*a^4 - 138*a^3 - 797/5*a^2 - 48/5*a + 59/5,
a^8 + 5*a^7 + a^6 - 24*a^5 - 20*a^4 + 27*a^3 + 23*a^2 + 4*a + 3
],
[
a,
17/94*a^13 - 41/47*a^12 - 85/47*a^11 + 1211/94*a^10 + 265/94*a^9 - 3265/47*a^8 + 1745/94*a^7 + 7844/47*a^6 - 2764/47*a^5 - 8227/47*a^4 + 4197/94*a^3 + 5787/94*a^2 - 526/47*a - 102/47,
-19/94*a^13 + 32/47*a^12 + 142/47*a^11 - 983/94*a^10 - 1673/94*a^9 + 2781/47*a^8 + 5343/94*a^7 - 7014/47*a^6 - 5357/47*a^5 + 7384/47*a^4 + 11621/94*a^3 - 4151/94*a^2 - 1552/47*a + 302/47,
-39/188*a^13 + 65/47*a^12 + 27/47*a^11 - 3685/188*a^10 + 3705/188*a^9 + 4587/47*a^8 - 27647/188*a^7 - 18971/94*a^6 + 34223/94*a^5 + 15263/94*a^4 - 63131/188*a^3 - 6403/188*a^2 + 4062/47*a - 447/47,
3/188*a^13 + 37/94*a^12 - 78/47*a^11 - 1047/188*a^10 + 4321/188*a^9 + 2559/94*a^8 - 22993/188*a^7 - 2526/47*a^6 + 27057/94*a^5 + 3779/94*a^4 - 53525/188*a^3 - 1279/188*a^2 + 7911/94*a - 432/47,
-79/94*a^13 + 323/94*a^12 + 489/47*a^11 - 4859/94*a^10 - 1911/47*a^9 + 26671/94*a^8 + 4509/94*a^7 - 64761/94*a^6 - 28/47*a^5 + 33230/47*a^4 + 745/94*a^3 - 9848/47*a^2 + 1231/94*a + 239/47,
-57/47*a^13 + 239/47*a^12 + 664/47*a^11 - 3560/47*a^10 - 2058/47*a^9 + 19130/47*a^8 - 797/47*a^7 - 44810/47*a^6 + 9594/47*a^5 + 44069/47*a^4 - 8189/47*a^3 - 13064/47*a^2 + 2297/47*a + 214/47,
73/47*a^13 - 330/47*a^12 - 777/47*a^11 + 4885/47*a^10 + 1572/47*a^9 - 26003/47*a^8 + 6556/47*a^7 + 59871/47*a^6 - 24794/47*a^5 - 56619/47*a^4 + 22598/47*a^3 + 14358/47*a^2 - 7260/47*a + 816/47,
73/47*a^13 - 613/94*a^12 - 871/47*a^11 + 4603/47*a^10 + 5917/94*a^9 - 49985/94*a^8 - 870/47*a^7 + 118379/94*a^6 - 7310/47*a^5 - 58123/47*a^4 + 5302/47*a^3 + 31301/94*a^2 - 4885/94*a + 17/47,
-231/188*a^13 + 535/94*a^12 + 554/47*a^11 - 15449/188*a^10 - 1461/188*a^9 + 39743/94*a^8 - 39791/188*a^7 - 43506/47*a^6 + 62913/94*a^5 + 76087/94*a^4 - 122299/188*a^3 - 32929/188*a^2 + 18491/94*a - 1046/47,
-12/47*a^13 + 33/47*a^12 + 214/47*a^11 - 559/47*a^10 - 1492/47*a^9 + 3451/47*a^8 + 5351/47*a^7 - 9451/47*a^6 - 10784/47*a^5 + 11034/47*a^4 + 10966/47*a^3 - 4002/47*a^2 - 3175/47*a + 520/47,
143/94*a^13 - 320/47*a^12 - 762/47*a^11 + 9407/94*a^10 + 3241/94*a^9 - 24896/47*a^8 + 11477/94*a^7 + 57121/47*a^6 - 22382/47*a^5 - 53959/47*a^4 + 39689/94*a^3 + 27833/94*a^2 - 5724/47*a + 552/47
]
*], q_expansions := [*
q + a*q^2 + (1/5*a^8 + 2/5*a^7 - 13/5*a^6 - 22/5*a^5 + 53/5*a^4 + 13*a^3 - 77/5*a^2 - 53/5*a + 14/5)*q^3 + (a^2 - 2)*q^4 + (a^7 + 4*a^6 - 3*a^5 - 23*a^4 - 4*a^3 + 34*a^2 + 12*a - 5)*q^5 + (-4/5*a^8 - 18/5*a^7 + 7/5*a^6 + 103/5*a^5 + 38/5*a^4 - 32*a^3 - 72/5*a^2 + 27/5*a - 1/5)*q^6 + (3/5*a^8 + 16/5*a^7 + 11/5*a^6 - 66/5*a^5 - 111/5*a^4 + 6*a^3 + 169/5*a^2 + 76/5*a - 23/5)*q^7 + (a^3 - 4*a)*q^8 + (-7/5*a^8 - 34/5*a^7 + 1/5*a^6 + 189/5*a^5 + 144/5*a^4 - 52*a^3 - 251/5*a^2 - 9/5*a + 2/5)*q^9 + (a^8 + 4*a^7 - 3*a^6 - 23*a^5 - 4*a^4 + 34*a^3 + 12*a^2 - 5*a)*q^10 + (-3/5*a^8 - 21/5*a^7 - 31/5*a^6 + 76/5*a^5 + 216/5*a^4 + 3*a^3 - 309/5*a^2 - 176/5*a + 28/5)*q^11 + (4/5*a^8 + 23/5*a^7 + 13/5*a^6 - 118/5*a^5 - 158/5*a^4 + 26*a^3 + 257/5*a^2 + 53/5*a - 24/5)*q^12 + (2/5*a^8 + 14/5*a^7 + 19/5*a^6 - 64/5*a^5 - 169/5*a^4 + 2*a^3 + 291/5*a^2 + 164/5*a - 42/5)*q^13 + (-2/5*a^8 - 4/5*a^7 + 21/5*a^6 + 39/5*a^5 - 51/5*a^4 - 16*a^3 + 19/5*a^2 + 16/5*a - 3/5)*q^14 + (1/5*a^8 + 12/5*a^7 + 32/5*a^6 - 37/5*a^5 - 197/5*a^4 - 8*a^3 + 298/5*a^2 + 147/5*a - 46/5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-2/5*a^8 - 19/5*a^7 - 39/5*a^6 + 79/5*a^5 + 284/5*a^4 + a^3 - 461/5*a^2 - 199/5*a + 42/5)*q^17 + (8/5*a^8 + 36/5*a^7 - 14/5*a^6 - 206/5*a^5 - 71/5*a^4 + 66*a^3 + 124/5*a^2 - 89/5*a + 7/5)*q^18 + (-2*a^8 - 9*a^7 + 2*a^6 + 49*a^5 + 30*a^4 - 66*a^3 - 54*a^2)*q^19 + (-2*a^8 - 10*a^7 - 2*a^6 + 52*a^5 + 53*a^4 - 63*a^3 - 92*a^2 - 11*a + 9)*q^20 + (13/5*a^8 + 61/5*a^7 - 9/5*a^6 - 346/5*a^5 - 241/5*a^4 + 98*a^3 + 459/5*a^2 + 1/5*a - 28/5)*q^21 + (-3/5*a^8 - 16/5*a^7 - 11/5*a^6 + 66/5*a^5 + 96/5*a^4 - 12*a^3 - 119/5*a^2 - 11/5*a + 3/5)*q^22 + (3/5*a^8 + 21/5*a^7 + 31/5*a^6 - 86/5*a^5 - 251/5*a^4 - a^3 + 409/5*a^2 + 216/5*a - 53/5)*q^23 + (7/5*a^8 + 29/5*a^7 - 16/5*a^6 - 164/5*a^5 - 54/5*a^4 + 49*a^3 + 121/5*a^2 - 26/5*a - 2/5)*q^24 + (a^8 + a^7 - 16*a^6 - 17*a^5 + 71*a^4 + 65*a^3 - 100*a^2 - 69*a + 15)*q^25 + (2/5*a^8 + 9/5*a^7 - 6/5*a^6 - 69/5*a^5 - 44/5*a^4 + 25*a^3 + 126/5*a^2 - 16/5*a - 2/5)*q^26 + (9/5*a^8 + 48/5*a^7 + 18/5*a^6 - 253/5*a^5 - 298/5*a^4 + 62*a^3 + 502/5*a^2 + 73/5*a - 39/5)*q^27 + (2/5*a^8 - 1/5*a^7 - 41/5*a^6 - 19/5*a^5 + 196/5*a^4 + 25*a^3 - 284/5*a^2 - 181/5*a + 48/5)*q^28 + (-a^8 - 5*a^7 - a^6 + 26*a^5 + 26*a^4 - 33*a^3 - 45*a^2 - 2*a + 2)*q^29 + (6/5*a^8 + 27/5*a^7 - 8/5*a^6 - 147/5*a^5 - 67/5*a^4 + 43*a^3 + 128/5*a^2 - 33/5*a - 1/5)*q^30 + (-19/5*a^8 - 93/5*a^7 - 3/5*a^6 + 513/5*a^5 + 438/5*a^4 - 138*a^3 - 797/5*a^2 - 48/5*a + 59/5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-8/5*a^8 - 36/5*a^7 + 14/5*a^6 + 221/5*a^5 + 121/5*a^4 - 69*a^3 - 264/5*a^2 + 34/5*a + 13/5)*q^33 + (-7/5*a^8 - 29/5*a^7 + 21/5*a^6 + 184/5*a^5 + 59/5*a^4 - 59*a^3 - 161/5*a^2 + 16/5*a + 2/5)*q^34 + (-22/5*a^8 - 109/5*a^7 - 19/5*a^6 + 554/5*a^5 + 529/5*a^4 - 132*a^3 - 871/5*a^2 - 89/5*a + 67/5)*q^35 + (2/5*a^8 + 14/5*a^7 + 24/5*a^6 - 49/5*a^5 - 174/5*a^4 - 4*a^3 + 261/5*a^2 + 129/5*a - 12/5)*q^36 + (a^8 + 5*a^7 + a^6 - 24*a^5 - 20*a^4 + 27*a^3 + 23*a^2 + 4*a + 3)*q^37 + O(q^38),
q + a*q^2 + (17/94*a^13 - 41/47*a^12 - 85/47*a^11 + 1211/94*a^10 + 265/94*a^9 - 3265/47*a^8 + 1745/94*a^7 + 7844/47*a^6 - 2764/47*a^5 - 8227/47*a^4 + 4197/94*a^3 + 5787/94*a^2 - 526/47*a - 102/47)*q^3 + (a^2 - 2)*q^4 + (-19/94*a^13 + 32/47*a^12 + 142/47*a^11 - 983/94*a^10 - 1673/94*a^9 + 2781/47*a^8 + 5343/94*a^7 - 7014/47*a^6 - 5357/47*a^5 + 7384/47*a^4 + 11621/94*a^3 - 4151/94*a^2 - 1552/47*a + 302/47)*q^5 + (10/47*a^13 - 51/47*a^12 - 100/47*a^11 + 787/47*a^10 + 84/47*a^9 - 4372/47*a^8 + 1690/47*a^7 + 10547/47*a^6 - 5082/47*a^5 - 10558/47*a^4 + 4194/47*a^3 + 2959/47*a^2 - 1122/47*a + 68/47)*q^6 + (-39/188*a^13 + 65/47*a^12 + 27/47*a^11 - 3685/188*a^10 + 3705/188*a^9 + 4587/47*a^8 - 27647/188*a^7 - 18971/94*a^6 + 34223/94*a^5 + 15263/94*a^4 - 63131/188*a^3 - 6403/188*a^2 + 4062/47*a - 447/47)*q^7 + (a^3 - 4*a)*q^8 + (45/47*a^13 - 206/47*a^12 - 450/47*a^11 + 3001/47*a^10 + 566/47*a^9 - 15679/47*a^8 + 6148/47*a^7 + 35312/47*a^6 - 20331/47*a^5 - 32659/47*a^4 + 18920/47*a^3 + 8357/47*a^2 - 5378/47*a + 635/47)*q^9 + (-25/47*a^13 + 104/47*a^12 + 297/47*a^11 - 1568/47*a^10 - 962/47*a^9 + 8533/47*a^8 - 136/47*a^7 - 20234/47*a^6 + 3869/47*a^5 + 19956/47*a^4 - 3529/47*a^3 - 5447/47*a^2 + 1442/47*a - 76/47)*q^10 + (3/188*a^13 + 37/94*a^12 - 78/47*a^11 - 1047/188*a^10 + 4321/188*a^9 + 2559/94*a^8 - 22993/188*a^7 - 2526/47*a^6 + 27057/94*a^5 + 3779/94*a^4 - 53525/188*a^3 - 1279/188*a^2 + 7911/94*a - 432/47)*q^11 + (-8/47*a^13 + 22/47*a^12 + 127/47*a^11 - 357/47*a^10 - 697/47*a^9 + 2050/47*a^8 + 1562/47*a^7 - 5110/47*a^6 - 1330/47*a^5 + 5758/47*a^4 + 292/47*a^3 - 2809/47*a^2 - 80/47*a + 284/47)*q^12 + (-79/94*a^13 + 323/94*a^12 + 489/47*a^11 - 4859/94*a^10 - 1911/47*a^9 + 26671/94*a^8 + 4509/94*a^7 - 64761/94*a^6 - 28/47*a^5 + 33230/47*a^4 + 745/94*a^3 - 9848/47*a^2 + 1231/94*a + 239/47)*q^13 + (13/94*a^13 - 12/47*a^12 - 112/47*a^11 + 351/94*a^10 + 1491/94*a^9 - 896/47*a^8 - 4853/94*a^7 + 1843/47*a^6 + 4024/47*a^5 - 1265/47*a^4 - 6185/94*a^3 + 129/94*a^2 + 723/47*a - 78/47)*q^14 + (-13/47*a^13 + 71/47*a^12 + 83/47*a^11 - 1009/47*a^10 + 577/47*a^9 + 4941/47*a^8 - 5863/47*a^7 - 9514/47*a^6 + 15358/47*a^5 + 5632/47*a^4 - 14542/47*a^3 + 1093/47*a^2 + 4382/47*a - 784/47)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-57/47*a^13 + 239/47*a^12 + 664/47*a^11 - 3560/47*a^10 - 2058/47*a^9 + 19130/47*a^8 - 797/47*a^7 - 44810/47*a^6 + 9594/47*a^5 + 44069/47*a^4 - 8189/47*a^3 - 13064/47*a^2 + 2297/47*a + 214/47)*q^17 + (64/47*a^13 - 270/47*a^12 - 734/47*a^11 + 4031/47*a^10 + 2051/47*a^9 - 21617/47*a^8 + 2732/47*a^7 + 50139/47*a^6 - 16009/47*a^5 - 48085/47*a^4 + 15242/47*a^3 + 13072/47*a^2 - 4765/47*a + 360/47)*q^18 + (73/47*a^13 - 330/47*a^12 - 777/47*a^11 + 4885/47*a^10 + 1572/47*a^9 - 26003/47*a^8 + 6556/47*a^7 + 59871/47*a^6 - 24794/47*a^5 - 56619/47*a^4 + 22598/47*a^3 + 14358/47*a^2 - 7260/47*a + 816/47)*q^19 + (-27/47*a^13 + 133/47*a^12 + 223/47*a^11 - 1904/47*a^10 + 356/47*a^9 + 9727/47*a^8 - 7477/47*a^7 - 21253/47*a^6 + 21420/47*a^5 + 18928/47*a^4 - 20893/47*a^3 - 4657/47*a^2 + 6028/47*a - 804/47)*q^20 + (43/94*a^13 - 112/47*a^12 - 168/47*a^11 + 3229/94*a^10 - 889/94*a^9 - 8253/47*a^8 + 13753/94*a^7 + 17734/47*a^6 - 19297/47*a^5 - 14658/47*a^4 + 38451/94*a^3 + 4541/94*a^2 - 6365/47*a + 776/47)*q^21 + (23/47*a^13 - 75/47*a^12 - 324/47*a^11 + 1138/47*a^10 + 1575/47*a^9 - 6211/47*a^8 - 3069/47*a^7 + 14703/47*a^6 + 2167/47*a^5 - 14498/47*a^4 - 205/47*a^3 + 4263/47*a^2 - 522/47*a + 6/47)*q^22 + (73/47*a^13 - 613/94*a^12 - 871/47*a^11 + 4603/47*a^10 + 5917/94*a^9 - 49985/94*a^8 - 870/47*a^7 + 118379/94*a^6 - 7310/47*a^5 - 58123/47*a^4 + 5302/47*a^3 + 31301/94*a^2 - 4885/94*a + 17/47)*q^23 + (-46/47*a^13 + 197/47*a^12 + 507/47*a^11 - 2887/47*a^10 - 1270/47*a^9 + 15242/47*a^8 - 2698/47*a^7 - 34952/47*a^6 + 12962/47*a^5 + 33320/47*a^4 - 12421/47*a^3 - 9278/47*a^2 + 3488/47*a - 200/47)*q^24 + (-40/47*a^13 + 157/47*a^12 + 494/47*a^11 - 2302/47*a^10 - 1981/47*a^9 + 12224/47*a^8 + 2875/47*a^7 - 28323/47*a^6 - 2279/47*a^5 + 26957/47*a^4 + 3575/47*a^3 - 6713/47*a^2 - 682/47*a + 245/47)*q^25 + (-151/94*a^13 + 331/47*a^12 + 849/47*a^11 - 9905/94*a^10 - 4455/94*a^9 + 26626/47*a^8 - 7565/94*a^7 - 61885/47*a^6 + 18615/47*a^5 + 59188/47*a^4 - 31783/94*a^3 - 31159/94*a^2 + 4979/47*a - 316/47)*q^26 + (-28/47*a^13 + 124/47*a^12 + 280/47*a^11 - 1790/47*a^10 - 301/47*a^9 + 9149/47*a^8 - 4403/47*a^7 - 19671/47*a^6 + 14897/47*a^5 + 16581/47*a^4 - 15381/47*a^3 - 3275/47*a^2 + 5172/47*a - 604/47)*q^27 + (93/94*a^13 - 216/47*a^12 - 418/47*a^11 + 6177/94*a^10 - 375/94*a^9 - 15611/47*a^8 + 21921/94*a^7 + 33174/47*a^6 - 33083/47*a^5 - 28034/47*a^4 + 65249/94*a^3 + 13179/94*a^2 - 8982/47*a + 946/47)*q^28 + (-231/188*a^13 + 535/94*a^12 + 554/47*a^11 - 15449/188*a^10 - 1461/188*a^9 + 39743/94*a^8 - 39791/188*a^7 - 43506/47*a^6 + 62913/94*a^5 + 76087/94*a^4 - 122299/188*a^3 - 32929/188*a^2 + 18491/94*a - 1046/47)*q^29 + (-7/47*a^13 + 31/47*a^12 + 70/47*a^11 - 424/47*a^10 - 181/47*a^9 + 2158/47*a^8 - 102/47*a^7 - 5000/47*a^6 + 822/47*a^5 + 4815/47*a^4 - 896/47*a^3 - 948/47*a^2 + 776/47*a - 104/47)*q^30 + (-12/47*a^13 + 33/47*a^12 + 214/47*a^11 - 559/47*a^10 - 1492/47*a^9 + 3451/47*a^8 + 5351/47*a^7 - 9451/47*a^6 - 10784/47*a^5 + 11034/47*a^4 + 10966/47*a^3 - 4002/47*a^2 - 3175/47*a + 520/47)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (83/94*a^13 - 214/47*a^12 - 321/47*a^11 + 6095/94*a^10 - 1681/94*a^9 - 15352/47*a^8 + 25495/94*a^7 + 32483/47*a^6 - 34584/47*a^5 - 26985/47*a^4 + 63875/94*a^3 + 11301/94*a^2 - 8656/47*a + 912/47)*q^33 + (-103/47*a^13 + 436/47*a^12 + 1171/47*a^11 - 6447/47*a^10 - 3328/47*a^9 + 34372/47*a^8 - 3542/47*a^7 - 79668/47*a^6 + 22979/47*a^5 + 76684/47*a^4 - 21785/47*a^3 - 21073/47*a^2 + 7054/47*a - 456/47)*q^34 + (-51/94*a^13 + 123/47*a^12 + 255/47*a^11 - 3633/94*a^10 - 701/94*a^9 + 9654/47*a^8 - 5987/94*a^7 - 22263/47*a^6 + 8950/47*a^5 + 21344/47*a^4 - 11839/94*a^3 - 11627/94*a^2 + 591/47*a - 164/47)*q^35 + (24/47*a^13 - 66/47*a^12 - 381/47*a^11 + 977/47*a^10 + 2467/47*a^9 - 5398/47*a^8 - 8493/47*a^7 + 13591/47*a^6 + 16257/47*a^5 - 14736/47*a^4 - 14976/47*a^3 + 4761/47*a^2 + 3436/47*a - 758/47)*q^36 + (143/94*a^13 - 320/47*a^12 - 762/47*a^11 + 9407/94*a^10 + 3241/94*a^9 - 24896/47*a^8 + 11477/94*a^7 + 57121/47*a^6 - 22382/47*a^5 - 53959/47*a^4 + 39689/94*a^3 + 27833/94*a^2 - 5724/47*a + 552/47)*q^37 + O(q^38)
*]> ;  // time = 4.181 seconds




J[285] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 285, 285, 285, 285, 285, 285, 285, 95, 95, 57, 57, 57, 19, 15 ], new_dimensions := [ 1, 1, 1, 2, 2, 2, 2, 3, 4, 1, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 2, 2, 2, 2, 6, 8, 2, 2, 2, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 47, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 1, 1, 19, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 19, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 5, 47, 1, 1, 1, 1, 0, 1, 1, 1, 81, 1, 3, 3, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 7, 1, 5, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 81, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 1, -1, -1, -2, -2, -4, 2, -1, -4, 4, 0, 0 ],
[ 1, -1, 1, 4, 4, 2, 2, -1, -4, -2, 0, -6 ],
[ -1, 1, -1, -2, -6, 0, -6, 1, -8, 4, 0, 4 ],
[ 2, -2, -2, 4, 0, 8, -8, 2, 4, -4, -4, 8 ],
[ 0, -2, 2, -2, 6, -6, -8, -2, 8, 2, 12, 2 ],
[ 2, 2, -2, 0, 4, -4, 8, -2, 4, 0, -12, -4 ],
[ 0, 2, 2, -2, 6, -2, 0, 2, 0, 6, 4, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 - 2*x - 1,
x^2 - 7,
x^2 - 2*x - 1,
x^2 - 3
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, 1, -1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 1, 3, 1 ],
[ 5, 1, 1 ],
[ 47, 1, 1 ],
[ 19, 3, 3 ],
[ 1, 7, 1 ],
[ 3, 3, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 3, 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 3, 0, 1, 3, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1, 1, 1/9 ], eigenvalues := [*
[ 1, -1, -1, -2, -2, -4, 2, -1, -4, 4, 0, 0 ],
[ 1, -1, 1, 4, 4, 2, 2, -1, -4, -2, 0, -6 ],
[ -1, 1, -1, -2, -6, 0, -6, 1, -8, 4, 0, 4 ],
[
a,
-1,
-1,
a + 1,
-a + 1,
-a + 5,
-2*a - 2,
1,
-4*a + 6,
5*a - 7,
-6*a + 4,
-5*a + 9
],
[
a,
-1,
1,
-a - 1,
a + 3,
-a - 3,
-4,
-1,
-2*a + 4,
-3*a + 1,
6,
-a + 1
],
[
a,
1,
-1,
-a + 1,
-3*a + 5,
-a - 1,
-2*a + 6,
-1,
4*a - 2,
a - 1,
2*a - 8,
-a - 1
],
[
a,
1,
1,
a - 1,
-a + 3,
-a - 1,
0,
1,
-2*a,
-3*a + 3,
-4*a + 2,
3*a - 1
]
*], q_expansions := [*
q + q^2 - q^3 - q^4 - q^5 - q^6 - 2*q^7 - 3*q^8 + q^9 - q^10 - 2*q^11 + q^12 - 4*q^13 - 2*q^14 + q^15 - q^16 + 2*q^17 + q^18 - q^19 + q^20 + 2*q^21 - 2*q^22 - 4*q^23 + 3*q^24 + q^25 - 4*q^26 - q^27 + 2*q^28 + 4*q^29 + q^30 + 5*q^32 + 2*q^33 + 2*q^34 + 2*q^35 - q^36 + O(q^38),
q + q^2 - q^3 - q^4 + q^5 - q^6 + 4*q^7 - 3*q^8 + q^9 + q^10 + 4*q^11 + q^12 + 2*q^13 + 4*q^14 - q^15 - q^16 + 2*q^17 + q^18 - q^19 - q^20 - 4*q^21 + 4*q^22 - 4*q^23 + 3*q^24 + q^25 + 2*q^26 - q^27 - 4*q^28 - 2*q^29 - q^30 + 5*q^32 - 4*q^33 + 2*q^34 + 4*q^35 - q^36 - 6*q^37 + O(q^38),
q - q^2 + q^3 - q^4 - q^5 - q^6 - 2*q^7 + 3*q^8 + q^9 + q^10 - 6*q^11 - q^12 + 2*q^14 - q^15 - q^16 - 6*q^17 - q^18 + q^19 + q^20 - 2*q^21 + 6*q^22 - 8*q^23 + 3*q^24 + q^25 + q^27 + 2*q^28 + 4*q^29 + q^30 - 5*q^32 - 6*q^33 + 6*q^34 + 2*q^35 - q^36 + 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (2*a - 1)*q^4 - q^5 - a*q^6 + (a + 1)*q^7 + (a + 2)*q^8 + q^9 - a*q^10 + (-a + 1)*q^11 + (-2*a + 1)*q^12 + (-a + 5)*q^13 + (3*a + 1)*q^14 + q^15 + 3*q^16 + (-2*a - 2)*q^17 + a*q^18 + q^19 + (-2*a + 1)*q^20 + (-a - 1)*q^21 + (-a - 1)*q^22 + (-4*a + 6)*q^23 + (-a - 2)*q^24 + q^25 + (3*a - 1)*q^26 - q^27 + (5*a + 1)*q^28 + (5*a - 7)*q^29 + a*q^30 + (-6*a + 4)*q^31 + (a - 4)*q^32 + (a - 1)*q^33 + (-6*a - 2)*q^34 + (-a - 1)*q^35 + (2*a - 1)*q^36 + (-5*a + 9)*q^37 + O(q^38),
q + a*q^2 - q^3 + 5*q^4 + q^5 - a*q^6 + (-a - 1)*q^7 + 3*a*q^8 + q^9 + a*q^10 + (a + 3)*q^11 - 5*q^12 + (-a - 3)*q^13 + (-a - 7)*q^14 - q^15 + 11*q^16 - 4*q^17 + a*q^18 - q^19 + 5*q^20 + (a + 1)*q^21 + (3*a + 7)*q^22 + (-2*a + 4)*q^23 - 3*a*q^24 + q^25 + (-3*a - 7)*q^26 - q^27 + (-5*a - 5)*q^28 + (-3*a + 1)*q^29 - a*q^30 + 6*q^31 + 5*a*q^32 + (-a - 3)*q^33 - 4*a*q^34 + (-a - 1)*q^35 + 5*q^36 + (-a + 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (2*a - 1)*q^4 - q^5 + a*q^6 + (-a + 1)*q^7 + (a + 2)*q^8 + q^9 - a*q^10 + (-3*a + 5)*q^11 + (2*a - 1)*q^12 + (-a - 1)*q^13 + (-a - 1)*q^14 - q^15 + 3*q^16 + (-2*a + 6)*q^17 + a*q^18 - q^19 + (-2*a + 1)*q^20 + (-a + 1)*q^21 + (-a - 3)*q^22 + (4*a - 2)*q^23 + (a + 2)*q^24 + q^25 + (-3*a - 1)*q^26 + q^27 + (-a - 3)*q^28 + (a - 1)*q^29 - a*q^30 + (2*a - 8)*q^31 + (a - 4)*q^32 + (-3*a + 5)*q^33 + (2*a - 2)*q^34 + (a - 1)*q^35 + (2*a - 1)*q^36 + (-a - 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + q^4 + q^5 + a*q^6 + (a - 1)*q^7 - a*q^8 + q^9 + a*q^10 + (-a + 3)*q^11 + q^12 + (-a - 1)*q^13 + (-a + 3)*q^14 + q^15 - 5*q^16 + a*q^18 + q^19 + q^20 + (a - 1)*q^21 + (3*a - 3)*q^22 - 2*a*q^23 - a*q^24 + q^25 + (-a - 3)*q^26 + q^27 + (a - 1)*q^28 + (-3*a + 3)*q^29 + a*q^30 + (-4*a + 2)*q^31 - 3*a*q^32 + (-a + 3)*q^33 + (a - 1)*q^35 + q^36 + (3*a - 1)*q^37 + O(q^38)
*]> ;  // time = 82.009 seconds




J[286] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 286, 286, 286, 286, 286, 286, 286, 143, 143, 143, 26, 26, 11 ], new_dimensions := [ 1, 1, 1, 1, 1, 1, 3, 1, 4, 6, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 1, 3, 2, 8, 12, 2, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 15, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 139, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 139, 1, 0, 1, 1, 7, 81, 1, 15, 1, 13, 1, 1, 1, 1, 1, 0, 9, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 9, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 1, 1, 81, 1, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, 1, -1, -1, -1, -4, -8, -8, 0, 7 ],
[ -1, -2, 3, -1, -1, 1, 6, 8, -3, 9, 2, -10 ],
[ 1, 2, -1, 1, -1, -1, 2, -4, 1, 7, -6, -2 ],
[ 1, -1, -3, -5, -1, 1, 7, 0, -4, -8, 0, -3 ],
[ 1, -1, 1, 3, 1, 1, 3, 0, 4, 0, -8, -7 ],
[ 1, 2, 1, -3, 1, 1, -6, 0, 1, -3, 10, 2 ],
[ -3, 1, 2, -4, 3, -3, 3, -12, 5, 13, -2, 7 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^3 - x^2 - 10*x + 8
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ -1, -1, -1 ],
[ 1, -1, 1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 5, 1, 3 ],
[ 3, 5, 1 ],
[ 13, 1, 1 ],
[ 5, 1, 5 ],
[ 1, 1, 1 ],
[ 139, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 3, 1, 1 ],
[ 13, 1, 1 ],
[ 5, 1, 5 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 5, 1, 1 ], torsion_lower_bounds := [ 1, 3, 1, 1, 1, 1, 1 ], l_ratios := [ 0, 1/3, 3, 0, 1, 1, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 0, 1/25, 1, 1 ], eigenvalues := [*
[ -1, -1, -1, 1, -1, -1, -1, -4, -8, -8, 0, 7 ],
[ -1, -2, 3, -1, -1, 1, 6, 8, -3, 9, 2, -10 ],
[ 1, 2, -1, 1, -1, -1, 2, -4, 1, 7, -6, -2 ],
[ 1, -1, -3, -5, -1, 1, 7, 0, -4, -8, 0, -3 ],
[ 1, -1, 1, 3, 1, 1, 3, 0, 4, 0, -8, -7 ],
[ 1, 2, 1, -3, 1, 1, -6, 0, 1, -3, 10, 2 ],
[
-1,
a,
-1/2*a^2 + 1/2*a + 4,
-1/2*a^2 + 1/2*a + 2,
1,
-1,
a^2 - 6,
-4,
-1/2*a^2 - 5/2*a + 6,
-1/2*a^2 - 1/2*a + 8,
a^2 + a - 8,
-a^2 - 2*a + 10
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 + q^7 - q^8 - 2*q^9 + q^10 - q^11 - q^12 - q^13 - q^14 + q^15 + q^16 - q^17 + 2*q^18 - 4*q^19 - q^20 - q^21 + q^22 - 8*q^23 + q^24 - 4*q^25 + q^26 + 5*q^27 + q^28 - 8*q^29 - q^30 - q^32 + q^33 + q^34 - q^35 - 2*q^36 + 7*q^37 + O(q^38),
q - q^2 - 2*q^3 + q^4 + 3*q^5 + 2*q^6 - q^7 - q^8 + q^9 - 3*q^10 - q^11 - 2*q^12 + q^13 + q^14 - 6*q^15 + q^16 + 6*q^17 - q^18 + 8*q^19 + 3*q^20 + 2*q^21 + q^22 - 3*q^23 + 2*q^24 + 4*q^25 - q^26 + 4*q^27 - q^28 + 9*q^29 + 6*q^30 + 2*q^31 - q^32 + 2*q^33 - 6*q^34 - 3*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 - q^5 + 2*q^6 + q^7 + q^8 + q^9 - q^10 - q^11 + 2*q^12 - q^13 + q^14 - 2*q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 - q^20 + 2*q^21 - q^22 + q^23 + 2*q^24 - 4*q^25 - q^26 - 4*q^27 + q^28 + 7*q^29 - 2*q^30 - 6*q^31 + q^32 - 2*q^33 + 2*q^34 - q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 3*q^5 - q^6 - 5*q^7 + q^8 - 2*q^9 - 3*q^10 - q^11 - q^12 + q^13 - 5*q^14 + 3*q^15 + q^16 + 7*q^17 - 2*q^18 - 3*q^20 + 5*q^21 - q^22 - 4*q^23 - q^24 + 4*q^25 + q^26 + 5*q^27 - 5*q^28 - 8*q^29 + 3*q^30 + q^32 + q^33 + 7*q^34 + 15*q^35 - 2*q^36 - 3*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + 3*q^7 + q^8 - 2*q^9 + q^10 + q^11 - q^12 + q^13 + 3*q^14 - q^15 + q^16 + 3*q^17 - 2*q^18 + q^20 - 3*q^21 + q^22 + 4*q^23 - q^24 - 4*q^25 + q^26 + 5*q^27 + 3*q^28 - q^30 - 8*q^31 + q^32 - q^33 + 3*q^34 + 3*q^35 - 2*q^36 - 7*q^37 + O(q^38),
q + q^2 + 2*q^3 + q^4 + q^5 + 2*q^6 - 3*q^7 + q^8 + q^9 + q^10 + q^11 + 2*q^12 + q^13 - 3*q^14 + 2*q^15 + q^16 - 6*q^17 + q^18 + q^20 - 6*q^21 + q^22 + q^23 + 2*q^24 - 4*q^25 + q^26 - 4*q^27 - 3*q^28 - 3*q^29 + 2*q^30 + 10*q^31 + q^32 + 2*q^33 - 6*q^34 - 3*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a^2 + 1/2*a + 4)*q^5 - a*q^6 + (-1/2*a^2 + 1/2*a + 2)*q^7 - q^8 + (a^2 - 3)*q^9 + (1/2*a^2 - 1/2*a - 4)*q^10 + q^11 + a*q^12 - q^13 + (1/2*a^2 - 1/2*a - 2)*q^14 + (-a + 4)*q^15 + q^16 + (a^2 - 6)*q^17 + (-a^2 + 3)*q^18 - 4*q^19 + (-1/2*a^2 + 1/2*a + 4)*q^20 + (-3*a + 4)*q^21 - q^22 + (-1/2*a^2 - 5/2*a + 6)*q^23 - a*q^24 + (-3/2*a^2 - 1/2*a + 13)*q^25 + q^26 + (a^2 + 4*a - 8)*q^27 + (-1/2*a^2 + 1/2*a + 2)*q^28 + (-1/2*a^2 - 1/2*a + 8)*q^29 + (a - 4)*q^30 + (a^2 + a - 8)*q^31 - q^32 + a*q^33 + (-a^2 + 6)*q^34 + (-1/2*a^2 - 3/2*a + 10)*q^35 + (a^2 - 3)*q^36 + (-a^2 - 2*a + 10)*q^37 + O(q^38)
*]> ;  // time = 107.98 seconds




J[287] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 287, 287, 287, 287, 287, 287, 41 ], new_dimensions := [ 2, 2, 3, 3, 5, 6, 3 ], dimensions := [ 2, 2, 3, 3, 5, 6, 6 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 19, 1, 1, 0, 1, 1, 97, 13, 1, 1, 1, 0, 61, 1, 1, 1, 1, 1, 61, 0, 1, 1, 1, 1, 97, 1, 1, 0, 37, 1, 19, 13, 1, 1, 37, 0 ], ap_traces := [
[ -1, -1, 1, -2, -2, -8, -4, -1, -5, -5, 5, -10 ],
[ -1, -3, -1, 2, 0, -6, -6, -3, 3, 9, -17, 2 ],
[ 4, 5, 2, -3, -4, 7, 3, -11, -13, 2, 0, 3 ],
[ 1, -1, 6, 3, -6, 9, 1, 13, -11, 10, -2, 3 ],
[ -1, 4, -5, 5, 2, 5, 13, 0, 2, -5, 17, -7 ],
[ -1, -4, -1, -6, 6, 7, 7, 2, 20, -9, -27, 19 ]
], hecke_fields := [
x^2 + x - 1,
x^2 + x - 1,
x^3 - 4*x^2 + 3*x + 1,
x^3 - x^2 - 4*x + 3,
x^5 + x^4 - 6*x^3 - 4*x^2 + 6*x + 3,
x^6 + x^5 - 10*x^4 - 10*x^3 + 23*x^2 + 24*x + 5
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 19, 1 ],
[ 13, 1 ],
[ 1, 1 ],
[ 21, 3 ],
[ 37, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 19, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 21, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 21, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 21, 1 ], l_ratios := [ 0, 0, 1, 1, 1/21, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 1, 1 ], eigenvalues := [*
[
a,
-a - 1,
a + 1,
-1,
-1,
-2*a - 5,
-2*a - 3,
3*a + 1,
-a - 3,
-3*a - 4,
5*a + 5,
2*a - 4
],
[
a,
a - 1,
-a - 1,
1,
-2*a - 1,
-3,
4*a - 1,
-3*a - 3,
-a + 1,
3*a + 6,
-a - 9,
6*a + 4
],
[
a,
-a + 3,
-2*a^2 + 4*a + 2,
-1,
2*a^2 - 6*a,
-a^2 + 5*a - 1,
-a^2 - 2*a + 7,
3*a^2 - 8*a - 3,
-2*a^2 + 7*a - 7,
-4*a^2 + 12*a - 2,
-6*a^2 + 18*a - 4,
3*a^2 - 9*a + 3
],
[
a,
a^2 - a - 3,
2,
1,
-2,
-a^2 + 6,
-2*a^2 + a + 6,
a + 4,
-a^2 + a - 1,
-2*a + 4,
-2*a,
5*a^2 - 14
],
[
a,
a + 1,
a^4 - 7*a^2 + a + 6,
1,
-a^4 - a^3 + 3*a^2 + 2*a + 3,
-a^4 - a^3 + 6*a^2 + 3*a - 4,
a^4 + 2*a^3 - 4*a^2 - 7*a + 3,
-a^4 + a^3 + 6*a^2 - 6*a - 4,
2*a^4 - 12*a^2 + a + 9,
2*a^4 + a^3 - 10*a^2 - 3*a + 3,
-a^4 + 7*a^2 - 3*a - 4,
-2*a^4 + 13*a^2 - 3*a - 13
],
[
a,
-a^3 + 5*a,
a^5 - 9*a^3 - a^2 + 19*a + 6,
-1,
a^5 + a^4 - 11*a^3 - 8*a^2 + 30*a + 15,
a^5 + a^4 - 10*a^3 - 8*a^2 + 22*a + 14,
a^3 + a^2 - 5*a - 3,
-a^4 - a^3 + 6*a^2 + 4*a - 2,
-a^3 + 5*a + 4,
2*a^5 + a^4 - 22*a^3 - 11*a^2 + 59*a + 27,
a^5 - 11*a^3 - 3*a^2 + 29*a + 10,
2*a^5 - 19*a^3 - 4*a^2 + 42*a + 23
]
*], q_expansions := [*
q + a*q^2 + (-a - 1)*q^3 + (-a - 1)*q^4 + (a + 1)*q^5 - q^6 - q^7 + (-2*a - 1)*q^8 + (a - 1)*q^9 + q^10 - q^11 + (a + 2)*q^12 + (-2*a - 5)*q^13 - a*q^14 + (-a - 2)*q^15 + 3*a*q^16 + (-2*a - 3)*q^17 + (-2*a + 1)*q^18 + (3*a + 1)*q^19 + (-a - 2)*q^20 + (a + 1)*q^21 - a*q^22 + (-a - 3)*q^23 + (a + 3)*q^24 + (a - 3)*q^25 + (-3*a - 2)*q^26 + (4*a + 3)*q^27 + (a + 1)*q^28 + (-3*a - 4)*q^29 + (-a - 1)*q^30 + (5*a + 5)*q^31 + (a + 5)*q^32 + (a + 1)*q^33 + (-a - 2)*q^34 + (-a - 1)*q^35 + a*q^36 + (2*a - 4)*q^37 + O(q^38),
q + a*q^2 + (a - 1)*q^3 + (-a - 1)*q^4 + (-a - 1)*q^5 + (-2*a + 1)*q^6 + q^7 + (-2*a - 1)*q^8 + (-3*a - 1)*q^9 - q^10 + (-2*a - 1)*q^11 + a*q^12 - 3*q^13 + a*q^14 + a*q^15 + 3*a*q^16 + (4*a - 1)*q^17 + (2*a - 3)*q^18 + (-3*a - 3)*q^19 + (a + 2)*q^20 + (a - 1)*q^21 + (a - 2)*q^22 + (-a + 1)*q^23 + (3*a - 1)*q^24 + (a - 3)*q^25 - 3*a*q^26 + (2*a + 1)*q^27 + (-a - 1)*q^28 + (3*a + 6)*q^29 + (-a + 1)*q^30 + (-a - 9)*q^31 + (a + 5)*q^32 + (3*a - 1)*q^33 + (-5*a + 4)*q^34 + (-a - 1)*q^35 + (a + 4)*q^36 + (6*a + 4)*q^37 + O(q^38),
q + a*q^2 + (-a + 3)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 + 4*a + 2)*q^5 + (-a^2 + 3*a)*q^6 - q^7 + (4*a^2 - 7*a - 1)*q^8 + (a^2 - 6*a + 6)*q^9 + (-4*a^2 + 8*a + 2)*q^10 + (2*a^2 - 6*a)*q^11 + (-a^2 + 5*a - 5)*q^12 + (-a^2 + 5*a - 1)*q^13 - a*q^14 + (-2*a^2 + 4*a + 4)*q^15 + (7*a^2 - 13*a)*q^16 + (-a^2 - 2*a + 7)*q^17 + (-2*a^2 + 3*a - 1)*q^18 + (3*a^2 - 8*a - 3)*q^19 + (-4*a^2 + 6*a)*q^20 + (a - 3)*q^21 + (2*a^2 - 6*a - 2)*q^22 + (-2*a^2 + 7*a - 7)*q^23 + (3*a^2 - 8*a + 1)*q^24 + (-4*a^2 + 12*a - 1)*q^25 + (a^2 + 2*a + 1)*q^26 + (5*a^2 - 18*a + 10)*q^27 + (-a^2 + 2)*q^28 + (-4*a^2 + 12*a - 2)*q^29 + (-4*a^2 + 10*a + 2)*q^30 + (-6*a^2 + 18*a - 4)*q^31 + (7*a^2 - 7*a - 5)*q^32 + (4*a^2 - 12*a + 2)*q^33 + (-6*a^2 + 10*a + 1)*q^34 + (2*a^2 - 4*a - 2)*q^35 + (-7*a^2 + 17*a - 10)*q^36 + (3*a^2 - 9*a + 3)*q^37 + O(q^38),
q + a*q^2 + (a^2 - a - 3)*q^3 + (a^2 - 2)*q^4 + 2*q^5 + (a - 3)*q^6 + q^7 + (a^2 - 3)*q^8 + (-2*a^2 - a + 9)*q^9 + 2*a*q^10 - 2*q^11 + (-a^2 - a + 6)*q^12 + (-a^2 + 6)*q^13 + a*q^14 + (2*a^2 - 2*a - 6)*q^15 + (-a^2 + a + 1)*q^16 + (-2*a^2 + a + 6)*q^17 + (-3*a^2 + a + 6)*q^18 + (a + 4)*q^19 + (2*a^2 - 4)*q^20 + (a^2 - a - 3)*q^21 - 2*a*q^22 + (-a^2 + a - 1)*q^23 + (-2*a^2 + 9)*q^24 - q^25 + (-a^2 + 2*a + 3)*q^26 + (4*a^2 - a - 15)*q^27 + (a^2 - 2)*q^28 + (-2*a + 4)*q^29 + (2*a - 6)*q^30 - 2*a*q^31 + (-2*a^2 - 3*a + 9)*q^32 + (-2*a^2 + 2*a + 6)*q^33 + (-a^2 - 2*a + 6)*q^34 + 2*q^35 + (2*a^2 - 4*a - 9)*q^36 + (5*a^2 - 14)*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (a^2 - 2)*q^4 + (a^4 - 7*a^2 + a + 6)*q^5 + (a^2 + a)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (a^2 + 2*a - 2)*q^9 + (-a^4 - a^3 + 5*a^2 - 3)*q^10 + (-a^4 - a^3 + 3*a^2 + 2*a + 3)*q^11 + (a^3 + a^2 - 2*a - 2)*q^12 + (-a^4 - a^3 + 6*a^2 + 3*a - 4)*q^13 + a*q^14 + (-a^3 - 2*a^2 + a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + 2*a^3 - 4*a^2 - 7*a + 3)*q^17 + (a^3 + 2*a^2 - 2*a)*q^18 + (-a^4 + a^3 + 6*a^2 - 6*a - 4)*q^19 + (-2*a^4 - a^3 + 10*a^2 + a - 9)*q^20 + (a + 1)*q^21 + (-3*a^3 - 2*a^2 + 9*a + 3)*q^22 + (2*a^4 - 12*a^2 + a + 9)*q^23 + (a^4 + a^3 - 4*a^2 - 4*a)*q^24 + (2*a^4 + 3*a^3 - 10*a^2 - 9*a + 10)*q^25 + (-a^2 + 2*a + 3)*q^26 + (a^3 + 3*a^2 - 3*a - 5)*q^27 + (a^2 - 2)*q^28 + (2*a^4 + a^3 - 10*a^2 - 3*a + 3)*q^29 + (-a^4 - 2*a^3 + a^2 + 3*a)*q^30 + (-a^4 + 7*a^2 - 3*a - 4)*q^31 + (-a^4 - 2*a^3 + 4*a^2 + 6*a - 3)*q^32 + (-a^4 - 4*a^3 + a^2 + 11*a + 6)*q^33 + (a^4 + 2*a^3 - 3*a^2 - 3*a - 3)*q^34 + (a^4 - 7*a^2 + a + 6)*q^35 + (a^4 + 2*a^3 - 4*a^2 - 4*a + 4)*q^36 + (-2*a^4 + 13*a^2 - 3*a - 13)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 5*a)*q^3 + (a^2 - 2)*q^4 + (a^5 - 9*a^3 - a^2 + 19*a + 6)*q^5 + (-a^4 + 5*a^2)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^5 + 10*a^3 + 2*a^2 - 24*a - 8)*q^9 + (-a^5 + a^4 + 9*a^3 - 4*a^2 - 18*a - 5)*q^10 + (a^5 + a^4 - 11*a^3 - 8*a^2 + 30*a + 15)*q^11 + (-a^5 + 7*a^3 - 10*a)*q^12 + (a^5 + a^4 - 10*a^3 - 8*a^2 + 22*a + 14)*q^13 - a*q^14 + (-2*a^5 - a^4 + 20*a^3 + 7*a^2 - 47*a - 15)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^3 + a^2 - 5*a - 3)*q^17 + (a^5 - 8*a^3 - a^2 + 16*a + 5)*q^18 + (-a^4 - a^3 + 6*a^2 + 4*a - 2)*q^19 + (-a^4 + 4*a^3 + 7*a^2 - 19*a - 7)*q^20 + (a^3 - 5*a)*q^21 + (-a^4 + 2*a^3 + 7*a^2 - 9*a - 5)*q^22 + (-a^3 + 5*a + 4)*q^23 + (a^5 - a^4 - 10*a^3 + 3*a^2 + 24*a + 5)*q^24 + (-2*a^5 - a^4 + 22*a^3 + 11*a^2 - 61*a - 24)*q^25 + (2*a^3 - a^2 - 10*a - 5)*q^26 + (2*a^5 + a^4 - 20*a^3 - 9*a^2 + 46*a + 20)*q^27 + (-a^2 + 2)*q^28 + (2*a^5 + a^4 - 22*a^3 - 11*a^2 + 59*a + 27)*q^29 + (a^5 - 13*a^3 - a^2 + 33*a + 10)*q^30 + (a^5 - 11*a^3 - 3*a^2 + 29*a + 10)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3*a^5 - 2*a^4 + 29*a^3 + 17*a^2 - 69*a - 30)*q^33 + (a^4 + a^3 - 5*a^2 - 3*a)*q^34 + (-a^5 + 9*a^3 + a^2 - 19*a - 6)*q^35 + (a^5 + 2*a^4 - 11*a^3 - 11*a^2 + 29*a + 11)*q^36 + (2*a^5 - 19*a^3 - 4*a^2 + 42*a + 23)*q^37 + O(q^38)
*]> ;  // time = 40.08 seconds




J[290] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 290, 290, 290, 290, 290, 145, 145, 145, 145, 58, 58, 29 ], new_dimensions := [ 1, 2, 2, 3, 3, 1, 2, 3, 3, 1, 1, 2 ], dimensions := [ 1, 2, 2, 3, 3, 2, 4, 6, 6, 2, 2, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 13, 9, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 49, 1, 23, 1, 1, 1, 1, 1, 0, 1, 1, 1, 625, 1, 1, 13, 1, 1, 1, 1, 1, 0, 1, 5, 1, 3, 1, 9, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 5, 1, 0, 1, 1, 1, 1, 1, 7, 1, 49, 625, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -1, -2, 2, -6, 2, -2, -6, -1, -6, -2 ],
[ -2, 1, -2, 5, -2, 9, 3, 6, 7, 2, -5, -2 ],
[ -2, 1, 2, 3, 2, -1, -1, 6, -3, -2, 17, 6 ],
[ 3, 3, -3, 3, 0, 3, 3, 0, -15, -3, -9, 0 ],
[ 3, -1, 3, -1, 2, 5, -5, 2, 1, 3, -5, -4 ]
], hecke_fields := [
x - 1,
x^2 - x - 3,
x^2 - x - 3,
x^3 - 3*x^2 - 3*x + 8,
x^3 + x^2 - 7*x + 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 23, 1, 3 ],
[ 13, 27, 1 ],
[ 3, 7, 1 ],
[ 49, 7, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 3 ],
[ 1, 27, 1 ],
[ 3, 1, 1 ],
[ 49, 7, 1 ]
], torsion_upper_bounds := [ 1, 3, 3, 3, 7 ], torsion_lower_bounds := [ 1, 3, 3, 3, 1 ], l_ratios := [ 0, 1/3, 3, 1/3, 7 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 1/49 ], eigenvalues := [*
[ -1, 0, -1, -2, 2, -6, 2, -2, -6, -1, -6, -2 ],
[
-1,
a,
-1,
-a + 3,
2*a - 2,
a + 4,
-3*a + 3,
-2*a + 4,
-a + 4,
1,
-3*a - 1,
6*a - 4
],
[
-1,
a,
1,
a + 1,
-2*a + 2,
-a,
a - 1,
-2*a + 4,
-3*a,
-1,
-a + 9,
-2*a + 4
],
[
1,
a,
-1,
-a^2 + 6,
-2*a + 2,
2*a^2 - 3*a - 6,
a^2 - 2*a - 2,
-2*a^2 + 4*a + 6,
-2*a^2 + 3*a + 2,
-1,
a^2 - 2*a - 6,
-2*a^2 + 10
],
[
1,
a,
1,
-a^2 - 2*a + 4,
2*a^2 + 4*a - 8,
-2*a^2 - 5*a + 10,
a^2 + 2*a - 6,
-2*a,
-a,
1,
-3*a^2 - 4*a + 12,
2*a^2 + 4*a - 10
]
*], q_expansions := [*
q - q^2 + q^4 - q^5 - 2*q^7 - q^8 - 3*q^9 + q^10 + 2*q^11 - 6*q^13 + 2*q^14 + q^16 + 2*q^17 + 3*q^18 - 2*q^19 - q^20 - 2*q^22 - 6*q^23 + q^25 + 6*q^26 - 2*q^28 - q^29 - 6*q^31 - q^32 - 2*q^34 + 2*q^35 - 3*q^36 - 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (-a + 3)*q^7 - q^8 + a*q^9 + q^10 + (2*a - 2)*q^11 + a*q^12 + (a + 4)*q^13 + (a - 3)*q^14 - a*q^15 + q^16 + (-3*a + 3)*q^17 - a*q^18 + (-2*a + 4)*q^19 - q^20 + (2*a - 3)*q^21 + (-2*a + 2)*q^22 + (-a + 4)*q^23 - a*q^24 + q^25 + (-a - 4)*q^26 + (-2*a + 3)*q^27 + (-a + 3)*q^28 + q^29 + a*q^30 + (-3*a - 1)*q^31 - q^32 + 6*q^33 + (3*a - 3)*q^34 + (a - 3)*q^35 + a*q^36 + (6*a - 4)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 + (a + 1)*q^7 - q^8 + a*q^9 - q^10 + (-2*a + 2)*q^11 + a*q^12 - a*q^13 + (-a - 1)*q^14 + a*q^15 + q^16 + (a - 1)*q^17 - a*q^18 + (-2*a + 4)*q^19 + q^20 + (2*a + 3)*q^21 + (2*a - 2)*q^22 - 3*a*q^23 - a*q^24 + q^25 + a*q^26 + (-2*a + 3)*q^27 + (a + 1)*q^28 - q^29 - a*q^30 + (-a + 9)*q^31 - q^32 - 6*q^33 + (-a + 1)*q^34 + (a + 1)*q^35 + a*q^36 + (-2*a + 4)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + (-a^2 + 6)*q^7 + q^8 + (a^2 - 3)*q^9 - q^10 + (-2*a + 2)*q^11 + a*q^12 + (2*a^2 - 3*a - 6)*q^13 + (-a^2 + 6)*q^14 - a*q^15 + q^16 + (a^2 - 2*a - 2)*q^17 + (a^2 - 3)*q^18 + (-2*a^2 + 4*a + 6)*q^19 - q^20 + (-3*a^2 + 3*a + 8)*q^21 + (-2*a + 2)*q^22 + (-2*a^2 + 3*a + 2)*q^23 + a*q^24 + q^25 + (2*a^2 - 3*a - 6)*q^26 + (3*a^2 - 3*a - 8)*q^27 + (-a^2 + 6)*q^28 - q^29 - a*q^30 + (a^2 - 2*a - 6)*q^31 + q^32 + (-2*a^2 + 2*a)*q^33 + (a^2 - 2*a - 2)*q^34 + (a^2 - 6)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 + 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 + (-a^2 - 2*a + 4)*q^7 + q^8 + (a^2 - 3)*q^9 + q^10 + (2*a^2 + 4*a - 8)*q^11 + a*q^12 + (-2*a^2 - 5*a + 10)*q^13 + (-a^2 - 2*a + 4)*q^14 + a*q^15 + q^16 + (a^2 + 2*a - 6)*q^17 + (a^2 - 3)*q^18 - 2*a*q^19 + q^20 + (-a^2 - 3*a + 4)*q^21 + (2*a^2 + 4*a - 8)*q^22 - a*q^23 + a*q^24 + q^25 + (-2*a^2 - 5*a + 10)*q^26 + (-a^2 + a - 4)*q^27 + (-a^2 - 2*a + 4)*q^28 + q^29 + a*q^30 + (-3*a^2 - 4*a + 12)*q^31 + q^32 + (2*a^2 + 6*a - 8)*q^33 + (a^2 + 2*a - 6)*q^34 + (-a^2 - 2*a + 4)*q^35 + (a^2 - 3)*q^36 + (2*a^2 + 4*a - 10)*q^37 + O(q^38)
*]> ;  // time = 119.99 seconds




J[291] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 291, 291, 291, 291, 291, 291, 291, 291, 97, 97 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 2, 7, 3, 4 ], dimensions := [ 1, 1, 1, 1, 2, 2, 2, 7, 6, 8 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 5, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 11, 1, 1, 1, 23, 3, 1, 1, 1, 0, 1, 1, 1, 13, 1, 1, 5, 1, 11, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 0, 139, 1, 1, 1, 1, 1, 13, 1, 1, 139, 0, 1, 1, 1, 1, 23, 1, 1, 11, 1, 1, 0 ], ap_traces := [
[ -1, -1, 0, 2, -4, -2, -8, -2, -4, 0, 8, 10 ],
[ -1, -1, -2, -4, 4, 6, 2, -8, 4, 6, 8, -2 ],
[ 2, -1, 1, 2, 4, 0, 2, -2, -8, -3, -1, 4 ],
[ -2, -1, 3, -2, 0, -4, 6, 6, 0, 7, 7, 4 ],
[ -1, -2, -6, 3, -3, -3, 5, -8, 0, -11, -5, -10 ],
[ 3, -2, 6, -3, -7, 7, -1, 4, 8, 7, -9, -14 ],
[ -1, 2, -4, -7, 1, -9, 1, -8, 6, -7, -5, -6 ],
[ 0, 7, 4, 9, -3, 11, -5, 6, -10, 3, 9, 4 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + x - 3,
x^2 - 3*x + 1,
x^2 + x - 1,
x^7 - 11*x^5 + x^4 + 34*x^3 - 5*x^2 - 24*x - 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 23, 1 ],
[ 13, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 6811, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 6811, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 1, 49 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 49 ], l_ratios := [ 0, 1, 1, 1, 0, 1, 0, 139/49 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1, 0, 1 ], eigenvalues := [*
[ -1, -1, 0, 2, -4, -2, -8, -2, -4, 0, 8, 10 ],
[ -1, -1, -2, -4, 4, 6, 2, -8, 4, 6, 8, -2 ],
[ 2, -1, 1, 2, 4, 0, 2, -2, -8, -3, -1, 4 ],
[ -2, -1, 3, -2, 0, -4, 6, 6, 0, 7, 7, 4 ],
[
a,
-1,
-3,
-a + 1,
-a - 2,
a - 1,
-3*a + 1,
2*a - 3,
2*a + 1,
a - 5,
3*a - 1,
-5
],
[
a,
-1,
3,
-3*a + 3,
-a - 2,
-a + 5,
-5*a + 7,
2*a - 1,
-2*a + 7,
-a + 5,
3*a - 9,
-7
],
[
a,
1,
-2*a - 3,
a - 3,
3*a + 2,
-a - 5,
a + 1,
-2*a - 5,
-4*a + 1,
5*a - 1,
-a - 3,
8*a + 1
],
[
a,
1,
-1/2*a^6 + 9/2*a^4 - 1/2*a^3 - 10*a^2 + 5/2*a + 4,
1/2*a^6 + 1/2*a^5 - 5*a^4 - 7/2*a^3 + 25/2*a^2 + 3*a - 2,
a^4 - a^3 - 7*a^2 + 5*a + 6,
a^3 - 5*a + 2,
-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 8,
1/2*a^6 + 1/2*a^5 - 4*a^4 - 9/2*a^3 + 11/2*a^2 + 8*a + 4,
1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 25/2*a^2 - 5*a - 6,
-1/2*a^6 + 11/2*a^4 - 3/2*a^3 - 15*a^2 + 15/2*a + 4,
a^4 - 6*a^2 + 5,
-2*a^5 - a^4 + 16*a^3 + 7*a^2 - 26*a - 8
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 + q^6 + 2*q^7 + 3*q^8 + q^9 - 4*q^11 + q^12 - 2*q^13 - 2*q^14 - q^16 - 8*q^17 - q^18 - 2*q^19 - 2*q^21 + 4*q^22 - 4*q^23 - 3*q^24 - 5*q^25 + 2*q^26 - q^27 - 2*q^28 + 8*q^31 - 5*q^32 + 4*q^33 + 8*q^34 - q^36 + 10*q^37 + O(q^38),
q - q^2 - q^3 - q^4 - 2*q^5 + q^6 - 4*q^7 + 3*q^8 + q^9 + 2*q^10 + 4*q^11 + q^12 + 6*q^13 + 4*q^14 + 2*q^15 - q^16 + 2*q^17 - q^18 - 8*q^19 + 2*q^20 + 4*q^21 - 4*q^22 + 4*q^23 - 3*q^24 - q^25 - 6*q^26 - q^27 + 4*q^28 + 6*q^29 - 2*q^30 + 8*q^31 - 5*q^32 - 4*q^33 - 2*q^34 + 8*q^35 - q^36 - 2*q^37 + O(q^38),
q + 2*q^2 - q^3 + 2*q^4 + q^5 - 2*q^6 + 2*q^7 + q^9 + 2*q^10 + 4*q^11 - 2*q^12 + 4*q^14 - q^15 - 4*q^16 + 2*q^17 + 2*q^18 - 2*q^19 + 2*q^20 - 2*q^21 + 8*q^22 - 8*q^23 - 4*q^25 - q^27 + 4*q^28 - 3*q^29 - 2*q^30 - q^31 - 8*q^32 - 4*q^33 + 4*q^34 + 2*q^35 + 2*q^36 + 4*q^37 + O(q^38),
q - 2*q^2 - q^3 + 2*q^4 + 3*q^5 + 2*q^6 - 2*q^7 + q^9 - 6*q^10 - 2*q^12 - 4*q^13 + 4*q^14 - 3*q^15 - 4*q^16 + 6*q^17 - 2*q^18 + 6*q^19 + 6*q^20 + 2*q^21 + 4*q^25 + 8*q^26 - q^27 - 4*q^28 + 7*q^29 + 6*q^30 + 7*q^31 + 8*q^32 - 12*q^34 - 6*q^35 + 2*q^36 + 4*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a + 1)*q^4 - 3*q^5 - a*q^6 + (-a + 1)*q^7 - 3*q^8 + q^9 - 3*a*q^10 + (-a - 2)*q^11 + (a - 1)*q^12 + (a - 1)*q^13 + (2*a - 3)*q^14 + 3*q^15 + (-a - 2)*q^16 + (-3*a + 1)*q^17 + a*q^18 + (2*a - 3)*q^19 + (3*a - 3)*q^20 + (a - 1)*q^21 + (-a - 3)*q^22 + (2*a + 1)*q^23 + 3*q^24 + 4*q^25 + (-2*a + 3)*q^26 - q^27 + (-3*a + 4)*q^28 + (a - 5)*q^29 + 3*a*q^30 + (3*a - 1)*q^31 + (-a + 3)*q^32 + (a + 2)*q^33 + (4*a - 9)*q^34 + (3*a - 3)*q^35 + (-a + 1)*q^36 - 5*q^37 + O(q^38),
q + a*q^2 - q^3 + (3*a - 3)*q^4 + 3*q^5 - a*q^6 + (-3*a + 3)*q^7 + (4*a - 3)*q^8 + q^9 + 3*a*q^10 + (-a - 2)*q^11 + (-3*a + 3)*q^12 + (-a + 5)*q^13 + (-6*a + 3)*q^14 - 3*q^15 + (3*a + 2)*q^16 + (-5*a + 7)*q^17 + a*q^18 + (2*a - 1)*q^19 + (9*a - 9)*q^20 + (3*a - 3)*q^21 + (-5*a + 1)*q^22 + (-2*a + 7)*q^23 + (-4*a + 3)*q^24 + 4*q^25 + (2*a + 1)*q^26 - q^27 - 9*a*q^28 + (-a + 5)*q^29 - 3*a*q^30 + (3*a - 9)*q^31 + (3*a + 3)*q^32 + (a + 2)*q^33 + (-8*a + 5)*q^34 + (-9*a + 9)*q^35 + (3*a - 3)*q^36 - 7*q^37 + O(q^38),
q + a*q^2 + q^3 + (-a - 1)*q^4 + (-2*a - 3)*q^5 + a*q^6 + (a - 3)*q^7 + (-2*a - 1)*q^8 + q^9 + (-a - 2)*q^10 + (3*a + 2)*q^11 + (-a - 1)*q^12 + (-a - 5)*q^13 + (-4*a + 1)*q^14 + (-2*a - 3)*q^15 + 3*a*q^16 + (a + 1)*q^17 + a*q^18 + (-2*a - 5)*q^19 + (3*a + 5)*q^20 + (a - 3)*q^21 + (-a + 3)*q^22 + (-4*a + 1)*q^23 + (-2*a - 1)*q^24 + (8*a + 8)*q^25 + (-4*a - 1)*q^26 + q^27 + (3*a + 2)*q^28 + (5*a - 1)*q^29 + (-a - 2)*q^30 + (-a - 3)*q^31 + (a + 5)*q^32 + (3*a + 2)*q^33 + q^34 + (5*a + 7)*q^35 + (-a - 1)*q^36 + (8*a + 1)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-1/2*a^6 + 9/2*a^4 - 1/2*a^3 - 10*a^2 + 5/2*a + 4)*q^5 + a*q^6 + (1/2*a^6 + 1/2*a^5 - 5*a^4 - 7/2*a^3 + 25/2*a^2 + 3*a - 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^5 + 7*a^3 - 8*a - 2)*q^10 + (a^4 - a^3 - 7*a^2 + 5*a + 6)*q^11 + (a^2 - 2)*q^12 + (a^3 - 5*a + 2)*q^13 + (1/2*a^6 + 1/2*a^5 - 4*a^4 - 9/2*a^3 + 11/2*a^2 + 10*a + 2)*q^14 + (-1/2*a^6 + 9/2*a^4 - 1/2*a^3 - 10*a^2 + 5/2*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 8)*q^17 + a*q^18 + (1/2*a^6 + 1/2*a^5 - 4*a^4 - 9/2*a^3 + 11/2*a^2 + 8*a + 4)*q^19 + (-2*a^4 + a^3 + 12*a^2 - 7*a - 8)*q^20 + (1/2*a^6 + 1/2*a^5 - 5*a^4 - 7/2*a^3 + 25/2*a^2 + 3*a - 2)*q^21 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 6*a)*q^22 + (1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 25/2*a^2 - 5*a - 6)*q^23 + (a^3 - 4*a)*q^24 + (-a^6 + 9*a^4 - 19*a^2 + 6)*q^25 + (a^4 - 5*a^2 + 2*a)*q^26 + q^27 + (-1/2*a^6 + 1/2*a^5 + 5*a^4 - 9/2*a^3 - 25/2*a^2 + 8*a + 6)*q^28 + (-1/2*a^6 + 11/2*a^4 - 3/2*a^3 - 15*a^2 + 15/2*a + 4)*q^29 + (-a^5 + 7*a^3 - 8*a - 2)*q^30 + (a^4 - 6*a^2 + 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - a^3 - 7*a^2 + 5*a + 6)*q^33 + (-a^6 - a^5 + 9*a^4 + 7*a^3 - 18*a^2 - 8*a)*q^34 + (a^5 - a^4 - 7*a^3 + 7*a^2 + 6*a - 6)*q^35 + (a^2 - 2)*q^36 + (-2*a^5 - a^4 + 16*a^3 + 7*a^2 - 26*a - 8)*q^37 + O(q^38)
*]> ;  // time = 47.281 seconds




J[293] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 293, 293 ], new_dimensions := [ 8, 16 ], dimensions := [ 8, 16 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -8, -1, -13, -9, -8, -2, -15, -8, 7, -9, -23 ],
[ 3, 10, 1, 15, 9, 10, -4, 19, 4, -7, 7, 19 ]
], hecke_fields := [
x^8 + 3*x^7 - 4*x^6 - 15*x^5 + 4*x^4 + 21*x^3 - 2*x^2 - 8*x + 1,
x^16 - 3*x^15 - 22*x^14 + 69*x^13 + 184*x^12 - 621*x^11 - 716*x^10 + 2758*x^9 + 1234*x^8 - 6287*x^7 - 554*x^6 + 7023*x^5 - 572*x^4 - 3385*x^3 + 508*x^2 + 526*x - 111
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 73 ]
], tamagawa_numbers := [
[ 1 ],
[ 73 ]
], torsion_upper_bounds := [ 1, 73 ], torsion_lower_bounds := [ 1, 73 ], l_ratios := [ 0, 1/73 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
a^5 + a^4 - 5*a^3 - 3*a^2 + 5*a,
-a^6 - 3*a^5 + 3*a^4 + 12*a^3 - a^2 - 10*a,
a^6 + 2*a^5 - 4*a^4 - 6*a^3 + 4*a^2 + a - 2,
-2*a^7 - 4*a^6 + 10*a^5 + 17*a^4 - 16*a^3 - 17*a^2 + 9*a + 1,
a^7 + 3*a^6 - 4*a^5 - 15*a^4 + 2*a^3 + 19*a^2 + 4*a - 6,
2*a^7 + 7*a^6 - 3*a^5 - 29*a^4 - 12*a^3 + 30*a^2 + 14*a - 9,
-a^7 - 5*a^6 + 25*a^4 + 13*a^3 - 34*a^2 - 12*a + 8,
2*a^7 + 6*a^6 - 6*a^5 - 27*a^4 - 2*a^3 + 29*a^2 + 8*a - 5,
-a^7 - 5*a^6 + 23*a^4 + 12*a^3 - 25*a^2 - 11*a + 5,
-a^6 - 2*a^5 + 6*a^4 + 10*a^3 - 13*a^2 - 12*a + 8,
-3*a^7 - 9*a^6 + 9*a^5 + 38*a^4 - 2*a^3 - 37*a^2 + a + 2
],
[
a,
-577/16858*a^15 + 4393/33716*a^14 + 16563/33716*a^13 - 18220/8429*a^12 - 74523/33716*a^11 + 435367/33716*a^10 + 21555/8429*a^9 - 286976/8429*a^8 + 130715/33716*a^7 + 1398031/33716*a^6 - 320453/33716*a^5 - 230781/8429*a^4 + 82231/8429*a^3 + 483617/33716*a^2 - 38240/8429*a - 18467/8429,
761/33716*a^15 - 713/33716*a^14 - 17781/33716*a^13 + 6135/16858*a^12 + 163023/33716*a^11 - 65719/33716*a^10 - 739285/33716*a^9 + 44693/33716*a^8 + 1715335/33716*a^7 + 154804/8429*a^6 - 1882511/33716*a^5 - 1693565/33716*a^4 + 697325/33716*a^3 + 319291/8429*a^2 + 78445/33716*a - 86901/16858,
297/16858*a^15 - 479/33716*a^14 - 3143/8429*a^13 + 949/33716*a^12 + 115053/33716*a^11 + 34451/16858*a^10 - 597641/33716*a^9 - 139484/8429*a^8 + 1843485/33716*a^7 + 751603/16858*a^6 - 1559611/16858*a^5 - 1306309/33716*a^4 + 1221403/16858*a^3 - 53941/33716*a^2 - 576815/33716*a + 54207/8429,
-233/33716*a^15 + 1511/67432*a^14 + 8529/67432*a^13 - 16297/67432*a^12 - 49515/33716*a^11 + 18855/67432*a^10 + 844103/67432*a^9 + 245827/67432*a^8 - 4050371/67432*a^7 - 567485/67432*a^6 + 4635547/33716*a^5 - 340967/67432*a^4 - 8679221/67432*a^3 + 1068839/67432*a^2 + 1152697/33716*a - 303691/67432,
-623/33716*a^15 + 193/8429*a^14 + 5855/16858*a^13 - 9325/33716*a^12 - 82399/33716*a^11 + 6083/16858*a^10 + 130703/16858*a^9 + 62912/8429*a^8 - 155665/16858*a^7 - 1292109/33716*a^6 - 175301/33716*a^5 + 611969/8429*a^4 + 172165/8429*a^3 - 1923829/33716*a^2 - 471027/33716*a + 411913/33716,
5121/67432*a^15 - 20349/67432*a^14 - 59089/67432*a^13 + 79407/16858*a^12 + 58193/67432*a^11 - 1662399/67432*a^10 + 1575357/67432*a^9 + 2934123/67432*a^8 - 7273265/67432*a^7 + 145400/8429*a^6 + 12534279/67432*a^5 - 7704035/67432*a^4 - 9352905/67432*a^3 + 1452333/16858*a^2 + 2408533/67432*a - 229595/16858,
-1175/16858*a^15 - 6285/67432*a^14 + 169263/67432*a^13 + 8299/67432*a^12 - 248807/8429*a^11 + 947657/67432*a^10 + 10419633/67432*a^9 - 7553201/67432*a^8 - 25892511/67432*a^7 + 21334795/67432*a^6 + 14788541/33716*a^5 - 24100153/67432*a^4 - 14102421/67432*a^3 + 9874977/67432*a^2 + 1128119/33716*a - 1024209/67432,
-89/16858*a^15 - 763/67432*a^14 + 19937/67432*a^13 - 25799/67432*a^12 - 59937/16858*a^11 + 571695/67432*a^10 + 1027195/67432*a^9 - 3749195/67432*a^8 - 1173729/67432*a^7 + 10430077/67432*a^6 - 867699/33716*a^5 - 12637907/67432*a^4 + 3065513/67432*a^3 + 5895535/67432*a^2 - 301955/33716*a - 589459/67432,
3885/33716*a^15 - 11349/33716*a^14 - 71413/33716*a^13 + 103847/16858*a^12 + 522739/33716*a^11 - 1459075/33716*a^10 - 2073633/33716*a^9 + 5057349/33716*a^8 + 5231307/33716*a^7 - 2358918/8429*a^6 - 8467211/33716*a^5 + 9665959/33716*a^4 + 7114909/33716*a^3 - 1254647/8429*a^2 - 1876887/33716*a + 443941/16858,
5441/33716*a^15 - 2335/8429*a^14 - 66207/16858*a^13 + 220255/33716*a^12 + 1248809/33716*a^11 - 997553/16858*a^10 - 2874303/16858*a^9 + 2172635/8429*a^8 + 6711855/16858*a^7 - 18695269/33716*a^6 - 15276237/33716*a^5 + 4657938/8429*a^4 + 1932769/8429*a^3 - 7449369/33716*a^2 - 1475651/33716*a + 857921/33716,
4927/33716*a^15 - 2054/8429*a^14 - 110779/33716*a^13 + 171783/33716*a^12 + 244061/8429*a^11 - 1399111/33716*a^10 - 2122319/16858*a^9 + 5594357/33716*a^8 + 2351622/8429*a^7 - 2849107/8429*a^6 - 9947321/33716*a^5 + 2797941/8429*a^4 + 4322749/33716*a^3 - 4462107/33716*a^2 - 395485/16858*a + 225443/16858
]
*], q_expansions := [*
q + a*q^2 + (a^5 + a^4 - 5*a^3 - 3*a^2 + 5*a)*q^3 + (a^2 - 2)*q^4 + (-a^6 - 3*a^5 + 3*a^4 + 12*a^3 - a^2 - 10*a)*q^5 + (a^6 + a^5 - 5*a^4 - 3*a^3 + 5*a^2)*q^6 + (a^6 + 2*a^5 - 4*a^4 - 6*a^3 + 4*a^2 + a - 2)*q^7 + (a^3 - 4*a)*q^8 + (a^7 + 2*a^6 - 7*a^5 - 10*a^4 + 18*a^3 + 12*a^2 - 15*a - 1)*q^9 + (-a^7 - 3*a^6 + 3*a^5 + 12*a^4 - a^3 - 10*a^2)*q^10 + (-2*a^7 - 4*a^6 + 10*a^5 + 17*a^4 - 16*a^3 - 17*a^2 + 9*a + 1)*q^11 + (a^7 + a^6 - 7*a^5 - 5*a^4 + 15*a^3 + 6*a^2 - 10*a)*q^12 + (a^7 + 3*a^6 - 4*a^5 - 15*a^4 + 2*a^3 + 19*a^2 + 4*a - 6)*q^13 + (a^7 + 2*a^6 - 4*a^5 - 6*a^4 + 4*a^3 + a^2 - 2*a)*q^14 + (-a^7 - 2*a^6 + 7*a^5 + 11*a^4 - 16*a^3 - 13*a^2 + 12*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (2*a^7 + 7*a^6 - 3*a^5 - 29*a^4 - 12*a^3 + 30*a^2 + 14*a - 9)*q^17 + (-a^7 - 3*a^6 + 5*a^5 + 14*a^4 - 9*a^3 - 13*a^2 + 7*a - 1)*q^18 + (-a^7 - 5*a^6 + 25*a^4 + 13*a^3 - 34*a^2 - 12*a + 8)*q^19 + (a^6 + 3*a^5 - 3*a^4 - 13*a^3 + 12*a + 1)*q^20 + (-2*a^7 - 5*a^6 + 6*a^5 + 18*a^4 - a^3 - 11*a^2 + a - 1)*q^21 + (2*a^7 + 2*a^6 - 13*a^5 - 8*a^4 + 25*a^3 + 5*a^2 - 15*a + 2)*q^22 + (2*a^7 + 6*a^6 - 6*a^5 - 27*a^4 - 2*a^3 + 29*a^2 + 8*a - 5)*q^23 + (-2*a^7 - 5*a^6 + 8*a^5 + 21*a^4 - 9*a^3 - 18*a^2 + 8*a - 1)*q^24 + (2*a^7 + 6*a^6 - 7*a^5 - 27*a^4 + 4*a^3 + 28*a^2 + a - 4)*q^25 + (-2*a^4 - 2*a^3 + 6*a^2 + 2*a - 1)*q^26 + (-3*a^7 - 7*a^6 + 14*a^5 + 29*a^4 - 22*a^3 - 23*a^2 + 17*a - 5)*q^27 + (-a^7 - 2*a^6 + 5*a^5 + 8*a^4 - 8*a^3 - 8*a^2 + 6*a + 3)*q^28 + (-a^7 - 5*a^6 + 23*a^4 + 12*a^3 - 25*a^2 - 11*a + 5)*q^29 + (a^7 + 3*a^6 - 4*a^5 - 12*a^4 + 8*a^3 + 10*a^2 - 10*a + 1)*q^30 + (-a^6 - 2*a^5 + 6*a^4 + 10*a^3 - 13*a^2 - 12*a + 8)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^7 + 4*a^6 - 12*a^5 - 18*a^4 + 29*a^3 + 18*a^2 - 26*a + 4)*q^33 + (a^7 + 5*a^6 + a^5 - 20*a^4 - 12*a^3 + 18*a^2 + 7*a - 2)*q^34 + (2*a^7 + 7*a^6 - 3*a^5 - 27*a^4 - 10*a^3 + 19*a^2 + 8*a + 1)*q^35 + (-2*a^7 - 3*a^6 + 13*a^5 + 15*a^4 - 28*a^3 - 19*a^2 + 21*a + 3)*q^36 + (-3*a^7 - 9*a^6 + 9*a^5 + 38*a^4 - 2*a^3 - 37*a^2 + a + 2)*q^37 + O(q^38),
q + a*q^2 + (-577/16858*a^15 + 4393/33716*a^14 + 16563/33716*a^13 - 18220/8429*a^12 - 74523/33716*a^11 + 435367/33716*a^10 + 21555/8429*a^9 - 286976/8429*a^8 + 130715/33716*a^7 + 1398031/33716*a^6 - 320453/33716*a^5 - 230781/8429*a^4 + 82231/8429*a^3 + 483617/33716*a^2 - 38240/8429*a - 18467/8429)*q^3 + (a^2 - 2)*q^4 + (761/33716*a^15 - 713/33716*a^14 - 17781/33716*a^13 + 6135/16858*a^12 + 163023/33716*a^11 - 65719/33716*a^10 - 739285/33716*a^9 + 44693/33716*a^8 + 1715335/33716*a^7 + 154804/8429*a^6 - 1882511/33716*a^5 - 1693565/33716*a^4 + 697325/33716*a^3 + 319291/8429*a^2 + 78445/33716*a - 86901/16858)*q^5 + (931/33716*a^15 - 8825/33716*a^14 + 3373/16858*a^13 + 137813/33716*a^12 - 281267/33716*a^11 - 185011/8429*a^10 + 508707/8429*a^9 + 1554751/33716*a^8 - 5857167/33716*a^7 - 959769/33716*a^6 + 3590709/16858*a^5 - 82791/8429*a^4 - 3422673/33716*a^3 + 108318/8429*a^2 + 133284/8429*a - 64047/16858)*q^6 + (297/16858*a^15 - 479/33716*a^14 - 3143/8429*a^13 + 949/33716*a^12 + 115053/33716*a^11 + 34451/16858*a^10 - 597641/33716*a^9 - 139484/8429*a^8 + 1843485/33716*a^7 + 751603/16858*a^6 - 1559611/16858*a^5 - 1306309/33716*a^4 + 1221403/16858*a^3 - 53941/33716*a^2 - 576815/33716*a + 54207/8429)*q^7 + (a^3 - 4*a)*q^8 + (-6493/67432*a^15 + 15609/67432*a^14 + 114805/67432*a^13 - 122391/33716*a^12 - 789151/67432*a^11 + 1292555/67432*a^10 + 2819513/67432*a^9 - 2376333/67432*a^8 - 6046011/67432*a^7 - 62305/16858*a^6 + 7703439/67432*a^5 + 3916345/67432*a^4 - 4410473/67432*a^3 - 252993/8429*a^2 + 589083/67432*a + 103289/33716)*q^9 + (785/16858*a^15 - 1039/33716*a^14 - 40239/33716*a^13 + 22999/33716*a^12 + 203431/16858*a^11 - 194409/33716*a^10 - 2054145/33716*a^9 + 776261/33716*a^8 + 5403623/33716*a^7 - 1460917/33716*a^6 - 1759517/8429*a^5 + 1132617/33716*a^4 + 3853149/33716*a^3 - 308143/33716*a^2 - 143522/8429*a + 84471/33716)*q^10 + (-233/33716*a^15 + 1511/67432*a^14 + 8529/67432*a^13 - 16297/67432*a^12 - 49515/33716*a^11 + 18855/67432*a^10 + 844103/67432*a^9 + 245827/67432*a^8 - 4050371/67432*a^7 - 567485/67432*a^6 + 4635547/33716*a^5 - 340967/67432*a^4 - 8679221/67432*a^3 + 1068839/67432*a^2 + 1152697/33716*a - 303691/67432)*q^11 + (-931/8429*a^15 + 9221/16858*a^14 + 10112/8429*a^13 - 306811/33716*a^12 - 12847/33716*a^11 + 915345/16858*a^10 - 1185387/33716*a^9 - 4710213/33716*a^8 + 2315999/16858*a^7 + 2450565/16858*a^6 - 6228671/33716*a^5 - 1043893/33716*a^4 + 2926859/33716*a^3 - 453523/16858*a^2 - 77970/8429*a + 251077/33716)*q^12 + (-623/33716*a^15 + 193/8429*a^14 + 5855/16858*a^13 - 9325/33716*a^12 - 82399/33716*a^11 + 6083/16858*a^10 + 130703/16858*a^9 + 62912/8429*a^8 - 155665/16858*a^7 - 1292109/33716*a^6 - 175301/33716*a^5 + 611969/8429*a^4 + 172165/8429*a^3 - 1923829/33716*a^2 - 471027/33716*a + 411913/33716)*q^13 + (1303/33716*a^15 + 124/8429*a^14 - 40037/33716*a^13 + 5757/33716*a^12 + 109444/8429*a^11 - 172337/33716*a^10 - 549047/8429*a^9 + 1110489/33716*a^8 + 1309421/8429*a^7 - 1395073/16858*a^6 - 5477971/33716*a^5 + 1391287/16858*a^4 + 1956749/33716*a^3 - 878567/33716*a^2 - 23904/8429*a + 32967/16858)*q^14 + (3143/33716*a^15 - 1527/33716*a^14 - 92887/33716*a^13 + 37965/16858*a^12 + 1004213/33716*a^11 - 987525/33716*a^10 - 5120447/33716*a^9 + 5359527/33716*a^8 + 12997241/33716*a^7 - 3321223/8429*a^6 - 15984413/33716*a^5 + 14449993/33716*a^4 + 8619091/33716*a^3 - 1483825/8429*a^2 - 1584757/33716*a + 378501/16858)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (5121/67432*a^15 - 20349/67432*a^14 - 59089/67432*a^13 + 79407/16858*a^12 + 58193/67432*a^11 - 1662399/67432*a^10 + 1575357/67432*a^9 + 2934123/67432*a^8 - 7273265/67432*a^7 + 145400/8429*a^6 + 12534279/67432*a^5 - 7704035/67432*a^4 - 9352905/67432*a^3 + 1452333/16858*a^2 + 2408533/67432*a - 229595/16858)*q^17 + (-1935/33716*a^15 - 28041/67432*a^14 + 203235/67432*a^13 + 405561/67432*a^12 - 1369799/33716*a^11 - 1829475/67432*a^10 + 15531361/67432*a^9 + 1966351/67432*a^8 - 41070711/67432*a^7 + 4106317/67432*a^6 + 12379171/16858*a^5 - 8124469/67432*a^4 - 24002749/67432*a^3 + 3887527/67432*a^2 + 452737/8429*a - 720723/67432)*q^18 + (-1175/16858*a^15 - 6285/67432*a^14 + 169263/67432*a^13 + 8299/67432*a^12 - 248807/8429*a^11 + 947657/67432*a^10 + 10419633/67432*a^9 - 7553201/67432*a^8 - 25892511/67432*a^7 + 21334795/67432*a^6 + 14788541/33716*a^5 - 24100153/67432*a^4 - 14102421/67432*a^3 + 9874977/67432*a^2 + 1128119/33716*a - 1024209/67432)*q^19 + (2149/33716*a^15 - 4273/33716*a^14 - 49769/33716*a^13 + 46721/16858*a^12 + 454515/33716*a^11 - 798587/33716*a^10 - 2075229/33716*a^9 + 3376857/33716*a^8 + 4979003/33716*a^7 - 1851680/8429*a^6 - 6128471/33716*a^5 + 8138319/33716*a^4 + 3611657/33716*a^3 - 981494/8429*a^2 - 898239/33716*a + 260937/16858)*q^20 + (-3727/67432*a^15 + 34749/67432*a^14 + 2283/67432*a^13 - 315879/33716*a^12 + 698567/67432*a^11 + 4351209/67432*a^10 - 6199965/67432*a^9 - 14307941/67432*a^8 + 21373537/67432*a^7 + 5839007/16858*a^6 - 33476305/67432*a^5 - 17215569/67432*a^4 + 22724119/67432*a^3 + 1910969/33716*a^2 - 4949557/67432*a + 28470/8429)*q^21 + (113/67432*a^15 - 1723/67432*a^14 + 15857/67432*a^13 - 6643/33716*a^12 - 270531/67432*a^11 + 510447/67432*a^10 + 1531055/67432*a^9 - 3475327/67432*a^8 - 3497227/67432*a^7 + 4506465/33716*a^6 + 2931751/67432*a^5 - 8945773/67432*a^4 - 508571/67432*a^3 + 1271061/33716*a^2 - 58575/67432*a - 25863/33716)*q^22 + (-89/16858*a^15 - 763/67432*a^14 + 19937/67432*a^13 - 25799/67432*a^12 - 59937/16858*a^11 + 571695/67432*a^10 + 1027195/67432*a^9 - 3749195/67432*a^8 - 1173729/67432*a^7 + 10430077/67432*a^6 - 867699/33716*a^5 - 12637907/67432*a^4 + 3065513/67432*a^3 + 5895535/67432*a^2 - 301955/33716*a - 589459/67432)*q^23 + (1352/8429*a^15 - 11915/16858*a^14 - 63347/33716*a^13 + 396743/33716*a^12 + 20155/8429*a^11 - 2371683/33716*a^10 + 1490923/33716*a^9 + 1529478/8429*a^8 - 1699331/8429*a^7 - 6372229/33716*a^6 + 10746923/33716*a^5 + 1459059/33716*a^4 - 1666860/8429*a^3 + 178342/8429*a^2 + 1143629/33716*a - 39294/8429)*q^24 + (a^5 - a^4 - 8*a^3 + 6*a^2 + 11*a - 2)*q^25 + (-1097/33716*a^15 - 499/8429*a^14 + 16831/16858*a^13 + 32233/33716*a^12 - 374717/33716*a^11 - 92331/16858*a^10 + 984941/16858*a^9 + 114363/8429*a^8 - 2604455/16858*a^7 - 520443/33716*a^6 + 6823205/33716*a^5 + 83076/8429*a^4 - 1008171/8429*a^3 - 154543/33716*a^2 + 739611/33716*a - 69153/33716)*q^26 + (-2391/16858*a^15 + 21931/67432*a^14 + 188033/67432*a^13 - 386241/67432*a^12 - 743351/33716*a^11 + 2535427/67432*a^10 + 6212625/67432*a^9 - 7797103/67432*a^8 - 15059699/67432*a^7 + 12008445/67432*a^6 + 10430123/33716*a^5 - 9886125/67432*a^4 - 14378143/67432*a^3 + 4822557/67432*a^2 + 865695/16858*a - 859003/67432)*q^27 + (3217/33716*a^15 - 10413/33716*a^14 - 29503/16858*a^13 + 98063/16858*a^12 + 101680/8429*a^11 - 350261/8429*a^10 - 1287903/33716*a^9 + 2372827/16858*a^8 + 1714845/33716*a^7 - 7762521/33716*a^6 - 129951/33716*a^5 + 5314683/33716*a^4 - 338381/8429*a^3 - 324829/16858*a^2 + 267093/16858*a - 289023/33716)*q^28 + (3885/33716*a^15 - 11349/33716*a^14 - 71413/33716*a^13 + 103847/16858*a^12 + 522739/33716*a^11 - 1459075/33716*a^10 - 2073633/33716*a^9 + 5057349/33716*a^8 + 5231307/33716*a^7 - 2358918/8429*a^6 - 8467211/33716*a^5 + 9665959/33716*a^4 + 7114909/33716*a^3 - 1254647/8429*a^2 - 1876887/33716*a + 443941/16858)*q^29 + (3951/16858*a^15 - 23741/33716*a^14 - 140937/33716*a^13 + 425901/33716*a^12 + 482139/16858*a^11 - 2870059/33716*a^10 - 3308867/33716*a^9 + 9118779/33716*a^8 + 6475149/33716*a^7 - 14243191/33716*a^6 - 1905824/8429*a^5 + 10416887/33716*a^4 + 4703755/33716*a^3 - 3181401/33716*a^2 - 224054/8429*a + 348873/33716)*q^30 + (5441/33716*a^15 - 2335/8429*a^14 - 66207/16858*a^13 + 220255/33716*a^12 + 1248809/33716*a^11 - 997553/16858*a^10 - 2874303/16858*a^9 + 2172635/8429*a^8 + 6711855/16858*a^7 - 18695269/33716*a^6 - 15276237/33716*a^5 + 4657938/8429*a^4 + 1932769/8429*a^3 - 7449369/33716*a^2 - 1475651/33716*a + 857921/33716)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (7627/67432*a^15 - 26485/67432*a^14 - 118883/67432*a^13 + 120843/16858*a^12 + 557463/67432*a^11 - 3324969/67432*a^10 - 57837/67432*a^9 + 10753195/67432*a^8 - 6422889/67432*a^7 - 4137811/16858*a^6 + 17473811/67432*a^5 + 10022511/67432*a^4 - 15934065/67432*a^3 + 92679/33716*a^2 + 3452181/67432*a - 559909/33716)*q^33 + (-2493/33716*a^15 + 53573/67432*a^14 - 35721/67432*a^13 - 884071/67432*a^12 + 758871/33716*a^11 + 5241993/67432*a^10 - 11189595/67432*a^9 - 13592579/67432*a^8 + 33358927/67432*a^7 + 15371313/67432*a^6 - 21834409/33716*a^5 - 6423693/67432*a^4 + 23143917/67432*a^3 - 192935/67432*a^2 - 1806013/33716*a + 568431/67432)*q^34 + (-310/8429*a^15 + 1323/16858*a^14 + 16159/16858*a^13 - 19198/8429*a^12 - 153209/16858*a^11 + 408081/16858*a^10 + 328446/8429*a^9 - 1017757/8429*a^8 - 1273781/16858*a^7 + 4983679/16858*a^6 + 1043581/16858*a^5 - 2853271/8429*a^4 - 265542/8429*a^3 + 2585371/16858*a^2 + 127797/8429*a - 153261/8429)*q^35 + (-26665/67432*a^15 + 86877/67432*a^14 + 442981/67432*a^13 - 768977/33716*a^12 - 2654443/67432*a^11 + 10175331/67432*a^10 + 7000785/67432*a^9 - 31542465/67432*a^8 - 8132351/67432*a^7 + 5983893/8429*a^6 + 3647663/67432*a^5 - 34049079/67432*a^4 - 391477/67432*a^3 + 1204468/8429*a^2 + 136731/67432*a - 421363/33716)*q^36 + (4927/33716*a^15 - 2054/8429*a^14 - 110779/33716*a^13 + 171783/33716*a^12 + 244061/8429*a^11 - 1399111/33716*a^10 - 2122319/16858*a^9 + 5594357/33716*a^8 + 2351622/8429*a^7 - 2849107/8429*a^6 - 9947321/33716*a^5 + 2797941/8429*a^4 + 4322749/33716*a^3 - 4462107/33716*a^2 - 395485/16858*a + 225443/16858)*q^37 + O(q^38)
*]> ;  // time = 4.84 seconds




J[295] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 295, 295, 295, 295, 59 ], new_dimensions := [ 3, 3, 6, 7, 5 ], dimensions := [ 3, 3, 6, 7, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 107, 1, 1, 0, 1, 1, 1, 1, 1, 0, 6629, 1, 107, 1, 6629, 0 ], ap_traces := [
[ -1, -1, -3, 0, -9, 1, -12, -1, -3, -12, -7, 6 ],
[ -3, -3, 3, -6, 3, -9, -18, 3, -3, -12, 3, -6 ],
[ 2, 1, 6, 2, 3, 11, 16, -5, 11, 6, -11, 10 ],
[ 1, 3, -7, -4, 3, -9, 24, 3, 3, 4, -1, -24 ]
], hecke_fields := [
x^3 + x^2 - 2*x - 1,
x^3 + 3*x^2 - 3,
x^6 - 2*x^5 - 6*x^4 + 11*x^3 + 8*x^2 - 11*x - 3,
x^7 - x^6 - 10*x^5 + 7*x^4 + 27*x^3 - 11*x^2 - 10*x - 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 107, 1 ],
[ 5, 1 ],
[ 6629, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 107, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 5, 1 ], l_ratios := [ 0, 0, 1/5, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-a^2 - a + 1,
-1,
2*a^2 + a - 3,
-a^2 - 2*a - 2,
2*a^2 - 3,
-a^2 - 2*a - 3,
2*a^2 + 5*a - 2,
-3*a^2 + 4,
-3*a^2 + 1,
-2*a^2 - 3*a,
-4*a^2 + 4*a + 10
],
[
a,
a^2 + a - 3,
1,
-2*a^2 - 3*a + 1,
-a^2 + 4,
2*a^2 + 2*a - 7,
-a^2 - 2*a - 5,
-3*a - 2,
3*a^2 + 8*a - 2,
a^2 + 4*a - 3,
-2*a^2 - 5*a + 2,
-4*a^2 - 8*a + 2
],
[
a,
-a^5 + a^4 + 6*a^3 - 4*a^2 - 7*a + 1,
1,
a^5 - 7*a^3 - a^2 + 10*a + 3,
a^4 - a^3 - 5*a^2 + 3*a + 4,
-a^4 + a^3 + 4*a^2 - 3*a + 1,
a^5 - a^4 - 7*a^3 + 5*a^2 + 10*a,
a^3 - a^2 - 3*a + 1,
a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 5*a - 1,
-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 8,
-a^3 + a^2 + a - 3,
-a^5 - a^4 + 7*a^3 + 8*a^2 - 10*a - 9
],
[
a,
a^5 - 3*a^4 - 4*a^3 + 14*a^2 - a - 3,
-1,
a^6 - a^5 - 10*a^4 + 8*a^3 + 25*a^2 - 15*a - 4,
-a^6 + 2*a^5 + 5*a^4 - 8*a^3 - 3*a^2 - 2*a + 3,
-2*a^6 + 4*a^5 + 15*a^4 - 23*a^3 - 30*a^2 + 23*a + 7,
a^6 - a^5 - 9*a^4 + 6*a^3 + 21*a^2 - 9*a - 1,
a^6 - 2*a^5 - 10*a^4 + 16*a^3 + 27*a^2 - 30*a - 6,
3*a^6 - 5*a^5 - 24*a^4 + 31*a^3 + 51*a^2 - 40*a - 14,
-a^6 + 3*a^5 + 5*a^4 - 14*a^3 - 5*a^2 + a + 5,
-3*a^6 + 4*a^5 + 26*a^4 - 24*a^3 - 59*a^2 + 30*a + 12,
-3*a^5 + 9*a^4 + 9*a^3 - 40*a^2 + 18*a + 3
]
*], q_expansions := [*
q + a*q^2 + (-a^2 - a + 1)*q^3 + (a^2 - 2)*q^4 - q^5 + (-a - 1)*q^6 + (2*a^2 + a - 3)*q^7 + (-a^2 - 2*a + 1)*q^8 + (a - 1)*q^9 - a*q^10 + (-a^2 - 2*a - 2)*q^11 + (a^2 + a - 2)*q^12 + (2*a^2 - 3)*q^13 + (-a^2 + a + 2)*q^14 + (a^2 + a - 1)*q^15 + (-3*a^2 - a + 3)*q^16 + (-a^2 - 2*a - 3)*q^17 + (a^2 - a)*q^18 + (2*a^2 + 5*a - 2)*q^19 + (-a^2 + 2)*q^20 + (a^2 - 4)*q^21 + (-a^2 - 4*a - 1)*q^22 + (-3*a^2 + 4)*q^23 + (2*a + 3)*q^24 + q^25 + (-2*a^2 + a + 2)*q^26 + (4*a^2 + 3*a - 5)*q^27 + (-2*a^2 - 2*a + 5)*q^28 + (-3*a^2 + 1)*q^29 + (a + 1)*q^30 + (-2*a^2 - 3*a)*q^31 + (4*a^2 + a - 5)*q^32 + (3*a^2 + 5*a)*q^33 + (-a^2 - 5*a - 1)*q^34 + (-2*a^2 - a + 3)*q^35 + (-2*a^2 + 3)*q^36 + (-4*a^2 + 4*a + 10)*q^37 + O(q^38),
q + a*q^2 + (a^2 + a - 3)*q^3 + (a^2 - 2)*q^4 + q^5 + (-2*a^2 - 3*a + 3)*q^6 + (-2*a^2 - 3*a + 1)*q^7 + (-3*a^2 - 4*a + 3)*q^8 + (-2*a^2 - 3*a + 3)*q^9 + a*q^10 + (-a^2 + 4)*q^11 + (a^2 + a)*q^12 + (2*a^2 + 2*a - 7)*q^13 + (3*a^2 + a - 6)*q^14 + (a^2 + a - 3)*q^15 + (3*a^2 + 3*a - 5)*q^16 + (-a^2 - 2*a - 5)*q^17 + (3*a^2 + 3*a - 6)*q^18 + (-3*a - 2)*q^19 + (a^2 - 2)*q^20 + (a^2 + 4*a)*q^21 + (3*a^2 + 4*a - 3)*q^22 + (3*a^2 + 8*a - 2)*q^23 + (2*a^2 + 6*a - 3)*q^24 + q^25 + (-4*a^2 - 7*a + 6)*q^26 + (3*a + 3)*q^27 + (-4*a^2 + 7)*q^28 + (a^2 + 4*a - 3)*q^29 + (-2*a^2 - 3*a + 3)*q^30 + (-2*a^2 - 5*a + 2)*q^31 + (3*a + 3)*q^32 + (a^2 + a - 6)*q^33 + (a^2 - 5*a - 3)*q^34 + (-2*a^2 - 3*a + 1)*q^35 + (-2*a^2 + 3)*q^36 + (-4*a^2 - 8*a + 2)*q^37 + O(q^38),
q + a*q^2 + (-a^5 + a^4 + 6*a^3 - 4*a^2 - 7*a + 1)*q^3 + (a^2 - 2)*q^4 + q^5 + (-a^5 + 7*a^3 + a^2 - 10*a - 3)*q^6 + (a^5 - 7*a^3 - a^2 + 10*a + 3)*q^7 + (a^3 - 4*a)*q^8 + (-a^3 - a^2 + 5*a + 4)*q^9 + a*q^10 + (a^4 - a^3 - 5*a^2 + 3*a + 4)*q^11 + (-a^4 + 6*a^2 - 5)*q^12 + (-a^4 + a^3 + 4*a^2 - 3*a + 1)*q^13 + (2*a^5 - a^4 - 12*a^3 + 2*a^2 + 14*a + 3)*q^14 + (-a^5 + a^4 + 6*a^3 - 4*a^2 - 7*a + 1)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 10*a)*q^17 + (-a^4 - a^3 + 5*a^2 + 4*a)*q^18 + (a^3 - a^2 - 3*a + 1)*q^19 + (a^2 - 2)*q^20 + (a^4 + a^3 - 5*a^2 - 7*a)*q^21 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 4*a)*q^22 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 5*a - 1)*q^23 + (a^5 - 8*a^3 - 2*a^2 + 15*a + 6)*q^24 + q^25 + (-a^5 + a^4 + 4*a^3 - 3*a^2 + a)*q^26 + (-a^5 + 9*a^3 + a^2 - 18*a - 5)*q^27 + (a^5 - 6*a^3 + 5*a)*q^28 + (-a^5 - a^4 + 9*a^3 + 7*a^2 - 18*a - 8)*q^29 + (-a^5 + 7*a^3 + a^2 - 10*a - 3)*q^30 + (-a^3 + a^2 + a - 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - 6*a^2 - 2*a + 7)*q^33 + (a^5 - a^4 - 6*a^3 + 2*a^2 + 11*a + 3)*q^34 + (a^5 - 7*a^3 - a^2 + 10*a + 3)*q^35 + (-a^5 - a^4 + 7*a^3 + 6*a^2 - 10*a - 8)*q^36 + (-a^5 - a^4 + 7*a^3 + 8*a^2 - 10*a - 9)*q^37 + O(q^38),
q + a*q^2 + (a^5 - 3*a^4 - 4*a^3 + 14*a^2 - a - 3)*q^3 + (a^2 - 2)*q^4 - q^5 + (a^6 - 3*a^5 - 4*a^4 + 14*a^3 - a^2 - 3*a)*q^6 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 25*a^2 - 15*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + 2*a^5 + 8*a^4 - 14*a^3 - 17*a^2 + 22*a + 7)*q^9 - a*q^10 + (-a^6 + 2*a^5 + 5*a^4 - 8*a^3 - 3*a^2 - 2*a + 3)*q^11 + (-2*a^6 + 4*a^5 + 13*a^4 - 20*a^3 - 20*a^2 + 12*a + 7)*q^12 + (-2*a^6 + 4*a^5 + 15*a^4 - 23*a^3 - 30*a^2 + 23*a + 7)*q^13 + (a^4 - 2*a^3 - 4*a^2 + 6*a + 1)*q^14 + (-a^5 + 3*a^4 + 4*a^3 - 14*a^2 + a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - a^5 - 9*a^4 + 6*a^3 + 21*a^2 - 9*a - 1)*q^17 + (a^6 - 2*a^5 - 7*a^4 + 10*a^3 + 11*a^2 - 3*a - 1)*q^18 + (a^6 - 2*a^5 - 10*a^4 + 16*a^3 + 27*a^2 - 30*a - 6)*q^19 + (-a^2 + 2)*q^20 + (a^6 - 4*a^5 + a^4 + 14*a^3 - 25*a^2 + 14*a + 7)*q^21 + (a^6 - 5*a^5 - a^4 + 24*a^3 - 13*a^2 - 7*a - 1)*q^22 + (3*a^6 - 5*a^5 - 24*a^4 + 31*a^3 + 51*a^2 - 40*a - 14)*q^23 + (-a^5 + 2*a^4 + 6*a^3 - 8*a^2 - 7*a - 2)*q^24 + q^25 + (2*a^6 - 5*a^5 - 9*a^4 + 24*a^3 + a^2 - 13*a - 2)*q^26 + (a^6 + a^5 - 14*a^4 - 4*a^3 + 43*a^2 - 3*a - 4)*q^27 + (-2*a^6 + 3*a^5 + 18*a^4 - 20*a^3 - 44*a^2 + 31*a + 8)*q^28 + (-a^6 + 3*a^5 + 5*a^4 - 14*a^3 - 5*a^2 + a + 5)*q^29 + (-a^6 + 3*a^5 + 4*a^4 - 14*a^3 + a^2 + 3*a)*q^30 + (-3*a^6 + 4*a^5 + 26*a^4 - 24*a^3 - 59*a^2 + 30*a + 12)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3*a^4 + 4*a^3 + 18*a^2 - 18*a - 11)*q^33 + (a^5 - a^4 - 6*a^3 + 2*a^2 + 9*a + 1)*q^34 + (-a^6 + a^5 + 10*a^4 - 8*a^3 - 25*a^2 + 15*a + 4)*q^35 + (a^6 - a^5 - 13*a^4 + 12*a^3 + 42*a^2 - 35*a - 13)*q^36 + (-3*a^5 + 9*a^4 + 9*a^3 - 40*a^2 + 18*a + 3)*q^37 + O(q^38)
*]> ;  // time = 41.311 seconds




J[298] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 298, 298, 298, 298, 298, 149, 149 ], new_dimensions := [ 1, 1, 2, 3, 5, 3, 9 ], dimensions := [ 1, 1, 2, 3, 5, 6, 18 ], intersection_graph := [ 0, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 9, 1, 1, 0, 1, 1, 1, 69, 5, 1, 1, 0, 1, 13, 1, 1, 1, 1, 1, 0, 29, 1, 1, 1, 1, 13, 29, 0, 1, 1, 9, 69, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -4, 4, 2, -5, -7, -7, 3, -8, 2, -4 ],
[ 1, -2, -2, -2, 0, -5, -7, 1, -1, 8, 4, 0 ],
[ -2, 2, 2, 2, 6, -4, 10, 2, 4, 4, -10, 0 ],
[ -3, -5, 1, -4, -5, 0, -9, -2, -19, -1, -4, 7 ],
[ 5, 1, 5, 0, -3, 6, 9, -8, 1, 7, 0, -13 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2*x - 2,
x^3 + 5*x^2 + 4*x - 5,
x^5 - x^4 - 10*x^3 + 11*x^2 + 12*x - 2
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 9, 1 ],
[ 69, 1 ],
[ 13, 1 ],
[ 725, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 9, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 725, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 25 ], torsion_lower_bounds := [ 1, 1, 1, 1, 25 ], l_ratios := [ 0, 0, 1, 0, 29/25 ], analytic_sha_upper_bounds := [ 0, 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 0, 1 ], eigenvalues := [*
[ -1, 0, -4, 4, 2, -5, -7, -7, 3, -8, 2, -4 ],
[ 1, -2, -2, -2, 0, -5, -7, 1, -1, 8, 4, 0 ],
[
-1,
a,
-a + 2,
-a + 2,
a + 2,
a - 3,
5,
-2*a + 3,
-a + 3,
-2*a + 4,
-a - 4,
0
],
[
-1,
a,
-a^2 - 3*a + 1,
2*a^2 + 4*a - 6,
-3*a^2 - 8*a + 2,
0,
a^2 + 4*a - 2,
2*a^2 + 6*a - 2,
a^2 + 3*a - 7,
4*a^2 + 9*a - 8,
2*a + 2,
-3*a^2 - 5*a + 11
],
[
1,
a,
2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 13/5*a + 18/5,
-3/5*a^4 - 1/5*a^3 + 22/5*a^2 - 7/5*a - 2/5,
-1/5*a^4 + 3/5*a^3 + 9/5*a^2 - 29/5*a - 4/5,
3/5*a^4 + 6/5*a^3 - 17/5*a^2 - 33/5*a - 3/5,
-2/5*a^4 + 1/5*a^3 + 18/5*a^2 - 18/5*a - 3/5,
-a^3 - a^2 + 6*a + 1,
-4/5*a^4 - 8/5*a^3 + 31/5*a^2 + 39/5*a - 21/5,
1/5*a^4 + 7/5*a^3 - 4/5*a^2 - 36/5*a + 4/5,
-1/5*a^4 + 3/5*a^3 + 14/5*a^2 - 19/5*a - 24/5,
7/5*a^4 - 6/5*a^3 - 68/5*a^2 + 68/5*a + 48/5
]
*], q_expansions := [*
q - q^2 + q^4 - 4*q^5 + 4*q^7 - q^8 - 3*q^9 + 4*q^10 + 2*q^11 - 5*q^13 - 4*q^14 + q^16 - 7*q^17 + 3*q^18 - 7*q^19 - 4*q^20 - 2*q^22 + 3*q^23 + 11*q^25 + 5*q^26 + 4*q^28 - 8*q^29 + 2*q^31 - q^32 + 7*q^34 - 16*q^35 - 3*q^36 - 4*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^5 - 2*q^6 - 2*q^7 + q^8 + q^9 - 2*q^10 - 2*q^12 - 5*q^13 - 2*q^14 + 4*q^15 + q^16 - 7*q^17 + q^18 + q^19 - 2*q^20 + 4*q^21 - q^23 - 2*q^24 - q^25 - 5*q^26 + 4*q^27 - 2*q^28 + 8*q^29 + 4*q^30 + 4*q^31 + q^32 - 7*q^34 + 4*q^35 + q^36 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a + 2)*q^5 - a*q^6 + (-a + 2)*q^7 - q^8 + (2*a - 1)*q^9 + (a - 2)*q^10 + (a + 2)*q^11 + a*q^12 + (a - 3)*q^13 + (a - 2)*q^14 - 2*q^15 + q^16 + 5*q^17 + (-2*a + 1)*q^18 + (-2*a + 3)*q^19 + (-a + 2)*q^20 - 2*q^21 + (-a - 2)*q^22 + (-a + 3)*q^23 - a*q^24 + (-2*a + 1)*q^25 + (-a + 3)*q^26 + 4*q^27 + (-a + 2)*q^28 + (-2*a + 4)*q^29 + 2*q^30 + (-a - 4)*q^31 - q^32 + (4*a + 2)*q^33 - 5*q^34 + (-2*a + 6)*q^35 + (2*a - 1)*q^36 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 - 3*a + 1)*q^5 - a*q^6 + (2*a^2 + 4*a - 6)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 + 3*a - 1)*q^10 + (-3*a^2 - 8*a + 2)*q^11 + a*q^12 + (-2*a^2 - 4*a + 6)*q^14 + (2*a^2 + 5*a - 5)*q^15 + q^16 + (a^2 + 4*a - 2)*q^17 + (-a^2 + 3)*q^18 + (2*a^2 + 6*a - 2)*q^19 + (-a^2 - 3*a + 1)*q^20 + (-6*a^2 - 14*a + 10)*q^21 + (3*a^2 + 8*a - 2)*q^22 + (a^2 + 3*a - 7)*q^23 - a*q^24 + (-2*a^2 - 5*a + 1)*q^25 + (-5*a^2 - 10*a + 5)*q^27 + (2*a^2 + 4*a - 6)*q^28 + (4*a^2 + 9*a - 8)*q^29 + (-2*a^2 - 5*a + 5)*q^30 + (2*a + 2)*q^31 - q^32 + (7*a^2 + 14*a - 15)*q^33 + (-a^2 - 4*a + 2)*q^34 + (4*a^2 + 12*a - 6)*q^35 + (a^2 - 3)*q^36 + (-3*a^2 - 5*a + 11)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 13/5*a + 18/5)*q^5 + a*q^6 + (-3/5*a^4 - 1/5*a^3 + 22/5*a^2 - 7/5*a - 2/5)*q^7 + q^8 + (a^2 - 3)*q^9 + (2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 13/5*a + 18/5)*q^10 + (-1/5*a^4 + 3/5*a^3 + 9/5*a^2 - 29/5*a - 4/5)*q^11 + a*q^12 + (3/5*a^4 + 6/5*a^3 - 17/5*a^2 - 33/5*a - 3/5)*q^13 + (-3/5*a^4 - 1/5*a^3 + 22/5*a^2 - 7/5*a - 2/5)*q^14 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 6/5*a + 4/5)*q^15 + q^16 + (-2/5*a^4 + 1/5*a^3 + 18/5*a^2 - 18/5*a - 3/5)*q^17 + (a^2 - 3)*q^18 + (-a^3 - a^2 + 6*a + 1)*q^19 + (2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 13/5*a + 18/5)*q^20 + (-4/5*a^4 - 8/5*a^3 + 26/5*a^2 + 34/5*a - 6/5)*q^21 + (-1/5*a^4 + 3/5*a^3 + 9/5*a^2 - 29/5*a - 4/5)*q^22 + (-4/5*a^4 - 8/5*a^3 + 31/5*a^2 + 39/5*a - 21/5)*q^23 + a*q^24 + (a^4 - a^3 - 10*a^2 + 10*a + 9)*q^25 + (3/5*a^4 + 6/5*a^3 - 17/5*a^2 - 33/5*a - 3/5)*q^26 + (a^3 - 6*a)*q^27 + (-3/5*a^4 - 1/5*a^3 + 22/5*a^2 - 7/5*a - 2/5)*q^28 + (1/5*a^4 + 7/5*a^3 - 4/5*a^2 - 36/5*a + 4/5)*q^29 + (1/5*a^4 + 2/5*a^3 - 9/5*a^2 - 6/5*a + 4/5)*q^30 + (-1/5*a^4 + 3/5*a^3 + 14/5*a^2 - 19/5*a - 24/5)*q^31 + q^32 + (2/5*a^4 - 1/5*a^3 - 18/5*a^2 + 8/5*a - 2/5)*q^33 + (-2/5*a^4 + 1/5*a^3 + 18/5*a^2 - 18/5*a - 3/5)*q^34 - 2*q^35 + (a^2 - 3)*q^36 + (7/5*a^4 - 6/5*a^3 - 68/5*a^2 + 68/5*a + 48/5)*q^37 + O(q^38)
*]> ;  // time = 60.9 seconds




J[299] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 299, 299, 299, 299, 299, 299, 299, 23 ], new_dimensions := [ 2, 2, 2, 2, 2, 3, 10, 2 ], dimensions := [ 2, 2, 2, 2, 2, 3, 10, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 5, 1, 5, 1, 1, 1, 1, 0, 17, 1, 1, 1, 1, 1, 5, 17, 0, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 11, 1, 5, 1, 5, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 289, 1, 1, 1, 1, 11, 1, 289, 0 ], ap_traces := [
[ 1, -1, -3, -2, -3, -2, -1, -4, -2, 1, 1, -6 ],
[ 0, 0, 2, 2, -6, 2, 4, 10, -2, 8, 12, 2 ],
[ 1, 1, 1, 2, 5, 2, -12, 5, -2, 4, -4, 10 ],
[ -1, -1, 3, 2, 3, 2, 3, -8, -2, -11, 11, 14 ],
[ -1, -1, -1, -4, 1, 2, -3, 2, 2, -7, -13, -14 ],
[ 0, -1, 1, 2, 5, 3, 2, 1, -3, 10, -12, 8 ],
[ 1, 3, 3, -2, 3, -10, -3, 2, 10, 17, 5, 16 ]
], hecke_fields := [
x^2 - x - 1,
x^2 - 5,
x^2 - x - 4,
x^2 + x - 5,
x^2 + x - 1,
x^3 + x^2 - 9*x - 5,
x^10 - x^9 - 19*x^8 + 18*x^7 + 127*x^6 - 109*x^5 - 357*x^4 + 252*x^3 + 400*x^2 - 192*x - 128
], atkin_lehners := [
[ 1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 3, 3 ],
[ 289, 7 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ],
[ 3, 1 ],
[ 1, 7 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 3, 7 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 3, 7 ], l_ratios := [ 0, 1, 1, 1, 0, 1/3, 1/7 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1, 1 ], eigenvalues := [*
[
a,
-a,
-a - 1,
-1,
a - 2,
-1,
3*a - 2,
2*a - 3,
-1,
-3*a + 2,
-3*a + 2,
-2*a - 2
],
[
a,
0,
a + 1,
-a + 1,
-a - 3,
1,
2,
-a + 5,
-1,
-2*a + 4,
-2*a + 6,
a + 1
],
[
a,
-a + 1,
-a + 1,
2*a,
-a + 3,
1,
-6,
-a + 3,
-1,
2,
-4*a,
-2*a + 6
],
[
a,
a,
-a + 1,
1,
a + 2,
1,
a + 2,
-2*a - 5,
-1,
-a - 6,
a + 6,
-2*a + 6
],
[
a,
a,
-a - 1,
-2*a - 3,
-a,
1,
3*a,
4*a + 3,
1,
3*a - 2,
a - 6,
2*a - 6
],
[
0,
a,
-1/2*a^2 + 7/2,
a + 1,
-1/2*a^2 - a + 9/2,
1,
-a^2 + 7,
1/2*a^2 + a - 5/2,
-1,
-a^2 - 2*a + 9,
-4,
a^2 - a - 4
],
[
a,
-3/16*a^9 - 3/16*a^8 + 47/16*a^7 + 11/4*a^6 - 233/16*a^5 - 195/16*a^4 + 397/16*a^3 + 141/8*a^2 - 23/2*a - 7,
7/32*a^9 + 9/32*a^8 - 117/32*a^7 - 65/16*a^6 + 649/32*a^5 + 565/32*a^4 - 1379/32*a^3 - 199/8*a^2 + 61/2*a + 11,
-3/16*a^9 + 1/16*a^8 + 51/16*a^7 - a^6 - 289/16*a^5 + 73/16*a^4 + 617/16*a^3 - 29/8*a^2 - 25*a - 4,
7/32*a^9 + 13/32*a^8 - 105/32*a^7 - 95/16*a^6 + 481/32*a^5 + 849/32*a^4 - 711/32*a^3 - 39*a^2 + 21/2*a + 15,
-1,
5/16*a^9 + 3/16*a^8 - 87/16*a^7 - 23/8*a^6 + 507/16*a^5 + 231/16*a^4 - 1121/16*a^3 - 119/4*a^2 + 47*a + 22,
-13/32*a^9 - 15/32*a^8 + 227/32*a^7 + 117/16*a^6 - 1355/32*a^5 - 1179/32*a^4 + 3245/32*a^3 + 68*a^2 - 165/2*a - 35,
1,
-1/16*a^9 - 7/16*a^8 + 11/16*a^7 + 51/8*a^6 - 15/16*a^5 - 443/16*a^4 - 99/16*a^3 + 143/4*a^2 + 9*a - 8,
-5/8*a^9 - 7/8*a^8 + 83/8*a^7 + 53/4*a^6 - 459/8*a^5 - 499/8*a^4 + 989/8*a^3 + 100*a^2 - 93*a - 44,
-1/8*a^8 - 3/8*a^7 + 11/8*a^6 + 23/4*a^5 - 15/8*a^4 - 203/8*a^3 - 107/8*a^2 + 27*a + 22
]
*], q_expansions := [*
q + a*q^2 - a*q^3 + (a - 1)*q^4 + (-a - 1)*q^5 + (-a - 1)*q^6 - q^7 + (-2*a + 1)*q^8 + (a - 2)*q^9 + (-2*a - 1)*q^10 + (a - 2)*q^11 - q^12 - q^13 - a*q^14 + (2*a + 1)*q^15 - 3*a*q^16 + (3*a - 2)*q^17 + (-a + 1)*q^18 + (2*a - 3)*q^19 - a*q^20 + a*q^21 + (-a + 1)*q^22 - q^23 + (a + 2)*q^24 + (3*a - 3)*q^25 - a*q^26 + (4*a - 1)*q^27 + (-a + 1)*q^28 + (-3*a + 2)*q^29 + (3*a + 2)*q^30 + (-3*a + 2)*q^31 + (a - 5)*q^32 + (a - 1)*q^33 + (a + 3)*q^34 + (a + 1)*q^35 + (-2*a + 3)*q^36 + (-2*a - 2)*q^37 + O(q^38),
q + a*q^2 + 3*q^4 + (a + 1)*q^5 + (-a + 1)*q^7 + a*q^8 - 3*q^9 + (a + 5)*q^10 + (-a - 3)*q^11 + q^13 + (a - 5)*q^14 - q^16 + 2*q^17 - 3*a*q^18 + (-a + 5)*q^19 + (3*a + 3)*q^20 + (-3*a - 5)*q^22 - q^23 + (2*a + 1)*q^25 + a*q^26 + (-3*a + 3)*q^28 + (-2*a + 4)*q^29 + (-2*a + 6)*q^31 - 3*a*q^32 + 2*a*q^34 - 4*q^35 - 9*q^36 + (a + 1)*q^37 + O(q^38),
q + a*q^2 + (-a + 1)*q^3 + (a + 2)*q^4 + (-a + 1)*q^5 - 4*q^6 + 2*a*q^7 + (a + 4)*q^8 + (-a + 2)*q^9 - 4*q^10 + (-a + 3)*q^11 + (-2*a - 2)*q^12 + q^13 + (2*a + 8)*q^14 + (-a + 5)*q^15 + 3*a*q^16 - 6*q^17 + (a - 4)*q^18 + (-a + 3)*q^19 + (-2*a - 2)*q^20 - 8*q^21 + (2*a - 4)*q^22 - q^23 - 4*a*q^24 - a*q^25 + a*q^26 + (a + 3)*q^27 + (6*a + 8)*q^28 + 2*q^29 + (4*a - 4)*q^30 - 4*a*q^31 + (a + 4)*q^32 + (-3*a + 7)*q^33 - 6*a*q^34 - 8*q^35 - a*q^36 + (-2*a + 6)*q^37 + O(q^38),
q + a*q^2 + a*q^3 + (-a + 3)*q^4 + (-a + 1)*q^5 + (-a + 5)*q^6 + q^7 + (2*a - 5)*q^8 + (-a + 2)*q^9 + (2*a - 5)*q^10 + (a + 2)*q^11 + (4*a - 5)*q^12 + q^13 + a*q^14 + (2*a - 5)*q^15 + (-5*a + 4)*q^16 + (a + 2)*q^17 + (3*a - 5)*q^18 + (-2*a - 5)*q^19 + (-5*a + 8)*q^20 + a*q^21 + (a + 5)*q^22 - q^23 + (-7*a + 10)*q^24 + (-3*a + 1)*q^25 + a*q^26 - 5*q^27 + (-a + 3)*q^28 + (-a - 6)*q^29 + (-7*a + 10)*q^30 + (a + 6)*q^31 + (5*a - 15)*q^32 + (a + 5)*q^33 + (a + 5)*q^34 + (-a + 1)*q^35 + (-6*a + 11)*q^36 + (-2*a + 6)*q^37 + O(q^38),
q + a*q^2 + a*q^3 + (-a - 1)*q^4 + (-a - 1)*q^5 + (-a + 1)*q^6 + (-2*a - 3)*q^7 + (-2*a - 1)*q^8 + (-a - 2)*q^9 - q^10 - a*q^11 - q^12 + q^13 + (-a - 2)*q^14 - q^15 + 3*a*q^16 + 3*a*q^17 + (-a - 1)*q^18 + (4*a + 3)*q^19 + (a + 2)*q^20 + (-a - 2)*q^21 + (a - 1)*q^22 + q^23 + (a - 2)*q^24 + (a - 3)*q^25 + a*q^26 + (-4*a - 1)*q^27 + (3*a + 5)*q^28 + (3*a - 2)*q^29 - a*q^30 + (a - 6)*q^31 + (a + 5)*q^32 + (a - 1)*q^33 + (-3*a + 3)*q^34 + (3*a + 5)*q^35 + (2*a + 3)*q^36 + (2*a - 6)*q^37 + O(q^38),
q + a*q^3 - 2*q^4 + (-1/2*a^2 + 7/2)*q^5 + (a + 1)*q^7 + (a^2 - 3)*q^9 + (-1/2*a^2 - a + 9/2)*q^11 - 2*a*q^12 + q^13 + (1/2*a^2 - a - 5/2)*q^15 + 4*q^16 + (-a^2 + 7)*q^17 + (1/2*a^2 + a - 5/2)*q^19 + (a^2 - 7)*q^20 + (a^2 + a)*q^21 - q^23 + (-a^2 - a + 6)*q^25 + (-a^2 + 3*a + 5)*q^27 + (-2*a - 2)*q^28 + (-a^2 - 2*a + 9)*q^29 - 4*q^31 + (-1/2*a^2 - 5/2)*q^33 + (-a + 1)*q^35 + (-2*a^2 + 6)*q^36 + (a^2 - a - 4)*q^37 + O(q^38),
q + a*q^2 + (-3/16*a^9 - 3/16*a^8 + 47/16*a^7 + 11/4*a^6 - 233/16*a^5 - 195/16*a^4 + 397/16*a^3 + 141/8*a^2 - 23/2*a - 7)*q^3 + (a^2 - 2)*q^4 + (7/32*a^9 + 9/32*a^8 - 117/32*a^7 - 65/16*a^6 + 649/32*a^5 + 565/32*a^4 - 1379/32*a^3 - 199/8*a^2 + 61/2*a + 11)*q^5 + (-3/8*a^9 - 5/8*a^8 + 49/8*a^7 + 37/4*a^6 - 261/8*a^5 - 337/8*a^4 + 519/8*a^3 + 127/2*a^2 - 43*a - 24)*q^6 + (-3/16*a^9 + 1/16*a^8 + 51/16*a^7 - a^6 - 289/16*a^5 + 73/16*a^4 + 617/16*a^3 - 29/8*a^2 - 25*a - 4)*q^7 + (a^3 - 4*a)*q^8 + (5/16*a^9 + 3/16*a^8 - 87/16*a^7 - 23/8*a^6 + 507/16*a^5 + 231/16*a^4 - 1137/16*a^3 - 115/4*a^2 + 52*a + 20)*q^9 + (1/2*a^9 + 1/2*a^8 - 8*a^7 - 15/2*a^6 + 83/2*a^5 + 35*a^4 - 80*a^3 - 57*a^2 + 53*a + 28)*q^10 + (7/32*a^9 + 13/32*a^8 - 105/32*a^7 - 95/16*a^6 + 481/32*a^5 + 849/32*a^4 - 711/32*a^3 - 39*a^2 + 21/2*a + 15)*q^11 + (-5/8*a^9 - 5/8*a^8 + 81/8*a^7 + 19/2*a^6 - 431/8*a^5 - 357/8*a^4 + 867/8*a^3 + 287/4*a^2 - 73*a - 34)*q^12 - q^13 + (-1/8*a^9 - 3/8*a^8 + 19/8*a^7 + 23/4*a^6 - 127/8*a^5 - 227/8*a^4 + 349/8*a^3 + 50*a^2 - 40*a - 24)*q^14 + (-3/32*a^9 - 1/32*a^8 + 45/32*a^7 + 3/16*a^6 - 181/32*a^5 + 43/32*a^4 + 51/32*a^3 - 17/2*a^2 + 21/2*a + 9)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (5/16*a^9 + 3/16*a^8 - 87/16*a^7 - 23/8*a^6 + 507/16*a^5 + 231/16*a^4 - 1121/16*a^3 - 119/4*a^2 + 47*a + 22)*q^17 + (1/2*a^9 + 1/2*a^8 - 17/2*a^7 - 8*a^6 + 97/2*a^5 + 81/2*a^4 - 215/2*a^3 - 73*a^2 + 80*a + 40)*q^18 + (-13/32*a^9 - 15/32*a^8 + 227/32*a^7 + 117/16*a^6 - 1355/32*a^5 - 1179/32*a^4 + 3245/32*a^3 + 68*a^2 - 165/2*a - 35)*q^19 + (9/16*a^9 + 15/16*a^8 - 147/16*a^7 - 111/8*a^6 + 783/16*a^5 + 1011/16*a^4 - 1549/16*a^3 - 389/4*a^2 + 63*a + 42)*q^20 + (-3/16*a^9 - 3/16*a^8 + 55/16*a^7 + 13/4*a^6 - 353/16*a^5 - 307/16*a^4 + 933/16*a^3 + 361/8*a^2 - 54*a - 30)*q^21 + (5/8*a^9 + 7/8*a^8 - 79/8*a^7 - 51/4*a^6 + 403/8*a^5 + 447/8*a^4 - 753/8*a^3 - 77*a^2 + 57*a + 28)*q^22 + q^23 + (-1/2*a^9 - 1/2*a^8 + 17/2*a^7 + 7*a^6 - 95/2*a^5 - 61/2*a^4 + 199/2*a^3 + 50*a^2 - 68*a - 32)*q^24 + (1/8*a^8 - 1/8*a^7 - 19/8*a^6 + 9/4*a^5 + 111/8*a^4 - 93/8*a^3 - 205/8*a^2 + 27/2*a + 14)*q^25 - a*q^26 + (-1/4*a^9 - 5/8*a^8 + 29/8*a^7 + 73/8*a^6 - 31/2*a^5 - 311/8*a^4 + 149/8*a^3 + 355/8*a^2 - 9/2*a - 3)*q^27 + (-1/8*a^9 - 1/8*a^8 + 13/8*a^7 + 2*a^6 - 47/8*a^5 - 81/8*a^4 + 35/8*a^3 + 69/4*a^2 + 2*a - 8)*q^28 + (-1/16*a^9 - 7/16*a^8 + 11/16*a^7 + 51/8*a^6 - 15/16*a^5 - 443/16*a^4 - 99/16*a^3 + 143/4*a^2 + 9*a - 8)*q^29 + (-1/8*a^9 - 3/8*a^8 + 15/8*a^7 + 25/4*a^6 - 71/8*a^5 - 255/8*a^4 + 121/8*a^3 + 48*a^2 - 9*a - 12)*q^30 + (-5/8*a^9 - 7/8*a^8 + 83/8*a^7 + 53/4*a^6 - 459/8*a^5 - 499/8*a^4 + 989/8*a^3 + 100*a^2 - 93*a - 44)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-3/32*a^9 - 5/32*a^8 + 65/32*a^7 + 49/16*a^6 - 493/32*a^5 - 625/32*a^4 + 1495/32*a^3 + 357/8*a^2 - 91/2*a - 29)*q^33 + (1/2*a^9 + 1/2*a^8 - 17/2*a^7 - 8*a^6 + 97/2*a^5 + 83/2*a^4 - 217/2*a^3 - 78*a^2 + 82*a + 40)*q^34 + (-3/16*a^9 + 5/16*a^8 + 55/16*a^7 - 19/4*a^6 - 329/16*a^5 + 325/16*a^4 + 693/16*a^3 - 119/8*a^2 - 49/2*a - 16)*q^35 + (3/8*a^9 + 5/8*a^8 - 49/8*a^7 - 37/4*a^6 + 253/8*a^5 + 337/8*a^4 - 455/8*a^3 - 125/2*a^2 + 32*a + 24)*q^36 + (-1/8*a^8 - 3/8*a^7 + 11/8*a^6 + 23/4*a^5 - 15/8*a^4 - 203/8*a^3 - 107/8*a^2 + 27*a + 22)*q^37 + O(q^38)
*]> ;  // time = 43.43 seconds




J[301] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 301, 301, 301, 301, 43, 43 ], new_dimensions := [ 4, 5, 5, 7, 1, 2 ], dimensions := [ 4, 5, 5, 7, 2, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 17, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 17, 1, 1, 0 ], ap_traces := [
[ -4, -3, -4, 4, -15, 1, -1, -8, -5, -16, 3, -11 ],
[ 0, -3, -6, -5, -16, -2, -8, -10, -2, -4, -6, 9 ],
[ 1, 5, 4, -5, 13, -1, 1, 18, -5, 2, -3, -9 ],
[ 4, 1, 0, 7, 16, -2, 4, 0, 6, 12, 8, -7 ]
], hecke_fields := [
x^4 + 4*x^3 + 2*x^2 - 5*x - 3,
x^5 - 6*x^3 + x^2 + 5*x - 2,
x^5 - x^4 - 6*x^3 + 5*x^2 + 6*x - 1,
x^7 - 4*x^6 - 3*x^5 + 25*x^4 - 13*x^3 - 23*x^2 + 11*x + 2
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 7, 1 ],
[ 1, 1 ],
[ 17, 1 ],
[ 11, 1 ]
], tamagawa_numbers := [
[ 7, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 11, 1 ]
], torsion_upper_bounds := [ 21, 1, 1, 11 ], torsion_lower_bounds := [ 1, 1, 1, 11 ], l_ratios := [ 0, 0, 1, 1/11 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-a^3 - 2*a^2 + 2*a + 1,
-a^2 - 2*a,
1,
-a^3 - 3*a^2 + a,
3*a^3 + 8*a^2 - 2*a - 7,
a^3 + 3*a^2 - 3*a - 6,
a^2 + 4*a - 1,
a^3 + 5*a^2 + a - 9,
-4*a^3 - 12*a^2 + 2*a + 9,
5*a^3 + 13*a^2 - 6*a - 13,
-a^3 - 6*a^2 - 4*a + 5
],
[
a,
a^4 + a^3 - 6*a^2 - 5*a + 4,
-2*a^4 - 2*a^3 + 11*a^2 + 8*a - 8,
-1,
3*a^4 + a^3 - 17*a^2 - 4*a + 7,
-2*a^4 - a^3 + 12*a^2 + 2*a - 9,
5*a^4 + 3*a^3 - 27*a^2 - 10*a + 13,
3*a^4 + 2*a^3 - 15*a^2 - 7*a + 4,
-4*a^4 - 3*a^3 + 21*a^2 + 13*a - 11,
-3*a^4 + 16*a^2 - a - 8,
4*a^4 + 3*a^3 - 25*a^2 - 12*a + 19,
7*a^4 + 3*a^3 - 38*a^2 - 9*a + 22
],
[
a,
-a^3 + 4*a + 1,
a^4 - 5*a^2 + a + 3,
-1,
a^4 - a^3 - 5*a^2 + 4*a + 5,
-a^3 - 2*a^2 + 4*a + 5,
-a^4 + a^3 + 7*a^2 - 6*a - 7,
2*a^3 + a^2 - 8*a + 1,
-2*a^4 + a^3 + 9*a^2 - 5*a - 3,
a^4 - 6*a^2 - 3*a + 6,
a^4 + a^3 - 5*a^2 - 5*a + 2,
-a^3 + 2*a^2 + 4*a - 7
],
[
a,
-a^5 + a^4 + 7*a^3 - 5*a^2 - 8*a + 2,
a^6 - 2*a^5 - 6*a^4 + 11*a^3 + 4*a^2 - 6*a,
1,
-a^6 + 3*a^5 + 5*a^4 - 18*a^3 + a^2 + 13*a + 1,
a^6 - a^5 - 8*a^4 + 6*a^3 + 14*a^2 - 7*a - 3,
-a^6 + a^5 + 7*a^4 - 4*a^3 - 9*a^2 - 3*a + 3,
-a^6 + 2*a^5 + 7*a^4 - 13*a^3 - 10*a^2 + 15*a + 4,
2*a^6 - 2*a^5 - 16*a^4 + 11*a^3 + 29*a^2 - 9*a - 7,
-3*a^6 + 5*a^5 + 19*a^4 - 29*a^3 - 14*a^2 + 22*a - 2,
-a^5 + 2*a^4 + 5*a^3 - 10*a^2 - a + 5,
3*a^5 - 5*a^4 - 19*a^3 + 25*a^2 + 18*a - 8
]
*], q_expansions := [*
q + a*q^2 + (-a^3 - 2*a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 - 2*a)*q^5 + (2*a^3 + 4*a^2 - 4*a - 3)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (3*a^3 + 7*a^2 - 6*a - 8)*q^9 + (-a^3 - 2*a^2)*q^10 + (-a^3 - 3*a^2 + a)*q^11 + (-2*a^3 - 4*a^2 + 3*a + 4)*q^12 + (3*a^3 + 8*a^2 - 2*a - 7)*q^13 + a*q^14 + a*q^15 + (-4*a^3 - 8*a^2 + 5*a + 7)*q^16 + (a^3 + 3*a^2 - 3*a - 6)*q^17 + (-5*a^3 - 12*a^2 + 7*a + 9)*q^18 + (a^2 + 4*a - 1)*q^19 + (2*a^3 + 4*a^2 - a - 3)*q^20 + (-a^3 - 2*a^2 + 2*a + 1)*q^21 + (a^3 + 3*a^2 - 5*a - 3)*q^22 + (a^3 + 5*a^2 + a - 9)*q^23 + (-a^2 + 2*a)*q^24 + (2*a^2 + 5*a - 2)*q^25 + (-4*a^3 - 8*a^2 + 8*a + 9)*q^26 + (-5*a^3 - 13*a^2 + 9*a + 13)*q^27 + (a^2 - 2)*q^28 + (-4*a^3 - 12*a^2 + 2*a + 9)*q^29 + a^2*q^30 + (5*a^3 + 13*a^2 - 6*a - 13)*q^31 + (6*a^3 + 13*a^2 - 5*a - 12)*q^32 + (6*a^3 + 13*a^2 - 11*a - 9)*q^33 + (-a^3 - 5*a^2 - a + 3)*q^34 + (-a^2 - 2*a)*q^35 + (2*a^3 + 3*a^2 - 4*a + 1)*q^36 + (-a^3 - 6*a^2 - 4*a + 5)*q^37 + O(q^38),
q + a*q^2 + (a^4 + a^3 - 6*a^2 - 5*a + 4)*q^3 + (a^2 - 2)*q^4 + (-2*a^4 - 2*a^3 + 11*a^2 + 8*a - 8)*q^5 + (a^4 - 6*a^2 - a + 2)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-3*a^4 - a^3 + 17*a^2 + 5*a - 9)*q^9 + (-2*a^4 - a^3 + 10*a^2 + 2*a - 4)*q^10 + (3*a^4 + a^3 - 17*a^2 - 4*a + 7)*q^11 + (-2*a^4 - 2*a^3 + 10*a^2 + 7*a - 6)*q^12 + (-2*a^4 - a^3 + 12*a^2 + 2*a - 9)*q^13 - a*q^14 + (4*a^4 + 2*a^3 - 20*a^2 - 5*a + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (5*a^4 + 3*a^3 - 27*a^2 - 10*a + 13)*q^17 + (-a^4 - a^3 + 8*a^2 + 6*a - 6)*q^18 + (3*a^4 + 2*a^3 - 15*a^2 - 7*a + 4)*q^19 + (3*a^4 + 2*a^3 - 18*a^2 - 10*a + 12)*q^20 + (-a^4 - a^3 + 6*a^2 + 5*a - 4)*q^21 + (a^4 + a^3 - 7*a^2 - 8*a + 6)*q^22 + (-4*a^4 - 3*a^3 + 21*a^2 + 13*a - 11)*q^23 + (-4*a^4 - 2*a^3 + 21*a^2 + 6*a - 8)*q^24 + (-3*a^4 + 16*a^2 - 5)*q^25 + (-a^4 + 4*a^2 + a - 4)*q^26 + (-a^4 - a^3 + 5*a^2 + 2*a - 4)*q^27 + (-a^2 + 2)*q^28 + (-3*a^4 + 16*a^2 - a - 8)*q^29 + (2*a^4 + 4*a^3 - 9*a^2 - 14*a + 8)*q^30 + (4*a^4 + 3*a^3 - 25*a^2 - 12*a + 19)*q^31 + (-2*a^3 - a^2 + 7*a + 2)*q^32 + (-3*a^4 - 4*a^3 + 19*a^2 + 22*a - 14)*q^33 + (3*a^4 + 3*a^3 - 15*a^2 - 12*a + 10)*q^34 + (2*a^4 + 2*a^3 - 11*a^2 - 8*a + 8)*q^35 + (5*a^4 + 4*a^3 - 27*a^2 - 11*a + 16)*q^36 + (7*a^4 + 3*a^3 - 38*a^2 - 9*a + 22)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 4*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^4 - 5*a^2 + a + 3)*q^5 + (-a^4 + 4*a^2 + a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (-a^4 - a^3 + 5*a^2 + 3*a - 1)*q^9 + (a^4 + a^3 - 4*a^2 - 3*a + 1)*q^10 + (a^4 - a^3 - 5*a^2 + 4*a + 5)*q^11 + (-a^4 + 6*a^2 - 2*a - 3)*q^12 + (-a^3 - 2*a^2 + 4*a + 5)*q^13 - a*q^14 + (a^4 - 6*a^2 + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 + a^3 + 7*a^2 - 6*a - 7)*q^17 + (-2*a^4 - a^3 + 8*a^2 + 5*a - 1)*q^18 + (2*a^3 + a^2 - 8*a + 1)*q^19 + (2*a^3 + 2*a^2 - 7*a - 5)*q^20 + (a^3 - 4*a - 1)*q^21 + (a^3 - a^2 - a + 1)*q^22 + (-2*a^4 + a^3 + 9*a^2 - 5*a - 3)*q^23 + (a^4 - 5*a^2 + a - 1)*q^24 + (2*a^4 - 10*a^2 + 3*a + 4)*q^25 + (-a^4 - 2*a^3 + 4*a^2 + 5*a)*q^26 + (-2*a^4 + a^3 + 11*a^2 - 5*a - 5)*q^27 + (-a^2 + 2)*q^28 + (a^4 - 6*a^2 - 3*a + 6)*q^29 + (a^4 - 5*a^2 - a + 1)*q^30 + (a^4 + a^3 - 5*a^2 - 5*a + 2)*q^31 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 1)*q^32 + (a^4 - 2*a^3 - 5*a^2 + 6*a + 8)*q^33 + (a^3 - a^2 - a - 1)*q^34 + (-a^4 + 5*a^2 - a - 3)*q^35 + (-a^4 - 2*a^3 + 5*a^2 + 5*a)*q^36 + (-a^3 + 2*a^2 + 4*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-a^5 + a^4 + 7*a^3 - 5*a^2 - 8*a + 2)*q^3 + (a^2 - 2)*q^4 + (a^6 - 2*a^5 - 6*a^4 + 11*a^3 + 4*a^2 - 6*a)*q^5 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 8*a^2 + 2*a)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (a^4 - a^3 - 7*a^2 + 5*a + 7)*q^9 + (2*a^6 - 3*a^5 - 14*a^4 + 17*a^3 + 17*a^2 - 11*a - 2)*q^10 + (-a^6 + 3*a^5 + 5*a^4 - 18*a^3 + a^2 + 13*a + 1)*q^11 + (-3*a^6 + 6*a^5 + 18*a^4 - 35*a^3 - 11*a^2 + 27*a - 2)*q^12 + (a^6 - a^5 - 8*a^4 + 6*a^3 + 14*a^2 - 7*a - 3)*q^13 + a*q^14 + (a^6 - 2*a^5 - 6*a^4 + 11*a^3 + 3*a^2 - 5*a + 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^6 + a^5 + 7*a^4 - 4*a^3 - 9*a^2 - 3*a + 3)*q^17 + (a^5 - a^4 - 7*a^3 + 5*a^2 + 7*a)*q^18 + (-a^6 + 2*a^5 + 7*a^4 - 13*a^3 - 10*a^2 + 15*a + 4)*q^19 + (3*a^6 - 4*a^5 - 21*a^4 + 21*a^3 + 27*a^2 - 12*a - 4)*q^20 + (-a^5 + a^4 + 7*a^3 - 5*a^2 - 8*a + 2)*q^21 + (-a^6 + 2*a^5 + 7*a^4 - 12*a^3 - 10*a^2 + 12*a + 2)*q^22 + (2*a^6 - 2*a^5 - 16*a^4 + 11*a^3 + 29*a^2 - 9*a - 7)*q^23 + (-4*a^6 + 7*a^5 + 26*a^4 - 40*a^3 - 26*a^2 + 27*a + 6)*q^24 + (-2*a^6 + 3*a^5 + 13*a^4 - 16*a^3 - 11*a^2 + 7*a - 3)*q^25 + (3*a^6 - 5*a^5 - 19*a^4 + 27*a^3 + 16*a^2 - 14*a - 2)*q^26 + (3*a^6 - 8*a^5 - 15*a^4 + 48*a^3 - 4*a^2 - 40*a + 4)*q^27 + (a^2 - 2)*q^28 + (-3*a^6 + 5*a^5 + 19*a^4 - 29*a^3 - 14*a^2 + 22*a - 2)*q^29 + (2*a^6 - 3*a^5 - 14*a^4 + 16*a^3 + 18*a^2 - 9*a - 2)*q^30 + (-a^5 + 2*a^4 + 5*a^3 - 10*a^2 - a + 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^5 + a^4 + 16*a^3 - 3*a^2 - 26*a - 6)*q^33 + (-3*a^6 + 4*a^5 + 21*a^4 - 22*a^3 - 26*a^2 + 14*a + 2)*q^34 + (a^6 - 2*a^5 - 6*a^4 + 11*a^3 + 4*a^2 - 6*a)*q^35 + (a^6 - a^5 - 9*a^4 + 7*a^3 + 21*a^2 - 10*a - 14)*q^36 + (3*a^5 - 5*a^4 - 19*a^3 + 25*a^2 + 18*a - 8)*q^37 + O(q^38)
*]> ;  // time = 39.449 seconds




J[302] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 302, 302, 302, 302, 302, 302, 151, 151, 151 ], new_dimensions := [ 1, 1, 1, 2, 4, 4, 3, 3, 6 ], dimensions := [ 1, 1, 1, 2, 4, 4, 6, 6, 12 ], intersection_graph := [ 0, 1, 1, 1, 9, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 3, 5, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 9, 1, 1, 1, 0, 1, 1, 3, 431, 1, 1, 1, 1, 1, 0, 41, 1, 1, 1, 1, 1, 7, 1, 41, 0, 1, 1, 3, 3, 5, 1, 3, 1, 1, 0, 4489, 1, 5, 1, 1, 431, 1, 1, 4489, 0 ], ap_traces := [
[ -1, 2, 2, 4, -4, 0, -6, 0, 0, 6, 0, -2 ],
[ 1, -1, -4, -2, 2, -6, 3, 0, -6, 0, -3, -2 ],
[ 1, -3, 0, -2, -6, -2, -5, -8, 6, 8, 9, 2 ],
[ -2, -2, 0, -4, 4, -8, -10, 0, 4, 0, -6, -12 ],
[ -4, 0, -4, 2, 0, 14, 12, 12, 2, -4, 0, 12 ],
[ 4, 2, 0, 6, 0, 6, -4, 4, -6, -4, 4, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 1,
x^4 - 10*x^2 - 6*x + 9,
x^4 - 2*x^3 - 4*x^2 + 8*x - 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 15, 1 ],
[ 5, 1 ],
[ 7, 1 ],
[ 3879, 3 ],
[ 779, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 15, 1 ],
[ 5, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 779, 1 ]
], torsion_upper_bounds := [ 1, 5, 1, 1, 3, 19 ], torsion_lower_bounds := [ 1, 1, 1, 1, 3, 19 ], l_ratios := [ 1, 0, 0, 0, 1/3, 41/19 ], analytic_sha_upper_bounds := [ 1, 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 2, 2, 4, -4, 0, -6, 0, 0, 6, 0, -2 ],
[ 1, -1, -4, -2, 2, -6, 3, 0, -6, 0, -3, -2 ],
[ 1, -3, 0, -2, -6, -2, -5, -8, 6, 8, 9, 2 ],
[
-1,
a,
0,
-2*a - 4,
-2*a,
2*a - 2,
-5,
2*a + 2,
4*a + 6,
-4*a - 4,
4*a + 1,
-2*a - 8
],
[
-1,
a,
2/3*a^3 - a^2 - 14/3*a + 1,
-1/3*a^3 + 7/3*a + 2,
-a^2 + 2*a + 5,
1/3*a^3 - 7/3*a + 2,
3,
-2/3*a^3 + a^2 + 14/3*a + 1,
-1/3*a^3 + 1/3*a + 2,
2/3*a^3 - 20/3*a - 4,
2/3*a^3 - 3*a^2 - 8/3*a + 12,
2/3*a^3 - 2*a^2 - 14/3*a + 10
],
[
1,
a,
-a^2 + 3,
a^3 - 5*a + 2,
-2*a^3 + a^2 + 8*a - 3,
-a^3 + 2*a^2 + 3*a - 4,
-1,
2*a^3 - a^2 - 10*a + 5,
a^3 - 2*a^2 - 3*a + 4,
-2*a,
-2*a^3 + a^2 + 8*a - 2,
2*a^2 + 4*a - 10
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 + 2*q^5 - 2*q^6 + 4*q^7 - q^8 + q^9 - 2*q^10 - 4*q^11 + 2*q^12 - 4*q^14 + 4*q^15 + q^16 - 6*q^17 - q^18 + 2*q^20 + 8*q^21 + 4*q^22 - 2*q^24 - q^25 - 4*q^27 + 4*q^28 + 6*q^29 - 4*q^30 - q^32 - 8*q^33 + 6*q^34 + 8*q^35 + q^36 - 2*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - 4*q^5 - q^6 - 2*q^7 + q^8 - 2*q^9 - 4*q^10 + 2*q^11 - q^12 - 6*q^13 - 2*q^14 + 4*q^15 + q^16 + 3*q^17 - 2*q^18 - 4*q^20 + 2*q^21 + 2*q^22 - 6*q^23 - q^24 + 11*q^25 - 6*q^26 + 5*q^27 - 2*q^28 + 4*q^30 - 3*q^31 + q^32 - 2*q^33 + 3*q^34 + 8*q^35 - 2*q^36 - 2*q^37 + O(q^38),
q + q^2 - 3*q^3 + q^4 - 3*q^6 - 2*q^7 + q^8 + 6*q^9 - 6*q^11 - 3*q^12 - 2*q^13 - 2*q^14 + q^16 - 5*q^17 + 6*q^18 - 8*q^19 + 6*q^21 - 6*q^22 + 6*q^23 - 3*q^24 - 5*q^25 - 2*q^26 - 9*q^27 - 2*q^28 + 8*q^29 + 9*q^31 + q^32 + 18*q^33 - 5*q^34 + 6*q^36 + 2*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - a*q^6 + (-2*a - 4)*q^7 - q^8 + (-2*a - 2)*q^9 - 2*a*q^11 + a*q^12 + (2*a - 2)*q^13 + (2*a + 4)*q^14 + q^16 - 5*q^17 + (2*a + 2)*q^18 + (2*a + 2)*q^19 - 2*q^21 + 2*a*q^22 + (4*a + 6)*q^23 - a*q^24 - 5*q^25 + (-2*a + 2)*q^26 + (-a - 2)*q^27 + (-2*a - 4)*q^28 + (-4*a - 4)*q^29 + (4*a + 1)*q^31 - q^32 + (4*a - 2)*q^33 + 5*q^34 + (-2*a - 2)*q^36 + (-2*a - 8)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (2/3*a^3 - a^2 - 14/3*a + 1)*q^5 - a*q^6 + (-1/3*a^3 + 7/3*a + 2)*q^7 - q^8 + (a^2 - 3)*q^9 + (-2/3*a^3 + a^2 + 14/3*a - 1)*q^10 + (-a^2 + 2*a + 5)*q^11 + a*q^12 + (1/3*a^3 - 7/3*a + 2)*q^13 + (1/3*a^3 - 7/3*a - 2)*q^14 + (-a^3 + 2*a^2 + 5*a - 6)*q^15 + q^16 + 3*q^17 + (-a^2 + 3)*q^18 + (-2/3*a^3 + a^2 + 14/3*a + 1)*q^19 + (2/3*a^3 - a^2 - 14/3*a + 1)*q^20 + (-a^2 + 3)*q^21 + (a^2 - 2*a - 5)*q^22 + (-1/3*a^3 + 1/3*a + 2)*q^23 - a*q^24 + (-2*a + 3)*q^25 + (-1/3*a^3 + 7/3*a - 2)*q^26 + (a^3 - 6*a)*q^27 + (-1/3*a^3 + 7/3*a + 2)*q^28 + (2/3*a^3 - 20/3*a - 4)*q^29 + (a^3 - 2*a^2 - 5*a + 6)*q^30 + (2/3*a^3 - 3*a^2 - 8/3*a + 12)*q^31 - q^32 + (-a^3 + 2*a^2 + 5*a)*q^33 - 3*q^34 + (2/3*a^3 - 14/3*a - 6)*q^35 + (a^2 - 3)*q^36 + (2/3*a^3 - 2*a^2 - 14/3*a + 10)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a^2 + 3)*q^5 + a*q^6 + (a^3 - 5*a + 2)*q^7 + q^8 + (a^2 - 3)*q^9 + (-a^2 + 3)*q^10 + (-2*a^3 + a^2 + 8*a - 3)*q^11 + a*q^12 + (-a^3 + 2*a^2 + 3*a - 4)*q^13 + (a^3 - 5*a + 2)*q^14 + (-a^3 + 3*a)*q^15 + q^16 - q^17 + (a^2 - 3)*q^18 + (2*a^3 - a^2 - 10*a + 5)*q^19 + (-a^2 + 3)*q^20 + (2*a^3 - a^2 - 6*a + 1)*q^21 + (-2*a^3 + a^2 + 8*a - 3)*q^22 + (a^3 - 2*a^2 - 3*a + 4)*q^23 + a*q^24 + (2*a^3 - 2*a^2 - 8*a + 5)*q^25 + (-a^3 + 2*a^2 + 3*a - 4)*q^26 + (a^3 - 6*a)*q^27 + (a^3 - 5*a + 2)*q^28 - 2*a*q^29 + (-a^3 + 3*a)*q^30 + (-2*a^3 + a^2 + 8*a - 2)*q^31 + q^32 + (-3*a^3 + 13*a - 2)*q^33 - q^34 + (-2*a^2 + 4)*q^35 + (a^2 - 3)*q^36 + (2*a^2 + 4*a - 10)*q^37 + O(q^38)
*]> ;  // time = 64.231 seconds




J[303] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 303, 303, 303, 303, 303, 101, 101 ], new_dimensions := [ 1, 1, 2, 6, 7, 1, 7 ], dimensions := [ 1, 1, 2, 6, 7, 2, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 7, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1103, 1, 1, 1, 3, 1, 0, 1, 7, 1, 1, 1, 1103, 1, 0 ], ap_traces := [
[ 0, 1, -3, 0, -2, -3, -7, -5, -5, 6, 7, 10 ],
[ -2, 1, -1, -2, -6, 1, -5, 7, -3, -6, -1, -10 ],
[ 0, -2, -2, -4, 4, -6, -6, -6, 2, 4, 2, -8 ],
[ 1, 6, 6, 0, 10, 0, 12, -10, 4, 8, -2, -6 ],
[ 0, -7, 6, 6, -10, 10, 20, 2, 6, -10, 10, 8 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 - 2,
x^6 - x^5 - 7*x^4 + 5*x^3 + 13*x^2 - 4*x - 6,
x^7 - 12*x^5 + 40*x^3 + x^2 - 24*x - 4
], atkin_lehners := [
[ -1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 7, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 51, 1 ],
[ 1103, 1 ]
], tamagawa_numbers := [
[ 7, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 51, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 17, 1 ], torsion_lower_bounds := [ 1, 1, 1, 17, 1 ], l_ratios := [ 0, 0, 0, 3/17, 1 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1, 1 ], eigenvalues := [*
[ 0, 1, -3, 0, -2, -3, -7, -5, -5, 6, 7, 10 ],
[ -2, 1, -1, -2, -6, 1, -5, 7, -3, -6, -1, -10 ],
[
a,
-1,
-a - 1,
-a - 2,
2,
2*a - 3,
-a - 3,
-3,
3*a + 1,
2*a + 2,
2*a + 1,
-4
],
[
a,
1,
a^4 - a^3 - 5*a^2 + 3*a + 5,
-a^5 + a^4 + 5*a^3 - 5*a^2 - 3*a + 4,
-2*a^4 + a^3 + 11*a^2 - 4*a - 8,
2*a^5 - 2*a^4 - 11*a^3 + 9*a^2 + 10*a - 5,
-a^4 + a^3 + 3*a^2 - 3*a + 3,
-a^5 + 2*a^4 + 7*a^3 - 11*a^2 - 10*a + 7,
-2*a^5 + 3*a^4 + 11*a^3 - 13*a^2 - 13*a + 7,
2*a^5 - 11*a^3 - 3*a^2 + 10*a + 8,
-2*a^4 - a^3 + 11*a^2 + 4*a - 9,
2*a^4 + a^3 - 7*a^2 - 6*a - 2
],
[
a,
-1,
a^6 + a^5 - 8*a^4 - 6*a^3 + 14*a^2 + 3*a - 3,
-a^6 - 2*a^5 + 8*a^4 + 12*a^3 - 14*a^2 - 5*a + 4,
-a^3 - a^2 + 6*a + 2,
-a^6 - 3*a^5 + 5*a^4 + 20*a^3 + 4*a^2 - 18*a - 3,
a^6 + 3*a^5 - 6*a^4 - 20*a^3 + 2*a^2 + 17*a + 5,
-a^5 + 7*a^3 - a^2 - 8*a + 3,
a^6 + 3*a^5 - 6*a^4 - 18*a^3 + 2*a^2 + 7*a + 3,
a^3 - a^2 - 6*a + 2,
-a^6 - a^5 + 7*a^4 + 8*a^3 - 8*a^2 - 14*a + 3,
-2*a^5 - 4*a^4 + 13*a^3 + 23*a^2 - 12*a - 6
]
*], q_expansions := [*
q + q^3 - 2*q^4 - 3*q^5 + q^9 - 2*q^11 - 2*q^12 - 3*q^13 - 3*q^15 + 4*q^16 - 7*q^17 - 5*q^19 + 6*q^20 - 5*q^23 + 4*q^25 + q^27 + 6*q^29 + 7*q^31 - 2*q^33 - 2*q^36 + 10*q^37 + O(q^38),
q - 2*q^2 + q^3 + 2*q^4 - q^5 - 2*q^6 - 2*q^7 + q^9 + 2*q^10 - 6*q^11 + 2*q^12 + q^13 + 4*q^14 - q^15 - 4*q^16 - 5*q^17 - 2*q^18 + 7*q^19 - 2*q^20 - 2*q^21 + 12*q^22 - 3*q^23 - 4*q^25 - 2*q^26 + q^27 - 4*q^28 - 6*q^29 + 2*q^30 - q^31 + 8*q^32 - 6*q^33 + 10*q^34 + 2*q^35 + 2*q^36 - 10*q^37 + O(q^38),
q + a*q^2 - q^3 + (-a - 1)*q^5 - a*q^6 + (-a - 2)*q^7 - 2*a*q^8 + q^9 + (-a - 2)*q^10 + 2*q^11 + (2*a - 3)*q^13 + (-2*a - 2)*q^14 + (a + 1)*q^15 - 4*q^16 + (-a - 3)*q^17 + a*q^18 - 3*q^19 + (a + 2)*q^21 + 2*a*q^22 + (3*a + 1)*q^23 + 2*a*q^24 + (2*a - 2)*q^25 + (-3*a + 4)*q^26 - q^27 + (2*a + 2)*q^29 + (a + 2)*q^30 + (2*a + 1)*q^31 - 2*q^33 + (-3*a - 2)*q^34 + (3*a + 4)*q^35 - 4*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (a^4 - a^3 - 5*a^2 + 3*a + 5)*q^5 + a*q^6 + (-a^5 + a^4 + 5*a^3 - 5*a^2 - 3*a + 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 5*a)*q^10 + (-2*a^4 + a^3 + 11*a^2 - 4*a - 8)*q^11 + (a^2 - 2)*q^12 + (2*a^5 - 2*a^4 - 11*a^3 + 9*a^2 + 10*a - 5)*q^13 + (-2*a^4 + 10*a^2 - 6)*q^14 + (a^4 - a^3 - 5*a^2 + 3*a + 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 + a^3 + 3*a^2 - 3*a + 3)*q^17 + a*q^18 + (-a^5 + 2*a^4 + 7*a^3 - 11*a^2 - 10*a + 7)*q^19 + (2*a^2 - 2*a - 4)*q^20 + (-a^5 + a^4 + 5*a^3 - 5*a^2 - 3*a + 4)*q^21 + (-2*a^5 + a^4 + 11*a^3 - 4*a^2 - 8*a)*q^22 + (-2*a^5 + 3*a^4 + 11*a^3 - 13*a^2 - 13*a + 7)*q^23 + (a^3 - 4*a)*q^24 + (a^5 - 8*a^3 + 12*a + 2)*q^25 + (3*a^4 - a^3 - 16*a^2 + 3*a + 12)*q^26 + q^27 + (-2*a^4 + 10*a^2 - 8)*q^28 + (2*a^5 - 11*a^3 - 3*a^2 + 10*a + 8)*q^29 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 5*a)*q^30 + (-2*a^4 - a^3 + 11*a^2 + 4*a - 9)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^4 + a^3 + 11*a^2 - 4*a - 8)*q^33 + (-a^5 + a^4 + 3*a^3 - 3*a^2 + 3*a)*q^34 + (a^5 - a^4 - 5*a^3 + 3*a^2 + 3*a + 2)*q^35 + (a^2 - 2)*q^36 + (2*a^4 + a^3 - 7*a^2 - 6*a - 2)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^6 + a^5 - 8*a^4 - 6*a^3 + 14*a^2 + 3*a - 3)*q^5 - a*q^6 + (-a^6 - 2*a^5 + 8*a^4 + 12*a^3 - 14*a^2 - 5*a + 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^6 + 4*a^5 - 6*a^4 - 26*a^3 + 2*a^2 + 21*a + 4)*q^10 + (-a^3 - a^2 + 6*a + 2)*q^11 + (-a^2 + 2)*q^12 + (-a^6 - 3*a^5 + 5*a^4 + 20*a^3 + 4*a^2 - 18*a - 3)*q^13 + (-2*a^6 - 4*a^5 + 12*a^4 + 26*a^3 - 4*a^2 - 20*a - 4)*q^14 + (-a^6 - a^5 + 8*a^4 + 6*a^3 - 14*a^2 - 3*a + 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 + 3*a^5 - 6*a^4 - 20*a^3 + 2*a^2 + 17*a + 5)*q^17 + a*q^18 + (-a^5 + 7*a^3 - a^2 - 8*a + 3)*q^19 + (2*a^6 + 4*a^5 - 10*a^4 - 26*a^3 - 8*a^2 + 22*a + 10)*q^20 + (a^6 + 2*a^5 - 8*a^4 - 12*a^3 + 14*a^2 + 5*a - 4)*q^21 + (-a^4 - a^3 + 6*a^2 + 2*a)*q^22 + (a^6 + 3*a^5 - 6*a^4 - 18*a^3 + 2*a^2 + 7*a + 3)*q^23 + (-a^3 + 4*a)*q^24 + (2*a^6 + 5*a^5 - 12*a^4 - 32*a^3 + 4*a^2 + 22*a + 8)*q^25 + (-3*a^6 - 7*a^5 + 20*a^4 + 44*a^3 - 17*a^2 - 27*a - 4)*q^26 - q^27 + (-2*a^6 - 8*a^5 + 10*a^4 + 52*a^3 + 10*a^2 - 42*a - 16)*q^28 + (a^3 - a^2 - 6*a + 2)*q^29 + (-a^6 - 4*a^5 + 6*a^4 + 26*a^3 - 2*a^2 - 21*a - 4)*q^30 + (-a^6 - a^5 + 7*a^4 + 8*a^3 - 8*a^2 - 14*a + 3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^3 + a^2 - 6*a - 2)*q^33 + (3*a^6 + 6*a^5 - 20*a^4 - 38*a^3 + 16*a^2 + 29*a + 4)*q^34 + (-a^6 - 4*a^5 + 4*a^4 + 24*a^3 + 12*a^2 - 13*a - 16)*q^35 + (a^2 - 2)*q^36 + (-2*a^5 - 4*a^4 + 13*a^3 + 23*a^2 - 12*a - 6)*q^37 + O(q^38)
*]> ;  // time = 46.139 seconds




J[305] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 305, 305, 305, 305, 61, 61 ], new_dimensions := [ 3, 4, 7, 7, 1, 3 ], dimensions := [ 3, 4, 7, 7, 2, 6 ], intersection_graph := [ 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 37, 1, 1, 0, 1, 1, 139, 1, 1, 1, 0, 9, 1, 3, 1, 1, 9, 0, 1, 1, 37, 139, 1, 1, 0 ], ap_traces := [
[ 0, 0, -3, -6, -6, -3, 0, -15, 9, 3, -15, 3 ],
[ -3, -6, 4, -10, -2, -1, -4, -7, -13, 5, -21, -15 ],
[ -2, 0, -7, 12, 2, 9, -4, 13, -5, 7, 35, 9 ],
[ 2, 6, 7, 8, -6, 5, -2, 9, 5, -13, 17, 1 ]
], hecke_fields := [
x^3 - 3*x + 1,
x^4 + 3*x^3 - x^2 - 6*x - 1,
x^7 + 2*x^6 - 11*x^5 - 19*x^4 + 35*x^3 + 48*x^2 - 25*x - 27,
x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 19*x^3 - 36*x^2 + 5*x + 1
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 3, 1 ],
[ 37, 1 ],
[ 417, 3 ],
[ 279, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 37, 1 ],
[ 1, 3 ],
[ 279, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 31 ], torsion_lower_bounds := [ 1, 1, 3, 31 ], l_ratios := [ 0, 0, 1/3, 9/31 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-a,
-1,
-2*a^2 - a + 2,
-a^2 + a,
3*a^2 + 4*a - 7,
3*a^2 - a - 6,
-a - 5,
a^2 + 2*a + 1,
-3*a^2 - 5*a + 7,
a - 5,
-2*a^2 + a + 5
],
[
a,
-a^3 - 2*a^2 + 2*a + 1,
1,
a^3 + 2*a^2 - 2*a - 5,
a^2 - a - 4,
-a^2 - 2*a + 1,
-2*a^3 - a^2 + 7*a - 2,
-2*a^2 - a + 3,
2*a^3 + a^2 - 8*a - 3,
3*a^3 + 5*a^2 - 4*a - 2,
2*a^2 + 5*a - 7,
-2*a^2 - a + 1
],
[
a,
-1/2*a^5 + 4*a^3 - 1/2*a^2 - 11/2*a - 1/2,
-1,
a^4 - 7*a^2 + 2*a + 8,
1/2*a^6 - 5*a^4 + 1/2*a^3 + 25/2*a^2 - 3/2*a - 6,
-a^2 + 5,
a^4 + a^3 - 6*a^2 - 3*a + 3,
-a^4 - a^3 + 5*a^2 + 3*a + 2,
-a^6 + 10*a^4 - a^3 - 26*a^2 + a + 15,
a^6 - 11*a^4 + a^3 + 33*a^2 - 3*a - 21,
1/2*a^6 + a^5 - 5*a^4 - 15/2*a^3 + 29/2*a^2 + 19/2*a - 4,
-a^5 - a^4 + 7*a^3 + 6*a^2 - 8*a - 7
],
[
a,
-1/2*a^6 + a^5 + 4*a^4 - 15/2*a^3 - 15/2*a^2 + 27/2*a,
1,
a^4 - 2*a^3 - 5*a^2 + 8*a + 2,
a^6 - 3/2*a^5 - 10*a^4 + 13*a^3 + 49/2*a^2 - 55/2*a - 1/2,
a^6 - a^5 - 10*a^4 + 9*a^3 + 25*a^2 - 22*a - 2,
-a^5 + a^4 + 7*a^3 - 5*a^2 - 10*a + 4,
a^4 - a^3 - 5*a^2 + 3*a + 2,
-a^5 + 10*a^3 - 23*a + 4,
-a^5 + 3*a^4 + 2*a^3 - 13*a^2 + 11*a - 2,
-a^6 + 3/2*a^5 + 8*a^4 - 9*a^3 - 31/2*a^2 + 23/2*a + 7/2,
-a^4 + a^3 + 5*a^2 - 5*a
]
*], q_expansions := [*
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 - q^5 - a^2*q^6 + (-2*a^2 - a + 2)*q^7 + (-a - 1)*q^8 + (a^2 - 3)*q^9 - a*q^10 + (-a^2 + a)*q^11 + (-a + 1)*q^12 + (3*a^2 + 4*a - 7)*q^13 + (-a^2 - 4*a + 2)*q^14 + a*q^15 + (-3*a^2 - a + 4)*q^16 + (3*a^2 - a - 6)*q^17 - q^18 + (-a - 5)*q^19 + (-a^2 + 2)*q^20 + (a^2 + 4*a - 2)*q^21 + (a^2 - 3*a + 1)*q^22 + (a^2 + 2*a + 1)*q^23 + (a^2 + a)*q^24 + q^25 + (4*a^2 + 2*a - 3)*q^26 + (3*a + 1)*q^27 + (a - 3)*q^28 + (-3*a^2 - 5*a + 7)*q^29 + a^2*q^30 + (a - 5)*q^31 + (-a^2 - 3*a + 5)*q^32 + (-a^2 + 3*a - 1)*q^33 + (-a^2 + 3*a - 3)*q^34 + (2*a^2 + a - 2)*q^35 + (-2*a^2 - a + 6)*q^36 + (-2*a^2 + a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 + q^5 + (a^3 + a^2 - 5*a - 1)*q^6 + (a^3 + 2*a^2 - 2*a - 5)*q^7 + (a^3 - 4*a)*q^8 + (3*a^3 + 5*a^2 - 7*a - 4)*q^9 + a*q^10 + (a^2 - a - 4)*q^11 + (a - 1)*q^12 + (-a^2 - 2*a + 1)*q^13 + (-a^3 - a^2 + a + 1)*q^14 + (-a^3 - 2*a^2 + 2*a + 1)*q^15 + (-3*a^3 - 5*a^2 + 6*a + 5)*q^16 + (-2*a^3 - a^2 + 7*a - 2)*q^17 + (-4*a^3 - 4*a^2 + 14*a + 3)*q^18 + (-2*a^2 - a + 3)*q^19 + (a^2 - 2)*q^20 + (a^3 + 3*a^2 - a - 3)*q^21 + (a^3 - a^2 - 4*a)*q^22 + (2*a^3 + a^2 - 8*a - 3)*q^23 + (-2*a^3 - a^2 + 9*a + 2)*q^24 + q^25 + (-a^3 - 2*a^2 + a)*q^26 + (-4*a^3 - 4*a^2 + 13*a - 1)*q^27 + (-4*a^2 - a + 9)*q^28 + (3*a^3 + 5*a^2 - 4*a - 2)*q^29 + (a^3 + a^2 - 5*a - 1)*q^30 + (2*a^2 + 5*a - 7)*q^31 + (2*a^3 + 3*a^2 - 5*a - 3)*q^32 + (a^3 + 3*a^2 + 2*a - 2)*q^33 + (5*a^3 + 5*a^2 - 14*a - 2)*q^34 + (a^3 + 2*a^2 - 2*a - 5)*q^35 + (2*a^3 - 7*a + 4)*q^36 + (-2*a^2 - a + 1)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^5 + 4*a^3 - 1/2*a^2 - 11/2*a - 1/2)*q^3 + (a^2 - 2)*q^4 - q^5 + (-1/2*a^6 + 4*a^4 - 1/2*a^3 - 11/2*a^2 - 1/2*a)*q^6 + (a^4 - 7*a^2 + 2*a + 8)*q^7 + (a^3 - 4*a)*q^8 + (-a^3 - a^2 + 5*a + 4)*q^9 - a*q^10 + (1/2*a^6 - 5*a^4 + 1/2*a^3 + 25/2*a^2 - 3/2*a - 6)*q^11 + (a^6 - 1/2*a^5 - 10*a^4 + 4*a^3 + 49/2*a^2 - 3/2*a - 25/2)*q^12 + (-a^2 + 5)*q^13 + (a^5 - 7*a^3 + 2*a^2 + 8*a)*q^14 + (1/2*a^5 - 4*a^3 + 1/2*a^2 + 11/2*a + 1/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + a^3 - 6*a^2 - 3*a + 3)*q^17 + (-a^4 - a^3 + 5*a^2 + 4*a)*q^18 + (-a^4 - a^3 + 5*a^2 + 3*a + 2)*q^19 + (-a^2 + 2)*q^20 + (-a^5 + 9*a^3 - 18*a - 4)*q^21 + (-a^6 + 1/2*a^5 + 10*a^4 - 5*a^3 - 51/2*a^2 + 13/2*a + 27/2)*q^22 + (-a^6 + 10*a^4 - a^3 - 26*a^2 + a + 15)*q^23 + (-3/2*a^6 + a^5 + 15*a^4 - 19/2*a^3 - 77/2*a^2 + 27/2*a + 27)*q^24 + q^25 + (-a^3 + 5*a)*q^26 + (-a^4 + a^3 + 9*a^2 - 7*a - 14)*q^27 + (a^6 - 9*a^4 + 2*a^3 + 22*a^2 - 4*a - 16)*q^28 + (a^6 - 11*a^4 + a^3 + 33*a^2 - 3*a - 21)*q^29 + (1/2*a^6 - 4*a^4 + 1/2*a^3 + 11/2*a^2 + 1/2*a)*q^30 + (1/2*a^6 + a^5 - 5*a^4 - 15/2*a^3 + 29/2*a^2 + 19/2*a - 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - 6*a^2 + 3)*q^33 + (a^5 + a^4 - 6*a^3 - 3*a^2 + 3*a)*q^34 + (-a^4 + 7*a^2 - 2*a - 8)*q^35 + (-a^5 - a^4 + 7*a^3 + 6*a^2 - 10*a - 8)*q^36 + (-a^5 - a^4 + 7*a^3 + 6*a^2 - 8*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-1/2*a^6 + a^5 + 4*a^4 - 15/2*a^3 - 15/2*a^2 + 27/2*a)*q^3 + (a^2 - 2)*q^4 + q^5 + (-1/2*a^5 + a^4 + 2*a^3 - 9/2*a^2 + 5/2*a + 1/2)*q^6 + (a^4 - 2*a^3 - 5*a^2 + 8*a + 2)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + 2*a^5 + 8*a^4 - 14*a^3 - 16*a^2 + 22*a + 2)*q^9 + a*q^10 + (a^6 - 3/2*a^5 - 10*a^4 + 13*a^3 + 49/2*a^2 - 55/2*a - 1/2)*q^11 + (1/2*a^6 - a^5 - 6*a^4 + 21/2*a^3 + 35/2*a^2 - 53/2*a)*q^12 + (a^6 - a^5 - 10*a^4 + 9*a^3 + 25*a^2 - 22*a - 2)*q^13 + (a^5 - 2*a^4 - 5*a^3 + 8*a^2 + 2*a)*q^14 + (-1/2*a^6 + a^5 + 4*a^4 - 15/2*a^3 - 15/2*a^2 + 27/2*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^5 + a^4 + 7*a^3 - 5*a^2 - 10*a + 4)*q^17 + (-a^5 + 3*a^4 + 3*a^3 - 14*a^2 + 7*a + 1)*q^18 + (a^4 - a^3 - 5*a^2 + 3*a + 2)*q^19 + (a^2 - 2)*q^20 + (-a^6 + 2*a^5 + 10*a^4 - 18*a^3 - 26*a^2 + 40*a + 3)*q^21 + (1/2*a^6 - a^5 - 4*a^4 + 11/2*a^3 + 17/2*a^2 - 11/2*a - 1)*q^22 + (-a^5 + 10*a^3 - 23*a + 4)*q^23 + (-1/2*a^5 + 4*a^3 + 1/2*a^2 - 15/2*a - 3/2)*q^24 + q^25 + (a^6 - a^5 - 8*a^4 + 6*a^3 + 14*a^2 - 7*a - 1)*q^26 + (-a^6 + 2*a^5 + 9*a^4 - 14*a^3 - 22*a^2 + 20*a + 8)*q^27 + (a^6 - 2*a^5 - 7*a^4 + 12*a^3 + 12*a^2 - 16*a - 4)*q^28 + (-a^5 + 3*a^4 + 2*a^3 - 13*a^2 + 11*a - 2)*q^29 + (-1/2*a^5 + a^4 + 2*a^3 - 9/2*a^2 + 5/2*a + 1/2)*q^30 + (-a^6 + 3/2*a^5 + 8*a^4 - 9*a^3 - 31/2*a^2 + 23/2*a + 7/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^6 - 3*a^5 - 19*a^4 + 24*a^3 + 47*a^2 - 47*a - 10)*q^33 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 10*a^2 + 4*a)*q^34 + (a^4 - 2*a^3 - 5*a^2 + 8*a + 2)*q^35 + (a^6 - a^5 - 13*a^4 + 14*a^3 + 39*a^2 - 43*a - 4)*q^36 + (-a^4 + a^3 + 5*a^2 - 5*a)*q^37 + O(q^38)
*]> ;  // time = 42.32 seconds




J[307] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 307, 307, 307, 307, 307, 307, 307 ], new_dimensions := [ 1, 1, 1, 1, 2, 9, 10 ], dimensions := [ 1, 1, 1, 1, 2, 9, 10 ], intersection_graph := [ 0, 1, 1, 1, 1, 13, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 11, 1, 1, 1, 1, 0, 3, 5, 1, 1, 1, 1, 3, 0, 107, 1, 13, 5, 11, 5, 107, 0, 1, 1, 1, 1, 1, 1, 1, 0 ], ap_traces := [
[ 0, 0, 4, 0, 3, 6, -1, -1, -2, 0, 4, 3 ],
[ 1, 2, 0, 3, 5, 0, -5, -1, 6, -6, -4, -9 ],
[ 2, 0, 2, 3, -4, 0, 3, 1, 2, 6, -4, -6 ],
[ 2, 2, 0, -3, 1, 6, 2, -4, -6, 0, 2, 3 ],
[ -1, -3, 6, 5, 7, -4, 11, 1, 0, -3, -5, 8 ],
[ 3, 1, 5, -5, 0, -3, 3, -1, 16, 21, -4, 23 ],
[ -7, -4, -15, -3, -10, -11, -17, 1, -20, -22, 1, -28 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + x - 3,
x^9 - 3*x^8 - 11*x^7 + 30*x^6 + 46*x^5 - 87*x^4 - 91*x^3 + 50*x^2 + 62*x + 13,
x^10 + 7*x^9 + 10*x^8 - 28*x^7 - 73*x^6 + 16*x^5 + 128*x^4 + 26*x^3 - 69*x^2 - 18*x - 1
], atkin_lehners := [
[ -1 ],
[ -1 ],
[ -1 ],
[ -1 ],
[ -1 ],
[ -1 ],
[ 1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 3 ],
[ 17 ],
[ 1 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 1 ],
[ 3 ],
[ 17 ],
[ 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 3, 17, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 3, 17, 1 ], l_ratios := [ 1, 1, 1, 1, 1/3, 1/17, 0 ], analytic_sha_upper_bounds := [ 1, 1, 1, 1, 1, 1, 0 ], analytic_sha_lower_bounds := [ 1, 1, 1, 1, 1, 1, 0 ], eigenvalues := [*
[ 0, 0, 4, 0, 3, 6, -1, -1, -2, 0, 4, 3 ],
[ 1, 2, 0, 3, 5, 0, -5, -1, 6, -6, -4, -9 ],
[ 2, 0, 2, 3, -4, 0, 3, 1, 2, 6, -4, -6 ],
[ 2, 2, 0, -3, 1, 6, 2, -4, -6, 0, 2, 3 ],
[
a,
-a - 2,
3,
-a + 2,
-a + 3,
2*a - 1,
a + 6,
3*a + 2,
0,
-3*a - 3,
-3*a - 4,
2*a + 5
],
[
a,
-a^8 + 2*a^7 + 11*a^6 - 18*a^5 - 38*a^4 + 44*a^3 + 39*a^2 - 24*a - 13,
a^7 - a^6 - 11*a^5 + 5*a^4 + 36*a^3 + 3*a^2 - 24*a - 9,
a^7 - a^6 - 12*a^5 + 5*a^4 + 44*a^3 + 5*a^2 - 36*a - 13,
a^8 - 2*a^7 - 10*a^6 + 15*a^5 + 31*a^4 - 26*a^3 - 23*a^2 + 6*a + 3,
a^8 - a^7 - 12*a^6 + 6*a^5 + 45*a^4 - 2*a^3 - 45*a^2 - 8*a + 6,
-a^8 + 3*a^7 + 9*a^6 - 27*a^5 - 26*a^4 + 71*a^3 + 27*a^2 - 47*a - 14,
-a^8 + 13*a^6 + 6*a^5 - 52*a^4 - 39*a^3 + 51*a^2 + 32*a - 1,
-a^8 - 2*a^7 + 15*a^6 + 29*a^5 - 61*a^4 - 120*a^3 + 38*a^2 + 94*a + 24,
-a^6 + 2*a^5 + 8*a^4 - 12*a^3 - 19*a^2 + 13*a + 13,
-2*a^8 + 2*a^7 + 23*a^6 - 10*a^5 - 80*a^4 - 9*a^3 + 59*a^2 + 29*a + 4,
-a^7 + 2*a^6 + 9*a^5 - 13*a^4 - 26*a^3 + 17*a^2 + 20*a + 3
],
[
a,
a^9 + 6*a^8 + 5*a^7 - 29*a^6 - 48*a^5 + 37*a^4 + 91*a^3 - 7*a^2 - 52*a - 6,
-a^9 - 6*a^8 - 4*a^7 + 34*a^6 + 50*a^5 - 57*a^4 - 111*a^3 + 22*a^2 + 69*a + 7,
-a^9 - 8*a^8 - 16*a^7 + 22*a^6 + 95*a^5 + 21*a^4 - 143*a^3 - 56*a^2 + 71*a + 9,
2*a^8 + 10*a^7 + 3*a^6 - 46*a^5 - 42*a^4 + 58*a^3 + 50*a^2 - 23*a - 6,
a^9 + 7*a^8 + 8*a^7 - 35*a^6 - 67*a^5 + 49*a^4 + 129*a^3 - 12*a^2 - 75*a - 12,
-a^9 - 7*a^8 - 10*a^7 + 24*a^6 + 58*a^5 - 10*a^4 - 68*a^3 - 6*a^2 + 20*a - 2,
2*a^8 + 12*a^7 + 10*a^6 - 51*a^5 - 71*a^4 + 57*a^3 + 76*a^2 - 23*a - 6,
2*a^9 + 12*a^8 + 10*a^7 - 56*a^6 - 88*a^5 + 72*a^4 + 150*a^3 - 25*a^2 - 75*a - 7,
3*a^9 + 19*a^8 + 23*a^7 - 67*a^6 - 146*a^5 + 25*a^4 + 173*a^3 + 35*a^2 - 41*a - 8,
-2*a^9 - 11*a^8 - 6*a^7 + 50*a^6 + 55*a^5 - 63*a^4 - 61*a^3 + 28*a^2 + 2*a + 1,
-2*a^9 - 14*a^8 - 21*a^7 + 48*a^6 + 131*a^5 - 11*a^4 - 180*a^3 - 35*a^2 + 70*a + 3
]
*], q_expansions := [*
q - 2*q^4 + 4*q^5 - 3*q^9 + 3*q^11 + 6*q^13 + 4*q^16 - q^17 - q^19 - 8*q^20 - 2*q^23 + 11*q^25 + 4*q^31 + 6*q^36 + 3*q^37 + O(q^38),
q + q^2 + 2*q^3 - q^4 + 2*q^6 + 3*q^7 - 3*q^8 + q^9 + 5*q^11 - 2*q^12 + 3*q^14 - q^16 - 5*q^17 + q^18 - q^19 + 6*q^21 + 5*q^22 + 6*q^23 - 6*q^24 - 5*q^25 - 4*q^27 - 3*q^28 - 6*q^29 - 4*q^31 + 5*q^32 + 10*q^33 - 5*q^34 - q^36 - 9*q^37 + O(q^38),
q + 2*q^2 + 2*q^4 + 2*q^5 + 3*q^7 - 3*q^9 + 4*q^10 - 4*q^11 + 6*q^14 - 4*q^16 + 3*q^17 - 6*q^18 + q^19 + 4*q^20 - 8*q^22 + 2*q^23 - q^25 + 6*q^28 + 6*q^29 - 4*q^31 - 8*q^32 + 6*q^34 + 6*q^35 - 6*q^36 - 6*q^37 + O(q^38),
q + 2*q^2 + 2*q^3 + 2*q^4 + 4*q^6 - 3*q^7 + q^9 + q^11 + 4*q^12 + 6*q^13 - 6*q^14 - 4*q^16 + 2*q^17 + 2*q^18 - 4*q^19 - 6*q^21 + 2*q^22 - 6*q^23 - 5*q^25 + 12*q^26 - 4*q^27 - 6*q^28 + 2*q^31 - 8*q^32 + 2*q^33 + 4*q^34 + 2*q^36 + 3*q^37 + O(q^38),
q + a*q^2 + (-a - 2)*q^3 + (-a + 1)*q^4 + 3*q^5 + (-a - 3)*q^6 + (-a + 2)*q^7 - 3*q^8 + (3*a + 4)*q^9 + 3*a*q^10 + (-a + 3)*q^11 + q^12 + (2*a - 1)*q^13 + (3*a - 3)*q^14 + (-3*a - 6)*q^15 + (-a - 2)*q^16 + (a + 6)*q^17 + (a + 9)*q^18 + (3*a + 2)*q^19 + (-3*a + 3)*q^20 + (-a - 1)*q^21 + (4*a - 3)*q^22 + (3*a + 6)*q^24 + 4*q^25 + (-3*a + 6)*q^26 + (-4*a - 11)*q^27 + (-4*a + 5)*q^28 + (-3*a - 3)*q^29 + (-3*a - 9)*q^30 + (-3*a - 4)*q^31 + (-a + 3)*q^32 + (-2*a - 3)*q^33 + (5*a + 3)*q^34 + (-3*a + 6)*q^35 + (2*a - 5)*q^36 + (2*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^8 + 2*a^7 + 11*a^6 - 18*a^5 - 38*a^4 + 44*a^3 + 39*a^2 - 24*a - 13)*q^3 + (a^2 - 2)*q^4 + (a^7 - a^6 - 11*a^5 + 5*a^4 + 36*a^3 + 3*a^2 - 24*a - 9)*q^5 + (-a^8 + 12*a^6 + 8*a^5 - 43*a^4 - 52*a^3 + 26*a^2 + 49*a + 13)*q^6 + (a^7 - a^6 - 12*a^5 + 5*a^4 + 44*a^3 + 5*a^2 - 36*a - 13)*q^7 + (a^3 - 4*a)*q^8 + (a^7 - a^6 - 12*a^5 + 7*a^4 + 41*a^3 - 6*a^2 - 26*a - 3)*q^9 + (a^8 - a^7 - 11*a^6 + 5*a^5 + 36*a^4 + 3*a^3 - 24*a^2 - 9*a)*q^10 + (a^8 - 2*a^7 - 10*a^6 + 15*a^5 + 31*a^4 - 26*a^3 - 23*a^2 + 6*a + 3)*q^11 + (-a^8 - 3*a^7 + 16*a^6 + 39*a^5 - 63*a^4 - 153*a^3 + 21*a^2 + 123*a + 39)*q^12 + (a^8 - a^7 - 12*a^6 + 6*a^5 + 45*a^4 - 2*a^3 - 45*a^2 - 8*a + 6)*q^13 + (a^8 - a^7 - 12*a^6 + 5*a^5 + 44*a^4 + 5*a^3 - 36*a^2 - 13*a)*q^14 + (a^8 - 2*a^7 - 10*a^6 + 15*a^5 + 32*a^4 - 29*a^3 - 29*a^2 + 19*a + 13)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^8 + 3*a^7 + 9*a^6 - 27*a^5 - 26*a^4 + 71*a^3 + 27*a^2 - 47*a - 14)*q^17 + (a^8 - a^7 - 12*a^6 + 7*a^5 + 41*a^4 - 6*a^3 - 26*a^2 - 3*a)*q^18 + (-a^8 + 13*a^6 + 6*a^5 - 52*a^4 - 39*a^3 + 51*a^2 + 32*a - 1)*q^19 + (2*a^8 - 2*a^7 - 23*a^6 + 12*a^5 + 80*a^4 - 5*a^3 - 65*a^2 - 14*a + 5)*q^20 + (-a^8 + 2*a^7 + 10*a^6 - 15*a^5 - 30*a^4 + 27*a^3 + 16*a^2 - 13*a)*q^21 + (a^8 + a^7 - 15*a^6 - 15*a^5 + 61*a^4 + 68*a^3 - 44*a^2 - 59*a - 13)*q^22 + (-a^8 - 2*a^7 + 15*a^6 + 29*a^5 - 61*a^4 - 120*a^3 + 38*a^2 + 94*a + 24)*q^23 + (-4*a^8 + 5*a^7 + 45*a^6 - 33*a^5 - 154*a^4 + 34*a^3 + 121*a^2 + 3*a - 13)*q^24 + (-a^7 + a^6 + 13*a^5 - 7*a^4 - 50*a^3 + 4*a^2 + 44*a + 11)*q^25 + (2*a^8 - a^7 - 24*a^6 - a^5 + 85*a^4 + 46*a^3 - 58*a^2 - 56*a - 13)*q^26 + (a^8 - 12*a^6 - 7*a^5 + 41*a^4 + 46*a^3 - 17*a^2 - 43*a - 13)*q^27 + (2*a^8 - 3*a^7 - 23*a^6 + 22*a^5 + 82*a^4 - 33*a^3 - 73*a^2 + 10*a + 13)*q^28 + (-a^6 + 2*a^5 + 8*a^4 - 12*a^3 - 19*a^2 + 13*a + 13)*q^29 + (a^8 + a^7 - 15*a^6 - 14*a^5 + 58*a^4 + 62*a^3 - 31*a^2 - 49*a - 13)*q^30 + (-2*a^8 + 2*a^7 + 23*a^6 - 10*a^5 - 80*a^4 - 9*a^3 + 59*a^2 + 29*a + 4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^8 + 12*a^6 + 8*a^5 - 41*a^4 - 53*a^3 + 16*a^2 + 46*a + 13)*q^33 + (-2*a^7 + 3*a^6 + 20*a^5 - 16*a^4 - 64*a^3 + 3*a^2 + 48*a + 13)*q^34 + (-a^8 + 12*a^6 + 6*a^5 - 40*a^4 - 40*a^3 + 14*a^2 + 36*a + 13)*q^35 + (2*a^8 - 3*a^7 - 21*a^6 + 19*a^5 + 67*a^4 - 17*a^3 - 41*a^2 - 10*a - 7)*q^36 + (-a^7 + 2*a^6 + 9*a^5 - 13*a^4 - 26*a^3 + 17*a^2 + 20*a + 3)*q^37 + O(q^38),
q + a*q^2 + (a^9 + 6*a^8 + 5*a^7 - 29*a^6 - 48*a^5 + 37*a^4 + 91*a^3 - 7*a^2 - 52*a - 6)*q^3 + (a^2 - 2)*q^4 + (-a^9 - 6*a^8 - 4*a^7 + 34*a^6 + 50*a^5 - 57*a^4 - 111*a^3 + 22*a^2 + 69*a + 7)*q^5 + (-a^9 - 5*a^8 - a^7 + 25*a^6 + 21*a^5 - 37*a^4 - 33*a^3 + 17*a^2 + 12*a + 1)*q^6 + (-a^9 - 8*a^8 - 16*a^7 + 22*a^6 + 95*a^5 + 21*a^4 - 143*a^3 - 56*a^2 + 71*a + 9)*q^7 + (a^3 - 4*a)*q^8 + (a^8 + 5*a^7 - 27*a^5 - 14*a^4 + 47*a^3 + 17*a^2 - 29*a - 2)*q^9 + (a^9 + 6*a^8 + 6*a^7 - 23*a^6 - 41*a^5 + 17*a^4 + 48*a^3 - 11*a - 1)*q^10 + (2*a^8 + 10*a^7 + 3*a^6 - 46*a^5 - 42*a^4 + 58*a^3 + 50*a^2 - 23*a - 6)*q^11 + (-3*a^8 - 13*a^7 + 6*a^6 + 75*a^5 + 21*a^4 - 139*a^3 - 43*a^2 + 87*a + 11)*q^12 + (a^9 + 7*a^8 + 8*a^7 - 35*a^6 - 67*a^5 + 49*a^4 + 129*a^3 - 12*a^2 - 75*a - 12)*q^13 + (-a^9 - 6*a^8 - 6*a^7 + 22*a^6 + 37*a^5 - 15*a^4 - 30*a^3 + 2*a^2 - 9*a - 1)*q^14 + (-2*a^9 - 12*a^8 - 10*a^7 + 57*a^6 + 92*a^5 - 73*a^4 - 165*a^3 + 22*a^2 + 88*a + 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^9 - 7*a^8 - 10*a^7 + 24*a^6 + 58*a^5 - 10*a^4 - 68*a^3 - 6*a^2 + 20*a - 2)*q^17 + (a^9 + 5*a^8 - 27*a^6 - 14*a^5 + 47*a^4 + 17*a^3 - 29*a^2 - 2*a)*q^18 + (2*a^8 + 12*a^7 + 10*a^6 - 51*a^5 - 71*a^4 + 57*a^3 + 76*a^2 - 23*a - 6)*q^19 + (a^9 + 8*a^8 + 13*a^7 - 36*a^6 - 99*a^5 + 34*a^4 + 196*a^3 + 14*a^2 - 121*a - 13)*q^20 + (-a^8 - 4*a^7 + 6*a^6 + 33*a^5 - 8*a^4 - 85*a^3 - 2*a^2 + 67*a)*q^21 + (2*a^9 + 10*a^8 + 3*a^7 - 46*a^6 - 42*a^5 + 58*a^4 + 50*a^3 - 23*a^2 - 6*a)*q^22 + (2*a^9 + 12*a^8 + 10*a^7 - 56*a^6 - 88*a^5 + 72*a^4 + 150*a^3 - 25*a^2 - 75*a - 7)*q^23 + (-a^9 - 3*a^8 + 8*a^7 + 25*a^6 - 21*a^5 - 65*a^4 + 23*a^3 + 53*a^2 - 13*a - 2)*q^24 + (2*a^9 + 11*a^8 + a^7 - 80*a^6 - 84*a^5 + 174*a^4 + 246*a^3 - 95*a^2 - 175*a - 16)*q^25 + (-2*a^8 - 7*a^7 + 6*a^6 + 33*a^5 + a^4 - 38*a^3 - 6*a^2 + 6*a + 1)*q^26 + (3*a^6 + 10*a^5 - 8*a^4 - 42*a^3 - 4*a^2 + 40*a + 8)*q^27 + (3*a^9 + 20*a^8 + 26*a^7 - 80*a^6 - 189*a^5 + 56*a^4 + 314*a^3 + 34*a^2 - 161*a - 19)*q^28 + (3*a^9 + 19*a^8 + 23*a^7 - 67*a^6 - 146*a^5 + 25*a^4 + 173*a^3 + 35*a^2 - 41*a - 8)*q^29 + (2*a^9 + 10*a^8 + a^7 - 54*a^6 - 41*a^5 + 91*a^4 + 74*a^3 - 50*a^2 - 32*a - 2)*q^30 + (-2*a^9 - 11*a^8 - 6*a^7 + 50*a^6 + 55*a^5 - 63*a^4 - 61*a^3 + 28*a^2 + 2*a + 1)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-2*a^9 - 13*a^8 - 16*a^7 + 52*a^6 + 118*a^5 - 35*a^4 - 193*a^3 - 26*a^2 + 96*a + 15)*q^33 + (-4*a^7 - 15*a^6 + 6*a^5 + 60*a^4 + 20*a^3 - 49*a^2 - 20*a - 1)*q^34 + (2*a^9 + 15*a^8 + 26*a^7 - 50*a^6 - 166*a^5 + 2*a^4 + 266*a^3 + 54*a^2 - 140*a - 7)*q^35 + (-2*a^9 - 12*a^8 - 9*a^7 + 59*a^6 + 85*a^5 - 83*a^4 - 149*a^3 + 33*a^2 + 76*a + 5)*q^36 + (-2*a^9 - 14*a^8 - 21*a^7 + 48*a^6 + 131*a^5 - 11*a^4 - 180*a^3 - 35*a^2 + 70*a + 3)*q^37 + O(q^38)
*]> ;  // time = 6.809 seconds




J[309] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 309, 309, 309, 309, 103, 103 ], new_dimensions := [ 1, 3, 5, 8, 2, 6 ], dimensions := [ 1, 3, 5, 8, 4, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 5, 1, 0, 1, 1, 1, 89, 1, 1, 0, 1, 9, 1, 1, 1, 1, 0, 25, 1, 1, 1, 9, 25, 0, 1, 5, 89, 1, 1, 1, 0 ], ap_traces := [
[ -1, 1, -1, -2, -2, -5, 0, -8, 1, -2, 5, 2 ],
[ 1, -3, 1, -2, 8, -3, 4, 12, 7, 0, 7, -6 ],
[ -2, -5, -5, -2, -12, 1, -10, -16, -5, -16, -13, 4 ],
[ -1, 8, -1, 6, 6, 9, -4, 16, -11, 0, 17, -6 ]
], hecke_fields := [
x - 1,
x^3 - x^2 - 3*x + 1,
x^5 + 2*x^4 - 4*x^3 - 6*x^2 + 4*x + 1,
x^8 + x^7 - 13*x^6 - 11*x^5 + 52*x^4 + 35*x^3 - 59*x^2 - 27*x + 1
], atkin_lehners := [
[ -1, -1 ],
[ 1, -1 ],
[ 1, 1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 89, 1 ],
[ 9, 1 ],
[ 325, 1 ]
], tamagawa_numbers := [
[ 5, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 325, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 13 ], torsion_lower_bounds := [ 1, 1, 1, 13 ], l_ratios := [ 0, 1, 0, 25/13 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1 ], eigenvalues := [*
[ -1, 1, -1, -2, -2, -5, 0, -8, 1, -2, 5, 2 ],
[
a,
-1,
a,
-a^2 + 2*a + 1,
-a^2 + 5,
-2*a^2 + 2*a + 3,
-2*a + 2,
2*a^2 - 2*a,
a + 2,
-a^2 - 2*a + 3,
-2*a + 3,
a^2 - 4*a - 3
],
[
a,
-1,
a^4 + a^3 - 5*a^2 - 3*a + 3,
-2*a^4 - 3*a^3 + 7*a^2 + 6*a - 4,
2*a^3 + 2*a^2 - 6*a - 4,
2*a^4 + 3*a^3 - 5*a^2 - 6*a - 1,
-3*a^3 - a^2 + 10*a - 4,
-a^4 - 2*a^3 + 4*a^2 + 7*a - 6,
3*a^3 + a^2 - 10*a + 1,
-2*a^4 - 3*a^3 + 7*a^2 + 8*a - 6,
-a^4 - 3*a^3 + 3*a^2 + 9*a - 5,
-2*a^3 - 2*a^2 + 10*a + 4
],
[
a,
1,
-1/2*a^7 + 11/2*a^5 - 18*a^3 - 3/2*a^2 + 17*a + 7/2,
a^6 - 8*a^4 + a^3 + 13*a^2 - 3*a,
-a^6 - a^5 + 8*a^4 + 6*a^3 - 14*a^2 - 5*a + 3,
1/2*a^7 - 11/2*a^5 - a^4 + 18*a^3 + 15/2*a^2 - 18*a - 11/2,
-a^5 + 7*a^3 - a^2 - 8*a + 1,
a^5 + a^4 - 6*a^3 - 6*a^2 + 3*a + 7,
1/2*a^7 - 9/2*a^5 - a^4 + 10*a^3 + 15/2*a^2 - 6*a - 13/2,
a^6 + 2*a^5 - 6*a^4 - 13*a^3 + 3*a^2 + 13*a + 2,
-1/2*a^7 + 13/2*a^5 - 26*a^3 + 1/2*a^2 + 29*a + 1/2,
a^6 - 3*a^5 - 10*a^4 + 24*a^3 + 24*a^2 - 37*a - 9
]
*], q_expansions := [*
q - q^2 + q^3 - q^4 - q^5 - q^6 - 2*q^7 + 3*q^8 + q^9 + q^10 - 2*q^11 - q^12 - 5*q^13 + 2*q^14 - q^15 - q^16 - q^18 - 8*q^19 + q^20 - 2*q^21 + 2*q^22 + q^23 + 3*q^24 - 4*q^25 + 5*q^26 + q^27 + 2*q^28 - 2*q^29 + q^30 + 5*q^31 - 5*q^32 - 2*q^33 + 2*q^35 - q^36 + 2*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + a*q^5 - a*q^6 + (-a^2 + 2*a + 1)*q^7 + (a^2 - a - 1)*q^8 + q^9 + a^2*q^10 + (-a^2 + 5)*q^11 + (-a^2 + 2)*q^12 + (-2*a^2 + 2*a + 3)*q^13 + (a^2 - 2*a + 1)*q^14 - a*q^15 + (-2*a^2 + 2*a + 3)*q^16 + (-2*a + 2)*q^17 + a*q^18 + (2*a^2 - 2*a)*q^19 + (a^2 + a - 1)*q^20 + (a^2 - 2*a - 1)*q^21 + (-a^2 + 2*a + 1)*q^22 + (a + 2)*q^23 + (-a^2 + a + 1)*q^24 + (a^2 - 5)*q^25 + (-3*a + 2)*q^26 - q^27 + (a^2 - 3)*q^28 + (-a^2 - 2*a + 3)*q^29 - a^2*q^30 + (-2*a + 3)*q^31 + (-2*a^2 - a + 4)*q^32 + (a^2 - 5)*q^33 + (-2*a^2 + 2*a)*q^34 + (a^2 - 2*a + 1)*q^35 + (a^2 - 2)*q^36 + (a^2 - 4*a - 3)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^4 + a^3 - 5*a^2 - 3*a + 3)*q^5 - a*q^6 + (-2*a^4 - 3*a^3 + 7*a^2 + 6*a - 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 - a^3 + 3*a^2 - a - 1)*q^10 + (2*a^3 + 2*a^2 - 6*a - 4)*q^11 + (-a^2 + 2)*q^12 + (2*a^4 + 3*a^3 - 5*a^2 - 6*a - 1)*q^13 + (a^4 - a^3 - 6*a^2 + 4*a + 2)*q^14 + (-a^4 - a^3 + 5*a^2 + 3*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^3 - a^2 + 10*a - 4)*q^17 + a*q^18 + (-a^4 - 2*a^3 + 4*a^2 + 7*a - 6)*q^19 + (-a^4 - 3*a^3 + 3*a^2 + 9*a - 5)*q^20 + (2*a^4 + 3*a^3 - 7*a^2 - 6*a + 4)*q^21 + (2*a^4 + 2*a^3 - 6*a^2 - 4*a)*q^22 + (3*a^3 + a^2 - 10*a + 1)*q^23 + (-a^3 + 4*a)*q^24 + (a^4 + 5*a^3 - a^2 - 13*a + 4)*q^25 + (-a^4 + 3*a^3 + 6*a^2 - 9*a - 2)*q^26 - q^27 + (a^4 + 4*a^3 - 4*a^2 - 14*a + 7)*q^28 + (-2*a^4 - 3*a^3 + 7*a^2 + 8*a - 6)*q^29 + (a^4 + a^3 - 3*a^2 + a + 1)*q^30 + (-a^4 - 3*a^3 + 3*a^2 + 9*a - 5)*q^31 + (-2*a^4 - 4*a^3 + 6*a^2 + 8*a - 1)*q^32 + (-2*a^3 - 2*a^2 + 6*a + 4)*q^33 + (-3*a^4 - a^3 + 10*a^2 - 4*a)*q^34 + (-2*a^3 + 4*a^2 + 14*a - 14)*q^35 + (a^2 - 2)*q^36 + (-2*a^3 - 2*a^2 + 10*a + 4)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-1/2*a^7 + 11/2*a^5 - 18*a^3 - 3/2*a^2 + 17*a + 7/2)*q^5 + a*q^6 + (a^6 - 8*a^4 + a^3 + 13*a^2 - 3*a)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (1/2*a^7 - a^6 - 11/2*a^5 + 8*a^4 + 16*a^3 - 25/2*a^2 - 10*a + 1/2)*q^10 + (-a^6 - a^5 + 8*a^4 + 6*a^3 - 14*a^2 - 5*a + 3)*q^11 + (a^2 - 2)*q^12 + (1/2*a^7 - 11/2*a^5 - a^4 + 18*a^3 + 15/2*a^2 - 18*a - 11/2)*q^13 + (a^7 - 8*a^5 + a^4 + 13*a^3 - 3*a^2)*q^14 + (-1/2*a^7 + 11/2*a^5 - 18*a^3 - 3/2*a^2 + 17*a + 7/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^5 + 7*a^3 - a^2 - 8*a + 1)*q^17 + a*q^18 + (a^5 + a^4 - 6*a^3 - 6*a^2 + 3*a + 7)*q^19 + (-1/2*a^7 + a^6 + 5/2*a^5 - 10*a^4 + 6*a^3 + 45/2*a^2 - 20*a - 15/2)*q^20 + (a^6 - 8*a^4 + a^3 + 13*a^2 - 3*a)*q^21 + (-a^7 - a^6 + 8*a^5 + 6*a^4 - 14*a^3 - 5*a^2 + 3*a)*q^22 + (1/2*a^7 - 9/2*a^5 - a^4 + 10*a^3 + 15/2*a^2 - 6*a - 13/2)*q^23 + (a^3 - 4*a)*q^24 + (1/2*a^7 - a^6 - 7/2*a^5 + 10*a^4 + 2*a^3 - 49/2*a^2 + 6*a + 23/2)*q^25 + (-1/2*a^7 + a^6 + 9/2*a^5 - 8*a^4 - 10*a^3 + 23/2*a^2 + 8*a - 1/2)*q^26 + q^27 + (-a^7 + 3*a^6 + 12*a^5 - 23*a^4 - 40*a^3 + 33*a^2 + 33*a - 1)*q^28 + (a^6 + 2*a^5 - 6*a^4 - 13*a^3 + 3*a^2 + 13*a + 2)*q^29 + (1/2*a^7 - a^6 - 11/2*a^5 + 8*a^4 + 16*a^3 - 25/2*a^2 - 10*a + 1/2)*q^30 + (-1/2*a^7 + 13/2*a^5 - 26*a^3 + 1/2*a^2 + 29*a + 1/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 - a^5 + 8*a^4 + 6*a^3 - 14*a^2 - 5*a + 3)*q^33 + (-a^6 + 7*a^4 - a^3 - 8*a^2 + a)*q^34 + (-a^6 + a^5 + 8*a^4 - 10*a^3 - 12*a^2 + 19*a - 1)*q^35 + (a^2 - 2)*q^36 + (a^6 - 3*a^5 - 10*a^4 + 24*a^3 + 24*a^2 - 37*a - 9)*q^37 + O(q^38)
*]> ;  // time = 45.05 seconds




J[310] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 310, 310, 310, 310, 310, 155, 155, 155, 155, 155, 62, 62, 31 ], new_dimensions := [ 1, 1, 2, 2, 3, 1, 1, 1, 4, 4, 1, 2, 2 ], dimensions := [ 1, 1, 2, 2, 3, 2, 2, 2, 8, 8, 2, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 1, 5, 3, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 25, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 2401, 1, 1, 1, 23, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0, 121, 1, 1, 1, 1, 5, 1, 1, 25, 2401, 1, 1, 121, 0 ], ap_traces := [
[ 1, 2, -1, 0, 2, 0, 2, -4, -4, -4, -1, -8 ],
[ 1, -2, -1, -4, 0, -4, 0, -4, -6, 6, 1, 8 ],
[ -2, -2, -2, 0, -2, -6, -8, 4, -8, -2, -2, -10 ],
[ -2, 0, 2, -4, 4, 4, 0, 0, 4, 16, -2, 4 ],
[ 3, 2, 3, 0, 0, -8, 0, 8, -2, -2, 3, -8 ]
], hecke_fields := [
x - 1,
x - 1,
x^2 + 2*x - 2,
x^2 - 6,
x^3 - 2*x^2 - 4*x + 4
], atkin_lehners := [
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, 1, 1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 3, 1, 1 ],
[ 3, 1, 1 ],
[ 3, 1, 1 ],
[ 23, 1, 1 ],
[ 25, 5, 1 ]
], tamagawa_numbers := [
[ 3, 1, 1 ],
[ 3, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 25, 5, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 5 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 3, 0, 0, 1, 5 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1/25 ], eigenvalues := [*
[ 1, 2, -1, 0, 2, 0, 2, -4, -4, -4, -1, -8 ],
[ 1, -2, -1, -4, 0, -4, 0, -4, -6, 6, 1, 8 ],
[
-1,
a,
-1,
-2*a - 2,
-a - 2,
a - 2,
-4,
2*a + 4,
2*a - 2,
a,
-1,
-a - 6
],
[
-1,
a,
1,
-2,
a + 2,
a + 2,
-2*a,
-2*a,
2,
-a + 8,
-1,
-a + 2
],
[
1,
a,
1,
-a^2 + 4,
a^2 - 3*a - 2,
-a - 2,
-a^2 + 4,
2*a^2 - 2*a - 4,
-a^2 + 2*a + 2,
-3*a^2 + 5*a + 8,
1,
2*a^2 - a - 10
]
*], q_expansions := [*
q + q^2 + 2*q^3 + q^4 - q^5 + 2*q^6 + q^8 + q^9 - q^10 + 2*q^11 + 2*q^12 - 2*q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 - q^20 + 2*q^22 - 4*q^23 + 2*q^24 + q^25 - 4*q^27 - 4*q^29 - 2*q^30 - q^31 + q^32 + 4*q^33 + 2*q^34 + q^36 - 8*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - q^5 - 2*q^6 - 4*q^7 + q^8 + q^9 - q^10 - 2*q^12 - 4*q^13 - 4*q^14 + 2*q^15 + q^16 + q^18 - 4*q^19 - q^20 + 8*q^21 - 6*q^23 - 2*q^24 + q^25 - 4*q^26 + 4*q^27 - 4*q^28 + 6*q^29 + 2*q^30 + q^31 + q^32 + 4*q^35 + q^36 + 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (-2*a - 2)*q^7 - q^8 + (-2*a - 1)*q^9 + q^10 + (-a - 2)*q^11 + a*q^12 + (a - 2)*q^13 + (2*a + 2)*q^14 - a*q^15 + q^16 - 4*q^17 + (2*a + 1)*q^18 + (2*a + 4)*q^19 - q^20 + (2*a - 4)*q^21 + (a + 2)*q^22 + (2*a - 2)*q^23 - a*q^24 + q^25 + (-a + 2)*q^26 - 4*q^27 + (-2*a - 2)*q^28 + a*q^29 + a*q^30 - q^31 - q^32 - 2*q^33 + 4*q^34 + (2*a + 2)*q^35 + (-2*a - 1)*q^36 + (-a - 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + q^5 - a*q^6 - 2*q^7 - q^8 + 3*q^9 - q^10 + (a + 2)*q^11 + a*q^12 + (a + 2)*q^13 + 2*q^14 + a*q^15 + q^16 - 2*a*q^17 - 3*q^18 - 2*a*q^19 + q^20 - 2*a*q^21 + (-a - 2)*q^22 + 2*q^23 - a*q^24 + q^25 + (-a - 2)*q^26 - 2*q^28 + (-a + 8)*q^29 - a*q^30 - q^31 - q^32 + (2*a + 6)*q^33 + 2*a*q^34 - 2*q^35 + 3*q^36 + (-a + 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + q^5 + a*q^6 + (-a^2 + 4)*q^7 + q^8 + (a^2 - 3)*q^9 + q^10 + (a^2 - 3*a - 2)*q^11 + a*q^12 + (-a - 2)*q^13 + (-a^2 + 4)*q^14 + a*q^15 + q^16 + (-a^2 + 4)*q^17 + (a^2 - 3)*q^18 + (2*a^2 - 2*a - 4)*q^19 + q^20 + (-2*a^2 + 4)*q^21 + (a^2 - 3*a - 2)*q^22 + (-a^2 + 2*a + 2)*q^23 + a*q^24 + q^25 + (-a - 2)*q^26 + (2*a^2 - 2*a - 4)*q^27 + (-a^2 + 4)*q^28 + (-3*a^2 + 5*a + 8)*q^29 + a*q^30 + q^31 + q^32 + (-a^2 + 2*a - 4)*q^33 + (-a^2 + 4)*q^34 + (-a^2 + 4)*q^35 + (a^2 - 3)*q^36 + (2*a^2 - a - 10)*q^37 + O(q^38)
*]> ;  // time = 129.66 seconds




J[311] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 311, 311 ], new_dimensions := [ 4, 22 ], dimensions := [ 4, 22 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -1, -2, -1, -4, -4, -6, -7, -6, 2, -6, -6, -11 ],
[ 2, 2, 1, 8, 6, 12, 9, 16, -2, 24, 10, 27 ]
], hecke_fields := [
x^4 + x^3 - 3*x^2 - x + 1,
x^22 - 2*x^21 - 35*x^20 + 70*x^19 + 517*x^18 - 1033*x^17 - 4195*x^16 + 8357*x^15 + 20417*x^14 - 40403*x^13 - 61287*x^12 + 119701*x^11 + 113017*x^10 - 215615*x^9 - 124399*x^8 + 228609*x^7 + 76453*x^6 - 133295*x^5 - 23503*x^4 + 36742*x^3 + 3587*x^2 - 3200*x - 473
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 155 ]
], tamagawa_numbers := [
[ 1 ],
[ 155 ]
], torsion_upper_bounds := [ 1, 155 ], torsion_lower_bounds := [ 1, 155 ], l_ratios := [ 0, 1/155 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-a^3 - a^2 + 2*a,
a^3 + a^2 - 3*a - 1,
a^3 - 3*a,
-1,
a^2 + a - 3,
-3*a^3 - 3*a^2 + 7*a,
-a^3 - a^2 + 2*a - 1,
3*a^2 + 3*a - 4,
-a^3 - 2*a^2 + 3*a + 1,
a^3 + 2*a^2 + a - 3,
-4*a^3 - 8*a^2 + 7*a + 6
],
[
a,
-1333218028123436678/106341562018576649119*a^21 + 1367946423136236257/106341562018576649119*a^20 + 49328489263264063408/106341562018576649119*a^19 - 48698618113739814119/106341562018576649119*a^18 - 780071490285978038489/106341562018576649119*a^17 + 731764058773877640305/106341562018576649119*a^16 + 6883435129930837071209/106341562018576649119*a^15 - 6029718454604453812991/106341562018576649119*a^14 - 37117408682963362048611/106341562018576649119*a^13 + 29643589741202443321628/106341562018576649119*a^12 + 125904278451589035925849/106341562018576649119*a^11 - 88764078616540344648331/106341562018576649119*a^10 - 266400248133720180154691/106341562018576649119*a^9 + 159042733994278329421197/106341562018576649119*a^8 + 336261615438596631255820/106341562018576649119*a^7 - 162008001244132052237259/106341562018576649119*a^6 - 230084343080867524283273/106341562018576649119*a^5 + 85032171085335940948597/106341562018576649119*a^4 + 71086649415902837709445/106341562018576649119*a^3 - 17051195074052769029465/106341562018576649119*a^2 - 6284781941061791629214/106341562018576649119*a - 2035191172956196509/2473059581827363933,
-21242974024529590/106341562018576649119*a^21 - 1434491652110563978/106341562018576649119*a^20 + 3209217338769634321/106341562018576649119*a^19 + 48282217898366329351/106341562018576649119*a^18 - 94578303848943192367/106341562018576649119*a^17 - 676590780104692901915/106341562018576649119*a^16 + 1270815302353166006692/106341562018576649119*a^15 + 5102603103564094427213/106341562018576649119*a^14 - 9439579417621543494677/106341562018576649119*a^13 - 22357866355125222974699/106341562018576649119*a^12 + 41280678241435124160901/106341562018576649119*a^11 + 57441564627509462184517/106341562018576649119*a^10 - 106882614769975285857639/106341562018576649119*a^9 - 83882843771650414225579/106341562018576649119*a^8 + 158593036380613931304765/106341562018576649119*a^7 + 66319079553842412941717/106341562018576649119*a^6 - 126427357236440356717803/106341562018576649119*a^5 - 28369596568106140688094/106341562018576649119*a^4 + 47782658911006380501745/106341562018576649119*a^3 + 8238984211089590694971/106341562018576649119*a^2 - 6439892278957108980653/106341562018576649119*a - 30557112079337671866/2473059581827363933,
504418815307781939/106341562018576649119*a^21 - 1021065885099576655/106341562018576649119*a^20 - 16604493185137817773/106341562018576649119*a^19 + 33056103831567470983/106341562018576649119*a^18 + 226015020692329680027/106341562018576649119*a^17 - 435479859114799908685/106341562018576649119*a^16 - 1641199345467818455453/106341562018576649119*a^15 + 2956466065705411278227/106341562018576649119*a^14 + 6861291586789371631471/106341562018576649119*a^13 - 10597470554231302540041/106341562018576649119*a^12 - 16835996047441621774817/106341562018576649119*a^11 + 16674122550262725807072/106341562018576649119*a^10 + 24918511100968457522896/106341562018576649119*a^9 + 4438859628397342489851/106341562018576649119*a^8 - 26019738542206463779319/106341562018576649119*a^7 - 47775179818655449476697/106341562018576649119*a^6 + 24030985031406062666739/106341562018576649119*a^5 + 52435121331955185077307/106341562018576649119*a^4 - 16943596953875463472297/106341562018576649119*a^3 - 19178717695756638586794/106341562018576649119*a^2 + 5034806783502259963324/106341562018576649119*a + 39595990210148060592/2473059581827363933,
-949531404212230610/106341562018576649119*a^21 + 1404606076267666588/106341562018576649119*a^20 + 31860596932911204463/106341562018576649119*a^19 - 46971051976902102427/106341562018576649119*a^18 - 443194299396015920727/106341562018576649119*a^17 + 654211796697056201475/106341562018576649119*a^16 + 3289263238009343513027/106341562018576649119*a^15 - 4909640949988760976063/106341562018576649119*a^14 - 13911354804136965503755/106341562018576649119*a^13 + 21492498277511827879899/106341562018576649119*a^12 + 32809246067622506014675/106341562018576649119*a^11 - 55848212667582391995663/106341562018576649119*a^10 - 37152948138636735453445/106341562018576649119*a^9 + 85393270687204170694965/106341562018576649119*a^8 + 5583375858342452495631/106341562018576649119*a^7 - 76499001320510405514675/106341562018576649119*a^6 + 25817695878266203276277/106341562018576649119*a^5 + 39666285577392711382787/106341562018576649119*a^4 - 19730812320902394420787/106341562018576649119*a^3 - 10921342107175992074971/106341562018576649119*a^2 + 3730720089149782086801/106341562018576649119*a + 28348484555942980958/2473059581827363933,
321226424163746048/106341562018576649119*a^21 + 3801901583102434231/106341562018576649119*a^20 - 18552232937067380885/106341562018576649119*a^19 - 129228358922459727636/106341562018576649119*a^18 + 415822499184604316188/106341562018576649119*a^17 + 1838181668057575308290/106341562018576649119*a^16 - 4909941181790293676126/106341562018576649119*a^15 - 14192061774488959599914/106341562018576649119*a^14 + 33996329744624815911691/106341562018576649119*a^13 + 64611826293534390239510/106341562018576649119*a^12 - 143009619717835957566812/106341562018576649119*a^11 - 177164866440755054595842/106341562018576649119*a^10 + 363135701598845915429974/106341562018576649119*a^9 + 289742407609106508486970/106341562018576649119*a^8 - 534122568544790467437490/106341562018576649119*a^7 - 275603753317877822408499/106341562018576649119*a^6 + 420748487273236095304854/106341562018576649119*a^5 + 145078038418898400990846/106341562018576649119*a^4 - 153245015674186693664582/106341562018576649119*a^3 - 38930610655526174141722/106341562018576649119*a^2 + 18299352733124579928085/106341562018576649119*a + 96767738356241061887/2473059581827363933,
4452381647471694094/106341562018576649119*a^21 - 9068371874454525600/106341562018576649119*a^20 - 153992947179709981857/106341562018576649119*a^19 + 309305459277894660434/106341562018576649119*a^18 + 2241142934119782305766/106341562018576649119*a^17 - 4414101082400495089032/106341562018576649119*a^16 - 17849102933154097864728/106341562018576649119*a^15 + 34138690020226395806430/106341562018576649119*a^14 + 84888616078482178708090/106341562018576649119*a^13 - 154986667317321532177050/106341562018576649119*a^12 - 247940630886815257914596/106341562018576649119*a^11 + 419002856056921869273834/106341562018576649119*a^10 + 444151988255289405124854/106341562018576649119*a^9 - 657580637032014020631760/106341562018576649119*a^8 - 476755702015183905849788/106341562018576649119*a^7 + 565228902091487119925104/106341562018576649119*a^6 + 285426523932612121998880/106341562018576649119*a^5 - 239125370165520923828736/106341562018576649119*a^4 - 80207143469841117045912/106341562018576649119*a^3 + 39063917958108087392762/106341562018576649119*a^2 + 6022433751456583734384/106341562018576649119*a - 13918998523744547471/2473059581827363933,
2060947601905836306/106341562018576649119*a^21 - 4832671238044683175/106341562018576649119*a^20 - 68573303399040677761/106341562018576649119*a^19 + 163608169101819422096/106341562018576649119*a^18 + 945067357347588828552/106341562018576649119*a^17 - 2310696191041279916506/106341562018576649119*a^16 - 6945163366149052550342/106341562018576649119*a^15 + 17606989366145028973364/106341562018576649119*a^14 + 29110744005390982374894/106341562018576649119*a^13 - 78197087165562781870272/106341562018576649119*a^12 - 68512622918921845946016/106341562018576649119*a^11 + 204416013113214253913886/106341562018576649119*a^10 + 80351459485752749582826/106341562018576649119*a^9 - 304229490665913015656534/106341562018576649119*a^8 - 24090178091362483895616/106341562018576649119*a^7 + 240402390067988455671396/106341562018576649119*a^6 - 34263402855534371727222/106341562018576649119*a^5 - 89455854323221778141268/106341562018576649119*a^4 + 26829327840793157634146/106341562018576649119*a^3 + 12894732713698986951570/106341562018576649119*a^2 - 4229275899838336784401/106341562018576649119*a - 16475863908380734115/2473059581827363933,
-183828183402467739/106341562018576649119*a^21 + 1039361525618415970/106341562018576649119*a^20 + 6101367191790319672/106341562018576649119*a^19 - 36335263579768053016/106341562018576649119*a^18 - 86097238365453050162/106341562018576649119*a^17 + 535013726770783983898/106341562018576649119*a^16 + 679936098218707440588/106341562018576649119*a^15 - 4304659386907177462172/106341562018576649119*a^14 - 3352483334807843958878/106341562018576649119*a^13 + 20525485479955595004164/106341562018576649119*a^12 + 10989624956073174280880/106341562018576649119*a^11 - 58778429143237160633642/106341562018576649119*a^10 - 24843801449515718243784/106341562018576649119*a^9 + 97604340848147573252008/106341562018576649119*a^8 + 38249882878989736086178/106341562018576649119*a^7 - 85409928933297878885242/106341562018576649119*a^6 - 36526711348597203705336/106341562018576649119*a^5 + 31341260738901659239774/106341562018576649119*a^4 + 18666517891163488220250/106341562018576649119*a^3 - 1652994415952016698357/106341562018576649119*a^2 - 3937341625041663583766/106341562018576649119*a - 5194141489789705256/2473059581827363933,
-4949554546469626151/106341562018576649119*a^21 + 5638410761951578121/106341562018576649119*a^20 + 176207117842749094505/106341562018576649119*a^19 - 191397314944231603028/106341562018576649119*a^18 - 2660490697073345263440/106341562018576649119*a^17 + 2707190973281190920048/106341562018576649119*a^16 + 22216248394573400487934/106341562018576649119*a^15 - 20597631528218833688502/106341562018576649119*a^14 - 112317687824702088138006/106341562018576649119*a^13 + 90712069956071996243772/106341562018576649119*a^12 + 354554649317530165235914/106341562018576649119*a^11 - 231162104592895901963896/106341562018576649119*a^10 - 697751720167008818836016/106341562018576649119*a^9 + 319889567020050596788750/106341562018576649119*a^8 + 831647493859939158411512/106341562018576649119*a^7 - 199844244260598778871414/106341562018576649119*a^6 - 560612132770439918559736/106341562018576649119*a^5 + 15800073124336849081422/106341562018576649119*a^4 + 188323919933396899399728/106341562018576649119*a^3 + 26727855000532543053163/106341562018576649119*a^2 - 23537886238855188251027/106341562018576649119*a - 114397190965483473771/2473059581827363933,
-132904553112721313/106341562018576649119*a^21 - 1176708245964174219/106341562018576649119*a^20 + 9904292068140553639/106341562018576649119*a^19 + 39065139067194949432/106341562018576649119*a^18 - 246905618631975767242/106341562018576649119*a^17 - 538471726425906035698/106341562018576649119*a^16 + 3080826924353390203226/106341562018576649119*a^15 + 3987676782018307963186/106341562018576649119*a^14 - 22005835609083581847834/106341562018576649119*a^13 - 17217508630054096872000/106341562018576649119*a^12 + 94182905922897950077050/106341562018576649119*a^11 + 44530024615877316807794/106341562018576649119*a^10 - 240788420412776223839324/106341562018576649119*a^9 - 70388526602452924678018/106341562018576649119*a^8 + 352048707552451713628708/106341562018576649119*a^7 + 71335855328798875924316/106341562018576649119*a^6 - 268841807668535375834654/106341562018576649119*a^5 - 45754557196087629322204/106341562018576649119*a^4 + 89914375314152864848222/106341562018576649119*a^3 + 16149501277969156542849/106341562018576649119*a^2 - 8829343406548919375683/106341562018576649119*a - 46380259482200347787/2473059581827363933,
7394664530843307306/106341562018576649119*a^21 - 7606811372112628985/106341562018576649119*a^20 - 265748373574771212515/106341562018576649119*a^19 + 262649542497701585053/106341562018576649119*a^18 + 4059724885732822776975/106341562018576649119*a^17 - 3798927284152887127595/106341562018576649119*a^16 - 34396095662365500835307/106341562018576649119*a^15 + 29807565684935758419707/106341562018576649119*a^14 + 176999555379210375255647/106341562018576649119*a^13 - 137367368061688512257791/106341562018576649119*a^12 - 570418410750884597129585/106341562018576649119*a^11 + 376728273526138216865739/106341562018576649119*a^10 + 1147527903105757245029711/106341562018576649119*a^9 - 597146212364599738977311/106341562018576649119*a^8 - 1393620714368475271214341/106341562018576649119*a^7 + 510797249529005350919693/106341562018576649119*a^6 + 946073752160513183531115/106341562018576649119*a^5 - 205880561965320549938131/106341562018576649119*a^4 - 309538691264250150171849/106341562018576649119*a^3 + 23820849468389444377459/106341562018576649119*a^2 + 33753100856119673756800/106341562018576649119*a + 68552604153275274946/2473059581827363933
]
*], q_expansions := [*
q + a*q^2 + (-a^3 - a^2 + 2*a)*q^3 + (a^2 - 2)*q^4 + (a^3 + a^2 - 3*a - 1)*q^5 + (-a^2 - a + 1)*q^6 + (a^3 - 3*a)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + a^2 - 2*a - 2)*q^9 - q^10 - q^11 + (a^3 + a^2 - 3*a)*q^12 + (a^2 + a - 3)*q^13 + (-a^3 + a - 1)*q^14 + (a^2 + a - 2)*q^15 + (-a^3 - 3*a^2 + a + 3)*q^16 + (-3*a^3 - 3*a^2 + 7*a)*q^17 + (a^2 - a - 1)*q^18 + (-a^3 - a^2 + 2*a - 1)*q^19 + (-2*a^3 - 2*a^2 + 5*a + 2)*q^20 + (a^2 + 2*a - 2)*q^21 - a*q^22 + (3*a^2 + 3*a - 4)*q^23 + (2*a^2 + 3*a - 3)*q^24 + (-a^3 - 2*a^2 + 2*a - 1)*q^25 + (a^3 + a^2 - 3*a)*q^26 + (4*a^3 + 4*a^2 - 8*a - 1)*q^27 + (-a^3 - 2*a^2 + 4*a + 1)*q^28 + (-a^3 - 2*a^2 + 3*a + 1)*q^29 + (a^3 + a^2 - 2*a)*q^30 + (a^3 + 2*a^2 + a - 3)*q^31 + (-4*a^3 - 2*a^2 + 10*a + 1)*q^32 + (a^3 + a^2 - 2*a)*q^33 + (-2*a^2 - 3*a + 3)*q^34 + (-a^2 + 3)*q^35 + (-a^3 - 3*a^2 + 3*a + 4)*q^36 + (-4*a^3 - 8*a^2 + 7*a + 6)*q^37 + O(q^38),
q + a*q^2 + (-1333218028123436678/106341562018576649119*a^21 + 1367946423136236257/106341562018576649119*a^20 + 49328489263264063408/106341562018576649119*a^19 - 48698618113739814119/106341562018576649119*a^18 - 780071490285978038489/106341562018576649119*a^17 + 731764058773877640305/106341562018576649119*a^16 + 6883435129930837071209/106341562018576649119*a^15 - 6029718454604453812991/106341562018576649119*a^14 - 37117408682963362048611/106341562018576649119*a^13 + 29643589741202443321628/106341562018576649119*a^12 + 125904278451589035925849/106341562018576649119*a^11 - 88764078616540344648331/106341562018576649119*a^10 - 266400248133720180154691/106341562018576649119*a^9 + 159042733994278329421197/106341562018576649119*a^8 + 336261615438596631255820/106341562018576649119*a^7 - 162008001244132052237259/106341562018576649119*a^6 - 230084343080867524283273/106341562018576649119*a^5 + 85032171085335940948597/106341562018576649119*a^4 + 71086649415902837709445/106341562018576649119*a^3 - 17051195074052769029465/106341562018576649119*a^2 - 6284781941061791629214/106341562018576649119*a - 2035191172956196509/2473059581827363933)*q^3 + (a^2 - 2)*q^4 + (-21242974024529590/106341562018576649119*a^21 - 1434491652110563978/106341562018576649119*a^20 + 3209217338769634321/106341562018576649119*a^19 + 48282217898366329351/106341562018576649119*a^18 - 94578303848943192367/106341562018576649119*a^17 - 676590780104692901915/106341562018576649119*a^16 + 1270815302353166006692/106341562018576649119*a^15 + 5102603103564094427213/106341562018576649119*a^14 - 9439579417621543494677/106341562018576649119*a^13 - 22357866355125222974699/106341562018576649119*a^12 + 41280678241435124160901/106341562018576649119*a^11 + 57441564627509462184517/106341562018576649119*a^10 - 106882614769975285857639/106341562018576649119*a^9 - 83882843771650414225579/106341562018576649119*a^8 + 158593036380613931304765/106341562018576649119*a^7 + 66319079553842412941717/106341562018576649119*a^6 - 126427357236440356717803/106341562018576649119*a^5 - 28369596568106140688094/106341562018576649119*a^4 + 47782658911006380501745/106341562018576649119*a^3 + 8238984211089590694971/106341562018576649119*a^2 - 6439892278957108980653/106341562018576649119*a - 30557112079337671866/2473059581827363933)*q^5 + (-1298489633110637099/106341562018576649119*a^21 + 2665858278943779678/106341562018576649119*a^20 + 44626643854900753341/106341562018576649119*a^19 - 90797769746161275963/106341562018576649119*a^18 - 645450164277632448069/106341562018576649119*a^17 + 1290585501953020206999/106341562018576649119*a^16 + 5111984606423106505055/106341562018576649119*a^15 - 9897096202767155393885/106341562018576649119*a^14 - 24222418249068768779606/106341562018576649119*a^13 + 44195345161987972241263/106341562018576649119*a^12 + 70823452567863149144947/106341562018576649119*a^11 - 115723946249293737117165/106341562018576649119*a^10 - 128419071139556469905773/106341562018576649119*a^9 + 170410625958069231949298/106341562018576649119*a^8 + 142777638947138683283643/106341562018576649119*a^7 - 128155825176746419940139/106341562018576649119*a^6 - 92679125973377551045413/106341562018576649119*a^5 + 39752026100917705466411/106341562018576649119*a^4 + 31933901715258541393611/106341562018576649119*a^3 - 1502528874183024265228/106341562018576649119*a^2 - 4353810910432113819487/106341562018576649119*a - 14665398309357803458/2473059581827363933)*q^6 + (504418815307781939/106341562018576649119*a^21 - 1021065885099576655/106341562018576649119*a^20 - 16604493185137817773/106341562018576649119*a^19 + 33056103831567470983/106341562018576649119*a^18 + 226015020692329680027/106341562018576649119*a^17 - 435479859114799908685/106341562018576649119*a^16 - 1641199345467818455453/106341562018576649119*a^15 + 2956466065705411278227/106341562018576649119*a^14 + 6861291586789371631471/106341562018576649119*a^13 - 10597470554231302540041/106341562018576649119*a^12 - 16835996047441621774817/106341562018576649119*a^11 + 16674122550262725807072/106341562018576649119*a^10 + 24918511100968457522896/106341562018576649119*a^9 + 4438859628397342489851/106341562018576649119*a^8 - 26019738542206463779319/106341562018576649119*a^7 - 47775179818655449476697/106341562018576649119*a^6 + 24030985031406062666739/106341562018576649119*a^5 + 52435121331955185077307/106341562018576649119*a^4 - 16943596953875463472297/106341562018576649119*a^3 - 19178717695756638586794/106341562018576649119*a^2 + 5034806783502259963324/106341562018576649119*a + 39595990210148060592/2473059581827363933)*q^7 + (a^3 - 4*a)*q^8 + (2046403089845571866/106341562018576649119*a^21 - 3320501250721280963/106341562018576649119*a^20 - 69436507984912614568/106341562018576649119*a^19 + 114229840938650420436/106341562018576649119*a^18 + 984593027842667859606/106341562018576649119*a^17 - 1647333477805559999578/106341562018576649119*a^16 - 7554077366172048872258/106341562018576649119*a^15 + 12913841625992631704837/106341562018576649119*a^14 + 33934916106603120681242/106341562018576649119*a^13 - 59748486152308080949246/106341562018576649119*a^12 - 90354129204143133078118/106341562018576649119*a^11 + 166314229434478003793370/106341562018576649119*a^10 + 138283868513786033925878/106341562018576649119*a^9 - 274038136524740361292930/106341562018576649119*a^8 - 113182368936346686594406/106341562018576649119*a^7 + 255694038610765851693374/106341562018576649119*a^6 + 42269138950209474008131/106341562018576649119*a^5 - 122382397121220694901858/106341562018576649119*a^4 - 3796040728454798420212/106341562018576649119*a^3 + 23868564658330153413544/106341562018576649119*a^2 - 540233279487050585897/106341562018576649119*a - 13505670722752196027/2473059581827363933)*q^9 + (-1476977600159623158/106341562018576649119*a^21 + 2465713247911098671/106341562018576649119*a^20 + 49769226080083400651/106341562018576649119*a^19 - 83595686278261394337/106341562018576649119*a^18 - 698534772272031968385/106341562018576649119*a^17 + 1181701026320264376642/106341562018576649119*a^16 + 5280130637487088210843/106341562018576649119*a^15 - 9005861616962722855647/106341562018576649119*a^14 - 23216146234638291999469/106341562018576649119*a^13 + 39978760092393779178571/106341562018576649119*a^12 + 59984369861219678637107/106341562018576649119*a^11 - 104481797574645025184609/106341562018576649119*a^10 - 88463147615949361773429/106341562018576649119*a^9 + 155950431654936474838355/106341562018576649119*a^8 + 71175414602616097982027/106341562018576649119*a^7 - 124803268143342995973533/106341562018576649119*a^6 - 31201178790705812387144/106341562018576649119*a^5 + 47283385292507861547975/106341562018576649119*a^4 + 9019493562698856890751/106341562018576649119*a^3 - 6363693731131121341323/106341562018576649119*a^2 - 1381933336290014578238/106341562018576649119*a - 233672714269825490/2473059581827363933)*q^10 + (-949531404212230610/106341562018576649119*a^21 + 1404606076267666588/106341562018576649119*a^20 + 31860596932911204463/106341562018576649119*a^19 - 46971051976902102427/106341562018576649119*a^18 - 443194299396015920727/106341562018576649119*a^17 + 654211796697056201475/106341562018576649119*a^16 + 3289263238009343513027/106341562018576649119*a^15 - 4909640949988760976063/106341562018576649119*a^14 - 13911354804136965503755/106341562018576649119*a^13 + 21492498277511827879899/106341562018576649119*a^12 + 32809246067622506014675/106341562018576649119*a^11 - 55848212667582391995663/106341562018576649119*a^10 - 37152948138636735453445/106341562018576649119*a^9 + 85393270687204170694965/106341562018576649119*a^8 + 5583375858342452495631/106341562018576649119*a^7 - 76499001320510405514675/106341562018576649119*a^6 + 25817695878266203276277/106341562018576649119*a^5 + 39666285577392711382787/106341562018576649119*a^4 - 19730812320902394420787/106341562018576649119*a^3 - 10921342107175992074971/106341562018576649119*a^2 + 3730720089149782086801/106341562018576649119*a + 28348484555942980958/2473059581827363933)*q^11 + (2735315068969378836/106341562018576649119*a^21 - 3556386150244017638/106341562018576649119*a^20 - 98560473954944805849/106341562018576649119*a^19 + 123266212268046560352/106341562018576649119*a^18 + 1509388691521688160710/106341562018576649119*a^17 - 1798707522023771405860/106341562018576649119*a^16 - 12812488598723235299960/106341562018576649119*a^15 + 14348281499360016496659/106341562018576649119*a^14 + 65967285881345625627588/106341562018576649119*a^13 - 68044261058993353384722/106341562018576649119*a^12 - 212101995579495437581464/106341562018576649119*a^11 + 195860488958789092408572/106341562018576649119*a^10 + 423237279982359574157795/106341562018576649119*a^9 - 336838640910748120037252/106341562018576649119*a^8 - 503832639518150045886488/106341562018576649119*a^7 + 330610304435094091558952/106341562018576649119*a^6 + 326838536617170381921752/106341562018576649119*a^5 - 168648842302412644241380/106341562018576649119*a^4 - 95966721606237671392660/106341562018576649119*a^3 + 34406261551641279513556/106341562018576649119*a^2 + 7783784928867158992934/106341562018576649119*a - 10213003618304615071/2473059581827363933)*q^12 + (321226424163746048/106341562018576649119*a^21 + 3801901583102434231/106341562018576649119*a^20 - 18552232937067380885/106341562018576649119*a^19 - 129228358922459727636/106341562018576649119*a^18 + 415822499184604316188/106341562018576649119*a^17 + 1838181668057575308290/106341562018576649119*a^16 - 4909941181790293676126/106341562018576649119*a^15 - 14192061774488959599914/106341562018576649119*a^14 + 33996329744624815911691/106341562018576649119*a^13 + 64611826293534390239510/106341562018576649119*a^12 - 143009619717835957566812/106341562018576649119*a^11 - 177164866440755054595842/106341562018576649119*a^10 + 363135701598845915429974/106341562018576649119*a^9 + 289742407609106508486970/106341562018576649119*a^8 - 534122568544790467437490/106341562018576649119*a^7 - 275603753317877822408499/106341562018576649119*a^6 + 420748487273236095304854/106341562018576649119*a^5 + 145078038418898400990846/106341562018576649119*a^4 - 153245015674186693664582/106341562018576649119*a^3 - 38930610655526174141722/106341562018576649119*a^2 + 18299352733124579928085/106341562018576649119*a + 96767738356241061887/2473059581827363933)*q^13 + (-12228254484012777/106341562018576649119*a^21 + 1050165350634550092/106341562018576649119*a^20 - 2253213239977264747/106341562018576649119*a^19 - 34769506821793582436/106341562018576649119*a^18 + 85584777098138834302/106341562018576649119*a^17 + 474837584748326778652/106341562018576649119*a^16 - 1258961973821722385996/106341562018576649119*a^15 - 3437427365349612217092/106341562018576649119*a^14 + 9782562840649011141376/106341562018576649119*a^13 + 14078319886326409920676/106341562018576649119*a^12 - 43705314060894080073167/106341562018576649119*a^11 - 32089390148671133877067/106341562018576649119*a^10 + 113199122490984745267336/106341562018576649119*a^9 + 36729457663266301650342/106341562018576649119*a^8 - 163089860767352170769548/106341562018576649119*a^7 - 14533346655319789915628/106341562018576649119*a^6 + 119671627318405978636312/106341562018576649119*a^5 - 5088241537696664559980/106341562018576649119*a^4 - 37712073807795162589532/106341562018576649119*a^3 + 3225456492993246148131/106341562018576649119*a^2 + 3316767788021268810256/106341562018576649119*a + 5548606968385601329/2473059581827363933)*q^14 + (-3742303588968530107/106341562018576649119*a^21 + 3342400388448693194/106341562018576649119*a^20 + 133746740179511662120/106341562018576649119*a^19 - 113314885334183648100/106341562018576649119*a^18 - 2030356591407612687132/106341562018576649119*a^17 + 1601516699860616206053/106341562018576649119*a^16 + 17075571556833547170124/106341562018576649119*a^15 - 12186624276226513165584/106341562018576649119*a^14 - 87078358215154879522920/106341562018576649119*a^13 + 53795495238609565759988/106341562018576649119*a^12 + 277365657525005451628137/106341562018576649119*a^11 - 138266908354537623105784/106341562018576649119*a^10 - 549017649597967552746466/106341562018576649119*a^9 + 196895002163903242319749/106341562018576649119*a^8 + 650546317324946249637884/106341562018576649119*a^7 - 137489413085018415956440/106341562018576649119*a^6 - 422988250481854722664560/106341562018576649119*a^5 + 32138160482011131466836/106341562018576649119*a^4 + 126213526087593167637433/106341562018576649119*a^3 + 5730202195059084526405/106341562018576649119*a^2 - 10657578977563476319208/106341562018576649119*a - 43494269503448039318/2473059581827363933)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (4452381647471694094/106341562018576649119*a^21 - 9068371874454525600/106341562018576649119*a^20 - 153992947179709981857/106341562018576649119*a^19 + 309305459277894660434/106341562018576649119*a^18 + 2241142934119782305766/106341562018576649119*a^17 - 4414101082400495089032/106341562018576649119*a^16 - 17849102933154097864728/106341562018576649119*a^15 + 34138690020226395806430/106341562018576649119*a^14 + 84888616078482178708090/106341562018576649119*a^13 - 154986667317321532177050/106341562018576649119*a^12 - 247940630886815257914596/106341562018576649119*a^11 + 419002856056921869273834/106341562018576649119*a^10 + 444151988255289405124854/106341562018576649119*a^9 - 657580637032014020631760/106341562018576649119*a^8 - 476755702015183905849788/106341562018576649119*a^7 + 565228902091487119925104/106341562018576649119*a^6 + 285426523932612121998880/106341562018576649119*a^5 - 239125370165520923828736/106341562018576649119*a^4 - 80207143469841117045912/106341562018576649119*a^3 + 39063917958108087392762/106341562018576649119*a^2 + 6022433751456583734384/106341562018576649119*a - 13918998523744547471/2473059581827363933)*q^17 + (772304928969862769/106341562018576649119*a^21 + 2187600159682400742/106341562018576649119*a^20 - 29018375350539610184/106341562018576649119*a^19 - 73397369607492795116/106341562018576649119*a^18 + 466600914004915738000/106341562018576649119*a^17 + 1030583595730125105612/106341562018576649119*a^16 - 4187948995846812379325/106341562018576649119*a^15 - 7846495778773920106880/106341562018576649119*a^14 + 22932337886722559152752/106341562018576649119*a^13 + 35063776963222429873424/106341562018576649119*a^12 - 78642266823126794138696/106341562018576649119*a^11 - 92994469491290961653844/106341562018576649119*a^10 + 167197065692312616594660/106341562018576649119*a^9 + 141388129037352607964128/106341562018576649119*a^8 - 212132125355740487021020/106341562018576649119*a^7 - 114184516477754031863167/106341562018576649119*a^6 + 150392902739744806976612/106341562018576649119*a^5 + 44300571092185677146386/106341562018576649119*a^4 - 51320377668775848087028/106341562018576649119*a^3 - 7880681162763116869239/106341562018576649119*a^2 + 5967746046427485542039/106341562018576649119*a + 22510433988301290526/2473059581827363933)*q^18 + (2060947601905836306/106341562018576649119*a^21 - 4832671238044683175/106341562018576649119*a^20 - 68573303399040677761/106341562018576649119*a^19 + 163608169101819422096/106341562018576649119*a^18 + 945067357347588828552/106341562018576649119*a^17 - 2310696191041279916506/106341562018576649119*a^16 - 6945163366149052550342/106341562018576649119*a^15 + 17606989366145028973364/106341562018576649119*a^14 + 29110744005390982374894/106341562018576649119*a^13 - 78197087165562781870272/106341562018576649119*a^12 - 68512622918921845946016/106341562018576649119*a^11 + 204416013113214253913886/106341562018576649119*a^10 + 80351459485752749582826/106341562018576649119*a^9 - 304229490665913015656534/106341562018576649119*a^8 - 24090178091362483895616/106341562018576649119*a^7 + 240402390067988455671396/106341562018576649119*a^6 - 34263402855534371727222/106341562018576649119*a^5 - 89455854323221778141268/106341562018576649119*a^4 + 26829327840793157634146/106341562018576649119*a^3 + 12894732713698986951570/106341562018576649119*a^2 - 4229275899838336784401/106341562018576649119*a - 16475863908380734115/2473059581827363933)*q^19 + (-445756004359088465/106341562018576649119*a^21 + 943993378717718077/106341562018576649119*a^20 + 13374311055372958081/106341562018576649119*a^19 - 31501788786239454401/106341562018576649119*a^18 - 154860226946739960838/106341562018576649119*a^17 + 437391165026854866863/106341562018576649119*a^16 + 795609582864915862375/106341562018576649119*a^15 - 3265900779307454837009/106341562018576649119*a^14 - 816407051612388284749/106341562018576649119*a^13 + 14180576390487300102159/106341562018576649119*a^12 - 10247458340808221870653/106341562018576649119*a^11 - 36422699433728155694777/106341562018576649119*a^10 + 51257135936469899341463/106341562018576649119*a^9 + 55206565663659965201143/106341562018576649119*a^8 - 104338968709679568055841/106341562018576649119*a^7 - 50919969433386968972004/106341562018576649119*a^6 + 103264370552111606137971/106341562018576649119*a^5 + 31045282162359515184465/106341562018576649119*a^4 - 47661900568079008273577/106341562018576649119*a^3 - 12561983106696627700434/106341562018576649119*a^2 + 8143408310689821359636/106341562018576649119*a + 44867470556919488994/2473059581827363933)*q^20 + (-2249893811685617514/106341562018576649119*a^21 + 4889151217053188472/106341562018576649119*a^20 + 78448856556918336317/106341562018576649119*a^19 - 165965583596167928108/106341562018576649119*a^18 - 1156614060025552531081/106341562018576649119*a^17 + 2352019130624422535113/106341562018576649119*a^16 + 9411342247030654010618/106341562018576649119*a^15 - 17995360684792647361044/106341562018576649119*a^14 - 46423948334502659938116/106341562018576649119*a^13 + 80250391160832653875260/106341562018576649119*a^12 + 144429564505690955661176/106341562018576649119*a^11 - 210078747092599937527244/106341562018576649119*a^10 - 288095361393536824443956/106341562018576649119*a^9 + 309201303395171840828680/106341562018576649119*a^8 + 367366130426128360182060/106341562018576649119*a^7 - 230047035257201422215924/106341562018576649119*a^6 - 284482773420770565536964/106341562018576649119*a^5 + 65025589344599718946708/106341562018576649119*a^4 + 117881342225203702773187/106341562018576649119*a^3 + 2447208805807854457205/106341562018576649119*a^2 - 19239928901254527029690/106341562018576649119*a - 49267649801016415541/2473059581827363933)*q^21 + (-494456732156794632/106341562018576649119*a^21 - 1373002214516866887/106341562018576649119*a^20 + 19496146317954040273/106341562018576649119*a^19 + 47713436581707304643/106341562018576649119*a^18 - 326654143854178018655/106341562018576649119*a^17 - 694021002660963895923/106341562018576649119*a^16 + 3025592995012850231707/106341562018576649119*a^15 + 5475227875664146860615/106341562018576649119*a^14 - 16871419046874925455931/106341562018576649119*a^13 - 25384685102332471380395/106341562018576649119*a^12 + 57811645948025824251947/106341562018576649119*a^11 + 70160242571216931396925/106341562018576649119*a^10 - 119339943032015932280185/106341562018576649119*a^9 - 112537381294254823157759/106341562018576649119*a^8 + 140572423465043422006815/106341562018576649119*a^7 + 98412220324503870102607/106341562018576649119*a^6 - 86901502947076567777163/106341562018576649119*a^5 - 42047648914102450447617/106341562018576649119*a^4 + 23966340746389784997649/106341562018576649119*a^3 + 7136689236059053284871/106341562018576649119*a^2 - 1819515657573589770806/106341562018576649119*a - 10444845446334536710/2473059581827363933)*q^22 + (-183828183402467739/106341562018576649119*a^21 + 1039361525618415970/106341562018576649119*a^20 + 6101367191790319672/106341562018576649119*a^19 - 36335263579768053016/106341562018576649119*a^18 - 86097238365453050162/106341562018576649119*a^17 + 535013726770783983898/106341562018576649119*a^16 + 679936098218707440588/106341562018576649119*a^15 - 4304659386907177462172/106341562018576649119*a^14 - 3352483334807843958878/106341562018576649119*a^13 + 20525485479955595004164/106341562018576649119*a^12 + 10989624956073174280880/106341562018576649119*a^11 - 58778429143237160633642/106341562018576649119*a^10 - 24843801449515718243784/106341562018576649119*a^9 + 97604340848147573252008/106341562018576649119*a^8 + 38249882878989736086178/106341562018576649119*a^7 - 85409928933297878885242/106341562018576649119*a^6 - 36526711348597203705336/106341562018576649119*a^5 + 31341260738901659239774/106341562018576649119*a^4 + 18666517891163488220250/106341562018576649119*a^3 - 1652994415952016698357/106341562018576649119*a^2 - 3937341625041663583766/106341562018576649119*a - 5194141489789705256/2473059581827363933)*q^23 + (4511223253916014232/106341562018576649119*a^21 - 8156163098904105945/106341562018576649119*a^20 - 157459130269611464850/106341562018576649119*a^19 + 276826340356841854424/106341562018576649119*a^18 + 2317773272776861827866/106341562018576649119*a^17 - 3919012888302731496938/106341562018576649119*a^16 - 18734715744863295445903/106341562018576649119*a^15 + 29914550523732128720746/106341562018576649119*a^14 + 90915510170713997285398/106341562018576649119*a^13 - 132853431271545061342058/106341562018576649119*a^12 - 273206365247640821929358/106341562018576649119*a^11 + 345548069331234760483913/106341562018576649119*a^10 + 509774459964197437498434/106341562018576649119*a^9 - 504383432169566751965520/106341562018576649119*a^8 - 580262616061204001327458/106341562018576649119*a^7 + 374027144002747301653322/106341562018576649119*a^6 + 381313231762615809794066/106341562018576649119*a^5 - 111182663742085771542974/106341562018576649119*a^4 - 129962488142948720465978/106341562018576649119*a^3 + 977267524840045638658/106341562018576649119*a^2 + 17021470885979141466121/106341562018576649119*a + 59419262377378774112/2473059581827363933)*q^24 + (-719816243709360152/106341562018576649119*a^21 + 3480636582222939563/106341562018576649119*a^20 + 20974008119275552707/106341562018576649119*a^19 - 118897405477588296255/106341562018576649119*a^18 - 229919874272320623243/106341562018576649119*a^17 + 1694847346023944139209/106341562018576649119*a^16 + 1024365485846039534061/106341562018576649119*a^15 - 13039838467624206709527/106341562018576649119*a^14 + 358740843870346752281/106341562018576649119*a^13 + 58505328019139688374477/106341562018576649119*a^12 - 21828299221105886443334/106341562018576649119*a^11 - 154545795270897105008091/106341562018576649119*a^10 + 87825063743642909970975/106341562018576649119*a^9 + 232062869301826606115644/106341562018576649119*a^8 - 156531603625948067533695/106341562018576649119*a^7 - 183078835958843793038639/106341562018576649119*a^6 + 135467093277583434283893/106341562018576649119*a^5 + 64932817451593238462845/106341562018576649119*a^4 - 53115752474249641776155/106341562018576649119*a^3 - 8139381250059636113759/106341562018576649119*a^2 + 7474549838328303569920/106341562018576649119*a + 24983920957800688425/2473059581827363933)*q^25 + (4444354431429926327/106341562018576649119*a^21 - 7309308091336269205/106341562018576649119*a^20 - 151714208613921950996/106341562018576649119*a^19 + 249748437891947609372/106341562018576649119*a^18 + 2170008564218724975874/106341562018576649119*a^17 - 3562396332423379004766/106341562018576649119*a^16 - 16876551001225385323050/106341562018576649119*a^15 + 27437849842473612849675/106341562018576649119*a^14 + 77590337509022221816854/106341562018576649119*a^13 - 123322615860112453523036/106341562018576649119*a^12 - 215615990639579620287490/106341562018576649119*a^11 + 326831654819131828323158/106341562018576649119*a^10 + 359003643055172612626490/106341562018576649119*a^9 - 494162322605244622812338/106341562018576649119*a^8 - 349039004919527642695731/106341562018576649119*a^7 + 396189763466645218697110/106341562018576649119*a^6 + 187895914627804930459006/106341562018576649119*a^5 - 145695231027066170298438/106341562018576649119*a^4 - 50733111932150531437338/106341562018576649119*a^3 + 17147113549649222853909/106341562018576649119*a^2 + 5188937306642353014741/106341562018576649119*a + 3533490665801206528/2473059581827363933)*q^26 + (-352284225223252022/106341562018576649119*a^21 + 2845168931599921220/106341562018576649119*a^20 + 8336344563743999271/106341562018576649119*a^19 - 99082035402916844873/106341562018576649119*a^18 - 47531220165652833382/106341562018576649119*a^17 + 1449078797750534236601/106341562018576649119*a^16 - 414797840351158752689/106341562018576649119*a^15 - 11555907204671722096607/106341562018576649119*a^14 + 7173057466625397070929/106341562018576649119*a^13 + 54669563080241202467654/106341562018576649119*a^12 - 42058554506695254106363/106341562018576649119*a^11 - 156952658430579100530203/106341562018576649119*a^10 + 126747017976260365443049/106341562018576649119*a^9 + 270777843566910619082773/106341562018576649119*a^8 - 206155218592006223084826/106341562018576649119*a^7 - 272110890152956370642859/106341562018576649119*a^6 + 174672823246396058360079/106341562018576649119*a^5 + 149033777499581949774553/106341562018576649119*a^4 - 68116683806157067981879/106341562018576649119*a^3 - 36914964703432353737948/106341562018576649119*a^2 + 8953094622225115223125/106341562018576649119*a + 43244097974126713324/2473059581827363933)*q^27 + (16871211050960660/106341562018576649119*a^21 - 639070376718558632/106341562018576649119*a^20 - 704542637637052500/106341562018576649119*a^19 + 25794577003238498045/106341562018576649119*a^18 + 10175756481682219957/106341562018576649119*a^17 - 439299783152556168141/106341562018576649119*a^16 - 52837151691080528797/106341562018576649119*a^15 + 4119294981038277452931/106341562018576649119*a^14 - 138321453169901571397/106341562018576649119*a^13 - 23259805984993166057084/106341562018576649119*a^12 + 3046336236202923092244/106341562018576649119*a^11 + 81232878027478965671401/106341562018576649119*a^10 - 15744159629241028308305/106341562018576649119*a^9 - 173488762653703561195273/106341562018576649119*a^8 + 40301619458428814580203/106341562018576649119*a^7 + 216156873695783106429687/106341562018576649119*a^6 - 54780176781955273003673/106341562018576649119*a^5 - 142869717136843285041977/106341562018576649119*a^4 + 37561940926995770545259/106341562018576649119*a^3 + 41718065928368699814943/106341562018576649119*a^2 - 9870153881712779955901/106341562018576649119*a - 79326491219620261731/2473059581827363933)*q^28 + (-4949554546469626151/106341562018576649119*a^21 + 5638410761951578121/106341562018576649119*a^20 + 176207117842749094505/106341562018576649119*a^19 - 191397314944231603028/106341562018576649119*a^18 - 2660490697073345263440/106341562018576649119*a^17 + 2707190973281190920048/106341562018576649119*a^16 + 22216248394573400487934/106341562018576649119*a^15 - 20597631528218833688502/106341562018576649119*a^14 - 112317687824702088138006/106341562018576649119*a^13 + 90712069956071996243772/106341562018576649119*a^12 + 354554649317530165235914/106341562018576649119*a^11 - 231162104592895901963896/106341562018576649119*a^10 - 697751720167008818836016/106341562018576649119*a^9 + 319889567020050596788750/106341562018576649119*a^8 + 831647493859939158411512/106341562018576649119*a^7 - 199844244260598778871414/106341562018576649119*a^6 - 560612132770439918559736/106341562018576649119*a^5 + 15800073124336849081422/106341562018576649119*a^4 + 188323919933396899399728/106341562018576649119*a^3 + 26727855000532543053163/106341562018576649119*a^2 - 23537886238855188251027/106341562018576649119*a - 114397190965483473771/2473059581827363933)*q^29 + (-4142206789488367020/106341562018576649119*a^21 + 2766114565613108375/106341562018576649119*a^20 + 148646365893613459390/106341562018576649119*a^19 - 95585635910882621813/106341562018576649119*a^18 - 2264282907543875394478/106341562018576649119*a^17 + 1376608001110563371259/106341562018576649119*a^16 + 19087806816783492938615/106341562018576649119*a^15 - 10671745839184400328301/106341562018576649119*a^14 - 97404796666485956153133/106341562018576649119*a^13 + 48011097467891146960428/106341562018576649119*a^12 + 309690573548584399232223/106341562018576649119*a^11 - 126073724883511185643647/106341562018576649119*a^10 - 610001786171546376701056/106341562018576649119*a^9 + 185007493160850072857191/106341562018576649119*a^8 + 718034868085488283274723/106341562018576649119*a^7 - 136877914194443690394089/106341562018576649119*a^6 - 466692196409549089145729/106341562018576649119*a^5 + 38258164836065804532612/106341562018576649119*a^4 + 143229920660940817717799/106341562018576649119*a^3 + 2766063996066641174601/106341562018576649119*a^2 - 13845625073347562033074/106341562018576649119*a - 41165339478653831177/2473059581827363933)*q^30 + (-132904553112721313/106341562018576649119*a^21 - 1176708245964174219/106341562018576649119*a^20 + 9904292068140553639/106341562018576649119*a^19 + 39065139067194949432/106341562018576649119*a^18 - 246905618631975767242/106341562018576649119*a^17 - 538471726425906035698/106341562018576649119*a^16 + 3080826924353390203226/106341562018576649119*a^15 + 3987676782018307963186/106341562018576649119*a^14 - 22005835609083581847834/106341562018576649119*a^13 - 17217508630054096872000/106341562018576649119*a^12 + 94182905922897950077050/106341562018576649119*a^11 + 44530024615877316807794/106341562018576649119*a^10 - 240788420412776223839324/106341562018576649119*a^9 - 70388526602452924678018/106341562018576649119*a^8 + 352048707552451713628708/106341562018576649119*a^7 + 71335855328798875924316/106341562018576649119*a^6 - 268841807668535375834654/106341562018576649119*a^5 - 45754557196087629322204/106341562018576649119*a^4 + 89914375314152864848222/106341562018576649119*a^3 + 16149501277969156542849/106341562018576649119*a^2 - 8829343406548919375683/106341562018576649119*a - 46380259482200347787/2473059581827363933)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1006495042118223334/106341562018576649119*a^21 - 5837465978972957077/106341562018576649119*a^20 - 30060645769735490952/106341562018576649119*a^19 + 195512224103113106461/106341562018576649119*a^18 + 346714791065022627065/106341562018576649119*a^17 - 2724629993380080843565/106341562018576649119*a^16 - 1801507725219849119889/106341562018576649119*a^15 + 20399173913522690726623/106341562018576649119*a^14 + 2501816494514050819683/106341562018576649119*a^13 - 88321838110296443051387/106341562018576649119*a^12 + 15688079072925932736055/106341562018576649119*a^11 + 221350366634349870944903/106341562018576649119*a^10 - 77429910519443275365569/106341562018576649119*a^9 - 303112090167529668807735/106341562018576649119*a^8 + 135145380976671634633313/106341562018576649119*a^7 + 194967501932903735915569/106341562018576649119*a^6 - 102473588037526024969487/106341562018576649119*a^5 - 32556072526807797835445/106341562018576649119*a^4 + 28789543729733679305901/106341562018576649119*a^3 - 9348612469908886632777/106341562018576649119*a^2 - 1583834343778972683170/106341562018576649119*a + 22024900338083014717/2473059581827363933)*q^33 + (-163608579511137412/106341562018576649119*a^21 + 1840410481799311433/106341562018576649119*a^20 - 2361256045123926146/106341562018576649119*a^19 - 60738377623083540832/106341562018576649119*a^18 + 185209159437764910070/106341562018576649119*a^17 + 828638077989658859602/106341562018576649119*a^16 - 3069863407694551737128/106341562018576649119*a^15 - 6015660017947399609108/106341562018576649119*a^14 + 24902908385477324302832/106341562018576649119*a^13 + 24932483141782458024382/106341562018576649119*a^12 - 113951679527087385472060/106341562018576649119*a^11 - 59042828397019046296744/106341562018576649119*a^10 + 302419631887595301446050/106341562018576649119*a^9 + 77116122548647367749718/106341562018576649119*a^8 - 452625613955369395210142/106341562018576649119*a^7 - 54971410161541306569702/106341562018576649119*a^6 + 354354841534218540430994/106341562018576649119*a^5 + 24437182390686109245370/106341562018576649119*a^4 - 124525488533296897008986/106341562018576649119*a^3 - 9948259218024382980794/106341562018576649119*a^2 + 13649104335388405559547/106341562018576649119*a + 48976198122188635034/2473059581827363933)*q^34 + (-3229700687340763982/106341562018576649119*a^21 + 7737086920446803710/106341562018576649119*a^20 + 106381235166050629089/106341562018576649119*a^19 - 262015042159619387671/106341562018576649119*a^18 - 1446159258894733761513/106341562018576649119*a^17 + 3702051152123841607427/106341562018576649119*a^16 + 10428867785229687369663/106341562018576649119*a^15 - 28235954384274523463250/106341562018576649119*a^14 - 42604862684218626355034/106341562018576649119*a^13 + 125723366914348543343543/106341562018576649119*a^12 + 97270044638881937773841/106341562018576649119*a^11 - 330801525223516647890469/106341562018576649119*a^10 - 114273910130507915658541/106341562018576649119*a^9 + 499989209909604519359403/106341562018576649119*a^8 + 59493184004550343315955/106341562018576649119*a^7 - 407415705716671360116998/106341562018576649119*a^6 - 18045187244393863729842/106341562018576649119*a^5 + 155272284488725782390971/106341562018576649119*a^4 + 15805298199278316026709/106341562018576649119*a^3 - 17898132518519438907763/106341562018576649119*a^2 - 5808257435761813451995/106341562018576649119*a - 28354937548076875652/2473059581827363933)*q^35 + (-360596162069017452/106341562018576649119*a^21 + 4653299664848148657/106341562018576649119*a^20 + 11414301334442040190/106341562018576649119*a^19 - 161140416149804154445/106341562018576649119*a^18 - 140811468329342373223/106341562018576649119*a^17 + 2346537136792881935786/106341562018576649119*a^16 + 807506662169034477103/106341562018576649119*a^15 - 18663495100040392411595/106341562018576649119*a^14 - 1602619204814446033153/106341562018576649119*a^13 + 88186957663265347283499/106341562018576649119*a^12 - 4731883385626238809677/106341562018576649119*a^11 - 252714979334030371556153/106341562018576649119*a^10 + 31340919269617501050307/106341562018576649119*a^9 + 432018108552662194165671/106341562018576649119*a^8 - 64375636111932016432676/106341562018576649119*a^7 - 420040203216319814688493/106341562018576649119*a^6 + 62706678698804586923979/106341562018576649119*a^5 + 211595899319244226376495/106341562018576649119*a^4 - 28664627406064217887413/106341562018576649119*a^3 - 44539641050447719037452/106341562018576649119*a^2 + 4519790993174617525212/106341562018576649119*a + 35506695664172882513/2473059581827363933)*q^36 + (7394664530843307306/106341562018576649119*a^21 - 7606811372112628985/106341562018576649119*a^20 - 265748373574771212515/106341562018576649119*a^19 + 262649542497701585053/106341562018576649119*a^18 + 4059724885732822776975/106341562018576649119*a^17 - 3798927284152887127595/106341562018576649119*a^16 - 34396095662365500835307/106341562018576649119*a^15 + 29807565684935758419707/106341562018576649119*a^14 + 176999555379210375255647/106341562018576649119*a^13 - 137367368061688512257791/106341562018576649119*a^12 - 570418410750884597129585/106341562018576649119*a^11 + 376728273526138216865739/106341562018576649119*a^10 + 1147527903105757245029711/106341562018576649119*a^9 - 597146212364599738977311/106341562018576649119*a^8 - 1393620714368475271214341/106341562018576649119*a^7 + 510797249529005350919693/106341562018576649119*a^6 + 946073752160513183531115/106341562018576649119*a^5 - 205880561965320549938131/106341562018576649119*a^4 - 309538691264250150171849/106341562018576649119*a^3 + 23820849468389444377459/106341562018576649119*a^2 + 33753100856119673756800/106341562018576649119*a + 68552604153275274946/2473059581827363933)*q^37 + O(q^38)
*]> ;  // time = 6.64 seconds




J[313] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 313, 313, 313 ], new_dimensions := [ 2, 11, 12 ], dimensions := [ 2, 11, 12 ], intersection_graph := [ 0, 1, 41, 1, 0, 1, 41, 1, 0 ], ap_traces := [
[ 1, 3, 3, 2, 0, 7, 4, -2, 5, -16, 13, -16 ],
[ -8, -8, -6, -14, -11, -7, -15, 1, -44, -17, -3, -3 ],
[ 6, 1, -1, 6, 9, -8, 7, -1, 41, 29, -14, 5 ]
], hecke_fields := [
x^2 - x - 1,
x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 - 62*x^6 + 190*x^5 + 196*x^4 - 76*x^3 - 122*x^2 + 2*x + 17,
x^12 - 6*x^11 - 2*x^10 + 69*x^9 - 68*x^8 - 268*x^7 + 399*x^6 + 368*x^5 - 701*x^4 - 57*x^3 + 262*x^2 - 22*x - 19
], atkin_lehners := [
[ -1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 13 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 13 ]
], torsion_upper_bounds := [ 1, 1, 13 ], torsion_lower_bounds := [ 1, 1, 13 ], l_ratios := [ 1, 0, 1/13 ], analytic_sha_upper_bounds := [ 1, 0, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1 ], eigenvalues := [*
[
a,
-a + 2,
a + 1,
2*a,
-2*a + 1,
-3*a + 5,
2*a + 1,
-2*a,
a + 2,
-8,
3*a + 5,
-2*a - 7
],
[
a,
-29/13*a^10 - 184/13*a^9 - 159/13*a^8 + 1023/13*a^7 + 1831/13*a^6 - 1251/13*a^5 - 3525/13*a^4 + 133/13*a^3 + 2052/13*a^2 + 138/13*a - 290/13,
3/13*a^10 + 15/13*a^9 - 10/13*a^8 - 126/13*a^7 - 37/13*a^6 + 341/13*a^5 + 132/13*a^4 - 302/13*a^3 - 76/13*a^2 + 31/13*a + 4/13,
73/13*a^10 + 482/13*a^9 + 502/13*a^8 - 2559/13*a^7 - 5238/13*a^6 + 2582/13*a^5 + 9959/13*a^4 + 577/13*a^3 - 5875/13*a^2 - 602/13*a + 834/13,
-8/13*a^10 - 66/13*a^9 - 125/13*a^8 + 271/13*a^7 + 1013/13*a^6 + 135/13*a^5 - 1860/13*a^4 - 850/13*a^3 + 1117/13*a^2 + 368/13*a - 197/13,
73/13*a^10 + 482/13*a^9 + 502/13*a^8 - 2546/13*a^7 - 5199/13*a^6 + 2517/13*a^5 + 9751/13*a^4 + 655/13*a^3 - 5641/13*a^2 - 641/13*a + 795/13,
-3*a^10 - 20*a^9 - 21*a^8 + 107*a^7 + 217*a^6 - 114*a^5 - 408*a^4 - 6*a^3 + 232*a^2 + 11*a - 31,
-36/13*a^10 - 232/13*a^9 - 218/13*a^8 + 1252/13*a^7 + 2368/13*a^6 - 1349/13*a^5 - 4405/13*a^4 - 211/13*a^3 + 2459/13*a^2 + 395/13*a - 373/13,
16/13*a^10 + 106/13*a^9 + 107/13*a^8 - 581/13*a^7 - 1142/13*a^6 + 692/13*a^5 + 2225/13*a^4 - 120/13*a^3 - 1389/13*a^2 + 31/13*a + 186/13,
18/13*a^10 + 116/13*a^9 + 109/13*a^8 - 639/13*a^7 - 1236/13*a^6 + 720/13*a^5 + 2495/13*a^4 + 99/13*a^3 - 1587/13*a^2 - 152/13*a + 245/13,
-47/13*a^10 - 300/13*a^9 - 268/13*a^8 + 1662/13*a^7 + 3054/13*a^6 - 2010/13*a^5 - 5981/13*a^4 + 190/13*a^3 + 3678/13*a^2 + 251/13*a - 561/13,
16/13*a^10 + 132/13*a^9 + 237/13*a^8 - 607/13*a^7 - 2026/13*a^6 + 107/13*a^5 + 4019/13*a^4 + 1167/13*a^3 - 2663/13*a^2 - 567/13*a + 433/13
],
[
a,
a^10 - 3*a^9 - 12*a^8 + 35*a^7 + 54*a^6 - 139*a^5 - 112*a^4 + 200*a^3 + 100*a^2 - 47*a - 17,
a^11 - 4*a^10 - 9*a^9 + 47*a^8 + 18*a^7 - 190*a^6 + 34*a^5 + 290*a^4 - 113*a^3 - 105*a^2 + 33*a + 8,
-3/2*a^11 + 11/2*a^10 + 31/2*a^9 - 67*a^8 - 47*a^7 + 283*a^6 + 27/2*a^5 - 919/2*a^4 + 99*a^3 + 387/2*a^2 - 69/2*a - 33/2,
a^11 - 5*a^10 - 7*a^9 + 63*a^8 - 11*a^7 - 279*a^6 + 172*a^5 + 491*a^4 - 344*a^3 - 260*a^2 + 95*a + 32,
-a^11 + 2*a^10 + 15*a^9 - 22*a^8 - 92*a^7 + 77*a^6 + 276*a^5 - 72*a^4 - 355*a^3 - 52*a^2 + 80*a + 14,
a^11 - 4*a^10 - 9*a^9 + 47*a^8 + 19*a^7 - 193*a^6 + 27*a^5 + 313*a^4 - 102*a^3 - 151*a^2 + 36*a + 18,
3*a^11 - 12*a^10 - 27*a^9 + 141*a^8 + 55*a^7 - 573*a^6 + 95*a^5 + 892*a^4 - 326*a^3 - 357*a^2 + 96*a + 33,
-7/2*a^11 + 29/2*a^10 + 63/2*a^9 - 176*a^8 - 57*a^7 + 743*a^6 - 333/2*a^5 - 2431/2*a^4 + 498*a^3 + 1075/2*a^2 - 307/2*a - 101/2,
-a^11 + 4*a^10 + 9*a^9 - 46*a^8 - 22*a^7 + 185*a^6 - 2*a^5 - 296*a^4 + 46*a^3 + 147*a^2 - 19*a - 15,
3/2*a^11 - 15/2*a^10 - 17/2*a^9 + 88*a^8 - 32*a^7 - 364*a^6 + 581/2*a^5 + 1225/2*a^4 - 527*a^3 - 689/2*a^2 + 285/2*a + 77/2,
4*a^11 - 14*a^10 - 44*a^9 + 171*a^8 + 159*a^7 - 720*a^6 - 183*a^5 + 1141*a^4 - 31*a^3 - 411*a^2 + 39*a + 31
]
*], q_expansions := [*
q + a*q^2 + (-a + 2)*q^3 + (a - 1)*q^4 + (a + 1)*q^5 + (a - 1)*q^6 + 2*a*q^7 + (-2*a + 1)*q^8 + (-3*a + 2)*q^9 + (2*a + 1)*q^10 + (-2*a + 1)*q^11 + (2*a - 3)*q^12 + (-3*a + 5)*q^13 + (2*a + 2)*q^14 + q^15 - 3*a*q^16 + (2*a + 1)*q^17 + (-a - 3)*q^18 - 2*a*q^19 + a*q^20 + (2*a - 2)*q^21 + (-a - 2)*q^22 + (a + 2)*q^23 + (-3*a + 4)*q^24 + (3*a - 3)*q^25 + (2*a - 3)*q^26 + (-2*a + 1)*q^27 + 2*q^28 - 8*q^29 + a*q^30 + (3*a + 5)*q^31 + (a - 5)*q^32 + (-3*a + 4)*q^33 + (3*a + 2)*q^34 + (4*a + 2)*q^35 + (2*a - 5)*q^36 + (-2*a - 7)*q^37 + O(q^38),
q + a*q^2 + (-29/13*a^10 - 184/13*a^9 - 159/13*a^8 + 1023/13*a^7 + 1831/13*a^6 - 1251/13*a^5 - 3525/13*a^4 + 133/13*a^3 + 2052/13*a^2 + 138/13*a - 290/13)*q^3 + (a^2 - 2)*q^4 + (3/13*a^10 + 15/13*a^9 - 10/13*a^8 - 126/13*a^7 - 37/13*a^6 + 341/13*a^5 + 132/13*a^4 - 302/13*a^3 - 76/13*a^2 + 31/13*a + 4/13)*q^5 + (48/13*a^10 + 305/13*a^9 + 269/13*a^8 - 1678/13*a^7 - 3049/13*a^6 + 1985/13*a^5 + 5817/13*a^4 - 152/13*a^3 - 3400/13*a^2 - 232/13*a + 493/13)*q^6 + (73/13*a^10 + 482/13*a^9 + 502/13*a^8 - 2559/13*a^7 - 5238/13*a^6 + 2582/13*a^5 + 9959/13*a^4 + 577/13*a^3 - 5875/13*a^2 - 602/13*a + 834/13)*q^7 + (a^3 - 4*a)*q^8 + (-4*a^10 - 27*a^9 - 30*a^8 + 142*a^7 + 303*a^6 - 138*a^5 - 576*a^4 - 39*a^3 + 348*a^2 + 35*a - 55)*q^9 + (-9/13*a^10 - 58/13*a^9 - 48/13*a^8 + 326/13*a^7 + 527/13*a^6 - 438/13*a^5 - 890/13*a^4 + 152/13*a^3 + 397/13*a^2 - 2/13*a - 51/13)*q^10 + (-8/13*a^10 - 66/13*a^9 - 125/13*a^8 + 271/13*a^7 + 1013/13*a^6 + 135/13*a^5 - 1860/13*a^4 - 850/13*a^3 + 1117/13*a^2 + 368/13*a - 197/13)*q^11 + (-21/13*a^10 - 131/13*a^9 - 112/13*a^8 + 713/13*a^7 + 1299/13*a^6 - 801/13*a^5 - 2510/13*a^4 - 18/13*a^3 + 1520/13*a^2 + 121/13*a - 236/13)*q^12 + (73/13*a^10 + 482/13*a^9 + 502/13*a^8 - 2546/13*a^7 - 5199/13*a^6 + 2517/13*a^5 + 9751/13*a^4 + 655/13*a^3 - 5641/13*a^2 - 641/13*a + 795/13)*q^13 + (-102/13*a^10 - 666/13*a^9 - 661/13*a^8 + 3595/13*a^7 + 7108/13*a^6 - 3911/13*a^5 - 13731/13*a^4 - 327/13*a^3 + 8304/13*a^2 + 688/13*a - 1241/13)*q^14 + (10*a^10 + 66*a^9 + 68*a^8 - 353*a^7 - 715*a^6 + 369*a^5 + 1371*a^4 + 58*a^3 - 826*a^2 - 77*a + 123)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^10 - 20*a^9 - 21*a^8 + 107*a^7 + 217*a^6 - 114*a^5 - 408*a^4 - 6*a^3 + 232*a^2 + 11*a - 31)*q^17 + (5*a^10 + 34*a^9 + 38*a^8 - 181*a^7 - 386*a^6 + 184*a^5 + 745*a^4 + 44*a^3 - 453*a^2 - 47*a + 68)*q^18 + (-36/13*a^10 - 232/13*a^9 - 218/13*a^8 + 1252/13*a^7 + 2368/13*a^6 - 1349/13*a^5 - 4405/13*a^4 - 211/13*a^3 + 2459/13*a^2 + 395/13*a - 373/13)*q^19 + (8/13*a^10 + 66/13*a^9 + 112/13*a^8 - 310/13*a^7 - 922/13*a^6 + 138/13*a^5 + 1652/13*a^4 + 317/13*a^3 - 948/13*a^2 - 95/13*a + 145/13)*q^20 + (-64/13*a^10 - 437/13*a^9 - 506/13*a^8 + 2285/13*a^7 + 5062/13*a^6 - 2131/13*a^5 - 9784/13*a^4 - 820/13*a^3 + 6063/13*a^2 + 617/13*a - 939/13)*q^21 + (-2/13*a^10 + 3/13*a^9 + 63/13*a^8 + 45/13*a^7 - 361/13*a^6 - 340/13*a^5 + 718/13*a^4 + 509/13*a^3 - 608/13*a^2 - 181/13*a + 136/13)*q^22 + (16/13*a^10 + 106/13*a^9 + 107/13*a^8 - 581/13*a^7 - 1142/13*a^6 + 692/13*a^5 + 2225/13*a^4 - 120/13*a^3 - 1389/13*a^2 + 31/13*a + 186/13)*q^23 + (-59/13*a^10 - 386/13*a^9 - 371/13*a^8 + 2114/13*a^7 + 3995/13*a^6 - 2490/13*a^5 - 7536/13*a^4 + 228/13*a^3 + 4359/13*a^2 + 270/13*a - 629/13)*q^24 + (-12*a^10 - 79*a^9 - 80*a^8 + 427*a^7 + 854*a^6 - 465*a^5 - 1660*a^4 - 45*a^3 + 1019*a^2 + 90*a - 157)*q^25 + (-102/13*a^10 - 666/13*a^9 - 648/13*a^8 + 3634/13*a^7 + 7043/13*a^6 - 4119/13*a^5 - 13653/13*a^4 - 93/13*a^3 + 8265/13*a^2 + 649/13*a - 1241/13)*q^26 + (68/13*a^10 + 457/13*a^9 + 497/13*a^8 - 2427/13*a^7 - 5081/13*a^6 + 2473/13*a^5 + 9687/13*a^4 + 478/13*a^3 - 5770/13*a^2 - 554/13*a + 823/13)*q^27 + (4/13*a^10 + 7/13*a^9 - 61/13*a^8 - 116/13*a^7 + 241/13*a^6 + 485/13*a^5 - 253/13*a^4 - 602/13*a^3 - 6/13*a^2 + 167/13*a + 66/13)*q^28 + (18/13*a^10 + 116/13*a^9 + 109/13*a^8 - 639/13*a^7 - 1236/13*a^6 + 720/13*a^5 + 2495/13*a^4 + 99/13*a^3 - 1587/13*a^2 - 152/13*a + 245/13)*q^29 + (-14*a^10 - 92*a^9 - 93*a^8 + 495*a^7 + 989*a^6 - 529*a^5 - 1902*a^4 - 66*a^3 + 1143*a^2 + 103*a - 170)*q^30 + (-47/13*a^10 - 300/13*a^9 - 268/13*a^8 + 1662/13*a^7 + 3054/13*a^6 - 2010/13*a^5 - 5981/13*a^4 + 190/13*a^3 + 3678/13*a^2 + 251/13*a - 561/13)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (105/13*a^10 + 694/13*a^9 + 716/13*a^8 - 3734/13*a^7 - 7587/13*a^6 + 3966/13*a^5 + 14760/13*a^4 + 597/13*a^3 - 9017/13*a^2 - 787/13*a + 1349/13)*q^33 + (4*a^10 + 27*a^9 + 29*a^8 - 146*a^7 - 300*a^6 + 162*a^5 + 582*a^4 + 4*a^3 - 355*a^2 - 25*a + 51)*q^34 + (-14/13*a^10 - 83/13*a^9 - 40/13*a^8 + 497/13*a^7 + 593/13*a^6 - 794/13*a^5 - 915/13*a^4 + 430/13*a^3 + 190/13*a^2 - 32/13*a + 16/13)*q^35 + (2*a^10 + 12*a^9 + 9*a^8 - 65*a^7 - 112*a^6 + 71*a^5 + 216*a^4 + 5*a^3 - 133*a^2 - 12*a + 25)*q^36 + (16/13*a^10 + 132/13*a^9 + 237/13*a^8 - 607/13*a^7 - 2026/13*a^6 + 107/13*a^5 + 4019/13*a^4 + 1167/13*a^3 - 2663/13*a^2 - 567/13*a + 433/13)*q^37 + O(q^38),
q + a*q^2 + (a^10 - 3*a^9 - 12*a^8 + 35*a^7 + 54*a^6 - 139*a^5 - 112*a^4 + 200*a^3 + 100*a^2 - 47*a - 17)*q^3 + (a^2 - 2)*q^4 + (a^11 - 4*a^10 - 9*a^9 + 47*a^8 + 18*a^7 - 190*a^6 + 34*a^5 + 290*a^4 - 113*a^3 - 105*a^2 + 33*a + 8)*q^5 + (a^11 - 3*a^10 - 12*a^9 + 35*a^8 + 54*a^7 - 139*a^6 - 112*a^5 + 200*a^4 + 100*a^3 - 47*a^2 - 17*a)*q^6 + (-3/2*a^11 + 11/2*a^10 + 31/2*a^9 - 67*a^8 - 47*a^7 + 283*a^6 + 27/2*a^5 - 919/2*a^4 + 99*a^3 + 387/2*a^2 - 69/2*a - 33/2)*q^7 + (a^3 - 4*a)*q^8 + (-3*a^11 + 12*a^10 + 28*a^9 - 145*a^8 - 61*a^7 + 608*a^6 - 94*a^5 - 981*a^4 + 356*a^3 + 412*a^2 - 106*a - 37)*q^9 + (2*a^11 - 7*a^10 - 22*a^9 + 86*a^8 + 78*a^7 - 365*a^6 - 78*a^5 + 588*a^4 - 48*a^3 - 229*a^2 + 30*a + 19)*q^10 + (a^11 - 5*a^10 - 7*a^9 + 63*a^8 - 11*a^7 - 279*a^6 + 172*a^5 + 491*a^4 - 344*a^3 - 260*a^2 + 95*a + 32)*q^11 + (3*a^11 - 12*a^10 - 28*a^9 + 146*a^8 + 59*a^7 - 619*a^6 + 110*a^5 + 1025*a^4 - 390*a^3 - 479*a^2 + 116*a + 53)*q^12 + (-a^11 + 2*a^10 + 15*a^9 - 22*a^8 - 92*a^7 + 77*a^6 + 276*a^5 - 72*a^4 - 355*a^3 - 52*a^2 + 80*a + 14)*q^13 + (-7/2*a^11 + 25/2*a^10 + 73/2*a^9 - 149*a^8 - 119*a^7 + 612*a^6 + 185/2*a^5 - 1905/2*a^4 + 108*a^3 + 717/2*a^2 - 99/2*a - 57/2)*q^14 + (-a^11 + 4*a^10 + 9*a^9 - 47*a^8 - 18*a^7 + 190*a^6 - 35*a^5 - 288*a^4 + 119*a^3 + 96*a^2 - 42*a - 3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^11 - 4*a^10 - 9*a^9 + 47*a^8 + 19*a^7 - 193*a^6 + 27*a^5 + 313*a^4 - 102*a^3 - 151*a^2 + 36*a + 18)*q^17 + (-6*a^11 + 22*a^10 + 62*a^9 - 265*a^8 - 196*a^7 + 1103*a^6 + 123*a^5 - 1747*a^4 + 241*a^3 + 680*a^2 - 103*a - 57)*q^18 + (3*a^11 - 12*a^10 - 27*a^9 + 141*a^8 + 55*a^7 - 573*a^6 + 95*a^5 + 892*a^4 - 326*a^3 - 357*a^2 + 96*a + 33)*q^19 + (3*a^11 - 10*a^10 - 34*a^9 + 120*a^8 + 135*a^7 - 496*a^6 - 216*a^5 + 774*a^4 + 111*a^3 - 284*a^2 - 3*a + 22)*q^20 + (2*a^11 - 4*a^10 - 31*a^9 + 48*a^8 + 189*a^7 - 186*a^6 - 545*a^5 + 208*a^4 + 662*a^3 + 103*a^2 - 141*a - 33)*q^21 + (a^11 - 5*a^10 - 6*a^9 + 57*a^8 - 11*a^7 - 227*a^6 + 123*a^5 + 357*a^4 - 203*a^3 - 167*a^2 + 54*a + 19)*q^22 + (-7/2*a^11 + 29/2*a^10 + 63/2*a^9 - 176*a^8 - 57*a^7 + 743*a^6 - 333/2*a^5 - 2431/2*a^4 + 498*a^3 + 1075/2*a^2 - 307/2*a - 101/2)*q^23 + (4*a^11 - 16*a^10 - 37*a^9 + 193*a^8 + 77*a^7 - 809*a^6 + 145*a^5 + 1313*a^4 - 508*a^3 - 576*a^2 + 153*a + 57)*q^24 + (2*a^11 - 7*a^10 - 22*a^9 + 86*a^8 + 78*a^7 - 364*a^6 - 80*a^5 + 581*a^4 - 35*a^3 - 218*a^2 + 9*a + 21)*q^25 + (-4*a^11 + 13*a^10 + 47*a^9 - 160*a^8 - 191*a^7 + 675*a^6 + 296*a^5 - 1056*a^4 - 109*a^3 + 342*a^2 - 8*a - 19)*q^26 + (2*a^11 - 6*a^10 - 24*a^9 + 70*a^8 + 107*a^7 - 276*a^6 - 215*a^5 + 386*a^4 + 175*a^3 - 70*a^2 - 17*a - 4)*q^27 + (-11/2*a^11 + 37/2*a^10 + 123/2*a^9 - 223*a^8 - 232*a^7 + 923*a^6 + 617/2*a^5 - 2853/2*a^4 - 39*a^3 + 961/2*a^2 - 73/2*a - 67/2)*q^28 + (-a^11 + 4*a^10 + 9*a^9 - 46*a^8 - 22*a^7 + 185*a^6 - 2*a^5 - 296*a^4 + 46*a^3 + 147*a^2 - 19*a - 15)*q^29 + (-2*a^11 + 7*a^10 + 22*a^9 - 86*a^8 - 78*a^7 + 364*a^6 + 80*a^5 - 582*a^4 + 39*a^3 + 220*a^2 - 25*a - 19)*q^30 + (3/2*a^11 - 15/2*a^10 - 17/2*a^9 + 88*a^8 - 32*a^7 - 364*a^6 + 581/2*a^5 + 1225/2*a^4 - 527*a^3 - 689/2*a^2 + 285/2*a + 77/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^11 - 7*a^10 - 22*a^9 + 84*a^8 + 84*a^7 - 347*a^6 - 130*a^5 + 536*a^4 + 73*a^3 - 177*a^2 - 11*a + 7)*q^33 + (2*a^11 - 7*a^10 - 22*a^9 + 87*a^8 + 75*a^7 - 372*a^6 - 55*a^5 + 599*a^4 - 94*a^3 - 226*a^2 + 40*a + 19)*q^34 + (-a^11 + 3*a^10 + 12*a^9 - 34*a^8 - 57*a^7 + 131*a^6 + 137*a^5 - 184*a^4 - 154*a^3 + 47*a^2 + 27*a + 1)*q^35 + (-8*a^11 + 26*a^10 + 93*a^9 - 314*a^8 - 383*a^7 + 1301*a^6 + 649*a^5 - 2003*a^4 - 374*a^3 + 645*a^2 + 23*a - 40)*q^36 + (4*a^11 - 14*a^10 - 44*a^9 + 171*a^8 + 159*a^7 - 720*a^6 - 183*a^5 + 1141*a^4 - 31*a^3 - 411*a^2 + 39*a + 31)*q^37 + O(q^38)
*]> ;  // time = 4.889 seconds




J[314] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 314, 314, 314, 157, 157 ], new_dimensions := [ 1, 6, 7, 5, 7 ], dimensions := [ 1, 6, 7, 10, 14 ], intersection_graph := [ 0, 1, 1, 5, 1, 1, 0, 1, 1, 2147, 1, 1, 0, 709, 1, 5, 1, 709, 0, 1, 1, 2147, 1, 1, 0 ], ap_traces := [
[ -1, 0, 0, -3, -2, -1, 3, -4, -1, 0, -6, -1 ],
[ -6, 3, 1, 3, 9, 4, -7, 17, -3, -5, 18, 14 ],
[ 7, -1, 3, 4, -1, 7, 4, 1, 0, 5, 0, -3 ]
], hecke_fields := [
x - 1,
x^6 - 3*x^5 - 9*x^4 + 26*x^3 + 20*x^2 - 43*x - 25,
x^7 + x^6 - 17*x^5 - 6*x^4 + 84*x^3 - 19*x^2 - 73*x + 4
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 6441, 3 ],
[ 56011, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 56011, 1 ]
], torsion_upper_bounds := [ 1, 3, 79 ], torsion_lower_bounds := [ 1, 3, 79 ], l_ratios := [ 0, 1/3, 709/79 ], analytic_sha_upper_bounds := [ 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1 ], eigenvalues := [*
[ -1, 0, 0, -3, -2, -1, 3, -4, -1, 0, -6, -1 ],
[
-1,
a,
-5/13*a^5 + 8/13*a^4 + 51/13*a^3 - 56/13*a^2 - 103/13*a + 24/13,
-2/13*a^5 - 2/13*a^4 + 23/13*a^3 + 14/13*a^2 - 49/13*a - 6/13,
5/13*a^5 + 5/13*a^4 - 64/13*a^3 - 61/13*a^2 + 181/13*a + 171/13,
8/13*a^5 - 18/13*a^4 - 66/13*a^3 + 126/13*a^2 + 92/13*a - 80/13,
8/13*a^5 - 5/13*a^4 - 92/13*a^3 - 4/13*a^2 + 248/13*a + 154/13,
6/13*a^5 - 7/13*a^4 - 56/13*a^3 + 36/13*a^2 + 82/13*a + 70/13,
-6/13*a^5 - 6/13*a^4 + 82/13*a^3 + 81/13*a^2 - 264/13*a - 226/13,
7/13*a^5 - 19/13*a^4 - 48/13*a^3 + 133/13*a^2 + 9/13*a - 109/13,
2/13*a^5 + 2/13*a^4 - 10/13*a^3 - 40/13*a^2 - 16/13*a + 136/13,
-10/13*a^5 + 16/13*a^4 + 76/13*a^3 - 86/13*a^2 - 76/13*a + 22/13
],
[
1,
a,
-1/3*a^5 + 11/3*a^3 - 4/3*a^2 - 19/3*a + 4/3,
1/15*a^6 + 7/15*a^5 - a^4 - 71/15*a^3 + 26/5*a^2 + 28/5*a + 1/15,
-1/15*a^6 - 2/15*a^5 + 4/3*a^4 + 2/5*a^3 - 41/5*a^2 + 86/15*a + 74/15,
-1/15*a^6 + 1/5*a^5 + a^4 - 8/5*a^3 - 38/15*a^2 - 29/15*a + 49/15,
1/15*a^6 - 1/5*a^5 - 4/3*a^4 + 34/15*a^3 + 88/15*a^2 - 91/15*a - 13/5,
2/15*a^6 + 4/15*a^5 - a^4 - 32/15*a^3 - 4/15*a^2 + 68/15*a + 4/5,
1/5*a^6 + 1/15*a^5 - 3*a^4 - 8/15*a^3 + 169/15*a^2 + 7/15*a - 97/15,
-1/3*a^6 - 2/3*a^5 + 14/3*a^4 + 6*a^3 - 17*a^2 - 16/3*a + 8/3,
2/15*a^6 + 4/15*a^5 - 8/3*a^4 - 14/5*a^3 + 72/5*a^2 + 38/15*a - 118/15,
-7/15*a^6 - 3/5*a^5 + 19/3*a^4 + 62/15*a^3 - 346/15*a^2 + 37/15*a + 51/5
]
*], q_expansions := [*
q - q^2 + q^4 - 3*q^7 - q^8 - 3*q^9 - 2*q^11 - q^13 + 3*q^14 + q^16 + 3*q^17 + 3*q^18 - 4*q^19 + 2*q^22 - q^23 - 5*q^25 + q^26 - 3*q^28 - 6*q^31 - q^32 - 3*q^34 - 3*q^36 - q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-5/13*a^5 + 8/13*a^4 + 51/13*a^3 - 56/13*a^2 - 103/13*a + 24/13)*q^5 - a*q^6 + (-2/13*a^5 - 2/13*a^4 + 23/13*a^3 + 14/13*a^2 - 49/13*a - 6/13)*q^7 - q^8 + (a^2 - 3)*q^9 + (5/13*a^5 - 8/13*a^4 - 51/13*a^3 + 56/13*a^2 + 103/13*a - 24/13)*q^10 + (5/13*a^5 + 5/13*a^4 - 64/13*a^3 - 61/13*a^2 + 181/13*a + 171/13)*q^11 + a*q^12 + (8/13*a^5 - 18/13*a^4 - 66/13*a^3 + 126/13*a^2 + 92/13*a - 80/13)*q^13 + (2/13*a^5 + 2/13*a^4 - 23/13*a^3 - 14/13*a^2 + 49/13*a + 6/13)*q^14 + (-7/13*a^5 + 6/13*a^4 + 74/13*a^3 - 3/13*a^2 - 191/13*a - 125/13)*q^15 + q^16 + (8/13*a^5 - 5/13*a^4 - 92/13*a^3 - 4/13*a^2 + 248/13*a + 154/13)*q^17 + (-a^2 + 3)*q^18 + (6/13*a^5 - 7/13*a^4 - 56/13*a^3 + 36/13*a^2 + 82/13*a + 70/13)*q^19 + (-5/13*a^5 + 8/13*a^4 + 51/13*a^3 - 56/13*a^2 - 103/13*a + 24/13)*q^20 + (-8/13*a^5 + 5/13*a^4 + 66/13*a^3 - 9/13*a^2 - 92/13*a - 50/13)*q^21 + (-5/13*a^5 - 5/13*a^4 + 64/13*a^3 + 61/13*a^2 - 181/13*a - 171/13)*q^22 + (-6/13*a^5 - 6/13*a^4 + 82/13*a^3 + 81/13*a^2 - 264/13*a - 226/13)*q^23 - a*q^24 + (-4/13*a^5 + 22/13*a^4 + 7/13*a^3 - 180/13*a^2 + 97/13*a + 287/13)*q^25 + (-8/13*a^5 + 18/13*a^4 + 66/13*a^3 - 126/13*a^2 - 92/13*a + 80/13)*q^26 + (a^3 - 6*a)*q^27 + (-2/13*a^5 - 2/13*a^4 + 23/13*a^3 + 14/13*a^2 - 49/13*a - 6/13)*q^28 + (7/13*a^5 - 19/13*a^4 - 48/13*a^3 + 133/13*a^2 + 9/13*a - 109/13)*q^29 + (7/13*a^5 - 6/13*a^4 - 74/13*a^3 + 3/13*a^2 + 191/13*a + 125/13)*q^30 + (2/13*a^5 + 2/13*a^4 - 10/13*a^3 - 40/13*a^2 - 16/13*a + 136/13)*q^31 - q^32 + (20/13*a^5 - 19/13*a^4 - 191/13*a^3 + 81/13*a^2 + 386/13*a + 125/13)*q^33 + (-8/13*a^5 + 5/13*a^4 + 92/13*a^3 + 4/13*a^2 - 248/13*a - 154/13)*q^34 + (-17/13*a^5 + 22/13*a^4 + 163/13*a^3 - 115/13*a^2 - 345/13*a - 38/13)*q^35 + (a^2 - 3)*q^36 + (-10/13*a^5 + 16/13*a^4 + 76/13*a^3 - 86/13*a^2 - 76/13*a + 22/13)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-1/3*a^5 + 11/3*a^3 - 4/3*a^2 - 19/3*a + 4/3)*q^5 + a*q^6 + (1/15*a^6 + 7/15*a^5 - a^4 - 71/15*a^3 + 26/5*a^2 + 28/5*a + 1/15)*q^7 + q^8 + (a^2 - 3)*q^9 + (-1/3*a^5 + 11/3*a^3 - 4/3*a^2 - 19/3*a + 4/3)*q^10 + (-1/15*a^6 - 2/15*a^5 + 4/3*a^4 + 2/5*a^3 - 41/5*a^2 + 86/15*a + 74/15)*q^11 + a*q^12 + (-1/15*a^6 + 1/5*a^5 + a^4 - 8/5*a^3 - 38/15*a^2 - 29/15*a + 49/15)*q^13 + (1/15*a^6 + 7/15*a^5 - a^4 - 71/15*a^3 + 26/5*a^2 + 28/5*a + 1/15)*q^14 + (-1/3*a^6 + 11/3*a^4 - 4/3*a^3 - 19/3*a^2 + 4/3*a)*q^15 + q^16 + (1/15*a^6 - 1/5*a^5 - 4/3*a^4 + 34/15*a^3 + 88/15*a^2 - 91/15*a - 13/5)*q^17 + (a^2 - 3)*q^18 + (2/15*a^6 + 4/15*a^5 - a^4 - 32/15*a^3 - 4/15*a^2 + 68/15*a + 4/5)*q^19 + (-1/3*a^5 + 11/3*a^3 - 4/3*a^2 - 19/3*a + 4/3)*q^20 + (2/5*a^6 + 2/15*a^5 - 13/3*a^4 - 2/5*a^3 + 103/15*a^2 + 74/15*a - 4/15)*q^21 + (-1/15*a^6 - 2/15*a^5 + 4/3*a^4 + 2/5*a^3 - 41/5*a^2 + 86/15*a + 74/15)*q^22 + (1/5*a^6 + 1/15*a^5 - 3*a^4 - 8/15*a^3 + 169/15*a^2 + 7/15*a - 97/15)*q^23 + a*q^24 + (-2/3*a^4 + 1/3*a^3 + 20/3*a^2 - 7*a - 11/3)*q^25 + (-1/15*a^6 + 1/5*a^5 + a^4 - 8/5*a^3 - 38/15*a^2 - 29/15*a + 49/15)*q^26 + (a^3 - 6*a)*q^27 + (1/15*a^6 + 7/15*a^5 - a^4 - 71/15*a^3 + 26/5*a^2 + 28/5*a + 1/15)*q^28 + (-1/3*a^6 - 2/3*a^5 + 14/3*a^4 + 6*a^3 - 17*a^2 - 16/3*a + 8/3)*q^29 + (-1/3*a^6 + 11/3*a^4 - 4/3*a^3 - 19/3*a^2 + 4/3*a)*q^30 + (2/15*a^6 + 4/15*a^5 - 8/3*a^4 - 14/5*a^3 + 72/5*a^2 + 38/15*a - 118/15)*q^31 + q^32 + (-1/15*a^6 + 1/5*a^5 - 13/5*a^3 + 67/15*a^2 + 1/15*a + 4/15)*q^33 + (1/15*a^6 - 1/5*a^5 - 4/3*a^4 + 34/15*a^3 + 88/15*a^2 - 91/15*a - 13/5)*q^34 + (2/15*a^6 - 1/15*a^5 - 4/3*a^4 + 11/5*a^3 + 11/15*a^2 - 39/5*a + 4/5)*q^35 + (a^2 - 3)*q^36 + (-7/15*a^6 - 3/5*a^5 + 19/3*a^4 + 62/15*a^3 - 346/15*a^2 + 37/15*a + 51/5)*q^37 + O(q^38)
*]> ;  // time = 68.721 seconds




J[317] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 317, 317 ], new_dimensions := [ 11, 15 ], dimensions := [ 11, 15 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -3, -11, -4, -20, -10, -16, -7, -31, 0, 12, -12, -16 ],
[ 1, 11, 2, 20, 6, 14, 5, 31, 0, -2, 12, 14 ]
], hecke_fields := [
x^11 + 3*x^10 - 10*x^9 - 32*x^8 + 31*x^7 + 109*x^6 - 42*x^5 - 147*x^4 + 35*x^3 + 68*x^2 - 19*x - 1,
x^15 - x^14 - 22*x^13 + 22*x^12 + 188*x^11 - 184*x^10 - 786*x^9 + 723*x^8 + 1666*x^7 - 1315*x^6 - 1715*x^5 + 910*x^4 + 829*x^3 - 168*x^2 - 129*x + 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 79 ]
], tamagawa_numbers := [
[ 1 ],
[ 79 ]
], torsion_upper_bounds := [ 1, 79 ], torsion_lower_bounds := [ 1, 79 ], l_ratios := [ 0, 1/79 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
113/1046*a^10 - 154/523*a^9 - 1081/523*a^8 + 2021/523*a^7 + 12971/1046*a^6 - 9125/523*a^5 - 14011/523*a^4 + 33587/1046*a^3 + 8762/523*a^2 - 10392/523*a + 1175/1046,
234/523*a^10 + 834/523*a^9 - 1950/523*a^8 - 8588/523*a^7 + 3603/523*a^6 + 27458/523*a^5 + 2/523*a^4 - 33780/523*a^3 - 1733/523*a^2 + 13352/523*a - 964/523,
-250/523*a^10 - 596/523*a^9 + 2432/523*a^8 + 5322/523*a^7 - 7041/523*a^6 - 12072/523*a^5 + 7673/523*a^4 + 5045/523*a^3 - 2109/523*a^2 + 3374/523*a - 1822/523,
7/523*a^10 + 92/523*a^9 + 116/523*a^8 - 990/523*a^7 - 1830/523*a^6 + 3271/523*a^5 + 6285/523*a^4 - 4001/523*a^3 - 4922/523*a^2 + 2031/523*a - 1723/523,
59/523*a^10 + 103/523*a^9 - 666/523*a^8 - 574/523*a^7 + 2806/523*a^6 - 1494/523*a^5 - 5976/523*a^4 + 9761/523*a^3 + 4165/523*a^2 - 9704/523*a + 794/523,
-677/523*a^10 - 1501/523*a^9 + 7385/523*a^8 + 14981/523*a^7 - 25638/523*a^6 - 44243/523*a^5 + 33797/523*a^4 + 43567/523*a^3 - 13575/523*a^2 - 8595/523*a - 273/523,
365/1046*a^10 + 456/523*a^9 - 1608/523*a^8 - 3770/523*a^7 + 7759/1046*a^6 + 6867/523*a^5 - 4435/523*a^4 + 427/1046*a^3 + 5415/523*a^2 - 3645/523*a - 7507/1046,
-77/523*a^10 - 1012/523*a^9 - 753/523*a^8 + 10890/523*a^7 + 11239/523*a^6 - 37550/523*a^5 - 28341/523*a^4 + 51333/523*a^3 + 14917/523*a^2 - 22864/523*a + 2740/523,
-573/523*a^10 - 956/523*a^9 + 6867/523*a^8 + 9014/523*a^7 - 28395/523*a^6 - 24485/523*a^5 + 50592/523*a^4 + 24021/523*a^3 - 33580/523*a^2 - 8530/523*a + 3715/523,
182/523*a^10 + 823/523*a^9 - 1168/523*a^8 - 9004/523*a^7 - 1033/523*a^6 + 32223/523*a^5 + 12786/523*a^4 - 47542/523*a^3 - 13958/523*a^2 + 26133/523*a - 1912/523,
-947/1046*a^10 - 769/523*a^9 + 6125/523*a^8 + 8241/523*a^7 - 54497/1046*a^6 - 27563/523*a^5 + 49786/523*a^4 + 65647/1046*a^3 - 33909/523*a^2 - 9285/523*a + 8805/1046
],
[
a,
-2929/9028*a^14 + 3305/4514*a^13 + 31073/4514*a^12 - 35302/2257*a^11 - 248773/4514*a^10 + 573563/4514*a^9 + 919473/4514*a^8 - 4378801/9028*a^7 - 3005667/9028*a^6 + 1935368/2257*a^5 + 1592783/9028*a^4 - 5224775/9028*a^3 - 38286/2257*a^2 + 248643/2257*a - 29861/9028,
6887/4514*a^14 - 10787/4514*a^13 - 144831/4514*a^12 + 232879/4514*a^11 + 1153635/4514*a^10 - 1909601/4514*a^9 - 4281777/4514*a^8 + 3670378/2257*a^7 + 7216765/4514*a^6 - 12991581/4514*a^5 - 2205724/2257*a^4 + 8622515/4514*a^3 + 846049/4514*a^2 - 1576987/4514*a + 2893/2257,
-175/122*a^14 + 251/122*a^13 + 3703/122*a^12 - 5485/122*a^11 - 29711/122*a^10 + 45521/122*a^9 + 111249/122*a^8 - 88481/61*a^7 - 189781/122*a^6 + 316101/122*a^5 + 59244/61*a^4 - 210853/122*a^3 - 22725/122*a^2 + 38633/122*a - 55/61,
93/4514*a^14 - 1741/4514*a^13 - 2817/4514*a^12 + 35583/4514*a^11 + 30911/4514*a^10 - 277307/4514*a^9 - 158111/4514*a^8 + 512581/2257*a^7 + 392617/4514*a^6 - 1800053/4514*a^5 - 224672/2257*a^4 + 1279815/4514*a^3 + 214893/4514*a^2 - 246421/4514*a - 3148/2257,
-2172/2257*a^14 + 2583/2257*a^13 + 45696/2257*a^12 - 56593/2257*a^11 - 365097/2257*a^10 + 469928/2257*a^9 + 1366782/2257*a^8 - 1822073/2257*a^7 - 2356643/2257*a^6 + 3225372/2257*a^5 + 1542585/2257*a^4 - 2096010/2257*a^3 - 333769/2257*a^2 + 368683/2257*a + 6380/2257,
-1331/2257*a^14 + 3359/4514*a^13 + 55369/4514*a^12 - 73415/4514*a^11 - 434575/4514*a^10 + 608867/4514*a^9 + 1576641/4514*a^8 - 2363585/4514*a^7 - 1269561/2257*a^6 + 4210995/4514*a^5 + 1333379/4514*a^4 - 1396928/2257*a^3 - 103501/4514*a^2 + 509893/4514*a - 20707/4514,
-5113/9028*a^14 + 2227/2257*a^13 + 27379/2257*a^12 - 96937/4514*a^11 - 222537/2257*a^10 + 400941/2257*a^9 + 845411/2257*a^8 - 6220667/9028*a^7 - 5890799/9028*a^6 + 5556089/4514*a^5 + 3910273/9028*a^4 - 7456363/9028*a^3 - 501477/4514*a^2 + 676885/4514*a + 58729/9028,
16115/4514*a^14 - 24093/4514*a^13 - 339749/4514*a^12 + 524035/4514*a^11 + 2711963/4514*a^10 - 4328791/4514*a^9 - 10072577/4514*a^8 + 8377156/2257*a^7 + 16914173/4514*a^6 - 29824007/4514*a^5 - 5050561/2257*a^4 + 19893597/4514*a^3 + 1706727/4514*a^2 - 3701483/4514*a + 27260/2257,
1553/2257*a^14 - 921/2257*a^13 - 32698/2257*a^12 + 22740/2257*a^11 + 261188/2257*a^10 - 208659/2257*a^9 - 974375/2257*a^8 + 875377/2257*a^7 + 1658616/2257*a^6 - 1630991/2257*a^5 - 1029345/2257*a^4 + 1063558/2257*a^3 + 161992/2257*a^2 - 187810/2257*a + 11815/2257,
6683/4514*a^14 - 5559/2257*a^13 - 70600/2257*a^12 + 120478/2257*a^11 + 564211/2257*a^10 - 992156/2257*a^9 - 2093468/2257*a^8 + 7663319/4514*a^7 + 6987355/4514*a^6 - 6818910/2257*a^5 - 4089421/4514*a^4 + 9143453/4514*a^3 + 354317/2257*a^2 - 866859/2257*a + 10787/4514,
20437/9028*a^14 - 6599/2257*a^13 - 216293/4514*a^12 + 292305/4514*a^11 + 1735175/4514*a^10 - 1228459/2257*a^9 - 6487451/4514*a^8 + 19324327/9028*a^7 + 22018405/9028*a^6 - 8716942/2257*a^5 - 13481329/9028*a^4 + 23502269/9028*a^3 + 606540/2257*a^2 - 2236959/4514*a + 8909/9028
]
*], q_expansions := [*
q + a*q^2 + (113/1046*a^10 - 154/523*a^9 - 1081/523*a^8 + 2021/523*a^7 + 12971/1046*a^6 - 9125/523*a^5 - 14011/523*a^4 + 33587/1046*a^3 + 8762/523*a^2 - 10392/523*a + 1175/1046)*q^3 + (a^2 - 2)*q^4 + (234/523*a^10 + 834/523*a^9 - 1950/523*a^8 - 8588/523*a^7 + 3603/523*a^6 + 27458/523*a^5 + 2/523*a^4 - 33780/523*a^3 - 1733/523*a^2 + 13352/523*a - 964/523)*q^5 + (-647/1046*a^10 - 516/523*a^9 + 3829/523*a^8 + 4734/523*a^7 - 30567/1046*a^6 - 11638/523*a^5 + 25099/523*a^4 + 13569/1046*a^3 - 14234/523*a^2 + 1661/523*a + 113/1046)*q^6 + (-250/523*a^10 - 596/523*a^9 + 2432/523*a^8 + 5322/523*a^7 - 7041/523*a^6 - 12072/523*a^5 + 7673/523*a^4 + 5045/523*a^3 - 2109/523*a^2 + 3374/523*a - 1822/523)*q^7 + (a^3 - 4*a)*q^8 + (-385/1046*a^10 + 85/523*a^9 + 3086/523*a^8 - 1540/523*a^7 - 33761/1046*a^6 + 9156/523*a^5 + 36624/523*a^4 - 41445/1046*a^3 - 27298/523*a^2 + 14491/523*a + 2717/1046)*q^9 + (132/523*a^10 + 390/523*a^9 - 1100/523*a^8 - 3651/523*a^7 + 1952/523*a^6 + 9830/523*a^5 + 618/523*a^4 - 9923/523*a^3 - 2560/523*a^2 + 3482/523*a + 234/523)*q^10 + (7/523*a^10 + 92/523*a^9 + 116/523*a^8 - 990/523*a^7 - 1830/523*a^6 + 3271/523*a^5 + 6285/523*a^4 - 4001/523*a^3 - 4922/523*a^2 + 2031/523*a - 1723/523)*q^11 + (683/1046*a^10 + 902/523*a^9 - 3456/523*a^8 - 9297/523*a^7 + 21305/1046*a^6 + 29762/523*a^5 - 12748/523*a^4 - 72997/1046*a^3 + 6135/523*a^2 + 14694/523*a - 2997/1046)*q^12 + (59/523*a^10 + 103/523*a^9 - 666/523*a^8 - 574/523*a^7 + 2806/523*a^6 - 1494/523*a^5 - 5976/523*a^4 + 9761/523*a^3 + 4165/523*a^2 - 9704/523*a + 794/523)*q^13 + (154/523*a^10 - 68/523*a^9 - 2678/523*a^8 + 709/523*a^7 + 15178/523*a^6 - 2827/523*a^5 - 31705/523*a^4 + 6641/523*a^3 + 20374/523*a^2 - 6572/523*a - 250/523)*q^14 + (-418/523*a^10 - 1235/523*a^9 + 3832/523*a^8 + 12346/523*a^7 - 9145/523*a^6 - 37230/523*a^5 + 3796/523*a^4 + 41447/523*a^3 + 6712/523*a^2 - 13990/523*a - 3879/523)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-677/523*a^10 - 1501/523*a^9 + 7385/523*a^8 + 14981/523*a^7 - 25638/523*a^6 - 44243/523*a^5 + 33797/523*a^4 + 43567/523*a^3 - 13575/523*a^2 - 8595/523*a - 273/523)*q^17 + (1325/1046*a^10 + 1161/523*a^9 - 7700/523*a^8 - 10913/523*a^7 + 60277/1046*a^6 + 28539/523*a^5 - 49020/523*a^4 - 41121/1046*a^3 + 27581/523*a^2 - 2299/523*a - 385/1046)*q^18 + (365/1046*a^10 + 456/523*a^9 - 1608/523*a^8 - 3770/523*a^7 + 7759/1046*a^6 + 6867/523*a^5 - 4435/523*a^4 + 427/1046*a^3 + 5415/523*a^2 - 3645/523*a - 7507/1046)*q^19 + (-474/523*a^10 - 1448/523*a^9 + 4473/523*a^8 + 15036/523*a^7 - 11764/523*a^6 - 48754/523*a^5 + 9477/523*a^4 + 60380/523*a^3 - 2028/523*a^2 - 23962/523*a + 2060/523)*q^20 + (703/523*a^10 + 1768/523*a^9 - 7253/523*a^8 - 17388/523*a^7 + 23772/523*a^6 + 50490/523*a^5 - 32867/523*a^4 - 51330/523*a^3 + 19426/523*a^2 + 15018/523*a - 3437/523)*q^21 + (71/523*a^10 + 186/523*a^9 - 766/523*a^8 - 2047/523*a^7 + 2508/523*a^6 + 6579/523*a^5 - 2972/523*a^4 - 5167/523*a^3 + 1555/523*a^2 - 1590/523*a + 7/523)*q^22 + (-77/523*a^10 - 1012/523*a^9 - 753/523*a^8 + 10890/523*a^7 + 11239/523*a^6 - 37550/523*a^5 - 28341/523*a^4 + 51333/523*a^3 + 14917/523*a^2 - 22864/523*a + 2740/523)*q^23 + (1049/1046*a^10 + 991/523*a^9 - 6027/523*a^8 - 9402/523*a^7 + 46211/1046*a^6 + 24871/523*a^5 - 36496/523*a^4 - 38773/1046*a^3 + 19940/523*a^2 + 1668/523*a + 457/1046)*q^24 + (389/523*a^10 + 1078/523*a^9 - 3939/523*a^8 - 11532/523*a^7 + 11347/523*a^6 + 38771/523*a^5 - 7569/523*a^4 - 48257/523*a^3 - 6419/523*a^2 + 18352/523*a + 2948/523)*q^25 + (-74/523*a^10 - 76/523*a^9 + 1314/523*a^8 + 977/523*a^7 - 7925/523*a^6 - 3498/523*a^5 + 18434/523*a^4 + 2100/523*a^3 - 13716/523*a^2 + 1915/523*a + 59/523)*q^26 + (-33/523*a^10 - 359/523*a^9 - 248/523*a^8 + 3920/523*a^7 + 4742/523*a^6 - 14225/523*a^5 - 16106/523*a^4 + 21701/523*a^3 + 16853/523*a^2 - 10546/523*a - 2412/523)*q^27 + (-30/523*a^10 + 54/523*a^9 + 773/523*a^8 - 240/523*a^7 - 5531/523*a^6 - 1093/523*a^5 + 13933/523*a^4 + 4894/523*a^3 - 12826/523*a^2 - 4072/523*a + 3798/523)*q^28 + (-573/523*a^10 - 956/523*a^9 + 6867/523*a^8 + 9014/523*a^7 - 28395/523*a^6 - 24485/523*a^5 + 50592/523*a^4 + 24021/523*a^3 - 33580/523*a^2 - 8530/523*a + 3715/523)*q^29 + (19/523*a^10 - 348/523*a^9 - 1030/523*a^8 + 3813/523*a^7 + 8332/523*a^6 - 13760/523*a^5 - 19999/523*a^4 + 21342/523*a^3 + 14434/523*a^2 - 11821/523*a - 418/523)*q^30 + (182/523*a^10 + 823/523*a^9 - 1168/523*a^8 - 9004/523*a^7 - 1033/523*a^6 + 32223/523*a^5 + 12786/523*a^4 - 47542/523*a^3 - 13958/523*a^2 + 26133/523*a - 1912/523)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (696/523*a^10 + 1676/523*a^9 - 7369/523*a^8 - 16921/523*a^7 + 25079/523*a^6 + 52449/523*a^5 - 35491/523*a^4 - 61450/523*a^3 + 19641/523*a^2 + 22924/523*a - 2760/523)*q^33 + (530/523*a^10 + 615/523*a^9 - 6683/523*a^8 - 4651/523*a^7 + 29550/523*a^6 + 5363/523*a^5 - 55952/523*a^4 + 10120/523*a^3 + 37441/523*a^2 - 13136/523*a - 677/523)*q^34 + (-290/523*a^10 - 1047/523*a^9 + 2591/523*a^8 + 11278/523*a^7 - 6222/523*a^6 - 38982/523*a^5 + 5679/523*a^4 + 53759/523*a^3 - 5961/523*a^2 - 25416/523*a + 4811/523)*q^35 + (-883/1046*a^10 - 1245/523*a^9 + 4115/523*a^8 + 12681/523*a^7 - 19825/1046*a^6 - 39507/523*a^5 + 3579/523*a^4 + 91677/1046*a^3 + 7247/523*a^2 - 16587/523*a - 4109/1046)*q^36 + (-947/1046*a^10 - 769/523*a^9 + 6125/523*a^8 + 8241/523*a^7 - 54497/1046*a^6 - 27563/523*a^5 + 49786/523*a^4 + 65647/1046*a^3 - 33909/523*a^2 - 9285/523*a + 8805/1046)*q^37 + O(q^38),
q + a*q^2 + (-2929/9028*a^14 + 3305/4514*a^13 + 31073/4514*a^12 - 35302/2257*a^11 - 248773/4514*a^10 + 573563/4514*a^9 + 919473/4514*a^8 - 4378801/9028*a^7 - 3005667/9028*a^6 + 1935368/2257*a^5 + 1592783/9028*a^4 - 5224775/9028*a^3 - 38286/2257*a^2 + 248643/2257*a - 29861/9028)*q^3 + (a^2 - 2)*q^4 + (6887/4514*a^14 - 10787/4514*a^13 - 144831/4514*a^12 + 232879/4514*a^11 + 1153635/4514*a^10 - 1909601/4514*a^9 - 4281777/4514*a^8 + 3670378/2257*a^7 + 7216765/4514*a^6 - 12991581/4514*a^5 - 2205724/2257*a^4 + 8622515/4514*a^3 + 846049/4514*a^2 - 1576987/4514*a + 2893/2257)*q^5 + (3681/9028*a^14 - 573/2257*a^13 - 38385/4514*a^12 + 26553/4514*a^11 + 304095/4514*a^10 - 115812/2257*a^9 - 1130567/4514*a^8 + 1874047/9028*a^7 + 3889837/9028*a^6 - 857613/2257*a^5 - 2559385/9028*a^4 + 2274997/9028*a^3 + 125625/2257*a^2 - 203851/4514*a + 2929/9028)*q^6 + (-175/122*a^14 + 251/122*a^13 + 3703/122*a^12 - 5485/122*a^11 - 29711/122*a^10 + 45521/122*a^9 + 111249/122*a^8 - 88481/61*a^7 - 189781/122*a^6 + 316101/122*a^5 + 59244/61*a^4 - 210853/122*a^3 - 22725/122*a^2 + 38633/122*a - 55/61)*q^7 + (a^3 - 4*a)*q^8 + (-2215/9028*a^14 + 1063/4514*a^13 + 11513/2257*a^12 - 12182/2257*a^11 - 90758/2257*a^10 + 211717/4514*a^9 + 334714/2257*a^8 - 1723911/9028*a^7 - 2272699/9028*a^6 + 1622361/4514*a^5 + 1468925/9028*a^4 - 2355755/9028*a^3 - 159411/4514*a^2 + 129331/2257*a + 23731/9028)*q^9 + (-1950/2257*a^14 + 6683/4514*a^13 + 81365/4514*a^12 - 141121/4514*a^11 - 642393/4514*a^10 + 1131405/4514*a^9 + 2361455/4514*a^8 - 4256977/4514*a^7 - 1967588/2257*a^6 + 7399757/4514*a^5 + 2355345/4514*a^4 - 2431637/2257*a^3 - 419971/4514*a^2 + 894209/4514*a - 6887/4514)*q^10 + (93/4514*a^14 - 1741/4514*a^13 - 2817/4514*a^12 + 35583/4514*a^11 + 30911/4514*a^10 - 277307/4514*a^9 - 158111/4514*a^8 + 512581/2257*a^7 + 392617/4514*a^6 - 1800053/4514*a^5 - 224672/2257*a^4 + 1279815/4514*a^3 + 214893/4514*a^2 - 246421/4514*a - 3148/2257)*q^11 + (7247/9028*a^14 - 2252/2257*a^13 - 38042/2257*a^12 + 99289/4514*a^11 + 302287/2257*a^10 - 415530/2257*a^9 - 1116302/2257*a^8 + 6514893/9028*a^7 + 7421397/9028*a^6 - 5864707/4514*a^5 - 4260279/9028*a^4 + 7900501/9028*a^3 + 258497/4514*a^2 - 755683/4514*a + 56041/9028)*q^12 + (-2172/2257*a^14 + 2583/2257*a^13 + 45696/2257*a^12 - 56593/2257*a^11 - 365097/2257*a^10 + 469928/2257*a^9 + 1366782/2257*a^8 - 1822073/2257*a^7 - 2356643/2257*a^6 + 3225372/2257*a^5 + 1542585/2257*a^4 - 2096010/2257*a^3 - 333769/2257*a^2 + 368683/2257*a + 6380/2257)*q^13 + (38/61*a^14 - 147/122*a^13 - 1635/122*a^12 + 3189/122*a^11 + 13321/122*a^10 - 26301/122*a^9 - 50437/122*a^8 + 101769/122*a^7 + 42988/61*a^6 - 181637/122*a^5 - 51603/122*a^4 + 61175/61*a^3 + 9233/122*a^2 - 22685/122*a + 175/122)*q^14 + (1754/2257*a^14 - 2354/2257*a^13 - 37039/2257*a^12 + 52321/2257*a^11 + 295888/2257*a^10 - 440837/2257*a^9 - 1097461/2257*a^8 + 1733355/2257*a^7 + 1830949/2257*a^6 - 3107239/2257*a^5 - 1070187/2257*a^4 + 2037843/2257*a^3 + 175475/2257*a^2 - 355637/2257*a + 10439/2257)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1331/2257*a^14 + 3359/4514*a^13 + 55369/4514*a^12 - 73415/4514*a^11 - 434575/4514*a^10 + 608867/4514*a^9 + 1576641/4514*a^8 - 2363585/4514*a^7 - 1269561/2257*a^6 + 4210995/4514*a^5 + 1333379/4514*a^4 - 1396928/2257*a^3 - 103501/4514*a^2 + 509893/4514*a - 20707/4514)*q^17 + (-89/9028*a^14 - 1339/4514*a^13 + 1/4514*a^12 + 13347/2257*a^11 + 7937/4514*a^10 - 201067/4514*a^9 - 61233/4514*a^8 + 1417491/9028*a^7 + 331997/9028*a^6 - 582450/2257*a^5 - 340105/9028*a^4 + 1517413/9028*a^3 + 36301/2257*a^2 - 65501/2257*a + 2215/9028)*q^18 + (-5113/9028*a^14 + 2227/2257*a^13 + 27379/2257*a^12 - 96937/4514*a^11 - 222537/2257*a^10 + 400941/2257*a^9 + 845411/2257*a^8 - 6220667/9028*a^7 - 5890799/9028*a^6 + 5556089/4514*a^5 + 3910273/9028*a^4 - 7456363/9028*a^3 - 501477/4514*a^2 + 676885/4514*a + 58729/9028)*q^19 + (-10991/4514*a^14 + 17139/4514*a^13 + 234341/4514*a^12 - 374951/4514*a^11 - 1893465/4514*a^10 + 3115257/4514*a^9 + 7126277/4514*a^8 - 6059644/2257*a^7 - 12162273/4514*a^6 + 21650007/4514*a^5 + 3754311/2257*a^4 - 14431901/4514*a^3 - 1453089/4514*a^2 + 2643987/4514*a - 3836/2257)*q^20 + (-3123/4514*a^14 + 7645/4514*a^13 + 66639/4514*a^12 - 162359/4514*a^11 - 537831/4514*a^10 + 1311447/4514*a^9 + 2014395/4514*a^8 - 2489516/2257*a^7 - 3384875/4514*a^6 + 8751885/4514*a^5 + 984551/2257*a^4 - 5835967/4514*a^3 - 316815/4514*a^2 + 1048499/4514*a - 12453/2257)*q^21 + (-824/2257*a^14 - 771/4514*a^13 + 33537/4514*a^12 + 13427/4514*a^11 - 260195/4514*a^10 - 85013/4514*a^9 + 957923/4514*a^8 + 237679/4514*a^7 - 838879/2257*a^6 - 289849/4514*a^5 + 1195185/4514*a^4 + 68898/2257*a^3 - 230797/4514*a^2 + 5701/4514*a - 93/4514)*q^22 + (16115/4514*a^14 - 24093/4514*a^13 - 339749/4514*a^12 + 524035/4514*a^11 + 2711963/4514*a^10 - 4328791/4514*a^9 - 10072577/4514*a^8 + 8377156/2257*a^7 + 16914173/4514*a^6 - 29824007/4514*a^5 - 5050561/2257*a^4 + 19893597/4514*a^3 + 1706727/4514*a^2 - 3701483/4514*a + 27260/2257)*q^23 + (-9123/9028*a^14 + 5925/4514*a^13 + 48171/2257*a^12 - 64875/2257*a^11 - 386263/2257*a^10 + 1078715/4514*a^9 + 1449395/2257*a^8 - 8400199/9028*a^7 - 9979283/9028*a^6 + 7514615/4514*a^5 + 6424501/9028*a^4 - 10040763/9028*a^3 - 649435/4514*a^2 + 451577/2257*a - 13105/9028)*q^24 + (-5105/2257*a^14 + 9098/2257*a^13 + 108400/2257*a^12 - 196492/2257*a^11 - 871059/2257*a^10 + 1612624/2257*a^9 + 3251577/2257*a^8 - 6205967/2257*a^7 - 5463992/2257*a^6 + 10997985/2257*a^5 + 3227404/2257*a^4 - 7312562/2257*a^3 - 555857/2257*a^2 + 1334514/2257*a - 17143/2257)*q^25 + (411/2257*a^14 - 2088/2257*a^13 - 8809/2257*a^12 + 43239/2257*a^11 + 70280/2257*a^10 - 340410/2257*a^9 - 251717/2257*a^8 + 1261909/2257*a^7 + 369192/2257*a^6 - 2182395/2257*a^5 - 119490/2257*a^4 + 1466819/2257*a^3 + 3787/2257*a^2 - 273808/2257*a + 2172/2257)*q^26 + (5322/2257*a^14 - 7894/2257*a^13 - 112716/2257*a^12 + 171183/2257*a^11 + 905568/2257*a^10 - 1409537/2257*a^9 - 3397812/2257*a^8 + 5436707/2257*a^7 + 5817353/2257*a^6 - 9637613/2257*a^5 - 3661217/2257*a^4 + 6378388/2257*a^3 + 711953/2257*a^2 - 1157163/2257*a + 8471/2257)*q^27 + (279/122*a^14 - 465/122*a^13 - 5889/122*a^12 + 10003/122*a^11 + 47105/122*a^10 - 81743/122*a^9 - 175677/122*a^8 + 156642/61*a^7 + 297865/122*a^6 - 553465/122*a^5 - 91893/61*a^4 + 367935/122*a^3 + 35533/122*a^2 - 67287/122*a + 72/61)*q^28 + (1553/2257*a^14 - 921/2257*a^13 - 32698/2257*a^12 + 22740/2257*a^11 + 261188/2257*a^10 - 208659/2257*a^9 - 974375/2257*a^8 + 875377/2257*a^7 + 1658616/2257*a^6 - 1630991/2257*a^5 - 1029345/2257*a^4 + 1063558/2257*a^3 + 161992/2257*a^2 - 187810/2257*a + 11815/2257)*q^29 + (-600/2257*a^14 + 1549/2257*a^13 + 13733/2257*a^12 - 33864/2257*a^11 - 118101/2257*a^10 + 281183/2257*a^9 + 465213/2257*a^8 - 1091215/2257*a^7 - 800729/2257*a^6 + 1937923/2257*a^5 + 441703/2257*a^4 - 1278591/2257*a^3 - 60965/2257*a^2 + 236705/2257*a - 1754/2257)*q^30 + (6683/4514*a^14 - 5559/2257*a^13 - 70600/2257*a^12 + 120478/2257*a^11 + 564211/2257*a^10 - 992156/2257*a^9 - 2093468/2257*a^8 + 7663319/4514*a^7 + 6987355/4514*a^6 - 6818910/2257*a^5 - 4089421/4514*a^4 + 9143453/4514*a^3 + 354317/2257*a^2 - 866859/2257*a + 10787/4514)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-5320/2257*a^14 + 9070/2257*a^13 + 112437/2257*a^12 - 195536/2257*a^11 - 899103/2257*a^10 + 1601340/2257*a^9 + 3339904/2257*a^8 - 6148501/2257*a^7 - 5585952/2257*a^6 + 10875806/2257*a^5 + 3285677/2257*a^4 - 7243545/2257*a^3 - 575916/2257*a^2 + 1362250/2257*a - 355/2257)*q^33 + (697/4514*a^14 - 3195/4514*a^13 - 14851/4514*a^12 + 65881/4514*a^11 + 119059/4514*a^10 - 515691/4514*a^9 - 438959/4514*a^8 + 947885/2257*a^7 + 710465/4514*a^6 - 3231951/4514*a^5 - 185718/2257*a^4 + 2103297/4514*a^3 + 62677/4514*a^2 - 364105/4514*a + 1331/2257)*q^34 + (7394/2257*a^14 - 12852/2257*a^13 - 155747/2257*a^12 + 276300/2257*a^11 + 1240825/2257*a^10 - 2256541/2257*a^9 - 4591136/2257*a^8 + 8641388/2257*a^7 + 7647447/2257*a^6 - 15242003/2257*a^5 - 4480545/2257*a^4 + 10090598/2257*a^3 + 784658/2257*a^2 - 1840368/2257*a + 9322/2257)*q^35 + (1663/9028*a^14 - 1552/2257*a^13 - 18379/4514*a^12 + 65031/4514*a^11 + 153777/4514*a^10 - 259822/2257*a^9 - 597937/4514*a^8 + 3928093/9028*a^7 + 2098563/9028*a^6 - 1745546/2257*a^5 - 1339447/9028*a^4 + 4930495/9028*a^3 + 90172/2257*a^2 - 521957/4514*a - 47373/9028)*q^36 + (20437/9028*a^14 - 6599/2257*a^13 - 216293/4514*a^12 + 292305/4514*a^11 + 1735175/4514*a^10 - 1228459/2257*a^9 - 6487451/4514*a^8 + 19324327/9028*a^7 + 22018405/9028*a^6 - 8716942/2257*a^5 - 13481329/9028*a^4 + 23502269/9028*a^3 + 606540/2257*a^2 - 2236959/4514*a + 8909/9028)*q^37 + O(q^38)
*]> ;  // time = 5.511 seconds




J[318] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 318, 318, 318, 318, 318, 318, 318, 159, 159, 106, 106, 106, 106, 53, 53 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 2, 4, 5, 1, 1, 1, 1, 1, 3 ], dimensions := [ 1, 1, 1, 1, 1, 2, 2, 8, 10, 2, 2, 2, 2, 4, 12 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 17, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 43, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 3, 1, 1, 43, 1, 0, 1, 1, 1, 3, 3, 49, 1, 1, 17, 1, 1, 11, 1, 1, 1, 0, 1, 1, 1, 1, 1, 11449, 3, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 25, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 49, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 13, 1, 11449, 1, 25, 1, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, 0, -1, -2, -7, 2, -5, -4, -1, -2 ],
[ -1, -1, 4, 1, -1, -4, 6, -1, 9, -3, -8, 12 ],
[ -1, 1, 0, 5, -3, -4, 6, 5, -3, 3, 8, -4 ],
[ 1, -1, 0, 1, 5, 0, 2, -1, 3, -1, -4, 0 ],
[ 1, -1, -3, -4, -5, -2, 5, 6, -7, -8, 1, 2 ],
[ -2, 2, 1, 0, 3, 12, -9, -2, 3, -2, -1, 12 ],
[ 2, 2, 1, 1, -2, -2, -5, 3, 0, -7, 1, 2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1,
x^2 - x - 10,
x^2 - x - 4
], atkin_lehners := [
[ 1, 1, 1 ],
[ 1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, 1, 1 ],
[ -1, 1, -1 ],
[ 1, -1, 1 ],
[ -1, -1, -1 ]
], component_group_orders := [
[ 1, 3, 1 ],
[ 17, 3, 1 ],
[ 3, 3, 1 ],
[ 1, 5, 1 ],
[ 11, 1, 1 ],
[ 43, 5, 1 ],
[ 13, 13, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 1, 1, 1 ],
[ 11, 1, 1 ],
[ 1, 5, 1 ],
[ 13, 13, 1 ]
], torsion_upper_bounds := [ 1, 1, 3, 1, 1, 1, 13 ], torsion_lower_bounds := [ 1, 1, 3, 1, 1, 1, 1 ], l_ratios := [ 0, 1, 1/3, 1, 0, 5, 1 ], analytic_sha_upper_bounds := [ 0, 1, 1, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 1, 1, 0, 1, 1/169 ], eigenvalues := [*
[ -1, -1, -1, 0, -1, -2, -7, 2, -5, -4, -1, -2 ],
[ -1, -1, 4, 1, -1, -4, 6, -1, 9, -3, -8, 12 ],
[ -1, 1, 0, 5, -3, -4, 6, 5, -3, 3, 8, -4 ],
[ 1, -1, 0, 1, 5, 0, 2, -1, 3, -1, -4, 0 ],
[ 1, -1, -3, -4, -5, -2, 5, 6, -7, -8, 1, 2 ],
[
-1,
1,
a,
0,
-a + 2,
6,
-a - 4,
-2*a,
-a + 2,
2*a - 2,
3*a - 2,
6
],
[
1,
1,
a,
-a + 1,
-1,
-2*a,
-a - 2,
a + 1,
2*a - 1,
-a - 3,
a,
2*a
]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - q^8 + q^9 + q^10 - q^11 - q^12 - 2*q^13 + q^15 + q^16 - 7*q^17 - q^18 + 2*q^19 - q^20 + q^22 - 5*q^23 + q^24 - 4*q^25 + 2*q^26 - q^27 - 4*q^29 - q^30 - q^31 - q^32 + q^33 + 7*q^34 + q^36 - 2*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + 4*q^5 + q^6 + q^7 - q^8 + q^9 - 4*q^10 - q^11 - q^12 - 4*q^13 - q^14 - 4*q^15 + q^16 + 6*q^17 - q^18 - q^19 + 4*q^20 - q^21 + q^22 + 9*q^23 + q^24 + 11*q^25 + 4*q^26 - q^27 + q^28 - 3*q^29 + 4*q^30 - 8*q^31 - q^32 + q^33 - 6*q^34 + 4*q^35 + q^36 + 12*q^37 + O(q^38),
q - q^2 + q^3 + q^4 - q^6 + 5*q^7 - q^8 + q^9 - 3*q^11 + q^12 - 4*q^13 - 5*q^14 + q^16 + 6*q^17 - q^18 + 5*q^19 + 5*q^21 + 3*q^22 - 3*q^23 - q^24 - 5*q^25 + 4*q^26 + q^27 + 5*q^28 + 3*q^29 + 8*q^31 - q^32 - 3*q^33 - 6*q^34 + q^36 - 4*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^6 + q^7 + q^8 + q^9 + 5*q^11 - q^12 + q^14 + q^16 + 2*q^17 + q^18 - q^19 - q^21 + 5*q^22 + 3*q^23 - q^24 - 5*q^25 - q^27 + q^28 - q^29 - 4*q^31 + q^32 - 5*q^33 + 2*q^34 + q^36 + O(q^38),
q + q^2 - q^3 + q^4 - 3*q^5 - q^6 - 4*q^7 + q^8 + q^9 - 3*q^10 - 5*q^11 - q^12 - 2*q^13 - 4*q^14 + 3*q^15 + q^16 + 5*q^17 + q^18 + 6*q^19 - 3*q^20 + 4*q^21 - 5*q^22 - 7*q^23 - q^24 + 4*q^25 - 2*q^26 - q^27 - 4*q^28 - 8*q^29 + 3*q^30 + q^31 + q^32 + 5*q^33 + 5*q^34 + 12*q^35 + q^36 + 2*q^37 + O(q^38),
q - q^2 + q^3 + q^4 + a*q^5 - q^6 - q^8 + q^9 - a*q^10 + (-a + 2)*q^11 + q^12 + 6*q^13 + a*q^15 + q^16 + (-a - 4)*q^17 - q^18 - 2*a*q^19 + a*q^20 + (a - 2)*q^22 + (-a + 2)*q^23 - q^24 + (a + 5)*q^25 - 6*q^26 + q^27 + (2*a - 2)*q^29 - a*q^30 + (3*a - 2)*q^31 - q^32 + (-a + 2)*q^33 + (a + 4)*q^34 + q^36 + 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + a*q^5 + q^6 + (-a + 1)*q^7 + q^8 + q^9 + a*q^10 - q^11 + q^12 - 2*a*q^13 + (-a + 1)*q^14 + a*q^15 + q^16 + (-a - 2)*q^17 + q^18 + (a + 1)*q^19 + a*q^20 + (-a + 1)*q^21 - q^22 + (2*a - 1)*q^23 + q^24 + (a - 1)*q^25 - 2*a*q^26 + q^27 + (-a + 1)*q^28 + (-a - 3)*q^29 + a*q^30 + a*q^31 + q^32 - q^33 + (-a - 2)*q^34 - 4*q^35 + q^36 + 2*a*q^37 + O(q^38)
*]> ;  // time = 190.27 seconds




J[319] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 319, 319, 319, 319, 319, 29, 11 ], new_dimensions := [ 1, 3, 4, 7, 8, 2, 1 ], dimensions := [ 1, 3, 4, 7, 8, 4, 2 ], intersection_graph := [ 0, 1, 1, 1, 23, 1, 1, 1, 0, 1, 1, 1, 17, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 15, 23, 1, 1, 1, 0, 167, 1, 1, 17, 1, 1, 167, 0, 1, 1, 3, 1, 15, 1, 1, 0 ], ap_traces := [
[ 2, -3, 1, 4, -1, 6, 4, -2, 3, 1, -7, -11 ],
[ 0, 0, -6, -3, 3, -6, -12, -12, 0, 3, -9, 15 ],
[ -2, -3, -5, 1, -4, -2, -4, -2, -1, -4, -10, -8 ],
[ 3, 0, 4, 1, 7, 0, 18, 10, 4, -7, -13, -5 ],
[ 0, 4, 10, -7, -8, -4, 12, -10, 0, 8, 5, 9 ]
], hecke_fields := [
x - 1,
x^3 - 3*x - 1,
x^4 + 2*x^3 - 3*x^2 - 3*x + 2,
x^7 - 3*x^6 - 4*x^5 + 15*x^4 + x^3 - 14*x^2 + 1,
x^8 - 13*x^6 - x^5 + 50*x^4 + 7*x^3 - 54*x^2 - 5*x + 1
], atkin_lehners := [
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 1, 1 ],
[ 17, 3 ],
[ 1, 1 ],
[ 5, 15 ],
[ 167, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 17, 3 ],
[ 1, 1 ],
[ 5, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 5, 1 ], torsion_lower_bounds := [ 1, 1, 1, 5, 1 ], l_ratios := [ 1, 0, 0, 1/5, 1 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 2, -3, 1, 4, -1, 6, 4, -2, 3, 1, -7, -11 ],
[
a,
-a,
-2*a^2 + a + 2,
2*a^2 - 2*a - 5,
1,
a^2 + a - 4,
-a^2 + a - 2,
a - 4,
-4*a^2 + 4*a + 8,
1,
3*a^2 - 2*a - 9,
4*a^2 - a - 3
],
[
a,
-a^3 - 2*a^2 + 2*a + 1,
a^3 + 2*a^2 - 2*a - 3,
a^3 + 2*a^2 - 3*a - 2,
-1,
-2*a^3 - 5*a^2 + a + 4,
3*a^2 + 5*a - 6,
a,
-a^3 - 4*a^2 - a + 5,
-1,
-a^2 + 2*a + 1,
2*a^3 + 2*a^2 - 5*a - 1
],
[
a,
-a^4 + a^3 + 5*a^2 - 3*a - 3,
a^5 - a^4 - 6*a^3 + 4*a^2 + 7*a - 1,
a^6 - 3*a^5 - 4*a^4 + 14*a^3 + 2*a^2 - 11*a - 1,
1,
a^5 - 2*a^4 - 4*a^3 + 6*a^2 + 2*a + 1,
a^6 - 3*a^5 - 4*a^4 + 15*a^3 + a^2 - 15*a + 3,
-3*a^6 + 8*a^5 + 13*a^4 - 38*a^3 - 6*a^2 + 28*a + 1,
a^6 - 4*a^5 - 2*a^4 + 19*a^3 - 7*a^2 - 15*a + 4,
-1,
a^6 - 4*a^5 - a^4 + 17*a^3 - 13*a^2 - 6*a + 7,
-a^6 + 5*a^5 + a^4 - 25*a^3 + 9*a^2 + 20*a
],
[
a,
-1/9*a^7 - 1/9*a^6 + 16/9*a^5 + 10/9*a^4 - 26/3*a^3 - 25/9*a^2 + 113/9*a + 14/9,
4/9*a^7 - 2/9*a^6 - 49/9*a^5 + 17/9*a^4 + 56/3*a^3 - 26/9*a^2 - 143/9*a + 13/9,
-2/9*a^7 - 1/3*a^6 + 3*a^5 + 34/9*a^4 - 12*a^3 - 98/9*a^2 + 13*a + 29/9,
-1,
2/3*a^7 - 2/9*a^6 - 73/9*a^5 + 16/9*a^4 + 86/3*a^3 - 2*a^2 - 254/9*a - 13/9,
1/3*a^6 - 1/3*a^5 - 8/3*a^4 + 3*a^3 + 3*a^2 - 17/3*a + 11/3,
1/9*a^7 + 2/9*a^6 - 20/9*a^5 - 8/3*a^4 + 37/3*a^3 + 64/9*a^2 - 148/9*a - 2/3,
-4/9*a^7 - 5/9*a^6 + 50/9*a^5 + 6*a^4 - 61/3*a^3 - 139/9*a^2 + 181/9*a + 10/3,
1,
1/9*a^7 - 4/3*a^5 + 4/9*a^4 + 4*a^3 - 23/9*a^2 - 2/3*a + 14/9,
7/9*a^7 - 31/3*a^5 - 8/9*a^4 + 40*a^3 + 55/9*a^2 - 116/3*a - 19/9
]
*], q_expansions := [*
q + 2*q^2 - 3*q^3 + 2*q^4 + q^5 - 6*q^6 + 4*q^7 + 6*q^9 + 2*q^10 - q^11 - 6*q^12 + 6*q^13 + 8*q^14 - 3*q^15 - 4*q^16 + 4*q^17 + 12*q^18 - 2*q^19 + 2*q^20 - 12*q^21 - 2*q^22 + 3*q^23 - 4*q^25 + 12*q^26 - 9*q^27 + 8*q^28 + q^29 - 6*q^30 - 7*q^31 - 8*q^32 + 3*q^33 + 8*q^34 + 4*q^35 + 12*q^36 - 11*q^37 + O(q^38),
q + a*q^2 - a*q^3 + (a^2 - 2)*q^4 + (-2*a^2 + a + 2)*q^5 - a^2*q^6 + (2*a^2 - 2*a - 5)*q^7 + (-a + 1)*q^8 + (a^2 - 3)*q^9 + (a^2 - 4*a - 2)*q^10 + q^11 + (-a - 1)*q^12 + (a^2 + a - 4)*q^13 + (-2*a^2 + a + 2)*q^14 + (-a^2 + 4*a + 2)*q^15 + (-3*a^2 + a + 4)*q^16 + (-a^2 + a - 2)*q^17 + q^18 + (a - 4)*q^19 + (-a - 3)*q^20 + (2*a^2 - a - 2)*q^21 + a*q^22 + (-4*a^2 + 4*a + 8)*q^23 + (a^2 - a)*q^24 + (5*a^2 - 4*a - 5)*q^25 + (a^2 - a + 1)*q^26 + (3*a - 1)*q^27 + (-3*a^2 + 8)*q^28 + q^29 + (4*a^2 - a - 1)*q^30 + (3*a^2 - 2*a - 9)*q^31 + (a^2 - 3*a - 5)*q^32 - a*q^33 + (a^2 - 5*a - 1)*q^34 + (5*a - 4)*q^35 + (-2*a^2 + a + 6)*q^36 + (4*a^2 - a - 3)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^3 + 2*a^2 - 2*a - 3)*q^5 + (-a^2 - 2*a + 2)*q^6 + (a^3 + 2*a^2 - 3*a - 2)*q^7 + (a^3 - 4*a)*q^8 + (a^3 + a^2 - 3*a)*q^9 + (a^2 - 2)*q^10 - q^11 + (a^3 + 2*a^2 - 2*a - 2)*q^12 + (-2*a^3 - 5*a^2 + a + 4)*q^13 + (a - 2)*q^14 + (a^3 + 3*a^2 - a - 5)*q^15 + (-2*a^3 - 3*a^2 + 3*a + 2)*q^16 + (3*a^2 + 5*a - 6)*q^17 + (-a^3 + 3*a - 2)*q^18 + a*q^19 + (-a^3 - 4*a^2 + 2*a + 6)*q^20 + (2*a^2 + 3*a - 6)*q^21 - a*q^22 + (-a^3 - 4*a^2 - a + 5)*q^23 + (3*a^2 + 5*a - 6)*q^24 + (-3*a^3 - 7*a^2 + 5*a + 6)*q^25 + (-a^3 - 5*a^2 - 2*a + 4)*q^26 + (2*a^3 + 6*a^2 - a - 7)*q^27 + (-2*a^3 - 3*a^2 + 4*a + 4)*q^28 - q^29 + (a^3 + 2*a^2 - 2*a - 2)*q^30 + (-a^2 + 2*a + 1)*q^31 + (-a^3 - 3*a^2 + 4*a + 4)*q^32 + (a^3 + 2*a^2 - 2*a - 1)*q^33 + (3*a^3 + 5*a^2 - 6*a)*q^34 + (-2*a^3 - 6*a^2 + 3*a + 10)*q^35 + (-2*a^2 + a + 2)*q^36 + (2*a^3 + 2*a^2 - 5*a - 1)*q^37 + O(q^38),
q + a*q^2 + (-a^4 + a^3 + 5*a^2 - 3*a - 3)*q^3 + (a^2 - 2)*q^4 + (a^5 - a^4 - 6*a^3 + 4*a^2 + 7*a - 1)*q^5 + (-a^5 + a^4 + 5*a^3 - 3*a^2 - 3*a)*q^6 + (a^6 - 3*a^5 - 4*a^4 + 14*a^3 + 2*a^2 - 11*a - 1)*q^7 + (a^3 - 4*a)*q^8 + (-2*a^6 + 5*a^5 + 9*a^4 - 23*a^3 - 7*a^2 + 17*a + 5)*q^9 + (a^6 - a^5 - 6*a^4 + 4*a^3 + 7*a^2 - a)*q^10 + q^11 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 13*a^2 + 6*a + 6)*q^12 + (a^5 - 2*a^4 - 4*a^3 + 6*a^2 + 2*a + 1)*q^13 + (-a^4 + a^3 + 3*a^2 - a - 1)*q^14 + (2*a^6 - 5*a^5 - 9*a^4 + 23*a^3 + 5*a^2 - 17*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - 3*a^5 - 4*a^4 + 15*a^3 + a^2 - 15*a + 3)*q^17 + (-a^6 + a^5 + 7*a^4 - 5*a^3 - 11*a^2 + 5*a + 2)*q^18 + (-3*a^6 + 8*a^5 + 13*a^4 - 38*a^3 - 6*a^2 + 28*a + 1)*q^19 + (2*a^6 - 4*a^5 - 9*a^4 + 18*a^3 + 5*a^2 - 14*a + 1)*q^20 + (-2*a^6 + 6*a^5 + 9*a^4 - 31*a^3 - 7*a^2 + 31*a + 5)*q^21 + a*q^22 + (a^6 - 4*a^5 - 2*a^4 + 19*a^3 - 7*a^2 - 15*a + 4)*q^23 + (-2*a^6 + 5*a^5 + 8*a^4 - 22*a^3 - 2*a^2 + 12*a + 1)*q^24 + (a^6 - 3*a^5 - 3*a^4 + 14*a^3 - 2*a^2 - 10*a - 1)*q^25 + (a^6 - 2*a^5 - 4*a^4 + 6*a^3 + 2*a^2 + a)*q^26 + (3*a^6 - 9*a^5 - 13*a^4 + 47*a^3 + 9*a^2 - 48*a - 8)*q^27 + (-2*a^6 + 5*a^5 + 9*a^4 - 25*a^3 - 5*a^2 + 21*a + 2)*q^28 - q^29 + (a^6 - a^5 - 7*a^4 + 3*a^3 + 11*a^2 - 2)*q^30 + (a^6 - 4*a^5 - a^4 + 17*a^3 - 13*a^2 - 6*a + 7)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^4 + a^3 + 5*a^2 - 3*a - 3)*q^33 + (-a^2 + 3*a - 1)*q^34 + (-a^4 - a^3 + 7*a^2 + a - 5)*q^35 + (2*a^6 - 7*a^5 - 8*a^4 + 36*a^3 + 5*a^2 - 32*a - 9)*q^36 + (-a^6 + 5*a^5 + a^4 - 25*a^3 + 9*a^2 + 20*a)*q^37 + O(q^38),
q + a*q^2 + (-1/9*a^7 - 1/9*a^6 + 16/9*a^5 + 10/9*a^4 - 26/3*a^3 - 25/9*a^2 + 113/9*a + 14/9)*q^3 + (a^2 - 2)*q^4 + (4/9*a^7 - 2/9*a^6 - 49/9*a^5 + 17/9*a^4 + 56/3*a^3 - 26/9*a^2 - 143/9*a + 13/9)*q^5 + (-1/9*a^7 + 1/3*a^6 + a^5 - 28/9*a^4 - 2*a^3 + 59/9*a^2 + a + 1/9)*q^6 + (-2/9*a^7 - 1/3*a^6 + 3*a^5 + 34/9*a^4 - 12*a^3 - 98/9*a^2 + 13*a + 29/9)*q^7 + (a^3 - 4*a)*q^8 + (-1/3*a^7 + 1/9*a^6 + 41/9*a^5 - 8/9*a^4 - 58/3*a^3 + a^2 + 217/9*a + 20/9)*q^9 + (-2/9*a^7 + 1/3*a^6 + 7/3*a^5 - 32/9*a^4 - 6*a^3 + 73/9*a^2 + 11/3*a - 4/9)*q^10 - q^11 + (5/9*a^7 - 2/9*a^6 - 61/9*a^5 + 4/3*a^4 + 74/3*a^3 + 5/9*a^2 - 230/9*a - 3)*q^12 + (2/3*a^7 - 2/9*a^6 - 73/9*a^5 + 16/9*a^4 + 86/3*a^3 - 2*a^2 - 254/9*a - 13/9)*q^13 + (-1/3*a^7 + 1/9*a^6 + 32/9*a^5 - 8/9*a^4 - 28/3*a^3 + a^2 + 19/9*a + 2/9)*q^14 + (-1/9*a^7 + 1/9*a^6 + 17/9*a^5 - 2*a^4 - 28/3*a^3 + 71/9*a^2 + 115/9*a - 5/3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (1/3*a^6 - 1/3*a^5 - 8/3*a^4 + 3*a^3 + 3*a^2 - 17/3*a + 11/3)*q^17 + (1/9*a^7 + 2/9*a^6 - 11/9*a^5 - 8/3*a^4 + 10/3*a^3 + 55/9*a^2 + 5/9*a + 1/3)*q^18 + (1/9*a^7 + 2/9*a^6 - 20/9*a^5 - 8/3*a^4 + 37/3*a^3 + 64/9*a^2 - 148/9*a - 2/3)*q^19 + (-5/9*a^7 - 1/9*a^6 + 64/9*a^5 + 4/3*a^4 - 83/3*a^3 - 23/9*a^2 + 272/9*a - 8/3)*q^20 + (-11/9*a^7 - 1/9*a^6 + 136/9*a^5 + 8/3*a^4 - 158/3*a^3 - 119/9*a^2 + 389/9*a + 8)*q^21 - a*q^22 + (-4/9*a^7 - 5/9*a^6 + 50/9*a^5 + 6*a^4 - 61/3*a^3 - 139/9*a^2 + 181/9*a + 10/3)*q^23 + (-2/9*a^6 - 1/9*a^5 + 28/9*a^4 + 2/3*a^3 - 26/3*a^2 - 20/9*a - 7/9)*q^24 + (11/9*a^7 - 47/3*a^5 - 10/9*a^4 + 59*a^3 + 62/9*a^2 - 190/3*a + 10/9)*q^25 + (-2/9*a^7 + 5/9*a^6 + 22/9*a^5 - 14/3*a^4 - 20/3*a^3 + 70/9*a^2 + 17/9*a - 2/3)*q^26 + (1/9*a^7 + 2/9*a^6 - 11/9*a^5 - 8/3*a^4 + 10/3*a^3 + 55/9*a^2 - 4/9*a + 13/3)*q^27 + (5/9*a^7 - 1/9*a^6 - 65/9*a^5 - 2/9*a^4 + 82/3*a^3 + 53/9*a^2 - 247/9*a - 55/9)*q^28 + q^29 + (1/9*a^7 + 4/9*a^6 - 19/9*a^5 - 34/9*a^4 + 26/3*a^3 + 61/9*a^2 - 20/9*a + 1/9)*q^30 + (1/9*a^7 - 4/3*a^5 + 4/9*a^4 + 4*a^3 - 23/9*a^2 - 2/3*a + 14/9)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/9*a^7 + 1/9*a^6 - 16/9*a^5 - 10/9*a^4 + 26/3*a^3 + 25/9*a^2 - 113/9*a - 14/9)*q^33 + (1/3*a^7 - 1/3*a^6 - 8/3*a^5 + 3*a^4 + 3*a^3 - 17/3*a^2 + 11/3*a)*q^34 + (-1/3*a^7 + 1/9*a^6 + 32/9*a^5 - 8/9*a^4 - 22/3*a^3 + a^2 - 71/9*a + 2/9)*q^35 + (8/9*a^7 - 35/3*a^5 - 4/9*a^4 + 44*a^3 + 41/9*a^2 - 142/3*a - 41/9)*q^36 + (7/9*a^7 - 31/3*a^5 - 8/9*a^4 + 40*a^3 + 55/9*a^2 - 116/3*a - 19/9)*q^37 + O(q^38)
*]> ;  // time = 44.041 seconds




J[321] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 321, 321, 321, 321, 107, 107 ], new_dimensions := [ 2, 2, 6, 7, 2, 7 ], dimensions := [ 2, 2, 6, 7, 4, 14 ], intersection_graph := [ 0, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 41, 1, 1, 0, 1, 29, 1, 1, 1, 1, 0, 1, 14051, 5, 1, 29, 1, 0, 1, 1, 41, 1, 14051, 1, 0 ], ap_traces := [
[ -1, -2, 2, -4, -6, -2, 2, -8, -4, -2, -12, 2 ],
[ -1, 2, -6, -2, -4, -2, -6, 0, -8, -2, -4, 2 ],
[ 3, 6, 6, 0, 6, -8, 4, -4, 14, 10, 12, -12 ],
[ 0, -7, -8, 6, 4, 6, -10, 8, 6, 0, 16, 10 ]
], hecke_fields := [
x^2 + x - 1,
x^2 + x - 1,
x^6 - 3*x^5 - 5*x^4 + 18*x^3 + x^2 - 19*x + 3,
x^7 - 14*x^5 - x^4 + 55*x^3 + 8*x^2 - 46*x - 19
], atkin_lehners := [
[ 1, 1 ],
[ -1, -1 ],
[ -1, 1 ],
[ 1, -1 ]
], component_group_orders := [
[ 5, 1 ],
[ 41, 1 ],
[ 261, 1 ],
[ 14051, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 41, 1 ],
[ 261, 1 ],
[ 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 9, 1 ], torsion_lower_bounds := [ 1, 1, 9, 1 ], l_ratios := [ 0, 0, 29/9, 1 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[
a,
-1,
1,
-2,
-2*a - 4,
-1,
-4*a - 1,
2*a - 3,
4*a,
2*a,
-6,
1
],
[
a,
1,
-3,
-2*a - 2,
-2,
-1,
4*a - 1,
2*a + 1,
-4,
-2*a - 2,
-2,
8*a + 5
],
[
a,
1,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 13/2*a,
-1/2*a^5 + 1/2*a^4 + 3*a^3 - 5/2*a^2 - 5/2*a + 2,
-a^5 + 3/2*a^4 + 13/2*a^3 - 7*a^2 - 19/2*a + 9/2,
1/2*a^4 + 1/2*a^3 - 4*a^2 - 5/2*a + 7/2,
-1/2*a^5 - 1/2*a^4 + 5*a^3 + 5/2*a^2 - 21/2*a,
a^5 - a^4 - 7*a^3 + 4*a^2 + 10*a - 1,
a^5 - 3/2*a^4 - 11/2*a^3 + 6*a^2 + 9/2*a + 3/2,
-2*a^5 + 4*a^4 + 12*a^3 - 20*a^2 - 12*a + 12,
5/2*a^5 - 9/2*a^4 - 15*a^3 + 47/2*a^2 + 27/2*a - 13,
-a^5 + 1/2*a^4 + 13/2*a^3 - 19/2*a - 11/2
],
[
a,
-1,
-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - 5/2*a^3 - 31/4*a^2 + 25/4*a + 13/4,
1/2*a^6 - 7*a^4 + a^3 + 26*a^2 - 7*a - 27/2,
-3/4*a^6 + 1/4*a^5 + 41/4*a^4 - 4*a^3 - 151/4*a^2 + 67/4*a + 93/4,
-1/2*a^6 + 1/2*a^5 + 7*a^4 - 11/2*a^3 - 55/2*a^2 + 15*a + 21,
a^6 - 1/2*a^5 - 27/2*a^4 + 6*a^3 + 97/2*a^2 - 39/2*a - 28,
-1/2*a^6 + 1/2*a^5 + 11/2*a^4 - 4*a^3 - 33/2*a^2 + 11/2*a + 27/2,
a^6 - a^5 - 27/2*a^4 + 21/2*a^3 + 50*a^2 - 55/2*a - 63/2,
-2*a,
-3/4*a^6 + 3/4*a^5 + 41/4*a^4 - 17/2*a^3 - 153/4*a^2 + 87/4*a + 107/4,
1/4*a^6 - 3/4*a^5 - 11/4*a^4 + 7*a^3 + 33/4*a^2 - 53/4*a - 19/4
]
*], q_expansions := [*
q + a*q^2 - q^3 + (-a - 1)*q^4 + q^5 - a*q^6 - 2*q^7 + (-2*a - 1)*q^8 + q^9 + a*q^10 + (-2*a - 4)*q^11 + (a + 1)*q^12 - q^13 - 2*a*q^14 - q^15 + 3*a*q^16 + (-4*a - 1)*q^17 + a*q^18 + (2*a - 3)*q^19 + (-a - 1)*q^20 + 2*q^21 + (-2*a - 2)*q^22 + 4*a*q^23 + (2*a + 1)*q^24 - 4*q^25 - a*q^26 - q^27 + (2*a + 2)*q^28 + 2*a*q^29 - a*q^30 - 6*q^31 + (a + 5)*q^32 + (2*a + 4)*q^33 + (3*a - 4)*q^34 - 2*q^35 + (-a - 1)*q^36 + q^37 + O(q^38),
q + a*q^2 + q^3 + (-a - 1)*q^4 - 3*q^5 + a*q^6 + (-2*a - 2)*q^7 + (-2*a - 1)*q^8 + q^9 - 3*a*q^10 - 2*q^11 + (-a - 1)*q^12 - q^13 - 2*q^14 - 3*q^15 + 3*a*q^16 + (4*a - 1)*q^17 + a*q^18 + (2*a + 1)*q^19 + (3*a + 3)*q^20 + (-2*a - 2)*q^21 - 2*a*q^22 - 4*q^23 + (-2*a - 1)*q^24 + 4*q^25 - a*q^26 + q^27 + (2*a + 4)*q^28 + (-2*a - 2)*q^29 - 3*a*q^30 - 2*q^31 + (a + 5)*q^32 - 2*q^33 + (-5*a + 4)*q^34 + (6*a + 6)*q^35 + (-a - 1)*q^36 + (8*a + 5)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 13/2*a)*q^5 + a*q^6 + (-1/2*a^5 + 1/2*a^4 + 3*a^3 - 5/2*a^2 - 5/2*a + 2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (a^5 - 3/2*a^4 - 13/2*a^3 + 6*a^2 + 19/2*a - 3/2)*q^10 + (-a^5 + 3/2*a^4 + 13/2*a^3 - 7*a^2 - 19/2*a + 9/2)*q^11 + (a^2 - 2)*q^12 + (1/2*a^4 + 1/2*a^3 - 4*a^2 - 5/2*a + 7/2)*q^13 + (-a^5 + 1/2*a^4 + 13/2*a^3 - 2*a^2 - 15/2*a + 3/2)*q^14 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 13/2*a)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1/2*a^5 - 1/2*a^4 + 5*a^3 + 5/2*a^2 - 21/2*a)*q^17 + a*q^18 + (a^5 - a^4 - 7*a^3 + 4*a^2 + 10*a - 1)*q^19 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 7/2*a^2 + 9/2*a - 3)*q^20 + (-1/2*a^5 + 1/2*a^4 + 3*a^3 - 5/2*a^2 - 5/2*a + 2)*q^21 + (-3/2*a^5 + 3/2*a^4 + 11*a^3 - 17/2*a^2 - 29/2*a + 3)*q^22 + (a^5 - 3/2*a^4 - 11/2*a^3 + 6*a^2 + 9/2*a + 3/2)*q^23 + (a^3 - 4*a)*q^24 + (a^5 - 3/2*a^4 - 17/2*a^3 + 9*a^2 + 31/2*a - 13/2)*q^25 + (1/2*a^5 + 1/2*a^4 - 4*a^3 - 5/2*a^2 + 7/2*a)*q^26 + q^27 + (-3/2*a^5 + 1/2*a^4 + 10*a^3 - 3/2*a^2 - 25/2*a - 1)*q^28 + (-2*a^5 + 4*a^4 + 12*a^3 - 20*a^2 - 12*a + 12)*q^29 + (a^5 - 3/2*a^4 - 13/2*a^3 + 6*a^2 + 19/2*a - 3/2)*q^30 + (5/2*a^5 - 9/2*a^4 - 15*a^3 + 47/2*a^2 + 27/2*a - 13)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^5 + 3/2*a^4 + 13/2*a^3 - 7*a^2 - 19/2*a + 9/2)*q^33 + (-2*a^5 + 5/2*a^4 + 23/2*a^3 - 10*a^2 - 19/2*a + 3/2)*q^34 + (a^5 - a^4 - 7*a^3 + 4*a^2 + 10*a)*q^35 + (a^2 - 2)*q^36 + (-a^5 + 1/2*a^4 + 13/2*a^3 - 19/2*a - 11/2)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-1/4*a^6 + 1/4*a^5 + 11/4*a^4 - 5/2*a^3 - 31/4*a^2 + 25/4*a + 13/4)*q^5 - a*q^6 + (1/2*a^6 - 7*a^4 + a^3 + 26*a^2 - 7*a - 27/2)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (1/4*a^6 - 3/4*a^5 - 11/4*a^4 + 6*a^3 + 33/4*a^2 - 33/4*a - 19/4)*q^10 + (-3/4*a^6 + 1/4*a^5 + 41/4*a^4 - 4*a^3 - 151/4*a^2 + 67/4*a + 93/4)*q^11 + (-a^2 + 2)*q^12 + (-1/2*a^6 + 1/2*a^5 + 7*a^4 - 11/2*a^3 - 55/2*a^2 + 15*a + 21)*q^13 + (3/2*a^4 - 3/2*a^3 - 11*a^2 + 19/2*a + 19/2)*q^14 + (1/4*a^6 - 1/4*a^5 - 11/4*a^4 + 5/2*a^3 + 31/4*a^2 - 25/4*a - 13/4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^6 - 1/2*a^5 - 27/2*a^4 + 6*a^3 + 97/2*a^2 - 39/2*a - 28)*q^17 + a*q^18 + (-1/2*a^6 + 1/2*a^5 + 11/2*a^4 - 4*a^3 - 33/2*a^2 + 11/2*a + 27/2)*q^19 + (-1/4*a^6 + 1/4*a^5 + 3/4*a^4 - 1/2*a^3 + 21/4*a^2 - 23/4*a - 7/4)*q^20 + (-1/2*a^6 + 7*a^4 - a^3 - 26*a^2 + 7*a + 27/2)*q^21 + (1/4*a^6 - 1/4*a^5 - 19/4*a^4 + 7/2*a^3 + 91/4*a^2 - 45/4*a - 57/4)*q^22 + (a^6 - a^5 - 27/2*a^4 + 21/2*a^3 + 50*a^2 - 55/2*a - 63/2)*q^23 + (-a^3 + 4*a)*q^24 + (a^6 - a^5 - 25/2*a^4 + 21/2*a^3 + 43*a^2 - 55/2*a - 53/2)*q^25 + (1/2*a^6 - 6*a^4 + 19*a^2 - 2*a - 19/2)*q^26 - q^27 + (-a^6 + 3/2*a^5 + 25/2*a^4 - 13*a^3 - 85/2*a^2 + 47/2*a + 27)*q^28 - 2*a*q^29 + (-1/4*a^6 + 3/4*a^5 + 11/4*a^4 - 6*a^3 - 33/4*a^2 + 33/4*a + 19/4)*q^30 + (-3/4*a^6 + 3/4*a^5 + 41/4*a^4 - 17/2*a^3 - 153/4*a^2 + 87/4*a + 107/4)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3/4*a^6 - 1/4*a^5 - 41/4*a^4 + 4*a^3 + 151/4*a^2 - 67/4*a - 93/4)*q^33 + (-1/2*a^6 + 1/2*a^5 + 7*a^4 - 13/2*a^3 - 55/2*a^2 + 18*a + 19)*q^34 + (-5/4*a^6 + 3/4*a^5 + 69/4*a^4 - 21/2*a^3 - 257/4*a^2 + 139/4*a + 157/4)*q^35 + (a^2 - 2)*q^36 + (1/4*a^6 - 3/4*a^5 - 11/4*a^4 + 7*a^3 + 33/4*a^2 - 53/4*a - 19/4)*q^37 + O(q^38)
*]> ;  // time = 48.751 seconds




J[322] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 322, 322, 322, 322, 322, 322, 322, 161, 161, 161, 161, 46, 23, 14 ], new_dimensions := [ 1, 1, 1, 1, 2, 2, 3, 1, 2, 3, 5, 1, 2, 1 ], dimensions := [ 1, 1, 1, 1, 2, 2, 3, 2, 4, 6, 10, 2, 8, 2 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 0, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 5, 1, 11, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 1, 1, 361, 1, 7, 1, 1, 1, 1, 1, 1, 25, 1, 1, 0, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 25, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 361, 1, 25, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 0 ], ap_traces := [
[ -1, 2, 0, 1, 4, 0, 6, -6, -1, 10, 4, -2 ],
[ -1, 0, -2, 1, -4, 4, -8, -2, 1, 2, -6, -10 ],
[ 1, -2, -2, -1, -2, -4, -6, 0, 1, -2, 4, 0 ],
[ 1, 2, -2, 1, 6, -4, -2, 4, 1, -10, -8, -8 ],
[ -2, -2, -2, -2, 0, -4, -10, 0, -2, -4, 2, 12 ],
[ 2, -2, 2, 2, 0, 4, 2, -4, 2, 16, -10, 8 ],
[ 3, 2, 4, -3, -4, 2, 8, 0, -3, -10, -2, -10 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x^2 + 2*x - 4,
x^2 + 2*x - 2,
x^3 - 2*x^2 - 6*x + 8
], atkin_lehners := [
[ 1, -1, 1 ],
[ 1, -1, -1 ],
[ -1, 1, -1 ],
[ -1, -1, -1 ],
[ 1, 1, 1 ],
[ -1, -1, -1 ],
[ -1, 1, 1 ]
], component_group_orders := [
[ 7, 1, 1 ],
[ 1, 3, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 5, 1, 1 ],
[ 11, 11, 1 ],
[ 11, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1 ],
[ 1, 3, 1 ],
[ 5, 1, 1 ],
[ 1, 1, 1 ],
[ 1, 1, 1 ],
[ 11, 11, 1 ],
[ 11, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 11, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1 ], l_ratios := [ 1, 0, 0, 1, 0, 1, 11 ], analytic_sha_upper_bounds := [ 1, 0, 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 0, 1, 0, 1/121, 1 ], eigenvalues := [*
[ -1, 2, 0, 1, 4, 0, 6, -6, -1, 10, 4, -2 ],
[ -1, 0, -2, 1, -4, 4, -8, -2, 1, 2, -6, -10 ],
[ 1, -2, -2, -1, -2, -4, -6, 0, 1, -2, 4, 0 ],
[ 1, 2, -2, 1, 6, -4, -2, 4, 1, -10, -8, -8 ],
[
-1,
a,
-a - 2,
-1,
0,
-2*a - 4,
a - 4,
2*a + 2,
-1,
-2,
a + 2,
6
],
[
1,
a,
a + 2,
1,
-2*a - 2,
-2*a,
-a,
-2,
1,
8,
3*a - 2,
-2*a + 2
],
[
1,
a,
-a + 2,
-1,
-a^2 + 4,
-a^2 + 6,
a^2 - a - 2,
a^2 - 2*a - 4,
-1,
a^2 + 2*a - 10,
-a^2 + a + 4,
-2*a^2 + 2*a + 6
]
*], q_expansions := [*
q - q^2 + 2*q^3 + q^4 - 2*q^6 + q^7 - q^8 + q^9 + 4*q^11 + 2*q^12 - q^14 + q^16 + 6*q^17 - q^18 - 6*q^19 + 2*q^21 - 4*q^22 - q^23 - 2*q^24 - 5*q^25 - 4*q^27 + q^28 + 10*q^29 + 4*q^31 - q^32 + 8*q^33 - 6*q^34 + q^36 - 2*q^37 + O(q^38),
q - q^2 + q^4 - 2*q^5 + q^7 - q^8 - 3*q^9 + 2*q^10 - 4*q^11 + 4*q^13 - q^14 + q^16 - 8*q^17 + 3*q^18 - 2*q^19 - 2*q^20 + 4*q^22 + q^23 - q^25 - 4*q^26 + q^28 + 2*q^29 - 6*q^31 - q^32 + 8*q^34 - 2*q^35 - 3*q^36 - 10*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - 2*q^5 - 2*q^6 - q^7 + q^8 + q^9 - 2*q^10 - 2*q^11 - 2*q^12 - 4*q^13 - q^14 + 4*q^15 + q^16 - 6*q^17 + q^18 - 2*q^20 + 2*q^21 - 2*q^22 + q^23 - 2*q^24 - q^25 - 4*q^26 + 4*q^27 - q^28 - 2*q^29 + 4*q^30 + 4*q^31 + q^32 + 4*q^33 - 6*q^34 + 2*q^35 + q^36 + O(q^38),
q + q^2 + 2*q^3 + q^4 - 2*q^5 + 2*q^6 + q^7 + q^8 + q^9 - 2*q^10 + 6*q^11 + 2*q^12 - 4*q^13 + q^14 - 4*q^15 + q^16 - 2*q^17 + q^18 + 4*q^19 - 2*q^20 + 2*q^21 + 6*q^22 + q^23 + 2*q^24 - q^25 - 4*q^26 - 4*q^27 + q^28 - 10*q^29 - 4*q^30 - 8*q^31 + q^32 + 12*q^33 - 2*q^34 - 2*q^35 + q^36 - 8*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a - 2)*q^5 - a*q^6 - q^7 - q^8 + (-2*a + 1)*q^9 + (a + 2)*q^10 + a*q^12 + (-2*a - 4)*q^13 + q^14 - 4*q^15 + q^16 + (a - 4)*q^17 + (2*a - 1)*q^18 + (2*a + 2)*q^19 + (-a - 2)*q^20 - a*q^21 - q^23 - a*q^24 + (2*a + 3)*q^25 + (2*a + 4)*q^26 + (2*a - 8)*q^27 - q^28 - 2*q^29 + 4*q^30 + (a + 2)*q^31 - q^32 + (-a + 4)*q^34 + (a + 2)*q^35 + (-2*a + 1)*q^36 + 6*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a + 2)*q^5 + a*q^6 + q^7 + q^8 + (-2*a - 1)*q^9 + (a + 2)*q^10 + (-2*a - 2)*q^11 + a*q^12 - 2*a*q^13 + q^14 + 2*q^15 + q^16 - a*q^17 + (-2*a - 1)*q^18 - 2*q^19 + (a + 2)*q^20 + a*q^21 + (-2*a - 2)*q^22 + q^23 + a*q^24 + (2*a + 1)*q^25 - 2*a*q^26 - 4*q^27 + q^28 + 8*q^29 + 2*q^30 + (3*a - 2)*q^31 + q^32 + (2*a - 4)*q^33 - a*q^34 + (a + 2)*q^35 + (-2*a - 1)*q^36 + (-2*a + 2)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-a + 2)*q^5 + a*q^6 - q^7 + q^8 + (a^2 - 3)*q^9 + (-a + 2)*q^10 + (-a^2 + 4)*q^11 + a*q^12 + (-a^2 + 6)*q^13 - q^14 + (-a^2 + 2*a)*q^15 + q^16 + (a^2 - a - 2)*q^17 + (a^2 - 3)*q^18 + (a^2 - 2*a - 4)*q^19 + (-a + 2)*q^20 - a*q^21 + (-a^2 + 4)*q^22 - q^23 + a*q^24 + (a^2 - 4*a - 1)*q^25 + (-a^2 + 6)*q^26 + (2*a^2 - 8)*q^27 - q^28 + (a^2 + 2*a - 10)*q^29 + (-a^2 + 2*a)*q^30 + (-a^2 + a + 4)*q^31 + q^32 + (-2*a^2 - 2*a + 8)*q^33 + (a^2 - a - 2)*q^34 + (a - 2)*q^35 + (a^2 - 3)*q^36 + (-2*a^2 + 2*a + 6)*q^37 + O(q^38)
*]> ;  // time = 130.291 seconds




J[323] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 323, 323, 323, 323, 323, 323, 19, 17 ], new_dimensions := [ 1, 2, 4, 5, 6, 7, 1, 1 ], dimensions := [ 1, 2, 4, 5, 6, 7, 2, 2 ], intersection_graph := [ 0, 1, 1, 1, 7, 1, 5, 1, 1, 0, 1, 1, 17, 1, 1, 1, 1, 1, 0, 1, 1, 1, 7, 3, 1, 1, 1, 0, 1, 1, 1, 1, 7, 17, 1, 1, 0, 1, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 7, 1, 3, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 0 ], ap_traces := [
[ 0, 3, -2, 4, -2, 6, -1, 1, 0, -9, -9, 2 ],
[ -1, 1, 4, 2, -4, 4, -2, 2, 2, 9, -7, 14 ],
[ 0, -1, -7, -11, -2, -10, 4, 4, -3, -10, 1, -21 ],
[ -3, -3, -3, -5, 0, -20, -5, -5, 5, 6, -3, -19 ],
[ 2, -3, -1, 5, 2, 14, -6, 6, -1, -16, 9, 1 ],
[ 1, 3, 7, 1, 2, 20, 7, -7, -3, 10, 21, 21 ]
], hecke_fields := [
x - 1,
x^2 + x - 4,
x^4 - 6*x^2 - x + 7,
x^5 + 3*x^4 - 2*x^3 - 7*x^2 + 2*x + 1,
x^6 - 2*x^5 - 9*x^4 + 15*x^3 + 23*x^2 - 23*x - 21,
x^7 - x^6 - 10*x^5 + 9*x^4 + 26*x^3 - 19*x^2 - 12*x + 8
], atkin_lehners := [
[ 1, -1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 5, 1 ],
[ 1, 1 ],
[ 7, 3 ],
[ 1, 1 ],
[ 9, 9 ],
[ 5, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 7, 3 ],
[ 1, 1 ],
[ 1, 9 ],
[ 5, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 9, 5 ], torsion_lower_bounds := [ 1, 1, 1, 1, 9, 5 ], l_ratios := [ 1, 1, 0, 0, 1/9, 1/5 ], analytic_sha_upper_bounds := [ 1, 1, 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 0, 1, 1 ], eigenvalues := [*
[ 0, 3, -2, 4, -2, 6, -1, 1, 0, -9, -9, 2 ],
[
a,
a + 1,
2,
-2*a,
-2,
2,
-1,
1,
-2*a,
a + 5,
a - 3,
-2*a + 6
],
[
a,
a^3 - 2*a^2 - 4*a + 5,
-a^3 + a^2 + 3*a - 4,
-a^3 + 2*a^2 + 3*a - 8,
-2*a^3 + 4*a^2 + 7*a - 11,
-2*a^3 + a^2 + 7*a - 4,
1,
1,
3*a^3 - 8*a^2 - 9*a + 21,
2*a^3 - a^2 - 7*a - 1,
3*a^3 - 4*a^2 - 7*a + 10,
a^3 + 2*a^2 - 3*a - 12
],
[
a,
-a^3 - 2*a^2 + 2*a + 1,
a^4 + 3*a^3 - a^2 - 6*a - 1,
a^3 + 2*a^2 - a - 2,
-2*a^4 - 6*a^3 + 2*a^2 + 9*a - 1,
-a^2 - a - 2,
-1,
-1,
a^4 + 5*a^3 + 4*a^2 - 8*a - 4,
-3*a^4 - 10*a^3 + 5*a^2 + 24*a - 4,
a^3 - 2*a^2 - 9*a + 4,
4*a^4 + 11*a^3 - 8*a^2 - 21*a + 2
],
[
a,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 6*a - 1/2,
-a^4 + a^3 + 7*a^2 - 4*a - 9,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 7*a + 1/2,
1/2*a^5 - 1/2*a^4 - 5*a^3 + 5/2*a^2 + 11*a + 3/2,
-a^5 + a^4 + 8*a^3 - 4*a^2 - 13*a - 1,
-1,
1,
-1/2*a^5 - 1/2*a^4 + 4*a^3 + 11/2*a^2 - 8*a - 21/2,
a^4 - 9*a^2 + 12,
1/2*a^5 - 1/2*a^4 - 4*a^3 + 9/2*a^2 + 5*a - 11/2,
-a^3 + 3*a + 2
],
[
a,
1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 13*a^2 - 7/2*a - 5,
a^6 - 10*a^4 + 26*a^2 + a - 10,
-a^3 + 5*a,
-a^6 + 11*a^4 + a^3 - 33*a^2 - 6*a + 18,
-a^2 - a + 6,
1,
-1,
-a^4 + a^3 + 6*a^2 - 4*a - 4,
3/2*a^6 - 1/2*a^5 - 15*a^4 + 7/2*a^3 + 39*a^2 - 5/2*a - 15,
-3/2*a^6 + 1/2*a^5 + 14*a^4 - 9/2*a^3 - 32*a^2 + 11/2*a + 13,
-3*a^6 + a^5 + 30*a^4 - 6*a^3 - 78*a^2 + 36
]
*], q_expansions := [*
q + 3*q^3 - 2*q^4 - 2*q^5 + 4*q^7 + 6*q^9 - 2*q^11 - 6*q^12 + 6*q^13 - 6*q^15 + 4*q^16 - q^17 + q^19 + 4*q^20 + 12*q^21 - q^25 + 9*q^27 - 8*q^28 - 9*q^29 - 9*q^31 - 6*q^33 - 8*q^35 - 12*q^36 + 2*q^37 + O(q^38),
q + a*q^2 + (a + 1)*q^3 + (-a + 2)*q^4 + 2*q^5 + 4*q^6 - 2*a*q^7 + (a - 4)*q^8 + (a + 2)*q^9 + 2*a*q^10 - 2*q^11 + (2*a - 2)*q^12 + 2*q^13 + (2*a - 8)*q^14 + (2*a + 2)*q^15 - 3*a*q^16 - q^17 + (a + 4)*q^18 + q^19 + (-2*a + 4)*q^20 - 8*q^21 - 2*a*q^22 - 2*a*q^23 - 4*a*q^24 - q^25 + 2*a*q^26 + (-a + 3)*q^27 + (-6*a + 8)*q^28 + (a + 5)*q^29 + 8*q^30 + (a - 3)*q^31 + (a - 4)*q^32 + (-2*a - 2)*q^33 - a*q^34 - 4*a*q^35 + a*q^36 + (-2*a + 6)*q^37 + O(q^38),
q + a*q^2 + (a^3 - 2*a^2 - 4*a + 5)*q^3 + (a^2 - 2)*q^4 + (-a^3 + a^2 + 3*a - 4)*q^5 + (-2*a^3 + 2*a^2 + 6*a - 7)*q^6 + (-a^3 + 2*a^2 + 3*a - 8)*q^7 + (a^3 - 4*a)*q^8 + (3*a^3 - 3*a^2 - 10*a + 8)*q^9 + (a^3 - 3*a^2 - 5*a + 7)*q^10 + (-2*a^3 + 4*a^2 + 7*a - 11)*q^11 + (-2*a^2 - a + 4)*q^12 + (-2*a^3 + a^2 + 7*a - 4)*q^13 + (2*a^3 - 3*a^2 - 9*a + 7)*q^14 + (-2*a^3 + 5*a^2 + 9*a - 13)*q^15 + (a - 3)*q^16 + q^17 + (-3*a^3 + 8*a^2 + 11*a - 21)*q^18 + q^19 + (-a^3 - a^2 + 2*a + 1)*q^20 + (-4*a^3 + 7*a^2 + 16*a - 19)*q^21 + (4*a^3 - 5*a^2 - 13*a + 14)*q^22 + (3*a^3 - 8*a^2 - 9*a + 21)*q^23 + (2*a^3 - 5*a^2 - 8*a + 14)*q^24 + (3*a^3 - 2*a^2 - 9*a + 4)*q^25 + (a^3 - 5*a^2 - 6*a + 14)*q^26 + (a^3 - 3*a^2 - 5*a + 11)*q^27 + (-a^3 - a^2 + 3*a + 2)*q^28 + (2*a^3 - a^2 - 7*a - 1)*q^29 + (5*a^3 - 3*a^2 - 15*a + 14)*q^30 + (3*a^3 - 4*a^2 - 7*a + 10)*q^31 + (-2*a^3 + a^2 + 5*a)*q^32 + (-5*a^3 + 6*a^2 + 18*a - 20)*q^33 + a*q^34 + (4*a^3 - 5*a^2 - 13*a + 18)*q^35 + (2*a^3 - a^2 - 4*a + 5)*q^36 + (a^3 + 2*a^2 - 3*a - 12)*q^37 + O(q^38),
q + a*q^2 + (-a^3 - 2*a^2 + 2*a + 1)*q^3 + (a^2 - 2)*q^4 + (a^4 + 3*a^3 - a^2 - 6*a - 1)*q^5 + (-a^4 - 2*a^3 + 2*a^2 + a)*q^6 + (a^3 + 2*a^2 - a - 2)*q^7 + (a^3 - 4*a)*q^8 + (-a^4 - a^3 + 5*a^2 + a - 3)*q^9 + (a^3 + a^2 - 3*a - 1)*q^10 + (-2*a^4 - 6*a^3 + 2*a^2 + 9*a - 1)*q^11 + (a^4 + 2*a^3 - 2*a^2 - 2*a - 1)*q^12 + (-a^2 - a - 2)*q^13 + (a^4 + 2*a^3 - a^2 - 2*a)*q^14 + (a^4 + 4*a^3 + a^2 - 8*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - q^17 + (2*a^4 + 3*a^3 - 6*a^2 - a + 1)*q^18 - q^19 + (-a^4 - 5*a^3 - a^2 + 11*a + 2)*q^20 + (-a^2 - 2*a - 1)*q^21 + (-2*a^3 - 5*a^2 + 3*a + 2)*q^22 + (a^4 + 5*a^3 + 4*a^2 - 8*a - 4)*q^23 + (a^4 + 4*a^3 + a^2 - 5*a - 1)*q^24 + (-3*a^4 - 11*a^3 + 22*a + 1)*q^25 + (-a^3 - a^2 - 2*a)*q^26 + (2*a^4 + 5*a^3 - 3*a^2 - 5*a - 3)*q^27 + (-a^4 - a^3 + a^2 + 3)*q^28 + (-3*a^4 - 10*a^3 + 5*a^2 + 24*a - 4)*q^29 + (a^4 + 3*a^3 - a^2 - 4*a - 1)*q^30 + (a^3 - 2*a^2 - 9*a + 4)*q^31 + (-3*a^4 - 6*a^3 + 7*a^2 + 10*a - 1)*q^32 + (a^4 + a^3 - 2*a^2 + 7*a + 1)*q^33 - a*q^34 + (-2*a^4 - 6*a^3 + a^2 + 11*a + 2)*q^35 + (-a^4 + 3*a^2 - 5*a + 4)*q^36 + (4*a^4 + 11*a^3 - 8*a^2 - 21*a + 2)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 6*a - 1/2)*q^3 + (a^2 - 2)*q^4 + (-a^4 + a^3 + 7*a^2 - 4*a - 9)*q^5 + (1/2*a^5 + 1/2*a^4 - 5*a^3 - 11/2*a^2 + 11*a + 21/2)*q^6 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 5/2*a^2 + 7*a + 1/2)*q^7 + (a^3 - 4*a)*q^8 + (-a^5 + 9*a^3 + 2*a^2 - 17*a - 8)*q^9 + (-a^5 + a^4 + 7*a^3 - 4*a^2 - 9*a)*q^10 + (1/2*a^5 - 1/2*a^4 - 5*a^3 + 5/2*a^2 + 11*a + 3/2)*q^11 + (1/2*a^5 + 1/2*a^4 - 5*a^3 - 11/2*a^2 + 10*a + 23/2)*q^12 + (-a^5 + a^4 + 8*a^3 - 4*a^2 - 13*a - 1)*q^13 + (1/2*a^5 + 1/2*a^4 - 5*a^3 - 9/2*a^2 + 12*a + 21/2)*q^14 + (a^5 - 8*a^3 - 4*a^2 + 12*a + 15)*q^15 + (a^4 - 6*a^2 + 4)*q^16 - q^17 + (-2*a^5 + 17*a^3 + 6*a^2 - 31*a - 21)*q^18 + q^19 + (-a^5 + 9*a^3 - 15*a - 3)*q^20 + (-a^2 + 5)*q^21 + (1/2*a^5 - 1/2*a^4 - 5*a^3 - 1/2*a^2 + 13*a + 21/2)*q^22 + (-1/2*a^5 - 1/2*a^4 + 4*a^3 + 11/2*a^2 - 8*a - 21/2)*q^23 + (1/2*a^5 - 3/2*a^4 - 3*a^3 + 19/2*a^2 + a - 21/2)*q^24 + (-a^5 + 9*a^3 + 3*a^2 - 20*a - 8)*q^25 + (-a^5 - a^4 + 11*a^3 + 10*a^2 - 24*a - 21)*q^26 + (a^5 + a^4 - 9*a^3 - 10*a^2 + 17*a + 16)*q^27 + (1/2*a^5 + 1/2*a^4 - 4*a^3 - 9/2*a^2 + 8*a + 19/2)*q^28 + (a^4 - 9*a^2 + 12)*q^29 + (2*a^5 + a^4 - 19*a^3 - 11*a^2 + 38*a + 21)*q^30 + (1/2*a^5 - 1/2*a^4 - 4*a^3 + 9/2*a^2 + 5*a - 11/2)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - a^3 - 8*a^2 + 5*a + 15)*q^33 - a*q^34 + (-a^2 - a + 6)*q^35 + (-2*a^5 - a^4 + 18*a^3 + 11*a^2 - 33*a - 26)*q^36 + (-a^3 + 3*a + 2)*q^37 + O(q^38),
q + a*q^2 + (1/2*a^6 - 1/2*a^5 - 5*a^4 + 7/2*a^3 + 13*a^2 - 7/2*a - 5)*q^3 + (a^2 - 2)*q^4 + (a^6 - 10*a^4 + 26*a^2 + a - 10)*q^5 + (-a^4 + 6*a^2 + a - 4)*q^6 + (-a^3 + 5*a)*q^7 + (a^3 - 4*a)*q^8 + (-a^6 + 10*a^4 - 26*a^2 - 2*a + 12)*q^9 + (a^6 - 9*a^4 + 20*a^2 + 2*a - 8)*q^10 + (-a^6 + 11*a^4 + a^3 - 33*a^2 - 6*a + 18)*q^11 + (-a^6 + 10*a^4 - a^3 - 25*a^2 + 3*a + 10)*q^12 + (-a^2 - a + 6)*q^13 + (-a^4 + 5*a^2)*q^14 + (a^4 - 7*a^2 + 6)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + q^17 + (-a^6 + 9*a^4 - 21*a^2 + 8)*q^18 - q^19 + (-a^6 + a^5 + 11*a^4 - 6*a^3 - 31*a^2 + 2*a + 12)*q^20 + (a^6 - 11*a^4 - a^3 + 34*a^2 + 5*a - 20)*q^21 + (-a^6 + a^5 + 10*a^4 - 7*a^3 - 25*a^2 + 6*a + 8)*q^22 + (-a^4 + a^3 + 6*a^2 - 4*a - 4)*q^23 + (-a^6 + 10*a^4 + a^3 - 28*a^2 - 4*a + 16)*q^24 + (2*a^6 - 21*a^4 - a^3 + 58*a^2 + 8*a - 25)*q^25 + (-a^3 - a^2 + 6*a)*q^26 + (-1/2*a^6 + 1/2*a^5 + 5*a^4 - 7/2*a^3 - 12*a^2 + 5/2*a + 3)*q^27 + (-a^5 + 7*a^3 - 10*a)*q^28 + (3/2*a^6 - 1/2*a^5 - 15*a^4 + 7/2*a^3 + 39*a^2 - 5/2*a - 15)*q^29 + (a^5 - 7*a^3 + 6*a)*q^30 + (-3/2*a^6 + 1/2*a^5 + 14*a^4 - 9/2*a^3 - 32*a^2 + 11/2*a + 13)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2*a^6 - a^5 - 20*a^4 + 9*a^3 + 51*a^2 - 17*a - 18)*q^33 + a*q^34 + (3*a^6 - a^5 - 30*a^4 + 5*a^3 + 77*a^2 + 6*a - 32)*q^35 + (a^6 - a^5 - 11*a^4 + 5*a^3 + 33*a^2 - 16)*q^36 + (-3*a^6 + a^5 + 30*a^4 - 6*a^3 - 78*a^2 + 36)*q^37 + O(q^38)
*]> ;  // time = 48.319 seconds




J[326] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 326, 326, 326, 326, 326, 163, 163, 163 ], new_dimensions := [ 1, 1, 1, 5, 6, 1, 5, 7 ], dimensions := [ 1, 1, 1, 5, 6, 2, 10, 14 ], intersection_graph := [ 0, 1, 1, 1, 1, 3, 3, 1, 1, 0, 1, 17, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 5, 1, 17, 1, 0, 1, 1, 1, 611, 1, 1, 1, 1, 0, 3, 549, 1, 3, 1, 1, 1, 3, 0, 9, 1, 3, 1, 1, 1, 549, 9, 0, 1, 1, 3, 5, 611, 1, 1, 1, 0 ], ap_traces := [
[ -1, 0, -1, -1, 0, -5, 6, -6, -3, -1, -3, -2 ],
[ -1, -2, -3, -1, 0, 5, 0, 2, -3, 9, 5, 2 ],
[ 1, -2, -1, -3, -4, -1, 0, -2, -1, 3, -9, 6 ],
[ -5, 3, 9, 4, -1, 1, 2, 7, -4, 3, 16, 19 ],
[ 6, 5, 0, 5, 1, -4, 4, 7, -1, -14, 3, -9 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x^5 - 3*x^4 - 8*x^3 + 27*x^2 - 5*x - 17,
x^6 - 5*x^5 + 29*x^3 - 25*x^2 - 35*x + 36
], atkin_lehners := [
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 1 ],
[ 9, 3 ],
[ 5, 1 ],
[ 611, 1 ],
[ 67527, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 3 ],
[ 5, 1 ],
[ 1, 1 ],
[ 67527, 1 ]
], torsion_upper_bounds := [ 1, 3, 1, 1, 41 ], torsion_lower_bounds := [ 1, 3, 1, 1, 41 ], l_ratios := [ 0, 1/3, 0, 1, 1647/41 ], analytic_sha_upper_bounds := [ 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, 0, -1, -1, 0, -5, 6, -6, -3, -1, -3, -2 ],
[ -1, -2, -3, -1, 0, 5, 0, 2, -3, 9, 5, 2 ],
[ 1, -2, -1, -3, -4, -1, 0, -2, -1, 3, -9, 6 ],
[
-1,
a,
-7/13*a^4 + 10/13*a^3 + 68/13*a^2 - 84/13*a - 32/13,
4/13*a^4 - 2/13*a^3 - 50/13*a^2 + 22/13*a + 100/13,
-3/13*a^4 - 5/13*a^3 + 31/13*a^2 + 42/13*a - 49/13,
6/13*a^4 - 3/13*a^3 - 62/13*a^2 + 33/13*a + 72/13,
8/13*a^4 - 4/13*a^3 - 74/13*a^2 + 18/13*a + 70/13,
10/13*a^4 - 18/13*a^3 - 99/13*a^2 + 120/13*a + 120/13,
14/13*a^4 - 20/13*a^3 - 136/13*a^2 + 142/13*a + 116/13,
-14/13*a^4 + 20/13*a^3 + 123/13*a^2 - 168/13*a - 38/13,
-4/13*a^4 + 2/13*a^3 + 50/13*a^2 - 22/13*a - 48/13,
-3/13*a^4 - 5/13*a^3 + 57/13*a^2 + 42/13*a - 127/13
],
[
1,
a,
a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 7*a - 7,
-3*a^5 + 7*a^4 + 18*a^3 - 37*a^2 - 23*a + 41,
3*a^5 - 8*a^4 - 17*a^3 + 44*a^2 + 19*a - 48,
a^5 - 3*a^4 - 7*a^3 + 19*a^2 + 12*a - 23,
2*a^2 - 2*a - 6,
-2*a^5 + 4*a^4 + 14*a^3 - 23*a^2 - 22*a + 30,
3*a^5 - 5*a^4 - 20*a^3 + 23*a^2 + 27*a - 21,
-5*a^5 + 11*a^4 + 32*a^3 - 60*a^2 - 43*a + 65,
-a^5 + 5*a^4 + 2*a^3 - 27*a^2 + 3*a + 27,
-a^5 + 4*a^4 + 3*a^3 - 22*a^2 + 3*a + 22
]
*], q_expansions := [*
q - q^2 + q^4 - q^5 - q^7 - q^8 - 3*q^9 + q^10 - 5*q^13 + q^14 + q^16 + 6*q^17 + 3*q^18 - 6*q^19 - q^20 - 3*q^23 - 4*q^25 + 5*q^26 - q^28 - q^29 - 3*q^31 - q^32 - 6*q^34 + q^35 - 3*q^36 - 2*q^37 + O(q^38),
q - q^2 - 2*q^3 + q^4 - 3*q^5 + 2*q^6 - q^7 - q^8 + q^9 + 3*q^10 - 2*q^12 + 5*q^13 + q^14 + 6*q^15 + q^16 - q^18 + 2*q^19 - 3*q^20 + 2*q^21 - 3*q^23 + 2*q^24 + 4*q^25 - 5*q^26 + 4*q^27 - q^28 + 9*q^29 - 6*q^30 + 5*q^31 - q^32 + 3*q^35 + q^36 + 2*q^37 + O(q^38),
q + q^2 - 2*q^3 + q^4 - q^5 - 2*q^6 - 3*q^7 + q^8 + q^9 - q^10 - 4*q^11 - 2*q^12 - q^13 - 3*q^14 + 2*q^15 + q^16 + q^18 - 2*q^19 - q^20 + 6*q^21 - 4*q^22 - q^23 - 2*q^24 - 4*q^25 - q^26 + 4*q^27 - 3*q^28 + 3*q^29 + 2*q^30 - 9*q^31 + q^32 + 8*q^33 + 3*q^35 + q^36 + 6*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-7/13*a^4 + 10/13*a^3 + 68/13*a^2 - 84/13*a - 32/13)*q^5 - a*q^6 + (4/13*a^4 - 2/13*a^3 - 50/13*a^2 + 22/13*a + 100/13)*q^7 - q^8 + (a^2 - 3)*q^9 + (7/13*a^4 - 10/13*a^3 - 68/13*a^2 + 84/13*a + 32/13)*q^10 + (-3/13*a^4 - 5/13*a^3 + 31/13*a^2 + 42/13*a - 49/13)*q^11 + a*q^12 + (6/13*a^4 - 3/13*a^3 - 62/13*a^2 + 33/13*a + 72/13)*q^13 + (-4/13*a^4 + 2/13*a^3 + 50/13*a^2 - 22/13*a - 100/13)*q^14 + (-11/13*a^4 + 12/13*a^3 + 105/13*a^2 - 67/13*a - 119/13)*q^15 + q^16 + (8/13*a^4 - 4/13*a^3 - 74/13*a^2 + 18/13*a + 70/13)*q^17 + (-a^2 + 3)*q^18 + (10/13*a^4 - 18/13*a^3 - 99/13*a^2 + 120/13*a + 120/13)*q^19 + (-7/13*a^4 + 10/13*a^3 + 68/13*a^2 - 84/13*a - 32/13)*q^20 + (10/13*a^4 - 18/13*a^3 - 86/13*a^2 + 120/13*a + 68/13)*q^21 + (3/13*a^4 + 5/13*a^3 - 31/13*a^2 - 42/13*a + 49/13)*q^22 + (14/13*a^4 - 20/13*a^3 - 136/13*a^2 + 142/13*a + 116/13)*q^23 - a*q^24 + (-16/13*a^4 + 21/13*a^3 + 148/13*a^2 - 179/13*a - 49/13)*q^25 + (-6/13*a^4 + 3/13*a^3 + 62/13*a^2 - 33/13*a - 72/13)*q^26 + (a^3 - 6*a)*q^27 + (4/13*a^4 - 2/13*a^3 - 50/13*a^2 + 22/13*a + 100/13)*q^28 + (-14/13*a^4 + 20/13*a^3 + 123/13*a^2 - 168/13*a - 38/13)*q^29 + (11/13*a^4 - 12/13*a^3 - 105/13*a^2 + 67/13*a + 119/13)*q^30 + (-4/13*a^4 + 2/13*a^3 + 50/13*a^2 - 22/13*a - 48/13)*q^31 - q^32 + (-14/13*a^4 + 7/13*a^3 + 123/13*a^2 - 64/13*a - 51/13)*q^33 + (-8/13*a^4 + 4/13*a^3 + 74/13*a^2 - 18/13*a - 70/13)*q^34 + (-8/13*a^4 + 30/13*a^3 + 48/13*a^2 - 226/13*a + 86/13)*q^35 + (a^2 - 3)*q^36 + (-3/13*a^4 - 5/13*a^3 + 57/13*a^2 + 42/13*a - 127/13)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 7*a - 7)*q^5 + a*q^6 + (-3*a^5 + 7*a^4 + 18*a^3 - 37*a^2 - 23*a + 41)*q^7 + q^8 + (a^2 - 3)*q^9 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 7*a - 7)*q^10 + (3*a^5 - 8*a^4 - 17*a^3 + 44*a^2 + 19*a - 48)*q^11 + a*q^12 + (a^5 - 3*a^4 - 7*a^3 + 19*a^2 + 12*a - 23)*q^13 + (-3*a^5 + 7*a^4 + 18*a^3 - 37*a^2 - 23*a + 41)*q^14 + (3*a^5 - 6*a^4 - 20*a^3 + 32*a^2 + 28*a - 36)*q^15 + q^16 + (2*a^2 - 2*a - 6)*q^17 + (a^2 - 3)*q^18 + (-2*a^5 + 4*a^4 + 14*a^3 - 23*a^2 - 22*a + 30)*q^19 + (a^5 - 2*a^4 - 6*a^3 + 9*a^2 + 7*a - 7)*q^20 + (-8*a^5 + 18*a^4 + 50*a^3 - 98*a^2 - 64*a + 108)*q^21 + (3*a^5 - 8*a^4 - 17*a^3 + 44*a^2 + 19*a - 48)*q^22 + (3*a^5 - 5*a^4 - 20*a^3 + 23*a^2 + 27*a - 21)*q^23 + a*q^24 + (-3*a^5 + 7*a^4 + 19*a^3 - 39*a^2 - 26*a + 44)*q^25 + (a^5 - 3*a^4 - 7*a^3 + 19*a^2 + 12*a - 23)*q^26 + (a^3 - 6*a)*q^27 + (-3*a^5 + 7*a^4 + 18*a^3 - 37*a^2 - 23*a + 41)*q^28 + (-5*a^5 + 11*a^4 + 32*a^3 - 60*a^2 - 43*a + 65)*q^29 + (3*a^5 - 6*a^4 - 20*a^3 + 32*a^2 + 28*a - 36)*q^30 + (-a^5 + 5*a^4 + 2*a^3 - 27*a^2 + 3*a + 27)*q^31 + q^32 + (7*a^5 - 17*a^4 - 43*a^3 + 94*a^2 + 57*a - 108)*q^33 + (2*a^2 - 2*a - 6)*q^34 + (3*a^5 - 7*a^4 - 18*a^3 + 35*a^2 + 23*a - 35)*q^35 + (a^2 - 3)*q^36 + (-a^5 + 4*a^4 + 3*a^3 - 22*a^2 + 3*a + 22)*q^37 + O(q^38)
*]> ;  // time = 72.73 seconds




J[327] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 327, 327, 327, 327, 109, 109, 109 ], new_dimensions := [ 1, 3, 6, 9, 1, 3, 4 ], dimensions := [ 1, 3, 6, 9, 2, 6, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 13, 1, 1, 1, 0, 1, 1, 1, 107, 1, 1, 1, 0, 1, 139, 1, 1, 1, 1, 1, 0, 1, 1, 1, 13, 1, 139, 1, 0, 1, 1, 1, 107, 1, 1, 1, 0 ], ap_traces := [
[ -1, 1, -1, -2, -1, -4, -4, -7, 1, 7, -2, -6 ],
[ -3, -3, -3, -2, -1, -2, -8, 5, -9, -7, 6, -12 ],
[ 4, -6, 5, -2, 7, 6, 14, -15, 9, 5, -14, 8 ],
[ 3, 9, 1, 6, -5, 6, 0, 13, -5, -3, 18, 16 ]
], hecke_fields := [
x - 1,
x^3 + 3*x^2 - x - 5,
x^6 - 4*x^5 - 2*x^4 + 20*x^3 - 8*x^2 - 16*x + 1,
x^9 - 3*x^8 - 11*x^7 + 35*x^6 + 34*x^5 - 122*x^4 - 29*x^3 + 127*x^2 + 9*x - 5
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 13, 1 ],
[ 107, 1 ],
[ 7645, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 7645, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 55 ], torsion_lower_bounds := [ 1, 1, 1, 55 ], l_ratios := [ 0, 0, 1, 139/55 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1 ], eigenvalues := [*
[ -1, 1, -1, -2, -1, -4, -4, -7, 1, 7, -2, -6 ],
[
a,
-1,
-1,
-a^2 - 2*a + 1,
a^2 + a - 3,
-a^2 - 2*a + 1,
2*a^2 + 2*a - 8,
a^2 + a - 1,
a - 2,
a^2 + 2*a - 4,
4*a + 6,
-3*a^2 - 2*a + 5
],
[
a,
-1,
1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 5/2*a^2 + 19/2*a + 1/2,
-a^5 + 2*a^4 + 5*a^3 - 8*a^2 - 3*a + 1,
-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 5/2*a^2 - 19/2*a + 3/2,
a^5 - a^4 - 7*a^3 + 3*a^2 + 11*a + 3,
-a^4 + a^3 + 5*a^2 - 4*a + 1,
1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 1/2*a^2 + 23/2*a + 5/2,
-5/2*a^5 + 11/2*a^4 + 27/2*a^3 - 47/2*a^2 - 31/2*a + 17/2,
-3/2*a^5 + 11/2*a^4 + 7/2*a^3 - 47/2*a^2 + 15/2*a + 17/2,
-a^5 + 2*a^4 + 5*a^3 - 6*a^2 - 7*a - 5,
2*a^3 - 12*a
],
[
a,
1,
-1/6*a^8 - 1/6*a^7 + 8/3*a^6 + 7/3*a^5 - 40/3*a^4 - 10*a^3 + 125/6*a^2 + 85/6*a - 1/3,
-1/3*a^8 + 2/3*a^7 + 13/3*a^6 - 22/3*a^5 - 53/3*a^4 + 22*a^3 + 68/3*a^2 - 44/3*a + 1/3,
3*a^8 - 7/2*a^7 - 79/2*a^6 + 33*a^5 + 163*a^4 - 72*a^3 - 217*a^2 - 5/2*a + 23/2,
-4/3*a^8 + 5/3*a^7 + 52/3*a^6 - 46/3*a^5 - 212/3*a^4 + 30*a^3 + 278/3*a^2 + 31/3*a - 2/3,
-7/3*a^8 + 8/3*a^7 + 91/3*a^6 - 73/3*a^5 - 368/3*a^4 + 48*a^3 + 473/3*a^2 + 43/3*a - 11/3,
8/3*a^8 - 17/6*a^7 - 211/6*a^6 + 77/3*a^5 + 433/3*a^4 - 48*a^3 - 562/3*a^2 - 163/6*a + 35/6,
-a^8 + 3/2*a^7 + 25/2*a^6 - 16*a^5 - 47*a^4 + 48*a^3 + 53*a^2 - 69/2*a - 5/2,
-3/2*a^8 + 3/2*a^7 + 20*a^6 - 13*a^5 - 84*a^4 + 20*a^3 + 231/2*a^2 + 49/2*a - 9,
-11/3*a^8 + 13/3*a^7 + 143/3*a^6 - 122/3*a^5 - 577/3*a^4 + 88*a^3 + 736/3*a^2 + 11/3*a - 13/3,
-5/3*a^8 + 4/3*a^7 + 68/3*a^6 - 32/3*a^5 - 292/3*a^4 + 10*a^3 + 409/3*a^2 + 116/3*a - 22/3
]
*], q_expansions := [*
q - q^2 + q^3 - q^4 - q^5 - q^6 - 2*q^7 + 3*q^8 + q^9 + q^10 - q^11 - q^12 - 4*q^13 + 2*q^14 - q^15 - q^16 - 4*q^17 - q^18 - 7*q^19 + q^20 - 2*q^21 + q^22 + q^23 + 3*q^24 - 4*q^25 + 4*q^26 + q^27 + 2*q^28 + 7*q^29 + q^30 - 2*q^31 - 5*q^32 - q^33 + 4*q^34 + 2*q^35 - q^36 - 6*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 - q^5 - a*q^6 + (-a^2 - 2*a + 1)*q^7 + (-3*a^2 - 3*a + 5)*q^8 + q^9 - a*q^10 + (a^2 + a - 3)*q^11 + (-a^2 + 2)*q^12 + (-a^2 - 2*a + 1)*q^13 + (a^2 - 5)*q^14 + q^15 + (4*a^2 + 2*a - 11)*q^16 + (2*a^2 + 2*a - 8)*q^17 + a*q^18 + (a^2 + a - 1)*q^19 + (-a^2 + 2)*q^20 + (a^2 + 2*a - 1)*q^21 + (-2*a^2 - 2*a + 5)*q^22 + (a - 2)*q^23 + (3*a^2 + 3*a - 5)*q^24 - 4*q^25 + (a^2 - 5)*q^26 - q^27 + (-a^2 + 3)*q^28 + (a^2 + 2*a - 4)*q^29 + a*q^30 + (4*a + 6)*q^31 + (-4*a^2 - a + 10)*q^32 + (-a^2 - a + 3)*q^33 + (-4*a^2 - 6*a + 10)*q^34 + (a^2 + 2*a - 1)*q^35 + (a^2 - 2)*q^36 + (-3*a^2 - 2*a + 5)*q^37 + O(q^38),
q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 5/2*a^2 + 19/2*a + 1/2)*q^5 - a*q^6 + (-a^5 + 2*a^4 + 5*a^3 - 8*a^2 - 3*a + 1)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (3/2*a^5 - 7/2*a^4 - 15/2*a^3 + 27/2*a^2 + 17/2*a - 1/2)*q^10 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 5/2*a^2 - 19/2*a + 3/2)*q^11 + (-a^2 + 2)*q^12 + (a^5 - a^4 - 7*a^3 + 3*a^2 + 11*a + 3)*q^13 + (-2*a^5 + 3*a^4 + 12*a^3 - 11*a^2 - 15*a + 1)*q^14 + (-1/2*a^5 + 1/2*a^4 + 9/2*a^3 - 5/2*a^2 - 19/2*a - 1/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 + a^3 + 5*a^2 - 4*a + 1)*q^17 + a*q^18 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 1/2*a^2 + 23/2*a + 5/2)*q^19 + (3/2*a^5 - 7/2*a^4 - 15/2*a^3 + 31/2*a^2 + 9/2*a - 5/2)*q^20 + (a^5 - 2*a^4 - 5*a^3 + 8*a^2 + 3*a - 1)*q^21 + (-3/2*a^5 + 7/2*a^4 + 15/2*a^3 - 27/2*a^2 - 13/2*a + 1/2)*q^22 + (-5/2*a^5 + 11/2*a^4 + 27/2*a^3 - 47/2*a^2 - 31/2*a + 17/2)*q^23 + (-a^3 + 4*a)*q^24 + (5/2*a^5 - 13/2*a^4 - 25/2*a^3 + 57/2*a^2 + 19/2*a - 9/2)*q^25 + (3*a^5 - 5*a^4 - 17*a^3 + 19*a^2 + 19*a - 1)*q^26 - q^27 + (-3*a^5 + 4*a^4 + 19*a^3 - 15*a^2 - 25*a)*q^28 + (-3/2*a^5 + 11/2*a^4 + 7/2*a^3 - 47/2*a^2 + 15/2*a + 17/2)*q^29 + (-3/2*a^5 + 7/2*a^4 + 15/2*a^3 - 27/2*a^2 - 17/2*a + 1/2)*q^30 + (-a^5 + 2*a^4 + 5*a^3 - 6*a^2 - 7*a - 5)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^5 - 1/2*a^4 - 9/2*a^3 + 5/2*a^2 + 19/2*a - 3/2)*q^33 + (-a^5 + a^4 + 5*a^3 - 4*a^2 + a)*q^34 + (a^5 - 3*a^4 - 3*a^3 + 11*a^2 - 3*a + 1)*q^35 + (a^2 - 2)*q^36 + (2*a^3 - 12*a)*q^37 + O(q^38),
q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-1/6*a^8 - 1/6*a^7 + 8/3*a^6 + 7/3*a^5 - 40/3*a^4 - 10*a^3 + 125/6*a^2 + 85/6*a - 1/3)*q^5 + a*q^6 + (-1/3*a^8 + 2/3*a^7 + 13/3*a^6 - 22/3*a^5 - 53/3*a^4 + 22*a^3 + 68/3*a^2 - 44/3*a + 1/3)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-2/3*a^8 + 5/6*a^7 + 49/6*a^6 - 23/3*a^5 - 91/3*a^4 + 16*a^3 + 106/3*a^2 + 7/6*a - 5/6)*q^10 + (3*a^8 - 7/2*a^7 - 79/2*a^6 + 33*a^5 + 163*a^4 - 72*a^3 - 217*a^2 - 5/2*a + 23/2)*q^11 + (a^2 - 2)*q^12 + (-4/3*a^8 + 5/3*a^7 + 52/3*a^6 - 46/3*a^5 - 212/3*a^4 + 30*a^3 + 278/3*a^2 + 31/3*a - 2/3)*q^13 + (-1/3*a^8 + 2/3*a^7 + 13/3*a^6 - 19/3*a^5 - 56/3*a^4 + 13*a^3 + 83/3*a^2 + 10/3*a - 5/3)*q^14 + (-1/6*a^8 - 1/6*a^7 + 8/3*a^6 + 7/3*a^5 - 40/3*a^4 - 10*a^3 + 125/6*a^2 + 85/6*a - 1/3)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-7/3*a^8 + 8/3*a^7 + 91/3*a^6 - 73/3*a^5 - 368/3*a^4 + 48*a^3 + 473/3*a^2 + 43/3*a - 11/3)*q^17 + a*q^18 + (8/3*a^8 - 17/6*a^7 - 211/6*a^6 + 77/3*a^5 + 433/3*a^4 - 48*a^3 - 562/3*a^2 - 163/6*a + 35/6)*q^19 + (-5/6*a^8 + 7/6*a^7 + 31/3*a^6 - 37/3*a^5 - 116/3*a^4 + 36*a^3 + 265/6*a^2 - 139/6*a - 8/3)*q^20 + (-1/3*a^8 + 2/3*a^7 + 13/3*a^6 - 22/3*a^5 - 53/3*a^4 + 22*a^3 + 68/3*a^2 - 44/3*a + 1/3)*q^21 + (11/2*a^8 - 13/2*a^7 - 72*a^6 + 61*a^5 + 294*a^4 - 130*a^3 - 767/2*a^2 - 31/2*a + 15)*q^22 + (-a^8 + 3/2*a^7 + 25/2*a^6 - 16*a^5 - 47*a^4 + 48*a^3 + 53*a^2 - 69/2*a - 5/2)*q^23 + (a^3 - 4*a)*q^24 + (-1/6*a^8 - 1/6*a^7 + 8/3*a^6 + 7/3*a^5 - 40/3*a^4 - 8*a^3 + 125/6*a^2 + 25/6*a + 2/3)*q^25 + (-7/3*a^8 + 8/3*a^7 + 94/3*a^6 - 76/3*a^5 - 398/3*a^4 + 54*a^3 + 539/3*a^2 + 34/3*a - 20/3)*q^26 + q^27 + (1/3*a^8 - 2/3*a^7 - 10/3*a^6 + 22/3*a^5 + 23/3*a^4 - 26*a^3 + 1/3*a^2 + 92/3*a - 7/3)*q^28 + (-3/2*a^8 + 3/2*a^7 + 20*a^6 - 13*a^5 - 84*a^4 + 20*a^3 + 231/2*a^2 + 49/2*a - 9)*q^29 + (-2/3*a^8 + 5/6*a^7 + 49/6*a^6 - 23/3*a^5 - 91/3*a^4 + 16*a^3 + 106/3*a^2 + 7/6*a - 5/6)*q^30 + (-11/3*a^8 + 13/3*a^7 + 143/3*a^6 - 122/3*a^5 - 577/3*a^4 + 88*a^3 + 736/3*a^2 + 11/3*a - 13/3)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (3*a^8 - 7/2*a^7 - 79/2*a^6 + 33*a^5 + 163*a^4 - 72*a^3 - 217*a^2 - 5/2*a + 23/2)*q^33 + (-13/3*a^8 + 14/3*a^7 + 172/3*a^6 - 130/3*a^5 - 710/3*a^4 + 90*a^3 + 932/3*a^2 + 52/3*a - 35/3)*q^34 + (1/3*a^8 - 2/3*a^7 - 10/3*a^6 + 22/3*a^5 + 20/3*a^4 - 24*a^3 + 19/3*a^2 + 62/3*a - 22/3)*q^35 + (a^2 - 2)*q^36 + (-5/3*a^8 + 4/3*a^7 + 68/3*a^6 - 32/3*a^5 - 292/3*a^4 + 10*a^3 + 409/3*a^2 + 116/3*a - 22/3)*q^37 + O(q^38)
*]> ;  // time = 48.569 seconds




J[329] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 329, 329, 329, 329, 329, 329, 329, 47 ], new_dimensions := [ 1, 2, 3, 3, 3, 5, 6, 4 ], dimensions := [ 1, 2, 3, 3, 3, 5, 6, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 5, 1, 9, 1, 0, 1, 1, 1, 1, 13, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 37, 1, 19, 1, 1, 1, 1, 0, 1, 1, 83, 5, 1, 1, 37, 1, 0, 1, 31, 1, 13, 1, 1, 1, 1, 0, 1, 9, 1, 1, 19, 83, 31, 1, 0 ], ap_traces := [
[ -1, -1, 3, -1, 3, -6, 6, 8, 4, 2, 6, 9 ],
[ -2, 1, -3, 2, -7, 4, 4, 8, 8, -4, -2, 7 ],
[ -1, -2, -2, -3, -4, 1, 5, -4, -5, -6, -16, -12 ],
[ 1, 1, -1, -3, 1, -4, -10, 0, 10, -2, 18, -5 ],
[ -1, -4, 0, 3, 0, -11, -9, -10, 1, 6, -20, -4 ],
[ 1, 2, -4, -5, 4, 1, -3, -2, -7, 4, 10, 4 ],
[ 0, 3, 5, 6, 7, 5, -3, 0, 1, 6, 36, -13 ]
], hecke_fields := [
x - 1,
x^2 + x - 4,
x^3 + x^2 - 2*x - 1,
x^3 - x^2 - 5*x + 1,
x^3 + x^2 - 2*x - 1,
x^5 - x^4 - 11*x^3 + 12*x^2 + 28*x - 33,
x^6 - 12*x^4 + 5*x^3 + 36*x^2 - 29*x + 3
], atkin_lehners := [
[ 1, -1 ],
[ -1, 1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 9, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 19, 1 ],
[ 83, 1 ],
[ 31, 1 ],
[ 3, 3 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 83, 1 ],
[ 1, 1 ],
[ 3, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 3 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 3 ], l_ratios := [ 1, 1, 0, 1, 0, 1, 1/3 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 0, 1, 1 ], eigenvalues := [*
[ -1, -1, 3, -1, 3, -6, 6, 8, 4, 2, 6, 9 ],
[
-1,
a + 1,
a - 1,
1,
a - 3,
2,
2,
4,
4,
-2,
-2*a - 2,
3*a + 5
],
[
a,
-a^2 + 1,
-a - 1,
-1,
a^2 - 3,
a^2 - 2*a - 2,
3*a^2 + 4*a - 2,
2*a^2 + 5*a - 3,
-a^2 - 3*a - 1,
-4*a^2 + a + 5,
-5*a^2 - 3*a + 2,
-2*a^2 - 4*a - 2
],
[
a,
a^2 - a - 3,
1/2*a^2 - 2*a - 3/2,
-1,
-1/2*a^2 - a + 5/2,
-a - 1,
2*a - 4,
-a^2 + 2*a + 3,
-a^2 + 3*a + 6,
a^2 + 2*a - 5,
6,
2*a^2 - 9
],
[
a,
a^2 - 3,
-2*a^2 - a + 3,
1,
3*a^2 - 5,
-a^2 - 2,
-a^2 - 2*a - 2,
a - 3,
5*a^2 + 3*a - 7,
3*a + 3,
a^2 + a - 8,
2*a^2 + 8*a - 2
],
[
a,
-a^2 + 5,
a - 1,
-1,
-a^4 + 10*a^2 + a - 20,
a^3 - 2*a^2 - 6*a + 11,
-a^4 - a^3 + 9*a^2 + 5*a - 18,
a^4 + 2*a^3 - 11*a^2 - 12*a + 28,
-a^4 - a^3 + 9*a^2 + 6*a - 19,
a^4 + 2*a^3 - 9*a^2 - 12*a + 20,
a^4 - 10*a^2 - 2*a + 23,
-2*a^4 - 2*a^3 + 18*a^2 + 10*a - 34
],
[
a,
-a^3 + 6*a - 2,
1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 2*a^2 + 10*a - 3/2,
1,
-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + a^2 - 11*a + 15/2,
-a^5 - a^4 + 10*a^3 + 4*a^2 - 26*a + 8,
a^4 + a^3 - 7*a^2 - 3*a + 6,
-a^4 + 7*a^2 - 2*a - 4,
a^5 + 2*a^4 - 8*a^3 - 9*a^2 + 16*a - 6,
-a^4 - 2*a^3 + 5*a^2 + 8*a,
a^4 + 2*a^3 - 6*a^2 - 10*a + 11,
-a^5 - 2*a^4 + 10*a^3 + 10*a^2 - 29*a + 5
]
*], q_expansions := [*
q - q^2 - q^3 - q^4 + 3*q^5 + q^6 - q^7 + 3*q^8 - 2*q^9 - 3*q^10 + 3*q^11 + q^12 - 6*q^13 + q^14 - 3*q^15 - q^16 + 6*q^17 + 2*q^18 + 8*q^19 - 3*q^20 + q^21 - 3*q^22 + 4*q^23 - 3*q^24 + 4*q^25 + 6*q^26 + 5*q^27 + q^28 + 2*q^29 + 3*q^30 + 6*q^31 - 5*q^32 - 3*q^33 - 6*q^34 - 3*q^35 + 2*q^36 + 9*q^37 + O(q^38),
q - q^2 + (a + 1)*q^3 - q^4 + (a - 1)*q^5 + (-a - 1)*q^6 + q^7 + 3*q^8 + (a + 2)*q^9 + (-a + 1)*q^10 + (a - 3)*q^11 + (-a - 1)*q^12 + 2*q^13 - q^14 + (-a + 3)*q^15 - q^16 + 2*q^17 + (-a - 2)*q^18 + 4*q^19 + (-a + 1)*q^20 + (a + 1)*q^21 + (-a + 3)*q^22 + 4*q^23 + (3*a + 3)*q^24 - 3*a*q^25 - 2*q^26 + (-a + 3)*q^27 - q^28 - 2*q^29 + (a - 3)*q^30 + (-2*a - 2)*q^31 - 5*q^32 + (-3*a + 1)*q^33 - 2*q^34 + (a - 1)*q^35 + (-a - 2)*q^36 + (3*a + 5)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 1)*q^3 + (a^2 - 2)*q^4 + (-a - 1)*q^5 + (a^2 - a - 1)*q^6 - q^7 + (-a^2 - 2*a + 1)*q^8 + (a^2 - a - 3)*q^9 + (-a^2 - a)*q^10 + (a^2 - 3)*q^11 + (a - 1)*q^12 + (a^2 - 2*a - 2)*q^13 - a*q^14 + a*q^15 + (-3*a^2 - a + 3)*q^16 + (3*a^2 + 4*a - 2)*q^17 + (-2*a^2 - a + 1)*q^18 + (2*a^2 + 5*a - 3)*q^19 + q^20 + (a^2 - 1)*q^21 + (-a^2 - a + 1)*q^22 + (-a^2 - 3*a - 1)*q^23 + (-a^2 + a + 2)*q^24 + (a^2 + 2*a - 4)*q^25 + (-3*a^2 + 1)*q^26 + (3*a^2 + 2*a - 4)*q^27 + (-a^2 + 2)*q^28 + (-4*a^2 + a + 5)*q^29 + a^2*q^30 + (-5*a^2 - 3*a + 2)*q^31 + (4*a^2 + a - 5)*q^32 + (a^2 + a - 2)*q^33 + (a^2 + 4*a + 3)*q^34 + (a + 1)*q^35 + (-a^2 - a + 4)*q^36 + (-2*a^2 - 4*a - 2)*q^37 + O(q^38),
q + a*q^2 + (a^2 - a - 3)*q^3 + (a^2 - 2)*q^4 + (1/2*a^2 - 2*a - 3/2)*q^5 + (2*a - 1)*q^6 - q^7 + (a^2 + a - 1)*q^8 + (-a^2 + 7)*q^9 + (-3/2*a^2 + a - 1/2)*q^10 + (-1/2*a^2 - a + 5/2)*q^11 + (a + 6)*q^12 + (-a - 1)*q^13 - a*q^14 + (-1/2*a^2 - 3*a + 13/2)*q^15 + (4*a + 3)*q^16 + (2*a - 4)*q^17 + (-a^2 + 2*a + 1)*q^18 + (-a^2 + 2*a + 3)*q^19 + (-3/2*a^2 - 4*a + 9/2)*q^20 + (-a^2 + a + 3)*q^21 + (-3/2*a^2 + 1/2)*q^22 + (-a^2 + 3*a + 6)*q^23 + (a^2 + 2*a + 2)*q^24 + (2*a^2 - 3*a - 1)*q^25 + (-a^2 - a)*q^26 + (2*a^2 - 3*a - 12)*q^27 + (-a^2 + 2)*q^28 + (a^2 + 2*a - 5)*q^29 + (-7/2*a^2 + 4*a + 1/2)*q^30 + 6*q^31 + (2*a^2 + a + 2)*q^32 + (3/2*a^2 - 4*a - 13/2)*q^33 + (2*a^2 - 4*a)*q^34 + (-1/2*a^2 + 2*a + 3/2)*q^35 + (3*a^2 - 4*a - 13)*q^36 + (2*a^2 - 9)*q^37 + O(q^38),
q + a*q^2 + (a^2 - 3)*q^3 + (a^2 - 2)*q^4 + (-2*a^2 - a + 3)*q^5 + (-a^2 - a + 1)*q^6 + q^7 + (-a^2 - 2*a + 1)*q^8 + (-3*a^2 - a + 5)*q^9 + (a^2 - a - 2)*q^10 + (3*a^2 - 5)*q^11 + (-2*a^2 - a + 5)*q^12 + (-a^2 - 2)*q^13 + a*q^14 + (4*a^2 + 3*a - 8)*q^15 + (-3*a^2 - a + 3)*q^16 + (-a^2 - 2*a - 2)*q^17 + (2*a^2 - a - 3)*q^18 + (a - 3)*q^19 + (2*a^2 + 2*a - 5)*q^20 + (a^2 - 3)*q^21 + (-3*a^2 + a + 3)*q^22 + (5*a^2 + 3*a - 7)*q^23 + (3*a^2 + 3*a - 4)*q^24 + (-3*a^2 - 2*a + 4)*q^25 + (a^2 - 4*a - 1)*q^26 + (3*a^2 + 4*a - 4)*q^27 + (a^2 - 2)*q^28 + (3*a + 3)*q^29 + (-a^2 + 4)*q^30 + (a^2 + a - 8)*q^31 + (4*a^2 + a - 5)*q^32 + (-5*a^2 - 3*a + 12)*q^33 + (-a^2 - 4*a - 1)*q^34 + (-2*a^2 - a + 3)*q^35 + (3*a^2 + 3*a - 8)*q^36 + (2*a^2 + 8*a - 2)*q^37 + O(q^38),
q + a*q^2 + (-a^2 + 5)*q^3 + (a^2 - 2)*q^4 + (a - 1)*q^5 + (-a^3 + 5*a)*q^6 - q^7 + (a^3 - 4*a)*q^8 + (a^4 - 10*a^2 + 22)*q^9 + (a^2 - a)*q^10 + (-a^4 + 10*a^2 + a - 20)*q^11 + (-a^4 + 7*a^2 - 10)*q^12 + (a^3 - 2*a^2 - 6*a + 11)*q^13 - a*q^14 + (-a^3 + a^2 + 5*a - 5)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^4 - a^3 + 9*a^2 + 5*a - 18)*q^17 + (a^4 + a^3 - 12*a^2 - 6*a + 33)*q^18 + (a^4 + 2*a^3 - 11*a^2 - 12*a + 28)*q^19 + (a^3 - a^2 - 2*a + 2)*q^20 + (a^2 - 5)*q^21 + (-a^4 - a^3 + 13*a^2 + 8*a - 33)*q^22 + (-a^4 - a^3 + 9*a^2 + 6*a - 19)*q^23 + (-a^4 - 2*a^3 + 12*a^2 + 8*a - 33)*q^24 + (a^2 - 2*a - 4)*q^25 + (a^4 - 2*a^3 - 6*a^2 + 11*a)*q^26 + (3*a^4 + a^3 - 29*a^2 - 5*a + 62)*q^27 + (-a^2 + 2)*q^28 + (a^4 + 2*a^3 - 9*a^2 - 12*a + 20)*q^29 + (-a^4 + a^3 + 5*a^2 - 5*a)*q^30 + (a^4 - 10*a^2 - 2*a + 23)*q^31 + (a^4 + 3*a^3 - 12*a^2 - 16*a + 33)*q^32 + (-3*a^4 - 2*a^3 + 30*a^2 + 10*a - 67)*q^33 + (-2*a^4 - 2*a^3 + 17*a^2 + 10*a - 33)*q^34 + (-a + 1)*q^35 + (-a^3 + 2*a^2 + 5*a - 11)*q^36 + (-2*a^4 - 2*a^3 + 18*a^2 + 10*a - 34)*q^37 + O(q^38),
q + a*q^2 + (-a^3 + 6*a - 2)*q^3 + (a^2 - 2)*q^4 + (1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 2*a^2 + 10*a - 3/2)*q^5 + (-a^4 + 6*a^2 - 2*a)*q^6 + q^7 + (a^3 - 4*a)*q^8 + (-a^3 + 5*a - 2)*q^9 + (1/2*a^5 + 3/2*a^4 - 9/2*a^3 - 8*a^2 + 13*a - 3/2)*q^10 + (-1/2*a^5 - 1/2*a^4 + 9/2*a^3 + a^2 - 11*a + 15/2)*q^11 + (-a^5 + 8*a^3 - 2*a^2 - 12*a + 4)*q^12 + (-a^5 - a^4 + 10*a^3 + 4*a^2 - 26*a + 8)*q^13 + a*q^14 + (1/2*a^5 + 1/2*a^4 - 11/2*a^3 - 3*a^2 + 16*a - 3/2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (a^4 + a^3 - 7*a^2 - 3*a + 6)*q^17 + (-a^4 + 5*a^2 - 2*a)*q^18 + (-a^4 + 7*a^2 - 2*a - 4)*q^19 + (1/2*a^5 + 1/2*a^4 - 3/2*a^3 - a^2 - 7*a + 3/2)*q^20 + (-a^3 + 6*a - 2)*q^21 + (-1/2*a^5 - 3/2*a^4 + 7/2*a^3 + 7*a^2 - 7*a + 3/2)*q^22 + (a^5 + 2*a^4 - 8*a^3 - 9*a^2 + 16*a - 6)*q^23 + (-2*a^4 + 3*a^3 + 12*a^2 - 21*a + 3)*q^24 + (a^5 + a^4 - 10*a^3 - 4*a^2 + 26*a - 8)*q^25 + (-a^5 - 2*a^4 + 9*a^3 + 10*a^2 - 21*a + 3)*q^26 + (a^4 + 2*a^3 - 6*a^2 - 11*a + 7)*q^27 + (a^2 - 2)*q^28 + (-a^4 - 2*a^3 + 5*a^2 + 8*a)*q^29 + (1/2*a^5 + 1/2*a^4 - 11/2*a^3 - 2*a^2 + 13*a - 3/2)*q^30 + (a^4 + 2*a^3 - 6*a^2 - 10*a + 11)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (1/2*a^5 + 1/2*a^4 - 13/2*a^3 - a^2 + 22*a - 21/2)*q^33 + (a^5 + a^4 - 7*a^3 - 3*a^2 + 6*a)*q^34 + (1/2*a^5 + 1/2*a^4 - 9/2*a^3 - 2*a^2 + 10*a - 3/2)*q^35 + (-a^5 + 7*a^3 - 2*a^2 - 10*a + 4)*q^36 + (-a^5 - 2*a^4 + 10*a^3 + 10*a^2 - 29*a + 5)*q^37 + O(q^38)
*]> ;  // time = 47.721 seconds




J[330] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 330, 330, 330, 330, 330, 165, 165, 165, 110, 110, 110, 110, 66, 66, 66, 55, 55, 33, 30, 15, 11 ], new_dimensions := [ 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1 ], dimensions := [ 1, 1, 1, 1, 1, 4, 4, 6, 2, 2, 2, 4, 2, 2, 2, 4, 8, 4, 2, 4, 8 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 7, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 25, 5, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 49, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 5, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 5, 1, 1, 1, 0, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 49, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2401, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 81, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 25, 1, 1, 1, 25, 1, 2401, 81, 1, 1, 0 ], ap_traces := [
[ -1, -1, -1, 0, 1, 2, -2, 8, 4, 2, 8, -2 ],
[ -1, -1, 1, -4, 1, -2, -2, -8, 0, 2, -8, -10 ],
[ 1, -1, -1, 4, -1, 2, 2, 4, -4, 6, 0, -10 ],
[ 1, -1, 1, 0, 1, 6, 2, -4, 0, -10, 0, 6 ],
[ 1, 1, 1, 0, -1, -2, 2, -4, 0, -2, 0, -2 ]
], hecke_fields := [
x - 1,
x - 1,
x - 1,
x - 1,
x - 1
], atkin_lehners := [
[ 1, 1, 1, -1 ],
[ 1, 1, -1, -1 ],
[ -1, 1, 1, 1 ],
[ -1, 1, -1, -1 ],
[ -1, -1, -1, 1 ]
], component_group_orders := [
[ 1, 5, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 7, 5, 1, 1 ],
[ 1, 3, 1, 1 ],
[ 1, 1, 1, 1 ]
], tamagawa_numbers := [
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 7, 1, 1, 1 ],
[ 1, 1, 1, 1 ],
[ 1, 1, 1, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1 ], l_ratios := [ 1, 0, 7, 1, 1 ], analytic_sha_upper_bounds := [ 1, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 1, 1 ], eigenvalues := [*
[ -1, -1, -1, 0, 1, 2, -2, 8, 4, 2, 8, -2 ],
[ -1, -1, 1, -4, 1, -2, -2, -8, 0, 2, -8, -10 ],
[ 1, -1, -1, 4, -1, 2, 2, 4, -4, 6, 0, -10 ],
[ 1, -1, 1, 0, 1, 6, 2, -4, 0, -10, 0, 6 ],
[ 1, 1, 1, 0, -1, -2, 2, -4, 0, -2, 0, -2 ]
*], q_expansions := [*
q - q^2 - q^3 + q^4 - q^5 + q^6 - q^8 + q^9 + q^10 + q^11 - q^12 + 2*q^13 + q^15 + q^16 - 2*q^17 - q^18 + 8*q^19 - q^20 - q^22 + 4*q^23 + q^24 + q^25 - 2*q^26 - q^27 + 2*q^29 - q^30 + 8*q^31 - q^32 - q^33 + 2*q^34 + q^36 - 2*q^37 + O(q^38),
q - q^2 - q^3 + q^4 + q^5 + q^6 - 4*q^7 - q^8 + q^9 - q^10 + q^11 - q^12 - 2*q^13 + 4*q^14 - q^15 + q^16 - 2*q^17 - q^18 - 8*q^19 + q^20 + 4*q^21 - q^22 + q^24 + q^25 + 2*q^26 - q^27 - 4*q^28 + 2*q^29 + q^30 - 8*q^31 - q^32 - q^33 + 2*q^34 - 4*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 - q^5 - q^6 + 4*q^7 + q^8 + q^9 - q^10 - q^11 - q^12 + 2*q^13 + 4*q^14 + q^15 + q^16 + 2*q^17 + q^18 + 4*q^19 - q^20 - 4*q^21 - q^22 - 4*q^23 - q^24 + q^25 + 2*q^26 - q^27 + 4*q^28 + 6*q^29 + q^30 + q^32 + q^33 + 2*q^34 - 4*q^35 + q^36 - 10*q^37 + O(q^38),
q + q^2 - q^3 + q^4 + q^5 - q^6 + q^8 + q^9 + q^10 + q^11 - q^12 + 6*q^13 - q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 + q^20 + q^22 - q^24 + q^25 + 6*q^26 - q^27 - 10*q^29 - q^30 + q^32 - q^33 + 2*q^34 + q^36 + 6*q^37 + O(q^38),
q + q^2 + q^3 + q^4 + q^5 + q^6 + q^8 + q^9 + q^10 - q^11 + q^12 - 2*q^13 + q^15 + q^16 + 2*q^17 + q^18 - 4*q^19 + q^20 - q^22 + q^24 + q^25 - 2*q^26 + q^27 - 2*q^29 + q^30 + q^32 - q^33 + 2*q^34 + q^36 - 2*q^37 + O(q^38)
*]> ;  // time = 625.69 seconds




J[331] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 331, 331, 331, 331 ], new_dimensions := [ 1, 3, 7, 16 ], dimensions := [ 1, 3, 7, 16 ], intersection_graph := [ 0, 1, 3, 1, 1, 0, 53, 1, 3, 53, 0, 1, 1, 1, 1, 0 ], ap_traces := [
[ -1, -2, 1, 2, 0, -4, 1, -3, -8, -10, 7, -8 ],
[ -2, -1, -6, 3, -7, -13, -3, 6, -2, -2, -14, 11 ],
[ -2, 0, -13, -8, -10, 5, -17, -19, 15, -24, 4, 2 ],
[ 3, -1, 20, 1, 9, 8, 19, 2, 5, 32, -1, 1 ]
], hecke_fields := [
x - 1,
x^3 + 2*x^2 - 4*x - 7,
x^7 + 2*x^6 - 6*x^5 - 8*x^4 + 11*x^3 + 3*x^2 - 5*x + 1,
x^16 - 3*x^15 - 19*x^14 + 60*x^13 + 136*x^12 - 465*x^11 - 448*x^10 + 1747*x^9 + 657*x^8 - 3241*x^7 - 375*x^6 + 2695*x^5 + 230*x^4 - 855*x^3 - 110*x^2 + 56*x + 8
], atkin_lehners := [
[ 1 ],
[ 1 ],
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 55 ]
], tamagawa_numbers := [
[ 1 ],
[ 1 ],
[ 1 ],
[ 55 ]
], torsion_upper_bounds := [ 1, 1, 1, 55 ], torsion_lower_bounds := [ 1, 1, 1, 55 ], l_ratios := [ 0, 0, 0, 1/55 ], analytic_sha_upper_bounds := [ 0, 0, 0, 1 ], analytic_sha_lower_bounds := [ 0, 0, 0, 1 ], eigenvalues := [*
[ -1, -2, 1, 2, 0, -4, 1, -3, -8, -10, 7, -8 ],
[
a,
-a - 1,
-a^2 + 2,
a^2 - 3,
-a - 3,
-2*a^2 - a + 3,
2*a^2 - 9,
-a^2 + 6,
2*a^2 + 4*a - 6,
-2*a^2 - 2*a + 6,
a^2 + 4*a - 6,
-3*a^2 + 2*a + 17
],
[
a,
-a^6 - 3*a^5 + 4*a^4 + 13*a^3 - 4*a^2 - 9*a + 3,
4*a^6 + 10*a^5 - 19*a^4 - 42*a^3 + 23*a^2 + 25*a - 11,
-5*a^6 - 11*a^5 + 27*a^4 + 45*a^3 - 41*a^2 - 24*a + 13,
8*a^6 + 20*a^5 - 38*a^4 - 82*a^3 + 48*a^2 + 45*a - 20,
-7*a^6 - 17*a^5 + 34*a^4 + 70*a^3 - 42*a^2 - 38*a + 14,
-a^6 - 4*a^5 + 14*a^3 + 12*a^2 - a - 7,
-6*a^6 - 17*a^5 + 22*a^4 + 67*a^3 - 11*a^2 - 31*a + 2,
9*a^6 + 22*a^5 - 44*a^4 - 91*a^3 + 58*a^2 + 49*a - 21,
2*a^6 + 7*a^5 - 4*a^4 - 27*a^3 - 8*a^2 + 13*a - 1,
-11*a^6 - 27*a^5 + 55*a^4 + 113*a^3 - 77*a^2 - 65*a + 31,
2*a^6 + 7*a^5 - 3*a^4 - 26*a^3 - 16*a^2 + 6*a + 11
],
[
a,
-1069/10445*a^15 + 5881/10445*a^14 + 17079/10445*a^13 - 23704/2089*a^12 - 84578/10445*a^11 + 923333/10445*a^10 + 43752/10445*a^9 - 3472853/10445*a^8 + 749508/10445*a^7 + 6394904/10445*a^6 - 1779062/10445*a^5 - 5163977/10445*a^4 + 881194/10445*a^3 + 1507308/10445*a^2 - 64022/10445*a - 14094/2089,
-193/41780*a^15 + 3141/41780*a^14 + 8817/41780*a^13 - 34827/20890*a^12 - 31464/10445*a^11 + 604449/41780*a^10 + 402503/20890*a^9 - 2602543/41780*a^8 - 2497031/41780*a^7 + 1153919/8356*a^6 + 3522077/41780*a^5 - 6042977/41780*a^4 - 85673/2089*a^3 + 2150027/41780*a^2 + 44617/10445*a - 14807/10445,
-5839/10445*a^15 + 9898/10445*a^14 + 114836/10445*a^13 - 191702/10445*a^12 - 859383/10445*a^11 + 1427727/10445*a^10 + 3015533/10445*a^9 - 5069699/10445*a^8 - 4853023/10445*a^7 + 1713921/2089*a^6 + 2824461/10445*a^5 - 5994991/10445*a^4 - 56504/2089*a^3 + 1607476/10445*a^2 - 86331/10445*a - 91994/10445,
-3028/10445*a^15 + 5627/10445*a^14 + 58148/10445*a^13 - 21605/2089*a^12 - 419726/10445*a^11 + 793671/10445*a^10 + 1386534/10445*a^9 - 2758186/10445*a^8 - 1983964/10445*a^7 + 4488793/10445*a^6 + 864276/10445*a^5 - 2892759/10445*a^4 - 153317/10445*a^3 + 679861/10445*a^2 + 75441/10445*a - 4708/2089,
11711/20890*a^15 - 26481/20890*a^14 - 223473/20890*a^13 + 258476/10445*a^12 + 798976/10445*a^11 - 3881061/20890*a^10 - 2583287/10445*a^9 + 13914713/20890*a^8 + 6823439/20890*a^7 - 23859907/20890*a^6 - 249959/4178*a^5 + 17062757/20890*a^4 - 942881/10445*a^3 - 884743/4178*a^2 + 295971/10445*a + 126152/10445,
-1163/20890*a^15 - 2383/10445*a^14 + 2987/2089*a^13 + 101753/20890*a^12 - 150653/10445*a^11 - 169427/4178*a^10 + 303653/4178*a^9 + 3466543/20890*a^8 - 396958/2089*a^7 - 3587263/10445*a^6 + 2479577/10445*a^5 + 3404271/10445*a^4 - 2254001/20890*a^3 - 2106001/20890*a^2 + 304807/20890*a + 41803/10445,
-6259/41780*a^15 + 4297/8356*a^14 + 112473/41780*a^13 - 107181/10445*a^12 - 181532/10445*a^11 + 3317291/41780*a^10 + 464876/10445*a^9 - 2492457/8356*a^8 - 625319/41780*a^7 + 23200151/41780*a^6 - 4108631/41780*a^5 - 3899193/8356*a^4 + 2021913/20890*a^3 + 6198629/41780*a^2 - 99793/4178*a - 74482/10445,
2332/10445*a^15 + 3189/10445*a^14 - 10849/2089*a^13 - 69647/10445*a^12 + 500884/10445*a^11 + 118145/2089*a^10 - 467090/2089*a^9 - 2461587/10445*a^8 + 1148618/2089*a^7 + 5226699/10445*a^6 - 6978761/10445*a^5 - 5264758/10445*a^4 + 3388984/10445*a^3 + 2024199/10445*a^2 - 540218/10445*a - 148334/10445,
8807/20890*a^15 - 2953/4178*a^14 - 175709/20890*a^13 + 143826/10445*a^12 + 672947/10445*a^11 - 2163643/20890*a^10 - 2463261/10445*a^9 + 1563499/4178*a^8 + 8701507/20890*a^7 - 13635973/20890*a^6 - 6721027/20890*a^5 + 2012599/4178*a^4 + 1138871/10445*a^3 - 2636267/20890*a^2 - 20260/2089*a + 78272/10445,
-3206/10445*a^15 + 2533/20890*a^14 + 136337/20890*a^13 - 7403/4178*a^12 - 570112/10445*a^11 + 81712/10445*a^10 + 4752891/20890*a^9 - 9247/10445*a^8 - 10289071/20890*a^7 - 1564493/20890*a^6 + 10877949/20890*a^5 + 3457649/20890*a^4 - 4630483/20890*a^3 - 961108/10445*a^2 + 455799/20890*a + 18789/2089,
1789/2089*a^15 - 14424/10445*a^14 - 174664/10445*a^13 + 274689/10445*a^12 + 258721/2089*a^11 - 1996708/10445*a^10 - 4469182/10445*a^9 + 6817782/10445*a^8 + 7022272/10445*a^7 - 10685442/10445*a^6 - 3974896/10445*a^5 + 6155623/10445*a^4 + 595163/10445*a^3 - 1044086/10445*a^2 + 25213/10445*a + 5818/10445
]
*], q_expansions := [*
q - q^2 - 2*q^3 - q^4 + q^5 + 2*q^6 + 2*q^7 + 3*q^8 + q^9 - q^10 + 2*q^12 - 4*q^13 - 2*q^14 - 2*q^15 - q^16 + q^17 - q^18 - 3*q^19 - q^20 - 4*q^21 - 8*q^23 - 6*q^24 - 4*q^25 + 4*q^26 + 4*q^27 - 2*q^28 - 10*q^29 + 2*q^30 + 7*q^31 - 5*q^32 - q^34 + 2*q^35 - q^36 - 8*q^37 + O(q^38),
q + a*q^2 + (-a - 1)*q^3 + (a^2 - 2)*q^4 + (-a^2 + 2)*q^5 + (-a^2 - a)*q^6 + (a^2 - 3)*q^7 + (-2*a^2 + 7)*q^8 + (a^2 + 2*a - 2)*q^9 + (2*a^2 - 2*a - 7)*q^10 + (-a - 3)*q^11 + (a^2 - 2*a - 5)*q^12 + (-2*a^2 - a + 3)*q^13 + (-2*a^2 + a + 7)*q^14 + (-a^2 + 2*a + 5)*q^15 + (2*a^2 - a - 10)*q^16 + (2*a^2 - 9)*q^17 + (2*a + 7)*q^18 + (-a^2 + 6)*q^19 + (-4*a^2 + a + 10)*q^20 + (a^2 - a - 4)*q^21 + (-a^2 - 3*a)*q^22 + (2*a^2 + 4*a - 6)*q^23 + (-2*a^2 + a + 7)*q^24 + (4*a^2 - a - 15)*q^25 + (3*a^2 - 5*a - 14)*q^26 + (-a^2 - a - 2)*q^27 + (3*a^2 - a - 8)*q^28 + (-2*a^2 - 2*a + 6)*q^29 + (4*a^2 + a - 7)*q^30 + (a^2 + 4*a - 6)*q^31 + (-a^2 - 2*a)*q^32 + (a^2 + 4*a + 3)*q^33 + (-4*a^2 - a + 14)*q^34 + (-3*a^2 + a + 8)*q^35 + (3*a + 4)*q^36 + (-3*a^2 + 2*a + 17)*q^37 + O(q^38),
q + a*q^2 + (-a^6 - 3*a^5 + 4*a^4 + 13*a^3 - 4*a^2 - 9*a + 3)*q^3 + (a^2 - 2)*q^4 + (4*a^6 + 10*a^5 - 19*a^4 - 42*a^3 + 23*a^2 + 25*a - 11)*q^5 + (-a^6 - 2*a^5 + 5*a^4 + 7*a^3 - 6*a^2 - 2*a + 1)*q^6 + (-5*a^6 - 11*a^5 + 27*a^4 + 45*a^3 - 41*a^2 - 24*a + 13)*q^7 + (a^3 - 4*a)*q^8 + (a^6 + 2*a^5 - 6*a^4 - 7*a^3 + 11*a^2 - 2*a - 3)*q^9 + (2*a^6 + 5*a^5 - 10*a^4 - 21*a^3 + 13*a^2 + 9*a - 4)*q^10 + (8*a^6 + 20*a^5 - 38*a^4 - 82*a^3 + 48*a^2 + 45*a - 20)*q^11 + (2*a^6 + 5*a^5 - 9*a^4 - 21*a^3 + 9*a^2 + 14*a - 5)*q^12 + (-7*a^6 - 17*a^5 + 34*a^4 + 70*a^3 - 42*a^2 - 38*a + 14)*q^13 + (-a^6 - 3*a^5 + 5*a^4 + 14*a^3 - 9*a^2 - 12*a + 5)*q^14 + (-a^6 - a^5 + 7*a^4 + 2*a^3 - 11*a^2 + 6*a - 2)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^6 - 4*a^5 + 14*a^3 + 12*a^2 - a - 7)*q^17 + (a^4 - 5*a^2 + 2*a - 1)*q^18 + (-6*a^6 - 17*a^5 + 22*a^4 + 67*a^3 - 11*a^2 - 31*a + 2)*q^19 + (-7*a^6 - 18*a^5 + 33*a^4 + 75*a^3 - 43*a^2 - 44*a + 20)*q^20 + (a^6 + 4*a^5 - a^4 - 18*a^3 - 8*a^2 + 19*a - 3)*q^21 + (4*a^6 + 10*a^5 - 18*a^4 - 40*a^3 + 21*a^2 + 20*a - 8)*q^22 + (9*a^6 + 22*a^5 - 44*a^4 - 91*a^3 + 58*a^2 + 49*a - 21)*q^23 + (3*a^6 + 7*a^5 - 15*a^4 - 27*a^3 + 20*a^2 + 9*a - 4)*q^24 + (-4*a^6 - 10*a^5 + 20*a^4 + 45*a^3 - 26*a^2 - 33*a + 14)*q^25 + (-3*a^6 - 8*a^5 + 14*a^4 + 35*a^3 - 17*a^2 - 21*a + 7)*q^26 + (8*a^6 + 19*a^5 - 39*a^4 - 75*a^3 + 50*a^2 + 33*a - 14)*q^27 + (9*a^6 + 21*a^5 - 48*a^4 - 88*a^3 + 73*a^2 + 48*a - 25)*q^28 + (2*a^6 + 7*a^5 - 4*a^4 - 27*a^3 - 8*a^2 + 13*a - 1)*q^29 + (a^6 + a^5 - 6*a^4 + 9*a^2 - 7*a + 1)*q^30 + (-11*a^6 - 27*a^5 + 55*a^4 + 113*a^3 - 77*a^2 - 65*a + 31)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-a^6 - 2*a^5 + 5*a^4 + 7*a^3 - 6*a^2 - 2*a - 1)*q^33 + (-2*a^6 - 6*a^5 + 6*a^4 + 23*a^3 + 2*a^2 - 12*a + 1)*q^34 + (3*a^6 + 3*a^5 - 24*a^4 - 9*a^3 + 54*a^2 - 4*a - 14)*q^35 + (-2*a^6 - 3*a^5 + 12*a^4 + 9*a^3 - 20*a^2 + 3*a + 6)*q^36 + (2*a^6 + 7*a^5 - 3*a^4 - 26*a^3 - 16*a^2 + 6*a + 11)*q^37 + O(q^38),
q + a*q^2 + (-1069/10445*a^15 + 5881/10445*a^14 + 17079/10445*a^13 - 23704/2089*a^12 - 84578/10445*a^11 + 923333/10445*a^10 + 43752/10445*a^9 - 3472853/10445*a^8 + 749508/10445*a^7 + 6394904/10445*a^6 - 1779062/10445*a^5 - 5163977/10445*a^4 + 881194/10445*a^3 + 1507308/10445*a^2 - 64022/10445*a - 14094/2089)*q^3 + (a^2 - 2)*q^4 + (-193/41780*a^15 + 3141/41780*a^14 + 8817/41780*a^13 - 34827/20890*a^12 - 31464/10445*a^11 + 604449/41780*a^10 + 402503/20890*a^9 - 2602543/41780*a^8 - 2497031/41780*a^7 + 1153919/8356*a^6 + 3522077/41780*a^5 - 6042977/41780*a^4 - 85673/2089*a^3 + 2150027/41780*a^2 + 44617/10445*a - 14807/10445)*q^5 + (2674/10445*a^15 - 3232/10445*a^14 - 10876/2089*a^13 + 60806/10445*a^12 + 426248/10445*a^11 - 87032/2089*a^10 - 321062/2089*a^9 + 1451841/10445*a^8 + 586055/2089*a^7 - 2179937/10445*a^6 - 2283022/10445*a^5 + 1127064/10445*a^4 + 593313/10445*a^3 - 181612/10445*a^2 - 10606/10445*a + 8552/10445)*q^6 + (-5839/10445*a^15 + 9898/10445*a^14 + 114836/10445*a^13 - 191702/10445*a^12 - 859383/10445*a^11 + 1427727/10445*a^10 + 3015533/10445*a^9 - 5069699/10445*a^8 - 4853023/10445*a^7 + 1713921/2089*a^6 + 2824461/10445*a^5 - 5994991/10445*a^4 - 56504/2089*a^3 + 1607476/10445*a^2 - 86331/10445*a - 91994/10445)*q^7 + (a^3 - 4*a)*q^8 + (1988/10445*a^15 - 719/2089*a^14 - 39926/10445*a^13 + 70023/10445*a^12 + 310006/10445*a^11 - 525127/10445*a^10 - 1165718/10445*a^9 + 377466/2089*a^8 + 2172098/10445*a^7 - 3284252/10445*a^6 - 1856308/10445*a^5 + 500081/2089*a^4 + 672948/10445*a^3 - 801488/10445*a^2 - 10528/2089*a + 84701/10445)*q^9 + (1281/20890*a^15 + 515/4178*a^14 - 29037/20890*a^13 - 24902/10445*a^12 + 128676/10445*a^11 + 359271/20890*a^10 - 566343/10445*a^9 - 237023/4178*a^8 + 2572041/20890*a^7 + 1724851/20890*a^6 - 2761421/20890*a^5 - 166907/4178*a^4 + 496253/10445*a^3 + 78619/20890*a^2 - 2421/2089*a + 386/10445)*q^10 + (-3028/10445*a^15 + 5627/10445*a^14 + 58148/10445*a^13 - 21605/2089*a^12 - 419726/10445*a^11 + 793671/10445*a^10 + 1386534/10445*a^9 - 2758186/10445*a^8 - 1983964/10445*a^7 + 4488793/10445*a^6 + 864276/10445*a^5 - 2892759/10445*a^4 - 153317/10445*a^3 + 679861/10445*a^2 + 75441/10445*a - 4708/2089)*q^11 + (6928/10445*a^15 - 15336/10445*a^14 - 133792/10445*a^13 + 299624/10445*a^12 + 977406/10445*a^11 - 2254024/10445*a^10 - 3307141/10445*a^9 + 8119163/10445*a^8 + 4987481/10445*a^7 - 2814016/2089*a^6 - 2521242/10445*a^5 + 10306247/10445*a^4 + 68454/2089*a^3 - 2731082/10445*a^2 - 13148/10445*a + 119548/10445)*q^12 + (11711/20890*a^15 - 26481/20890*a^14 - 223473/20890*a^13 + 258476/10445*a^12 + 798976/10445*a^11 - 3881061/20890*a^10 - 2583287/10445*a^9 + 13914713/20890*a^8 + 6823439/20890*a^7 - 23859907/20890*a^6 - 249959/4178*a^5 + 17062757/20890*a^4 - 942881/10445*a^3 - 884743/4178*a^2 + 295971/10445*a + 126152/10445)*q^13 + (-7619/10445*a^15 + 779/2089*a^14 + 158638/10445*a^13 - 65279/10445*a^12 - 1287408/10445*a^11 + 399661/10445*a^10 + 5131034/10445*a^9 - 203360/2089*a^8 - 10354594/10445*a^7 + 634836/10445*a^6 + 9741114/10445*a^5 + 212090/2089*a^4 - 3384869/10445*a^3 - 728621/10445*a^2 + 46998/2089*a + 46712/10445)*q^14 + (19/20890*a^15 + 7419/20890*a^14 - 7319/20890*a^13 - 15024/2089*a^12 + 65239/10445*a^11 + 1168437/20890*a^10 - 451136/10445*a^9 - 4344267/20890*a^8 + 2915607/20890*a^7 + 7766491/20890*a^6 - 4179063/20890*a^5 - 5828803/20890*a^4 + 909453/10445*a^3 + 1369117/20890*a^2 - 34264/10445*a + 2566/2089)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1163/20890*a^15 - 2383/10445*a^14 + 2987/2089*a^13 + 101753/20890*a^12 - 150653/10445*a^11 - 169427/4178*a^10 + 303653/4178*a^9 + 3466543/20890*a^8 - 396958/2089*a^7 - 3587263/10445*a^6 + 2479577/10445*a^5 + 3404271/10445*a^4 - 2254001/20890*a^3 - 2106001/20890*a^2 + 304807/20890*a + 41803/10445)*q^17 + (2369/10445*a^15 - 2154/10445*a^14 - 49257/10445*a^13 + 39638/10445*a^12 + 399293/10445*a^11 - 275094/10445*a^10 - 1585706/10445*a^9 + 865982/10445*a^8 + 3158856/10445*a^7 - 1110808/10445*a^6 - 571451/2089*a^5 + 215708/10445*a^4 + 898252/10445*a^3 + 33208/2089*a^2 - 26627/10445*a - 15904/10445)*q^18 + (-6259/41780*a^15 + 4297/8356*a^14 + 112473/41780*a^13 - 107181/10445*a^12 - 181532/10445*a^11 + 3317291/41780*a^10 + 464876/10445*a^9 - 2492457/8356*a^8 - 625319/41780*a^7 + 23200151/41780*a^6 - 4108631/41780*a^5 - 3899193/8356*a^4 + 2021913/20890*a^3 + 6198629/41780*a^2 - 99793/4178*a - 74482/10445)*q^19 + (6611/20890*a^15 - 7839/20890*a^14 - 135481/20890*a^13 + 15279/2089*a^12 + 540396/10445*a^11 - 1163247/20890*a^10 - 2114014/10445*a^9 + 4332967/20890*a^8 + 8373603/20890*a^7 - 8050641/20890*a^6 - 7808907/20890*a^5 + 6740853/20890*a^4 + 1443667/10445*a^3 - 2033327/20890*a^2 - 124716/10445*a + 4898/2089)*q^20 + (-468/2089*a^15 - 339/2089*a^14 + 10080/2089*a^13 + 8176/2089*a^12 - 84887/2089*a^11 - 75939/2089*a^10 + 352554/2089*a^9 + 347203/2089*a^8 - 741957/2089*a^7 - 818000/2089*a^6 + 705878/2089*a^5 + 927895/2089*a^4 - 178848/2089*a^3 - 390330/2089*a^2 - 35802/2089*a + 31596/2089)*q^21 + (-3457/10445*a^15 + 616/10445*a^14 + 14731/2089*a^13 - 7918/10445*a^12 - 614349/10445*a^11 + 5998/2089*a^10 + 506346/2089*a^9 + 5432/10445*a^8 - 1064991/2089*a^7 - 271224/10445*a^6 + 5267701/10445*a^5 + 543123/10445*a^4 - 1909079/10445*a^3 - 257639/10445*a^2 + 146028/10445*a + 24224/10445)*q^22 + (2332/10445*a^15 + 3189/10445*a^14 - 10849/2089*a^13 - 69647/10445*a^12 + 500884/10445*a^11 + 118145/2089*a^10 - 467090/2089*a^9 - 2461587/10445*a^8 + 1148618/2089*a^7 + 5226699/10445*a^6 - 6978761/10445*a^5 - 5264758/10445*a^4 + 3388984/10445*a^3 + 2024199/10445*a^2 - 540218/10445*a - 148334/10445)*q^23 + (20/2089*a^15 + 4304/10445*a^14 - 7296/10445*a^13 - 86414/10445*a^12 + 23000/2089*a^11 + 666923/10445*a^10 - 773433/10445*a^9 - 2467897/10445*a^8 + 2523018/10445*a^7 + 4436632/10445*a^6 - 3798669/10445*a^5 - 3505298/10445*a^4 + 2005732/10445*a^3 + 1112156/10445*a^2 - 247208/10445*a - 72528/10445)*q^24 + (-2183/41780*a^15 - 2291/41780*a^14 + 13421/8356*a^13 + 10677/10445*a^12 - 196234/10445*a^11 - 58709/8356*a^10 + 224447/2089*a^9 + 845783/41780*a^8 - 2624627/8356*a^7 - 615541/41780*a^6 + 18137889/41780*a^5 - 1079553/41780*a^4 - 4449373/20890*a^3 + 903109/41780*a^2 + 431961/20890*a - 24151/10445)*q^25 + (4326/10445*a^15 - 482/10445*a^14 - 92854/10445*a^13 + 2628/10445*a^12 + 782277/10445*a^11 + 39977/10445*a^10 - 3272202/10445*a^9 - 435344/10445*a^8 + 7047722/10445*a^7 + 314183/2089*a^6 - 7249194/10445*a^5 - 2289646/10445*a^4 + 558919/2089*a^3 + 940076/10445*a^2 - 201756/10445*a - 46844/10445)*q^26 + (-4282/10445*a^15 + 8977/10445*a^14 + 83711/10445*a^13 - 179694/10445*a^12 - 623049/10445*a^11 + 1402252/10445*a^10 + 2179183/10445*a^9 - 5348441/10445*a^8 - 3527473/10445*a^7 + 10197999/10445*a^6 + 435060/2089*a^5 - 8880719/10445*a^4 - 411586/10445*a^3 + 592640/2089*a^2 + 8756/10445*a - 196308/10445)*q^27 + (-7284/10445*a^15 - 5919/10445*a^14 + 162189/10445*a^13 + 26436/2089*a^12 - 1424408/10445*a^11 - 1137732/10445*a^10 + 6262527/10445*a^9 + 4790487/10445*a^8 - 14352297/10445*a^7 - 10255221/10445*a^6 + 15944733/10445*a^5 + 10357483/10445*a^4 - 6677826/10445*a^3 - 3818052/10445*a^2 + 646038/10445*a + 48988/2089)*q^28 + (8807/20890*a^15 - 2953/4178*a^14 - 175709/20890*a^13 + 143826/10445*a^12 + 672947/10445*a^11 - 2163643/20890*a^10 - 2463261/10445*a^9 + 1563499/4178*a^8 + 8701507/20890*a^7 - 13635973/20890*a^6 - 6721027/20890*a^5 + 2012599/4178*a^4 + 1138871/10445*a^3 - 2636267/20890*a^2 - 20260/2089*a + 78272/10445)*q^29 + (3738/10445*a^15 - 3479/10445*a^14 - 15138/2089*a^13 + 63947/10445*a^12 + 588636/10445*a^11 - 89376/2089*a^10 - 437746/2089*a^9 + 1451562/10445*a^8 + 782807/2089*a^7 - 2085969/10445*a^6 - 2940004/10445*a^5 + 907268/10445*a^4 + 692681/10445*a^3 - 33219/10445*a^2 + 12298/10445*a - 76/10445)*q^30 + (-3206/10445*a^15 + 2533/20890*a^14 + 136337/20890*a^13 - 7403/4178*a^12 - 570112/10445*a^11 + 81712/10445*a^10 + 4752891/20890*a^9 - 9247/10445*a^8 - 10289071/20890*a^7 - 1564493/20890*a^6 + 10877949/20890*a^5 + 3457649/20890*a^4 - 4630483/20890*a^3 - 961108/10445*a^2 + 455799/20890*a + 18789/2089)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2598/10445*a^15 - 5751/10445*a^14 - 50172/10445*a^13 + 112359/10445*a^12 + 363916/10445*a^11 - 845259/10445*a^10 - 1194481/10445*a^9 + 3048603/10445*a^8 + 1579151/10445*a^7 - 1063612/2089*a^6 - 133367/10445*a^5 + 4020212/10445*a^4 - 156595/2089*a^3 - 1267002/10445*a^2 + 230082/10445*a + 123168/10445)*q^33 + (-1651/4178*a^15 + 7773/20890*a^14 + 171533/20890*a^13 - 71569/10445*a^12 - 138793/2089*a^11 + 997241/20890*a^10 + 2749152/10445*a^9 - 3205489/20890*a^8 - 10943809/20890*a^7 + 4523029/20890*a^6 + 9942827/20890*a^5 - 1986511/20890*a^4 - 1550183/10445*a^3 + 176877/20890*a^2 + 74367/10445*a + 4652/10445)*q^34 + (-4226/10445*a^15 + 4786/10445*a^14 + 85558/10445*a^13 - 89042/10445*a^12 - 667277/10445*a^11 + 626946/10445*a^10 + 2498769/10445*a^9 - 2032553/10445*a^8 - 4514259/10445*a^7 + 2855272/10445*a^6 + 669215/2089*a^5 - 1121647/10445*a^4 - 517293/10445*a^3 - 7364/2089*a^2 - 160347/10445*a + 16096/10445)*q^35 + (977/10445*a^15 + 2944/10445*a^14 - 4530/2089*a^13 - 62937/10445*a^12 + 206479/10445*a^11 + 105172/2089*a^10 - 188245/2089*a^9 - 2172237/10445*a^8 + 444585/2089*a^7 + 4599624/10445*a^6 - 2456131/10445*a^5 - 4647428/10445*a^4 + 845639/10445*a^3 + 1836939/10445*a^2 - 43288/10445*a - 188354/10445)*q^36 + (1789/2089*a^15 - 14424/10445*a^14 - 174664/10445*a^13 + 274689/10445*a^12 + 258721/2089*a^11 - 1996708/10445*a^10 - 4469182/10445*a^9 + 6817782/10445*a^8 + 7022272/10445*a^7 - 10685442/10445*a^6 - 3974896/10445*a^5 + 6155623/10445*a^4 + 595163/10445*a^3 - 1044086/10445*a^2 + 25213/10445*a + 5818/10445)*q^37 + O(q^38)
*]> ;  // time = 6.399 seconds




J[334] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 334, 334, 334, 334, 334, 334, 167, 167 ], new_dimensions := [ 1, 2, 2, 2, 3, 3, 2, 12 ], dimensions := [ 1, 2, 2, 2, 3, 3, 4, 24 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 0, 1, 7, 1, 1, 63, 1, 1, 1, 0, 1, 1, 1, 99, 1, 1, 7, 1, 0, 1, 1, 791, 1, 1, 1, 1, 1, 0, 11, 1, 1, 5, 1, 1, 1, 11, 0, 1, 1, 1, 63, 99, 791, 1, 1, 0 ], ap_traces := [
[ 1, 0, 3, 1, 0, -2, -2, 2, 2, -4, 1, -3 ],
[ -2, -1, -2, 0, -5, 0, -5, 0, -4, -12, -4, 3 ],
[ -2, 0, 2, -6, 0, 8, 4, 4, 12, 8, -10, -6 ],
[ 2, -3, -4, -6, -9, 2, 1, -2, 0, -16, 2, -3 ],
[ -3, -1, 0, 0, 11, -10, 9, -4, -10, 18, 4, 1 ],
[ 3, 1, -3, 3, 7, 2, 3, -4, 4, 4, -5, -4 ]
], hecke_fields := [
x - 1,
x^2 + x - 1,
x^2 - 8,
x^2 + 3*x + 1,
x^3 + x^2 - 5*x - 4,
x^3 - x^2 - 7*x + 8
], atkin_lehners := [
[ -1, 1 ],
[ 1, 1 ],
[ 1, -1 ],
[ -1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 5, 1 ],
[ 63, 1 ],
[ 99, 1 ],
[ 791, 1 ],
[ 77, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 99, 1 ],
[ 1, 1 ],
[ 77, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 7 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 7 ], l_ratios := [ 1, 0, 1, 0, 1, 11/7 ], analytic_sha_upper_bounds := [ 1, 0, 1, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 0, 1, 0, 1, 1 ], eigenvalues := [*
[ 1, 0, 3, 1, 0, -2, -2, 2, 2, -4, 1, -3 ],
[
-1,
a,
-1,
-2*a - 1,
-a - 3,
-2*a - 1,
3*a - 1,
2*a + 1,
2*a - 1,
-2*a - 7,
6*a + 1,
9*a + 6
],
[
-1,
a,
-1/2*a + 1,
-3,
a,
a + 4,
a + 2,
-2*a + 2,
-a + 6,
-a + 4,
-a - 5,
-3/2*a - 3
],
[
1,
a,
-2*a - 5,
-3,
a - 3,
4*a + 7,
-5*a - 7,
4*a + 5,
2*a + 3,
2*a - 5,
-4*a - 5,
-3*a - 6
],
[
-1,
a,
-a^2 + a + 4,
-a^2 + a + 4,
a^2,
-a^2 - a,
-a^2 - 2*a + 6,
a^2 + 3*a - 4,
-a^2 - a,
-a^2 + a + 10,
-3*a^2 - a + 12,
-a
],
[
1,
a,
-1,
1,
-a^2 - 2*a + 8,
-a^2 - a + 6,
-a^2 + 6,
a^2 - a - 6,
3*a^2 + a - 14,
a^2 + a - 4,
-2*a^2 - 2*a + 9,
a^2 + 2*a - 7
]
*], q_expansions := [*
q + q^2 + q^4 + 3*q^5 + q^7 + q^8 - 3*q^9 + 3*q^10 - 2*q^13 + q^14 + q^16 - 2*q^17 - 3*q^18 + 2*q^19 + 3*q^20 + 2*q^23 + 4*q^25 - 2*q^26 + q^28 - 4*q^29 + q^31 + q^32 - 2*q^34 + 3*q^35 - 3*q^36 - 3*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 - q^5 - a*q^6 + (-2*a - 1)*q^7 - q^8 + (-a - 2)*q^9 + q^10 + (-a - 3)*q^11 + a*q^12 + (-2*a - 1)*q^13 + (2*a + 1)*q^14 - a*q^15 + q^16 + (3*a - 1)*q^17 + (a + 2)*q^18 + (2*a + 1)*q^19 - q^20 + (a - 2)*q^21 + (a + 3)*q^22 + (2*a - 1)*q^23 - a*q^24 - 4*q^25 + (2*a + 1)*q^26 + (-4*a - 1)*q^27 + (-2*a - 1)*q^28 + (-2*a - 7)*q^29 + a*q^30 + (6*a + 1)*q^31 - q^32 + (-2*a - 1)*q^33 + (-3*a + 1)*q^34 + (2*a + 1)*q^35 + (-a - 2)*q^36 + (9*a + 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-1/2*a + 1)*q^5 - a*q^6 - 3*q^7 - q^8 + 5*q^9 + (1/2*a - 1)*q^10 + a*q^11 + a*q^12 + (a + 4)*q^13 + 3*q^14 + (a - 4)*q^15 + q^16 + (a + 2)*q^17 - 5*q^18 + (-2*a + 2)*q^19 + (-1/2*a + 1)*q^20 - 3*a*q^21 - a*q^22 + (-a + 6)*q^23 - a*q^24 + (-a - 2)*q^25 + (-a - 4)*q^26 + 2*a*q^27 - 3*q^28 + (-a + 4)*q^29 + (-a + 4)*q^30 + (-a - 5)*q^31 - q^32 + 8*q^33 + (-a - 2)*q^34 + (3/2*a - 3)*q^35 + 5*q^36 + (-3/2*a - 3)*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 + (-2*a - 5)*q^5 + a*q^6 - 3*q^7 + q^8 + (-3*a - 4)*q^9 + (-2*a - 5)*q^10 + (a - 3)*q^11 + a*q^12 + (4*a + 7)*q^13 - 3*q^14 + (a + 2)*q^15 + q^16 + (-5*a - 7)*q^17 + (-3*a - 4)*q^18 + (4*a + 5)*q^19 + (-2*a - 5)*q^20 - 3*a*q^21 + (a - 3)*q^22 + (2*a + 3)*q^23 + a*q^24 + (8*a + 16)*q^25 + (4*a + 7)*q^26 + (2*a + 3)*q^27 - 3*q^28 + (2*a - 5)*q^29 + (a + 2)*q^30 + (-4*a - 5)*q^31 + q^32 + (-6*a - 1)*q^33 + (-5*a - 7)*q^34 + (6*a + 15)*q^35 + (-3*a - 4)*q^36 + (-3*a - 6)*q^37 + O(q^38),
q - q^2 + a*q^3 + q^4 + (-a^2 + a + 4)*q^5 - a*q^6 + (-a^2 + a + 4)*q^7 - q^8 + (a^2 - 3)*q^9 + (a^2 - a - 4)*q^10 + a^2*q^11 + a*q^12 + (-a^2 - a)*q^13 + (a^2 - a - 4)*q^14 + (2*a^2 - a - 4)*q^15 + q^16 + (-a^2 - 2*a + 6)*q^17 + (-a^2 + 3)*q^18 + (a^2 + 3*a - 4)*q^19 + (-a^2 + a + 4)*q^20 + (2*a^2 - a - 4)*q^21 - a^2*q^22 + (-a^2 - a)*q^23 - a*q^24 + (a^2 - 3*a - 1)*q^25 + (a^2 + a)*q^26 + (-a^2 - a + 4)*q^27 + (-a^2 + a + 4)*q^28 + (-a^2 + a + 10)*q^29 + (-2*a^2 + a + 4)*q^30 + (-3*a^2 - a + 12)*q^31 - q^32 + (-a^2 + 5*a + 4)*q^33 + (a^2 + 2*a - 6)*q^34 + (a^2 - 3*a + 4)*q^35 + (a^2 - 3)*q^36 - a*q^37 + O(q^38),
q + q^2 + a*q^3 + q^4 - q^5 + a*q^6 + q^7 + q^8 + (a^2 - 3)*q^9 - q^10 + (-a^2 - 2*a + 8)*q^11 + a*q^12 + (-a^2 - a + 6)*q^13 + q^14 - a*q^15 + q^16 + (-a^2 + 6)*q^17 + (a^2 - 3)*q^18 + (a^2 - a - 6)*q^19 - q^20 + a*q^21 + (-a^2 - 2*a + 8)*q^22 + (3*a^2 + a - 14)*q^23 + a*q^24 - 4*q^25 + (-a^2 - a + 6)*q^26 + (a^2 + a - 8)*q^27 + q^28 + (a^2 + a - 4)*q^29 - a*q^30 + (-2*a^2 - 2*a + 9)*q^31 + q^32 + (-3*a^2 + a + 8)*q^33 + (-a^2 + 6)*q^34 - q^35 + (a^2 - 3)*q^36 + (a^2 + 2*a - 7)*q^37 + O(q^38)
*]> ;  // time = 71.439 seconds




J[335] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 335, 335, 335, 335, 335, 67, 67, 67 ], new_dimensions := [ 1, 2, 2, 7, 11, 1, 2, 2 ], dimensions := [ 1, 2, 2, 7, 11, 2, 4, 4 ], intersection_graph := [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 9, 1, 1, 1, 0, 179, 1, 1, 1, 1, 1, 1, 179, 0, 1, 1, 1, 59, 1, 1, 1, 1, 0, 1, 81, 1, 1, 1, 1, 1, 1, 0, 1, 25, 1, 9, 1, 1, 81, 1, 0, 1, 1, 1, 1, 59, 1, 25, 1, 0 ], ap_traces := [
[ 0, 0, 1, -2, -2, -2, -3, -1, -1, -9, 0, -3 ],
[ 0, 0, -2, -4, 0, -4, -6, -2, -6, 6, 4, -10 ],
[ 1, 0, -2, 0, -6, 12, -2, -4, 2, -10, 12, -6 ],
[ 2, 4, -7, 10, 6, 4, 17, 3, 5, -1, 0, 15 ],
[ 0, 0, 11, 4, 6, 4, 2, 10, -10, 26, -8, 12 ]
], hecke_fields := [
x - 1,
x^2 - 2,
x^2 - x - 1,
x^7 - 2*x^6 - 12*x^5 + 21*x^4 + 42*x^3 - 52*x^2 - 39*x - 6,
x^11 - 18*x^9 + 2*x^8 + 114*x^7 - 24*x^6 - 306*x^5 + 86*x^4 + 332*x^3 - 109*x^2 - 114*x + 46
], atkin_lehners := [
[ -1, -1 ],
[ 1, 1 ],
[ 1, -1 ],
[ 1, -1 ],
[ -1, 1 ]
], component_group_orders := [
[ 1, 1 ],
[ 9, 1 ],
[ 1, 1 ],
[ 177, 3 ],
[ 1377, 1 ]
], tamagawa_numbers := [
[ 1, 1 ],
[ 1, 1 ],
[ 1, 1 ],
[ 1, 3 ],
[ 1377, 1 ]
], torsion_upper_bounds := [ 1, 1, 1, 3, 17 ], torsion_lower_bounds := [ 1, 1, 1, 3, 17 ], l_ratios := [ 0, 0, 1, 1/3, 81/17 ], analytic_sha_upper_bounds := [ 0, 0, 1, 1, 1 ], analytic_sha_lower_bounds := [ 0, 0, 1, 1, 1 ], eigenvalues := [*
[ 0, 0, 1, -2, -2, -2, -3, -1, -1, -9, 0, -3 ],
[
a,
-a,
-1,
-2,
a,
-2,
a - 3,
-1,
-a - 3,
-2*a + 3,
3*a + 2,
3*a - 5
],
[
a,
2*a - 1,
-1,
2*a - 1,
2*a - 4,
6,
-6*a + 2,
4*a - 4,
-2*a + 2,
-4*a - 3,
-4*a + 8,
2*a - 4
],
[
a,
-2*a^6 + a^5 + 23*a^4 - 8*a^3 - 66*a^2 + 12*a + 10,
-1,
2*a^6 + 2*a^5 - 23*a^4 - 26*a^3 + 61*a^2 + 81*a + 20,
-2*a^5 + 22*a^3 + 2*a^2 - 58*a - 12,
3*a^6 - 4*a^5 - 34*a^4 + 39*a^3 + 100*a^2 - 90*a - 34,
-3*a^6 + 4*a^5 + 34*a^4 - 41*a^3 - 100*a^2 + 100*a + 39,
2*a^3 - 12*a - 1,
a^6 - 4*a^5 - 12*a^4 + 45*a^3 + 42*a^2 - 122*a - 39,
3*a^6 - 5*a^5 - 33*a^4 + 51*a^3 + 96*a^2 - 124*a - 45,
-2*a^6 + 10*a^5 + 22*a^4 - 108*a^3 - 74*a^2 + 282*a + 86,
7*a^6 - 8*a^5 - 80*a^4 + 79*a^3 + 236*a^2 - 186*a - 73
],
[
a,
43/5261*a^10 - 84/5261*a^9 - 1344/5261*a^8 + 1488/5261*a^7 + 13496/5261*a^6 - 9411/5261*a^5 - 54847/5261*a^4 + 24218/5261*a^3 + 84666/5261*a^2 - 17145/5261*a - 28424/5261,
1,
2136/5261*a^10 + 966/5261*a^9 - 37154/5261*a^8 - 11851/5261*a^7 + 223588/5261*a^6 + 42464/5261*a^5 - 550354/5261*a^4 - 52284/5261*a^3 + 499421/5261*a^2 + 31446/5261*a - 115048/5261,
-1271/5261*a^10 + 770/5261*a^9 + 22842/5261*a^8 - 13640/5261*a^7 - 141250/5261*a^6 + 78376/5261*a^5 + 351072/5261*a^4 - 160620/5261*a^3 - 307876/5261*a^2 + 86139/5261*a + 57128/5261,
1936/5261*a^10 + 1112/5261*a^9 - 34818/5261*a^8 - 16692/5261*a^7 + 219421/5261*a^6 + 85502/5261*a^5 - 576654/5261*a^4 - 176549/5261*a^3 + 579238/5261*a^2 + 109722/5261*a - 156334/5261,
-1169/5261*a^10 - 41/5261*a^9 + 20388/5261*a^8 - 2280/5261*a^7 - 123184/5261*a^6 + 27912/5261*a^5 + 306614/5261*a^4 - 76990/5261*a^3 - 293500/5261*a^2 + 41799/5261*a + 82077/5261,
1666/5261*a^10 + 783/5261*a^9 - 29560/5261*a^8 - 10864/5261*a^7 + 184597/5261*a^6 + 52588/5261*a^5 - 491156/5261*a^4 - 119399/5261*a^3 + 529424/5261*a^2 + 107018/5261*a - 153673/5261,
-769/5261*a^10 - 333/5261*a^9 + 15716/5261*a^8 + 7402/5261*a^7 - 114850/5261*a^6 - 58164/5261*a^5 + 359214/5261*a^4 + 182062/5261*a^3 - 453134/5261*a^2 - 177885/5261*a + 164649/5261,
-436/5261*a^10 - 2207/5261*a^9 + 6776/5261*a^8 + 34586/5261*a^7 - 38230/5261*a^6 - 176803/5261*a^5 + 105757/5261*a^4 + 327278/5261*a^3 - 149340/5261*a^2 - 160170/5261*a + 87187/5261,
1977/5261*a^10 + 1766/5261*a^9 - 34876/5261*a^8 - 26774/5261*a^7 + 214304/5261*a^6 + 136602/5261*a^5 - 547588/5261*a^4 - 276418/5261*a^3 + 549118/5261*a^2 + 171433/5261*a - 178542/5261,
-1793/5261*a^10 - 1269/5261*a^9 + 32306/5261*a^8 + 17970/5261*a^7 - 206472/5261*a^6 - 84866/5261*a^5 + 561262/5261*a^4 + 170832/5261*a^3 - 594982/5261*a^2 - 144961/5261*a + 180119/5261
]
*], q_expansions := [*
q - 2*q^4 + q^5 - 2*q^7 - 3*q^9 - 2*q^11 - 2*q^13 + 4*q^16 - 3*q^17 - q^19 - 2*q^20 - q^23 + q^25 + 4*q^28 - 9*q^29 - 2*q^35 + 6*q^36 - 3*q^37 + O(q^38),
q + a*q^2 - a*q^3 - q^5 - 2*q^6 - 2*q^7 - 2*a*q^8 - q^9 - a*q^10 + a*q^11 - 2*q^13 - 2*a*q^14 + a*q^15 - 4*q^16 + (a - 3)*q^17 - a*q^18 - q^19 + 2*a*q^21 + 2*q^22 + (-a - 3)*q^23 + 4*q^24 + q^25 - 2*a*q^26 + 4*a*q^27 + (-2*a + 3)*q^29 + 2*q^30 + (3*a + 2)*q^31 - 2*q^33 + (-3*a + 2)*q^34 + 2*q^35 + (3*a - 5)*q^37 + O(q^38),
q + a*q^2 + (2*a - 1)*q^3 + (a - 1)*q^4 - q^5 + (a + 2)*q^6 + (2*a - 1)*q^7 + (-2*a + 1)*q^8 + 2*q^9 - a*q^10 + (2*a - 4)*q^11 + (-a + 3)*q^12 + 6*q^13 + (a + 2)*q^14 + (-2*a + 1)*q^15 - 3*a*q^16 + (-6*a + 2)*q^17 + 2*a*q^18 + (4*a - 4)*q^19 + (-a + 1)*q^20 + 5*q^21 + (-2*a + 2)*q^22 + (-2*a + 2)*q^23 - 5*q^24 + q^25 + 6*a*q^26 + (-2*a + 1)*q^27 + (-a + 3)*q^28 + (-4*a - 3)*q^29 + (-a - 2)*q^30 + (-4*a + 8)*q^31 + (a - 5)*q^32 + (-6*a + 8)*q^33 + (-4*a - 6)*q^34 + (-2*a + 1)*q^35 + (2*a - 2)*q^36 + (2*a - 4)*q^37 + O(q^38),
q + a*q^2 + (-2*a^6 + a^5 + 23*a^4 - 8*a^3 - 66*a^2 + 12*a + 10)*q^3 + (a^2 - 2)*q^4 - q^5 + (-3*a^6 - a^5 + 34*a^4 + 18*a^3 - 92*a^2 - 68*a - 12)*q^6 + (2*a^6 + 2*a^5 - 23*a^4 - 26*a^3 + 61*a^2 + 81*a + 20)*q^7 + (a^3 - 4*a)*q^8 + (3*a^5 - 36*a^3 - 5*a^2 + 105*a + 31)*q^9 - a*q^10 + (-2*a^5 + 22*a^3 + 2*a^2 - 58*a - 12)*q^11 + (-3*a^6 - 4*a^5 + 35*a^4 + 50*a^3 - 92*a^2 - 153*a - 38)*q^12 + (3*a^6 - 4*a^5 - 34*a^4 + 39*a^3 + 100*a^2 - 90*a - 34)*q^13 + (6*a^6 + a^5 - 68*a^4 - 23*a^3 + 185*a^2 + 98*a + 12)*q^14 + (2*a^6 - a^5 - 23*a^4 + 8*a^3 + 66*a^2 - 12*a - 10)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-3*a^6 + 4*a^5 + 34*a^4 - 41*a^3 - 100*a^2 + 100*a + 39)*q^17 + (3*a^6 - 36*a^4 - 5*a^3 + 105*a^2 + 31*a)*q^18 + (2*a^3 - 12*a - 1)*q^19 + (-a^2 + 2)*q^20 + (-3*a^6 + 4*a^5 + 35*a^4 - 39*a^3 - 107*a^2 + 87*a + 38)*q^21 + (-2*a^6 + 22*a^4 + 2*a^3 - 58*a^2 - 12*a)*q^22 + (a^6 - 4*a^5 - 12*a^4 + 45*a^3 + 42*a^2 - 122*a - 39)*q^23 + (-4*a^6 + a^5 + 45*a^4 - 2*a^3 - 125*a^2 - 19*a + 6)*q^24 + q^25 + (2*a^6 + 2*a^5 - 24*a^4 - 26*a^3 + 66*a^2 + 83*a + 18)*q^26 + (-3*a^6 - a^5 + 35*a^4 + 17*a^3 - 98*a^2 - 66*a - 8)*q^27 + (9*a^6 - 103*a^4 - 15*a^3 + 288*a^2 + 84*a - 4)*q^28 + (3*a^6 - 5*a^5 - 33*a^4 + 51*a^3 + 96*a^2 - 124*a - 45)*q^29 + (3*a^6 + a^5 - 34*a^4 - 18*a^3 + 92*a^2 + 68*a + 12)*q^30 + (-2*a^6 + 10*a^5 + 22*a^4 - 108*a^3 - 74*a^2 + 282*a + 86)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-6*a^6 + 4*a^5 + 68*a^4 - 34*a^3 - 194*a^2 + 62*a + 36)*q^33 + (-2*a^6 - 2*a^5 + 22*a^4 + 26*a^3 - 56*a^2 - 78*a - 18)*q^34 + (-2*a^6 - 2*a^5 + 23*a^4 + 26*a^3 - 61*a^2 - 81*a - 20)*q^35 + (6*a^6 - 6*a^5 - 68*a^4 + 51*a^3 + 197*a^2 - 93*a - 44)*q^36 + (7*a^6 - 8*a^5 - 80*a^4 + 79*a^3 + 236*a^2 - 186*a - 73)*q^37 + O(q^38),
q + a*q^2 + (43/5261*a^10 - 84/5261*a^9 - 1344/5261*a^8 + 1488/5261*a^7 + 13496/5261*a^6 - 9411/5261*a^5 - 54847/5261*a^4 + 24218/5261*a^3 + 84666/5261*a^2 - 17145/5261*a - 28424/5261)*q^3 + (a^2 - 2)*q^4 + q^5 + (-84/5261*a^10 - 570/5261*a^9 + 1402/5261*a^8 + 8594/5261*a^7 - 8379/5261*a^6 - 41689/5261*a^5 + 20520/5261*a^4 + 70390/5261*a^3 - 12458/5261*a^2 - 23522/5261*a - 1978/5261)*q^6 + (2136/5261*a^10 + 966/5261*a^9 - 37154/5261*a^8 - 11851/5261*a^7 + 223588/5261*a^6 + 42464/5261*a^5 - 550354/5261*a^4 - 52284/5261*a^3 + 499421/5261*a^2 + 31446/5261*a - 115048/5261)*q^7 + (a^3 - 4*a)*q^8 + (-2405/5261*a^10 - 1664/5261*a^9 + 41769/5261*a^8 + 23464/5261*a^7 - 251736/5261*a^6 - 108264/5261*a^5 + 628092/5261*a^4 + 195152/5261*a^3 - 607584/5261*a^2 - 115666/5261*a + 188255/5261)*q^9 + a*q^10 + (-1271/5261*a^10 + 770/5261*a^9 + 22842/5261*a^8 - 13640/5261*a^7 - 141250/5261*a^6 + 78376/5261*a^5 + 351072/5261*a^4 - 160620/5261*a^3 - 307876/5261*a^2 + 86139/5261*a + 57128/5261)*q^11 + (-656/5261*a^10 + 58/5261*a^9 + 11450/5261*a^8 - 1779/5261*a^7 - 70697/5261*a^6 + 13638/5261*a^5 + 187308/5261*a^4 - 33006/5261*a^3 - 202010/5261*a^2 + 22736/5261*a + 60712/5261)*q^12 + (1936/5261*a^10 + 1112/5261*a^9 - 34818/5261*a^8 - 16692/5261*a^7 + 219421/5261*a^6 + 85502/5261*a^5 - 576654/5261*a^4 - 176549/5261*a^3 + 579238/5261*a^2 + 109722/5261*a - 156334/5261)*q^13 + (966/5261*a^10 + 1294/5261*a^9 - 16123/5261*a^8 - 19916/5261*a^7 + 93728/5261*a^6 + 103262/5261*a^5 - 235980/5261*a^4 - 209731/5261*a^3 + 264270/5261*a^2 + 128456/5261*a - 98256/5261)*q^14 + (43/5261*a^10 - 84/5261*a^9 - 1344/5261*a^8 + 1488/5261*a^7 + 13496/5261*a^6 - 9411/5261*a^5 - 54847/5261*a^4 + 24218/5261*a^3 + 84666/5261*a^2 - 17145/5261*a - 28424/5261)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-1169/5261*a^10 - 41/5261*a^9 + 20388/5261*a^8 - 2280/5261*a^7 - 123184/5261*a^6 + 27912/5261*a^5 + 306614/5261*a^4 - 76990/5261*a^3 - 293500/5261*a^2 + 41799/5261*a + 82077/5261)*q^17 + (-1664/5261*a^10 - 1521/5261*a^9 + 28274/5261*a^8 + 22434/5261*a^7 - 165984/5261*a^6 - 107838/5261*a^5 + 401982/5261*a^4 + 190876/5261*a^3 - 377811/5261*a^2 - 85915/5261*a + 110630/5261)*q^18 + (1666/5261*a^10 + 783/5261*a^9 - 29560/5261*a^8 - 10864/5261*a^7 + 184597/5261*a^6 + 52588/5261*a^5 - 491156/5261*a^4 - 119399/5261*a^3 + 529424/5261*a^2 + 107018/5261*a - 153673/5261)*q^19 + (a^2 - 2)*q^20 + (-1904/5261*a^10 - 2398/5261*a^9 + 35286/5261*a^8 + 38721/5261*a^7 - 237273/5261*a^6 - 211918/5261*a^5 + 707126/5261*a^4 + 457377/5261*a^3 - 883889/5261*a^2 - 319218/5261*a + 330450/5261)*q^21 + (770/5261*a^10 - 36/5261*a^9 - 11098/5261*a^8 + 3644/5261*a^7 + 47872/5261*a^6 - 37854/5261*a^5 - 51314/5261*a^4 + 114096/5261*a^3 - 52400/5261*a^2 - 87766/5261*a + 58466/5261)*q^22 + (-769/5261*a^10 - 333/5261*a^9 + 15716/5261*a^8 + 7402/5261*a^7 - 114850/5261*a^6 - 58164/5261*a^5 + 359214/5261*a^4 + 182062/5261*a^3 - 453134/5261*a^2 - 177885/5261*a + 164649/5261)*q^23 + (226/5261*a^10 + 782/5261*a^9 - 3271/5261*a^8 - 13101/5261*a^7 + 14652/5261*a^6 + 69950/5261*a^5 - 17630/5261*a^4 - 124998/5261*a^3 - 23852/5261*a^2 + 32972/5261*a + 34132/5261)*q^24 + q^25 + (1112/5261*a^10 + 30/5261*a^9 - 20564/5261*a^8 - 1283/5261*a^7 + 131966/5261*a^6 + 15762/5261*a^5 - 343045/5261*a^4 - 63514/5261*a^3 + 320746/5261*a^2 + 64370/5261*a - 89056/5261)*q^26 + (3334/5261*a^10 + 828/5261*a^9 - 60406/5261*a^8 - 10158/5261*a^7 + 387807/5261*a^6 + 44665/5261*a^5 - 1066225/5261*a^4 - 114711/5261*a^3 + 1184156/5261*a^2 + 145702/5261*a - 366172/5261)*q^27 + (-2978/5261*a^10 - 667/5261*a^9 + 52460/5261*a^8 + 7306/5261*a^7 - 320730/5261*a^6 - 25312/5261*a^5 + 807901/5261*a^4 + 48126/5261*a^3 - 765092/5261*a^2 - 51024/5261*a + 185660/5261)*q^28 + (-436/5261*a^10 - 2207/5261*a^9 + 6776/5261*a^8 + 34586/5261*a^7 - 38230/5261*a^6 - 176803/5261*a^5 + 105757/5261*a^4 + 327278/5261*a^3 - 149340/5261*a^2 - 160170/5261*a + 87187/5261)*q^29 + (-84/5261*a^10 - 570/5261*a^9 + 1402/5261*a^8 + 8594/5261*a^7 - 8379/5261*a^6 - 41689/5261*a^5 + 20520/5261*a^4 + 70390/5261*a^3 - 12458/5261*a^2 - 23522/5261*a - 1978/5261)*q^30 + (1977/5261*a^10 + 1766/5261*a^9 - 34876/5261*a^8 - 26774/5261*a^7 + 214304/5261*a^6 + 136602/5261*a^5 - 547588/5261*a^4 - 276418/5261*a^3 + 549118/5261*a^2 + 171433/5261*a - 178542/5261)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (2642/5261*a^10 + 3648/5261*a^9 - 46852/5261*a^8 - 57106/5261*a^7 + 297736/5261*a^6 + 300480/5261*a^5 - 836302/5261*a^4 - 618848/5261*a^3 + 1020398/5261*a^2 + 388338/5261*a - 414534/5261)*q^33 + (-41/5261*a^10 - 654/5261*a^9 + 58/5261*a^8 + 10082/5261*a^7 - 144/5261*a^6 - 51100/5261*a^5 + 23544/5261*a^4 + 94608/5261*a^3 - 85622/5261*a^2 - 51189/5261*a + 53774/5261)*q^34 + (2136/5261*a^10 + 966/5261*a^9 - 37154/5261*a^8 - 11851/5261*a^7 + 223588/5261*a^6 + 42464/5261*a^5 - 550354/5261*a^4 - 52284/5261*a^3 + 499421/5261*a^2 + 31446/5261*a - 115048/5261)*q^35 + (3289/5261*a^10 + 1650/5261*a^9 - 57776/5261*a^8 - 23216/5261*a^7 + 355698/5261*a^6 + 109326/5261*a^5 - 922204/5261*a^4 - 215667/5261*a^3 + 947877/5261*a^2 + 152266/5261*a - 299966/5261)*q^36 + (-1793/5261*a^10 - 1269/5261*a^9 + 32306/5261*a^8 + 17970/5261*a^7 - 206472/5261*a^6 - 84866/5261*a^5 + 561262/5261*a^4 + 170832/5261*a^3 - 594982/5261*a^2 - 144961/5261*a + 180119/5261)*q^37 + O(q^38)
*]> ;  // time = 47.28 seconds




J[337] := rec<recformat<levels, new_dimensions, dimensions, intersection_graph, ap_traces, hecke_fields, atkin_lehners, component_group_orders, tamagawa_numbers, torsion_upper_bounds, torsion_lower_bounds, l_ratios, analytic_sha_upper_bounds, analytic_sha_lower_bounds, eigenvalues, q_expansions> | levels := [ 337, 337 ], new_dimensions := [ 12, 15 ], dimensions := [ 12, 15 ], intersection_graph := [ 0, 1, 1, 0 ], ap_traces := [
[ -6, -11, -10, -13, -7, -6, -19, 1, -41, -7, -11, -5 ],
[ 3, 9, 10, 7, 9, -4, 15, 1, 45, 1, 11, -11 ]
], hecke_fields := [
x^12 + 6*x^11 + x^10 - 54*x^9 - 76*x^8 + 135*x^7 + 289*x^6 - 97*x^5 - 392*x^4 - 28*x^3 + 201*x^2 + 36*x - 27,
x^15 - 3*x^14 - 18*x^13 + 56*x^12 + 123*x^11 - 402*x^10 - 400*x^9 + 1395*x^8 + 643*x^7 - 2406*x^6 - 496*x^5 + 1843*x^4 + 200*x^3 - 388*x^2 - 69*x + 1
], atkin_lehners := [
[ 1 ],
[ -1 ]
], component_group_orders := [
[ 1 ],
[ 7 ]
], tamagawa_numbers := [
[ 1 ],
[ 7 ]
], torsion_upper_bounds := [ 1, 7 ], torsion_lower_bounds := [ 1, 7 ], l_ratios := [ 0, 1/7 ], analytic_sha_upper_bounds := [ 0, 1 ], analytic_sha_lower_bounds := [ 0, 1 ], eigenvalues := [*
[
a,
-41/27*a^11 - 23/3*a^10 + 148/27*a^9 + 679/9*a^8 + 1208/27*a^7 - 2122/9*a^6 - 5621/27*a^5 + 8552/27*a^4 + 7303/27*a^3 - 5185/27*a^2 - 316/3*a + 124/3,
76/27*a^11 + 40/3*a^10 - 356/27*a^9 - 1184/9*a^8 - 1393/27*a^7 + 3701/9*a^6 + 7618/27*a^5 - 14677/27*a^4 - 9914/27*a^3 + 8360/27*a^2 + 422/3*a - 182/3,
-49/27*a^11 - 22/3*a^10 + 356/27*a^9 + 671/9*a^8 - 362/27*a^7 - 2189/9*a^6 - 976/27*a^5 + 8845/27*a^4 + 1571/27*a^3 - 4607/27*a^2 - 68/3*a + 68/3,
2*a^11 + 26/3*a^10 - 13*a^9 - 268/3*a^8 - 3*a^7 + 895/3*a^6 + 107*a^5 - 1243/3*a^4 - 473/3*a^3 + 683/3*a^2 + 187/3*a - 37,
-5/3*a^11 - 22/3*a^10 + 31/3*a^9 + 224/3*a^8 + 20/3*a^7 - 731/3*a^6 - 293/3*a^5 + 976/3*a^4 + 401/3*a^3 - 491/3*a^2 - 146/3*a + 19,
29/27*a^11 + 14/3*a^10 - 187/27*a^9 - 439/9*a^8 - 107/27*a^7 + 1504/9*a^6 + 2018/27*a^5 - 6560/27*a^4 - 3319/27*a^3 + 4027/27*a^2 + 178/3*a - 94/3,
56/27*a^11 + 25/3*a^10 - 430/27*a^9 - 784/9*a^8 + 595/27*a^7 + 2677/9*a^6 + 830/27*a^5 - 11375/27*a^4 - 1960/27*a^3 + 6016/27*a^2 + 119/3*a - 82/3,
-65/27*a^11 - 31/3*a^10 + 421/27*a^9 + 946/9*a^8 + 62/27*a^7 - 3100/9*a^6 - 3161/27*a^5 + 12734/27*a^4 + 4678/27*a^3 - 6925/27*a^2 - 221/3*a + 109/3,
-20/27*a^11 - 2*a^10 + 223/27*a^9 + 175/9*a^8 - 982/27*a^7 - 502/9*a^6 + 2473/27*a^5 + 1304/27*a^4 - 3062/27*a^3 + 410/27*a^2 + 42*a - 53/3,
-43/9*a^11 - 68/3*a^10 + 209/9*a^9 + 227*a^8 + 739/9*a^7 - 729*a^6 - 4300/9*a^5 + 8977/9*a^4 + 5831/9*a^3 - 5249/9*a^2 - 790/3*a + 112,
-25/27*a^11 - 8/3*a^10 + 299/27*a^9 + 269/9*a^8 - 1376/27*a^7 - 1004/9*a^6 + 3314/27*a^5 + 4528/27*a^4 - 3877/27*a^3 - 2300/27*a^2 + 155/3*a + 20/3
],
[
a,
-1949/1618*a^14 + 1320/809*a^13 + 19977/809*a^12 - 22552/809*a^11 - 322023/1618*a^10 + 281379/1618*a^9 + 1285759/1618*a^8 - 383962/809*a^7 - 2607215/1618*a^6 + 826791/1618*a^5 + 2373167/1618*a^4 - 68300/809*a^3 - 287702/809*a^2 - 35427/809*a + 4591/1618,
971/1618*a^14 - 954/809*a^13 - 9264/809*a^12 + 16549/809*a^11 + 137225/1618*a^10 - 212741/1618*a^9 - 498023/1618*a^8 + 309926/809*a^7 + 915105/1618*a^6 - 797805/1618*a^5 - 761279/1618*a^4 + 176743/809*a^3 + 85396/809*a^2 - 10937/809*a - 3535/1618,
849/1618*a^14 - 685/809*a^13 - 8280/809*a^12 + 11507/809*a^11 + 125879/1618*a^10 - 139611/1618*a^9 - 470549/1618*a^8 + 180836/809*a^7 + 890021/1618*a^6 - 342519/1618*a^5 - 750325/1618*a^4 - 655/809*a^3 + 74829/809*a^2 + 24406/809*a + 7347/1618,
6103/3236*a^14 - 4299/1618*a^13 - 30978/809*a^12 + 36187/809*a^11 + 989877/3236*a^10 - 882049/3236*a^9 - 3925325/3236*a^8 + 575536/809*a^7 + 7937621/3236*a^6 - 2195013/3236*a^5 - 7252033/3236*a^4 - 12097/809*a^3 + 444324/809*a^2 + 86502/809*a + 9625/3236,
797/809*a^14 - 1207/809*a^13 - 16066/809*a^12 + 20440/809*a^11 + 127515/809*a^10 - 126146/809*a^9 - 503042/809*a^8 + 339199/809*a^7 + 1014207/809*a^6 - 356190/809*a^5 - 927323/809*a^4 + 52978/809*a^3 + 229839/809*a^2 + 28557/809*a + 142/809,
297/809*a^14 - 262/809*a^13 - 6462/809*a^12 + 4589/809*a^11 + 55127/809*a^10 - 29346/809*a^9 - 231190/809*a^8 + 81729/809*a^7 + 484013/809*a^6 - 86129/809*a^5 - 437957/809*a^4 - 221/809*a^3 + 89565/809*a^2 + 21112/809*a + 2553/809,
4399/3236*a^14 - 3433/1618*a^13 - 22077/809*a^12 + 29662/809*a^11 + 695493/3236*a^10 - 757317/3236*a^9 - 2709089/3236*a^8 + 543180/809*a^7 + 5356125/3236*a^6 - 2677477/3236*a^5 - 4752777/3236*a^4 + 248195/809*a^3 + 280212/809*a^2 + 2867/809*a - 18751/3236,
-843/3236*a^14 + 1189/1618*a^13 + 3519/809*a^12 - 10331/809*a^11 - 86489/3236*a^10 + 268213/3236*a^9 + 242333/3236*a^8 - 200875/809*a^7 - 326413/3236*a^6 + 1115229/3236*a^5 + 238737/3236*a^4 - 155353/809*a^3 - 30245/809*a^2 + 21947/809*a + 25751/3236,
-4577/1618*a^14 + 3043/809*a^13 + 47022/809*a^12 - 51190/809*a^11 - 760587/1618*a^10 + 620917/1618*a^9 + 3052801/1618*a^8 - 797474/809*a^7 - 6243287/1618*a^6 + 1420385/1618*a^5 + 5772927/1618*a^4 + 115904/809*a^3 - 730440/809*a^2 - 157784/809*a + 1711/1618,
-4961/3236*a^14 + 3147/1618*a^13 + 25232/809*a^12 - 25493/809*a^11 - 809243/3236*a^10 + 579087/3236*a^9 + 3227683/3236*a^8 - 319249/809*a^7 - 6582287/3236*a^6 + 505327/3236*a^5 + 6089839/3236*a^4 + 305414/809*a^3 - 382354/809*a^2 - 128732/809*a - 14779/3236,
177/809*a^14 - 197/809*a^13 - 3704/809*a^12 + 2694/809*a^11 + 31023/809*a^10 - 9350/809*a^9 - 133359/809*a^8 - 14689/809*a^7 + 310524/809*a^6 + 126765/809*a^5 - 365619/809*a^4 - 176698/809*a^3 + 164014/809*a^2 + 34858/809*a - 8971/809
]
*], q_expansions := [*
q + a*q^2 + (-41/27*a^11 - 23/3*a^10 + 148/27*a^9 + 679/9*a^8 + 1208/27*a^7 - 2122/9*a^6 - 5621/27*a^5 + 8552/27*a^4 + 7303/27*a^3 - 5185/27*a^2 - 316/3*a + 124/3)*q^3 + (a^2 - 2)*q^4 + (76/27*a^11 + 40/3*a^10 - 356/27*a^9 - 1184/9*a^8 - 1393/27*a^7 + 3701/9*a^6 + 7618/27*a^5 - 14677/27*a^4 - 9914/27*a^3 + 8360/27*a^2 + 422/3*a - 182/3)*q^5 + (13/9*a^11 + 7*a^10 - 59/9*a^9 - 212/3*a^8 - 277/9*a^7 + 692/3*a^6 + 1525/9*a^5 - 2923/9*a^4 - 2111/9*a^3 + 1799/9*a^2 + 96*a - 41)*q^6 + (-49/27*a^11 - 22/3*a^10 + 356/27*a^9 + 671/9*a^8 - 362/27*a^7 - 2189/9*a^6 - 976/27*a^5 + 8845/27*a^4 + 1571/27*a^3 - 4607/27*a^2 - 68/3*a + 68/3)*q^7 + (a^3 - 4*a)*q^8 + (11/9*a^11 + 19/3*a^10 - 34/9*a^9 - 62*a^8 - 377/9*a^7 + 193*a^6 + 1649/9*a^5 - 2363/9*a^4 - 2080/9*a^3 + 1492/9*a^2 + 254/3*a - 37)*q^9 + (-32/9*a^11 - 16*a^10 + 184/9*a^9 + 487/3*a^8 + 281/9*a^7 - 1594/3*a^6 - 2435/9*a^5 + 6626/9*a^4 + 3496/9*a^3 - 3826/9*a^2 - 162*a + 76)*q^10 + (2*a^11 + 26/3*a^10 - 13*a^9 - 268/3*a^8 - 3*a^7 + 895/3*a^6 + 107*a^5 - 1243/3*a^4 - 473/3*a^3 + 683/3*a^2 + 187/3*a - 37)*q^11 + (37/27*a^11 + 22/3*a^10 - 98/27*a^9 - 647/9*a^8 - 1453/27*a^7 + 2012/9*a^6 + 6256/27*a^5 - 8149/27*a^4 - 8117/27*a^3 + 5123/27*a^2 + 353/3*a - 131/3)*q^12 + (-5/3*a^11 - 22/3*a^10 + 31/3*a^9 + 224/3*a^8 + 20/3*a^7 - 731/3*a^6 - 293/3*a^5 + 976/3*a^4 + 401/3*a^3 - 491/3*a^2 - 146/3*a + 19)*q^13 + (32/9*a^11 + 15*a^10 - 211/9*a^9 - 454/3*a^8 + 16/9*a^7 + 1465/3*a^6 + 1364/9*a^5 - 5879/9*a^4 - 1993/9*a^3 + 3079/9*a^2 + 88*a - 49)*q^14 + (-a^11 - 14/3*a^10 + 5*a^9 + 139/3*a^8 + 15*a^7 - 442/3*a^6 - 89*a^5 + 610/3*a^4 + 347/3*a^3 - 371/3*a^2 - 127/3*a + 21)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (29/27*a^11 + 14/3*a^10 - 187/27*a^9 - 439/9*a^8 - 107/27*a^7 + 1504/9*a^6 + 2018/27*a^5 - 6560/27*a^4 - 3319/27*a^3 + 4027/27*a^2 + 178/3*a - 94/3)*q^17 + (-a^11 - 5*a^10 + 4*a^9 + 51*a^8 + 28*a^7 - 170*a^6 - 144*a^5 + 248*a^4 + 200*a^3 - 161*a^2 - 81*a + 33)*q^18 + (56/27*a^11 + 25/3*a^10 - 430/27*a^9 - 784/9*a^8 + 595/27*a^7 + 2677/9*a^6 + 830/27*a^5 - 11375/27*a^4 - 1960/27*a^3 + 6016/27*a^2 + 119/3*a - 82/3)*q^19 + (-8/27*a^11 - 8/3*a^10 - 89/27*a^9 + 217/9*a^8 + 1400/27*a^7 - 589/9*a^6 - 4670/27*a^5 + 2210/27*a^4 + 5662/27*a^3 - 1798/27*a^2 - 232/3*a + 76/3)*q^20 + (67/27*a^11 + 12*a^10 - 284/27*a^9 - 1061/9*a^8 - 1546/27*a^7 + 3299/9*a^6 + 7825/27*a^5 - 13138/27*a^4 - 10292/27*a^3 + 7847/27*a^2 + 151*a - 191/3)*q^21 + (-10/3*a^11 - 15*a^10 + 56/3*a^9 + 149*a^8 + 85/3*a^7 - 471*a^6 - 661/3*a^5 + 1879/3*a^4 + 851/3*a^3 - 1019/3*a^2 - 109*a + 54)*q^22 + (-65/27*a^11 - 31/3*a^10 + 421/27*a^9 + 946/9*a^8 + 62/27*a^7 - 3100/9*a^6 - 3161/27*a^5 + 12734/27*a^4 + 4678/27*a^3 - 6925/27*a^2 - 221/3*a + 109/3)*q^23 + (-34/9*a^11 - 19*a^10 + 137/9*a^9 + 575/3*a^8 + 901/9*a^7 - 1877/3*a^6 - 4570/9*a^5 + 7975/9*a^4 + 6275/9*a^3 - 5018/9*a^2 - 285*a + 119)*q^24 + (16/9*a^11 + 22/3*a^10 - 119/9*a^9 - 232/3*a^8 + 125/9*a^7 + 808/3*a^6 + 412/9*a^5 - 3589/9*a^4 - 824/9*a^3 + 2123/9*a^2 + 140/3*a - 37)*q^25 + (8/3*a^11 + 12*a^10 - 46/3*a^9 - 120*a^8 - 56/3*a^7 + 384*a^6 + 491/3*a^5 - 1559/3*a^4 - 631/3*a^3 + 859/3*a^2 + 79*a - 45)*q^26 + (-22/27*a^11 - 5*a^10 + 5/27*a^9 + 458/9*a^8 + 1501/27*a^7 - 1553/9*a^6 - 6268/27*a^5 + 7396/27*a^4 + 8744/27*a^3 - 5813/27*a^2 - 133*a + 167/3)*q^27 + (-73/27*a^11 - 37/3*a^10 + 386/27*a^9 + 1106/9*a^8 + 949/27*a^7 - 3506/9*a^6 - 6373/27*a^5 + 13963/27*a^4 + 8783/27*a^3 - 7706/27*a^2 - 395/3*a + 152/3)*q^28 + (-20/27*a^11 - 2*a^10 + 223/27*a^9 + 175/9*a^8 - 982/27*a^7 - 502/9*a^6 + 2473/27*a^5 + 1304/27*a^4 - 3062/27*a^3 + 410/27*a^2 + 42*a - 53/3)*q^29 + (4/3*a^11 + 6*a^10 - 23/3*a^9 - 61*a^8 - 37/3*a^7 + 200*a^6 + 319/3*a^5 - 829/3*a^4 - 455/3*a^3 + 476/3*a^2 + 57*a - 27)*q^30 + (-43/9*a^11 - 68/3*a^10 + 209/9*a^9 + 227*a^8 + 739/9*a^7 - 729*a^6 - 4300/9*a^5 + 8977/9*a^4 + 5831/9*a^3 - 5249/9*a^2 - 790/3*a + 112)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (4/9*a^11 + 5/3*a^10 - 23/9*a^9 - 12*a^8 + 29/9*a^7 + 12*a^6 - 221/9*a^5 + 278/9*a^4 + 637/9*a^3 - 481/9*a^2 - 125/3*a + 18)*q^33 + (-16/9*a^11 - 8*a^10 + 83/9*a^9 + 233/3*a^8 + 199/9*a^7 - 707/3*a^6 - 1249/9*a^5 + 2683/9*a^4 + 1613/9*a^3 - 1409/9*a^2 - 70*a + 29)*q^34 + (-161/27*a^11 - 28*a^10 + 784/27*a^9 + 2491/9*a^8 + 2633/27*a^7 - 7804/9*a^6 - 15056/27*a^5 + 30893/27*a^4 + 19666/27*a^3 - 17314/27*a^2 - 283*a + 364/3)*q^35 + (-13/9*a^11 - 23/3*a^10 + 41/9*a^9 + 76*a^8 + 439/9*a^7 - 241*a^6 - 1939/9*a^5 + 2998/9*a^4 + 2459/9*a^3 - 1904/9*a^2 - 301/3*a + 47)*q^36 + (-25/27*a^11 - 8/3*a^10 + 299/27*a^9 + 269/9*a^8 - 1376/27*a^7 - 1004/