CoCalc Public Fileswww / Tables / MotiveDecomp_N1-200_k2
Author: William A. Stein
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Gamma_0(11)
Weight 2

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J_0(11), dim = 1

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11A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 5
Torsion Bound  = 5
|L(1)/Omega|   = 1/5
Sha Bound      = 5

ANALYTIC INVARIANTS:

Omega+         = 1.2692093042795534217 + 0.3059862835737342116e-39i
Omega-         = 0.13729835100889706111e-38 + -2.9176332338769904587i
L(1)           = 0.25384186085591068434
w1             = -0.63460465213977671084 + -1.4588166169384952293i
w2             = -1.2692093042795534217 + -0.3059862835737342116e-39i
c4             = 495.99999999999527567 + -0.30608752059884439992e-36i
c6             = 20008.000000008749296 + -0.37493358120158091857e-34i
j              = -757.67263785907241536 + -0.20669731864407559281e-35i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + -1*q^3 + 2*q^4 + 1*q^5 + 2*q^6 + -2*q^7 + -2*q^9 + -2*q^10 + 1*q^11 + -2*q^12 + 4*q^13 + 4*q^14 + -1*q^15 + -4*q^16 + -2*q^17 + 4*q^18 + 2*q^20 + 2*q^21 + -2*q^22 + -1*q^23 + -4*q^25 + -8*q^26 + 5*q^27 + -4*q^28 + 2*q^30 + 7*q^31 + 8*q^32 + -1*q^33 + 4*q^34 + -2*q^35 + -4*q^36 + 3*q^37 + -4*q^39 + -8*q^41 + -4*q^42 + -6*q^43 + 2*q^44 + -2*q^45 + 2*q^46 + 8*q^47 + 4*q^48 + -3*q^49 + 8*q^50 + 2*q^51 + 8*q^52 + -6*q^53 + -10*q^54 + 1*q^55 + 5*q^59 + -2*q^60 + 12*q^61 + -14*q^62 + 4*q^63 + -8*q^64 + 4*q^65 + 2*q^66 + -7*q^67 + -4*q^68 + 1*q^69 + 4*q^70 + -3*q^71 + 4*q^73 + -6*q^74 + 4*q^75 + -2*q^77 + 8*q^78 + -10*q^79 + -4*q^80 + 1*q^81 + 16*q^82 + -6*q^83 + 4*q^84 + -2*q^85 + 12*q^86 + 15*q^89 + 4*q^90 + -8*q^91 + -2*q^92 + -7*q^93 + -16*q^94 + -8*q^96 + -7*q^97 + 6*q^98 + -2*q^99 + -8*q^100 + 2*q^101 + -4*q^102 + -16*q^103 + 2*q^105 + 12*q^106 + 18*q^107 + 10*q^108 + 10*q^109 + -2*q^110 + -3*q^111 + 8*q^112 + 9*q^113 + -1*q^115 + -8*q^117 + -10*q^118 + 4*q^119 + 1*q^121 + -24*q^122 + 8*q^123 + 14*q^124 + -9*q^125 + -8*q^126 + 8*q^127 + 6*q^129 + -8*q^130 + -18*q^131 + -2*q^132 + 14*q^134 + 5*q^135 + -7*q^137 + -2*q^138 + 10*q^139 + -4*q^140 + -8*q^141 + 6*q^142 + 4*q^143 + 8*q^144 + -8*q^146 + 3*q^147 + 6*q^148 + -10*q^149 + -8*q^150 + 2*q^151 + 4*q^153 + 4*q^154 + 7*q^155 + -8*q^156 + -7*q^157 + 20*q^158 + 6*q^159 + 8*q^160 + 2*q^161 + -2*q^162 + 4*q^163 + -16*q^164 + -1*q^165 + 12*q^166 + -12*q^167 + 3*q^169 + 4*q^170 + -12*q^172 + -6*q^173 + 8*q^175 + -4*q^176 + -5*q^177 + -30*q^178 + -15*q^179 + -4*q^180 + 7*q^181 + 16*q^182 + -12*q^183 + 3*q^185 + 14*q^186 + -2*q^187 + 16*q^188 + -10*q^189 + 17*q^191 + 8*q^192 + 4*q^193 + 14*q^194 + -4*q^195 + -6*q^196 + -2*q^197 + 4*q^198 +  ...

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Gamma_0(14)
Weight 2

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J_0(14), dim = 1

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14A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2*3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/2*3
Sha Bound      = 2*3

ANALYTIC INVARIANTS:

Omega+         = 1.9813419560668832342 + -0.57966734777994701199e-45i
Omega-         = -2.6509824793649734287i
L(1)           = 0.33022365934448053903
w1             = 0.99067097803344161708 + 1.3254912396824867143i
w2             = 0.99067097803344161708 + -1.3254912396824867143i
c4             = -214.99999999999363375 + 0.51627365772238651979e-11i
c6             = 5291.000000010010186 + -0.68978662053619098087e-8i
j              = 452.73209730191306582 + 0.84710694491255540172e-9i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -2*q^3 + 1*q^4 + 2*q^6 + 1*q^7 + -1*q^8 + 1*q^9 + -2*q^12 + -4*q^13 + -1*q^14 + 1*q^16 + 6*q^17 + -1*q^18 + 2*q^19 + -2*q^21 + 2*q^24 + -5*q^25 + 4*q^26 + 4*q^27 + 1*q^28 + -6*q^29 + -4*q^31 + -1*q^32 + -6*q^34 + 1*q^36 + 2*q^37 + -2*q^38 + 8*q^39 + 6*q^41 + 2*q^42 + 8*q^43 + -12*q^47 + -2*q^48 + 1*q^49 + 5*q^50 + -12*q^51 + -4*q^52 + 6*q^53 + -4*q^54 + -1*q^56 + -4*q^57 + 6*q^58 + -6*q^59 + 8*q^61 + 4*q^62 + 1*q^63 + 1*q^64 + -4*q^67 + 6*q^68 + -1*q^72 + 2*q^73 + -2*q^74 + 10*q^75 + 2*q^76 + -8*q^78 + 8*q^79 + -11*q^81 + -6*q^82 + -6*q^83 + -2*q^84 + -8*q^86 + 12*q^87 + -6*q^89 + -4*q^91 + 8*q^93 + 12*q^94 + 2*q^96 + -10*q^97 + -1*q^98 + -5*q^100 + 12*q^102 + -4*q^103 + 4*q^104 + -6*q^106 + 12*q^107 + 4*q^108 + 2*q^109 + -4*q^111 + 1*q^112 + 6*q^113 + 4*q^114 + -6*q^116 + -4*q^117 + 6*q^118 + 6*q^119 + -11*q^121 + -8*q^122 + -12*q^123 + -4*q^124 + -1*q^126 + -16*q^127 + -1*q^128 + -16*q^129 + 18*q^131 + 2*q^133 + 4*q^134 + -6*q^136 + 18*q^137 + 14*q^139 + 24*q^141 + 1*q^144 + -2*q^146 + -2*q^147 + 2*q^148 + -18*q^149 + -10*q^150 + 8*q^151 + -2*q^152 + 6*q^153 + 8*q^156 + -4*q^157 + -8*q^158 + -12*q^159 + 11*q^162 + -16*q^163 + 6*q^164 + 6*q^166 + -12*q^167 + 2*q^168 + 3*q^169 + 2*q^171 + 8*q^172 + -12*q^173 + -12*q^174 + -5*q^175 + 12*q^177 + 6*q^178 + -12*q^179 + 20*q^181 + 4*q^182 + -16*q^183 + -8*q^186 + -12*q^188 + 4*q^189 + 24*q^191 + -2*q^192 + 14*q^193 + 10*q^194 + 1*q^196 + -18*q^197 + 20*q^199 + 5*q^200 +  ...

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Gamma_0(15)
Weight 2

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J_0(15), dim = 1

-------------------------------------------------------
15A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2^3
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.4006030423326020232 + 0.11271976031056334584e-37i
Omega-         = 1.5962422221317835101i
L(1)           = 0.1750753802915752529
w1             = 1.5962422221317835101i
w2             = 1.4006030423326020232 + 0.11271976031056334584e-37i
c4             = 480.99999999999539535 + -0.11074053372419936509e-34i
c6             = 4879.0000000070087591 + -0.42890069723239564355e-33i
j              = 2198.2151308659332645 + -0.63852060580473614594e-34i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + -1*q^4 + 1*q^5 + 1*q^6 + 3*q^8 + 1*q^9 + -1*q^10 + -4*q^11 + 1*q^12 + -2*q^13 + -1*q^15 + -1*q^16 + 2*q^17 + -1*q^18 + 4*q^19 + -1*q^20 + 4*q^22 + -3*q^24 + 1*q^25 + 2*q^26 + -1*q^27 + -2*q^29 + 1*q^30 + -5*q^32 + 4*q^33 + -2*q^34 + -1*q^36 + -10*q^37 + -4*q^38 + 2*q^39 + 3*q^40 + 10*q^41 + 4*q^43 + 4*q^44 + 1*q^45 + 8*q^47 + 1*q^48 + -7*q^49 + -1*q^50 + -2*q^51 + 2*q^52 + -10*q^53 + 1*q^54 + -4*q^55 + -4*q^57 + 2*q^58 + -4*q^59 + 1*q^60 + -2*q^61 + 7*q^64 + -2*q^65 + -4*q^66 + 12*q^67 + -2*q^68 + -8*q^71 + 3*q^72 + 10*q^73 + 10*q^74 + -1*q^75 + -4*q^76 + -2*q^78 + -1*q^80 + 1*q^81 + -10*q^82 + 12*q^83 + 2*q^85 + -4*q^86 + 2*q^87 + -12*q^88 + -6*q^89 + -1*q^90 + -8*q^94 + 4*q^95 + 5*q^96 + 2*q^97 + 7*q^98 + -4*q^99 + -1*q^100 + 6*q^101 + 2*q^102 + -16*q^103 + -6*q^104 + 10*q^106 + -12*q^107 + 1*q^108 + 14*q^109 + 4*q^110 + 10*q^111 + 2*q^113 + 4*q^114 + 2*q^116 + -2*q^117 + 4*q^118 + -3*q^120 + 5*q^121 + 2*q^122 + -10*q^123 + 1*q^125 + -8*q^127 + 3*q^128 + -4*q^129 + 2*q^130 + -12*q^131 + -4*q^132 + -12*q^134 + -1*q^135 + 6*q^136 + -6*q^137 + -4*q^139 + -8*q^141 + 8*q^142 + 8*q^143 + -1*q^144 + -2*q^145 + -10*q^146 + 7*q^147 + 10*q^148 + 22*q^149 + 1*q^150 + -8*q^151 + 12*q^152 + 2*q^153 + -2*q^156 + 14*q^157 + 10*q^159 + -5*q^160 + -1*q^162 + -4*q^163 + -10*q^164 + 4*q^165 + -12*q^166 + -9*q^169 + -2*q^170 + 4*q^171 + -4*q^172 + -18*q^173 + -2*q^174 + 4*q^176 + 4*q^177 + 6*q^178 + 20*q^179 + -1*q^180 + -10*q^181 + 2*q^183 + -10*q^185 + -8*q^187 + -8*q^188 + -4*q^190 + 16*q^191 + -7*q^192 + 2*q^193 + -2*q^194 + 2*q^195 + 7*q^196 + 6*q^197 + 4*q^198 + -8*q^199 + 3*q^200 +  ...

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Gamma_0(17)
Weight 2

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J_0(17), dim = 1

-------------------------------------------------------
17A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 1.5470797535511201732 + -0.43447841757997306343e-33i
Omega-         = 0.33964661020505034238e-33 + 2.745739118089753672i
L(1)           = 0.3867699383877800433
w1             = -0.7735398767755600866 + -1.372869559044876836i
w2             = -1.5470797535511201732 + 0.43447841757997306343e-33i
c4             = 33.000000000249671654 + 0.23930515977994133707e-30i
c6             = 12014.999999576970406 + 0.14537826379428910875e-28i
j              = -0.43027502069356309261 + -0.83214684979929813881e-32i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^4 + -2*q^5 + 4*q^7 + 3*q^8 + -3*q^9 + 2*q^10 + -2*q^13 + -4*q^14 + -1*q^16 + 1*q^17 + 3*q^18 + -4*q^19 + 2*q^20 + 4*q^23 + -1*q^25 + 2*q^26 + -4*q^28 + 6*q^29 + 4*q^31 + -5*q^32 + -1*q^34 + -8*q^35 + 3*q^36 + -2*q^37 + 4*q^38 + -6*q^40 + -6*q^41 + 4*q^43 + 6*q^45 + -4*q^46 + 9*q^49 + 1*q^50 + 2*q^52 + 6*q^53 + 12*q^56 + -6*q^58 + -12*q^59 + -10*q^61 + -4*q^62 + -12*q^63 + 7*q^64 + 4*q^65 + 4*q^67 + -1*q^68 + 8*q^70 + -4*q^71 + -9*q^72 + -6*q^73 + 2*q^74 + 4*q^76 + 12*q^79 + 2*q^80 + 9*q^81 + 6*q^82 + -4*q^83 + -2*q^85 + -4*q^86 + 10*q^89 + -6*q^90 + -8*q^91 + -4*q^92 + 8*q^95 + 2*q^97 + -9*q^98 + 1*q^100 + -10*q^101 + 8*q^103 + -6*q^104 + -6*q^106 + 8*q^107 + 6*q^109 + -4*q^112 + -14*q^113 + -8*q^115 + -6*q^116 + 6*q^117 + 12*q^118 + 4*q^119 + -11*q^121 + 10*q^122 + -4*q^124 + 12*q^125 + 12*q^126 + 8*q^127 + 3*q^128 + -4*q^130 + 16*q^131 + -16*q^133 + -4*q^134 + 3*q^136 + -6*q^137 + -8*q^139 + 8*q^140 + 4*q^142 + 3*q^144 + -12*q^145 + 6*q^146 + 2*q^148 + -10*q^149 + -16*q^151 + -12*q^152 + -3*q^153 + -8*q^155 + -2*q^157 + -12*q^158 + 10*q^160 + 16*q^161 + -9*q^162 + 24*q^163 + 6*q^164 + 4*q^166 + -4*q^167 + -9*q^169 + 2*q^170 + 12*q^171 + -4*q^172 + 22*q^173 + -4*q^175 + -10*q^178 + 12*q^179 + -6*q^180 + -2*q^181 + 8*q^182 + 12*q^184 + 4*q^185 + -8*q^190 + -16*q^191 + 2*q^193 + -2*q^194 + -9*q^196 + -18*q^197 + -20*q^199 + -3*q^200 +  ...

-------------------------------------------------------
Gamma_0(19)
Weight 2

-------------------------------------------------------
J_0(19), dim = 1

-------------------------------------------------------
19A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 1.3597597334883108107 + 0.89357968985713309066e-31i
Omega-         = 0.29757051331387211599e-29 + -4.1270923917172404647i
L(1)           = 0.45325324449610360358
w1             = -0.67987986674415540537 + -2.0635461958586202323i
w2             = -1.3597597334883108107 + -0.89357968985713309066e-31i
c4             = 447.99999999980911037 + -0.68424641734672241246e-28i
c6             = 10088.000000136937544 + -0.61822617395497506154e-26i
j              = -13109.110945918256219 + -0.86384903441062371352e-25i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -2*q^4 + 3*q^5 + -1*q^7 + 1*q^9 + 3*q^11 + 4*q^12 + -4*q^13 + -6*q^15 + 4*q^16 + -3*q^17 + 1*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 + 8*q^39 + -6*q^41 + -1*q^43 + -6*q^44 + 3*q^45 + -3*q^47 + -8*q^48 + -6*q^49 + 6*q^51 + 8*q^52 + 12*q^53 + 9*q^55 + -2*q^57 + -6*q^59 + 12*q^60 + -1*q^61 + -1*q^63 + -8*q^64 + -12*q^65 + -4*q^67 + 6*q^68 + 6*q^71 + -7*q^73 + -8*q^75 + -2*q^76 + -3*q^77 + 8*q^79 + 12*q^80 + -11*q^81 + 12*q^83 + -4*q^84 + -9*q^85 + -12*q^87 + 12*q^89 + 4*q^91 + 8*q^93 + 3*q^95 + 8*q^97 + 3*q^99 + -8*q^100 + 6*q^101 + 14*q^103 + 6*q^105 + -18*q^107 + -8*q^108 + -16*q^109 + -4*q^111 + -4*q^112 + 6*q^113 + -12*q^116 + -4*q^117 + 3*q^119 + -2*q^121 + 12*q^123 + 8*q^124 + -3*q^125 + 2*q^127 + 2*q^129 + -15*q^131 + 12*q^132 + -1*q^133 + 12*q^135 + -3*q^137 + -13*q^139 + 6*q^140 + 6*q^141 + -12*q^143 + 4*q^144 + 18*q^145 + 12*q^147 + -4*q^148 + 21*q^149 + -10*q^151 + -3*q^153 + -12*q^155 + -16*q^156 + 14*q^157 + -24*q^159 + 20*q^163 + 12*q^164 + -18*q^165 + -18*q^167 + 3*q^169 + 1*q^171 + 2*q^172 + -18*q^173 + -4*q^175 + 12*q^176 + 12*q^177 + -18*q^179 + -6*q^180 + 2*q^181 + 2*q^183 + 6*q^185 + -9*q^187 + 6*q^188 + -4*q^189 + 3*q^191 + 16*q^192 + -4*q^193 + 24*q^195 + 12*q^196 + 18*q^197 + 11*q^199 +  ...

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Gamma_0(20)
Weight 2

-------------------------------------------------------
J_0(20), dim = 1

-------------------------------------------------------
20A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2*3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/2*3
Sha Bound      = 2*3

ANALYTIC INVARIANTS:

Omega+         = 2.8243751419591137995 + -0.60650242879223896752e-45i
Omega-         = -2.2741651990410812607i
L(1)           = 0.47072919032651896658
w1             = 1.4121875709795568997 + -1.1370825995205406303i
w2             = -1.4121875709795568997 + -1.1370825995205406303i
c4             = -176.00000000000231173 + -0.11690435302745935616e-11i
c6             = -2367.9999999979810162 + -0.24853222347605818446e-8i
j              = 851.84000000075352974 + -0.89802043514728136522e-9i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -1*q^5 + 2*q^7 + 1*q^9 + 2*q^13 + 2*q^15 + -6*q^17 + -4*q^19 + -4*q^21 + 6*q^23 + 1*q^25 + 4*q^27 + 6*q^29 + -4*q^31 + -2*q^35 + 2*q^37 + -4*q^39 + 6*q^41 + -10*q^43 + -1*q^45 + -6*q^47 + -3*q^49 + 12*q^51 + -6*q^53 + 8*q^57 + 12*q^59 + 2*q^61 + 2*q^63 + -2*q^65 + 2*q^67 + -12*q^69 + -12*q^71 + 2*q^73 + -2*q^75 + 8*q^79 + -11*q^81 + 6*q^83 + 6*q^85 + -12*q^87 + -6*q^89 + 4*q^91 + 8*q^93 + 4*q^95 + 2*q^97 + 6*q^101 + 14*q^103 + 4*q^105 + -6*q^107 + 2*q^109 + -4*q^111 + -6*q^113 + -6*q^115 + 2*q^117 + -12*q^119 + -11*q^121 + -12*q^123 + -1*q^125 + 2*q^127 + 20*q^129 + -8*q^133 + -4*q^135 + 18*q^137 + -4*q^139 + 12*q^141 + -6*q^145 + 6*q^147 + -6*q^149 + 20*q^151 + -6*q^153 + 4*q^155 + -22*q^157 + 12*q^159 + 12*q^161 + -10*q^163 + 18*q^167 + -9*q^169 + -4*q^171 + -6*q^173 + 2*q^175 + -24*q^177 + -12*q^179 + -10*q^181 + -4*q^183 + -2*q^185 + 8*q^189 + -12*q^191 + 26*q^193 + 4*q^195 + 18*q^197 + 8*q^199 +  ...

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Gamma_0(21)
Weight 2

-------------------------------------------------------
J_0(21), dim = 1

-------------------------------------------------------
21A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2^3
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.8044616215539682224 + 0.29472810292846279258e-27i
Omega-         = -1.9109897807518291966i
L(1)           = 0.2255577026942460278
w1             = -1.9109897807518291966i
w2             = -1.8044616215539682224 + -0.29472810292846279258e-27i
c4             = 192.99999999996502162 + -0.75525051905516522399e-25i
c6             = 575.00000003208539274 + -0.19302279967477339266e-23i
j              = 1811.3018392640124426 + -0.48372820272688486517e-24i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + -1*q^4 + -2*q^5 + -1*q^6 + -1*q^7 + 3*q^8 + 1*q^9 + 2*q^10 + 4*q^11 + -1*q^12 + -2*q^13 + 1*q^14 + -2*q^15 + -1*q^16 + -6*q^17 + -1*q^18 + 4*q^19 + 2*q^20 + -1*q^21 + -4*q^22 + 3*q^24 + -1*q^25 + 2*q^26 + 1*q^27 + 1*q^28 + -2*q^29 + 2*q^30 + -5*q^32 + 4*q^33 + 6*q^34 + 2*q^35 + -1*q^36 + 6*q^37 + -4*q^38 + -2*q^39 + -6*q^40 + 2*q^41 + 1*q^42 + -4*q^43 + -4*q^44 + -2*q^45 + -1*q^48 + 1*q^49 + 1*q^50 + -6*q^51 + 2*q^52 + 6*q^53 + -1*q^54 + -8*q^55 + -3*q^56 + 4*q^57 + 2*q^58 + 12*q^59 + 2*q^60 + -2*q^61 + -1*q^63 + 7*q^64 + 4*q^65 + -4*q^66 + 4*q^67 + 6*q^68 + -2*q^70 + 3*q^72 + -6*q^73 + -6*q^74 + -1*q^75 + -4*q^76 + -4*q^77 + 2*q^78 + -16*q^79 + 2*q^80 + 1*q^81 + -2*q^82 + -12*q^83 + 1*q^84 + 12*q^85 + 4*q^86 + -2*q^87 + 12*q^88 + -14*q^89 + 2*q^90 + 2*q^91 + -8*q^95 + -5*q^96 + 18*q^97 + -1*q^98 + 4*q^99 + 1*q^100 + 14*q^101 + 6*q^102 + 8*q^103 + -6*q^104 + 2*q^105 + -6*q^106 + 4*q^107 + -1*q^108 + -18*q^109 + 8*q^110 + 6*q^111 + 1*q^112 + -14*q^113 + -4*q^114 + 2*q^116 + -2*q^117 + -12*q^118 + 6*q^119 + -6*q^120 + 5*q^121 + 2*q^122 + 2*q^123 + 12*q^125 + 1*q^126 + 3*q^128 + -4*q^129 + -4*q^130 + 4*q^131 + -4*q^132 + -4*q^133 + -4*q^134 + -2*q^135 + -18*q^136 + -6*q^137 + 12*q^139 + -2*q^140 + -8*q^143 + -1*q^144 + 4*q^145 + 6*q^146 + 1*q^147 + -6*q^148 + 6*q^149 + 1*q^150 + 8*q^151 + 12*q^152 + -6*q^153 + 4*q^154 + 2*q^156 + -2*q^157 + 16*q^158 + 6*q^159 + 10*q^160 + -1*q^162 + 4*q^163 + -2*q^164 + -8*q^165 + 12*q^166 + -8*q^167 + -3*q^168 + -9*q^169 + -12*q^170 + 4*q^171 + 4*q^172 + -10*q^173 + 2*q^174 + 1*q^175 + -4*q^176 + 12*q^177 + 14*q^178 + -4*q^179 + 2*q^180 + -26*q^181 + -2*q^182 + -2*q^183 + -12*q^185 + -24*q^187 + -1*q^189 + 8*q^190 + -8*q^191 + 7*q^192 + 2*q^193 + -18*q^194 + 4*q^195 + -1*q^196 + 22*q^197 + -4*q^198 + 24*q^199 + -3*q^200 +  ...

-------------------------------------------------------
Gamma_0(22)
Weight 2

-------------------------------------------------------
J_0(22), dim = 2

-------------------------------------------------------
22A (old = 11A), dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

-------------------------------------------------------
Gamma_0(23)
Weight 2

-------------------------------------------------------
J_0(23), dim = 2

-------------------------------------------------------
23A (new) , dim = 2

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 5
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 11
Torsion Bound  = 11
|L(1)/Omega|   = 1/11
Sha Bound      = 11

ANALYTIC INVARIANTS:

Omega+         = 2.7327505324965964933 + 0.11649388849290241305e-24i
Omega-         = 5.8575268484637719828 + -0.81849091729712220778e-24i
L(1)           = 0.24843186659059968121

HECKE EIGENFORM:
a^2+a-1 = 0,
f(q) = 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 + 1*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 + -2*a*q^38 + (-6*a-3)*q^39 + (2*a-4)*q^40 + (-4*a-1)*q^41 + (-4*a-2)*q^42 + (4*a+6)*q^44 + 4*a*q^45 + a*q^46 + (-2*a-1)*q^47 + (3*a-6)*q^48 + (4*a+1)*q^49 + (3*a-4)*q^50 + (-6*a+2)*q^51 + (-3*a-3)*q^52 + (4*a-2)*q^53 + (-a+2)*q^54 + (-4*a-4)*q^55 + (-2*a-6)*q^56 + (4*a+2)*q^57 + -3*a*q^58 + (4*a+4)*q^59 + (4*a+2)*q^60 + (-8*a-2)*q^61 + (-3*a+6)*q^62 + (4*a+4)*q^63 + (-2*a+1)*q^64 + 6*a*q^65 + (2*a+6)*q^66 + (2*a-4)*q^67 + -2*a*q^68 + (-2*a-1)*q^69 + 4*a*q^70 + (2*a+11)*q^71 + (-4*a-2)*q^72 + (-4*a+9)*q^73 + (2*a-2)*q^74 + (-2*a+9)*q^75 + (2*a+2)*q^76 + (-8*a-12)*q^77 + (3*a-6)*q^78 + (-8*a-6)*q^79 + (-6*a+6)*q^80 + -11*q^81 + (3*a-4)*q^82 + (2*a-10)*q^83 + (6*a+8)*q^84 + (8*a-4)*q^85 + (6*a+3)*q^87 + (6*a+8)*q^88 + (-4*a-8)*q^89 + (-4*a+4)*q^90 + (6*a+6)*q^91 + (-a-1)*q^92 + -15*q^93 + (a-2)*q^94 + -4*a*q^95 + (-9*a-7)*q^96 + (6*a+14)*q^97 + (-3*a+4)*q^98 + (-4*a-8)*q^99 + (a+5)*q^100 + (4*a+2)*q^101 + (8*a-6)*q^102 + (-10*a+2)*q^103 + (-6*a-3)*q^104 + (-8*a-4)*q^105 + (-6*a+4)*q^106 + (12*a+6)*q^107 + (-a-3)*q^108 + -4*q^110 + (-2*a+4)*q^111 + 6*q^112 + (-2*a+10)*q^113 + (-2*a+4)*q^114 + 2*a*q^115 + (3*a+3)*q^116 + 6*q^117 + 4*q^118 + 4*a*q^119 + 10*a*q^120 + (12*a+9)*q^121 + (6*a-8)*q^122 + (-2*a+9)*q^123 + (-3*a-9)*q^124 + (-4*a-8)*q^125 + 4*q^126 + (6*a-11)*q^127 + (a-12)*q^128 + (-6*a+6)*q^130 + (6*a+15)*q^131 + (-8*a-14)*q^132 + (-4*a-4)*q^133 + (-6*a+2)*q^134 + (-2*a+4)*q^135 + (-6*a+2)*q^136 + (-16*a-12)*q^137 + (a-2)*q^138 + (-6*a-7)*q^139 + (-4*a-4)*q^140 + 5*q^141 + (9*a+2)*q^142 + (-6*a-12)*q^143 + 6*a*q^144 + -6*a*q^145 + (13*a-4)*q^146 + (2*a-9)*q^147 + 2*q^148 + (16*a+14)*q^149 + (11*a-2)*q^150 + (2*a+3)*q^151 + (4*a+2)*q^152 + (-4*a+4)*q^153 + (-4*a-8)*q^154 + (-6*a+12)*q^155 + (3*a+9)*q^156 + (-12*a-4)*q^157 + (2*a-8)*q^158 + (8*a-6)*q^159 + (8*a+2)*q^160 + (2*a+2)*q^161 + -11*a*q^162 + (2*a-7)*q^163 + (a+5)*q^164 + (4*a+12)*q^165 + (-12*a+2)*q^166 + (-4*a+4)*q^167 + (10*a+10)*q^168 + -4*q^169 + (-12*a+8)*q^170 + -4*q^171 + (8*a+18)*q^173 + (-3*a+6)*q^174 + (-2*a-10)*q^175 + (-6*a-6)*q^176 + (-4*a-12)*q^177 + (-4*a-4)*q^178 + (6*a-3)*q^179 + -4*q^180 + (14*a+8)*q^181 + 6*q^182 + (-4*a+18)*q^183 + (-2*a-1)*q^184 + (4*a-4)*q^185 + -15*a*q^186 + -4*q^187 + (a+3)*q^188 + (2*a+6)*q^189 + (4*a-4)*q^190 + (-10*a-20)*q^191 + (-4*a+3)*q^192 + (8*a+5)*q^193 + (8*a+6)*q^194 + (6*a-12)*q^195 + (-a-5)*q^196 + (-4*a+1)*q^197 + (-4*a-4)*q^198 + (6*a-16)*q^199 + (-2*a+9)*q^200 +  ...

-------------------------------------------------------
Gamma_0(24)
Weight 2

-------------------------------------------------------
J_0(24), dim = 1

-------------------------------------------------------
24A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2^3
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 2.1565156474997666435 + -0.99125450192921019734e-41i
Omega-         = 1.6857503548125960429i
L(1)           = 0.26956445593747083044
w1             = 2.1565156474997666435 + -0.99125450192921019734e-41i
w2             = -1.6857503548125960429i
c4             = 207.99999999997270926 + 0.55598426153455317657e-39i
c6             = -2240.0000000150646579 + 0.16471274396119639423e-37i
j              = 3905.7777778459245576 + -0.11186411152501882634e-36i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^5 + 1*q^9 + 4*q^11 + -2*q^13 + 2*q^15 + 2*q^17 + -4*q^19 + -8*q^23 + -1*q^25 + -1*q^27 + 6*q^29 + 8*q^31 + -4*q^33 + 6*q^37 + 2*q^39 + -6*q^41 + 4*q^43 + -2*q^45 + -7*q^49 + -2*q^51 + -2*q^53 + -8*q^55 + 4*q^57 + 4*q^59 + -2*q^61 + 4*q^65 + -4*q^67 + 8*q^69 + 8*q^71 + 10*q^73 + 1*q^75 + -8*q^79 + 1*q^81 + -4*q^83 + -4*q^85 + -6*q^87 + -6*q^89 + -8*q^93 + 8*q^95 + 2*q^97 + 4*q^99 + -18*q^101 + 16*q^103 + -12*q^107 + -2*q^109 + -6*q^111 + 18*q^113 + 16*q^115 + -2*q^117 + 5*q^121 + 6*q^123 + 12*q^125 + -8*q^127 + -4*q^129 + -4*q^131 + 2*q^135 + -6*q^137 + -12*q^139 + -8*q^143 + -12*q^145 + 7*q^147 + 14*q^149 + -16*q^151 + 2*q^153 + -16*q^155 + -2*q^157 + 2*q^159 + 12*q^163 + 8*q^165 + 24*q^167 + -9*q^169 + -4*q^171 + 6*q^173 + -4*q^177 + 12*q^179 + 6*q^181 + 2*q^183 + -12*q^185 + 8*q^187 + 2*q^193 + -4*q^195 + -18*q^197 + 16*q^199 +  ...

-------------------------------------------------------
Gamma_0(26)
Weight 2

-------------------------------------------------------
J_0(26), dim = 2

-------------------------------------------------------
26A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 1.5467299538318833526 + 0.5868132788120751371e-22i
Omega-         = 0.10905020355811993018e-21 + 3.4793434834315132576i
L(1)           = 0.51557665127729445088
w1             = -0.77336497691594167632 + 1.7396717417157566288i
w2             = 1.5467299538318833526 + 0.5868132788120751371e-22i
c4             = 216.99999999999457642 + -0.59802200343477242453e-19i
c6             = 6371.0000000067628017 + -0.55733495765730914546e-18i
j              = -581.3787551189112398 + 0.50643532147801631345e-18i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -3*q^5 + -1*q^6 + -1*q^7 + -1*q^8 + -2*q^9 + 3*q^10 + 6*q^11 + 1*q^12 + 1*q^13 + 1*q^14 + -3*q^15 + 1*q^16 + -3*q^17 + 2*q^18 + 2*q^19 + -3*q^20 + -1*q^21 + -6*q^22 + -1*q^24 + 4*q^25 + -1*q^26 + -5*q^27 + -1*q^28 + 6*q^29 + 3*q^30 + -4*q^31 + -1*q^32 + 6*q^33 + 3*q^34 + 3*q^35 + -2*q^36 + -7*q^37 + -2*q^38 + 1*q^39 + 3*q^40 + 1*q^42 + -1*q^43 + 6*q^44 + 6*q^45 + 3*q^47 + 1*q^48 + -6*q^49 + -4*q^50 + -3*q^51 + 1*q^52 + 5*q^54 + -18*q^55 + 1*q^56 + 2*q^57 + -6*q^58 + -6*q^59 + -3*q^60 + 8*q^61 + 4*q^62 + 2*q^63 + 1*q^64 + -3*q^65 + -6*q^66 + 14*q^67 + -3*q^68 + -3*q^70 + -3*q^71 + 2*q^72 + 2*q^73 + 7*q^74 + 4*q^75 + 2*q^76 + -6*q^77 + -1*q^78 + 8*q^79 + -3*q^80 + 1*q^81 + 12*q^83 + -1*q^84 + 9*q^85 + 1*q^86 + 6*q^87 + -6*q^88 + -6*q^89 + -6*q^90 + -1*q^91 + -4*q^93 + -3*q^94 + -6*q^95 + -1*q^96 + -10*q^97 + 6*q^98 + -12*q^99 + 4*q^100 + -12*q^101 + 3*q^102 + -4*q^103 + -1*q^104 + 3*q^105 + 12*q^107 + -5*q^108 + -7*q^109 + 18*q^110 + -7*q^111 + -1*q^112 + -6*q^113 + -2*q^114 + 6*q^116 + -2*q^117 + 6*q^118 + 3*q^119 + 3*q^120 + 25*q^121 + -8*q^122 + -4*q^124 + 3*q^125 + -2*q^126 + 20*q^127 + -1*q^128 + -1*q^129 + 3*q^130 + -21*q^131 + 6*q^132 + -2*q^133 + -14*q^134 + 15*q^135 + 3*q^136 + -13*q^139 + 3*q^140 + 3*q^141 + 3*q^142 + 6*q^143 + -2*q^144 + -18*q^145 + -2*q^146 + -6*q^147 + -7*q^148 + -6*q^149 + -4*q^150 + 17*q^151 + -2*q^152 + 6*q^153 + 6*q^154 + 12*q^155 + 1*q^156 + 14*q^157 + -8*q^158 + 3*q^160 + -1*q^162 + -16*q^163 + -18*q^165 + -12*q^166 + 1*q^168 + 1*q^169 + -9*q^170 + -4*q^171 + -1*q^172 + -6*q^174 + -4*q^175 + 6*q^176 + -6*q^177 + 6*q^178 + 3*q^179 + 6*q^180 + 20*q^181 + 1*q^182 + 8*q^183 + 21*q^185 + 4*q^186 + -18*q^187 + 3*q^188 + 5*q^189 + 6*q^190 + -18*q^191 + 1*q^192 + -4*q^193 + 10*q^194 + -3*q^195 + -6*q^196 + 3*q^197 + 12*q^198 + 2*q^199 + -4*q^200 +  ...

-------------------------------------------------------
26B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 7
Torsion Bound  = 7
|L(1)/Omega|   = 1/7
Sha Bound      = 7

ANALYTIC INVARIANTS:

Omega+         = 4.3467574468433882646 + 0.8947838753713410092e-22i
Omega-         = 0.61407734160525436911e-23 + 1.8040571933815642736i
L(1)           = 0.62096534954905546638
w1             = -2.1733787234216941323 + 0.90202859669078213679i
w2             = 0.61407734160525436911e-23 + 1.8040571933815642736i
c4             = 129.00000000016127829 + 0.5034237925688686126e-20i
c6             = -2240.9999998973346059 + 0.35654969074205170944e-19i
j              = -1290.0775242533624749 + -0.33549431741773713578e-18i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -3*q^3 + 1*q^4 + -1*q^5 + -3*q^6 + 1*q^7 + 1*q^8 + 6*q^9 + -1*q^10 + -2*q^11 + -3*q^12 + -1*q^13 + 1*q^14 + 3*q^15 + 1*q^16 + -3*q^17 + 6*q^18 + 6*q^19 + -1*q^20 + -3*q^21 + -2*q^22 + -4*q^23 + -3*q^24 + -4*q^25 + -1*q^26 + -9*q^27 + 1*q^28 + 2*q^29 + 3*q^30 + 4*q^31 + 1*q^32 + 6*q^33 + -3*q^34 + -1*q^35 + 6*q^36 + 3*q^37 + 6*q^38 + 3*q^39 + -1*q^40 + -3*q^42 + -5*q^43 + -2*q^44 + -6*q^45 + -4*q^46 + 13*q^47 + -3*q^48 + -6*q^49 + -4*q^50 + 9*q^51 + -1*q^52 + 12*q^53 + -9*q^54 + 2*q^55 + 1*q^56 + -18*q^57 + 2*q^58 + -10*q^59 + 3*q^60 + -8*q^61 + 4*q^62 + 6*q^63 + 1*q^64 + 1*q^65 + 6*q^66 + -2*q^67 + -3*q^68 + 12*q^69 + -1*q^70 + -5*q^71 + 6*q^72 + -10*q^73 + 3*q^74 + 12*q^75 + 6*q^76 + -2*q^77 + 3*q^78 + -4*q^79 + -1*q^80 + 9*q^81 + -3*q^84 + 3*q^85 + -5*q^86 + -6*q^87 + -2*q^88 + 6*q^89 + -6*q^90 + -1*q^91 + -4*q^92 + -12*q^93 + 13*q^94 + -6*q^95 + -3*q^96 + 14*q^97 + -6*q^98 + -12*q^99 + -4*q^100 + 4*q^101 + 9*q^102 + -8*q^103 + -1*q^104 + 3*q^105 + 12*q^106 + -4*q^107 + -9*q^108 + 19*q^109 + 2*q^110 + -9*q^111 + 1*q^112 + 2*q^113 + -18*q^114 + 4*q^115 + 2*q^116 + -6*q^117 + -10*q^118 + -3*q^119 + 3*q^120 + -7*q^121 + -8*q^122 + 4*q^124 + 9*q^125 + 6*q^126 + 16*q^127 + 1*q^128 + 15*q^129 + 1*q^130 + -1*q^131 + 6*q^132 + 6*q^133 + -2*q^134 + 9*q^135 + -3*q^136 + 12*q^137 + 12*q^138 + 7*q^139 + -1*q^140 + -39*q^141 + -5*q^142 + 2*q^143 + 6*q^144 + -2*q^145 + -10*q^146 + 18*q^147 + 3*q^148 + -18*q^149 + 12*q^150 + -9*q^151 + 6*q^152 + -18*q^153 + -2*q^154 + -4*q^155 + 3*q^156 + -10*q^157 + -4*q^158 + -36*q^159 + -1*q^160 + -4*q^161 + 9*q^162 + -4*q^163 + -6*q^165 + -3*q^168 + 1*q^169 + 3*q^170 + 36*q^171 + -5*q^172 + 20*q^173 + -6*q^174 + -4*q^175 + -2*q^176 + 30*q^177 + 6*q^178 + -9*q^179 + -6*q^180 + -1*q^182 + 24*q^183 + -4*q^184 + -3*q^185 + -12*q^186 + 6*q^187 + 13*q^188 + -9*q^189 + -6*q^190 + 10*q^191 + -3*q^192 + -16*q^193 + 14*q^194 + -3*q^195 + -6*q^196 + 9*q^197 + -12*q^198 + -10*q^199 + -4*q^200 +  ...

-------------------------------------------------------
Gamma_0(27)
Weight 2

-------------------------------------------------------
J_0(27), dim = 1

-------------------------------------------------------
27A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 1.7666387502854499573 + -0.1334392187887364652e-22i
Omega-         = 0.23112350666439109869e-22 + 3.0599080741143857498i
L(1)           = 0.5888795834284833191
w1             = 1.7666387502854499573 + -0.1334392187887364652e-22i
w2             = 0.88331937514272497866 + -1.5299540370571928749i
c4             = -0.18776672680640749198e-9 + -0.32522151079960285662e-9i
c6             = 5831.99999951216479 + 0.26430446760609271727e-18i
j              = -0.26906338489013003736e-32 + -0.32180958100195476755e-61i

HECKE EIGENFORM:
f(q) = q + -2*q^4 + -1*q^7 + 5*q^13 + 4*q^16 + -7*q^19 + -5*q^25 + 2*q^28 + -4*q^31 + 11*q^37 + 8*q^43 + -6*q^49 + -10*q^52 + -1*q^61 + -8*q^64 + 5*q^67 + -7*q^73 + 14*q^76 + 17*q^79 + -5*q^91 + -19*q^97 + 10*q^100 + -13*q^103 + 2*q^109 + -4*q^112 + -11*q^121 + 8*q^124 + 20*q^127 + 7*q^133 + 23*q^139 + -22*q^148 + -19*q^151 + 14*q^157 + -25*q^163 + 12*q^169 + -16*q^172 + 5*q^175 + -7*q^181 + 23*q^193 + 12*q^196 + 11*q^199 +  ...

-------------------------------------------------------
Gamma_0(28)
Weight 2

-------------------------------------------------------
J_0(28), dim = 2

-------------------------------------------------------
28A (old = 14A), dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

-------------------------------------------------------
Gamma_0(29)
Weight 2

-------------------------------------------------------
J_0(29), dim = 2

-------------------------------------------------------
29A (new) , dim = 2

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^3
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 7
Torsion Bound  = 7
|L(1)/Omega|   = 1/7
Sha Bound      = 7

ANALYTIC INVARIANTS:

Omega+         = 2.0406509598940708402 + -0.72907676164715401209e-20i
Omega-         = 9.6162259738752548483 + -0.18789996460360025936e-19i
L(1)           = 0.29152156569915297717

HECKE EIGENFORM:
a^2+2*a-1 = 0,
f(q) = q + a*q^2 + -a*q^3 + (-2*a-1)*q^4 + -1*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 + 1*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 + 1*q^29 + (-2*a+1)*q^30 + (-5*a-2)*q^31 + (a+4)*q^32 + -1*q^33 + -2*q^34 + (-2*a-2)*q^35 + (-2*a+6)*q^36 + -4*q^37 + 6*a*q^38 + (3*a-2)*q^39 + (-a+2)*q^40 + (6*a+10)*q^41 + (-6*a+2)*q^42 + (a+6)*q^43 + (-a-4)*q^44 + (2*a+2)*q^45 + (2*a-4)*q^46 + (3*a+4)*q^47 + -3*a*q^48 + 1*q^49 + -4*a*q^50 + 2*q^51 + (4*a-5)*q^52 + (-6*a-5)*q^53 + 1*q^54 + (-a-2)*q^55 + (-6*a-2)*q^56 + -6*a*q^57 + a*q^58 + (4*a+6)*q^59 + (3*a-2)*q^60 + 2*a*q^61 + (8*a-5)*q^62 + -8*q^63 + (2*a-5)*q^64 + (-2*a-1)*q^65 + -a*q^66 + (-4*a-4)*q^67 + (2*a+8)*q^68 + (-2*a+4)*q^69 + (2*a-2)*q^70 + (2*a-4)*q^71 + (6*a+2)*q^72 + 4*q^73 + -4*a*q^74 + 4*a*q^75 + (-12*a-6)*q^76 + (2*a+6)*q^77 + (-8*a+3)*q^78 + a*q^79 + -3*q^80 + (6*a+5)*q^81 + (-2*a+6)*q^82 + (-4*a-2)*q^83 + (10*a-2)*q^84 + (2*a+4)*q^85 + (4*a+1)*q^86 + -a*q^87 + (-2*a-3)*q^88 + (6*a+2)*q^89 + (-2*a+2)*q^90 + (-2*a+6)*q^91 + 14*q^92 + (-8*a+5)*q^93 + (-2*a+3)*q^94 + -6*q^95 + (-2*a-1)*q^96 + (-6*a-10)*q^97 + a*q^98 + (-2*a-6)*q^99 + (8*a+4)*q^100 + (-4*a-12)*q^101 + 2*a*q^102 + 2*a*q^103 + -7*a*q^104 + (-2*a+2)*q^105 + (7*a-6)*q^106 + (2*a-10)*q^107 + (-a-4)*q^108 + (-4*a+3)*q^109 + -1*q^110 + 4*a*q^111 + (6*a+6)*q^112 + (8*a+6)*q^113 + (12*a-6)*q^114 + (4*a+6)*q^115 + (-2*a-1)*q^116 + (2*a-6)*q^117 + (-2*a+4)*q^118 + (-4*a-12)*q^119 + (-4*a+1)*q^120 + (2*a-6)*q^121 + (-4*a+2)*q^122 + (2*a-6)*q^123 + (-11*a+12)*q^124 + 9*q^125 + -8*a*q^126 + (-4*a-14)*q^127 + (-11*a-6)*q^128 + (-4*a-1)*q^129 + (3*a-2)*q^130 + (-8*a+2)*q^131 + (2*a+1)*q^132 + (12*a+12)*q^133 + (4*a-4)*q^134 + (-a-2)*q^135 + (4*a+6)*q^136 + 12*q^137 + (8*a-2)*q^138 + 14*q^139 + (-2*a+6)*q^140 + (2*a-3)*q^141 + (-8*a+2)*q^142 + (a+4)*q^143 + (-6*a-6)*q^144 + -1*q^145 + 4*a*q^146 + -a*q^147 + (8*a+4)*q^148 + (2*a-3)*q^149 + (-8*a+4)*q^150 + (10*a+10)*q^151 + (6*a-12)*q^152 + (4*a+12)*q^153 + (2*a+2)*q^154 + (5*a+2)*q^155 + (13*a-4)*q^156 + (-6*a-6)*q^157 + (-2*a+1)*q^158 + (-7*a+6)*q^159 + (-a-4)*q^160 + (-4*a-20)*q^161 + (-7*a+6)*q^162 + (5*a+16)*q^163 + (-2*a-22)*q^164 + 1*q^165 + (6*a-4)*q^166 + (-2*a-8)*q^167 + (-10*a+6)*q^168 + (-4*a-8)*q^169 + 2*q^170 + (-12*a-12)*q^171 + (-9*a-8)*q^172 + (4*a+22)*q^173 + (2*a-1)*q^174 + (-8*a-8)*q^175 + (3*a+6)*q^176 + (2*a-4)*q^177 + (-10*a+6)*q^178 + (6*a+8)*q^179 + (2*a-6)*q^180 + (-8*a-11)*q^181 + (10*a-2)*q^182 + (4*a-2)*q^183 + (10*a+8)*q^184 + 4*q^185 + (21*a-8)*q^186 + (-4*a-10)*q^187 + (a-10)*q^188 + (2*a+6)*q^189 + -6*a*q^190 + (-8*a+6)*q^191 + (9*a-2)*q^192 + (-2*a-10)*q^193 + (2*a-6)*q^194 + (-3*a+2)*q^195 + (-2*a-1)*q^196 + 2*q^197 + (-2*a-2)*q^198 + (6*a+14)*q^199 + (-4*a+8)*q^200 +  ...

-------------------------------------------------------
Gamma_0(30)
Weight 2

-------------------------------------------------------
J_0(30), dim = 3

-------------------------------------------------------
30A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2*3
Torsion Bound  = 2^2*3
|L(1)/Omega|   = 1/2*3
Sha Bound      = 2^3*3

ANALYTIC INVARIANTS:

Omega+         = 3.3519482592414964497 + -0.24978584697288268586e-19i
Omega-         = 2.3167842226281642667i
L(1)           = 0.55865804320691607495
w1             = 1.6759741296207482248 + -1.1583921113140821333i
w2             = -1.6759741296207482248 + -1.1583921113140821333i
c4             = -71.000000000006388842 + -0.77649282879156822658e-11i
c6             = -1836.9999999906914853 + -0.31702887426627591104e-8i
j              = 165.69953703859572874 + -0.46793266070001681022e-9i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -1*q^5 + -1*q^6 + -4*q^7 + -1*q^8 + 1*q^9 + 1*q^10 + 1*q^12 + 2*q^13 + 4*q^14 + -1*q^15 + 1*q^16 + 6*q^17 + -1*q^18 + -4*q^19 + -1*q^20 + -4*q^21 + -1*q^24 + 1*q^25 + -2*q^26 + 1*q^27 + -4*q^28 + -6*q^29 + 1*q^30 + 8*q^31 + -1*q^32 + -6*q^34 + 4*q^35 + 1*q^36 + 2*q^37 + 4*q^38 + 2*q^39 + 1*q^40 + -6*q^41 + 4*q^42 + -4*q^43 + -1*q^45 + 1*q^48 + 9*q^49 + -1*q^50 + 6*q^51 + 2*q^52 + -6*q^53 + -1*q^54 + 4*q^56 + -4*q^57 + 6*q^58 + -1*q^60 + -10*q^61 + -8*q^62 + -4*q^63 + 1*q^64 + -2*q^65 + -4*q^67 + 6*q^68 + -4*q^70 + -1*q^72 + 2*q^73 + -2*q^74 + 1*q^75 + -4*q^76 + -2*q^78 + 8*q^79 + -1*q^80 + 1*q^81 + 6*q^82 + 12*q^83 + -4*q^84 + -6*q^85 + 4*q^86 + -6*q^87 + 18*q^89 + 1*q^90 + -8*q^91 + 8*q^93 + 4*q^95 + -1*q^96 + 2*q^97 + -9*q^98 + 1*q^100 + 18*q^101 + -6*q^102 + -4*q^103 + -2*q^104 + 4*q^105 + 6*q^106 + -12*q^107 + 1*q^108 + -10*q^109 + 2*q^111 + -4*q^112 + -18*q^113 + 4*q^114 + -6*q^116 + 2*q^117 + -24*q^119 + 1*q^120 + -11*q^121 + 10*q^122 + -6*q^123 + 8*q^124 + -1*q^125 + 4*q^126 + 20*q^127 + -1*q^128 + -4*q^129 + 2*q^130 + 16*q^133 + 4*q^134 + -1*q^135 + -6*q^136 + 6*q^137 + -4*q^139 + 4*q^140 + 1*q^144 + 6*q^145 + -2*q^146 + 9*q^147 + 2*q^148 + -6*q^149 + -1*q^150 + 8*q^151 + 4*q^152 + 6*q^153 + -8*q^155 + 2*q^156 + 2*q^157 + -8*q^158 + -6*q^159 + 1*q^160 + -1*q^162 + -4*q^163 + -6*q^164 + -12*q^166 + 4*q^168 + -9*q^169 + 6*q^170 + -4*q^171 + -4*q^172 + 18*q^173 + 6*q^174 + -4*q^175 + -18*q^178 + 24*q^179 + -1*q^180 + 14*q^181 + 8*q^182 + -10*q^183 + -2*q^185 + -8*q^186 + -4*q^189 + -4*q^190 + -24*q^191 + 1*q^192 + -22*q^193 + -2*q^194 + -2*q^195 + 9*q^196 + -6*q^197 + 8*q^199 + -1*q^200 +  ...

-------------------------------------------------------
30B (old = 15A), dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(31)
Weight 2

-------------------------------------------------------
J_0(31), dim = 2

-------------------------------------------------------
31A (new) , dim = 2

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 5
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 5
Torsion Bound  = 5
|L(1)/Omega|   = 1/5
Sha Bound      = 5

ANALYTIC INVARIANTS:

Omega+         = 2.24643861938020393 + -0.58316714178571559551e-18i
Omega-         = 14.573180834492855092 + 0.1606417351165064946e-17i
L(1)           = 0.44928772387604078599

HECKE EIGENFORM:
a^2-a-1 = 0,
f(q) = q + a*q^2 + -2*a*q^3 + (a-1)*q^4 + 1*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 + 1*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 + (-a-2)*q^38 + (4*a+4)*q^39 + (-2*a+1)*q^40 + 7*q^41 + (-2*a+2)*q^42 + (2*a-2)*q^43 + (2*a-2)*q^44 + (4*a+1)*q^45 + (2*a+6)*q^46 + (4*a-4)*q^47 + (6*a+6)*q^48 + (-8*a+6)*q^49 + -4*a*q^50 + (-4*a+4)*q^51 + -2*q^52 + (-4*a-4)*q^53 + (-12*a-4)*q^54 + 2*q^55 + (4*a-7)*q^56 + (2*a+4)*q^57 + (4*a-2)*q^58 + (2*a-1)*q^59 + -2*q^60 + (10*a-8)*q^61 + a*q^62 + (-2*a+5)*q^63 + (2*a+1)*q^64 + -2*a*q^65 + (-4*a-4)*q^66 + 8*q^67 + (4*a-6)*q^68 + (-4*a-12)*q^69 + (-a+2)*q^70 + (-10*a+7)*q^71 + (-6*a-7)*q^72 + (4*a+2)*q^73 + -2*a*q^74 + 8*a*q^75 + (a-3)*q^76 + (4*a-6)*q^77 + (8*a+4)*q^78 + (-6*a-2)*q^79 + -3*a*q^80 + (12*a+5)*q^81 + 7*a*q^82 + (-8*a-2)*q^83 + (-4*a+6)*q^84 + (-2*a+4)*q^85 + 2*q^86 + (-8*a+4)*q^87 + (-4*a+2)*q^88 + (6*a+2)*q^89 + (5*a+4)*q^90 + (2*a-4)*q^91 + (-4*a+10)*q^92 + -2*a*q^93 + 4*q^94 + (-2*a+1)*q^95 + (8*a-2)*q^96 + (-8*a-3)*q^97 + (-2*a-8)*q^98 + (8*a+2)*q^99 + (-4*a+4)*q^100 + -3*q^101 + -4*q^102 + (2*a+3)*q^103 + (2*a+4)*q^104 + (2*a-4)*q^105 + (-8*a-4)*q^106 + (-2*a+9)*q^107 + (-8*a+4)*q^108 + (-8*a-1)*q^109 + 2*a*q^110 + 4*a*q^111 + (3*a-6)*q^112 + (4*a-3)*q^113 + (6*a+2)*q^114 + (6*a-4)*q^115 + (6*a-8)*q^116 + (-10*a-8)*q^117 + (a+2)*q^118 + (10*a-16)*q^119 + (2*a+4)*q^120 + -7*q^121 + (2*a+10)*q^122 + -14*a*q^123 + (a-1)*q^124 + -9*q^125 + (3*a-2)*q^126 + (4*a+6)*q^127 + (a+12)*q^128 + -4*q^129 + (-2*a-2)*q^130 + 12*q^131 + -4*q^132 + (4*a-7)*q^133 + 8*a*q^134 + (-4*a-8)*q^135 + (-6*a+8)*q^136 + (-6*a+16)*q^137 + (-16*a-4)*q^138 + (12*a-6)*q^139 + (-3*a+5)*q^140 + -8*q^141 + (-3*a-10)*q^142 + -4*a*q^143 + (-15*a-12)*q^144 + (-2*a+6)*q^145 + (6*a+4)*q^146 + (4*a+16)*q^147 + (-2*a+2)*q^148 + 10*q^149 + (8*a+8)*q^150 + (-10*a+2)*q^151 + 5*q^152 + (6*a-4)*q^153 + (-2*a+4)*q^154 + 1*q^155 + 4*a*q^156 + (16*a-5)*q^157 + (-8*a-6)*q^158 + (16*a+8)*q^159 + (a-5)*q^160 + (-14*a+24)*q^161 + (17*a+12)*q^162 + (6*a+1)*q^163 + (7*a-7)*q^164 + -4*a*q^165 + (-10*a-8)*q^166 + -4*a*q^167 + (6*a-8)*q^168 + (4*a-9)*q^169 + (2*a-2)*q^170 + (-6*a-7)*q^171 + (-2*a+4)*q^172 + (8*a-10)*q^173 + (-4*a-8)*q^174 + (-8*a+12)*q^175 + -6*a*q^176 + (-2*a-4)*q^177 + (8*a+6)*q^178 + (6*a-8)*q^179 + (a+3)*q^180 + (-10*a+12)*q^181 + (-2*a+2)*q^182 + (-4*a-20)*q^183 + (2*a-16)*q^184 + -2*q^185 + (-2*a-2)*q^186 + (-4*a+8)*q^187 + (-4*a+8)*q^188 + (-12*a+16)*q^189 + (-a-2)*q^190 + (-10*a-3)*q^191 + (-6*a-4)*q^192 + (4*a-3)*q^193 + (-11*a-8)*q^194 + (4*a+4)*q^195 + (6*a-14)*q^196 + (12*a-8)*q^197 + (10*a+8)*q^198 + (-8*a-6)*q^199 + (8*a-4)*q^200 +  ...

-------------------------------------------------------
Gamma_0(32)
Weight 2

-------------------------------------------------------
J_0(32), dim = 1

-------------------------------------------------------
32A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 2.6220575542921198112 + -0.91609413137570631098e-45i
Omega-         = 2.6220575542921198112i
L(1)           = 0.65551438857302995281
w1             = 1.3110287771460599056 + -1.3110287771460599056i
w2             = -1.3110287771460599056 + -1.3110287771460599056i
c4             = -191.99999999970916329 + -0.13416186755951148267e-42i
c6             = 0.30044632178269532466e-38 + 0.25277970442954914368e-6i
j              = 1728 + -0.37083365438245488585e-48i

HECKE EIGENFORM:
f(q) = q + -2*q^5 + -3*q^9 + 6*q^13 + 2*q^17 + -1*q^25 + -10*q^29 + -2*q^37 + 10*q^41 + 6*q^45 + -7*q^49 + 14*q^53 + -10*q^61 + -12*q^65 + -6*q^73 + 9*q^81 + -4*q^85 + 10*q^89 + 18*q^97 + -2*q^101 + 6*q^109 + -14*q^113 + -18*q^117 + -11*q^121 + 12*q^125 + -22*q^137 + 20*q^145 + 14*q^149 + -6*q^153 + 22*q^157 + 23*q^169 + -26*q^173 + -18*q^181 + 4*q^185 + -14*q^193 + -2*q^197 +  ...

-------------------------------------------------------
Gamma_0(33)
Weight 2

-------------------------------------------------------
J_0(33), dim = 3

-------------------------------------------------------
33A (new) , dim = 1

CONGRUENCES:
Modular Degree = 3
Ker(ModPolar)  = Z/3 + Z/3
= B(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 1.4946782954854872405 + -0.69134435991759407882e-18i
Omega-         = 0.23229572832919744763e-17 + 1.3723166787329470489i
L(1)           = 0.37366957387137181013
w1             = -1.4946782954854872405 + 0.69134435991759407882e-18i
w2             = 0.23229572832919744763e-17 + 1.3723166787329470489i
c4             = 552.99999999996643275 + 0.27791562436978358775e-14i
c6             = -4085.00000005323332 + -0.86141572206278351666e-13i
j              = 1917.1782584598612555 + 0.5687529768019157528e-14i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^3 + -1*q^4 + -2*q^5 + -1*q^6 + 4*q^7 + -3*q^8 + 1*q^9 + -2*q^10 + 1*q^11 + 1*q^12 + -2*q^13 + 4*q^14 + 2*q^15 + -1*q^16 + -2*q^17 + 1*q^18 + 2*q^20 + -4*q^21 + 1*q^22 + 8*q^23 + 3*q^24 + -1*q^25 + -2*q^26 + -1*q^27 + -4*q^28 + -6*q^29 + 2*q^30 + -8*q^31 + 5*q^32 + -1*q^33 + -2*q^34 + -8*q^35 + -1*q^36 + 6*q^37 + 2*q^39 + 6*q^40 + -2*q^41 + -4*q^42 + -1*q^44 + -2*q^45 + 8*q^46 + 8*q^47 + 1*q^48 + 9*q^49 + -1*q^50 + 2*q^51 + 2*q^52 + 6*q^53 + -1*q^54 + -2*q^55 + -12*q^56 + -6*q^58 + -4*q^59 + -2*q^60 + 6*q^61 + -8*q^62 + 4*q^63 + 7*q^64 + 4*q^65 + -1*q^66 + -4*q^67 + 2*q^68 + -8*q^69 + -8*q^70 + -3*q^72 + -14*q^73 + 6*q^74 + 1*q^75 + 4*q^77 + 2*q^78 + -4*q^79 + 2*q^80 + 1*q^81 + -2*q^82 + 12*q^83 + 4*q^84 + 4*q^85 + 6*q^87 + -3*q^88 + -6*q^89 + -2*q^90 + -8*q^91 + -8*q^92 + 8*q^93 + 8*q^94 + -5*q^96 + 2*q^97 + 9*q^98 + 1*q^99 + 1*q^100 + 2*q^101 + 2*q^102 + 8*q^103 + 6*q^104 + 8*q^105 + 6*q^106 + -12*q^107 + 1*q^108 + -2*q^109 + -2*q^110 + -6*q^111 + -4*q^112 + -6*q^113 + -16*q^115 + 6*q^116 + -2*q^117 + -4*q^118 + -8*q^119 + -6*q^120 + 1*q^121 + 6*q^122 + 2*q^123 + 8*q^124 + 12*q^125 + 4*q^126 + -4*q^127 + -3*q^128 + 4*q^130 + -12*q^131 + 1*q^132 + -4*q^134 + 2*q^135 + 6*q^136 + 2*q^137 + -8*q^138 + -8*q^139 + 8*q^140 + -8*q^141 + -2*q^143 + -1*q^144 + 12*q^145 + -14*q^146 + -9*q^147 + -6*q^148 + -22*q^149 + 1*q^150 + 20*q^151 + -2*q^153 + 4*q^154 + 16*q^155 + -2*q^156 + 14*q^157 + -4*q^158 + -6*q^159 + -10*q^160 + 32*q^161 + 1*q^162 + 4*q^163 + 2*q^164 + 2*q^165 + 12*q^166 + 12*q^168 + -9*q^169 + 4*q^170 + -6*q^173 + 6*q^174 + -4*q^175 + -1*q^176 + 4*q^177 + -6*q^178 + 12*q^179 + 2*q^180 + 22*q^181 + -8*q^182 + -6*q^183 + -24*q^184 + -12*q^185 + 8*q^186 + -2*q^187 + -8*q^188 + -4*q^189 + 8*q^191 + -7*q^192 + -14*q^193 + 2*q^194 + -4*q^195 + -9*q^196 + -14*q^197 + 1*q^198 + 3*q^200 +  ...

-------------------------------------------------------
33B (old = 11A), dim = 1

CONGRUENCES:
Modular Degree = 3
Ker(ModPolar)  = Z/3 + Z/3
= A(Z/3 + Z/3)

-------------------------------------------------------
Gamma_0(34)
Weight 2

-------------------------------------------------------
J_0(34), dim = 3

-------------------------------------------------------
34A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/2*3
Sha Bound      = 2*3

ANALYTIC INVARIANTS:

Omega+         = 2.2478316631568517669 + -0.70737079076773911788e-17i
Omega-         = 0.42066769969407749568e-17 + 1.8641750574724360854i
L(1)           = 0.37463861052614196114
w1             = -2.2478316631568517669 + 0.70737079076773911788e-17i
w2             = 0.42066769969407749568e-17 + 1.8641750574724360854i
c4             = 144.99999999986304794 + 0.14168747947496565355e-14i
c6             = -1081.0000000817098705 + -0.1199521028435092289e-13i
j              = 2802.0450370329297368 + -0.1240356515218331531e-13i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -2*q^3 + 1*q^4 + -2*q^6 + -4*q^7 + 1*q^8 + 1*q^9 + 6*q^11 + -2*q^12 + 2*q^13 + -4*q^14 + 1*q^16 + -1*q^17 + 1*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 + 1*q^32 + -12*q^33 + -1*q^34 + 1*q^36 + -4*q^37 + -4*q^38 + -4*q^39 + 6*q^41 + 8*q^42 + 8*q^43 + 6*q^44 + -2*q^48 + 9*q^49 + -5*q^50 + 2*q^51 + 2*q^52 + -6*q^53 + 4*q^54 + -4*q^56 + 8*q^57 + -4*q^61 + -4*q^62 + -4*q^63 + 1*q^64 + -12*q^66 + 8*q^67 + -1*q^68 + 1*q^72 + 2*q^73 + -4*q^74 + 10*q^75 + -4*q^76 + -24*q^77 + -4*q^78 + 8*q^79 + -11*q^81 + 6*q^82 + 8*q^84 + 8*q^86 + 6*q^88 + -6*q^89 + -8*q^91 + 8*q^93 + -2*q^96 + 14*q^97 + 9*q^98 + 6*q^99 + -5*q^100 + 18*q^101 + 2*q^102 + -16*q^103 + 2*q^104 + -6*q^106 + -6*q^107 + 4*q^108 + -16*q^109 + 8*q^111 + -4*q^112 + -6*q^113 + 8*q^114 + 2*q^117 + 4*q^119 + 25*q^121 + -4*q^122 + -12*q^123 + -4*q^124 + -4*q^126 + -16*q^127 + 1*q^128 + -16*q^129 + -6*q^131 + -12*q^132 + 16*q^133 + 8*q^134 + -1*q^136 + 6*q^137 + 2*q^139 + 12*q^143 + 1*q^144 + 2*q^146 + -18*q^147 + -4*q^148 + 6*q^149 + 10*q^150 + -16*q^151 + -4*q^152 + -1*q^153 + -24*q^154 + -4*q^156 + 14*q^157 + 8*q^158 + 12*q^159 + -11*q^162 + 2*q^163 + 6*q^164 + 12*q^167 + 8*q^168 + -9*q^169 + -4*q^171 + 8*q^172 + 24*q^173 + 20*q^175 + 6*q^176 + -6*q^178 + 12*q^179 + -4*q^181 + -8*q^182 + 8*q^183 + 8*q^186 + -6*q^187 + -16*q^189 + -24*q^191 + -2*q^192 + -10*q^193 + 14*q^194 + 9*q^196 + -12*q^197 + 6*q^198 + -16*q^199 + -5*q^200 +  ...

-------------------------------------------------------
34B (old = 17A), dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(35)
Weight 2

-------------------------------------------------------
J_0(35), dim = 3

-------------------------------------------------------
35A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 2.1087337174047165359 + -0.11820507992192260061e-16i
Omega-         = 0.14248536742437420368e-16 + -2.2050442761017105106i
L(1)           = 0.70291123913490551197
w1             = -1.0543668587023582751 + 1.1025221380508552612i
w2             = 1.0543668587023582608 + 1.1025221380508552494i
c4             = -416.00000000001532848 + 0.65861142994399898675e-9i
c6             = 1447.9999991544513104 + 0.17828762769999045968e-7i
j              = 1679.0972828543355173 + -0.13958619309883181967e-8i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + -2*q^4 + -1*q^5 + 1*q^7 + -2*q^9 + -3*q^11 + -2*q^12 + 5*q^13 + -1*q^15 + 4*q^16 + 3*q^17 + 2*q^19 + 2*q^20 + 1*q^21 + -6*q^23 + 1*q^25 + -5*q^27 + -2*q^28 + 3*q^29 + -4*q^31 + -3*q^33 + -1*q^35 + 4*q^36 + 2*q^37 + 5*q^39 + -12*q^41 + -10*q^43 + 6*q^44 + 2*q^45 + 9*q^47 + 4*q^48 + 1*q^49 + 3*q^51 + -10*q^52 + 12*q^53 + 3*q^55 + 2*q^57 + 2*q^60 + 8*q^61 + -2*q^63 + -8*q^64 + -5*q^65 + -4*q^67 + -6*q^68 + -6*q^69 + 2*q^73 + 1*q^75 + -4*q^76 + -3*q^77 + -1*q^79 + -4*q^80 + 1*q^81 + 12*q^83 + -2*q^84 + -3*q^85 + 3*q^87 + -12*q^89 + 5*q^91 + 12*q^92 + -4*q^93 + -2*q^95 + -1*q^97 + 6*q^99 + -2*q^100 + 6*q^101 + 5*q^103 + -1*q^105 + 6*q^107 + 10*q^108 + -7*q^109 + 2*q^111 + 4*q^112 + 6*q^113 + 6*q^115 + -6*q^116 + -10*q^117 + 3*q^119 + -2*q^121 + -12*q^123 + 8*q^124 + -1*q^125 + -16*q^127 + -10*q^129 + -6*q^131 + 6*q^132 + 2*q^133 + 5*q^135 + -12*q^137 + 14*q^139 + 2*q^140 + 9*q^141 + -15*q^143 + -8*q^144 + -3*q^145 + 1*q^147 + -4*q^148 + -6*q^149 + -1*q^151 + -6*q^153 + 4*q^155 + -10*q^156 + 14*q^157 + 12*q^159 + -6*q^161 + 2*q^163 + 24*q^164 + 3*q^165 + -3*q^167 + 12*q^169 + -4*q^171 + 20*q^172 + -9*q^173 + 1*q^175 + -12*q^176 + 12*q^179 + -4*q^180 + 20*q^181 + 8*q^183 + -2*q^185 + -9*q^187 + -18*q^188 + -5*q^189 + 9*q^191 + -8*q^192 + -4*q^193 + -5*q^195 + -2*q^196 + -16*q^199 +  ...

-------------------------------------------------------
35B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 17
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^3
Torsion Bound  = 2^4
|L(1)/Omega|   = 1/2^4
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 2.9819742701053530871 + 0.46554152239434347155e-17i
Omega-         = 3.0828285833203041519 + 0.96584367389443946279e-17i
L(1)           = 0.18637339188158456794

HECKE EIGENFORM:
a^2+a-4 = 0,
f(q) = q + a*q^2 + (-a-1)*q^3 + (-a+2)*q^4 + 1*q^5 + -4*q^6 + -1*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 + 1*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 + -1*q^35 + a*q^36 + 6*q^37 + (-4*a+8)*q^38 + (-3*a-7)*q^39 + (a-4)*q^40 + -2*a*q^41 + 4*q^42 + (2*a+6)*q^43 + (2*a-2)*q^44 + (a+2)*q^45 + -8*q^46 + (3*a-1)*q^47 + 12*q^48 + 1*q^49 + a*q^50 + (3*a+7)*q^51 + 2*q^52 + 2*a*q^53 + (-4*a+4)*q^54 + (a+1)*q^55 + (-a+4)*q^56 + (2*a-6)*q^57 + (2*a-12)*q^58 + -4*q^59 + (-2*a+2)*q^60 + -6*a*q^61 + (-a-2)*q^63 + (a+4)*q^64 + (a+3)*q^65 + (-4*a-4)*q^66 + -4*a*q^67 + -2*q^68 + (2*a+10)*q^69 + -a*q^70 + 8*q^71 + (-3*a-4)*q^72 + (4*a-2)*q^73 + 6*a*q^74 + (-a-1)*q^75 + (8*a-12)*q^76 + (-a-1)*q^77 + (-4*a-12)*q^78 + (-a-5)*q^79 + -3*a*q^80 + -7*q^81 + (2*a-8)*q^82 + 4*q^83 + (2*a-2)*q^84 + (-a-3)*q^85 + (4*a+8)*q^86 + (a+13)*q^87 + -4*a*q^88 + (2*a+4)*q^89 + (a+4)*q^90 + (-a-3)*q^91 + (-4*a+4)*q^92 + (-4*a+12)*q^94 + (2*a-2)*q^95 + 4*a*q^96 + (-5*a-7)*q^97 + a*q^98 + (2*a+6)*q^99 + (-a+2)*q^100 + (4*a-6)*q^101 + (4*a+12)*q^102 + (-a+3)*q^103 + (-2*a-8)*q^104 + (a+1)*q^105 + (-2*a+8)*q^106 + (-6*a-2)*q^107 + (6*a-10)*q^108 + (3*a+13)*q^109 + 4*q^110 + (-6*a-6)*q^111 + 3*a*q^112 + -14*q^113 + (-8*a+8)*q^114 + (-2*a-2)*q^115 + (-8*a+10)*q^116 + (4*a+10)*q^117 + -4*a*q^118 + (a+3)*q^119 + 4*a*q^120 + (a-6)*q^121 + (6*a-24)*q^122 + 8*q^123 + 1*q^125 + (-a-4)*q^126 + (4*a+4)*q^127 + (a+12)*q^128 + (-6*a-14)*q^129 + (2*a+4)*q^130 + (-2*a-6)*q^131 + (2*a-6)*q^132 + (-2*a+2)*q^133 + (4*a-16)*q^134 + (a-3)*q^135 + (2*a+8)*q^136 + (2*a-12)*q^137 + (8*a+8)*q^138 + (2*a-10)*q^139 + (a-2)*q^140 + (a-11)*q^141 + 8*a*q^142 + (3*a+7)*q^143 + (-3*a-12)*q^144 + (-3*a-1)*q^145 + (-6*a+16)*q^146 + (-a-1)*q^147 + (-6*a+12)*q^148 + (-4*a+2)*q^149 + -4*q^150 + (7*a+11)*q^151 + (-12*a+16)*q^152 + (-4*a-10)*q^153 + -4*q^154 + (-2*a-2)*q^156 + (-4*a+10)*q^157 + (-4*a-4)*q^158 + -8*q^159 + (a-4)*q^160 + (2*a+2)*q^161 + -7*a*q^162 + (2*a-2)*q^163 + (-6*a+8)*q^164 + (-a-5)*q^165 + 4*a*q^166 + (7*a+11)*q^167 + -4*a*q^168 + 5*a*q^169 + (-2*a-4)*q^170 + 4*q^171 + 4*q^172 + (-a-7)*q^173 + (12*a+4)*q^174 + -1*q^175 + -12*q^176 + (4*a+4)*q^177 + (2*a+8)*q^178 + 20*q^179 + a*q^180 + (10*a+8)*q^181 + (-2*a-4)*q^182 + 24*q^183 + 8*a*q^184 + 6*q^185 + (-3*a-7)*q^187 + (10*a-14)*q^188 + (-a+3)*q^189 + (-4*a+8)*q^190 + (a-11)*q^191 + (-4*a-8)*q^192 + (-6*a+4)*q^193 + (-2*a-20)*q^194 + (-3*a-7)*q^195 + (-a+2)*q^196 + (-2*a-4)*q^197 + (4*a+8)*q^198 + (-4*a-12)*q^199 + (a-4)*q^200 +  ...

-------------------------------------------------------
Gamma_0(36)
Weight 2

-------------------------------------------------------
J_0(36), dim = 1

-------------------------------------------------------
36A (new) , dim = 1

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2*3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/2*3
Sha Bound      = 2*3

ANALYTIC INVARIANTS:

Omega+         = 4.2065463110251268671 + -0.24512255545791210966e-42i
Omega-         = 2.4286506450289842226i
L(1)           = 0.70109105183752114451
w1             = 2.1032731555125634335 + 1.2143253225144921113i
w2             = 2.1032731555125634335 + -1.2143253225144921113i
c4             = -0.52571389486013256708e-10 + 0.91056317614267246262e-10i
c6             = -864.00000602945746137 + -0.15104054686297026568e-39i
j              = -0.26906338489013003736e-32 + -0.52498895775224995052e-63i

HECKE EIGENFORM:
f(q) = q + -4*q^7 + 2*q^13 + 8*q^19 + -5*q^25 + -4*q^31 + -10*q^37 + 8*q^43 + 9*q^49 + 14*q^61 + -16*q^67 + -10*q^73 + -4*q^79 + -8*q^91 + 14*q^97 + 20*q^103 + 2*q^109 + -11*q^121 + 20*q^127 + -32*q^133 + -16*q^139 + -4*q^151 + 14*q^157 + 8*q^163 + -9*q^169 + 20*q^175 + 26*q^181 + 2*q^193 + -28*q^199 +  ...

-------------------------------------------------------
Gamma_0(37)
Weight 2

-------------------------------------------------------
J_0(37), dim = 2

-------------------------------------------------------
37A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.9934586462319601052 + -0.12785801847156390955e-15i
Omega-         = 0.27086382816623465246e-15 + -2.4513893819867898361i
L(1)           =
w1             = -2.9934586462319601052 + 0.12785801847156390955e-15i
w2             = -0.27086382816623465246e-15 + 2.4513893819867898361i
c4             = 47.999999999971709464 + -0.15500379532785060652e-13i
c6             = -216.00000000976399004 + 0.22379484748281594807e-12i
j              = 2988.9729731740208105 + -0.24066742978407140058e-11i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + -3*q^3 + 2*q^4 + -2*q^5 + 6*q^6 + -1*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 + -1*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 + -1*q^37 + 6*q^39 + -9*q^41 + -6*q^42 + 2*q^43 + -10*q^44 + -12*q^45 + -4*q^46 + -9*q^47 + 12*q^48 + -6*q^49 + 2*q^50 + -4*q^52 + 1*q^53 + 18*q^54 + 10*q^55 + -12*q^58 + 8*q^59 + 12*q^60 + -8*q^61 + 8*q^62 + -6*q^63 + -8*q^64 + 4*q^65 + -30*q^66 + 8*q^67 + -6*q^69 + -4*q^70 + 9*q^71 + -1*q^73 + 2*q^74 + 3*q^75 + 5*q^77 + -12*q^78 + 4*q^79 + 8*q^80 + 9*q^81 + 18*q^82 + -15*q^83 + 6*q^84 + -4*q^86 + -18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^92 + 12*q^93 + 18*q^94 + -24*q^96 + 4*q^97 + 12*q^98 + -30*q^99 + -2*q^100 + 3*q^101 + 18*q^103 + -6*q^105 + -2*q^106 + -12*q^107 + -18*q^108 + -16*q^109 + -20*q^110 + 3*q^111 + 4*q^112 + -18*q^113 + -4*q^115 + 12*q^116 + -12*q^117 + -16*q^118 + 14*q^121 + 16*q^122 + 27*q^123 + -8*q^124 + 12*q^125 + 12*q^126 + 1*q^127 + -6*q^129 + -8*q^130 + -12*q^131 + 30*q^132 + -16*q^134 + 18*q^135 + -6*q^137 + 12*q^138 + 4*q^139 + 4*q^140 + 27*q^141 + -18*q^142 + 10*q^143 + -24*q^144 + -12*q^145 + 2*q^146 + 18*q^147 + -2*q^148 + -5*q^149 + -6*q^150 + 16*q^151 + -10*q^154 + 8*q^155 + 12*q^156 + 23*q^157 + -8*q^158 + -3*q^159 + -16*q^160 + -2*q^161 + -18*q^162 + -18*q^163 + -18*q^164 + -30*q^165 + 30*q^166 + -12*q^167 + -9*q^169 + 4*q^172 + 9*q^173 + 36*q^174 + 1*q^175 + 20*q^176 + -24*q^177 + -8*q^178 + 18*q^179 + -24*q^180 + 5*q^181 + -4*q^182 + 24*q^183 + 2*q^185 + -24*q^186 + -18*q^188 + 9*q^189 + -4*q^191 + 24*q^192 + -26*q^193 + -8*q^194 + -12*q^195 + -12*q^196 + 3*q^197 + 60*q^198 + 2*q^199 +  ...

-------------------------------------------------------
37B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 2
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 1.0885215929042291958 + -0.58407040734934424174e-17i
Omega-         = 0.94135561290761948146e-16 + -1.7676106702337894123i
L(1)           = 0.3628405309680763986
w1             = -0.94135561290761948146e-16 + 1.7676106702337894123i
w2             = 1.0885215929042291958 + -0.58407040734934424174e-17i
c4             = 1119.9999999999677548 + 0.18129127932846696033e-13i
c6             = 36296.000000035998826 + 0.1582728301279095073e-11i
j              = 27736.323614470447545 + 0.16135807138535004293e-10i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + -2*q^4 + -1*q^7 + -2*q^9 + 3*q^11 + -2*q^12 + -4*q^13 + 4*q^16 + 6*q^17 + 2*q^19 + -1*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 + 1*q^37 + -4*q^39 + -9*q^41 + 8*q^43 + -6*q^44 + 3*q^47 + 4*q^48 + -6*q^49 + 6*q^51 + 8*q^52 + -3*q^53 + 2*q^57 + 12*q^59 + 8*q^61 + 2*q^63 + -8*q^64 + -4*q^67 + -12*q^68 + 6*q^69 + -15*q^71 + 11*q^73 + -5*q^75 + -4*q^76 + -3*q^77 + -10*q^79 + 1*q^81 + 9*q^83 + 2*q^84 + -6*q^87 + 6*q^89 + 4*q^91 + -12*q^92 + -4*q^93 + 8*q^97 + -6*q^99 + 10*q^100 + 3*q^101 + -4*q^103 + 12*q^107 + 10*q^108 + 2*q^109 + 1*q^111 + -4*q^112 + -6*q^113 + 12*q^116 + 8*q^117 + -6*q^119 + -2*q^121 + -9*q^123 + 8*q^124 + -7*q^127 + 8*q^129 + -6*q^131 + -6*q^132 + -2*q^133 + -6*q^137 + -4*q^139 + 3*q^141 + -12*q^143 + -8*q^144 + -6*q^147 + -2*q^148 + 15*q^149 + 8*q^151 + -12*q^153 + 8*q^156 + -13*q^157 + -3*q^159 + -6*q^161 + -16*q^163 + 18*q^164 + 18*q^167 + 3*q^169 + -4*q^171 + -16*q^172 + 9*q^173 + 5*q^175 + 12*q^176 + 12*q^177 + 18*q^179 + -7*q^181 + 8*q^183 + 18*q^187 + -6*q^188 + 5*q^189 + -24*q^191 + -8*q^192 + -4*q^193 + 12*q^196 + 15*q^197 + 2*q^199 +  ...

-------------------------------------------------------
Gamma_0(38)
Weight 2

-------------------------------------------------------
J_0(38), dim = 4

-------------------------------------------------------
38A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= B(Z/2 + Z/2) + C(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 1.8906322299422984681 + -0.25549454413743819076e-15i
Omega-         = 0.24413525194222918571e-15 + -1.202627757962398574i
L(1)           = 0.63021074331409948938
w1             = 0.94531611497114935613 + -0.60131387898119941475i
w2             = -0.945316114971149112 + -0.60131387898119915925i
c4             = -454.9999999998093033 + 0.35644607514515694776e-9i
c6             = -77293.000001309909373 + 0.7077822448960960584e-7i
j              = 26.822757678307073771 + -0.13698781073461575829e-10i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -1*q^6 + -1*q^7 + -1*q^8 + -2*q^9 + -6*q^11 + 1*q^12 + 5*q^13 + 1*q^14 + 1*q^16 + 3*q^17 + 2*q^18 + 1*q^19 + -1*q^21 + 6*q^22 + 3*q^23 + -1*q^24 + -5*q^25 + -5*q^26 + -5*q^27 + -1*q^28 + 9*q^29 + -4*q^31 + -1*q^32 + -6*q^33 + -3*q^34 + -2*q^36 + 2*q^37 + -1*q^38 + 5*q^39 + 1*q^42 + 8*q^43 + -6*q^44 + -3*q^46 + 1*q^48 + -6*q^49 + 5*q^50 + 3*q^51 + 5*q^52 + -3*q^53 + 5*q^54 + 1*q^56 + 1*q^57 + -9*q^58 + 9*q^59 + -10*q^61 + 4*q^62 + 2*q^63 + 1*q^64 + 6*q^66 + 5*q^67 + 3*q^68 + 3*q^69 + -6*q^71 + 2*q^72 + -7*q^73 + -2*q^74 + -5*q^75 + 1*q^76 + 6*q^77 + -5*q^78 + -10*q^79 + 1*q^81 + -6*q^83 + -1*q^84 + -8*q^86 + 9*q^87 + 6*q^88 + -12*q^89 + -5*q^91 + 3*q^92 + -4*q^93 + -1*q^96 + -10*q^97 + 6*q^98 + 12*q^99 + -5*q^100 + 18*q^101 + -3*q^102 + 14*q^103 + -5*q^104 + 3*q^106 + -9*q^107 + -5*q^108 + 11*q^109 + 2*q^111 + -1*q^112 + 6*q^113 + -1*q^114 + 9*q^116 + -10*q^117 + -9*q^118 + -3*q^119 + 25*q^121 + 10*q^122 + -4*q^124 + -2*q^126 + 2*q^127 + -1*q^128 + 8*q^129 + -6*q^132 + -1*q^133 + -5*q^134 + -3*q^136 + -9*q^137 + -3*q^138 + -4*q^139 + 6*q^142 + -30*q^143 + -2*q^144 + 7*q^146 + -6*q^147 + 2*q^148 + 5*q^150 + -10*q^151 + -1*q^152 + -6*q^153 + -6*q^154 + 5*q^156 + -22*q^157 + 10*q^158 + -3*q^159 + -3*q^161 + -1*q^162 + 20*q^163 + 6*q^166 + 12*q^167 + 1*q^168 + 12*q^169 + -2*q^171 + 8*q^172 + 6*q^173 + -9*q^174 + 5*q^175 + -6*q^176 + 9*q^177 + 12*q^178 + 2*q^181 + 5*q^182 + -10*q^183 + -3*q^184 + 4*q^186 + -18*q^187 + 5*q^189 + 3*q^191 + 1*q^192 + 14*q^193 + 10*q^194 + -6*q^196 + -12*q^198 + 11*q^199 + 5*q^200 +  ...

-------------------------------------------------------
38B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 5
Torsion Bound  = 5
|L(1)/Omega|   = 1/5
Sha Bound      = 5

ANALYTIC INVARIANTS:

Omega+         = 4.0962281652755201749 + 0.77398315064620442127e-15i
Omega-         = 0.36306476815698415383e-15 + 2.3559624213775919731i
L(1)           = 0.81924563305510403499
w1             = -2.0481140826377599059 + 1.1779812106887955996i
w2             = 0.36306476815698415383e-15 + 2.3559624213775919731i
c4             = 1.0000000001027878033 + 0.89942732848875459372e-13i
c6             = -1024.9999999249986985 + 0.10904498003954723252e-12i
j              = -0.16447368428531379042e-2 + -0.44414675388747314801e-15i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + -4*q^5 + -1*q^6 + 3*q^7 + 1*q^8 + -2*q^9 + -4*q^10 + 2*q^11 + -1*q^12 + -1*q^13 + 3*q^14 + 4*q^15 + 1*q^16 + 3*q^17 + -2*q^18 + -1*q^19 + -4*q^20 + -3*q^21 + 2*q^22 + -1*q^23 + -1*q^24 + 11*q^25 + -1*q^26 + 5*q^27 + 3*q^28 + -5*q^29 + 4*q^30 + -8*q^31 + 1*q^32 + -2*q^33 + 3*q^34 + -12*q^35 + -2*q^36 + -2*q^37 + -1*q^38 + 1*q^39 + -4*q^40 + -8*q^41 + -3*q^42 + 4*q^43 + 2*q^44 + 8*q^45 + -1*q^46 + 8*q^47 + -1*q^48 + 2*q^49 + 11*q^50 + -3*q^51 + -1*q^52 + -1*q^53 + 5*q^54 + -8*q^55 + 3*q^56 + 1*q^57 + -5*q^58 + 15*q^59 + 4*q^60 + 2*q^61 + -8*q^62 + -6*q^63 + 1*q^64 + 4*q^65 + -2*q^66 + 3*q^67 + 3*q^68 + 1*q^69 + -12*q^70 + 2*q^71 + -2*q^72 + 9*q^73 + -2*q^74 + -11*q^75 + -1*q^76 + 6*q^77 + 1*q^78 + -10*q^79 + -4*q^80 + 1*q^81 + -8*q^82 + -6*q^83 + -3*q^84 + -12*q^85 + 4*q^86 + 5*q^87 + 2*q^88 + 8*q^90 + -3*q^91 + -1*q^92 + 8*q^93 + 8*q^94 + 4*q^95 + -1*q^96 + -2*q^97 + 2*q^98 + -4*q^99 + 11*q^100 + 2*q^101 + -3*q^102 + -6*q^103 + -1*q^104 + 12*q^105 + -1*q^106 + -7*q^107 + 5*q^108 + -15*q^109 + -8*q^110 + 2*q^111 + 3*q^112 + 14*q^113 + 1*q^114 + 4*q^115 + -5*q^116 + 2*q^117 + 15*q^118 + 9*q^119 + 4*q^120 + -7*q^121 + 2*q^122 + 8*q^123 + -8*q^124 + -24*q^125 + -6*q^126 + 18*q^127 + 1*q^128 + -4*q^129 + 4*q^130 + 12*q^131 + -2*q^132 + -3*q^133 + 3*q^134 + -20*q^135 + 3*q^136 + -17*q^137 + 1*q^138 + -12*q^140 + -8*q^141 + 2*q^142 + -2*q^143 + -2*q^144 + 20*q^145 + 9*q^146 + -2*q^147 + -2*q^148 + -11*q^150 + 2*q^151 + -1*q^152 + -6*q^153 + 6*q^154 + 32*q^155 + 1*q^156 + -2*q^157 + -10*q^158 + 1*q^159 + -4*q^160 + -3*q^161 + 1*q^162 + -16*q^163 + -8*q^164 + 8*q^165 + -6*q^166 + -12*q^167 + -3*q^168 + -12*q^169 + -12*q^170 + 2*q^171 + 4*q^172 + -6*q^173 + 5*q^174 + 33*q^175 + 2*q^176 + -15*q^177 + 8*q^180 + 22*q^181 + -3*q^182 + -2*q^183 + -1*q^184 + 8*q^185 + 8*q^186 + 6*q^187 + 8*q^188 + 15*q^189 + 4*q^190 + 7*q^191 + -1*q^192 + -6*q^193 + -2*q^194 + -4*q^195 + 2*q^196 + 8*q^197 + -4*q^198 + -25*q^199 + 11*q^200 +  ...

-------------------------------------------------------
38C (old = 19A), dim = 1

CONGRUENCES:
Modular Degree = 3
Ker(ModPolar)  = Z/3 + Z/3
= A(Z/3 + Z/3)

-------------------------------------------------------
Gamma_0(39)
Weight 2

-------------------------------------------------------
J_0(39), dim = 3

-------------------------------------------------------
39A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 1.653375701346774334 + 0.15446361992811899919e-14i
Omega-         = 0.35046099624307500246e-14 + 2.2865886336506696131i
L(1)           = 0.41334392533669358351
w1             = -0.35046099624307500246e-14 + -2.2865886336506696131i
w2             = -1.653375701346774334 + -0.15446361992811899919e-14i
c4             = 216.99999999999760004 + -0.62973998578533171536e-12i
c6             = 2755.0000000006076606 + -0.20981738516535295304e-10i
j              = 6718.1545036252441239 + -0.12660338165564227238e-9i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^3 + -1*q^4 + 2*q^5 + -1*q^6 + -4*q^7 + -3*q^8 + 1*q^9 + 2*q^10 + 4*q^11 + 1*q^12 + 1*q^13 + -4*q^14 + -2*q^15 + -1*q^16 + 2*q^17 + 1*q^18 + -2*q^20 + 4*q^21 + 4*q^22 + 3*q^24 + -1*q^25 + 1*q^26 + -1*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 + -1*q^36 + -2*q^37 + -1*q^39 + -6*q^40 + 6*q^41 + 4*q^42 + -12*q^43 + -4*q^44 + 2*q^45 + 1*q^48 + 9*q^49 + -1*q^50 + -2*q^51 + -1*q^52 + 6*q^53 + -1*q^54 + 8*q^55 + 12*q^56 + -10*q^58 + 12*q^59 + 2*q^60 + -2*q^61 + 4*q^62 + -4*q^63 + 7*q^64 + 2*q^65 + -4*q^66 + -8*q^67 + -2*q^68 + -8*q^70 + -3*q^72 + 2*q^73 + -2*q^74 + 1*q^75 + -16*q^77 + -1*q^78 + 8*q^79 + -2*q^80 + 1*q^81 + 6*q^82 + 4*q^83 + -4*q^84 + 4*q^85 + -12*q^86 + 10*q^87 + -12*q^88 + -2*q^89 + 2*q^90 + -4*q^91 + -4*q^93 + -5*q^96 + 10*q^97 + 9*q^98 + 4*q^99 + 1*q^100 + -18*q^101 + -2*q^102 + -3*q^104 + 8*q^105 + 6*q^106 + 12*q^107 + 1*q^108 + -2*q^109 + 8*q^110 + 2*q^111 + 4*q^112 + -6*q^113 + 10*q^116 + 1*q^117 + 12*q^118 + -8*q^119 + 6*q^120 + 5*q^121 + -2*q^122 + -6*q^123 + -4*q^124 + -12*q^125 + -4*q^126 + -16*q^127 + -3*q^128 + 12*q^129 + 2*q^130 + 4*q^131 + 4*q^132 + -8*q^134 + -2*q^135 + -6*q^136 + 6*q^137 + 12*q^139 + 8*q^140 + 4*q^143 + -1*q^144 + -20*q^145 + 2*q^146 + -9*q^147 + 2*q^148 + -6*q^149 + 1*q^150 + 4*q^151 + 2*q^153 + -16*q^154 + 8*q^155 + 1*q^156 + -18*q^157 + 8*q^158 + -6*q^159 + 10*q^160 + 1*q^162 + 8*q^163 + -6*q^164 + -8*q^165 + 4*q^166 + -8*q^167 + -12*q^168 + 1*q^169 + 4*q^170 + 12*q^172 + 6*q^173 + 10*q^174 + 4*q^175 + -4*q^176 + -12*q^177 + -2*q^178 + 4*q^179 + -2*q^180 + -10*q^181 + -4*q^182 + 2*q^183 + -4*q^185 + -4*q^186 + 8*q^187 + 4*q^189 + 8*q^191 + -7*q^192 + 18*q^193 + 10*q^194 + -2*q^195 + -9*q^196 + 18*q^197 + 4*q^198 + 8*q^199 + 3*q^200 +  ...

-------------------------------------------------------
39B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2*7
Torsion Bound  = 2^2*7
|L(1)/Omega|   = 1/2^2*7
Sha Bound      = 2^2*7

ANALYTIC INVARIANTS:

Omega+         = 5.3485665640937583872 + 0.23816033991704107474e-14i
Omega-         = 2.926444751637510878 + 0.37044323325137031567e-15i
L(1)           = 0.1910202344319199424

HECKE EIGENFORM:
a^2+2*a-1 = 0,
f(q) = q + a*q^2 + 1*q^3 + (-2*a-1)*q^4 + (-2*a-2)*q^5 + a*q^6 + (2*a+2)*q^7 + (a-2)*q^8 + 1*q^9 + (2*a-2)*q^10 + -2*q^11 + (-2*a-1)*q^12 + -1*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 + 1*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 + (2*a-2)*q^38 + -1*q^39 + (6*a+2)*q^40 + (-2*a+6)*q^41 + (-2*a+2)*q^42 + -4*a*q^43 + (4*a+2)*q^44 + (-2*a-2)*q^45 + -4*a*q^46 + (-4*a-10)*q^47 + 3*q^48 + 1*q^49 + 3*a*q^50 + (4*a+6)*q^51 + (2*a+1)*q^52 + -2*q^53 + a*q^54 + (4*a+4)*q^55 + (-6*a-2)*q^56 + (-2*a-2)*q^57 + 2*a*q^58 + (4*a+6)*q^59 + (-2*a+6)*q^60 + (8*a+10)*q^61 + (-6*a+2)*q^62 + (2*a+2)*q^63 + (2*a-5)*q^64 + (2*a+2)*q^65 + -2*a*q^66 + (2*a+6)*q^67 + -14*q^68 + -4*q^69 + -8*a*q^70 + 2*q^71 + (a-2)*q^72 + (-4*a+2)*q^73 + (2*a-4)*q^74 + 3*q^75 + (-2*a+6)*q^76 + (-4*a-4)*q^77 + -a*q^78 + (-8*a-8)*q^79 + (-6*a-6)*q^80 + 1*q^81 + (10*a-2)*q^82 + (4*a+2)*q^83 + (2*a-6)*q^84 + (-4*a-20)*q^85 + (8*a-4)*q^86 + 2*q^87 + (-2*a+4)*q^88 + (2*a+14)*q^89 + (2*a-2)*q^90 + (-2*a-2)*q^91 + (8*a+4)*q^92 + (2*a-2)*q^93 + (-2*a-4)*q^94 + 8*q^95 + (a+4)*q^96 + (4*a+2)*q^97 + a*q^98 + -2*q^99 + (-6*a-3)*q^100 + (4*a+6)*q^101 + (-2*a+4)*q^102 + (-4*a+4)*q^103 + (-a+2)*q^104 + -8*q^105 + -2*a*q^106 + (-8*a-8)*q^107 + (-2*a-1)*q^108 + (8*a+2)*q^109 + (-4*a+4)*q^110 + (-4*a-6)*q^111 + (6*a+6)*q^112 + (-8*a-2)*q^113 + (2*a-2)*q^114 + (8*a+8)*q^115 + (-4*a-2)*q^116 + -1*q^117 + (-2*a+4)*q^118 + (4*a+20)*q^119 + (6*a+2)*q^120 + -7*q^121 + (-6*a+8)*q^122 + (-2*a+6)*q^123 + (10*a-2)*q^124 + (4*a+4)*q^125 + (-2*a+2)*q^126 + (4*a+4)*q^127 + (-11*a-6)*q^128 + -4*a*q^129 + (-2*a+2)*q^130 + -8*q^131 + (4*a+2)*q^132 + -8*q^133 + (2*a+2)*q^134 + (-2*a-2)*q^135 + (-10*a-8)*q^136 + (-2*a-10)*q^137 + -4*a*q^138 + (-8*a-4)*q^139 + (16*a+8)*q^140 + (-4*a-10)*q^141 + 2*a*q^142 + 2*q^143 + 3*q^144 + (-4*a-4)*q^145 + (10*a-4)*q^146 + 1*q^147 + 14*q^148 + (2*a-10)*q^149 + 3*a*q^150 + (6*a-6)*q^151 + (6*a+2)*q^152 + (4*a+6)*q^153 + (4*a-4)*q^154 + 8*a*q^155 + (2*a+1)*q^156 + -10*q^157 + (8*a-8)*q^158 + -2*q^159 + (-6*a-10)*q^160 + (-8*a-8)*q^161 + a*q^162 + (2*a+18)*q^163 + (-18*a-2)*q^164 + (4*a+4)*q^165 + (-6*a+4)*q^166 + (-4*a-2)*q^167 + (-6*a-2)*q^168 + 1*q^169 + (-12*a-4)*q^170 + (-2*a-2)*q^171 + (-12*a+8)*q^172 + (-4*a-10)*q^173 + 2*a*q^174 + (6*a+6)*q^175 + -6*q^176 + (4*a+6)*q^177 + (10*a+2)*q^178 + (-8*a-20)*q^179 + (-2*a+6)*q^180 + 14*q^181 + (2*a-2)*q^182 + (8*a+10)*q^183 + (-4*a+8)*q^184 + (4*a+20)*q^185 + (-6*a+2)*q^186 + (-8*a-12)*q^187 + (8*a+18)*q^188 + (2*a+2)*q^189 + 8*a*q^190 + 8*a*q^191 + (2*a-5)*q^192 + (8*a+2)*q^193 + (-6*a+4)*q^194 + (2*a+2)*q^195 + (-2*a-1)*q^196 + (6*a-2)*q^197 + -2*a*q^198 + (4*a+20)*q^199 + (3*a-6)*q^200 +  ...

-------------------------------------------------------
Gamma_0(40)
Weight 2

-------------------------------------------------------
J_0(40), dim = 3

-------------------------------------------------------
40A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 1.4844124734223870825 + 0.67078372006300930248e-15i
Omega-         = -2.0189058199784246674i
L(1)           = 0.37110311835559677063
w1             = 2.0189058199784246674i
w2             = 1.4844124734223870825 + 0.67078372006300930248e-15i
c4             = 335.99999999999671731 + -0.54929661408210525998e-12i
c6             = 5184.0000000025045332 + -0.16259390717621393208e-10i
j              = 5927.0400000143388291 + -0.1970980279574890631e-10i

HECKE EIGENFORM:
f(q) = q + 1*q^5 + -4*q^7 + -3*q^9 + 4*q^11 + -2*q^13 + 2*q^17 + 4*q^19 + 4*q^23 + 1*q^25 + -2*q^29 + -8*q^31 + -4*q^35 + 6*q^37 + -6*q^41 + -8*q^43 + -3*q^45 + 4*q^47 + 9*q^49 + 6*q^53 + 4*q^55 + -4*q^59 + -2*q^61 + 12*q^63 + -2*q^65 + 8*q^67 + -6*q^73 + -16*q^77 + 9*q^81 + -16*q^83 + 2*q^85 + -6*q^89 + 8*q^91 + 4*q^95 + -14*q^97 + -12*q^99 + 6*q^101 + 4*q^103 + 14*q^109 + 18*q^113 + 4*q^115 + 6*q^117 + -8*q^119 + 5*q^121 + 1*q^125 + -12*q^127 + 12*q^131 + -16*q^133 + 10*q^137 + 12*q^139 + -8*q^143 + -2*q^145 + -10*q^149 + -16*q^151 + -6*q^153 + -8*q^155 + -2*q^157 + -16*q^161 + 16*q^163 + 12*q^167 + -9*q^169 + -12*q^171 + 14*q^173 + -4*q^175 + 20*q^179 + -10*q^181 + 6*q^185 + 8*q^187 + 8*q^191 + -14*q^193 + 22*q^197 + 8*q^199 +  ...

-------------------------------------------------------
40B (old = 20A), dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(41)
Weight 2

-------------------------------------------------------
J_0(41), dim = 3

-------------------------------------------------------
41A (new) , dim = 3

CONGRUENCES:
Modular Degree = 1
Ker(ModPolar)  = {0}

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^2*37
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 2*5
Torsion Bound  = 2*5
|L(1)/Omega|   = 1/2*5
Sha Bound      = 2*5

ANALYTIC INVARIANTS:

Omega+         = 3.181260746093144769 + -0.15765626094486573315e-13i
Omega-         = 0.43262957132767340751e-13 + -24.672174470523593452i
L(1)           = 0.3181260746093144769

HECKE EIGENFORM:
a^3+a^2-5*a-1 = 0,
f(q) = 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 + (1/2*a^2-a-3/2)*q^38 + (-a^2+5)*q^39 + (-a^2+3*a)*q^40 + 1*q^41 + (-2*a^2-5*a-1)*q^42 + (a^2-5)*q^43 + (1/2*a^2-3*a+17/2)*q^44 + (-a^2-a)*q^45 + (-2*a-2)*q^46 + (3/2*a^2-3*a-13/2)*q^47 + (1/2*a^2+a+13/2)*q^48 + (2*a^2+5*a-6)*q^49 + (a^2+a+1)*q^50 + (a^2+2*a-3)*q^51 + (-a^2+4*a-5)*q^52 + (a^2+2*a-1)*q^53 + (a^2+1)*q^54 + (-a^2-4*a+3)*q^55 + (-3/2*a^2+a+1/2)*q^56 + (-2*a^2-a+11)*q^57 + (a^2+1)*q^58 + (-2*a^2-2*a+4)*q^59 + (a^2+2*a+3)*q^60 + (-a^2+2*a+5)*q^61 + (2*a^2+6*a)*q^62 + (1/2*a^2+3*a+1/2)*q^63 + (3*a^2-4*a-8)*q^64 + (2*a-2)*q^65 + (-2*a^2-3*a+1)*q^66 + (-3/2*a^2-a+9/2)*q^67 + (-2*a^2+4)*q^68 + (-2*a^2+14)*q^69 + (-3*a^2-6*a-1)*q^70 + (-3/2*a^2+a+25/2)*q^71 + (2*a^2-4*a-1)*q^72 + (4*a^2+a-15)*q^73 + (-3*a^2-3*a)*q^74 + (1/2*a^2-a-15/2)*q^75 + (3/2*a^2+3*a-25/2)*q^76 + (2*a^2+3*a-1)*q^77 + (a^2-1)*q^78 + (1/2*a^2-a+17/2)*q^79 + (4*a^2+a-3)*q^80 + (a^2-3*a-9)*q^81 + a*q^82 + (2*a^2+4*a-6)*q^83 + (-a^2-5*a-2)*q^84 + (2*a+2)*q^85 + (-a^2+1)*q^86 + (a^2-9)*q^87 + (-5/2*a^2+5*a-5/2)*q^88 + (-4*a^2-2*a+12)*q^89 + (-5*a-1)*q^90 + (-a^2+1)*q^91 + (2*a^2+2*a-16)*q^92 + (-4*a^2-8*a+8)*q^93 + (-9/2*a^2+a+3/2)*q^94 + (a^2+2*a-5)*q^95 + (3/2*a^2+7*a-5/2)*q^96 + (-2*a^2-4*a+8)*q^97 + (3*a^2+4*a+2)*q^98 + (-1/2*a^2+3*a+3/2)*q^99 + (-2*a^2+2*a+9)*q^100 + (3*a^2-5)*q^101 + (a^2+2*a+1)*q^102 + (a^2-6*a-7)*q^103 + (3*a^2-6*a+1)*q^104 + (3*a^2+8*a+1)*q^105 + (a^2+4*a+1)*q^106 + (4*a-4)*q^107 + (-3*a^2+2*a+11)*q^108 + (a^2-4*a-7)*q^109 + (-3*a^2-2*a-1)*q^110 + (3*a^2+6*a-3)*q^111 + (-1/2*a^2-9*a-1/2)*q^112 + (-4*a^2-5*a+15)*q^113 + (a^2+a-2)*q^114 + (2*a^2+4*a-6)*q^115 + (-3*a^2+2*a+11)*q^116 + (a^2-2*a-1)*q^117 + (-6*a-2)*q^118 + (-a^2-2*a-1)*q^119 + (-a^2-1)*q^120 + (-2*a^2-3*a+10)*q^121 + (3*a^2-1)*q^122 + (-1/2*a^2-a+3/2)*q^123 + (4*a^2+6*a-10)*q^124 + (-2*a^2+2*a+8)*q^125 + (5/2*a^2+3*a+1/2)*q^126 + (-2*a^2-2*a+12)*q^127 + (-3*a^2+5*a+7)*q^128 + (2*a^2+2*a-8)*q^129 + (2*a^2-2*a)*q^130 + (a^2-2*a-11)*q^131 + (-3*a^2-7*a+14)*q^132 + (-a^2-a+2)*q^133 + (1/2*a^2-3*a-3/2)*q^134 + (-2*a^2-2*a+4)*q^135 + (2*a^2-2*a-2)*q^136 + (-4*a^2-8*a+18)*q^137 + (2*a^2+4*a-2)*q^138 + (2*a^2+10*a-8)*q^139 + (-a^2-8*a-1)*q^140 + (4*a^2+5*a-9)*q^141 + (5/2*a^2+5*a-3/2)*q^142 + (a^2+4*a-13)*q^143 + (-4*a^2+3*a)*q^144 + (-2*a^2-2*a+4)*q^145 + (-3*a^2+5*a+4)*q^146 + (-1/2*a^2-5*a-25/2)*q^147 + (-9*a+3)*q^148 + (5*a^2+6*a-13)*q^149 + (-3/2*a^2-5*a+1/2)*q^150 + (1/2*a^2-3*a+13/2)*q^151 + (1/2*a^2-3*a+9/2)*q^152 + -2*a*q^153 + (a^2+9*a+2)*q^154 + (-2*a^2-8*a-6)*q^155 + (a^2+4*a-9)*q^156 + (3*a^2+8*a-13)*q^157 + (-3/2*a^2+11*a+1/2)*q^158 + (-a^2-4*a-3)*q^159 + (-a^2+11*a+4)*q^160 + (-2*a^2-4*a+2)*q^161 + (-4*a^2-4*a+1)*q^162 + (-2*a^2+2)*q^163 + (a^2-2)*q^164 + (a^2+4*a+7)*q^165 + (2*a^2+4*a+2)*q^166 + (1/2*a^2+3*a-11/2)*q^167 + (3*a+1)*q^168 + (-4*a-5)*q^169 + (2*a^2+2*a)*q^170 + (1/2*a^2-a-3/2)*q^171 + (-a^2-4*a+9)*q^172 + (2*a^2+4*a-16)*q^173 + (-a^2-4*a+1)*q^174 + (3/2*a^2+5*a-1/2)*q^175 + (13/2*a^2-9*a-39/2)*q^176 + (4*a+8)*q^177 + (2*a^2-8*a-4)*q^178 + (1/2*a^2-7*a-7/2)*q^179 + (-3*a^2+a)*q^180 + (-5*a^2-6*a+5)*q^181 + (a^2-4*a-1)*q^182 + (-3*a^2-4*a+7)*q^183 + (-2*a+6)*q^184 + (3*a^2+6*a+3)*q^185 + (-4*a^2-12*a-4)*q^186 + (-3*a^2-2*a+9)*q^187 + (5/2*a^2-15*a+17/2)*q^188 + (a^2+4*a-1)*q^189 + (a^2+1)*q^190 + (-1/2*a^2+9*a+19/2)*q^191 + (9/2*a^2+3*a-23/2)*q^192 + (-2*a^2-2*a-2)*q^193 + (-2*a^2-2*a-2)*q^194 + -4*q^195 + (-3*a^2+7*a+15)*q^196 + (-a^2+2*a+21)*q^197 + (7/2*a^2-a-1/2)*q^198 + (3/2*a^2+5*a+23/2)*q^199 + (2*a^2-3*a-4)*q^200 +  ...

-------------------------------------------------------
Gamma_0(42)
Weight 2

-------------------------------------------------------
J_0(42), dim = 5

-------------------------------------------------------
42A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= B(Z/2 + Z/2) + C(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 3.475447457496835589 + -0.66773145341333805804e-14i
Omega-         = 0.46797544746161905321e-14 + 1.576986771215808643i
L(1)           = 0.86886186437420889724
w1             = -1.7377237287484154546 + 0.78849338560790766014i
w2             = 0.46797544746161905321e-14 + 1.576986771215808643i
c4             = 192.99999999999337075 + 0.27145489463580715346e-11i
c6             = -5921.0000000142305431 + -0.91972665928933416094e-10i
j              = -445.7500620012151321 + -0.6240112902509787748e-11i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + -2*q^5 + -1*q^6 + -1*q^7 + 1*q^8 + 1*q^9 + -2*q^10 + -4*q^11 + -1*q^12 + 6*q^13 + -1*q^14 + 2*q^15 + 1*q^16 + 2*q^17 + 1*q^18 + -4*q^19 + -2*q^20 + 1*q^21 + -4*q^22 + 8*q^23 + -1*q^24 + -1*q^25 + 6*q^26 + -1*q^27 + -1*q^28 + -2*q^29 + 2*q^30 + 1*q^32 + 4*q^33 + 2*q^34 + 2*q^35 + 1*q^36 + -10*q^37 + -4*q^38 + -6*q^39 + -2*q^40 + -6*q^41 + 1*q^42 + -4*q^43 + -4*q^44 + -2*q^45 + 8*q^46 + -1*q^48 + 1*q^49 + -1*q^50 + -2*q^51 + 6*q^52 + 6*q^53 + -1*q^54 + 8*q^55 + -1*q^56 + 4*q^57 + -2*q^58 + 4*q^59 + 2*q^60 + 6*q^61 + -1*q^63 + 1*q^64 + -12*q^65 + 4*q^66 + 4*q^67 + 2*q^68 + -8*q^69 + 2*q^70 + 8*q^71 + 1*q^72 + 10*q^73 + -10*q^74 + 1*q^75 + -4*q^76 + 4*q^77 + -6*q^78 + -2*q^80 + 1*q^81 + -6*q^82 + -4*q^83 + 1*q^84 + -4*q^85 + -4*q^86 + 2*q^87 + -4*q^88 + -6*q^89 + -2*q^90 + -6*q^91 + 8*q^92 + 8*q^95 + -1*q^96 + -14*q^97 + 1*q^98 + -4*q^99 + -1*q^100 + -2*q^101 + -2*q^102 + 8*q^103 + 6*q^104 + -2*q^105 + 6*q^106 + 12*q^107 + -1*q^108 + -2*q^109 + 8*q^110 + 10*q^111 + -1*q^112 + -14*q^113 + 4*q^114 + -16*q^115 + -2*q^116 + 6*q^117 + 4*q^118 + -2*q^119 + 2*q^120 + 5*q^121 + 6*q^122 + 6*q^123 + 12*q^125 + -1*q^126 + 1*q^128 + 4*q^129 + -12*q^130 + -20*q^131 + 4*q^132 + 4*q^133 + 4*q^134 + 2*q^135 + 2*q^136 + 10*q^137 + -8*q^138 + 4*q^139 + 2*q^140 + 8*q^142 + -24*q^143 + 1*q^144 + 4*q^145 + 10*q^146 + -1*q^147 + -10*q^148 + 6*q^149 + 1*q^150 + -8*q^151 + -4*q^152 + 2*q^153 + 4*q^154 + -6*q^156 + -10*q^157 + -6*q^159 + -2*q^160 + -8*q^161 + 1*q^162 + 20*q^163 + -6*q^164 + -8*q^165 + -4*q^166 + -8*q^167 + 1*q^168 + 23*q^169 + -4*q^170 + -4*q^171 + -4*q^172 + 22*q^173 + 2*q^174 + 1*q^175 + -4*q^176 + -4*q^177 + -6*q^178 + -12*q^179 + -2*q^180 + -18*q^181 + -6*q^182 + -6*q^183 + 8*q^184 + 20*q^185 + -8*q^187 + 1*q^189 + 8*q^190 + -1*q^192 + 2*q^193 + -14*q^194 + 12*q^195 + 1*q^196 + -10*q^197 + -4*q^198 + 8*q^199 + -1*q^200 +  ...

-------------------------------------------------------
42B (old = 21A), dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + C(Z/2 + Z/2)

-------------------------------------------------------
42C (old = 14A), dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2) + B(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(43)
Weight 2

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J_0(43), dim = 3

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43A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 5.4686895299676266201 + 0.32821187184894358827e-13i
Omega-         = 0.3298848030949229151e-13 + -2.7263648363408786932i
L(1)           =
w1             = 2.7343447649837968158 + 1.3631824181704557572i
w2             = 0.3298848030949229151e-13 + -2.7263648363408786932i
c4             = 15.999999999944623588 + -0.12357626444677525174e-11i
c6             = -280.00000002220308548 + 0.1563844624687032145e-10i
j              = -95.2558139365050836 + 0.12061045657571366696e-10i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + -2*q^3 + 2*q^4 + -4*q^5 + 4*q^6 + 1*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 + -1*q^23 + 11*q^25 + 10*q^26 + 4*q^27 + -6*q^29 + -16*q^30 + -1*q^31 + 8*q^32 + -6*q^33 + 6*q^34 + 2*q^36 + 4*q^38 + 10*q^39 + 5*q^41 + -1*q^43 + 6*q^44 + -4*q^45 + 2*q^46 + 4*q^47 + 8*q^48 + -7*q^49 + -22*q^50 + 6*q^51 + -10*q^52 + -5*q^53 + -8*q^54 + -12*q^55 + 4*q^57 + 12*q^58 + -12*q^59 + 16*q^60 + 2*q^61 + 2*q^62 + -8*q^64 + 20*q^65 + 12*q^66 + -3*q^67 + -6*q^68 + 2*q^69 + 2*q^71 + 2*q^73 + -22*q^75 + -4*q^76 + -20*q^78 + -8*q^79 + 16*q^80 + -11*q^81 + -10*q^82 + 15*q^83 + 12*q^85 + 2*q^86 + 12*q^87 + -4*q^89 + 8*q^90 + -2*q^92 + 2*q^93 + -8*q^94 + 8*q^95 + -16*q^96 + 7*q^97 + 14*q^98 + 3*q^99 + 22*q^100 + -9*q^101 + -12*q^102 + 1*q^103 + 10*q^106 + -12*q^107 + 8*q^108 + 7*q^109 + 24*q^110 + -20*q^113 + -8*q^114 + 4*q^115 + -12*q^116 + -5*q^117 + 24*q^118 + -2*q^121 + -4*q^122 + -10*q^123 + -2*q^124 + -24*q^125 + 1*q^127 + 2*q^129 + -40*q^130 + 8*q^131 + -12*q^132 + 6*q^134 + -16*q^135 + 6*q^137 + -4*q^138 + 19*q^139 + -8*q^141 + -4*q^142 + -15*q^143 + -4*q^144 + 24*q^145 + -4*q^146 + 14*q^147 + 12*q^149 + 44*q^150 + -20*q^151 + -3*q^153 + 4*q^155 + 20*q^156 + -10*q^157 + 16*q^158 + 10*q^159 + -32*q^160 + 22*q^162 + 14*q^163 + 10*q^164 + 24*q^165 + -30*q^166 + -9*q^167 + 12*q^169 + -24*q^170 + -2*q^171 + -2*q^172 + 6*q^173 + -24*q^174 + -12*q^176 + 24*q^177 + 8*q^178 + 20*q^179 + -8*q^180 + 10*q^181 + -4*q^183 + -4*q^186 + -9*q^187 + 8*q^188 + -16*q^190 + -16*q^191 + 16*q^192 + 3*q^193 + -14*q^194 + -40*q^195 + -14*q^196 + 2*q^197 + -6*q^198 + 14*q^199 +  ...

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43B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^3
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 7
Torsion Bound  = 7
|L(1)/Omega|   = 2/7
Sha Bound      = 2*7

ANALYTIC INVARIANTS:

Omega+         = 2.0010226476244111036 + -0.15663436276163079176e-13i
Omega-         = 7.2792812035685855105 + -0.16272703740131209145e-12i
L(1)           = 0.57172075646411745818

HECKE EIGENFORM:
a^2-2 = 0,
f(q) = q + a*q^2 + -a*q^3 + (-a+2)*q^5 + -2*q^6 + (a-2)*q^7 + -2*a*q^8 + -1*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 + (-2*a-4)*q^38 + (-a-4)*q^39 + (-4*a+4)*q^40 + (-2*a-1)*q^41 + (-2*a+4)*q^42 + 1*q^43 + (a-2)*q^45 + (a-8)*q^46 + 6*q^47 + 4*a*q^48 + (-4*a-1)*q^49 + (a-8)*q^50 + (-5*a-4)*q^51 + (-2*a+11)*q^53 + 8*q^54 + (5*a-6)*q^55 + (4*a-4)*q^56 + (2*a+4)*q^57 + 6*q^58 + (2*a-2)*q^59 + (3*a+4)*q^61 + -3*a*q^62 + (-a+2)*q^63 + 8*q^64 + (3*a-2)*q^65 + (-4*a+2)*q^66 + (6*a+1)*q^67 + (-a+8)*q^69 + (-6*a+8)*q^70 + (-2*a-6)*q^71 + 2*a*q^72 + (3*a-12)*q^73 + -12*q^74 + (-a+8)*q^75 + (-5*a+6)*q^77 + (-4*a-2)*q^78 + (-2*a+2)*q^79 + (4*a-8)*q^80 + -5*q^81 + (-a-4)*q^82 + (4*a+9)*q^83 + (-a+6)*q^85 + a*q^86 + -6*q^87 + (2*a-8)*q^88 + (-3*a-6)*q^89 + (-2*a+2)*q^90 + (-3*a+2)*q^91 + 3*a*q^93 + 6*a*q^94 + -2*a*q^95 + (-2*a-1)*q^97 + (-a-8)*q^98 + (-2*a+1)*q^99 + (-2*a+3)*q^101 + (-4*a-10)*q^102 + (6*a+9)*q^103 + (-2*a-8)*q^104 + (6*a-8)*q^105 + (11*a-4)*q^106 + (-4*a-6)*q^107 + (12*a-3)*q^109 + (-6*a+10)*q^110 + 12*q^111 + (-4*a+8)*q^112 + (2*a-4)*q^113 + (4*a+4)*q^114 + (-9*a+10)*q^115 + (-2*a-1)*q^117 + (-2*a+4)*q^118 + (a-6)*q^119 + (-4*a+8)*q^120 + (-4*a-2)*q^121 + (4*a+6)*q^122 + (a+4)*q^123 + -4*a*q^125 + (2*a-2)*q^126 + (-2*a+1)*q^127 + 8*a*q^128 + -a*q^129 + (-2*a+6)*q^130 + (-4*a+4)*q^131 + 2*a*q^133 + (a+12)*q^134 + (8*a-8)*q^135 + (-10*a-8)*q^136 + (6*a-6)*q^137 + (8*a-2)*q^138 + (-6*a-3)*q^139 + -6*a*q^141 + (-6*a-4)*q^142 + 7*q^143 + 4*q^144 + (6*a-6)*q^145 + (-12*a+6)*q^146 + (a+8)*q^147 + -6*a*q^149 + (8*a-2)*q^150 + (-3*a+14)*q^151 + (4*a+8)*q^152 + (-2*a-5)*q^153 + (6*a-10)*q^154 + (3*a-6)*q^155 + -10*q^157 + (2*a-4)*q^158 + (-11*a+4)*q^159 + (9*a-10)*q^161 + -5*a*q^162 + (-3*a-16)*q^163 + (6*a-10)*q^165 + (9*a+8)*q^166 + (8*a-3)*q^167 + (4*a-8)*q^168 + (4*a-4)*q^169 + (6*a-2)*q^170 + (2*a+2)*q^171 + (-4*a+18)*q^173 + -6*a*q^174 + (9*a-10)*q^175 + (-8*a+4)*q^176 + (2*a-4)*q^177 + (-6*a-6)*q^178 + (-a-6)*q^179 + (-8*a-4)*q^181 + (2*a-6)*q^182 + (-4*a-6)*q^183 + (-2*a+16)*q^184 + (-12*a+12)*q^185 + 6*q^186 + (8*a+3)*q^187 + (-8*a+8)*q^189 + -4*q^190 + (10*a+8)*q^191 + -8*a*q^192 + (-12*a-1)*q^193 + (-a-4)*q^194 + (2*a-6)*q^195 + 10*a*q^197 + (a-4)*q^198 + (-4*a+2)*q^199 + (-2*a+16)*q^200 +  ...

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Gamma_0(126)
Weight 2

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J_0(126), dim = 17

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126A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^5 + Z/2^5
= B(Z/2 + Z/2) + C(Z/2^2 + Z/2^2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2^2
|L(1)/Omega|   = 1
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 0.91047388787702620531 + -0.60242415453336437638e-5i
Omega-         = 0.39835744385225279054e-5 + 2.0065589493432608134i
L(1)           = 0.91047388789695620368
w1             = 0.45523893572573236392 + 1.0032764625508577399i
w2             = 0.91047388787702620531 + -0.60242415453336437638e-5i
c4             = 1737.0135408652847117 + 0.62848727298202147444e-1i
c6             = 159865.44097987231177 + 4.7388967173406549057i
j              = -445.77411260755315263 + -0.27623639591761530262e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^4 + 2*q^5 + -1*q^7 + -1*q^8 + -2*q^10 + 4*q^11 + 6*q^13 + 1*q^14 + 1*q^16 + -2*q^17 + -4*q^19 + 2*q^20 + -4*q^22 + -8*q^23 + -1*q^25 + -6*q^26 + -1*q^28 + 2*q^29 + -1*q^32 + 2*q^34 + -2*q^35 + -10*q^37 + 4*q^38 + -2*q^40 + 6*q^41 + -4*q^43 + 4*q^44 + 8*q^46 + 1*q^49 + 1*q^50 + 6*q^52 + -6*q^53 + 8*q^55 + 1*q^56 + -2*q^58 + -4*q^59 + 6*q^61 + 1*q^64 + 12*q^65 + 4*q^67 + -2*q^68 + 2*q^70 + -8*q^71 + 10*q^73 + 10*q^74 + -4*q^76 + -4*q^77 + 2*q^80 + -6*q^82 + 4*q^83 + -4*q^85 + 4*q^86 + -4*q^88 + 6*q^89 + -6*q^91 + -8*q^92 + -8*q^95 + -14*q^97 + -1*q^98 + -1*q^100 + 2*q^101 + 8*q^103 + -6*q^104 + 6*q^106 + -12*q^107 + -2*q^109 + -8*q^110 + -1*q^112 + 14*q^113 + -16*q^115 + 2*q^116 + 4*q^118 + 2*q^119 + 5*q^121 + -6*q^122 + -12*q^125 + -1*q^128 + -12*q^130 + 20*q^131 + 4*q^133 + -4*q^134 + 2*q^136 + -10*q^137 + 4*q^139 + -2*q^140 + 8*q^142 + 24*q^143 + 4*q^145 + -10*q^146 + -10*q^148 + -6*q^149 + -8*q^151 + 4*q^152 + 4*q^154 + -10*q^157 + -2*q^160 + 8*q^161 + 20*q^163 + 6*q^164 + -4*q^166 + 8*q^167 + 23*q^169 + 4*q^170 + -4*q^172 + -22*q^173 + 1*q^175 + 4*q^176 + -6*q^178 + 12*q^179 + -18*q^181 + 6*q^182 + 8*q^184 + -20*q^185 + -8*q^187 + 8*q^190 + 2*q^193 + 14*q^194 + 1*q^196 + 10*q^197 + 8*q^199 + 1*q^200 +  ...

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126B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2*3
|L(1)/Omega|   = 1
Sha Bound      = 2^2*3^2

ANALYTIC INVARIANTS:

Omega+         = 1.5305412681735860539 + -0.27977524001043783921e-5i
Omega-         = 0.98370241506577126324e-5 + -3.4317714391077220031i
L(1)           = 1.5305412681761431292
w1             = 0.76526571557471769808 + 1.7158843206776609494i
w2             = 1.5305412681735860539 + -0.27977524001043783921e-5i
c4             = 225.00196234289696024 + 0.35811891506484604706e-2i
c6             = 6831.1287338921811809 + 0.92858670587681942126e-2i
j              = -558.0272041881647529 + -0.33242658676412082127e-1i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + 1*q^7 + 1*q^8 + -4*q^13 + 1*q^14 + 1*q^16 + -6*q^17 + 2*q^19 + -5*q^25 + -4*q^26 + 1*q^28 + 6*q^29 + -4*q^31 + 1*q^32 + -6*q^34 + 2*q^37 + 2*q^38 + -6*q^41 + 8*q^43 + 12*q^47 + 1*q^49 + -5*q^50 + -4*q^52 + -6*q^53 + 1*q^56 + 6*q^58 + 6*q^59 + 8*q^61 + -4*q^62 + 1*q^64 + -4*q^67 + -6*q^68 + 2*q^73 + 2*q^74 + 2*q^76 + 8*q^79 + -6*q^82 + 6*q^83 + 8*q^86 + 6*q^89 + -4*q^91 + 12*q^94 + -10*q^97 + 1*q^98 + -5*q^100 + -4*q^103 + -4*q^104 + -6*q^106 + -12*q^107 + 2*q^109 + 1*q^112 + -6*q^113 + 6*q^116 + 6*q^118 + -6*q^119 + -11*q^121 + 8*q^122 + -4*q^124 + -16*q^127 + 1*q^128 + -18*q^131 + 2*q^133 + -4*q^134 + -6*q^136 + -18*q^137 + 14*q^139 + 2*q^146 + 2*q^148 + 18*q^149 + 8*q^151 + 2*q^152 + -4*q^157 + 8*q^158 + -16*q^163 + -6*q^164 + 6*q^166 + 12*q^167 + 3*q^169 + 8*q^172 + 12*q^173 + -5*q^175 + 6*q^178 + 12*q^179 + 20*q^181 + -4*q^182 + 12*q^188 + -24*q^191 + 14*q^193 + -10*q^194 + 1*q^196 + 18*q^197 + 20*q^199 + -5*q^200 +  ...

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126C (old = 63A), dim = 1

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^5 + Z/2^5
= A(Z/2^2 + Z/2^2) + B(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2)

-------------------------------------------------------
126D (old = 63B), dim = 2

CONGRUENCES:
Modular Degree = 2^6*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2*3 + Z/2*3)

-------------------------------------------------------
126E (old = 42A), dim = 1

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^5 + Z/2^5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2^2 + Z/2^2) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
126F (old = 21A), dim = 1

CONGRUENCES:
Modular Degree = 2^9
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^5 + Z/2^5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2^2 + Z/2^2) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
126G (old = 14A), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^3*3 + Z/2^3*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2*3 + Z/2*3) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2)

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Gamma_0(127)
Weight 2

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J_0(127), dim = 10

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127A (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 3^4
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 48.959965729099162167 + 0.20146945081030438462e-3i
Omega-         = 0.4822219420678451976e-4 + -10.034845860390825337i
L(1)           =

HECKE EIGENFORM:
a^3+3*a^2-3 = 0,
f(q) = 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 + (-2*a^2-a+3)*q^38 + (a^2+a+3)*q^39 + (5*a^2+10*a-6)*q^40 + (-4*a^2-8*a)*q^41 + 3*q^42 + (6*a^2+6*a-15)*q^43 + (-4*a^2-5*a+1)*q^44 + (-4*a^2-9*a+3)*q^45 + (3*a^2-6)*q^46 + (2*a^2+8*a+1)*q^47 + (-a^2+a)*q^48 + (-2*a^2-3*a-1)*q^49 + (7*a^2+8*a-12)*q^50 + (6*a^2+14*a+3)*q^51 + (-5*a^2-a+7)*q^52 + (7*a^2+8*a-12)*q^53 + (-6*a^2-6*a+9)*q^54 + (-5*a^2-12*a+2)*q^55 + (2*a^2+6*a-3)*q^56 + (-a^2-a)*q^57 + (-4*a^2-3*a+3)*q^58 + (-a^2-4*a-1)*q^59 + (-a^2-4*a-3)*q^60 + (6*a^2+14*a-5)*q^61 + (4*a^2+8*a-9)*q^62 + (-3*a^2-6*a+3)*q^63 + (-3*a^2-3*a+10)*q^64 + (6*a^2+11*a-10)*q^65 + (-5*a^2-9*a)*q^66 + (-a^2-a+1)*q^67 + (-4*a^2+2*a+11)*q^68 + (3*a^2+6*a+3)*q^69 + (5*a^2+9*a-9)*q^70 + (-2*a^2-10*a-3)*q^71 + (3*a^2-12)*q^72 + (7*a^2+9*a-11)*q^73 + (10*a^2+10*a-12)*q^74 + (-a^2-4*a+3)*q^75 + (3*a^2+a-4)*q^76 + (-4*a^2-8*a+3)*q^77 + (-2*a^2+3*a+3)*q^78 + (7*a+10)*q^79 + (-5*a^2-8*a+11)*q^80 + (-3*a^2-6*a)*q^81 + (4*a^2-12)*q^82 + (-5*a^2-16*a+3)*q^83 + (-2*a^2-3*a)*q^84 + (-5*a^2-3*a+25)*q^85 + (-12*a^2-15*a+18)*q^86 + (-a^2+3*a+6)*q^87 + (5*a^2-a-18)*q^88 + (2*a^2-a-18)*q^89 + (3*a^2+3*a-12)*q^90 + (3*a^2+7*a-6)*q^91 + (-5*a^2+9)*q^92 + (-4*a^2-7*a+6)*q^93 + (2*a^2+a+6)*q^94 + (-a^2-2*a+1)*q^95 + (-6*a-9)*q^96 + (6*a^2+9*a-14)*q^97 + (3*a^2-a-6)*q^98 + (a^2+6*a+12)*q^99 + (-5*a^2-2*a+5)*q^100 + (7*a+1)*q^101 + (-4*a^2+3*a+18)*q^102 + (2*a^2+5*a)*q^103 + (4*a^2-a+3)*q^104 + (-4*a^2-9*a+3)*q^105 + (-13*a^2-12*a+21)*q^106 + (a^2-2*a+3)*q^107 + (6*a^2+3*a-6)*q^108 + (-2*a^2-6*a+7)*q^109 + (3*a^2+2*a-15)*q^110 + (-8*a-6)*q^111 + (-2*a^2-5*a+6)*q^112 + (2*a^2+7*a-4)*q^113 + (2*a^2-3)*q^114 + (2*a^2+6*a+3)*q^115 + (7*a^2+5*a-6)*q^116 + (4*a^2+3*a-12)*q^117 + (-a^2-a-3)*q^118 + (-5*a^2-4*a+18)*q^119 + (a^2-3*a-15)*q^120 + (3*a^2+11*a+5)*q^121 + (-4*a^2-5*a+18)*q^122 + (4*a^2+12*a+12)*q^123 + (2*a^2+a-4)*q^124 + (5*a^2+11*a-3)*q^125 + (3*a^2+3*a-9)*q^126 + -1*q^127 + (6*a^2+4*a-15)*q^128 + (3*a^2+12*a)*q^129 + (-7*a^2-10*a+18)*q^130 + (-6*a^2+a+19)*q^131 + (6*a^2+10*a+3)*q^132 + -a*q^133 + (2*a^2+a-3)*q^134 + (-6*a^2-9*a+15)*q^135 + (16*a^2+25*a-12)*q^136 + -11*q^137 + (-3*a^2+3*a+9)*q^138 + (-8*a^2-8*a+13)*q^139 + (-a-3)*q^140 + (a^2-8*a-18)*q^141 + (-4*a^2-3*a-6)*q^142 + (6*a^2+3*a-17)*q^143 + (-5*a^2-6*a+9)*q^144 + (a^2+4*a+3)*q^145 + (-12*a^2-11*a+21)*q^146 + (4*a^2+8*a+3)*q^147 + (-12*a^2-8*a+10)*q^148 + (-a^2-8*a+10)*q^149 + (-a^2+3*a-3)*q^150 + (-10*a^2-18*a+11)*q^151 + (-4*a^2-2*a+3)*q^152 + (-7*a^2-21*a-3)*q^153 + (4*a^2+3*a-12)*q^154 + (12*a^2+19*a-29)*q^155 + (7*a^2+a-12)*q^156 + (-7*a^2-9*a+4)*q^157 + (7*a^2+10*a)*q^158 + (-a^2+3*a-3)*q^159 + (-3*a^2-9*a-3)*q^160 + (3*a+3)*q^161 + (3*a^2-9)*q^162 + (-2*a^2-6*a-4)*q^163 + (-4*a^2+4*a+12)*q^164 + (a^2+11*a+21)*q^165 + (-a^2+3*a-15)*q^166 + (4*a^2+6*a-7)*q^167 + (3*a^2-12)*q^168 + (a^2-5*a-6)*q^169 + (12*a^2+25*a-15)*q^170 + (-a^2+3)*q^171 + (9*a^2+6*a-6)*q^172 + (-12*a^2-22*a+12)*q^173 + (6*a^2+6*a-3)*q^174 + (6*a^2+11*a-15)*q^175 + (-8*a^2-8*a+13)*q^176 + (5*a+9)*q^177 + (-7*a^2-18*a+6)*q^178 + (-6*a^2-5*a+16)*q^179 + (2*a^2+6*a+3)*q^180 + (-4*a^2-5*a+5)*q^181 + (-2*a^2-6*a+9)*q^182 + (a^2-8*a-24)*q^183 + (9*a^2+9*a-3)*q^184 + (6*a^2+6*a-22)*q^185 + (5*a^2+6*a-12)*q^186 + (-8*a^2-29*a-10)*q^187 + (-9*a^2-10*a+4)*q^188 + (-3*a^2-6*a+9)*q^189 + (a^2+a-3)*q^190 + (-5*a^2-11*a)*q^191 + (-4*a^2-11*a)*q^192 + (9*a^2+18*a-1)*q^193 + (-9*a^2-14*a+18)*q^194 + (3*a^2+2*a-15)*q^195 + (-6*a^2+11)*q^196 + (-6*a^2-13*a+11)*q^197 + (3*a^2+12*a+3)*q^198 + (6*a^2+6*a-17)*q^199 + (-a^2-11*a+9)*q^200 +  ...

-------------------------------------------------------
127B (new) , dim = 7

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 7*86235899
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 3*7
Torsion Bound  = 3*7
|L(1)/Omega|   = 2^3/3*7
Sha Bound      = 2^3*3*7

ANALYTIC INVARIANTS:

Omega+         = 11.14907636713405705 + 0.15784519461285016129e-3i
Omega-         = 0.38005609865724611542e-2 + -264.7849721862743494i
L(1)           = 4.2472671879053024425

HECKE EIGENFORM:
a^7-2*a^6-8*a^5+15*a^4+17*a^3-28*a^2-11*a+15 = 0,
f(q) = 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 + (-a^6+5*a^5+2*a^4-32*a^3+23*a^2+33*a-30)*q^38 + (-2*a^6-a^5+21*a^4+7*a^3-61*a^2-7*a+38)*q^39 + (a^6-12*a^4+40*a^2+a-30)*q^40 + (-a^6+2*a^5+7*a^4-12*a^3-12*a^2+12*a+9)*q^41 + (-a^6+4*a^5+5*a^4-27*a^3+5*a^2+28*a-15)*q^42 + (-3*a^6+8*a^5+17*a^4-51*a^3-5*a^2+54*a-19)*q^43 + (2*a^5-2*a^4-13*a^3+11*a^2+15*a-12)*q^44 + (-3*a^6+3*a^5+23*a^4-17*a^3-39*a^2+10*a+12)*q^45 + (3*a^6-6*a^5-20*a^4+36*a^3+24*a^2-33*a)*q^46 + (-2*a^5+2*a^4+15*a^3-11*a^2-24*a+12)*q^47 + (-3*a^6+5*a^5+20*a^4-30*a^3-24*a^2+27*a+1)*q^48 + (2*a^6-5*a^5-10*a^4+32*a^3-2*a^2-36*a+12)*q^49 + (-a^6-a^5+8*a^4+8*a^3-18*a^2-10*a+15)*q^50 + (5*a^6-8*a^5-35*a^4+47*a^3+53*a^2-42*a-15)*q^51 + (3*a^6-4*a^5-20*a^4+25*a^3+25*a^2-26*a-4)*q^52 + (-a^6+4*a^5+4*a^4-26*a^3+6*a^2+33*a-6)*q^53 + (3*a^6-4*a^5-23*a^4+25*a^3+41*a^2-24*a-15)*q^54 + (a^6-8*a^4+14*a^2-a-6)*q^55 + (a^6-4*a^5-5*a^4+25*a^3-3*a^2-28*a+15)*q^56 + (-a^6+5*a^5-30*a^3+30*a^2+27*a-31)*q^57 + (a^6-3*a^5-a^4+19*a^3-27*a^2-22*a+30)*q^58 + (-2*a^6+21*a^4-a^3-63*a^2+3*a+45)*q^59 + (2*a^6-17*a^4-3*a^3+41*a^2+5*a-27)*q^60 + (-a^6+9*a^4-24*a^2+2*a+20)*q^61 + (3*a^6-8*a^5-18*a^4+50*a^3+11*a^2-51*a+15)*q^62 + (-2*a^6+4*a^5+13*a^4-23*a^3-15*a^2+21*a-1)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (5*a^5-6*a^4-34*a^3+34*a^2+40*a-27)*q^65 + (-3*a^6+5*a^5+18*a^4-32*a^3-8*a^2+35*a-15)*q^66 + (2*a^6-9*a^5-3*a^4+57*a^3-49*a^2-61*a+62)*q^67 + (-a^6+a^5+10*a^4-7*a^3-24*a^2+8*a+15)*q^68 + (4*a^6-6*a^5-31*a^4+35*a^3+59*a^2-23*a-27)*q^69 + (-a^5+a^4+5*a^3-a^2-3*a)*q^70 + (a^6-2*a^5-9*a^4+12*a^3+20*a^2-8*a-6)*q^71 + (-5*a^6+8*a^5+35*a^4-48*a^3-53*a^2+42*a+15)*q^72 + (a^6+a^5-12*a^4-5*a^3+41*a^2-a-31)*q^73 + (-4*a^6+6*a^5+27*a^4-37*a^3-32*a^2+35*a)*q^74 + (6*a^5-7*a^4-41*a^3+43*a^2+47*a-41)*q^75 + (-a^6+4*a^5+5*a^4-24*a^3+a^2+25*a-7)*q^76 + (3*a^6-8*a^5-15*a^4+51*a^3-7*a^2-58*a+33)*q^77 + (-5*a^6+5*a^5+37*a^4-27*a^3-63*a^2+16*a+30)*q^78 + (-a^6+7*a^5-a^4-44*a^3+40*a^2+44*a-52)*q^79 + (2*a^6-2*a^5-15*a^4+11*a^3+25*a^2-7*a-9)*q^80 + (2*a^6-2*a^5-15*a^4+11*a^3+27*a^2-5*a-14)*q^81 + (-a^5+3*a^4+5*a^3-16*a^2-2*a+15)*q^82 + (2*a^6-10*a^5-3*a^4+65*a^3-45*a^2-71*a+57)*q^83 + (3*a^5-4*a^4-18*a^3+20*a^2+20*a-19)*q^84 + (-2*a^6+a^5+15*a^4-5*a^3-21*a^2-3*a)*q^85 + (2*a^6-7*a^5-6*a^4+46*a^3-30*a^2-52*a+45)*q^86 + (-3*a^6-3*a^5+34*a^4+22*a^3-108*a^2-29*a+75)*q^87 + (2*a^6-6*a^5-9*a^4+39*a^3-11*a^2-46*a+30)*q^88 + (2*a^6-3*a^5-14*a^4+18*a^3+20*a^2-14*a-3)*q^89 + (-3*a^6-a^5+28*a^4+12*a^3-74*a^2-21*a+45)*q^90 + (-3*a^6+11*a^5+10*a^4-72*a^3+36*a^2+81*a-59)*q^91 + (-2*a^5+3*a^4+13*a^3-21*a^2-15*a+21)*q^92 + (2*a^6+a^5-22*a^4-10*a^3+70*a^2+24*a-55)*q^93 + (-2*a^6+2*a^5+15*a^4-11*a^3-24*a^2+12*a)*q^94 + (2*a^6-6*a^5-11*a^4+39*a^3+a^2-41*a+9)*q^95 + (-3*a^6+6*a^5+17*a^4-39*a^3-3*a^2+44*a-15)*q^96 + (-2*a^6+5*a^5+12*a^4-34*a^3-10*a^2+42*a-1)*q^97 + (-a^6+6*a^5+2*a^4-36*a^3+20*a^2+34*a-30)*q^98 + (4*a^5-5*a^4-26*a^3+28*a^2+29*a-27)*q^99 + (-a^6-2*a^5+9*a^4+13*a^3-20*a^2-16*a+13)*q^100 + (-3*a^6+9*a^5+13*a^4-57*a^3+19*a^2+62*a-42)*q^101 + (2*a^6+5*a^5-28*a^4-32*a^3+98*a^2+40*a-75)*q^102 + (a^6-3*a^5-9*a^4+18*a^3+26*a^2-18*a-22)*q^103 + (-2*a^6+14*a^5-4*a^4-90*a^3+92*a^2+99*a-105)*q^104 + (3*a^6-3*a^5-23*a^4+19*a^3+37*a^2-16*a-12)*q^105 + (2*a^6-4*a^5-11*a^4+23*a^3+5*a^2-17*a+15)*q^106 + (4*a^6-6*a^5-31*a^4+36*a^3+64*a^2-31*a-42)*q^107 + (-a^5+4*a^4+6*a^3-24*a^2-8*a+25)*q^108 + (-a^6+13*a^4-a^3-45*a^2+29)*q^109 + (2*a^6-15*a^4-3*a^3+27*a^2+5*a-15)*q^110 + (-2*a^6+4*a^5+16*a^4-22*a^3-36*a^2+10*a+20)*q^111 + (a^5-2*a^4-8*a^3+12*a^2+12*a-13)*q^112 + (3*a^6-13*a^5-5*a^4+82*a^3-64*a^2-84*a+84)*q^113 + (3*a^6-8*a^5-15*a^4+47*a^3-a^2-42*a+15)*q^114 + (-3*a^6+6*a^5+21*a^4-35*a^3-31*a^2+26*a+3)*q^115 + (3*a^6-3*a^5-22*a^4+18*a^3+36*a^2-17*a-15)*q^116 + (-3*a^6+7*a^5+19*a^4-42*a^3-20*a^2+30*a-4)*q^117 + (-4*a^6+5*a^5+29*a^4-29*a^3-53*a^2+23*a+30)*q^118 + (-a^6-2*a^5+10*a^4+16*a^3-34*a^2-23*a+30)*q^119 + (6*a^6-9*a^5-45*a^4+55*a^3+77*a^2-47*a-30)*q^120 + (3*a^6-13*a^5-10*a^4+85*a^3-37*a^2-97*a+55)*q^121 + (-2*a^6+a^5+15*a^4-7*a^3-26*a^2+9*a+15)*q^122 + (2*a^6-6*a^5-8*a^4+38*a^3-20*a^2-36*a+36)*q^123 + (-4*a^5+5*a^4+26*a^3-33*a^2-30*a+35)*q^124 + (2*a^6-5*a^5-13*a^4+31*a^3+17*a^2-27*a-6)*q^125 + (-3*a^5+7*a^4+19*a^3-35*a^2-23*a+30)*q^126 + 1*q^127 + (2*a^6-4*a^5-15*a^4+23*a^3+28*a^2-21*a-15)*q^128 + (-3*a^6+4*a^5+24*a^4-26*a^3-46*a^2+29*a+14)*q^129 + (5*a^6-6*a^5-34*a^4+34*a^3+40*a^2-27*a)*q^130 + (-5*a^6+11*a^5+29*a^4-69*a^3-15*a^2+68*a-18)*q^131 + (-3*a^6+4*a^5+19*a^4-23*a^3-19*a^2+24*a-3)*q^132 + (2*a^6-9*a^5-6*a^4+56*a^3-28*a^2-60*a+43)*q^133 + (-5*a^6+13*a^5+27*a^4-83*a^3-5*a^2+84*a-30)*q^134 + (-a^6+a^5+9*a^4-5*a^3-19*a^2-4*a)*q^135 + (-3*a^6+4*a^5+26*a^4-21*a^3-64*a^2+12*a+45)*q^136 + (-3*a^6+6*a^5+21*a^4-37*a^3-29*a^2+34*a+9)*q^137 + (2*a^6+a^5-25*a^4-9*a^3+89*a^2+17*a-60)*q^138 + (5*a^6-10*a^5-31*a^4+63*a^3+27*a^2-66*a+5)*q^139 + (-a^6+a^5+7*a^4-3*a^3-13*a^2+2*a+6)*q^140 + (5*a^6-16*a^5-18*a^4+102*a^3-52*a^2-115*a+78)*q^141 + (-a^5-3*a^4+3*a^3+20*a^2+5*a-15)*q^142 + (-7*a^6+17*a^5+37*a^4-108*a^3+6*a^2+118*a-63)*q^143 + (-3*a^5+7*a^4+20*a^3-44*a^2-26*a+37)*q^144 + (2*a^6+4*a^5-23*a^4-29*a^3+71*a^2+39*a-45)*q^145 + (3*a^6-4*a^5-20*a^4+24*a^3+27*a^2-20*a-15)*q^146 + (-3*a^6+4*a^5+21*a^4-23*a^3-27*a^2+12*a+3)*q^147 + (-2*a^6+3*a^5+11*a^4-18*a^3-3*a^2+20*a-10)*q^148 + (5*a^6-2*a^5-46*a^4+9*a^3+121*a^2-3*a-81)*q^149 + (6*a^6-7*a^5-41*a^4+43*a^3+47*a^2-41*a)*q^150 + (-3*a^6+8*a^5+11*a^4-49*a^3+35*a^2+44*a-61)*q^151 + (4*a^6-13*a^5-13*a^4+82*a^3-49*a^2-84*a+75)*q^152 + (3*a^5-9*a^4-24*a^3+58*a^2+37*a-45)*q^153 + (-2*a^6+9*a^5+6*a^4-58*a^3+26*a^2+66*a-45)*q^154 + (-3*a^6+5*a^5+21*a^4-29*a^3-29*a^2+22*a)*q^155 + (-a^6-a^5+6*a^4+8*a^3-2*a^2-11*a-1)*q^156 + (7*a^5-17*a^4-44*a^3+102*a^2+45*a-94)*q^157 + (5*a^6-9*a^5-29*a^4+57*a^3+16*a^2-63*a+15)*q^158 + (4*a^6-3*a^5-33*a^4+15*a^3+65*a^2+3*a-24)*q^159 + (a^5+5*a^4-9*a^3-31*a^2+11*a+30)*q^160 + (-3*a^6+9*a^5+17*a^4-57*a^3-3*a^2+58*a-24)*q^161 + (2*a^6+a^5-19*a^4-7*a^3+51*a^2+8*a-30)*q^162 + (-2*a^6-2*a^5+24*a^4+16*a^3-84*a^2-30*a+74)*q^163 + (a^6-a^5-9*a^4+8*a^3+22*a^2-9*a-18)*q^164 + (-2*a^6-3*a^5+19*a^4+23*a^3-51*a^2-27*a+36)*q^165 + (-6*a^6+13*a^5+35*a^4-79*a^3-15*a^2+79*a-30)*q^166 + (-9*a^6+22*a^5+53*a^4-137*a^3-31*a^2+138*a-39)*q^167 + (5*a^6-12*a^5-28*a^4+74*a^3+10*a^2-75*a+30)*q^168 + (-a^5-a^4+10*a^3+4*a^2-19*a+6)*q^169 + (-3*a^6-a^5+25*a^4+13*a^3-59*a^2-22*a+30)*q^170 + (2*a^6-8*a^5-7*a^4+50*a^3-26*a^2-45*a+38)*q^171 + (3*a^6-6*a^5-18*a^4+38*a^3+14*a^2-41*a+8)*q^172 + (4*a^6-6*a^5-26*a^4+36*a^3+26*a^2-34*a+12)*q^173 + (-9*a^6+10*a^5+67*a^4-57*a^3-113*a^2+42*a+45)*q^174 + (-3*a^6+7*a^5+17*a^4-43*a^3-5*a^2+48*a-22)*q^175 + (-2*a^6+3*a^5+13*a^4-19*a^3-12*a^2+22*a-6)*q^176 + (-9*a^6+19*a^5+59*a^4-119*a^3-65*a^2+114*a)*q^177 + (a^6+2*a^5-12*a^4-14*a^3+42*a^2+19*a-30)*q^178 + (-2*a^6+a^5+20*a^4-9*a^3-51*a^2+18*a+24)*q^179 + (-a^6-2*a^5+11*a^4+11*a^3-27*a^2-8*a+21)*q^180 + (5*a^6-11*a^5-25*a^4+67*a^3-15*a^2-60*a+56)*q^181 + (5*a^6-14*a^5-27*a^4+87*a^3-3*a^2-92*a+45)*q^182 + (a^6+2*a^5-10*a^4-14*a^3+24*a^2+19*a-10)*q^183 + (-8*a^6+15*a^5+53*a^4-93*a^3-63*a^2+87*a)*q^184 + (2*a^6-6*a^5-14*a^4+38*a^3+20*a^2-32*a)*q^185 + (5*a^6-6*a^5-40*a^4+36*a^3+80*a^2-33*a-30)*q^186 + (3*a^6-5*a^5-19*a^4+33*a^3+13*a^2-38*a+15)*q^187 + (-2*a^6+3*a^5+15*a^4-20*a^3-22*a^2+26*a+6)*q^188 + (-4*a^6+10*a^5+23*a^4-63*a^3-11*a^2+67*a-25)*q^189 + (-2*a^6+5*a^5+9*a^4-33*a^3+15*a^2+31*a-30)*q^190 + (-a^6-a^5+12*a^4+8*a^3-42*a^2-21*a+39)*q^191 + (6*a^6-17*a^5-34*a^4+108*a^3+8*a^2-102*a+43)*q^192 + (6*a^6-16*a^5-27*a^4+101*a^3-31*a^2-103*a+71)*q^193 + (a^6-4*a^5-4*a^4+24*a^3-14*a^2-23*a+30)*q^194 + (2*a^6-10*a^5-9*a^4+61*a^3-7*a^2-47*a+27)*q^195 + (4*a^5-a^4-27*a^3+10*a^2+31*a-9)*q^196 + (-2*a^6-a^5+20*a^4+7*a^3-59*a^2-4*a+45)*q^197 + (4*a^6-5*a^5-26*a^4+28*a^3+29*a^2-27*a)*q^198 + (2*a^6-24*a^4+a^3+83*a^2-8*a-64)*q^199 + (-2*a^6+3*a^5+12*a^4-19*a^3-8*a^2+22*a-15)*q^200 +  ...

-------------------------------------------------------
Gamma_0(128)
Weight 2

-------------------------------------------------------
J_0(128), dim = 9

-------------------------------------------------------
128A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= E(Z/2) + F(Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 4.0364603130905652564 + -0.71200728175571729358e-5i
Omega-         = 0.83494087413874351119e-5 + -2.7473549125384309096i
L(1)           =
w1             = -2.0182343312496533219 + 1.3736810163056242334i
w2             = 2.0182259818409119345 + 1.3736738962328066762i
c4             = -32.000134246087482622 + -0.80621078125716336098e-3i
c6             = -639.99939758135516548 + 0.51106372443462252238e-2i
j              = 128.00171443091647618 + 0.10850824109614298551e-1i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -2*q^5 + -4*q^7 + 1*q^9 + 2*q^11 + -2*q^13 + 4*q^15 + -2*q^17 + -2*q^19 + 8*q^21 + 4*q^23 + -1*q^25 + 4*q^27 + 6*q^29 + -4*q^33 + 8*q^35 + -10*q^37 + 4*q^39 + -6*q^41 + -6*q^43 + -2*q^45 + -8*q^47 + 9*q^49 + 4*q^51 + 6*q^53 + -4*q^55 + 4*q^57 + -14*q^59 + -2*q^61 + -4*q^63 + 4*q^65 + -10*q^67 + -8*q^69 + 12*q^71 + 14*q^73 + 2*q^75 + -8*q^77 + -8*q^79 + -11*q^81 + 6*q^83 + 4*q^85 + -12*q^87 + -2*q^89 + 8*q^91 + 4*q^95 + -2*q^97 + 2*q^99 + 6*q^101 + -4*q^103 + -16*q^105 + 2*q^107 + 6*q^109 + 20*q^111 + 2*q^113 + -8*q^115 + -2*q^117 + 8*q^119 + -7*q^121 + 12*q^123 + 12*q^125 + 16*q^127 + 12*q^129 + 6*q^131 + 8*q^133 + -8*q^135 + 10*q^137 + 10*q^139 + 16*q^141 + -4*q^143 + -12*q^145 + -18*q^147 + -18*q^149 + 4*q^151 + -2*q^153 + -18*q^157 + -12*q^159 + -16*q^161 + -2*q^163 + 8*q^165 + -20*q^167 + -9*q^169 + -2*q^171 + -18*q^173 + 4*q^175 + 28*q^177 + 6*q^179 + -2*q^181 + 4*q^183 + 20*q^185 + -4*q^187 + -16*q^189 + -16*q^191 + -2*q^193 + -8*q^195 + 14*q^197 + -4*q^199 +  ...

-------------------------------------------------------
128B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= D(Z/2 + Z/2) + E(Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.8541966046306724016 + -0.39249424010954629991e-5i
Omega-         = 0.23206094852863514313e-4 + 1.9426612453578152818i
L(1)           = 1.4270983023166855448
w1             = -1.4271099053627626325 + -0.97132866020770709318i
w2             = -1.427086699267909769 + 0.97133258515010818865i
c4             = -128.00167471708680552 + 0.44056244655811219688e-2i
c6             = -5120.1632729551944016 + -0.25148710211464093079i
j              = 127.99709105457434442 + -0.23879736697634542676e-1i

HECKE EIGENFORM:
f(q) = q + 2*q^3 + 2*q^5 + -4*q^7 + 1*q^9 + -2*q^11 + 2*q^13 + 4*q^15 + -2*q^17 + 2*q^19 + -8*q^21 + 4*q^23 + -1*q^25 + -4*q^27 + -6*q^29 + -4*q^33 + -8*q^35 + 10*q^37 + 4*q^39 + -6*q^41 + 6*q^43 + 2*q^45 + -8*q^47 + 9*q^49 + -4*q^51 + -6*q^53 + -4*q^55 + 4*q^57 + 14*q^59 + 2*q^61 + -4*q^63 + 4*q^65 + 10*q^67 + 8*q^69 + 12*q^71 + 14*q^73 + -2*q^75 + 8*q^77 + -8*q^79 + -11*q^81 + -6*q^83 + -4*q^85 + -12*q^87 + -2*q^89 + -8*q^91 + 4*q^95 + -2*q^97 + -2*q^99 + -6*q^101 + -4*q^103 + -16*q^105 + -2*q^107 + -6*q^109 + 20*q^111 + 2*q^113 + 8*q^115 + 2*q^117 + 8*q^119 + -7*q^121 + -12*q^123 + -12*q^125 + 16*q^127 + 12*q^129 + -6*q^131 + -8*q^133 + -8*q^135 + 10*q^137 + -10*q^139 + -16*q^141 + -4*q^143 + -12*q^145 + 18*q^147 + 18*q^149 + 4*q^151 + -2*q^153 + 18*q^157 + -12*q^159 + -16*q^161 + 2*q^163 + -8*q^165 + -20*q^167 + -9*q^169 + 2*q^171 + 18*q^173 + 4*q^175 + 28*q^177 + -6*q^179 + 2*q^181 + 4*q^183 + 20*q^185 + 4*q^187 + 16*q^189 + -16*q^191 + -2*q^193 + 8*q^195 + -14*q^197 + -4*q^199 +  ...

-------------------------------------------------------
128C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= E(Z/2) + F(Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.7473456117270088606 + -0.2061705397948603804e-4i
Omega-         = 0.16420884239606138028e-4 + -4.0364480454453271578i
L(1)           = 1.3736728059021838481
w1             = -1.3736810163056242334 + 2.0182343312496533219i
w2             = 1.3736645954213846272 + 2.0182137141956738359i
c4             = -32.000481460122357456 + 0.19192445346341074704e-2i
c6             = 640.01192493315147127 + 0.13012562248718662881e-1i
j              = 128.0009310531538899 + -0.26144171397517625961e-1i

HECKE EIGENFORM:
f(q) = q + 2*q^3 + -2*q^5 + 4*q^7 + 1*q^9 + -2*q^11 + -2*q^13 + -4*q^15 + -2*q^17 + 2*q^19 + 8*q^21 + -4*q^23 + -1*q^25 + -4*q^27 + 6*q^29 + -4*q^33 + -8*q^35 + -10*q^37 + -4*q^39 + -6*q^41 + 6*q^43 + -2*q^45 + 8*q^47 + 9*q^49 + -4*q^51 + 6*q^53 + 4*q^55 + 4*q^57 + 14*q^59 + -2*q^61 + 4*q^63 + 4*q^65 + 10*q^67 + -8*q^69 + -12*q^71 + 14*q^73 + -2*q^75 + -8*q^77 + 8*q^79 + -11*q^81 + -6*q^83 + 4*q^85 + 12*q^87 + -2*q^89 + -8*q^91 + -4*q^95 + -2*q^97 + -2*q^99 + 6*q^101 + 4*q^103 + -16*q^105 + -2*q^107 + 6*q^109 + -20*q^111 + 2*q^113 + 8*q^115 + -2*q^117 + -8*q^119 + -7*q^121 + -12*q^123 + 12*q^125 + -16*q^127 + 12*q^129 + -6*q^131 + 8*q^133 + 8*q^135 + 10*q^137 + -10*q^139 + 16*q^141 + 4*q^143 + -12*q^145 + 18*q^147 + -18*q^149 + -4*q^151 + -2*q^153 + -18*q^157 + 12*q^159 + -16*q^161 + 2*q^163 + 8*q^165 + 20*q^167 + -9*q^169 + 2*q^171 + -18*q^173 + -4*q^175 + 28*q^177 + -6*q^179 + -2*q^181 + -4*q^183 + 20*q^185 + 4*q^187 + -16*q^189 + 16*q^191 + -2*q^193 + 8*q^195 + 14*q^197 + 4*q^199 +  ...

-------------------------------------------------------
128D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2 + Z/2) + E(Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.9426511760542716085 + -0.1139824777299692982e-4i
Omega-         = 0.48150798055232236495e-4 + -2.854197517627208482i
L(1)           = 0.97132558804385523048
w1             = -0.97134966342616342035 + 1.4271044579374907394i
w2             = 0.97130151262810818811 + 1.4270930596897177425i
c4             = -127.99885010125334077 + 0.19629147344083080239e-1i
c6             = 5120.2623961755920674 + -0.68184222032001829039e-1i
j              = 127.98465368551522258 + -0.51363719891569464958e-1i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + 2*q^5 + 4*q^7 + 1*q^9 + 2*q^11 + 2*q^13 + -4*q^15 + -2*q^17 + -2*q^19 + -8*q^21 + -4*q^23 + -1*q^25 + 4*q^27 + -6*q^29 + -4*q^33 + 8*q^35 + 10*q^37 + -4*q^39 + -6*q^41 + -6*q^43 + 2*q^45 + 8*q^47 + 9*q^49 + 4*q^51 + -6*q^53 + 4*q^55 + 4*q^57 + -14*q^59 + 2*q^61 + 4*q^63 + 4*q^65 + -10*q^67 + 8*q^69 + -12*q^71 + 14*q^73 + 2*q^75 + 8*q^77 + 8*q^79 + -11*q^81 + 6*q^83 + -4*q^85 + 12*q^87 + -2*q^89 + 8*q^91 + -4*q^95 + -2*q^97 + 2*q^99 + -6*q^101 + 4*q^103 + -16*q^105 + 2*q^107 + -6*q^109 + -20*q^111 + 2*q^113 + -8*q^115 + 2*q^117 + -8*q^119 + -7*q^121 + 12*q^123 + -12*q^125 + -16*q^127 + 12*q^129 + 6*q^131 + -8*q^133 + 8*q^135 + 10*q^137 + 10*q^139 + -16*q^141 + 4*q^143 + -12*q^145 + -18*q^147 + 18*q^149 + -4*q^151 + -2*q^153 + 18*q^157 + 12*q^159 + -16*q^161 + -2*q^163 + -8*q^165 + 20*q^167 + -9*q^169 + -2*q^171 + 18*q^173 + -4*q^175 + 28*q^177 + 6*q^179 + 2*q^181 + -4*q^183 + 20*q^185 + -4*q^187 + 16*q^189 + 16*q^191 + -2*q^193 + -8*q^195 + -14*q^197 + 4*q^199 +  ...

-------------------------------------------------------
128E (old = 64A), dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2
= A(Z/2) + B(Z/2) + C(Z/2) + D(Z/2) + F(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
128F (old = 32A), dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2
= A(Z/2) + B(Z/2 + Z/2) + C(Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(129)
Weight 2

-------------------------------------------------------
J_0(129), dim = 13

-------------------------------------------------------
129A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 4.4727895738058883333 + -0.14688453495041768766e-4i
Omega-         = 0.47662048772846684677e-5 + 1.1381032072627964727i
L(1)           =
w1             = -2.2363924038005055243 + 0.56905894785814575724i
w2             = 0.47662048772846684677e-5 + 1.1381032072627964727i
c4             = 927.98258693279047766 + 0.15555814318341026992e-1i
c6             = -28375.211858321085997 + -0.71229500842289951904i
j              = -229428.47879975312591 + -2.568698264190957195i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^4 + -2*q^5 + -2*q^7 + 1*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 + -1*q^23 + -1*q^25 + -1*q^27 + 4*q^28 + -5*q^31 + 5*q^33 + 4*q^35 + -2*q^36 + 8*q^37 + -3*q^39 + -7*q^41 + -1*q^43 + 10*q^44 + -2*q^45 + -8*q^47 + -4*q^48 + -3*q^49 + 3*q^51 + -6*q^52 + 3*q^53 + 10*q^55 + -2*q^57 + 12*q^59 + -4*q^60 + -8*q^61 + -2*q^63 + -8*q^64 + -6*q^65 + -15*q^67 + 6*q^68 + 1*q^69 + -14*q^71 + 12*q^73 + 1*q^75 + -4*q^76 + 10*q^77 + -16*q^79 + -8*q^80 + 1*q^81 + 15*q^83 + -4*q^84 + 6*q^85 + 10*q^89 + -6*q^91 + 2*q^92 + 5*q^93 + -4*q^95 + 11*q^97 + -5*q^99 + 2*q^100 + -9*q^101 + 5*q^103 + -4*q^105 + 2*q^108 + 11*q^109 + -8*q^111 + -8*q^112 + -4*q^113 + 2*q^115 + 3*q^117 + 6*q^119 + 14*q^121 + 7*q^123 + 10*q^124 + 12*q^125 + -3*q^127 + 1*q^129 + 16*q^131 + -10*q^132 + -4*q^133 + 2*q^135 + 18*q^137 + -5*q^139 + -8*q^140 + 8*q^141 + -15*q^143 + 4*q^144 + 3*q^147 + -16*q^148 + -16*q^149 + -2*q^151 + -3*q^153 + 10*q^155 + 6*q^156 + -6*q^157 + -3*q^159 + 2*q^161 + 16*q^163 + 14*q^164 + -10*q^165 + -1*q^167 + -4*q^169 + 2*q^171 + 2*q^172 + -10*q^173 + 2*q^175 + -20*q^176 + -12*q^177 + -26*q^179 + 4*q^180 + -10*q^181 + 8*q^183 + -16*q^185 + 15*q^187 + 16*q^188 + 2*q^189 + -8*q^191 + 8*q^192 + -21*q^193 + 6*q^195 + 6*q^196 + -14*q^197 + -14*q^199 +  ...

-------------------------------------------------------
129B (new) , dim = 1

CONGRUENCES:
Modular Degree = 3*5
Ker(ModPolar)  = Z/3*5 + Z/3*5
= D(Z/5 + Z/5) + E(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 3/2^2
Sha Bound      = 2^2*3

ANALYTIC INVARIANTS:

Omega+         = 1.072763467986929993 + 0.25333570038513219196e-5i
Omega-         = 0.11145560545432884935e-5 + -1.2083436251358185594i
L(1)           = 0.80457260099244096383
w1             = -0.11145560545432884935e-5 + 1.2083436251358185594i
w2             = 1.072763467986929993 + 0.25333570038513219196e-5i
c4             = 1417.0100360884478606 + -0.10920109551231645522e-1i
c6             = 22714.686397302571993 + -0.50660076120148683486i
j              = 2110.7675591911023956 + -0.10045975661090317007e-1i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^3 + -1*q^4 + 2*q^5 + 1*q^6 + -3*q^8 + 1*q^9 + 2*q^10 + -1*q^12 + -2*q^13 + 2*q^15 + -1*q^16 + -6*q^17 + 1*q^18 + 4*q^19 + -2*q^20 + -4*q^23 + -3*q^24 + -1*q^25 + -2*q^26 + 1*q^27 + -6*q^29 + 2*q^30 + 8*q^31 + 5*q^32 + -6*q^34 + -1*q^36 + 6*q^37 + 4*q^38 + -2*q^39 + -6*q^40 + 2*q^41 + -1*q^43 + 2*q^45 + -4*q^46 + 4*q^47 + -1*q^48 + -7*q^49 + -1*q^50 + -6*q^51 + 2*q^52 + -2*q^53 + 1*q^54 + 4*q^57 + -6*q^58 + -2*q^60 + 14*q^61 + 8*q^62 + 7*q^64 + -4*q^65 + 12*q^67 + 6*q^68 + -4*q^69 + 8*q^71 + -3*q^72 + 2*q^73 + 6*q^74 + -1*q^75 + -4*q^76 + -2*q^78 + -8*q^79 + -2*q^80 + 1*q^81 + 2*q^82 + -12*q^85 + -1*q^86 + -6*q^87 + 14*q^89 + 2*q^90 + 4*q^92 + 8*q^93 + 4*q^94 + 8*q^95 + 5*q^96 + -14*q^97 + -7*q^98 + 1*q^100 + -18*q^101 + -6*q^102 + -8*q^103 + 6*q^104 + -2*q^106 + -1*q^108 + -2*q^109 + 6*q^111 + -2*q^113 + 4*q^114 + -8*q^115 + 6*q^116 + -2*q^117 + -6*q^120 + -11*q^121 + 14*q^122 + 2*q^123 + -8*q^124 + -12*q^125 + 16*q^127 + -3*q^128 + -1*q^129 + -4*q^130 + -4*q^131 + 12*q^134 + 2*q^135 + 18*q^136 + -18*q^137 + -4*q^138 + -20*q^139 + 4*q^141 + 8*q^142 + -1*q^144 + -12*q^145 + 2*q^146 + -7*q^147 + -6*q^148 + -6*q^149 + -1*q^150 + 16*q^151 + -12*q^152 + -6*q^153 + 16*q^155 + 2*q^156 + 14*q^157 + -8*q^158 + -2*q^159 + 10*q^160 + 1*q^162 + -4*q^163 + -2*q^164 + -12*q^167 + -9*q^169 + -12*q^170 + 4*q^171 + 1*q^172 + -18*q^173 + -6*q^174 + 14*q^178 + 20*q^179 + -2*q^180 + 22*q^181 + 14*q^183 + 12*q^184 + 12*q^185 + 8*q^186 + -4*q^188 + 8*q^190 + 8*q^191 + 7*q^192 + 18*q^193 + -14*q^194 + -4*q^195 + 7*q^196 + 14*q^197 + 8*q^199 + 3*q^200 +  ...

-------------------------------------------------------
129C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*7 + Z/2*7
= D(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.7583281107447579001 + 0.96356486030688217142e-5i
Omega-         = 14.994152440116986141 + 0.15057801999289448318e-3i
L(1)           = 1.7583281107711596062

HECKE EIGENFORM:
a^2-2*a-1 = 0,
f(q) = q + a*q^2 + -1*q^3 + (2*a-1)*q^4 + (-a+2)*q^5 + -a*q^6 + (-2*a+3)*q^7 + (a+2)*q^8 + 1*q^9 + -1*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 + -1*q^27 + -7*q^28 + 3*a*q^29 + 1*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 + (3*a+4)*q^38 + 5*q^39 + (-2*a+3)*q^40 + (4*a-4)*q^41 + (a+2)*q^42 + 1*q^43 + (5*a-6)*q^44 + (-a+2)*q^45 + 6*a*q^46 + (7*a-8)*q^47 + -3*q^48 + (-4*a+6)*q^49 + (-4*a-2)*q^50 + 2*a*q^51 + (-10*a+5)*q^52 + (8*a-8)*q^53 + -a*q^54 + (-4*a+9)*q^55 + (-5*a+4)*q^56 + (-4*a+5)*q^57 + (6*a+3)*q^58 + (-8*a+10)*q^59 + (-a+4)*q^60 + (2*a-6)*q^61 + 4*a*q^62 + (-2*a+3)*q^63 + (-2*a-5)*q^64 + (5*a-10)*q^65 + (-2*a+1)*q^66 + -6*a*q^67 + (-6*a-4)*q^68 + -6*q^69 + (2*a-3)*q^70 + (-2*a+8)*q^71 + (a+2)*q^72 + (4*a-2)*q^73 + (-6*a-2)*q^74 + 2*a*q^75 + (2*a+13)*q^76 + (-7*a+14)*q^77 + 5*a*q^78 + (6*a-2)*q^79 + (-3*a+6)*q^80 + 1*q^81 + (4*a+4)*q^82 + (-a-6)*q^83 + 7*q^84 + 2*q^85 + a*q^86 + -3*a*q^87 + 7*q^88 + (-6*a+6)*q^89 + -1*q^90 + (10*a-15)*q^91 + (12*a-6)*q^92 + -4*q^93 + (6*a+7)*q^94 + (5*a-14)*q^95 + (-a+4)*q^96 + (2*a-3)*q^97 + (-2*a-4)*q^98 + (-a+4)*q^99 + (-6*a-4)*q^100 + (-4*a+4)*q^101 + (4*a+2)*q^102 + (6*a-12)*q^103 + (-5*a-10)*q^104 + (3*a-8)*q^105 + (8*a+8)*q^106 + (5*a-14)*q^107 + (-2*a+1)*q^108 + (-6*a-1)*q^109 + (a-4)*q^110 + (2*a+2)*q^111 + (-6*a+9)*q^112 + (-a-6)*q^113 + (-3*a-4)*q^114 + (-6*a+12)*q^115 + (9*a+6)*q^116 + -5*q^117 + (-6*a-8)*q^118 + (2*a+4)*q^119 + (2*a-3)*q^120 + (-6*a+6)*q^121 + (-2*a+2)*q^122 + (-4*a+4)*q^123 + (8*a-4)*q^124 + (5*a-8)*q^125 + (-a-2)*q^126 + (-2*a-6)*q^127 + (-11*a+6)*q^128 + -1*q^129 + 5*q^130 + (-4*a+4)*q^131 + (-5*a+6)*q^132 + (6*a-23)*q^133 + (-12*a-6)*q^134 + (a-2)*q^135 + (-8*a-2)*q^136 + (a+14)*q^137 + -6*a*q^138 + (-8*a+12)*q^139 + (7*a-14)*q^140 + (-7*a+8)*q^141 + (4*a-2)*q^142 + (5*a-20)*q^143 + 3*q^144 + -3*q^145 + (6*a+4)*q^146 + (4*a-6)*q^147 + (-10*a-2)*q^148 + (-2*a-2)*q^149 + (4*a+2)*q^150 + 16*q^151 + (11*a-6)*q^152 + -2*a*q^153 + -7*q^154 + (-4*a+8)*q^155 + (10*a-5)*q^156 + (6*a-6)*q^157 + (10*a+6)*q^158 + (-8*a+8)*q^159 + (4*a-9)*q^160 + (-12*a+18)*q^161 + a*q^162 + (10*a-5)*q^163 + (4*a+12)*q^164 + (4*a-9)*q^165 + (-8*a-1)*q^166 + (-a-2)*q^167 + (5*a-4)*q^168 + 12*q^169 + 2*a*q^170 + (4*a-5)*q^171 + (2*a-1)*q^172 + (-4*a+18)*q^173 + (-6*a-3)*q^174 + (2*a+4)*q^175 + (-3*a+12)*q^176 + (8*a-10)*q^177 + (-6*a-6)*q^178 + (6*a-6)*q^179 + (a-4)*q^180 + -15*q^181 + (5*a+10)*q^182 + (-2*a+6)*q^183 + (6*a+12)*q^184 + (2*a-2)*q^185 + -4*a*q^186 + (-4*a+2)*q^187 + (5*a+22)*q^188 + (2*a-3)*q^189 + (-4*a+5)*q^190 + (-8*a+10)*q^191 + (2*a+5)*q^192 + 14*q^193 + (a+2)*q^194 + (-5*a+10)*q^195 + -14*q^196 + (-14*a+12)*q^197 + (2*a-1)*q^198 + (-12*a+20)*q^199 + (-8*a-2)*q^200 +  ...

-------------------------------------------------------
129D (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^5*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^3*5 + Z/2^3*5
= A(Z/2 + Z/2) + B(Z/5 + Z/5) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^3*71
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 11
Torsion Bound  = 11
|L(1)/Omega|   = 2^2/11
Sha Bound      = 2^2*11

ANALYTIC INVARIANTS:

Omega+         = 2.8708855702397557915 + 0.26191502149008159726e-4i
Omega-         = 0.86563470581547505576e-4 + 5.5000656432973454694i
L(1)           = 1.0439583892215382592

HECKE EIGENFORM:
a^3+2*a^2-5*a-8 = 0,
f(q) = q + a*q^2 + 1*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 + 1*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 + 1*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 + (-3*a-8)*q^38 + 3*q^39 + -a^2*q^40 + (-a^2+2*a+1)*q^41 + (2*a^2+a-8)*q^42 + -1*q^43 + (4*a^2-5*a-14)*q^44 + (-a-2)*q^45 + (-4*a^2+6*a+24)*q^46 + (-4*a^2-3*a+16)*q^47 + (3*a^2-2*a-12)*q^48 + (-3*a^2-2*a+13)*q^49 + (2*a^2+4*a+8)*q^50 + (-a^2+5)*q^51 + (3*a^2-6)*q^52 + (a^2+2*a-5)*q^53 + a*q^54 + (a^2+2*a+2)*q^55 + (-3*a+8)*q^56 + (-a^2-2*a+2)*q^57 + -a^2*q^58 + (-2*a^2+12)*q^59 + (-3*a-4)*q^60 + (2*a^2-2*a-16)*q^61 + 8*q^62 + (-a^2+6)*q^63 + (3*a^2-8*a-8)*q^64 + (-3*a-6)*q^65 + (-3*a^2+8)*q^66 + (3*a^2+4*a-15)*q^67 + (-2*a^2+2*a+6)*q^68 + (3*a^2+2*a-9)*q^69 + (-a^2-4*a)*q^70 + (-2*a^2+2*a+18)*q^71 + (-2*a^2+a+8)*q^72 + (-2*a^2+4)*q^73 + (-2*a^2+2*a+16)*q^74 + (a^2+4*a-1)*q^75 + (-a^2-4*a-4)*q^76 + (a-6)*q^77 + 3*a*q^78 + (-2*a^2-2*a+16)*q^79 + (2*a^2+a)*q^80 + 1*q^81 + (4*a^2-4*a-8)*q^82 + (3*a^2-a-17)*q^83 + (-a^2+2*a+4)*q^84 + -2*q^85 + -a*q^86 + -a*q^87 + (-7*a^2+6*a+16)*q^88 + (-2*a-14)*q^89 + (-a^2-2*a)*q^90 + (-3*a^2+18)*q^91 + (8*a^2-14)*q^92 + (a^2+2*a-5)*q^93 + (5*a^2-4*a-32)*q^94 + (2*a^2+7*a+4)*q^95 + (-4*a^2+a+8)*q^96 + (-2*a^2+2*a+11)*q^97 + (4*a^2-2*a-24)*q^98 + (a^2-a-5)*q^99 + (-2*a^2+10*a+18)*q^100 + (a^2+2*a-1)*q^101 + (2*a^2-8)*q^102 + (3*a^2-11)*q^103 + (-6*a^2+3*a+24)*q^104 + (-a-4)*q^105 + 8*q^106 + (-2*a^2-a+8)*q^107 + (a^2-2)*q^108 + (-2*a-5)*q^109 + (7*a+8)*q^110 + (2*a^2+2*a-8)*q^111 + (-a^2+4*a-8)*q^112 + (2*a^2+3*a-12)*q^113 + (-3*a-8)*q^114 + (-2*a^2-10*a-6)*q^115 + (2*a^2-3*a-8)*q^116 + 3*q^117 + (4*a^2+2*a-16)*q^118 + (-2*a^2-2*a+14)*q^119 + -a^2*q^120 + (4*a^2-2*a-18)*q^121 + (-6*a^2-6*a+16)*q^122 + (-a^2+2*a+1)*q^123 + (-2*a^2+4*a+10)*q^124 + (-4*a^2-7*a+4)*q^125 + (2*a^2+a-8)*q^126 + (-3*a^2-4*a+13)*q^127 + (-6*a^2+5*a+8)*q^128 + -1*q^129 + (-3*a^2-6*a)*q^130 + (4*a^2+8*a-16)*q^131 + (4*a^2-5*a-14)*q^132 + (-3*a^2-4*a+12)*q^133 + (-2*a^2+24)*q^134 + (-a-2)*q^135 + (2*a^2-4*a)*q^136 + (-7*a-6)*q^137 + (-4*a^2+6*a+24)*q^138 + (a^2-6*a-5)*q^139 + (-2*a^2-3*a)*q^140 + (-4*a^2-3*a+16)*q^141 + (6*a^2+8*a-16)*q^142 + (3*a^2-3*a-15)*q^143 + (3*a^2-2*a-12)*q^144 + (a^2+2*a)*q^145 + (4*a^2-6*a-16)*q^146 + (-3*a^2-2*a+13)*q^147 + (2*a^2+2*a)*q^148 + (2*a^2-2*a-16)*q^149 + (2*a^2+4*a+8)*q^150 + (2*a^2+4*a-10)*q^151 + (-2*a^2-3*a+8)*q^152 + (-a^2+5)*q^153 + (a^2-6*a)*q^154 + (-2*a^2-4*a+2)*q^155 + (3*a^2-6)*q^156 + (4*a^2+6*a-6)*q^157 + (2*a^2+6*a-16)*q^158 + (a^2+2*a-5)*q^159 + (-a^2+10*a+16)*q^160 + (4*a^2+8*a-22)*q^161 + a*q^162 + (5*a^2-24)*q^163 + (-10*a^2+8*a+30)*q^164 + (a^2+2*a+2)*q^165 + (-7*a^2-2*a+24)*q^166 + (-a^2-a+15)*q^167 + (-3*a+8)*q^168 + -4*q^169 + -2*a*q^170 + (-a^2-2*a+2)*q^171 + (-a^2+2)*q^172 + (-4*a^2+4*a+22)*q^173 + -a^2*q^174 + (6*a^2+6*a-22)*q^175 + (12*a^2-9*a-28)*q^176 + (-2*a^2+12)*q^177 + (-2*a^2-14*a)*q^178 + (2*a-2)*q^179 + (-3*a-4)*q^180 + (-9*a^2-2*a+38)*q^181 + (6*a^2+3*a-24)*q^182 + (2*a^2-2*a-16)*q^183 + (-8*a^2+14*a+16)*q^184 + (-2*a^2-6*a)*q^185 + 8*q^186 + (-a^2+2*a-1)*q^187 + (-6*a^2-a+8)*q^188 + (-a^2+6)*q^189 + (3*a^2+14*a+16)*q^190 + (-2*a^2-4*a+24)*q^191 + (3*a^2-8*a-8)*q^192 + (-a^2-2*a+11)*q^193 + (6*a^2+a-16)*q^194 + (-3*a-6)*q^195 + (-4*a^2+6)*q^196 + (2*a^2+6*a-14)*q^197 + (-3*a^2+8)*q^198 + (-6*a^2+34)*q^199 + (10*a^2-32)*q^200 +  ...

-------------------------------------------------------
129E (old = 43A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/3 + Z/3) + D(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
129F (old = 43B), dim = 2

CONGRUENCES:
Modular Degree = 2^4*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*7 + Z/2*7
= A(Z/2 + Z/2) + C(Z/7 + Z/7) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(130)
Weight 2

-------------------------------------------------------
J_0(130), dim = 17

-------------------------------------------------------
130A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*3
Ker(ModPolar)  = Z/2^3*3 + Z/2^3*3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +--
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2*3
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 1.8921070967892356474 + -0.52699198028610505636e-6i
Omega-         = 0.20030983627909775906e-5 + 1.0000044608037834836i
L(1)           =
w1             = 1.8921070967892356474 + -0.52699198028610505636e-6i
w2             = -0.20030983627909775906e-5 + -1.0000044608037834836i
c4             = 1561.087335849838375 + 0.12455302194537229062e-1i
c6             = -61314.189179503952031 + -0.7412763039216895167i
j              = 146314.49881445187104 + 2.9844843902465929005i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -2*q^3 + 1*q^4 + 1*q^5 + 2*q^6 + -4*q^7 + -1*q^8 + 1*q^9 + -1*q^10 + -6*q^11 + -2*q^12 + 1*q^13 + 4*q^14 + -2*q^15 + 1*q^16 + -6*q^17 + -1*q^18 + 2*q^19 + 1*q^20 + 8*q^21 + 6*q^22 + 6*q^23 + 2*q^24 + 1*q^25 + -1*q^26 + 4*q^27 + -4*q^28 + -6*q^29 + 2*q^30 + 2*q^31 + -1*q^32 + 12*q^33 + 6*q^34 + -4*q^35 + 1*q^36 + 2*q^37 + -2*q^38 + -2*q^39 + -1*q^40 + -6*q^41 + -8*q^42 + 2*q^43 + -6*q^44 + 1*q^45 + -6*q^46 + -12*q^47 + -2*q^48 + 9*q^49 + -1*q^50 + 12*q^51 + 1*q^52 + 6*q^53 + -4*q^54 + -6*q^55 + 4*q^56 + -4*q^57 + 6*q^58 + 6*q^59 + -2*q^60 + 2*q^61 + -2*q^62 + -4*q^63 + 1*q^64 + 1*q^65 + -12*q^66 + -4*q^67 + -6*q^68 + -12*q^69 + 4*q^70 + -6*q^71 + -1*q^72 + -10*q^73 + -2*q^74 + -2*q^75 + 2*q^76 + 24*q^77 + 2*q^78 + -4*q^79 + 1*q^80 + -11*q^81 + 6*q^82 + 8*q^84 + -6*q^85 + -2*q^86 + 12*q^87 + 6*q^88 + -6*q^89 + -1*q^90 + -4*q^91 + 6*q^92 + -4*q^93 + 12*q^94 + 2*q^95 + 2*q^96 + 2*q^97 + -9*q^98 + -6*q^99 + 1*q^100 + 6*q^101 + -12*q^102 + -10*q^103 + -1*q^104 + 8*q^105 + -6*q^106 + 18*q^107 + 4*q^108 + -10*q^109 + 6*q^110 + -4*q^111 + -4*q^112 + -6*q^113 + 4*q^114 + 6*q^115 + -6*q^116 + 1*q^117 + -6*q^118 + 24*q^119 + 2*q^120 + 25*q^121 + -2*q^122 + 12*q^123 + 2*q^124 + 1*q^125 + 4*q^126 + 2*q^127 + -1*q^128 + -4*q^129 + -1*q^130 + -12*q^131 + 12*q^132 + -8*q^133 + 4*q^134 + 4*q^135 + 6*q^136 + -6*q^137 + 12*q^138 + -16*q^139 + -4*q^140 + 24*q^141 + 6*q^142 + -6*q^143 + 1*q^144 + -6*q^145 + 10*q^146 + -18*q^147 + 2*q^148 + 6*q^149 + 2*q^150 + -10*q^151 + -2*q^152 + -6*q^153 + -24*q^154 + 2*q^155 + -2*q^156 + -10*q^157 + 4*q^158 + -12*q^159 + -1*q^160 + -24*q^161 + 11*q^162 + 20*q^163 + -6*q^164 + 12*q^165 + -12*q^167 + -8*q^168 + 1*q^169 + 6*q^170 + 2*q^171 + 2*q^172 + -18*q^173 + -12*q^174 + -4*q^175 + -6*q^176 + -12*q^177 + 6*q^178 + 12*q^179 + 1*q^180 + 2*q^181 + 4*q^182 + -4*q^183 + -6*q^184 + 2*q^185 + 4*q^186 + 36*q^187 + -12*q^188 + -16*q^189 + -2*q^190 + -2*q^192 + 2*q^193 + -2*q^194 + -2*q^195 + 9*q^196 + 6*q^197 + 6*q^198 + -16*q^199 + -1*q^200 +  ...

-------------------------------------------------------
130B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4*5
Ker(ModPolar)  = Z/2^4*5 + Z/2^4*5
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2^2 + Z/2^2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/5 + Z/5)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 0.4432677685283933338 + 0.56720294500400998851e-5i
Omega-         = 0.66959682441791918942e-4 + -1.1048298142876011041i
L(1)           = 0.88653553712936563762
w1             = -0.66959682441791918942e-4 + 1.1048298142876011041i
w2             = 0.4432677685283933338 + 0.56720294500400998851e-5i
c4             = 40371.16924654171533 + -2.0674950911691453268i
c6             = 8110501.3529961517983 + -622.20547405661082851i
j              = 6329568.6140312209229 + 4738.6486296922490873i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 2*q^3 + 1*q^4 + -1*q^5 + 2*q^6 + -4*q^7 + 1*q^8 + 1*q^9 + -1*q^10 + -2*q^11 + 2*q^12 + -1*q^13 + -4*q^14 + -2*q^15 + 1*q^16 + 2*q^17 + 1*q^18 + 6*q^19 + -1*q^20 + -8*q^21 + -2*q^22 + 6*q^23 + 2*q^24 + 1*q^25 + -1*q^26 + -4*q^27 + -4*q^28 + 2*q^29 + -2*q^30 + -6*q^31 + 1*q^32 + -4*q^33 + 2*q^34 + 4*q^35 + 1*q^36 + -2*q^37 + 6*q^38 + -2*q^39 + -1*q^40 + 10*q^41 + -8*q^42 + -10*q^43 + -2*q^44 + -1*q^45 + 6*q^46 + -12*q^47 + 2*q^48 + 9*q^49 + 1*q^50 + 4*q^51 + -1*q^52 + 2*q^53 + -4*q^54 + 2*q^55 + -4*q^56 + 12*q^57 + 2*q^58 + 10*q^59 + -2*q^60 + 2*q^61 + -6*q^62 + -4*q^63 + 1*q^64 + 1*q^65 + -4*q^66 + -12*q^67 + 2*q^68 + 12*q^69 + 4*q^70 + 10*q^71 + 1*q^72 + 10*q^73 + -2*q^74 + 2*q^75 + 6*q^76 + 8*q^77 + -2*q^78 + -4*q^79 + -1*q^80 + -11*q^81 + 10*q^82 + -8*q^84 + -2*q^85 + -10*q^86 + 4*q^87 + -2*q^88 + -14*q^89 + -1*q^90 + 4*q^91 + 6*q^92 + -12*q^93 + -12*q^94 + -6*q^95 + 2*q^96 + 14*q^97 + 9*q^98 + -2*q^99 + 1*q^100 + 14*q^101 + 4*q^102 + -18*q^103 + -1*q^104 + 8*q^105 + 2*q^106 + 6*q^107 + -4*q^108 + -6*q^109 + 2*q^110 + -4*q^111 + -4*q^112 + 2*q^113 + 12*q^114 + -6*q^115 + 2*q^116 + -1*q^117 + 10*q^118 + -8*q^119 + -2*q^120 + -7*q^121 + 2*q^122 + 20*q^123 + -6*q^124 + -1*q^125 + -4*q^126 + -14*q^127 + 1*q^128 + -20*q^129 + 1*q^130 + 4*q^131 + -4*q^132 + -24*q^133 + -12*q^134 + 4*q^135 + 2*q^136 + -18*q^137 + 12*q^138 + -8*q^139 + 4*q^140 + -24*q^141 + 10*q^142 + 2*q^143 + 1*q^144 + -2*q^145 + 10*q^146 + 18*q^147 + -2*q^148 + 2*q^149 + 2*q^150 + 6*q^151 + 6*q^152 + 2*q^153 + 8*q^154 + 6*q^155 + -2*q^156 + 10*q^157 + -4*q^158 + 4*q^159 + -1*q^160 + -24*q^161 + -11*q^162 + -4*q^163 + 10*q^164 + 4*q^165 + 20*q^167 + -8*q^168 + 1*q^169 + -2*q^170 + 6*q^171 + -10*q^172 + 10*q^173 + 4*q^174 + -4*q^175 + -2*q^176 + 20*q^177 + -14*q^178 + -4*q^179 + -1*q^180 + 10*q^181 + 4*q^182 + 4*q^183 + 6*q^184 + 2*q^185 + -12*q^186 + -4*q^187 + -12*q^188 + 16*q^189 + -6*q^190 + 2*q^192 + 14*q^193 + 14*q^194 + 2*q^195 + 9*q^196 + -6*q^197 + -2*q^198 + 1*q^200 +  ...

-------------------------------------------------------
130C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.5647138888433678767 + -0.29434929882574729343e-5i
Omega-         = 0.1541935502045473717e-6 + -1.728083590980676848i
L(1)           = 0.78235694442306824108
w1             = 0.1541935502045473717e-6 + -1.728083590980676848i
w2             = -1.5647138888433678767 + 0.29434929882574729343e-5i
c4             = 321.00178556568831706 + 0.15741564954743781904e-2i
c6             = 2078.9317562408452067 + 0.53271490396272712004e-1i
j              = 1987.7254588004412971 + 0.10915986638400366471e-1i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + 1*q^5 + 1*q^8 + -3*q^9 + 1*q^10 + 1*q^13 + 1*q^16 + 2*q^17 + -3*q^18 + -8*q^19 + 1*q^20 + -4*q^23 + 1*q^25 + 1*q^26 + -2*q^29 + -4*q^31 + 1*q^32 + 2*q^34 + -3*q^36 + 6*q^37 + -8*q^38 + 1*q^40 + 10*q^41 + -3*q^45 + -4*q^46 + 8*q^47 + -7*q^49 + 1*q^50 + 1*q^52 + 6*q^53 + -2*q^58 + 8*q^59 + -2*q^61 + -4*q^62 + 1*q^64 + 1*q^65 + 4*q^67 + 2*q^68 + -12*q^71 + -3*q^72 + 10*q^73 + 6*q^74 + -8*q^76 + -8*q^79 + 1*q^80 + 9*q^81 + 10*q^82 + 12*q^83 + 2*q^85 + 10*q^89 + -3*q^90 + -4*q^92 + 8*q^94 + -8*q^95 + -14*q^97 + -7*q^98 + 1*q^100 + 6*q^101 + -4*q^103 + 1*q^104 + 6*q^106 + -2*q^109 + -14*q^113 + -4*q^115 + -2*q^116 + -3*q^117 + 8*q^118 + -11*q^121 + -2*q^122 + -4*q^124 + 1*q^125 + -20*q^127 + 1*q^128 + 1*q^130 + 4*q^131 + 4*q^134 + 2*q^136 + -6*q^137 + 4*q^139 + -12*q^142 + -3*q^144 + -2*q^145 + 10*q^146 + 6*q^148 + 6*q^149 + -20*q^151 + -8*q^152 + -6*q^153 + -4*q^155 + -18*q^157 + -8*q^158 + 1*q^160 + 9*q^162 + 20*q^163 + 10*q^164 + 12*q^166 + 16*q^167 + 1*q^169 + 2*q^170 + 24*q^171 + -18*q^173 + 10*q^178 + 4*q^179 + -3*q^180 + 22*q^181 + -4*q^184 + 6*q^185 + 8*q^188 + -8*q^190 + 18*q^193 + -14*q^194 + -7*q^196 + -26*q^197 + 24*q^199 + 1*q^200 +  ...

-------------------------------------------------------
130D (old = 65A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2^2 + Z/2^2) + C(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
130E (old = 65B), dim = 2

CONGRUENCES:
Modular Degree = 2^6*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + G(Z/3 + Z/3)

-------------------------------------------------------
130F (old = 65C), dim = 2

CONGRUENCES:
Modular Degree = 2^6*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + H(Z/7 + Z/7)

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130G (old = 26A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= A(Z/3 + Z/3) + E(Z/3 + Z/3) + H(Z/2 + Z/2 + Z/2 + Z/2)

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130H (old = 26B), dim = 1

CONGRUENCES:
Modular Degree = 2^2*5*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*5*7 + Z/2*5*7
= B(Z/5 + Z/5) + F(Z/7 + Z/7) + G(Z/2 + Z/2 + Z/2 + Z/2)

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Gamma_0(131)
Weight 2

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J_0(131), dim = 11

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131A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 4.171576759558201568 + 0.10015976789612757912e-4i
Omega-         = 0.7202020174348221578e-5 + 2.9651666311218320924i
L(1)           =
w1             = 2.0857919807891879581 + 1.4825883235493108526i
w2             = 2.0857847787690136099 + -1.4825783075725212398i
c4             = -32.001303341575744438 + 0.67754684856740203339e-3i
c6             = -440.01300076674596784 + -0.28417597709655417104e-2i
j              = 250.15090181653876239 + -0.16352185291716487283e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^4 + -2*q^5 + -1*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 + 1*q^21 + -2*q^23 + -1*q^25 + 5*q^27 + 2*q^28 + -2*q^31 + 2*q^35 + 4*q^36 + -8*q^37 + 3*q^39 + -3*q^41 + 3*q^43 + 4*q^45 + 10*q^47 + -4*q^48 + -6*q^49 + -4*q^51 + 6*q^52 + -9*q^53 + 2*q^57 + 1*q^59 + -4*q^60 + -15*q^61 + 2*q^63 + -8*q^64 + 6*q^65 + -6*q^67 + -8*q^68 + 2*q^69 + 10*q^71 + 4*q^73 + 1*q^75 + 4*q^76 + -8*q^79 + -8*q^80 + 1*q^81 + 4*q^83 + -2*q^84 + -8*q^85 + -11*q^89 + 3*q^91 + 4*q^92 + 2*q^93 + 4*q^95 + 12*q^97 + 2*q^100 + 11*q^101 + 4*q^103 + -2*q^105 + -3*q^107 + -10*q^108 + -7*q^109 + 8*q^111 + -4*q^112 + 10*q^113 + 4*q^115 + 6*q^117 + -4*q^119 + -11*q^121 + 3*q^123 + 4*q^124 + 12*q^125 + 18*q^127 + -3*q^129 + -1*q^131 + 2*q^133 + -10*q^135 + 20*q^137 + 18*q^139 + -4*q^140 + -10*q^141 + -8*q^144 + 6*q^147 + 16*q^148 + -12*q^149 + -9*q^151 + -8*q^153 + 4*q^155 + -6*q^156 + -4*q^157 + 9*q^159 + 2*q^161 + 2*q^163 + 6*q^164 + -24*q^167 + -4*q^169 + 4*q^171 + -6*q^172 + -14*q^173 + 1*q^175 + -1*q^177 + -19*q^179 + -8*q^180 + 8*q^181 + 15*q^183 + 16*q^185 + -20*q^188 + -5*q^189 + -11*q^191 + 8*q^192 + -2*q^193 + -6*q^195 + 12*q^196 + -24*q^197 + 4*q^199 +  ...

-------------------------------------------------------
131B (new) , dim = 10

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^7*5*46141*75619573
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 5*13
Torsion Bound  = 5*13
|L(1)/Omega|   = 2/5*13
Sha Bound      = 2*5*13

ANALYTIC INVARIANTS:

Omega+         = 51.153457622392299779 + -0.51879058898414516949e-5i
Omega-         = 615.13238137002149554 + -0.23809758228906203539e-2i
L(1)           = 1.5739525422274634724

HECKE EIGENFORM:
a^10-18*a^8+2*a^7+111*a^6-18*a^5-270*a^4+28*a^3+232*a^2+16*a-32 = 0,
f(q) = 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 + (-a^6-a^5+10*a^4+7*a^3-23*a^2-8*a+4)*q^38 + (1/16*a^9+1/2*a^8-5/8*a^7-57/8*a^6+11/16*a^5+253/8*a^4+63/8*a^3-171/4*a^2-16*a+4)*q^39 + (1/4*a^9+1/4*a^8-13/4*a^7-13/4*a^6+25/2*a^5+29/2*a^4-12*a^3-24*a^2-8*a+8)*q^40 + (-7/16*a^9-3/8*a^8+57/8*a^7+41/8*a^6-593/16*a^5-22*a^4+503/8*a^3+63/2*a^2-19*a-7)*q^41 + (1/2*a^6+1/2*a^5-7/2*a^4-5/2*a^3+2*a^2+2*a+2)*q^42 + (1/16*a^9-1/2*a^8-11/8*a^7+67/8*a^6+163/16*a^5-351/8*a^4-243/8*a^3+277/4*a^2+67/2*a-8)*q^43 + (1/8*a^9-1/4*a^8-2*a^7+7/2*a^6+89/8*a^5-59/4*a^4-103/4*a^3+41/2*a^2+20*a-4)*q^44 + (3/16*a^9-1/8*a^8-27/8*a^7+21/8*a^6+305/16*a^5-67/4*a^4-263/8*a^3+67/2*a^2+5*a-13)*q^45 + (1/4*a^9+1/2*a^8-4*a^7-7*a^6+81/4*a^5+61/2*a^4-63/2*a^3-42*a^2+2*a+8)*q^46 + (-1/4*a^9+4*a^7-a^6-85/4*a^5+10*a^4+83/2*a^3-23*a^2-23*a+4)*q^47 + (-1/4*a^9-1/4*a^8+13/4*a^7+15/4*a^6-25/2*a^5-18*a^4+12*a^3+23*a^2+8*a+4)*q^48 + (-1/8*a^9+1/8*a^8+9/4*a^7-7/4*a^6-99/8*a^5+55/8*a^4+81/4*a^3-17/4*a^2-2*a)*q^49 + (-1/4*a^9-1/2*a^8+13/4*a^7+27/4*a^6-12*a^5-117/4*a^4+17/2*a^3+87/2*a^2+10*a-10)*q^50 + (1/8*a^9+1/4*a^8-7/4*a^7-13/4*a^6+51/8*a^5+23/2*a^4+5/4*a^3-5*a^2-20*a-14)*q^51 + (1/8*a^9-2*a^7-1/2*a^6+81/8*a^5+9/2*a^4-75/4*a^3-8*a^2+10*a+2)*q^52 + (a^5-9*a^3+a^2+14*a+3)*q^53 + (-1/8*a^9-1/2*a^8+7/4*a^7+31/4*a^6-55/8*a^5-153/4*a^4+17/4*a^3+119/2*a^2+7*a-6)*q^54 + (1/2*a^8+1/2*a^7-15/2*a^6-6*a^5+73/2*a^4+45/2*a^3-123/2*a^2-27*a+19)*q^55 + (1/4*a^9+1/4*a^8-17/4*a^7-17/4*a^6+45/2*a^5+43/2*a^4-37*a^3-30*a^2+4*a)*q^56 + (-1/4*a^9+1/4*a^8+9/2*a^7-9/2*a^6-103/4*a^5+99/4*a^4+97/2*a^3-73/2*a^2-19*a-2)*q^57 + (-1/4*a^9+4*a^7-a^6-81/4*a^5+9*a^4+67/2*a^3-16*a^2-12*a+4)*q^58 + (3/16*a^9-25/8*a^7+1/8*a^6+265/16*a^5-1/8*a^4-225/8*a^3-25/4*a^2+13/2*a+8)*q^59 + (1/4*a^9-1/4*a^8-9/2*a^7+4*a^6+105/4*a^5-81/4*a^4-56*a^3+65/2*a^2+35*a-6)*q^60 + (-3/16*a^9+25/8*a^7-5/8*a^6-257/16*a^5+53/8*a^4+189/8*a^3-67/4*a^2-3/2*a+14)*q^61 + (1/4*a^9+1/2*a^8-7/2*a^7-15/2*a^6+59/4*a^5+37*a^4-31/2*a^3-61*a^2-8*a+12)*q^62 + (5/16*a^9+1/4*a^8-41/8*a^7-27/8*a^6+435/16*a^5+121/8*a^4-395/8*a^3-113/4*a^2+43/2*a+14)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (-1/8*a^9-1/8*a^8+7/4*a^7+3/2*a^6-65/8*a^5-45/8*a^4+29/2*a^3+19/4*a^2-13/2*a+4)*q^65 + (-1/4*a^9-1/2*a^8+15/4*a^7+27/4*a^6-18*a^5-113/4*a^4+26*a^3+77/2*a^2-8)*q^66 + (-1/4*a^9-1/4*a^8+4*a^7+3*a^6-81/4*a^5-41/4*a^4+63/2*a^3+17/2*a^2-2*a+4)*q^67 + (1/4*a^9+1/2*a^8-7/2*a^7-13/2*a^6+63/4*a^5+27*a^4-49/2*a^3-40*a^2+8*a+16)*q^68 + (3/8*a^9-25/4*a^7+3/4*a^6+277/8*a^5-27/4*a^4-283/4*a^3+21/2*a^2+45*a+8)*q^69 + (-3/8*a^9-1/4*a^8+6*a^7+7/2*a^6-247/8*a^5-67/4*a^4+207/4*a^3+55/2*a^2-13*a-2)*q^70 + (1/8*a^9+1/2*a^8-5/4*a^7-29/4*a^6+11/8*a^5+135/4*a^4+55/4*a^3-101/2*a^2-30*a+8)*q^71 + (1/4*a^9-1/4*a^8-15/4*a^7+21/4*a^6+18*a^5-65/2*a^4-27*a^3+60*a^2+4*a-16)*q^72 + (3/8*a^9+1/2*a^8-23/4*a^7-29/4*a^6+221/8*a^5+135/4*a^4-161/4*a^3-109/2*a^2+a+18)*q^73 + (-1/4*a^9+7/2*a^7-1/2*a^6-59/4*a^5+7/2*a^4+35/2*a^3-2*a^2+2*a)*q^74 + (-3/8*a^9-1/8*a^8+25/4*a^7+a^6-279/8*a^5-1/8*a^4+73*a^3-33/4*a^2-93/2*a+5)*q^75 + (-1/4*a^9+7/2*a^7-3/2*a^6-63/4*a^5+27/2*a^4+49/2*a^3-29*a^2-8*a+12)*q^76 + (7/16*a^9+5/8*a^8-57/8*a^7-71/8*a^6+589/16*a^5+77/2*a^4-477/8*a^3-49*a^2+17/2*a-1)*q^77 + (1/2*a^9+1/2*a^8-29/4*a^7-25/4*a^6+131/4*a^5+99/4*a^4-89/2*a^3-61/2*a^2+3*a+2)*q^78 + (-1/4*a^8+7/2*a^6-3/2*a^5-63/4*a^4+23/2*a^3+49/2*a^2-13*a-8)*q^79 + (3/4*a^8+1/4*a^7-41/4*a^6-13/4*a^5+44*a^4+33/2*a^3-63*a^2-28*a+12)*q^80 + (1/4*a^9-5/8*a^8-5*a^7+41/4*a^6+32*a^5-427/8*a^4-285/4*a^3+339/4*a^2+83/2*a-10)*q^81 + (-3/8*a^9-3/4*a^8+6*a^7+23/2*a^6-239/8*a^5-221/4*a^4+175/4*a^3+165/2*a^2-14)*q^82 + (-1/8*a^9-1/4*a^8+7/4*a^7+15/4*a^6-55/8*a^5-18*a^4+17/4*a^3+30*a^2+8*a-14)*q^83 + (-1/8*a^9+11/4*a^7+1/4*a^6-147/8*a^5-5/4*a^4+171/4*a^3+7/2*a^2-31*a-6)*q^84 + (1/8*a^9-1/4*a^8-11/4*a^7+15/4*a^6+155/8*a^5-18*a^4-199/4*a^3+28*a^2+41*a-6)*q^85 + (-1/2*a^9-1/4*a^8+33/4*a^7+13/4*a^6-171/4*a^5-27/2*a^4+135/2*a^3+19*a^2-9*a+2)*q^86 + (-1/4*a^9+1/4*a^8+4*a^7-9/2*a^6-83/4*a^5+99/4*a^4+36*a^3-81/2*a^2-9*a)*q^87 + (-1/4*a^9+1/4*a^8+15/4*a^7-13/4*a^6-18*a^5+25/2*a^4+31*a^3-16*a^2-12*a+8)*q^88 + (-1/4*a^9+9/2*a^7-1/2*a^6-111/4*a^5+11/2*a^4+131/2*a^3-15*a^2-44*a+5)*q^89 + (-1/8*a^9+9/4*a^7-7/4*a^6-107/8*a^5+71/4*a^4+113/4*a^3-77/2*a^2-16*a+6)*q^90 + 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(-1/4*a^9-3/8*a^8+9/2*a^7+4*a^6-107/4*a^5-79/8*a^4+109/2*a^3-5/4*a^2-26*a+17)*q^165 + (-1/4*a^9-1/2*a^8+4*a^7+7*a^6-81/4*a^5-59/2*a^4+67/2*a^3+37*a^2-12*a-4)*q^166 + (a^6-10*a^4+2*a^3+25*a^2-6*a-12)*q^167 + (1/2*a^8+1/2*a^7-11/2*a^6-9/2*a^5+16*a^4+12*a^3-6*a^2-8*a-8)*q^168 + (3/4*a^9+5/4*a^8-11*a^7-69/4*a^6+101/2*a^5+149/2*a^4-281/4*a^3-98*a^2+7/2*a+4)*q^169 + (-1/4*a^9-1/2*a^8+7/2*a^7+11/2*a^6-63/4*a^5-16*a^4+49/2*a^3+12*a^2-8*a+4)*q^170 + (3/8*a^9-3/4*a^8-25/4*a^7+55/4*a^6+253/8*a^5-157/2*a^4-171/4*a^3+137*a^2-8*a-34)*q^171 + (-3/8*a^9+1/4*a^8+7*a^7-4*a^6-343/8*a^5+81/4*a^4+375/4*a^3-63/2*a^2-57*a)*q^172 + (1/8*a^9+3/4*a^8-5/4*a^7-45/4*a^6+11/8*a^5+52*a^4+55/4*a^3-68*a^2-30*a)*q^173 + (1/4*a^9-1/2*a^8-4*a^7+7*a^6+81/4*a^5-63/2*a^4-67/2*a^3+49*a^2+4*a-8)*q^174 + (7/16*a^9-1/8*a^8-61/8*a^7+23/8*a^6+681/16*a^5-20*a^4-647/8*a^3+45*a^2+45*a-26)*q^175 + (-1/4*a^8+5/4*a^7+11/4*a^6-57/4*a^5-7*a^4+85/2*a^3+5*a^2-28*a)*q^176 + (-9/16*a^9-1/8*a^8+73/8*a^7+1/8*a^6-739/16*a^5+39/4*a^4+549/8*a^3-73/2*a^2+3*a+26)*q^177 + (a^5-2*a^4-8*a^3+14*a^2+9*a-8)*q^178 + (-1/8*a^9+1/4*a^8+11/4*a^7-4*a^6-141/8*a^5+77/4*a^4+33*a^3-47/2*a^2-19/2*a+7)*q^179 + (-3/8*a^9+1/4*a^8+21/4*a^7-19/4*a^6-181/8*a^5+28*a^4+123/4*a^3-54*a^2-2*a+22)*q^180 + (1/4*a^9+1/4*a^8-4*a^7-3*a^6+81/4*a^5+37/4*a^4-65/2*a^3+1/2*a^2+9*a-8)*q^181 + (-5/8*a^9-5/4*a^8+41/4*a^7+75/4*a^6-419/8*a^5-85*a^4+323/4*a^3+113*a^2-6*a-16)*q^182 + (3/16*a^9+1/8*a^8-31/8*a^7-11/8*a^6+417/16*a^5+9/2*a^4-499/8*a^3-14*a^2+40*a+28)*q^183 + (-1/2*a^9-1/2*a^8+15/2*a^7+15/2*a^6-36*a^5-36*a^4+56*a^3+56*a^2-8*a-16)*q^184 + (-1/4*a^9+1/4*a^8+5*a^7-5/2*a^6-127/4*a^5+23/4*a^4+72*a^3-7/2*a^2-49*a+10)*q^185 + (-1/2*a^8-1/2*a^7+15/2*a^6+9/2*a^5-37*a^4-9*a^3+57*a^2+6*a-4)*q^186 + (-1/2*a^8-1/2*a^7+8*a^6+8*a^5-79/2*a^4-77/2*a^3+58*a^2+49*a-6)*q^187 + (-1/2*a^8-3/2*a^7+15/2*a^6+33/2*a^5-36*a^4-48*a^3+54*a^2+38*a-8)*q^188 + (1/8*a^8+1/4*a^7-2*a^6-3*a^5+89/8*a^4+29/4*a^3-107/4*a^2+21/2*a+25)*q^189 + (a^8+1/2*a^7-29/2*a^6-11/2*a^5+131/2*a^4+18*a^3-97*a^2-22*a+20)*q^190 + (1/4*a^9+7/8*a^8-7/2*a^7-27/2*a^6+59/4*a^5+523/8*a^4-31/2*a^3-381/4*a^2-12*a+11)*q^191 + (-1/4*a^9+3/4*a^8+15/4*a^7-43/4*a^6-19*a^5+95/2*a^4+39*a^3-64*a^2-28*a)*q^192 + (5/16*a^9-1/2*a^8-45/8*a^7+75/8*a^6+535/16*a^5-439/8*a^4-585/8*a^3+401/4*a^2+53*a-25)*q^193 + (1/4*a^9+1/2*a^8-4*a^7-8*a^6+77/4*a^5+75/2*a^4-49/2*a^3-48*a^2-6*a+4)*q^194 + (1/4*a^8+3/4*a^7-17/4*a^6-31/4*a^5+25*a^4+39/2*a^3-97/2*a^2-10*a+17)*q^195 + (1/4*a^9+1/2*a^8-13/4*a^7-23/4*a^6+27/2*a^5+77/4*a^4-17*a^3-37/2*a^2-2*a+4)*q^196 + (1/4*a^9-1/4*a^8-9/2*a^7+5*a^6+109/4*a^5-125/4*a^4-60*a^3+127/2*a^2+32*a-24)*q^197 + (-1/8*a^9+1/4*a^8+2*a^7-2*a^6-81/8*a^5+1/4*a^4+75/4*a^3+25/2*a^2-10*a-4)*q^198 + (-1/2*a^9-1/4*a^8+8*a^7+3/2*a^6-43*a^5+17/4*a^4+171/2*a^3-47/2*a^2-49*a+12)*q^199 + (-1/4*a^9+1/4*a^8+15/4*a^7-21/4*a^6-20*a^5+65/2*a^4+48*a^3-64*a^2-40*a+24)*q^200 +  ...

-------------------------------------------------------
Gamma_0(132)
Weight 2

-------------------------------------------------------
J_0(132), dim = 19

-------------------------------------------------------
132A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3*5
Ker(ModPolar)  = Z/2*3*5 + Z/2*3*5
= B(Z/2) + D(Z/3 + Z/3) + F(Z/5 + Z/5) + G(Z/2)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.1888691194489433223 + -0.12025229597668254532e-4i
Omega-         = 0.79425182551325041168e-6 + 0.79625447818473800029i
L(1)           = 1.0944345597409877408
w1             = 1.0944349568503844178 + 0.39812122647757016602i
w2             = -0.79425182551325041168e-6 + -0.79625447818473800029i
c4             = 3712.1692271166152191 + 0.8415488759643329274e-2i
c6             = -262897.18912067504788 + -2.4026025946106754031i
j              = -4921.6270753856814279 + 0.21736335926426064205i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + 2*q^5 + 2*q^7 + 1*q^9 + -1*q^11 + 6*q^13 + -2*q^15 + -4*q^17 + -2*q^19 + -2*q^21 + -8*q^23 + -1*q^25 + -1*q^27 + 1*q^33 + 4*q^35 + -6*q^37 + -6*q^39 + 10*q^43 + 2*q^45 + -3*q^49 + 4*q^51 + 14*q^53 + -2*q^55 + 2*q^57 + -12*q^59 + -14*q^61 + 2*q^63 + 12*q^65 + 4*q^67 + 8*q^69 + 6*q^73 + 1*q^75 + -2*q^77 + 2*q^79 + 1*q^81 + 16*q^83 + -8*q^85 + -14*q^89 + 12*q^91 + -4*q^95 + -2*q^97 + -1*q^99 + 8*q^101 + -12*q^103 + -4*q^105 + 16*q^107 + -18*q^109 + 6*q^111 + -10*q^113 + -16*q^115 + 6*q^117 + -8*q^119 + 1*q^121 + -12*q^125 + -6*q^127 + -10*q^129 + 4*q^131 + -4*q^133 + -2*q^135 + 14*q^137 + 14*q^139 + -6*q^143 + 3*q^147 + -4*q^149 + 10*q^151 + -4*q^153 + -10*q^157 + -14*q^159 + -16*q^161 + 16*q^163 + 2*q^165 + -12*q^167 + 23*q^169 + -2*q^171 + 8*q^173 + -2*q^175 + 12*q^177 + -4*q^179 + 22*q^181 + 14*q^183 + -12*q^185 + 4*q^187 + -2*q^189 + 24*q^191 + 10*q^193 + -12*q^195 + 16*q^197 + 8*q^199 +  ...

-------------------------------------------------------
132B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= A(Z/2) + E(Z/3 + Z/3) + G(Z/2)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.6563135416774121032 + -0.13255506938916320368e-4i
Omega-         = 0.81896097052990116481e-5 + 3.0402463784369185381i
L(1)           = 1.3281567708552429232
w1             = -1.3281526760338534021 + 1.5201298169719287272i
w2             = 1.3281608656435587011 + 1.5201165614649898109i
c4             = -127.99962558605718496 + -0.15954782564313622082e-2i
c6             = 800.05214874489268139 + 0.30738616324112967138e-1i
j              = 1323.9165199288975536 + -0.12212549906724005241e-1i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 2*q^5 + -2*q^7 + 1*q^9 + 1*q^11 + -2*q^13 + 2*q^15 + 4*q^17 + -6*q^19 + -2*q^21 + -1*q^25 + 1*q^27 + -8*q^29 + -8*q^31 + 1*q^33 + -4*q^35 + 10*q^37 + -2*q^39 + 8*q^41 + -2*q^43 + 2*q^45 + -8*q^47 + -3*q^49 + 4*q^51 + -2*q^53 + 2*q^55 + -6*q^57 + 12*q^59 + 10*q^61 + -2*q^63 + -4*q^65 + 12*q^67 + 8*q^71 + 6*q^73 + -1*q^75 + -2*q^77 + -2*q^79 + 1*q^81 + 16*q^83 + 8*q^85 + -8*q^87 + -14*q^89 + 4*q^91 + -8*q^93 + -12*q^95 + -2*q^97 + 1*q^99 + -16*q^101 + 4*q^103 + -4*q^105 + -10*q^109 + 10*q^111 + 6*q^113 + -2*q^117 + -8*q^119 + 1*q^121 + 8*q^123 + -12*q^125 + -10*q^127 + -2*q^129 + 12*q^131 + 12*q^133 + 2*q^135 + -2*q^137 + -6*q^139 + -8*q^141 + -2*q^143 + -16*q^145 + -3*q^147 + 20*q^149 + -10*q^151 + 4*q^153 + -16*q^155 + 6*q^157 + -2*q^159 + 16*q^163 + 2*q^165 + 12*q^167 + -9*q^169 + -6*q^171 + 2*q^175 + 12*q^177 + -12*q^179 + -10*q^181 + 10*q^183 + 20*q^185 + 4*q^187 + -2*q^189 + 16*q^191 + -22*q^193 + -4*q^195 + 24*q^197 + -16*q^199 +  ...

-------------------------------------------------------
132C (old = 66A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
132D (old = 66B), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/3 + Z/3) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
132E (old = 66C), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3*5^2
Ker(ModPolar)  = Z/2^2*5 + Z/2^2*5 + Z/2^2*3*5 + Z/2^2*3*5
= B(Z/3 + Z/3) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
132F (old = 44A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3*5 + Z/2*3*5
= A(Z/5 + Z/5) + C(Z/3 + Z/3) + H(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
132G (old = 33A), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3^3
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2) + B(Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/3 + Z/3 + Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
132H (old = 11A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^3*5^2
Ker(ModPolar)  = Z/3 + Z/3 + Z/2*3*5 + Z/2*3*5 + Z/2*3*5 + Z/2*3*5
= E(Z/5 + Z/5 + Z/5 + Z/5) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/3 + Z/3 + Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
Gamma_0(133)
Weight 2

-------------------------------------------------------
J_0(133), dim = 11

-------------------------------------------------------
133A (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 15.318100017164133124 + -0.3530502798011764799e-3i
Omega-         = 6.3558964531687147172 + 0.1302663729413473287e-5i
L(1)           =

HECKE EIGENFORM:
a^2+3*a+1 = 0,
f(q) = q + a*q^2 + a*q^3 + (-3*a-3)*q^4 + (-2*a-3)*q^5 + (-3*a-1)*q^6 + -1*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 + 1*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 + -1*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 + -a*q^38 + a*q^39 + (6*a-1)*q^40 + (a+3)*q^41 + (3*a+1)*q^42 + -2*q^43 + (15*a+12)*q^44 + (-a+6)*q^45 + -3*a*q^46 + (-10*a-15)*q^47 + (11*a+3)*q^48 + 1*q^49 + (-6*a-3)*q^51 + (-3*a-3)*q^52 + (-5*a-12)*q^53 + (-3*a-2)*q^54 + (9*a+11)*q^55 + (-4*a-3)*q^56 + -a*q^57 + (-6*a-1)*q^58 + (-6*a-15)*q^59 + (12*a+3)*q^60 + (6*a+9)*q^61 + (-2*a-3)*q^62 + (3*a+4)*q^63 + (-6*a-7)*q^64 + (-2*a-3)*q^65 + (17*a+6)*q^66 + (-9*a-17)*q^67 + 9*a*q^68 + -3*a*q^69 + (-3*a-2)*q^70 + (-4*a-3)*q^71 + 11*a*q^72 + (3*a+12)*q^73 + (-13*a-6)*q^74 + (3*a+3)*q^76 + (-a+3)*q^77 + (-3*a-1)*q^78 + -10*q^79 + (-13*a-12)*q^80 + (6*a+10)*q^81 + -1*q^82 + 3*a*q^83 + (-6*a-3)*q^84 + (3*a-3)*q^85 + -2*a*q^86 + (-6*a-1)*q^87 + (-21*a-13)*q^88 + (6*a+18)*q^89 + (9*a+1)*q^90 + -1*q^91 + (9*a+9)*q^92 + (-2*a-3)*q^93 + (15*a+10)*q^94 + (2*a+3)*q^95 + (-12*a-3)*q^96 + (-12*a-17)*q^97 + a*q^98 + (14*a+15)*q^99 + (-4*a+3)*q^101 + (15*a+6)*q^102 + (6*a+11)*q^103 + (4*a+3)*q^104 + (-3*a-2)*q^105 + (3*a+5)*q^106 + (-4*a-9)*q^107 + (3*a-3)*q^108 + (12*a+21)*q^109 + (-16*a-9)*q^110 + (-13*a-6)*q^111 + (3*a-2)*q^112 + (-3*a-12)*q^113 + (3*a+1)*q^114 + (6*a+9)*q^115 + (15*a+12)*q^116 + (-3*a-4)*q^117 + (3*a+6)*q^118 + (-3*a-3)*q^119 + (-19*a-6)*q^120 + (-9*a-3)*q^121 + (-9*a-6)*q^122 + -1*q^123 + (-3*a-12)*q^124 + (10*a+15)*q^125 + (-5*a-3)*q^126 + (6*a+22)*q^127 + (5*a+12)*q^128 + -2*a*q^129 + (3*a+2)*q^130 + (-5*a-3)*q^131 + (-33*a-15)*q^132 + 1*q^133 + (10*a+9)*q^134 + -5*q^135 + (-15*a-3)*q^136 + (-4*a+6)*q^137 + (9*a+3)*q^138 + (-6*a-23)*q^139 + (3*a-3)*q^140 + (15*a+10)*q^141 + (9*a+4)*q^142 + (a-3)*q^143 + (-21*a-17)*q^144 + (9*a+11)*q^145 + (3*a-3)*q^146 + a*q^147 + (21*a+3)*q^148 + (16*a+27)*q^149 + (9*a+25)*q^151 + (-4*a-3)*q^152 + (6*a-3)*q^153 + (6*a+1)*q^154 + (-5*a-15)*q^155 + (6*a+3)*q^156 + (-3*a-9)*q^157 + -10*a*q^158 + (3*a+5)*q^159 + (15*a+15)*q^160 + 3*q^161 + (-8*a-6)*q^162 + (3*a-8)*q^163 + (-3*a-6)*q^164 + (-16*a-9)*q^165 + (-9*a-3)*q^166 + (4*a+3)*q^167 + (9*a+4)*q^168 + -12*q^169 + (-12*a-3)*q^170 + (3*a+4)*q^171 + (6*a+6)*q^172 + (10*a+6)*q^173 + (17*a+6)*q^174 + (20*a-3)*q^176 + (3*a+6)*q^177 + -6*q^178 + (5*a+3)*q^179 + (-24*a-21)*q^180 + (-9*a-25)*q^181 + -a*q^182 + (-9*a-6)*q^183 + (-12*a-9)*q^184 + (8*a-3)*q^185 + (3*a+2)*q^186 + (-15*a-12)*q^187 + (-15*a+15)*q^188 + (-2*a-3)*q^189 + (-3*a-2)*q^190 + (7*a+12)*q^191 + (11*a+6)*q^192 + (-9*a-5)*q^193 + (19*a+12)*q^194 + (3*a+2)*q^195 + (-3*a-3)*q^196 + (-15*a-24)*q^197 + (-27*a-14)*q^198 + (-6*a+1)*q^199 +  ...

-------------------------------------------------------
133B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 5
Torsion Bound  = 5
|L(1)/Omega|   = 2^2/5
Sha Bound      = 2^2*5

ANALYTIC INVARIANTS:

Omega+         = 2.7831242123631701701 + 0.16094643594867394859e-4i
Omega-         = 8.3651472701277099127 + -0.21058428687447086229e-3i
L(1)           = 2.2264993699277658869

HECKE EIGENFORM:
a^2-a-1 = 0,
f(q) = q + a*q^2 + (-a+2)*q^3 + (a-1)*q^4 + 1*q^5 + (a-1)*q^6 + 1*q^7 + (-2*a+1)*q^8 + (-3*a+2)*q^9 + a*q^10 + (a-1)*q^11 + (2*a-3)*q^12 + -1*q^13 + a*q^14 + (-a+2)*q^15 + -3*a*q^16 + (3*a-1)*q^17 + (-a-3)*q^18 + -1*q^19 + (a-1)*q^20 + (-a+2)*q^21 + 1*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 + 1*q^35 + (2*a-5)*q^36 + (4*a-9)*q^37 + -a*q^38 + (a-2)*q^39 + (-2*a+1)*q^40 + (-5*a+7)*q^41 + (a-1)*q^42 + (4*a+2)*q^43 + (-a+2)*q^44 + (-3*a+2)*q^45 + (-3*a-4)*q^46 + (4*a+1)*q^47 + (-3*a+3)*q^48 + 1*q^49 + -4*a*q^50 + (4*a-5)*q^51 + (-a+1)*q^52 + 3*a*q^53 + (-a-2)*q^54 + (a-1)*q^55 + (-2*a+1)*q^56 + (a-2)*q^57 + (2*a-1)*q^58 + (-2*a+11)*q^59 + (2*a-3)*q^60 + (-8*a+1)*q^61 + (4*a+9)*q^62 + (-3*a+2)*q^63 + (2*a+1)*q^64 + -1*q^65 + (-a+2)*q^66 + (-7*a+9)*q^67 + (-a+4)*q^68 + (-5*a+6)*q^69 + a*q^70 + (6*a-1)*q^71 + (-a+8)*q^72 + -7*a*q^73 + (-5*a+4)*q^74 + (4*a-8)*q^75 + (-a+1)*q^76 + (a-1)*q^77 + (-a+1)*q^78 + (-4*a+2)*q^79 + -3*a*q^80 + (6*a-2)*q^81 + (2*a-5)*q^82 + (-3*a+8)*q^83 + (2*a-3)*q^84 + (3*a-1)*q^85 + (6*a+4)*q^86 + (-4*a+7)*q^87 + (a-3)*q^88 + (-2*a+6)*q^89 + (-a-3)*q^90 + -1*q^91 + (a-5)*q^92 + (14*a-19)*q^93 + (5*a+4)*q^94 + -1*q^95 + (6*a-11)*q^96 + (4*a+1)*q^97 + a*q^98 + (2*a-5)*q^99 + (-4*a+4)*q^100 + (10*a-13)*q^101 + (-a+4)*q^102 + (-6*a-3)*q^103 + (2*a-1)*q^104 + (-a+2)*q^105 + (3*a+3)*q^106 + (-2*a+9)*q^107 + (a-3)*q^108 + (-2*a-9)*q^109 + 1*q^110 + (13*a-22)*q^111 + -3*a*q^112 + (-15*a+4)*q^113 + (-a+1)*q^114 + (-4*a+1)*q^115 + (3*a-4)*q^116 + (3*a-2)*q^117 + (9*a-2)*q^118 + (3*a-1)*q^119 + (-3*a+4)*q^120 + (-a-9)*q^121 + (-7*a-8)*q^122 + (-12*a+19)*q^123 + (-5*a+14)*q^124 + -9*q^125 + (-a-3)*q^126 + (-6*a+6)*q^127 + (a+12)*q^128 + 2*a*q^129 + -a*q^130 + (-9*a+9)*q^131 + (-3*a+5)*q^132 + -1*q^133 + (2*a-7)*q^134 + (-2*a+1)*q^135 + (-a-7)*q^136 + (8*a-6)*q^137 + (a-5)*q^138 + (-4*a-3)*q^139 + (a-1)*q^140 + (3*a-2)*q^141 + (5*a+6)*q^142 + (-a+1)*q^143 + (3*a+9)*q^144 + (-a+3)*q^145 + (-7*a-7)*q^146 + (-a+2)*q^147 + (-9*a+13)*q^148 + (4*a-17)*q^149 + (-4*a+4)*q^150 + (-13*a+11)*q^151 + (2*a-1)*q^152 + -11*q^153 + 1*q^154 + (9*a-5)*q^155 + (-2*a+3)*q^156 + (-7*a-1)*q^157 + (-2*a-4)*q^158 + (3*a-3)*q^159 + (a-5)*q^160 + (-4*a+1)*q^161 + (4*a+6)*q^162 + (11*a-14)*q^163 + (7*a-12)*q^164 + (2*a-3)*q^165 + (5*a-3)*q^166 + (4*a+1)*q^167 + (-3*a+4)*q^168 + -12*q^169 + (2*a+3)*q^170 + (3*a-2)*q^171 + (2*a+2)*q^172 + (2*a+18)*q^173 + (3*a-4)*q^174 + -4*q^175 + -3*q^176 + (-13*a+24)*q^177 + (4*a-2)*q^178 + (19*a-7)*q^179 + (2*a-5)*q^180 + (5*a-13)*q^181 + -a*q^182 + (-9*a+10)*q^183 + (2*a+9)*q^184 + (4*a-9)*q^185 + (-5*a+14)*q^186 + (-a+4)*q^187 + (a+3)*q^188 + (-2*a+1)*q^189 + -a*q^190 + (-13*a+6)*q^191 + a*q^192 + (5*a+9)*q^193 + (5*a+4)*q^194 + (a-2)*q^195 + (a-1)*q^196 + (9*a-14)*q^197 + (-3*a+2)*q^198 + (4*a+13)*q^199 + (8*a-4)*q^200 +  ...

-------------------------------------------------------
133C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2 + Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 13
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 3^2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 11.235403462858361494 + 0.10654669078090316087e-3i
Omega-         = 1.7678544325887595189 + -0.17083733879655364396e-4i
L(1)           =

HECKE EIGENFORM:
a^2+a-3 = 0,
f(q) = q + a*q^2 + (-a-2)*q^3 + (-a+1)*q^4 + -3*q^5 + (-a-3)*q^6 + 1*q^7 + -3*q^8 + (3*a+4)*q^9 + -3*a*q^10 + (-a-3)*q^11 + 1*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 + 1*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 + a*q^38 + (-a-4)*q^39 + 9*q^40 + (a+3)*q^41 + (-a-3)*q^42 + -10*q^43 + a*q^44 + (-9*a-12)*q^45 + -3*a*q^46 + (-4*a-3)*q^47 + (3*a+7)*q^48 + 1*q^49 + 4*a*q^50 + (2*a+3)*q^51 + (5*a-7)*q^52 + 3*a*q^53 + (-7*a-12)*q^54 + (3*a+9)*q^55 + -3*q^56 + (-a-2)*q^57 + (6*a-9)*q^58 + (4*a+3)*q^59 + -3*q^60 + (4*a+5)*q^61 + -3*q^62 + (3*a+4)*q^63 + (6*a+1)*q^64 + (-6*a+3)*q^65 + (5*a+12)*q^66 + (3*a+5)*q^67 + (5*a-6)*q^68 + (3*a+6)*q^69 + -3*a*q^70 + (-4*a+3)*q^71 + (-9*a-12)*q^72 + (-5*a-10)*q^73 + (a-6)*q^74 + (-4*a-8)*q^75 + (-a+1)*q^76 + (-a-3)*q^77 + (-3*a-3)*q^78 + (-4*a+2)*q^79 + (3*a+6)*q^80 + (6*a+22)*q^81 + (2*a+3)*q^82 + (3*a-6)*q^83 + 1*q^84 + (-3*a+9)*q^85 + -10*a*q^86 + 3*q^87 + (3*a+9)*q^88 + (2*a-6)*q^89 + (-3*a-27)*q^90 + (2*a-1)*q^91 + (3*a-3)*q^92 + (2*a+5)*q^93 + (a-12)*q^94 + -3*q^95 + (-2*a-3)*q^96 + (-2*a+5)*q^97 + a*q^98 + (-10*a-21)*q^99 + (-4*a+4)*q^100 + (-2*a-9)*q^101 + (a+6)*q^102 + (4*a-7)*q^103 + (-6*a+3)*q^104 + (3*a+6)*q^105 + (-3*a+9)*q^106 + (-4*a-15)*q^107 + (3*a+1)*q^108 + (4*a-1)*q^109 + (6*a+9)*q^110 + (3*a+8)*q^111 + (-a-2)*q^112 + (a+12)*q^113 + (-a-3)*q^114 + 9*q^115 + (-9*a+12)*q^116 + (-a+14)*q^117 + (-a+12)*q^118 + (a-3)*q^119 + (-9*a-18)*q^120 + (5*a+1)*q^121 + (a+12)*q^122 + (-4*a-9)*q^123 + (-a+2)*q^124 + 3*q^125 + (a+9)*q^126 + (6*a+2)*q^127 + (-3*a+12)*q^128 + (10*a+20)*q^129 + (9*a-18)*q^130 + (5*a-9)*q^131 + (-a-3)*q^132 + 1*q^133 + (2*a+9)*q^134 + (12*a+33)*q^135 + (-3*a+9)*q^136 + (-12*a-6)*q^137 + (3*a+9)*q^138 + 5*q^139 + (3*a-3)*q^140 + (7*a+18)*q^141 + (7*a-12)*q^142 + (-3*a-3)*q^143 + (-7*a-17)*q^144 + (9*a-9)*q^145 + (-5*a-15)*q^146 + (-a-2)*q^147 + (-3*a+5)*q^148 + (4*a+3)*q^149 + (-4*a-12)*q^150 + (-3*a-1)*q^151 + -3*q^152 + (-8*a-3)*q^153 + (-2*a-3)*q^154 + (3*a+3)*q^155 + (2*a-1)*q^156 + (-5*a-7)*q^157 + (6*a-12)*q^158 + (-3*a-9)*q^159 + (3*a-9)*q^160 + -3*q^161 + (16*a+18)*q^162 + (a+8)*q^163 + -a*q^164 + (-12*a-27)*q^165 + (-9*a+9)*q^166 + (2*a+9)*q^167 + (3*a+6)*q^168 + -8*a*q^169 + (12*a-9)*q^170 + (3*a+4)*q^171 + (10*a-10)*q^172 + (-6*a-6)*q^173 + 3*a*q^174 + 4*q^175 + (4*a+9)*q^176 + (-7*a-18)*q^177 + (-8*a+6)*q^178 + (9*a+9)*q^179 + (-6*a+15)*q^180 + (-a-13)*q^181 + (-3*a+6)*q^182 + (-9*a-22)*q^183 + 9*q^184 + (6*a+3)*q^185 + (3*a+6)*q^186 + (a+6)*q^187 + (-5*a+9)*q^188 + (-4*a-11)*q^189 + -3*a*q^190 + -11*a*q^191 + (-7*a-20)*q^192 + (7*a-7)*q^193 + (7*a-6)*q^194 + (3*a+12)*q^195 + (-a+1)*q^196 + 3*a*q^197 + (-11*a-30)*q^198 + (8*a+5)*q^199 + -12*q^200 +  ...

-------------------------------------------------------
133D (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^4*7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2 + Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 229
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2
Sha Bound      = 2^5

ANALYTIC INVARIANTS:

Omega+         = 3.1520100741498324536 + 0.54087267618313453593e-4i
Omega-         = 0.28342561309371749855e-4 + -3.7711730402624936434i
L(1)           = 1.5760050373069453486

HECKE EIGENFORM:
a^3-2*a^2-4*a+7 = 0,
f(q) = 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 + -1*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 + 1*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 + a*q^38 + (3*a^2-2*a-13)*q^39 + (-3*a^2+a+14)*q^40 + (6*a^2+a-27)*q^41 + (2*a^2-a-7)*q^42 + (2*a^2-2*a-8)*q^43 + (a^2-2*a+1)*q^44 + (5*a^2-2*a-25)*q^45 + (3*a^2+4*a-7)*q^46 + (3*a^2+a-10)*q^47 + (2*a^2-a-15)*q^48 + 1*q^49 + (-5*a^2-a+21)*q^50 + (-3*a^2+a+20)*q^51 + (-a+1)*q^52 + (-a^2-2*a+5)*q^53 + (a^2+7)*q^54 + (2*a^2-3*a-5)*q^55 + (-2*a^2+7)*q^56 + (-a^2+5)*q^57 + (-5*a^2-3*a+28)*q^58 + (-3*a^2+a+8)*q^59 + (a^2-a-2)*q^60 + (a^2+3*a-8)*q^61 + (3*a^2-3*a-14)*q^62 + (2*a^2-a-8)*q^63 + (-4*a^2+2*a+13)*q^64 + (-3*a^2+a+16)*q^65 + (-3*a^2+4*a+7)*q^66 + (2*a^2+3*a-11)*q^67 + (-3*a^2-4*a+13)*q^68 + (-5*a^2+21)*q^69 + (-a^2+7)*q^70 + (-a^2-3*a+6)*q^71 + (2*a^2-3*a-14)*q^72 + (-a^2-4*a+7)*q^73 + (a^2-2*a+7)*q^74 + (-4*a^2+4*a+20)*q^75 + (a^2-2)*q^76 + (a-3)*q^77 + (4*a^2-a-21)*q^78 + (-2*a^2-2*a+8)*q^79 + (-5*a^2+4*a+19)*q^80 + (-a^2+a+3)*q^81 + (13*a^2-3*a-42)*q^82 + (a^2+2*a+5)*q^83 + (a^2+a-4)*q^84 + (6*a^2-5*a-23)*q^85 + (2*a^2-14)*q^86 + (-7*a^2+7*a+30)*q^87 + (2*a^2-a-7)*q^88 + (-6*a^2+4*a+12)*q^89 + (8*a^2-5*a-35)*q^90 + (-a^2+a+4)*q^91 + (8*a^2+3*a-21)*q^92 + (7*a^2-3*a-34)*q^93 + (7*a^2+2*a-21)*q^94 + (a^2-a-4)*q^95 + (a^2-3*a)*q^96 + (3*a^2-3*a-20)*q^97 + a*q^98 + (-3*a^2+3*a+10)*q^99 + (-5*a^2-a+13)*q^100 + (-3*a^2+5*a+6)*q^101 + (-5*a^2+8*a+21)*q^102 + (-9*a^2+3*a+28)*q^103 + (-3*a^2+a+14)*q^104 + (-3*a^2+2*a+13)*q^105 + (-4*a^2+a+7)*q^106 + (a^2-a+10)*q^107 + (4*a^2+5*a-15)*q^108 + (-3*a^2+3*a+12)*q^109 + (a^2+3*a-14)*q^110 + (-5*a^2+4*a+17)*q^111 + (-2*a^2-a+10)*q^112 + (9*a^2-6*a-29)*q^113 + (-2*a^2+a+7)*q^114 + (3*a^2-3*a-14)*q^115 + (-5*a^2+2*a+9)*q^116 + (5*a^2-2*a-25)*q^117 + (-5*a^2-4*a+21)*q^118 + (2*a^2+a-11)*q^119 + (-7*a^2+4*a+35)*q^120 + (a^2-6*a-2)*q^121 + (5*a^2-4*a-7)*q^122 + (7*a^2-5*a-44)*q^123 + (-a^2+1)*q^124 + (a^2+3*a-10)*q^125 + (3*a^2-14)*q^126 + (-6*a+2)*q^127 + (-8*a^2+a+28)*q^128 + (6*a^2-4*a-26)*q^129 + (-5*a^2+4*a+21)*q^130 + (-2*a^2-a+13)*q^131 + (-3*a+5)*q^132 + -1*q^133 + (7*a^2-3*a-14)*q^134 + (5*a^2-a-30)*q^135 + (-5*a-7)*q^136 + (-4*a^2+4*a+18)*q^137 + (-10*a^2+a+35)*q^138 + (3*a^2-7*a-6)*q^139 + (a-1)*q^140 + (-a^2-2*a-1)*q^141 + (-5*a^2+2*a+7)*q^142 + (2*a^2-3*a-5)*q^143 + (5*a^2-6*a-24)*q^144 + (8*a^2-a-45)*q^145 + (-6*a^2+3*a+7)*q^146 + (-a^2+5)*q^147 + (2*a^2+5*a-11)*q^148 + (5*a^2-7*a-14)*q^149 + (-4*a^2+4*a+28)*q^150 + (-2*a^2+a+11)*q^151 + (2*a^2-7)*q^152 + (-7*a^2+7*a+32)*q^153 + (a^2-3*a)*q^154 + (-8*a^2+5*a+37)*q^155 + (a^2-a-2)*q^156 + (-4*a^2-5*a+21)*q^157 + (-6*a^2+14)*q^158 + (2*a^2-a-3)*q^159 + (-3*a+7)*q^160 + (-a^2-a)*q^161 + (-a^2-a+7)*q^162 + (5*a^2+2*a-15)*q^163 + (11*a^2+8*a-37)*q^164 + (5*a^2-5*a-18)*q^165 + (4*a^2+9*a-7)*q^166 + (-7*a^2-a+38)*q^167 + (-a^2+2*a+7)*q^168 + (-3*a^2+a+3)*q^169 + (7*a^2+a-42)*q^170 + (-2*a^2+a+8)*q^171 + (-2*a+2)*q^172 + (6*a^2-32)*q^173 + (-7*a^2+2*a+49)*q^174 + (3*a^2-a-11)*q^175 + (a^2+5*a-16)*q^176 + (-a^2+4*a+5)*q^177 + (-8*a^2-12*a+42)*q^178 + (8*a^2-5*a-25)*q^179 + (a^2+a-6)*q^180 + (5*a-5)*q^181 + (-a^2+7)*q^182 + (-a^2+2*a-5)*q^183 + (13*a^2+3*a-42)*q^184 + (3*a^2+a-22)*q^185 + (11*a^2-6*a-49)*q^186 + (-a^2-6*a+19)*q^187 + (10*a^2+5*a-29)*q^188 + (a^2-3*a-4)*q^189 + (a^2-7)*q^190 + (a^2+6*a-11)*q^191 + (-5*a^2+6*a+23)*q^192 + (-4*a^2+5*a+3)*q^193 + (3*a^2-8*a-21)*q^194 + (-9*a^2+4*a+45)*q^195 + (a^2-2)*q^196 + (a^2+8*a-3)*q^197 + (-3*a^2-2*a+21)*q^198 + (-a^2+5*a-10)*q^199 + (-a^2-5*a-7)*q^200 +  ...

-------------------------------------------------------
133E (old = 19A), dim = 1

CONGRUENCES:
Modular Degree = 3*7
Ker(ModPolar)  = Z/3*7 + Z/3*7
= C(Z/3 + Z/3) + D(Z/7 + Z/7)

-------------------------------------------------------
Gamma_0(134)
Weight 2

-------------------------------------------------------
J_0(134), dim = 16

-------------------------------------------------------
134A (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3*5^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*5^2 + Z/2*5^2
= B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + C(Z/5 + Z/5) + E(Z/5 + Z/5)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 11*43
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 2.1868549368270631485 + 0.41381266039961637543e-4i
Omega-         = 0.26910915711771711457e-4 + -3.1935916019485521228i
L(1)           = 0.72895164573952880519

HECKE EIGENFORM:
a^3-a^2-8*a+11 = 0,
f(q) = q + -1*q^2 + a*q^3 + 1*q^4 + (a^2+a-5)*q^5 + -a*q^6 + (-2*a^2-2*a+12)*q^7 + -1*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 + 1*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 + -1*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 + -2*q^38 + (a^2+6*a-11)*q^39 + (-a^2-a+5)*q^40 + (2*a^2-2*a-12)*q^41 + (4*a^2+4*a-22)*q^42 + (3*a^2+a-17)*q^43 + (-a^2-2*a+6)*q^44 + (2*a^2+2*a-7)*q^45 + (-a+4)*q^46 + (a^2+2*a-6)*q^47 + a*q^48 + (4*a+5)*q^49 + (-2*a^2-3*a+13)*q^50 + (-2*a^2-3*a+11)*q^51 + (a^2-2)*q^52 + (-2*a^2+a+10)*q^53 + (-a^2-2*a+11)*q^54 + (-3*a^2-5*a+14)*q^55 + (2*a^2+2*a-12)*q^56 + 2*a*q^57 + (-6*a^2-6*a+36)*q^59 + (2*a^2+3*a-11)*q^60 + (-2*a^2+a+18)*q^61 + (-4*a^2-2*a+22)*q^62 + (-2*a^2-4*a+8)*q^63 + 1*q^64 + (3*a^2+3*a-12)*q^65 + (3*a^2+2*a-11)*q^66 + 1*q^67 + (-a^2-a+5)*q^68 + (a^2-4*a)*q^69 + (2*a^2+4*a-6)*q^70 + (3*a^2+5*a-17)*q^71 + (-a^2+3)*q^72 + (3*a^2+4*a-26)*q^73 + (2*a^2+4*a-14)*q^74 + (5*a^2+3*a-22)*q^75 + 2*q^76 + (4*a^2+6*a-16)*q^77 + (-a^2-6*a+11)*q^78 + (-2*a^2+2*a+14)*q^79 + (a^2+a-5)*q^80 + (-3*a-2)*q^81 + (-2*a^2+2*a+12)*q^82 + (2*a^2-2*a-18)*q^83 + (-4*a^2-4*a+22)*q^84 + (-2*a^2-3*a+8)*q^85 + (-3*a^2-a+17)*q^86 + (a^2+2*a-6)*q^88 + (-2*a^2-a+18)*q^89 + (-2*a^2-2*a+7)*q^90 + (-4*a^2-6*a+20)*q^91 + (a-4)*q^92 + (6*a^2+10*a-44)*q^93 + (-a^2-2*a+6)*q^94 + (2*a^2+2*a-10)*q^95 + -a*q^96 + (-4*a^2-6*a+24)*q^97 + (-4*a-5)*q^98 + (-2*a^2-7*a+15)*q^99 + (2*a^2+3*a-13)*q^100 + (-2*a^2-a+18)*q^101 + (2*a^2+3*a-11)*q^102 + (-3*a+8)*q^103 + (-a^2+2)*q^104 + (-6*a^2-10*a+22)*q^105 + (2*a^2-a-10)*q^106 + (6*a^2+2*a-32)*q^107 + (a^2+2*a-11)*q^108 + (-a^2+3*a-3)*q^109 + (3*a^2+5*a-14)*q^110 + (-6*a^2-2*a+22)*q^111 + (-2*a^2-2*a+12)*q^112 + (4*a-4)*q^113 + -2*a*q^114 + (-2*a^2-a+9)*q^115 + (4*a^2-3*a-5)*q^117 + (6*a^2+6*a-36)*q^118 + (2*a^2+4*a-6)*q^119 + (-2*a^2-3*a+11)*q^120 + (5*a^2+5*a-30)*q^121 + (2*a^2-a-18)*q^122 + (4*a-22)*q^123 + (4*a^2+2*a-22)*q^124 + (-2*a^2+a+13)*q^125 + (2*a^2+4*a-8)*q^126 + (-5*a^2-3*a+31)*q^127 + -1*q^128 + (4*a^2+7*a-33)*q^129 + (-3*a^2-3*a+12)*q^130 + 6*a*q^131 + (-3*a^2-2*a+11)*q^132 + (-4*a^2-4*a+24)*q^133 + -1*q^134 + (-2*a^2+11)*q^135 + (a^2+a-5)*q^136 + (-2*a^2-2*a+16)*q^137 + (-a^2+4*a)*q^138 + (4*a^2+8*a-28)*q^139 + (-2*a^2-4*a+6)*q^140 + (3*a^2+2*a-11)*q^141 + (-3*a^2-5*a+17)*q^142 + (-3*a^2-9*a+21)*q^143 + (a^2-3)*q^144 + (-3*a^2-4*a+26)*q^146 + (4*a^2+5*a)*q^147 + (-2*a^2-4*a+14)*q^148 + 6*q^149 + (-5*a^2-3*a+22)*q^150 + (7*a^2+6*a-38)*q^151 + -2*q^152 + (-2*a^2-2*a+7)*q^153 + (-4*a^2-6*a+16)*q^154 + (2*a^2+4*a)*q^155 + (a^2+6*a-11)*q^156 + (4*a^2+6*a-20)*q^157 + (2*a^2-2*a-14)*q^158 + (-a^2-6*a+22)*q^159 + (-a^2-a+5)*q^160 + (4*a^2+4*a-26)*q^161 + (3*a+2)*q^162 + (2*a^2+2*a-20)*q^163 + (2*a^2-2*a-12)*q^164 + (-8*a^2-10*a+33)*q^165 + (-2*a^2+2*a+18)*q^166 + (a^2-2*a-14)*q^167 + (4*a^2+4*a-22)*q^168 + (5*a^2-3*a-20)*q^169 + (2*a^2+3*a-8)*q^170 + (2*a^2-6)*q^171 + (3*a^2+a-17)*q^172 + (-8*a^2-10*a+48)*q^173 + (-2*a^2-6*a-2)*q^175 + (-a^2-2*a+6)*q^176 + (-12*a^2-12*a+66)*q^177 + (2*a^2+a-18)*q^178 + (-4*a^2-a+32)*q^179 + (2*a^2+2*a-7)*q^180 + (4*a^2+6*a-32)*q^181 + (4*a^2+6*a-20)*q^182 + (-a^2+2*a+22)*q^183 + (-a+4)*q^184 + (-4*a^2-8*a+18)*q^185 + (-6*a^2-10*a+44)*q^186 + (3*a^2+5*a-14)*q^187 + (a^2+2*a-6)*q^188 + (6*a^2+4*a-44)*q^189 + (-2*a^2-2*a+10)*q^190 + (-4*a^2-4*a+32)*q^191 + a*q^192 + (6*a^2+7*a-38)*q^193 + (4*a^2+6*a-24)*q^194 + (6*a^2+12*a-33)*q^195 + (4*a+5)*q^196 + (a^2-4*a+6)*q^197 + (2*a^2+7*a-15)*q^198 + (-5*a^2-3*a+31)*q^199 + (-2*a^2-3*a+13)*q^200 +  ...

-------------------------------------------------------
134B (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3*19
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*19 + Z/2*19
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + D(Z/19 + Z/19)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 3^4
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 17
Torsion Bound  = 17
|L(1)/Omega|   = 19/17
Sha Bound      = 17*19

ANALYTIC INVARIANTS:

Omega+         = 4.1674252047560784488 + -0.15790861374394757034e-4i
Omega-         = 0.12755114542897079862e-3 + 9.0747460112435670746i
L(1)           = 4.6577105229961122363

HECKE EIGENFORM:
a^3-3*a^2+1 = 0,
f(q) = q + 1*q^2 + a*q^3 + 1*q^4 + (-a^2+a+1)*q^5 + a*q^6 + (2*a^2-6*a)*q^7 + 1*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 + 1*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 + 1*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 + (-4*a^2+12*a+2)*q^38 + (a^2-2*a-3)*q^39 + (-a^2+a+1)*q^40 + (2*a^2-6*a)*q^41 + -2*q^42 + (a^2-7*a+5)*q^43 + (-3*a^2+6*a+2)*q^44 + (-2*a^2-2*a-1)*q^45 + (4*a^2-9*a-4)*q^46 + (a^2-2*a+6)*q^47 + a*q^48 + (-4*a+5)*q^49 + (2*a^2+a-5)*q^50 + (2*a^2-3*a+1)*q^51 + (3*a^2-8*a-2)*q^52 + (-2*a^2+5*a-2)*q^53 + (3*a^2-6*a-1)*q^54 + (a^2+5*a+2)*q^55 + (2*a^2-6*a)*q^56 + (2*a+4)*q^57 + -4*q^58 + (-2*a^2+6*a)*q^59 + (-2*a^2+a+1)*q^60 + (-2*a^2+5*a+6)*q^61 + (-2*a+6)*q^62 + (-6*a^2+16*a)*q^63 + 1*q^64 + (3*a^2-7*a-4)*q^65 + (-3*a^2+2*a+3)*q^66 + -1*q^67 + (-a^2+5*a-3)*q^68 + (3*a^2-4*a-4)*q^69 + (2*a^2-4*a-2)*q^70 + (-a^2-a+7)*q^71 + (a^2-3)*q^72 + (3*a^2-12*a+6)*q^73 + (-6*a^2+16*a+2)*q^74 + (7*a^2-5*a-2)*q^75 + (-4*a^2+12*a+2)*q^76 + (4*a^2-6*a-12)*q^77 + (a^2-2*a-3)*q^78 + (-2*a^2+2*a+2)*q^79 + (-a^2+a+1)*q^80 + (-a+6)*q^81 + (2*a^2-6*a)*q^82 + (-6*a^2+18*a+6)*q^83 + -2*q^84 + (-2*a^2+a)*q^85 + (a^2-7*a+5)*q^86 + -4*a*q^87 + (-3*a^2+6*a+2)*q^88 + (6*a^2-19*a+2)*q^89 + (-2*a^2-2*a-1)*q^90 + (-4*a^2+6*a+16)*q^91 + (4*a^2-9*a-4)*q^92 + (-2*a^2+6*a)*q^93 + (a^2-2*a+6)*q^94 + (-6*a^2+10*a+6)*q^95 + a*q^96 + (-4*a^2+14*a+4)*q^97 + (-4*a+5)*q^98 + (2*a^2-15*a-3)*q^99 + (2*a^2+a-5)*q^100 + (6*a^2-13*a-10)*q^101 + (2*a^2-3*a+1)*q^102 + (4*a^2-5*a-8)*q^103 + (3*a^2-8*a-2)*q^104 + (2*a^2-2*a-2)*q^105 + (-2*a^2+5*a-2)*q^106 + (2*a^2+6*a-16)*q^107 + (3*a^2-6*a-1)*q^108 + (9*a^2-21*a-1)*q^109 + (a^2+5*a+2)*q^110 + (-2*a^2+2*a+6)*q^111 + (2*a^2-6*a)*q^112 + (-8*a^2+20*a-8)*q^113 + (2*a+4)*q^114 + (2*a^2-9*a-5)*q^115 + -4*q^116 + (-8*a^2+21*a+5)*q^117 + (-2*a^2+6*a)*q^118 + (-6*a^2+20*a-10)*q^119 + (-2*a^2+a+1)*q^120 + (-3*a^2+15*a+2)*q^121 + (-2*a^2+5*a+6)*q^122 + -2*q^123 + (-2*a+6)*q^124 + (-2*a^2-7*a-5)*q^125 + (-6*a^2+16*a)*q^126 + (7*a^2-17*a-1)*q^127 + 1*q^128 + (-4*a^2+5*a-1)*q^129 + (3*a^2-7*a-4)*q^130 + (-2*a+4)*q^131 + (-3*a^2+2*a+3)*q^132 + (4*a^2-4*a-24)*q^133 + -1*q^134 + (-2*a^2-4*a-1)*q^135 + (-a^2+5*a-3)*q^136 + (-2*a^2-2*a+8)*q^137 + (3*a^2-4*a-4)*q^138 + (4*a^2-16*a+4)*q^139 + (2*a^2-4*a-2)*q^140 + (a^2+6*a-1)*q^141 + (-a^2-a+7)*q^142 + (9*a^2-19*a-19)*q^143 + (a^2-3)*q^144 + (4*a^2-4*a-4)*q^145 + (3*a^2-12*a+6)*q^146 + (-4*a^2+5*a)*q^147 + (-6*a^2+16*a+2)*q^148 + (4*a^2-8*a-18)*q^149 + (7*a^2-5*a-2)*q^150 + (-a^2+2*a-10)*q^151 + (-4*a^2+12*a+2)*q^152 + (6*a^2-14*a+7)*q^153 + (4*a^2-6*a-12)*q^154 + (-2*a^2+4*a+4)*q^155 + (a^2-2*a-3)*q^156 + (-12*a^2+26*a+8)*q^157 + (-2*a^2+2*a+2)*q^158 + (-a^2-2*a+2)*q^159 + (-a^2+a+1)*q^160 + (-8*a^2+16*a+18)*q^161 + (-a+6)*q^162 + (2*a^2+2*a-12)*q^163 + (2*a^2-6*a)*q^164 + (8*a^2+2*a-1)*q^165 + (-6*a^2+18*a+6)*q^166 + (a^2-6*a+6)*q^167 + -2*q^168 + (-11*a^2+23*a+12)*q^169 + (-2*a^2+a)*q^170 + (14*a^2-32*a-6)*q^171 + (a^2-7*a+5)*q^172 + (4*a^2-14*a-4)*q^173 + -4*a*q^174 + (-10*a^2+26*a-2)*q^175 + (-3*a^2+6*a+2)*q^176 + 2*q^177 + (6*a^2-19*a+2)*q^178 + (4*a^2-a-16)*q^179 + (-2*a^2-2*a-1)*q^180 + (-2*a+20)*q^181 + (-4*a^2+6*a+16)*q^182 + (-a^2+6*a+2)*q^183 + (4*a^2-9*a-4)*q^184 + (-4*a^2+12*a+6)*q^185 + (-2*a^2+6*a)*q^186 + (a^2-11*a+6)*q^187 + (a^2-2*a+6)*q^188 + (-2*a^2+12)*q^189 + (-6*a^2+10*a+6)*q^190 + (8*a^2-20*a+8)*q^191 + a*q^192 + (6*a^2-27*a+2)*q^193 + (-4*a^2+14*a+4)*q^194 + (2*a^2-4*a-3)*q^195 + (-4*a+5)*q^196 + (11*a^2-28*a-2)*q^197 + (2*a^2-15*a-3)*q^198 + (-9*a^2+31*a-1)*q^199 + (2*a^2+a-5)*q^200 +  ...

-------------------------------------------------------
134C (old = 67A), dim = 1

CONGRUENCES:
Modular Degree = 5^3
Ker(ModPolar)  = Z/5 + Z/5 + Z/5^2 + Z/5^2
= A(Z/5 + Z/5) + E(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
134D (old = 67B), dim = 2

CONGRUENCES:
Modular Degree = 2^4*19
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*19 + Z/2*19
= B(Z/19 + Z/19) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
134E (old = 67C), dim = 2

CONGRUENCES:
Modular Degree = 2^4*5^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*5 + Z/2*5 + Z/2*5 + Z/2*5 + Z/2*5 + Z/2*5
= A(Z/5 + Z/5) + C(Z/5 + Z/5 + Z/5 + Z/5) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(135)
Weight 2

-------------------------------------------------------
J_0(135), dim = 13

-------------------------------------------------------
135A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= B(Z/2 + Z/2) + E(Z/3 + Z/3) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 3.7814138716658199599 + -0.31863440998510323184e-4i
Omega-         = 0.15655137957662894992e-4 + -1.7031820359093501569i
L(1)           =
w1             = -1.8906991082639311485 + -0.85157508623417582331i
w2             = -0.15655137957662894992e-4 + 1.7031820359093501569i
c4             = 144.00185546143236237 + -0.1031620380234081895e-1i
c6             = -3672.0663648447868282 + 0.65464863390671339101e-1i
j              = -491.52157281484698761 + 0.11317429047948574265i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + 2*q^4 + -1*q^5 + -3*q^7 + 2*q^10 + -2*q^11 + -5*q^13 + 6*q^14 + -4*q^16 + -8*q^17 + 1*q^19 + -2*q^20 + 4*q^22 + 6*q^23 + 1*q^25 + 10*q^26 + -6*q^28 + 2*q^29 + 8*q^32 + 16*q^34 + 3*q^35 + 5*q^37 + -2*q^38 + -10*q^41 + 4*q^43 + -4*q^44 + -12*q^46 + 4*q^47 + 2*q^49 + -2*q^50 + -10*q^52 + -2*q^53 + 2*q^55 + -4*q^58 + -8*q^59 + 7*q^61 + -8*q^64 + 5*q^65 + -9*q^67 + -16*q^68 + -6*q^70 + 2*q^71 + -5*q^73 + -10*q^74 + 2*q^76 + 6*q^77 + -3*q^79 + 4*q^80 + 20*q^82 + 6*q^83 + 8*q^85 + -8*q^86 + -12*q^89 + 15*q^91 + 12*q^92 + -8*q^94 + -1*q^95 + -13*q^97 + -4*q^98 + 2*q^100 + 17*q^103 + 4*q^106 + 6*q^107 + -10*q^109 + -4*q^110 + 12*q^112 + 10*q^113 + -6*q^115 + 4*q^116 + 16*q^118 + 24*q^119 + -7*q^121 + -14*q^122 + -1*q^125 + -8*q^127 + -10*q^130 + 12*q^131 + -3*q^133 + 18*q^134 + -6*q^137 + -13*q^139 + 6*q^140 + -4*q^142 + 10*q^143 + -2*q^145 + 10*q^146 + 10*q^148 + -4*q^149 + 1*q^151 + -12*q^154 + 2*q^157 + 6*q^158 + -8*q^160 + -18*q^161 + -19*q^163 + -20*q^164 + -12*q^166 + -12*q^167 + 12*q^169 + -16*q^170 + 8*q^172 + -12*q^173 + -3*q^175 + 8*q^176 + 24*q^178 + 22*q^179 + 5*q^181 + -30*q^182 + -5*q^185 + 16*q^187 + 8*q^188 + 2*q^190 + -4*q^191 + 5*q^193 + 26*q^194 + 4*q^196 + -17*q^199 +  ...

-------------------------------------------------------
135B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2^2*3^2 + Z/2^2*3^2
= A(Z/2 + Z/2) + C(Z/3 + Z/3) + F(Z/2 + Z/2) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 0.98332094942824377246 + 0.34373070918439187994e-5i
Omega-         = 0.10894233235477580192e-4 + -2.183182372852369675i
L(1)           = 1.9666418988685030319
w1             = -0.49165502759750414744 + -1.0915929050797307594i
w2             = -0.98332094942824377246 + -0.34373070918439187994e-5i
c4             = 1296.0874867236162616 + -0.14288638054166441343e-1i
c6             = 99152.080810568663537 + -2.3934834708084717095i
j              = -491.5449403329096331 + -0.96004230801754878074e-2i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 2*q^4 + 1*q^5 + -3*q^7 + 2*q^10 + 2*q^11 + -5*q^13 + -6*q^14 + -4*q^16 + 8*q^17 + 1*q^19 + 2*q^20 + 4*q^22 + -6*q^23 + 1*q^25 + -10*q^26 + -6*q^28 + -2*q^29 + -8*q^32 + 16*q^34 + -3*q^35 + 5*q^37 + 2*q^38 + 10*q^41 + 4*q^43 + 4*q^44 + -12*q^46 + -4*q^47 + 2*q^49 + 2*q^50 + -10*q^52 + 2*q^53 + 2*q^55 + -4*q^58 + 8*q^59 + 7*q^61 + -8*q^64 + -5*q^65 + -9*q^67 + 16*q^68 + -6*q^70 + -2*q^71 + -5*q^73 + 10*q^74 + 2*q^76 + -6*q^77 + -3*q^79 + -4*q^80 + 20*q^82 + -6*q^83 + 8*q^85 + 8*q^86 + 12*q^89 + 15*q^91 + -12*q^92 + -8*q^94 + 1*q^95 + -13*q^97 + 4*q^98 + 2*q^100 + 17*q^103 + 4*q^106 + -6*q^107 + -10*q^109 + 4*q^110 + 12*q^112 + -10*q^113 + -6*q^115 + -4*q^116 + 16*q^118 + -24*q^119 + -7*q^121 + 14*q^122 + 1*q^125 + -8*q^127 + -10*q^130 + -12*q^131 + -3*q^133 + -18*q^134 + 6*q^137 + -13*q^139 + -6*q^140 + -4*q^142 + -10*q^143 + -2*q^145 + -10*q^146 + 10*q^148 + 4*q^149 + 1*q^151 + -12*q^154 + 2*q^157 + -6*q^158 + -8*q^160 + 18*q^161 + -19*q^163 + 20*q^164 + -12*q^166 + 12*q^167 + 12*q^169 + 16*q^170 + 8*q^172 + 12*q^173 + -3*q^175 + -8*q^176 + 24*q^178 + -22*q^179 + 5*q^181 + 30*q^182 + 5*q^185 + 16*q^187 + -8*q^188 + 2*q^190 + 4*q^191 + 5*q^193 + -26*q^194 + 4*q^196 + -17*q^199 +  ...

-------------------------------------------------------
135C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3^2 + Z/2*3^2
= B(Z/3 + Z/3) + D(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 13
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3^2
|L(1)/Omega|   = 1/3
Sha Bound      = 3^3

ANALYTIC INVARIANTS:

Omega+         = 2.8222753994022361503 + 0.32095388121101678776e-4i
Omega-         = 4.5330589729737948296 + 0.97707261118843142837e-4i
L(1)           = 0.94075846652824440418

HECKE EIGENFORM:
a^2+a-3 = 0,
f(q) = q + a*q^2 + (-a+1)*q^4 + 1*q^5 + (2*a+2)*q^7 + -3*q^8 + a*q^10 + -2*a*q^11 + (-2*a+2)*q^13 + 6*q^14 + (-a-2)*q^16 + (-2*a-3)*q^17 + (-2*a-1)*q^19 + (-a+1)*q^20 + (2*a-6)*q^22 + -3*q^23 + 1*q^25 + (4*a-6)*q^26 + (2*a-4)*q^28 + (2*a+6)*q^29 + (2*a-1)*q^31 + (-a+3)*q^32 + (-a-6)*q^34 + (2*a+2)*q^35 + 2*q^37 + (a-6)*q^38 + -3*q^40 + 2*a*q^41 + (-2*a-4)*q^43 + (-4*a+6)*q^44 + -3*a*q^46 + 4*a*q^47 + (4*a+9)*q^49 + a*q^50 + (-6*a+8)*q^52 + (-2*a-3)*q^53 + -2*a*q^55 + (-6*a-6)*q^56 + (4*a+6)*q^58 + (-2*a-6)*q^59 + (4*a+5)*q^61 + (-3*a+6)*q^62 + (6*a+1)*q^64 + (-2*a+2)*q^65 + (-4*a-10)*q^67 + (-a+3)*q^68 + 6*q^70 + (2*a+12)*q^71 + (-2*a+8)*q^73 + 2*a*q^74 + (-3*a+5)*q^76 + -12*q^77 + (2*a-7)*q^79 + (-a-2)*q^80 + (-2*a+6)*q^82 + 3*q^83 + (-2*a-3)*q^85 + (-2*a-6)*q^86 + 6*a*q^88 + 6*a*q^89 + (4*a-8)*q^91 + (3*a-3)*q^92 + (-4*a+12)*q^94 + (-2*a-1)*q^95 + 8*q^97 + (5*a+12)*q^98 + (-a+1)*q^100 + 12*q^101 + -4*q^103 + (6*a-6)*q^104 + (-a-6)*q^106 + -7*q^109 + (2*a-6)*q^110 + (-4*a-10)*q^112 + (4*a-6)*q^113 + -3*q^115 + -2*a*q^116 + (-4*a-6)*q^118 + (-6*a-18)*q^119 + (-4*a+1)*q^121 + (a+12)*q^122 + (5*a-7)*q^124 + 1*q^125 + (4*a-10)*q^127 + (-3*a+12)*q^128 + (4*a-6)*q^130 + 6*q^131 + (-2*a-14)*q^133 + (-6*a-12)*q^134 + (6*a+9)*q^136 + (-6*a+3)*q^137 + -4*q^139 + (2*a-4)*q^140 + (10*a+6)*q^142 + (-8*a+12)*q^143 + (2*a+6)*q^145 + (10*a-6)*q^146 + (-2*a+2)*q^148 + -10*a*q^149 + (-8*a-4)*q^151 + (6*a+3)*q^152 + -12*a*q^154 + (2*a-1)*q^155 + (6*a-4)*q^157 + (-9*a+6)*q^158 + (-a+3)*q^160 + (-6*a-6)*q^161 + 2*q^163 + (4*a-6)*q^164 + 3*a*q^166 + -3*q^167 + (-12*a+3)*q^169 + (-a-6)*q^170 + 2*q^172 + (6*a+3)*q^173 + (2*a+2)*q^175 + (2*a+6)*q^176 + (-6*a+18)*q^178 + (4*a-12)*q^179 + -7*q^181 + (-12*a+12)*q^182 + 9*q^184 + 2*q^185 + (2*a+12)*q^187 + (8*a-12)*q^188 + (a-6)*q^190 + (8*a+6)*q^191 + (6*a+14)*q^193 + 8*a*q^194 + (-a-3)*q^196 + (6*a-9)*q^197 + (4*a+8)*q^199 + -3*q^200 +  ...

-------------------------------------------------------
135D (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/3 + Z/3) + F(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 13
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 4.5330582644562458353 + 0.7819035276668099161e-4i
Omega-         = 2.8223793101543174595 + 0.6954402110940295428e-4i
L(1)           = 1.5110194217101984494

HECKE EIGENFORM:
a^2-a-3 = 0,
f(q) = q + a*q^2 + (a+1)*q^4 + -1*q^5 + (-2*a+2)*q^7 + 3*q^8 + -a*q^10 + -2*a*q^11 + (2*a+2)*q^13 + -6*q^14 + (a-2)*q^16 + (-2*a+3)*q^17 + (2*a-1)*q^19 + (-a-1)*q^20 + (-2*a-6)*q^22 + 3*q^23 + 1*q^25 + (4*a+6)*q^26 + (-2*a-4)*q^28 + (2*a-6)*q^29 + (-2*a-1)*q^31 + (-a-3)*q^32 + (a-6)*q^34 + (2*a-2)*q^35 + 2*q^37 + (a+6)*q^38 + -3*q^40 + 2*a*q^41 + (2*a-4)*q^43 + (-4*a-6)*q^44 + 3*a*q^46 + 4*a*q^47 + (-4*a+9)*q^49 + a*q^50 + (6*a+8)*q^52 + (-2*a+3)*q^53 + 2*a*q^55 + (-6*a+6)*q^56 + (-4*a+6)*q^58 + (-2*a+6)*q^59 + (-4*a+5)*q^61 + (-3*a-6)*q^62 + (-6*a+1)*q^64 + (-2*a-2)*q^65 + (4*a-10)*q^67 + (-a-3)*q^68 + 6*q^70 + (2*a-12)*q^71 + (2*a+8)*q^73 + 2*a*q^74 + (3*a+5)*q^76 + 12*q^77 + (-2*a-7)*q^79 + (-a+2)*q^80 + (2*a+6)*q^82 + -3*q^83 + (2*a-3)*q^85 + (-2*a+6)*q^86 + -6*a*q^88 + 6*a*q^89 + (-4*a-8)*q^91 + (3*a+3)*q^92 + (4*a+12)*q^94 + (-2*a+1)*q^95 + 8*q^97 + (5*a-12)*q^98 + (a+1)*q^100 + -12*q^101 + -4*q^103 + (6*a+6)*q^104 + (a-6)*q^106 + -7*q^109 + (2*a+6)*q^110 + (4*a-10)*q^112 + (4*a+6)*q^113 + -3*q^115 + -2*a*q^116 + (4*a-6)*q^118 + (-6*a+18)*q^119 + (4*a+1)*q^121 + (a-12)*q^122 + (-5*a-7)*q^124 + -1*q^125 + (-4*a-10)*q^127 + (-3*a-12)*q^128 + (-4*a-6)*q^130 + -6*q^131 + (2*a-14)*q^133 + (-6*a+12)*q^134 + (-6*a+9)*q^136 + (-6*a-3)*q^137 + -4*q^139 + (2*a+4)*q^140 + (-10*a+6)*q^142 + (-8*a-12)*q^143 + (-2*a+6)*q^145 + (10*a+6)*q^146 + (2*a+2)*q^148 + -10*a*q^149 + (8*a-4)*q^151 + (6*a-3)*q^152 + 12*a*q^154 + (2*a+1)*q^155 + (-6*a-4)*q^157 + (-9*a-6)*q^158 + (a+3)*q^160 + (-6*a+6)*q^161 + 2*q^163 + (4*a+6)*q^164 + -3*a*q^166 + 3*q^167 + (12*a+3)*q^169 + (-a+6)*q^170 + 2*q^172 + (6*a-3)*q^173 + (-2*a+2)*q^175 + (2*a-6)*q^176 + (6*a+18)*q^178 + (4*a+12)*q^179 + -7*q^181 + (-12*a-12)*q^182 + 9*q^184 + -2*q^185 + (-2*a+12)*q^187 + (8*a+12)*q^188 + (-a-6)*q^190 + (8*a-6)*q^191 + (-6*a+14)*q^193 + 8*a*q^194 + (a-3)*q^196 + (6*a+9)*q^197 + (-4*a+8)*q^199 + 3*q^200 +  ...

-------------------------------------------------------
135E (old = 45A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= A(Z/3 + Z/3) + D(Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
135F (old = 27A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/3 + Z/3)

-------------------------------------------------------
135G (old = 15A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3^2 + Z/2*3^2
= B(Z/3 + Z/3) + C(Z/3 + Z/3) + E(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(136)
Weight 2

-------------------------------------------------------
J_0(136), dim = 15

-------------------------------------------------------
136A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2^2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.4336245572497696743 + -0.51242398011782771087e-5i
Omega-         = 0.10963901274029108145e-4 + -1.8159750410627385182i
L(1)           = 0.71681227862946376149
w1             = -0.10963901274029108145e-4 + 1.8159750410627385182i
w2             = 1.4336245572497696743 + -0.51242398011782771087e-5i
c4             = 400.00701248295133262 + 0.33363724631527179944e-2i
c6             = 5824.152967237879321 + 0.22262430259898067621i
j              = 3676.4703111449877413 + 0.21318975019498050845i

HECKE EIGENFORM:
f(q) = q + 2*q^3 + 1*q^9 + 2*q^11 + -6*q^13 + -1*q^17 + 4*q^19 + 4*q^23 + -5*q^25 + -4*q^27 + -8*q^31 + 4*q^33 + -4*q^37 + -12*q^39 + 6*q^41 + 8*q^43 + -8*q^47 + -7*q^49 + -2*q^51 + 10*q^53 + 8*q^57 + 12*q^61 + 8*q^67 + 8*q^69 + 12*q^71 + 2*q^73 + -10*q^75 + -4*q^79 + -11*q^81 + 16*q^83 + 10*q^89 + -16*q^93 + -18*q^97 + 2*q^99 + 10*q^101 + -18*q^107 + -8*q^111 + -6*q^113 + -6*q^117 + -7*q^121 + 12*q^123 + 8*q^127 + 16*q^129 + -2*q^131 + -10*q^137 + 6*q^139 + -16*q^141 + -12*q^143 + -14*q^147 + 6*q^149 + 8*q^151 + -1*q^153 + -2*q^157 + 20*q^159 + -2*q^163 + -8*q^167 + 23*q^169 + 4*q^171 + -24*q^173 + -12*q^179 + -20*q^181 + 24*q^183 + -2*q^187 + 16*q^191 + -10*q^193 + 20*q^197 + -4*q^199 +  ...

-------------------------------------------------------
136B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= A(Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 1.9435696833716899406 + 0.30265140875221941781e-5i
Omega-         = 0.17939689864112663437e-4 + 1.7365087913148398216i
L(1)           =
w1             = -1.9435696833716899406 + -0.30265140875221941781e-5i
w2             = 0.17939689864112663437e-4 + 1.7365087913148398216i
c4             = 208.00530125347841529 + 0.55110267347945029839e-2i
c6             = -1216.2594178867685579 + -0.16377241456037753855i
j              = 2067.9071057632392886 + 0.77213297651885442563e-1i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -2*q^5 + -2*q^7 + 1*q^9 + -6*q^11 + 2*q^13 + 4*q^15 + 1*q^17 + 4*q^21 + 6*q^23 + -1*q^25 + 4*q^27 + -10*q^29 + 2*q^31 + 12*q^33 + 4*q^35 + 6*q^37 + -4*q^39 + -6*q^41 + -8*q^43 + -2*q^45 + -3*q^49 + -2*q^51 + -10*q^53 + 12*q^55 + -8*q^59 + 14*q^61 + -2*q^63 + -4*q^65 + 4*q^67 + -12*q^69 + 2*q^71 + -14*q^73 + 2*q^75 + 12*q^77 + -10*q^79 + -11*q^81 + 8*q^83 + -2*q^85 + 20*q^87 + -10*q^89 + -4*q^91 + -4*q^93 + 2*q^97 + -6*q^99 + 10*q^101 + 8*q^103 + -8*q^105 + -18*q^107 + 6*q^109 + -12*q^111 + 10*q^113 + -12*q^115 + 2*q^117 + -2*q^119 + 25*q^121 + 12*q^123 + 12*q^125 + 4*q^127 + 16*q^129 + 14*q^131 + -8*q^135 + 6*q^137 + 14*q^139 + -12*q^143 + 20*q^145 + 6*q^147 + -10*q^149 + -12*q^151 + 1*q^153 + -4*q^155 + -2*q^157 + 20*q^159 + -12*q^161 + -22*q^163 + -24*q^165 + -6*q^167 + -9*q^169 + 6*q^173 + 2*q^175 + 16*q^177 + 8*q^179 + -2*q^181 + -28*q^183 + -12*q^185 + -6*q^187 + -8*q^189 + -6*q^193 + 8*q^195 + -10*q^197 + -14*q^199 +  ...

-------------------------------------------------------
136C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2^2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.1370218352802319386 + -0.16422002906441714468e-4i
Omega-         = 2.6776973250376600554 + 0.78740228738805634488e-4i
L(1)           = 0.56851091769941170382

HECKE EIGENFORM:
a^2+2*a-4 = 0,
f(q) = q + a*q^3 + 2*q^5 + -a*q^7 + (-2*a+1)*q^9 + -a*q^11 + (2*a+2)*q^13 + 2*a*q^15 + 1*q^17 + (-2*a-4)*q^19 + (2*a-4)*q^21 + -a*q^23 + -1*q^25 + (2*a-8)*q^27 + 2*q^29 + a*q^31 + (2*a-4)*q^33 + -2*a*q^35 + (-4*a-6)*q^37 + (-2*a+8)*q^39 + 2*q^41 + (2*a-4)*q^43 + (-4*a+2)*q^45 + (4*a+8)*q^47 + (-2*a-3)*q^49 + a*q^51 + -2*q^53 + -2*a*q^55 + -8*q^57 + (2*a+12)*q^59 + (4*a+2)*q^61 + (-5*a+8)*q^63 + (4*a+4)*q^65 + -12*q^67 + (2*a-4)*q^69 + (a+8)*q^71 + (4*a+10)*q^73 + -a*q^75 + (-2*a+4)*q^77 + (3*a+8)*q^79 + (-6*a+5)*q^81 + (-2*a+4)*q^83 + 2*q^85 + 2*a*q^87 + (2*a-10)*q^89 + (2*a-8)*q^91 + (-2*a+4)*q^93 + (-4*a-8)*q^95 + 2*q^97 + (-5*a+8)*q^99 + (-6*a-6)*q^101 + -8*q^103 + (4*a-8)*q^105 + -3*a*q^107 + 10*q^109 + (2*a-16)*q^111 + (4*a+10)*q^113 + -2*a*q^115 + (6*a-14)*q^117 + -a*q^119 + (-2*a-7)*q^121 + 2*a*q^123 + -12*q^125 + 2*a*q^127 + (-8*a+8)*q^129 + (9*a+8)*q^131 + 8*q^133 + (4*a-16)*q^135 + (2*a-10)*q^137 + (a-8)*q^139 + 16*q^141 + (2*a-8)*q^143 + 4*q^145 + (a-8)*q^147 + 6*q^149 + (-2*a+8)*q^151 + (-2*a+1)*q^153 + 2*a*q^155 + (-8*a-2)*q^157 + -2*a*q^159 + (-2*a+4)*q^161 + (-5*a-16)*q^163 + (4*a-8)*q^165 + (-3*a-16)*q^167 + 7*q^169 + (-2*a+12)*q^171 + 2*q^173 + a*q^175 + (8*a+8)*q^177 + (2*a+12)*q^179 + 10*q^181 + (-6*a+16)*q^183 + (-8*a-12)*q^185 + -a*q^187 + (12*a-8)*q^189 + (-4*a-8)*q^191 + (4*a+10)*q^193 + (-4*a+16)*q^195 + (4*a+2)*q^197 + (5*a+16)*q^199 +  ...

-------------------------------------------------------
136D (old = 68A), dim = 2

CONGRUENCES:
Modular Degree = 2^5*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/3 + Z/3 + Z/2*3 + Z/2*3) + F(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
136E (old = 34A), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2^3*3 + Z/2^3*3
= A(Z/2 + Z/2^2) + B(Z/2) + C(Z/2 + Z/2) + D(Z/3 + Z/3 + Z/2*3 + Z/2*3) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
136F (old = 17A), dim = 1

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2^2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(137)
Weight 2

-------------------------------------------------------
J_0(137), dim = 11

-------------------------------------------------------
137A (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 5^2*29
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 172.31125464576955489 + -0.8576313324930618267e-3i
Omega-         = 23.617872734615639459 + 0.84428906108446030828e-3i
L(1)           =

HECKE EIGENFORM:
a^4+3*a^3-4*a-1 = 0,
f(q) = 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 + (-a^3-a^2-3*a-2)*q^38 + (-5*a^3-9*a^2+5*a+5)*q^39 + (-a^3-2*a^2+7*a+2)*q^40 + (-2*a^3-2*a^2+9*a+2)*q^41 + (8*a^3+11*a^2-11*a-4)*q^42 + (2*a^3+2*a^2-9*a-7)*q^43 + (-3*a^3-10*a^2+13)*q^44 + (-a^3-2*a^2-4*a-1)*q^45 + (a^3-2*a^2-4*a)*q^46 + (-3*a-5)*q^47 + (2*a^2+5*a-3)*q^48 + (7*a^3+13*a^2-15*a-9)*q^49 + (-2*a^3-6*a^2+5*a+3)*q^50 + (a^3+8*a^2+6*a-5)*q^51 + (-4*a^2-2*a+5)*q^52 + (-a^3-4*a^2-a+4)*q^53 + (3*a^3+4*a^2-9*a-4)*q^54 + (-6*a^3-11*a^2+10*a+3)*q^55 + (-6*a^3-5*a^2+17*a+3)*q^56 + (8*a^2+12*a-3)*q^57 + (-2*a^3+a^2+7*a-1)*q^58 + (-7*a^3-12*a^2+13*a+11)*q^59 + (4*a^3+a^2-8*a-2)*q^60 + (-3*a^3-7*a^2+a+7)*q^61 + (-6*a^3-7*a^2+9*a+5)*q^62 + (2*a^3-2*a^2-11*a)*q^63 + (7*a^3+13*a^2-7*a-9)*q^64 + (7*a^3+8*a^2-17*a-5)*q^65 + (-3*a^3-7*a^2+2*a-1)*q^66 + (-a^3+4*a^2+11*a-6)*q^67 + (6*a^3+11*a^2-5*a-12)*q^68 + (3*a^3+4*a^2+a+4)*q^69 + (-14*a^3-16*a^2+31*a+9)*q^70 + (4*a^3+8*a^2-4*a-4)*q^71 + (-4*a^2-6*a-3)*q^72 + (-2*a^3+3*a-12)*q^73 + (a^3+3*a^2+a+2)*q^74 + (5*a^3+4*a^2-10*a+3)*q^75 + (6*a^3+11*a^2-4*a-11)*q^76 + (-13*a^3-25*a^2+19*a+17)*q^77 + (6*a^3+5*a^2-15*a-5)*q^78 + (-8*a^3-15*a^2+6*a+9)*q^79 + (5*a^3+9*a^2-10*a-3)*q^80 + (-a^2+a-1)*q^81 + (4*a^3+9*a^2-6*a-2)*q^82 + (3*a^3+14*a^2+8*a-15)*q^83 + (-5*a^3-3*a^2+6*a-2)*q^84 + (3*a^3+4*a^2)*q^85 + (-4*a^3-9*a^2+a+2)*q^86 + (a^3+5*a^2-6*a-14)*q^87 + (5*a^3+8*a^2-15*a-11)*q^88 + (3*a^3+6*a^2-3*a-1)*q^89 + (a^3-4*a^2-5*a-1)*q^90 + (4*a^3+5*a^2-16*a)*q^91 + (-5*a^3-6*a^2+8*a+9)*q^92 + (-5*a^3-7*a^2+6*a+12)*q^93 + (-3*a^2-5*a)*q^94 + (7*a^3+11*a^2-6*a-2)*q^95 + (-5*a^2-7*a+2)*q^96 + (a^3-3*a^2-a+8)*q^97 + (-8*a^3-15*a^2+19*a+7)*q^98 + (-3*a^3-5*a^2+12*a+14)*q^99 + (-6*a^3-9*a^2+7*a+12)*q^100 + (3*a^3+2*a^2-15*a-4)*q^101 + (5*a^3+6*a^2-a+1)*q^102 + (-4*a^3-4*a^2+9*a-10)*q^103 + (-6*a^3-8*a^2+9*a)*q^104 + (3*a^3+6*a^2-18*a-5)*q^105 + (-a^3-a^2-1)*q^106 + (-a^3-5*a^2+4*a+15)*q^107 + (3*a^3+9*a^2-11)*q^108 + (-4*a^3-6*a^2+4*a+4)*q^109 + (7*a^3+10*a^2-21*a-6)*q^110 + (-6*a^3-16*a^2-2*a+9)*q^111 + (11*a^3+19*a^2-19*a-12)*q^112 + (3*a^3+6*a^2-2*a-1)*q^113 + (8*a^3+12*a^2-3*a)*q^114 + (-4*a^3-a^2+12*a+3)*q^115 + (9*a^3+17*a^2-11*a-24)*q^116 + (3*a^3+4*a^2-a+4)*q^117 + (9*a^3+13*a^2-17*a-7)*q^118 + (8*a^2+8*a-7)*q^119 + (-11*a^3-16*a^2+12*a+4)*q^120 + (-3*a^3-16*a^2-4*a+30)*q^121 + (2*a^3+a^2-5*a-3)*q^122 + (-8*a^3-15*a^2+6*a+3)*q^123 + (a^3-9*a^2-5*a+16)*q^124 + (-3*a^3-a^2+13*a+3)*q^125 + (-8*a^3-11*a^2+8*a+2)*q^126 + (-3*a^2-a-2)*q^127 + (-10*a^3-15*a^2+17*a+13)*q^128 + (3*a^3+10*a^2+9*a+7)*q^129 + (-13*a^3-17*a^2+23*a+7)*q^130 + (-a^3+2*a^2+10*a+1)*q^131 + (4*a^3+14*a^2+a-15)*q^132 + (5*a^3+17*a^2-9)*q^133 + (7*a^3+11*a^2-10*a-1)*q^134 + (8*a^3+14*a^2-13*a-4)*q^135 + (-3*a^3-a^2+10*a+8)*q^136 + -1*q^137 + (-5*a^3+a^2+16*a+3)*q^138 + (-8*a^3-15*a^2+6*a+7)*q^139 + (8*a^3+5*a^2-15*a-4)*q^140 + (a^3+4*a^2+9*a+7)*q^141 + (-4*a^3-4*a^2+12*a+4)*q^142 + (-12*a^3-22*a^2+24*a+25)*q^143 + (2*a^3+4*a^2-7*a-8)*q^144 + (-5*a^2-3*a)*q^145 + (6*a^3+3*a^2-20*a-2)*q^146 + (11*a^3+13*a^2-24*a-2)*q^147 + (-4*a^3-13*a^2+15)*q^148 + (7*a^3+15*a^2-15*a-16)*q^149 + (-11*a^3-10*a^2+23*a+5)*q^150 + (-4*a^3-5*a^2+15*a+2)*q^151 + (-5*a^3-2*a^2+19*a+10)*q^152 + (3*a^3+a^2-13*a-12)*q^153 + (14*a^3+19*a^2-35*a-13)*q^154 + (2*a^3-a^2+a)*q^155 + (-3*a^3+3*a^2+9*a-4)*q^156 + (7*a^3+12*a^2-16*a-16)*q^157 + (9*a^3+6*a^2-23*a-8)*q^158 + (a^3+6*a^2+4*a-4)*q^159 + (-4*a^3-6*a^2+3*a+1)*q^160 + (a^3-a^2+5*a+7)*q^161 + (-a^3+a^2-a)*q^162 + (-a^3-4*a^2+3*a+3)*q^163 + (a^3-2*a^2-4*a)*q^164 + (-8*a^3-7*a^2+28*a+8)*q^165 + (5*a^3+8*a^2-3*a+3)*q^166 + (-9*a^2-15*a+4)*q^167 + (-4*a^3-16*a^2+3)*q^168 + (3*a^3+5*a^2-8*a-8)*q^169 + (-5*a^3+12*a+3)*q^170 + (3*a^3-2*a^2-20*a-13)*q^171 + (-a^3-3*a^2+4*a+10)*q^172 + (-11*a^3-20*a^2+14*a+19)*q^173 + (2*a^3-6*a^2-10*a+1)*q^174 + (-12*a^3-24*a^2+28*a+17)*q^175 + (-a^3+5*a^2+9*a-21)*q^176 + (-2*a^3-3*a^2+7*a-6)*q^177 + (-3*a^3-3*a^2+11*a+3)*q^178 + (3*a^3-a^2-20*a+6)*q^179 + (-5*a^3-a^2+11*a+3)*q^180 + (15*a^3+28*a^2-24*a-23)*q^181 + (-7*a^3-16*a^2+16*a+4)*q^182 + (5*a^3+11*a^2-8)*q^183 + (7*a^3+12*a^2-3*a-5)*q^184 + (3*a^3+a^2-14*a-4)*q^185 + (8*a^3+6*a^2-8*a-5)*q^186 + (8*a^3+21*a^2-13*a-38)*q^187 + (-3*a^3-5*a^2+6*a+10)*q^188 + (14*a^3+27*a^2-21*a-16)*q^189 + (-10*a^3-6*a^2+26*a+7)*q^190 + (4*a^3+12*a^2-4*a-12)*q^191 + (-5*a^3-11*a^2-8*a+6)*q^192 + (-13*a^3-30*a^2+7*a+25)*q^193 + (-6*a^3-a^2+12*a+1)*q^194 + (4*a^3+13*a^2-5*a-2)*q^195 + (-5*a^3-7*a^2+5*a+10)*q^196 + (5*a^3+10*a^2-19*a-19)*q^197 + (4*a^3+12*a^2+2*a-3)*q^198 + (12*a^3+25*a^2-9*a-14)*q^199 + (13*a^3+19*a^2-22*a-12)*q^200 +  ...

-------------------------------------------------------
137B (new) , dim = 7

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^2*401*895241
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 2*17
Torsion Bound  = 2*17
|L(1)/Omega|   = 2^3/17
Sha Bound      = 2^5*17

ANALYTIC INVARIANTS:

Omega+         = 4.1900792783688976205 + 0.22160378973949664891e-3i
Omega-         = 0.45069804167788745588e-2 + 106.06489400151161767i
L(1)           = 1.9718020161077451916

HECKE EIGENFORM:
a^7-10*a^5+28*a^3+3*a^2-19*a-7 = 0,
f(q) = 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 + (-a^6+8*a^4-16*a^2+2*a+7)*q^38 + (a^6-a^5-9*a^4+8*a^3+22*a^2-11*a-14)*q^39 + (2*a^6-2*a^5-20*a^4+17*a^3+52*a^2-31*a-28)*q^40 + (-3*a^6+a^5+26*a^4-12*a^3-57*a^2+27*a+24)*q^41 + (2*a^6+a^5-18*a^4-3*a^3+43*a^2-8*a-21)*q^42 + (5/2*a^6-1/2*a^5-49/2*a^4+13/2*a^3+127/2*a^2-17*a-57/2)*q^43 + (-3*a^6+2*a^5+29*a^4-19*a^3-75*a^2+37*a+37)*q^44 + (a^6-9*a^4+a^3+23*a^2-a-17)*q^45 + (1/2*a^6-3/2*a^5-11/2*a^4+19/2*a^3+27/2*a^2-9*a-7/2)*q^46 + (-3/2*a^6-1/2*a^5+27/2*a^4+5/2*a^3-61/2*a^2-3*a+23/2)*q^47 + (-5/2*a^6+1/2*a^5+45/2*a^4-13/2*a^3-103/2*a^2+13*a+49/2)*q^48 + (-6*a^6+a^5+55*a^4-15*a^3-133*a^2+38*a+65)*q^49 + (a^5+3*a^4-6*a^3-14*a^2+8*a+7)*q^50 + (a^6-2*a^5-11*a^4+15*a^3+33*a^2-21*a-21)*q^51 + (-a^6+2*a^5+12*a^4-15*a^3-35*a^2+23*a+20)*q^52 + (4*a^6-2*a^5-38*a^4+21*a^3+96*a^2-45*a-50)*q^53 + (-2*a^5-2*a^4+13*a^3+12*a^2-17*a-14)*q^54 + (3*a^6-a^5-27*a^4+13*a^3+62*a^2-32*a-22)*q^55 + (-a^6+a^5+10*a^4-8*a^3-28*a^2+13*a+21)*q^56 + (4*a^6-a^5-37*a^4+12*a^3+92*a^2-29*a-49)*q^57 + (a^6+a^5-8*a^4-4*a^3+18*a^2-3*a-7)*q^58 + (3*a^6-28*a^4+6*a^3+69*a^2-22*a-32)*q^59 + (-2*a^6+a^5+19*a^4-10*a^3-49*a^2+17*a+28)*q^60 + (-5*a^6+4*a^5+47*a^4-37*a^3-118*a^2+70*a+65)*q^61 + (1/2*a^6+1/2*a^5-3/2*a^4-7/2*a^3-7/2*a^2+8*a+7/2)*q^62 + (-8*a^6+4*a^5+77*a^4-39*a^3-198*a^2+77*a+107)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (a^6-2*a^5-10*a^4+14*a^3+23*a^2-20*a-10)*q^65 + (-a^6-a^5+8*a^4+5*a^3-16*a^2-2*a+7)*q^66 + (3/2*a^6-1/2*a^5-31/2*a^4+11/2*a^3+81/2*a^2-16*a-23/2)*q^67 + (a^6+a^5-7*a^4-5*a^3+10*a^2+a+1)*q^68 + (5*a^6-2*a^5-47*a^4+19*a^3+115*a^2-34*a-56)*q^69 + (-3*a^6+25*a^4-4*a^3-51*a^2+12*a+21)*q^70 + (-11/2*a^6+9/2*a^5+111/2*a^4-81/2*a^3-297/2*a^2+77*a+159/2)*q^71 + (-4*a^6+2*a^5+38*a^4-20*a^3-96*a^2+40*a+49)*q^72 + (2*a^6-2*a^5-19*a^4+17*a^3+46*a^2-25*a-21)*q^73 + (-3*a^4+15*a^2-3*a-7)*q^74 + (1/2*a^6-1/2*a^5-9/2*a^4+11/2*a^3+23/2*a^2-10*a-21/2)*q^75 + (-2*a^6+20*a^4-4*a^3-51*a^2+14*a+27)*q^76 + (6*a^6-2*a^5-56*a^4+23*a^3+137*a^2-53*a-67)*q^77 + (-a^6+a^5+8*a^4-6*a^3-14*a^2+5*a+7)*q^78 + (3/2*a^6-1/2*a^5-27/2*a^4+9/2*a^3+59/2*a^2-3*a-13/2)*q^79 + (2*a^6-19*a^4+4*a^3+49*a^2-18*a-24)*q^80 + (2*a^4+2*a^3-13*a^2-7*a+9)*q^81 + (a^6-4*a^5-12*a^4+27*a^3+36*a^2-33*a-21)*q^82 + (-5/2*a^6+1/2*a^5+49/2*a^4-15/2*a^3-127/2*a^2+22*a+65/2)*q^83 + (7*a^6-2*a^5-65*a^4+23*a^3+160*a^2-51*a-84)*q^84 + (-2*a^6+2*a^5+21*a^4-18*a^3-60*a^2+34*a+31)*q^85 + (-1/2*a^6+1/2*a^5+13/2*a^4-13/2*a^3-49/2*a^2+19*a+35/2)*q^86 + (-2*a^6+a^5+18*a^4-8*a^3-41*a^2+11*a+21)*q^87 + (4*a^6-3*a^5-39*a^4+27*a^3+100*a^2-52*a-49)*q^88 + (-a^6+8*a^4-9*a^2-2*a-14)*q^89 + (a^5+a^4-5*a^3-4*a^2+2*a+7)*q^90 + (3*a^6-28*a^4+5*a^3+70*a^2-21*a-33)*q^91 + (-1/2*a^6-3/2*a^5+5/2*a^4+21/2*a^3-3/2*a^2-18*a+5/2)*q^92 + (-a^6+a^5+11*a^4-8*a^3-34*a^2+18*a+21)*q^93 + (-1/2*a^6-3/2*a^5+5/2*a^4+23/2*a^3+3/2*a^2-17*a-21/2)*q^94 + (-3*a^6+27*a^4-5*a^3-64*a^2+17*a+32)*q^95 + (7/2*a^6-7/2*a^5-71/2*a^4+55/2*a^3+191/2*a^2-41*a-105/2)*q^96 + (-2*a^6-a^5+17*a^4+5*a^3-37*a^2-2*a+14)*q^97 + (a^6-5*a^5-15*a^4+35*a^3+56*a^2-49*a-42)*q^98 + (a^5-8*a^3+3*a^2+15*a-11)*q^99 + (-a^6+3*a^5+12*a^4-20*a^3-36*a^2+29*a+22)*q^100 + (-2*a^6+3*a^5+20*a^4-26*a^3-56*a^2+48*a+35)*q^101 + (-2*a^6-a^5+15*a^4+5*a^3-24*a^2-2*a+7)*q^102 + (-3*a^6+3*a^5+30*a^4-26*a^3-77*a^2+49*a+40)*q^103 + (2*a^6-19*a^4+5*a^3+48*a^2-17*a-21)*q^104 + (6*a^6-a^5-58*a^4+16*a^3+152*a^2-47*a-84)*q^105 + (-2*a^6+2*a^5+21*a^4-16*a^3-57*a^2+26*a+28)*q^106 + (-2*a^5-3*a^4+12*a^3+19*a^2-14*a-24)*q^107 + (2*a^6-2*a^5-23*a^4+16*a^3+69*a^2-26*a-42)*q^108 + (-a^6-a^5+9*a^4+5*a^3-21*a^2-2*a+5)*q^109 + (-a^6+3*a^5+13*a^4-22*a^3-41*a^2+35*a+21)*q^110 + (-3*a^6+2*a^5+28*a^4-19*a^3-69*a^2+33*a+42)*q^111 + (-a^6+2*a^5+14*a^4-16*a^3-52*a^2+28*a+37)*q^112 + (-4*a^6+a^5+38*a^4-10*a^3-96*a^2+17*a+44)*q^113 + (-a^6+3*a^5+12*a^4-20*a^3-41*a^2+27*a+28)*q^114 + (-6*a^6+4*a^5+60*a^4-38*a^3-159*a^2+82*a+81)*q^115 + (3*a^6-26*a^4+6*a^3+58*a^2-18*a-25)*q^116 + (-2*a^4-a^3+12*a^2+a-12)*q^117 + (2*a^5+6*a^4-15*a^3-31*a^2+25*a+21)*q^118 + (2*a^6+3*a^5-15*a^4-18*a^3+26*a^2+15*a-9)*q^119 + (a^6-a^5-12*a^4+9*a^3+39*a^2-20*a-28)*q^120 + (6*a^6-5*a^5-58*a^4+46*a^3+146*a^2-89*a-73)*q^121 + (4*a^6-3*a^5-37*a^4+22*a^3+85*a^2-30*a-35)*q^122 + (2*a^6-16*a^4+2*a^3+27*a^2-4*a-7)*q^123 + (-1/2*a^6+5/2*a^5+11/2*a^4-29/2*a^3-29/2*a^2+17*a+13/2)*q^124 + (-4*a^6+2*a^5+38*a^4-19*a^3-97*a^2+33*a+47)*q^125 + (4*a^6-3*a^5-39*a^4+26*a^3+101*a^2-45*a-56)*q^126 + (-3/2*a^6-1/2*a^5+27/2*a^4+9/2*a^3-59/2*a^2-9*a+25/2)*q^127 + (-2*a^5+12*a^3-3*a^2-13*a+7)*q^128 + (5*a^6-3*a^5-48*a^4+25*a^3+121*a^2-37*a-63)*q^129 + (-2*a^6+14*a^4-5*a^3-23*a^2+9*a+7)*q^130 + (1/2*a^6-5/2*a^5-13/2*a^4+39/2*a^3+43/2*a^2-36*a-33/2)*q^131 + (-3*a^6+27*a^4-4*a^3-65*a^2+14*a+35)*q^132 + (5*a^6-5*a^5-52*a^4+41*a^3+148*a^2-68*a-89)*q^133 + (-1/2*a^6-1/2*a^5+11/2*a^4-3/2*a^3-41/2*a^2+17*a+21/2)*q^134 + (5*a^6-3*a^5-48*a^4+30*a^3+125*a^2-59*a-70)*q^135 + (-a^6+a^5+9*a^4-8*a^3-20*a^2+14*a+7)*q^136 + 1*q^137 + (-2*a^6+3*a^5+19*a^4-25*a^3-49*a^2+39*a+35)*q^138 + (2*a^4-2*a^3-15*a^2+6*a+13)*q^139 + (-6*a^6+a^5+56*a^4-17*a^3-139*a^2+48*a+69)*q^140 + (-4*a^6+2*a^5+41*a^4-18*a^3-112*a^2+31*a+56)*q^141 + (9/2*a^6+1/2*a^5-81/2*a^4+11/2*a^3+187/2*a^2-25*a-77/2)*q^142 + (2*a^6-3*a^5-21*a^4+24*a^3+56*a^2-41*a-25)*q^143 + (-4*a^6+2*a^5+40*a^4-20*a^3-108*a^2+43*a+58)*q^144 + (-2*a^6+a^5+16*a^4-11*a^3-31*a^2+18*a+9)*q^145 + (-2*a^6+a^5+17*a^4-10*a^3-31*a^2+17*a+14)*q^146 + (-23/2*a^6+15/2*a^5+231/2*a^4-133/2*a^3-631/2*a^2+120*a+357/2)*q^147 + (2*a^6-3*a^5-20*a^4+21*a^3+53*a^2-31*a-32)*q^148 + (-3*a^6+2*a^5+32*a^4-18*a^3-90*a^2+34*a+45)*q^149 + (-1/2*a^6+1/2*a^5+11/2*a^4-5/2*a^3-23/2*a^2-a+7/2)*q^150 + (-2*a^6+a^5+20*a^4-11*a^3-51*a^2+24*a+23)*q^151 + (2*a^6-20*a^4+5*a^3+52*a^2-15*a-28)*q^152 + (4*a^6-2*a^5-39*a^4+20*a^3+101*a^2-43*a-51)*q^153 + (-2*a^6+4*a^5+23*a^4-31*a^3-71*a^2+47*a+42)*q^154 + (3*a^6-4*a^5-31*a^4+30*a^3+80*a^2-46*a-40)*q^155 + (-a^6+12*a^4-2*a^3-36*a^2+10*a+21)*q^156 + (3*a^6-5*a^5-34*a^4+39*a^3+107*a^2-68*a-76)*q^157 + (-1/2*a^6+3/2*a^5+9/2*a^4-25/2*a^3-15/2*a^2+22*a+21/2)*q^158 + (5*a^6-3*a^5-50*a^4+29*a^3+137*a^2-58*a-84)*q^159 + (-4*a^6+5*a^5+44*a^4-41*a^3-128*a^2+76*a+70)*q^160 + (2*a^6-2*a^5-24*a^4+17*a^3+81*a^2-33*a-61)*q^161 + (2*a^5+2*a^4-13*a^3-7*a^2+9*a)*q^162 + (-1/2*a^6+9/2*a^5+15/2*a^4-69/2*a^3-51/2*a^2+59*a+31/2)*q^163 + (2*a^6-4*a^5-25*a^4+32*a^3+78*a^2-56*a-41)*q^164 + (-5*a^6+2*a^5+48*a^4-21*a^3-122*a^2+47*a+63)*q^165 + (1/2*a^6-1/2*a^5-15/2*a^4+13/2*a^3+59/2*a^2-15*a-35/2)*q^166 + (5*a^6-47*a^4+6*a^3+114*a^2-24*a-38)*q^167 + (-6*a^6+3*a^5+59*a^4-30*a^3-158*a^2+65*a+91)*q^168 + (a^6+a^5-8*a^4-3*a^3+20*a^2-6*a-18)*q^169 + (2*a^6+a^5-18*a^4-4*a^3+40*a^2-7*a-14)*q^170 + (7*a^6-4*a^5-69*a^4+37*a^3+183*a^2-71*a-103)*q^171 + (-9/2*a^6+5/2*a^5+85/2*a^4-47/2*a^3-213/2*a^2+42*a+107/2)*q^172 + (6*a^6-a^5-56*a^4+20*a^3+138*a^2-63*a-62)*q^173 + (a^6-2*a^5-8*a^4+15*a^3+17*a^2-17*a-14)*q^174 + (3*a^6-28*a^4+5*a^3+69*a^2-19*a-30)*q^175 + (3*a^6-3*a^5-31*a^4+26*a^3+86*a^2-47*a-46)*q^176 + (4*a^6-3*a^5-40*a^4+27*a^3+107*a^2-44*a-63)*q^177 + (-2*a^5+19*a^3+a^2-33*a-7)*q^178 + (-11/2*a^6+3/2*a^5+103/2*a^4-37/2*a^3-255/2*a^2+40*a+117/2)*q^179 + (-a^6+a^5+13*a^4-6*a^3-44*a^2+9*a+34)*q^180 + (7*a^6-2*a^5-67*a^4+25*a^3+169*a^2-57*a-81)*q^181 + (2*a^5+5*a^4-14*a^3-30*a^2+24*a+21)*q^182 + (-4*a^6+a^5+40*a^4-16*a^3-115*a^2+51*a+77)*q^183 + (-5/2*a^6+1/2*a^5+43/2*a^4-13/2*a^3-87/2*a^2+11*a+7/2)*q^184 + (a^6+2*a^5-9*a^4-11*a^3+26*a^2+7*a-12)*q^185 + (a^6+a^5-8*a^4-6*a^3+21*a^2+2*a-7)*q^186 + (-6*a^6+a^5+54*a^4-17*a^3-125*a^2+48*a+53)*q^187 + (3/2*a^6-3/2*a^5-31/2*a^4+21/2*a^3+91/2*a^2-14*a-53/2)*q^188 + (-10*a^6+3*a^5+94*a^4-35*a^3-237*a^2+80*a+133)*q^189 + (-3*a^5-5*a^4+20*a^3+26*a^2-25*a-21)*q^190 + (9/2*a^6-3/2*a^5-81/2*a^4+39/2*a^3+195/2*a^2-51*a-97/2)*q^191 + (3/2*a^6-3/2*a^5-35/2*a^4+21/2*a^3+103/2*a^2-12*a-49/2)*q^192 + (4*a^6-2*a^5-41*a^4+18*a^3+110*a^2-35*a-48)*q^193 + (-a^6-3*a^5+5*a^4+19*a^3+4*a^2-24*a-14)*q^194 + (-4*a^6+a^5+34*a^4-13*a^3-73*a^2+24*a+35)*q^195 + (7*a^6-7*a^5-75*a^4+58*a^3+214*a^2-99*a-123)*q^196 + (-6*a^6+2*a^5+57*a^4-20*a^3-144*a^2+37*a+72)*q^197 + (a^6-8*a^4+3*a^3+15*a^2-11*a)*q^198 + (7/2*a^6-3/2*a^5-67/2*a^4+23/2*a^3+163/2*a^2-17*a-57/2)*q^199 + (3*a^6-26*a^4+4*a^3+60*a^2-13*a-21)*q^200 +  ...

-------------------------------------------------------
Gamma_0(138)
Weight 2

-------------------------------------------------------
J_0(138), dim = 21

-------------------------------------------------------
138A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 4.4583320351995843719 + 0.35623310282267623097e-5i
Omega-         = 0.2277564809739031786e-5 + 2.0149783479559358695i
L(1)           =
w1             = -2.2291648788173873164 + 1.0074873928124538214i
w2             = 0.2277564809739031786e-5 + 2.0149783479559358695i
c4             = 73.002753206290449953 + 0.61647018988929467187e-3i
c6             = -1349.06193692834085 + -0.35710403341572729024e-2i
j              = -469.84003434772454442 + -0.11975275019824798168e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + 1*q^4 + -2*q^5 + 1*q^6 + -2*q^7 + -1*q^8 + 1*q^9 + 2*q^10 + -6*q^11 + -1*q^12 + -2*q^13 + 2*q^14 + 2*q^15 + 1*q^16 + -1*q^18 + -2*q^20 + 2*q^21 + 6*q^22 + -1*q^23 + 1*q^24 + -1*q^25 + 2*q^26 + -1*q^27 + -2*q^28 + 6*q^29 + -2*q^30 + 8*q^31 + -1*q^32 + 6*q^33 + 4*q^35 + 1*q^36 + 2*q^39 + 2*q^40 + 10*q^41 + -2*q^42 + -12*q^43 + -6*q^44 + -2*q^45 + 1*q^46 + -8*q^47 + -1*q^48 + -3*q^49 + 1*q^50 + -2*q^52 + 2*q^53 + 1*q^54 + 12*q^55 + 2*q^56 + -6*q^58 + -12*q^59 + 2*q^60 + 4*q^61 + -8*q^62 + -2*q^63 + 1*q^64 + 4*q^65 + -6*q^66 + -12*q^67 + 1*q^69 + -4*q^70 + -1*q^72 + -10*q^73 + 1*q^75 + 12*q^77 + -2*q^78 + -6*q^79 + -2*q^80 + 1*q^81 + -10*q^82 + 14*q^83 + 2*q^84 + 12*q^86 + -6*q^87 + 6*q^88 + 2*q^90 + 4*q^91 + -1*q^92 + -8*q^93 + 8*q^94 + 1*q^96 + -6*q^97 + 3*q^98 + -6*q^99 + -1*q^100 + -6*q^101 + 14*q^103 + 2*q^104 + -4*q^105 + -2*q^106 + 14*q^107 + -1*q^108 + -16*q^109 + -12*q^110 + -2*q^112 + -8*q^113 + 2*q^115 + 6*q^116 + -2*q^117 + 12*q^118 + -2*q^120 + 25*q^121 + -4*q^122 + -10*q^123 + 8*q^124 + 12*q^125 + 2*q^126 + 12*q^127 + -1*q^128 + 12*q^129 + -4*q^130 + -8*q^131 + 6*q^132 + 12*q^134 + 2*q^135 + -12*q^137 + -1*q^138 + 12*q^139 + 4*q^140 + 8*q^141 + 12*q^143 + 1*q^144 + -12*q^145 + 10*q^146 + 3*q^147 + -18*q^149 + -1*q^150 + -12*q^151 + -12*q^154 + -16*q^155 + 2*q^156 + 16*q^157 + 6*q^158 + -2*q^159 + 2*q^160 + 2*q^161 + -1*q^162 + -12*q^163 + 10*q^164 + -12*q^165 + -14*q^166 + 8*q^167 + -2*q^168 + -9*q^169 + -12*q^172 + -18*q^173 + 6*q^174 + 2*q^175 + -6*q^176 + 12*q^177 + -16*q^179 + -2*q^180 + 8*q^181 + -4*q^182 + -4*q^183 + 1*q^184 + 8*q^186 + -8*q^188 + 2*q^189 + -1*q^192 + 14*q^193 + 6*q^194 + -4*q^195 + -3*q^196 + -6*q^197 + 6*q^198 + 2*q^199 + 1*q^200 +  ...

-------------------------------------------------------
138B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2^2 + Z/2^2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/3
Sha Bound      = 2^2*3

ANALYTIC INVARIANTS:

Omega+         = 3.0601734380655552255 + -0.82645712615746202064e-5i
Omega-         = 0.16824173245462234632e-5 + -0.97473343278923739723i
L(1)           = 1.0200578126922384121
w1             = -1.5300858778241153396 + -0.48736258410898791131i
w2             = -0.16824173245462234632e-5 + 0.97473343278923739723i
c4             = 1704.9736373393039067 + -0.12712385464552724706e-1i
c6             = -73619.72011979875971 + 0.68050848961724981555i
j              = -18473.059126679393636 + 0.83814459672462657736i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -1*q^6 + 2*q^7 + -1*q^8 + 1*q^9 + 1*q^12 + 2*q^13 + -2*q^14 + 1*q^16 + -1*q^18 + 2*q^19 + 2*q^21 + -1*q^23 + -1*q^24 + -5*q^25 + -2*q^26 + 1*q^27 + 2*q^28 + -6*q^29 + -4*q^31 + -1*q^32 + 1*q^36 + -10*q^37 + -2*q^38 + 2*q^39 + -6*q^41 + -2*q^42 + 2*q^43 + 1*q^46 + 1*q^48 + -3*q^49 + 5*q^50 + 2*q^52 + 12*q^53 + -1*q^54 + -2*q^56 + 2*q^57 + 6*q^58 + 12*q^59 + -10*q^61 + 4*q^62 + 2*q^63 + 1*q^64 + 14*q^67 + -1*q^69 + -1*q^72 + 2*q^73 + 10*q^74 + -5*q^75 + 2*q^76 + -2*q^78 + -10*q^79 + 1*q^81 + 6*q^82 + 2*q^84 + -2*q^86 + -6*q^87 + 12*q^89 + 4*q^91 + -1*q^92 + -4*q^93 + -1*q^96 + -10*q^97 + 3*q^98 + -5*q^100 + -18*q^101 + 14*q^103 + -2*q^104 + -12*q^106 + 1*q^108 + 2*q^109 + -10*q^111 + 2*q^112 + 12*q^113 + -2*q^114 + -6*q^116 + 2*q^117 + -12*q^118 + -11*q^121 + 10*q^122 + -6*q^123 + -4*q^124 + -2*q^126 + -4*q^127 + -1*q^128 + 2*q^129 + -12*q^131 + 4*q^133 + -14*q^134 + 12*q^137 + 1*q^138 + 20*q^139 + 1*q^144 + -2*q^146 + -3*q^147 + -10*q^148 + 5*q^150 + 8*q^151 + -2*q^152 + 2*q^156 + 14*q^157 + 10*q^158 + 12*q^159 + -2*q^161 + -1*q^162 + 8*q^163 + -6*q^164 + -24*q^167 + -2*q^168 + -9*q^169 + 2*q^171 + 2*q^172 + -6*q^173 + 6*q^174 + -10*q^175 + 12*q^177 + -12*q^178 + 12*q^179 + 2*q^181 + -4*q^182 + -10*q^183 + 1*q^184 + 4*q^186 + 2*q^189 + -12*q^191 + 1*q^192 + 14*q^193 + 10*q^194 + -3*q^196 + 18*q^197 + -10*q^199 + 5*q^200 +  ...

-------------------------------------------------------
138C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 2.9754574760763095729 + 0.19033688175521251957e-4i
Omega-         = 0.35752577821571904031e-5 + 2.4085308897333027505i
L(1)           = 1.4877287380685939112
w1             = -1.4877305256670458651 + -1.2042749617107391359i
w2             = -1.4877269504092637079 + 1.2042559280225636146i
c4             = -143.00085701462737685 + 0.37937661010052182852e-2i
c6             = -1672.964057751011958 + -0.23365600137170321106e-1i
j              = 882.93905851106314059 + -0.46427270806740073506e-1i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + 2*q^5 + -1*q^6 + 1*q^8 + 1*q^9 + 2*q^10 + -1*q^12 + -2*q^13 + -2*q^15 + 1*q^16 + 2*q^17 + 1*q^18 + -8*q^19 + 2*q^20 + -1*q^23 + -1*q^24 + -1*q^25 + -2*q^26 + -1*q^27 + -2*q^29 + -2*q^30 + -8*q^31 + 1*q^32 + 2*q^34 + 1*q^36 + 2*q^37 + -8*q^38 + 2*q^39 + 2*q^40 + 10*q^41 + 8*q^43 + 2*q^45 + -1*q^46 + 8*q^47 + -1*q^48 + -7*q^49 + -1*q^50 + -2*q^51 + -2*q^52 + 2*q^53 + -1*q^54 + 8*q^57 + -2*q^58 + -4*q^59 + -2*q^60 + 2*q^61 + -8*q^62 + 1*q^64 + -4*q^65 + 8*q^67 + 2*q^68 + 1*q^69 + 1*q^72 + -6*q^73 + 2*q^74 + 1*q^75 + -8*q^76 + 2*q^78 + 8*q^79 + 2*q^80 + 1*q^81 + 10*q^82 + -16*q^83 + 4*q^85 + 8*q^86 + 2*q^87 + 18*q^89 + 2*q^90 + -1*q^92 + 8*q^93 + 8*q^94 + -16*q^95 + -1*q^96 + 10*q^97 + -7*q^98 + -1*q^100 + -18*q^101 + -2*q^102 + 8*q^103 + -2*q^104 + 2*q^106 + 8*q^107 + -1*q^108 + 2*q^109 + -2*q^111 + -6*q^113 + 8*q^114 + -2*q^115 + -2*q^116 + -2*q^117 + -4*q^118 + -2*q^120 + -11*q^121 + 2*q^122 + -10*q^123 + -8*q^124 + -12*q^125 + 16*q^127 + 1*q^128 + -8*q^129 + -4*q^130 + -12*q^131 + 8*q^134 + -2*q^135 + 2*q^136 + 10*q^137 + 1*q^138 + -20*q^139 + -8*q^141 + 1*q^144 + -4*q^145 + -6*q^146 + 7*q^147 + 2*q^148 + 2*q^149 + 1*q^150 + 16*q^151 + -8*q^152 + 2*q^153 + -16*q^155 + 2*q^156 + -22*q^157 + 8*q^158 + -2*q^159 + 2*q^160 + 1*q^162 + -4*q^163 + 10*q^164 + -16*q^166 + -9*q^169 + 4*q^170 + -8*q^171 + 8*q^172 + 14*q^173 + 2*q^174 + 4*q^177 + 18*q^178 + 12*q^179 + 2*q^180 + 10*q^181 + -2*q^183 + -1*q^184 + 4*q^185 + 8*q^186 + 8*q^188 + -16*q^190 + 24*q^191 + -1*q^192 + -14*q^193 + 10*q^194 + 4*q^195 + -7*q^196 + 22*q^197 + 16*q^199 + -1*q^200 +  ...

-------------------------------------------------------
138D (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4*11
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^3*11 + Z/2^3*11
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/11 + Z/11)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 2^2*5
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2*11
|L(1)/Omega|   = 1
Sha Bound      = 2^4*11^2

ANALYTIC INVARIANTS:

Omega+         = 2.8764289263646414469 + -0.42741296084473874127e-5i
Omega-         = 0.93415030667513104775 + -0.18989041985620858871e-4i
L(1)           = 2.8764289263678169441

HECKE EIGENFORM:
a^2+2*a-4 = 0,
f(q) = q + 1*q^2 + 1*q^3 + 1*q^4 + a*q^5 + 1*q^6 + (-2*a-2)*q^7 + 1*q^8 + 1*q^9 + a*q^10 + (-a-4)*q^11 + 1*q^12 + (2*a+2)*q^13 + (-2*a-2)*q^14 + a*q^15 + 1*q^16 + -4*q^17 + 1*q^18 + (3*a+2)*q^19 + a*q^20 + (-2*a-2)*q^21 + (-a-4)*q^22 + 1*q^23 + 1*q^24 + (-2*a-1)*q^25 + (2*a+2)*q^26 + 1*q^27 + (-2*a-2)*q^28 + (-2*a-2)*q^29 + a*q^30 + -2*a*q^31 + 1*q^32 + (-a-4)*q^33 + -4*q^34 + (2*a-8)*q^35 + 1*q^36 + (a+10)*q^37 + (3*a+2)*q^38 + (2*a+2)*q^39 + a*q^40 + -2*q^41 + (-2*a-2)*q^42 + (a-6)*q^43 + (-a-4)*q^44 + a*q^45 + 1*q^46 + 4*q^47 + 1*q^48 + 13*q^49 + (-2*a-1)*q^50 + -4*q^51 + (2*a+2)*q^52 + (a+4)*q^53 + 1*q^54 + (-2*a-4)*q^55 + (-2*a-2)*q^56 + (3*a+2)*q^57 + (-2*a-2)*q^58 + (-4*a-4)*q^59 + a*q^60 + (-a+2)*q^61 + -2*a*q^62 + (-2*a-2)*q^63 + 1*q^64 + (-2*a+8)*q^65 + (-a-4)*q^66 + (3*a+6)*q^67 + -4*q^68 + 1*q^69 + (2*a-8)*q^70 + (4*a+4)*q^71 + 1*q^72 + (-2*a-2)*q^73 + (a+10)*q^74 + (-2*a-1)*q^75 + (3*a+2)*q^76 + (6*a+16)*q^77 + (2*a+2)*q^78 + (2*a+2)*q^79 + a*q^80 + 1*q^81 + -2*q^82 + (a+12)*q^83 + (-2*a-2)*q^84 + -4*a*q^85 + (a-6)*q^86 + (-2*a-2)*q^87 + (-a-4)*q^88 + (-2*a-8)*q^89 + a*q^90 + -20*q^91 + 1*q^92 + -2*a*q^93 + 4*q^94 + (-4*a+12)*q^95 + 1*q^96 + (2*a-2)*q^97 + 13*q^98 + (-a-4)*q^99 + (-2*a-1)*q^100 + (2*a+2)*q^101 + -4*q^102 + -6*q^103 + (2*a+2)*q^104 + (2*a-8)*q^105 + (a+4)*q^106 + (-7*a-4)*q^107 + 1*q^108 + (-a+6)*q^109 + (-2*a-4)*q^110 + (a+10)*q^111 + (-2*a-2)*q^112 + (2*a-8)*q^113 + (3*a+2)*q^114 + a*q^115 + (-2*a-2)*q^116 + (2*a+2)*q^117 + (-4*a-4)*q^118 + (8*a+8)*q^119 + a*q^120 + (6*a+9)*q^121 + (-a+2)*q^122 + -2*q^123 + -2*a*q^124 + (-2*a-8)*q^125 + (-2*a-2)*q^126 + -4*q^127 + 1*q^128 + (a-6)*q^129 + (-2*a+8)*q^130 + (2*a-12)*q^131 + (-a-4)*q^132 + (2*a-28)*q^133 + (3*a+6)*q^134 + a*q^135 + -4*q^136 + (-4*a+8)*q^137 + 1*q^138 + (-4*a-12)*q^139 + (2*a-8)*q^140 + 4*q^141 + (4*a+4)*q^142 + (-6*a-16)*q^143 + 1*q^144 + (2*a-8)*q^145 + (-2*a-2)*q^146 + 13*q^147 + (a+10)*q^148 + (-3*a-8)*q^149 + (-2*a-1)*q^150 + (-2*a-12)*q^151 + (3*a+2)*q^152 + -4*q^153 + (6*a+16)*q^154 + (4*a-8)*q^155 + (2*a+2)*q^156 + (-7*a+2)*q^157 + (2*a+2)*q^158 + (a+4)*q^159 + a*q^160 + (-2*a-2)*q^161 + 1*q^162 + -2*a*q^163 + -2*q^164 + (-2*a-4)*q^165 + (a+12)*q^166 + (4*a+12)*q^167 + (-2*a-2)*q^168 + 7*q^169 + -4*a*q^170 + (3*a+2)*q^171 + (a-6)*q^172 + (-6*a-10)*q^173 + (-2*a-2)*q^174 + (-2*a+18)*q^175 + (-a-4)*q^176 + (-4*a-4)*q^177 + (-2*a-8)*q^178 + (6*a+12)*q^179 + a*q^180 + (-a-10)*q^181 + -20*q^182 + (-a+2)*q^183 + 1*q^184 + (8*a+4)*q^185 + -2*a*q^186 + (4*a+16)*q^187 + 4*q^188 + (-2*a-2)*q^189 + (-4*a+12)*q^190 + (2*a+4)*q^191 + 1*q^192 + (8*a+14)*q^193 + (2*a-2)*q^194 + (-2*a+8)*q^195 + 13*q^196 + (4*a-2)*q^197 + (-a-4)*q^198 + (6*a+10)*q^199 + (-2*a-1)*q^200 +  ...

-------------------------------------------------------
138E (old = 69A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2^2 + Z/2^2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2)

-------------------------------------------------------
138F (old = 69B), dim = 2

CONGRUENCES:
Modular Degree = 2^5*11^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*11 + Z/2*11 + Z/2^3*11 + Z/2^3*11
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/11 + Z/11 + Z/11 + Z/11)

-------------------------------------------------------
138G (old = 46A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*5^2
Ker(ModPolar)  = Z/2^2*5 + Z/2^2*5 + Z/2^2*5 + Z/2^2*5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
138H (old = 23A), dim = 2

CONGRUENCES:
Modular Degree = 5^2*11^3
Ker(ModPolar)  = Z/11 + Z/11 + Z/5*11 + Z/5*11 + Z/5*11 + Z/5*11
= D(Z/11 + Z/11) + F(Z/11 + Z/11 + Z/11 + Z/11) + G(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
Gamma_0(139)
Weight 2

-------------------------------------------------------
J_0(139), dim = 11

-------------------------------------------------------
139A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/2*3 + Z/2*3)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.739663411206934431 + 0.23413692732151292135e-4i
Omega-         = 0.16848864065839701915e-4 + -5.8014258698456315588i
L(1)           = 1.7396634113644939347
w1             = -0.86984013003550013533 + 2.9007012280764497037i
w2             = 1.739663411206934431 + 0.23413692732151292135e-4i
c4             = 169.00951538345383618 + -0.92258555286721925982e-2i
c6             = 2251.1731504916854477 + -0.17830730032043597443i
j              = -34736.28590651191346 + 3.9220067276700594265i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 2*q^3 + -1*q^4 + -1*q^5 + 2*q^6 + 3*q^7 + -3*q^8 + 1*q^9 + -1*q^10 + 5*q^11 + -2*q^12 + -7*q^13 + 3*q^14 + -2*q^15 + -1*q^16 + -6*q^17 + 1*q^18 + -2*q^19 + 1*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 + -1*q^36 + 2*q^37 + -2*q^38 + -14*q^39 + 3*q^40 + -6*q^41 + 6*q^42 + -4*q^43 + -5*q^44 + -1*q^45 + 2*q^46 + 8*q^47 + -2*q^48 + 2*q^49 + -4*q^50 + -12*q^51 + 7*q^52 + -4*q^54 + -5*q^55 + -9*q^56 + -4*q^57 + 9*q^58 + 6*q^59 + 2*q^60 + 4*q^61 + 9*q^62 + 3*q^63 + 7*q^64 + 7*q^65 + 10*q^66 + 5*q^67 + 6*q^68 + 4*q^69 + -3*q^70 + 5*q^71 + -3*q^72 + -6*q^73 + 2*q^74 + -8*q^75 + 2*q^76 + 15*q^77 + -14*q^78 + -5*q^79 + 1*q^80 + -11*q^81 + -6*q^82 + 7*q^83 + -6*q^84 + 6*q^85 + -4*q^86 + 18*q^87 + -15*q^88 + 7*q^89 + -1*q^90 + -21*q^91 + -2*q^92 + 18*q^93 + 8*q^94 + 2*q^95 + 10*q^96 + -12*q^97 + 2*q^98 + 5*q^99 + 4*q^100 + 2*q^101 + -12*q^102 + -16*q^103 + 21*q^104 + -6*q^105 + 4*q^107 + 4*q^108 + -10*q^109 + -5*q^110 + 4*q^111 + -3*q^112 + 1*q^113 + -4*q^114 + -2*q^115 + -9*q^116 + -7*q^117 + 6*q^118 + -18*q^119 + 6*q^120 + 14*q^121 + 4*q^122 + -12*q^123 + -9*q^124 + 9*q^125 + 3*q^126 + 5*q^127 + -3*q^128 + -8*q^129 + 7*q^130 + -9*q^131 + -10*q^132 + -6*q^133 + 5*q^134 + 4*q^135 + 18*q^136 + -3*q^137 + 4*q^138 + 1*q^139 + 3*q^140 + 16*q^141 + 5*q^142 + -35*q^143 + -1*q^144 + -9*q^145 + -6*q^146 + 4*q^147 + -2*q^148 + -2*q^149 + -8*q^150 + -2*q^151 + 6*q^152 + -6*q^153 + 15*q^154 + -9*q^155 + 14*q^156 + -22*q^157 + -5*q^158 + -5*q^160 + 6*q^161 + -11*q^162 + 11*q^163 + 6*q^164 + -10*q^165 + 7*q^166 + -8*q^167 + -18*q^168 + 36*q^169 + 6*q^170 + -2*q^171 + 4*q^172 + 9*q^173 + 18*q^174 + -12*q^175 + -5*q^176 + 12*q^177 + 7*q^178 + -18*q^179 + 1*q^180 + 3*q^181 + -21*q^182 + 8*q^183 + -6*q^184 + -2*q^185 + 18*q^186 + -30*q^187 + -8*q^188 + -12*q^189 + 2*q^190 + 4*q^191 + 14*q^192 + -11*q^193 + -12*q^194 + 14*q^195 + -2*q^196 + 5*q^198 + 12*q^200 +  ...

-------------------------------------------------------
139B (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 7^2
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 60.271573172366143222 + 0.72030753173379435569e-3i
Omega-         = 0.12245184706081894806e-3 + 9.4077740579180380477i
L(1)           =

HECKE EIGENFORM:
a^3+2*a^2-a-1 = 0,
f(q) = 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 + (3*a^2+2*a+2)*q^38 + (2*a+5)*q^39 + (6*a^2+10*a-5)*q^40 + (-2*a-4)*q^41 + (-a^2-3*a)*q^42 + (-3*a^2-7*a+2)*q^43 + 7*a*q^44 + (-5*a^2-10*a+6)*q^45 + (-3*a^2-3*a+4)*q^46 + (-4*a^2-5*a+8)*q^47 + (-a^2-2*a+1)*q^48 + (-3*a^2-4*a+1)*q^49 + (5*a^2+5*a-6)*q^50 + (-2*a-3)*q^51 + (4*a^2+8*a-5)*q^52 + (3*a^2+9*a-4)*q^53 + (-2*a^2+3)*q^54 + (8*a^2+13*a-5)*q^55 + (a^2+a-6)*q^56 + (-2*a^2-9*a-7)*q^57 + (-3*a^2-7*a)*q^58 + (-2*a^2-3*a-2)*q^59 + (-4*a^2-9*a+2)*q^60 + (2*a^2+11*a+2)*q^61 + (-3*a^2-a)*q^62 + (-3*a^2-2*a+7)*q^63 + (-a^2+4*a+1)*q^64 + (11*a^2+18*a-14)*q^65 + (a^2+6*a+2)*q^66 + (-2*a^2-2*a+8)*q^67 + (-4*a^2-4*a+3)*q^68 + (3*a^2+5*a-5)*q^69 + (3*a^2+2*a-7)*q^70 + (6*a^2+3*a-9)*q^71 + (2*a^2-a-6)*q^72 + (9*a^2+13*a-5)*q^73 + (-4*a^2-6*a-1)*q^74 + (-5*a^2-9*a+7)*q^75 + (-8*a^2-9*a+3)*q^76 + -7*q^77 + (2*a^2+5*a)*q^78 + (5*a^2+7*a-1)*q^79 + (4*a^2+5*a-8)*q^80 + (-3*a^2-10*a-1)*q^81 + (-2*a^2-4*a)*q^82 + (3*a^2+a+4)*q^83 + (-a^2+a+5)*q^84 + (-5*a^2-10*a+6)*q^85 + (-a^2-a-3)*q^86 + (7*a^2+17*a+3)*q^87 + (3*a^2+4*a+6)*q^88 + (-9*a^2-12*a+11)*q^89 + (a-5)*q^90 + (5*a^2+6*a-13)*q^91 + (-5*a^2-9*a+11)*q^92 + (a^2+5*a+3)*q^93 + (3*a^2+4*a-4)*q^94 + (-9*a^2-21*a+5)*q^95 + (-2*a^2-6*a-7)*q^96 + (-9*a^2-10*a+9)*q^97 + (2*a^2-2*a-3)*q^98 + (3*a^2-3*a-8)*q^99 + (7*a^2+13*a-17)*q^100 + (-3*a^2-12*a-8)*q^101 + (-2*a^2-3*a)*q^102 + (-2*a^2+3*a+8)*q^103 + (-2*a^2-a+10)*q^104 + (-2*a^2+11)*q^105 + (3*a^2-a+3)*q^106 + (5*a+1)*q^107 + (-2*a^2-7*a+4)*q^108 + (-a^2+2*a-9)*q^109 + (-3*a^2+3*a+8)*q^110 + (6*a^2+17*a+6)*q^111 + (3*a^2+5*a-5)*q^112 + (a^2-7*a-13)*q^113 + (-5*a^2-9*a-2)*q^114 + (-16*a^2-22*a+29)*q^115 + (-a^2+3*a+11)*q^116 + (4*a^2+3*a-11)*q^117 + (a^2-4*a-2)*q^118 + (-3*a^2-2*a+7)*q^119 + (-a^2-6*a-10)*q^120 + (7*a^2+7*a-4)*q^121 + (7*a^2+4*a+2)*q^122 + (4*a^2+10*a+2)*q^123 + (5*a^2+3*a-1)*q^124 + (19*a^2+27*a-25)*q^125 + (4*a^2+4*a-3)*q^126 + (-4*a^2+4*a+14)*q^127 + (-4*a^2-14*a+5)*q^128 + (a^2+6*a+7)*q^129 + (-4*a^2-3*a+11)*q^130 + (4*a^2-2*a-6)*q^131 + (-7*a-7)*q^132 + (-3*a^2+2*a+12)*q^133 + (2*a^2+6*a-2)*q^134 + (-10*a^2-15*a+13)*q^135 + (2*a^2-a-6)*q^136 + (4*a^2+15*a+5)*q^137 + (-a^2-2*a+3)*q^138 + -1*q^139 + (10*a^2+18*a-15)*q^140 + (-4*a^2-7*a+5)*q^141 + (-9*a^2-3*a+6)*q^142 + (-a^2+a+12)*q^143 + (3*a^2+4*a-4)*q^144 + (-4*a^2+2*a+25)*q^145 + (-5*a^2+4*a+9)*q^146 + (2*a^2+5*a+4)*q^147 + (4*a^2+7*a+6)*q^148 + (7*a^2+14*a-13)*q^149 + (a^2+2*a-5)*q^150 + (4*a^2-2*a-19)*q^151 + (a^2-9*a-12)*q^152 + (-a+5)*q^153 + -7*a*q^154 + (2*a^2+8*a+1)*q^155 + (a^2-2*a-8)*q^156 + (9*a^2+5*a-23)*q^157 + (-3*a^2+4*a+5)*q^158 + (a^2-4*a-9)*q^159 + (-15*a^2-24*a+14)*q^160 + (-11*a^2-17*a+20)*q^161 + (-4*a^2-4*a-3)*q^162 + (-10*a^2-10*a+14)*q^163 + (2*a+6)*q^164 + (-3*a^2-11*a-13)*q^165 + (-5*a^2+7*a+3)*q^166 + (-13*a^2-24*a+9)*q^167 + (5*a^2+10*a-1)*q^168 + (-8*a^2-9*a+8)*q^169 + (a-5)*q^170 + (3*a^2+4*a+9)*q^171 + (7*a^2+10*a-5)*q^172 + (-2*a^2-5*a+2)*q^173 + (3*a^2+10*a+7)*q^174 + (17*a^2+27*a-30)*q^175 + (-2*a^2-5*a+3)*q^176 + (4*a^2+9*a+3)*q^177 + (6*a^2+2*a-9)*q^178 + (a^2+12*a+1)*q^179 + (11*a^2+15*a-12)*q^180 + (4*a^2+9*a-18)*q^181 + (-4*a^2-8*a+5)*q^182 + (-4*a^2-17*a-11)*q^183 + (7*a^2+12*a-13)*q^184 + (2*a^2+13*a+15)*q^185 + (3*a^2+4*a+1)*q^186 + (3*a^2-3*a-8)*q^187 + (6*a^2+9*a-13)*q^188 + (-4*a^2-6*a+11)*q^189 + (-3*a^2-4*a-9)*q^190 + (-10*a^2-14*a+5)*q^191 + (-5*a-4)*q^192 + (a^2-8*a+2)*q^193 + (8*a^2-9)*q^194 + (3*a^2-a-18)*q^195 + 7*a*q^196 + (-4*a^2+8*a+12)*q^197 + (-9*a^2-5*a+3)*q^198 + (-6*a^2-19*a+1)*q^199 + (-11*a^2-20*a+19)*q^200 +  ...

-------------------------------------------------------
139C (new) , dim = 7

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3 + Z/2*3
= A(Z/2*3 + Z/2*3) + B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 997*2151701
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 23
Torsion Bound  = 23
|L(1)/Omega|   = 2^3/23
Sha Bound      = 2^3*23

ANALYTIC INVARIANTS:

Omega+         = 5.4108602216947507288 + 0.32579544782680209051e-3i
Omega-         = 0.2283738339233846861e-2 + -114.15249972475226146i
L(1)           = 1.8820383413923652492

HECKE EIGENFORM:
a^7-a^6-11*a^5+8*a^4+35*a^3-10*a^2-32*a-8 = 0,
f(q) = 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 + (-a^5+7*a^3-8*a)*q^38 + (-a^5-a^4+8*a^3+8*a^2-12*a-10)*q^39 + (-a^6-a^5+8*a^4+9*a^3-14*a^2-16*a)*q^40 + (-a^6+3*a^5+10*a^4-25*a^3-28*a^2+44*a+27)*q^41 + (-a^5+a^4+7*a^3-5*a^2-8*a)*q^42 + (1/2*a^6+1/2*a^5-9/2*a^4-3*a^3+21/2*a^2+3*a-8)*q^43 + (a^6-a^5-9*a^4+8*a^3+21*a^2-15*a-10)*q^44 + (-1/4*a^6-9/4*a^5+5/4*a^4+39/2*a^3+17/4*a^2-33*a-13)*q^45 + (a^5+a^4-7*a^3-5*a^2+8*a+4)*q^46 + (a^6-a^5-11*a^4+9*a^3+31*a^2-18*a-15)*q^47 + (-a^4+a^3+8*a^2-8*a-8)*q^48 + (-a^6+3/2*a^5+21/2*a^4-27/2*a^3-30*a^2+47/2*a+20)*q^49 + (-a^6-a^5+7*a^4+10*a^3-6*a^2-19*a-6)*q^50 + (-3*a^5-a^4+24*a^3+8*a^2-34*a-12)*q^51 + (a^6-9*a^4+20*a^2-a-10)*q^52 + (1/2*a^6-3/2*a^5-9/2*a^4+13*a^3+21/2*a^2-23*a-4)*q^53 + (3*a^5+a^4-24*a^3-6*a^2+32*a+8)*q^54 + (-1/2*a^6+a^5+6*a^4-19/2*a^3-37/2*a^2+33/2*a+12)*q^55 + (a^4-2*a^3-6*a^2+8*a+8)*q^56 + (-a^6+2*a^5+11*a^4-18*a^3-34*a^2+36*a+24)*q^57 + (a^4+2*a^3-6*a^2-4*a-2)*q^58 + (-a^5+7*a^3-a^2-5*a)*q^59 + (a^6+3*a^5-6*a^4-26*a^3-2*a^2+42*a+20)*q^60 + (1/2*a^6+3/2*a^5-9/2*a^4-10*a^3+17/2*a^2+9*a+2)*q^61 + (-1/2*a^6-3/2*a^5+5/2*a^4+12*a^3+5/2*a^2-21*a-6)*q^62 + (3/4*a^6-3/4*a^5-25/4*a^4+5*a^3+45/4*a^2-5/2*a-6)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (3/2*a^5+3/2*a^4-27/2*a^3-12*a^2+49/2*a+20)*q^65 + (-a^5-2*a^4+11*a^3+12*a^2-26*a-8)*q^66 + (1/4*a^6-7/4*a^5-17/4*a^4+33/2*a^3+79/4*a^2-36*a-21)*q^67 + (a^6+2*a^5-8*a^4-16*a^3+11*a^2+24*a+4)*q^68 + (a^3-a^2-6*a+4)*q^69 + (1/2*a^6-1/2*a^5-7/2*a^4+3*a^3+13/2*a^2-6*a-6)*q^70 + (1/2*a^6-a^5-7*a^4+17/2*a^3+51/2*a^2-29/2*a-13)*q^71 + (-3*a^5-3*a^4+25*a^3+20*a^2-44*a-16)*q^72 + (1/2*a^6-5/2*a^5-11/2*a^4+19*a^3+33/2*a^2-23*a-14)*q^73 + (-2*a^5+13*a^3-9*a)*q^74 + (1/2*a^6+7/2*a^5-7/2*a^4-29*a^3+5/2*a^2+43*a+8)*q^75 + (-a^6+9*a^4-22*a^2+16)*q^76 + (-1/4*a^6+1/4*a^5+11/4*a^4-2*a^3-43/4*a^2+13/2*a+11)*q^77 + (-a^6-a^5+8*a^4+8*a^3-12*a^2-10*a)*q^78 + (-1/4*a^6-1/4*a^5+9/4*a^4+5/2*a^3-3/4*a^2-8*a-11)*q^79 + (-a^6+10*a^4-a^3-25*a^2+12)*q^80 + (a^6-2*a^5-11*a^4+19*a^3+33*a^2-38*a-19)*q^81 + (2*a^6-a^5-17*a^4+7*a^3+34*a^2-5*a-8)*q^82 + (-9/4*a^6+5/4*a^5+83/4*a^4-11*a^3-195/4*a^2+39/2*a+26)*q^83 + (-a^6+a^5+9*a^4-7*a^3-22*a^2+10*a+16)*q^84 + (3/2*a^6+3/2*a^5-25/2*a^4-13*a^3+37/2*a^2+23*a+8)*q^85 + (a^6+a^5-7*a^4-7*a^3+8*a^2+8*a+4)*q^86 + (2*a^6-3*a^5-17*a^4+24*a^3+33*a^2-37*a-20)*q^87 + (-a^6+3*a^5+9*a^4-24*a^3-22*a^2+40*a+16)*q^88 + (5/4*a^6-9/4*a^5-43/4*a^4+20*a^3+91/4*a^2-73/2*a-16)*q^89 + (-5/2*a^6-3/2*a^5+43/2*a^4+13*a^3-71/2*a^2-21*a-2)*q^90 + (-5/4*a^6+5/4*a^5+51/4*a^4-10*a^3-143/4*a^2+31/2*a+25)*q^91 + (2*a^5+2*a^4-15*a^3-13*a^2+24*a+16)*q^92 + (-2*a^6+5*a^5+19*a^4-42*a^3-45*a^2+69*a+26)*q^93 + (a^4-4*a^3-8*a^2+17*a+8)*q^94 + (a^6-a^5-11*a^4+9*a^3+34*a^2-14*a-28)*q^95 + (-2*a^6+a^5+19*a^4-10*a^3-44*a^2+24*a+16)*q^96 + (a^6-3*a^5-10*a^4+25*a^3+27*a^2-42*a-22)*q^97 + (1/2*a^6-1/2*a^5-11/2*a^4+5*a^3+27/2*a^2-12*a-8)*q^98 + (-5/2*a^6+6*a^5+23*a^4-101/2*a^3-103/2*a^2+167/2*a+27)*q^99 + (-1/2*a^6-7/2*a^5+7/2*a^4+27*a^3+7/2*a^2-41*a-18)*q^100 + (3/2*a^6-1/2*a^5-29/2*a^4+3*a^3+73/2*a^2+a-16)*q^101 + (-3*a^6-a^5+24*a^4+8*a^3-34*a^2-12*a)*q^102 + (2*a^6-2*a^5-19*a^4+18*a^3+45*a^2-34*a-26)*q^103 + (a^5+a^4-7*a^3-8*a^2+8*a+8)*q^104 + (1/2*a^6-3/2*a^5-13/2*a^4+14*a^3+47/2*a^2-25*a-26)*q^105 + (-a^6+a^5+9*a^4-7*a^3-18*a^2+12*a+4)*q^106 + (-2*a^6+a^5+19*a^4-9*a^3-46*a^2+16*a+25)*q^107 + (a^6+3*a^5-8*a^4-24*a^3+10*a^2+40*a)*q^108 + (-1/2*a^6-1/2*a^5+11/2*a^4+6*a^3-35/2*a^2-16*a+10)*q^109 + (1/2*a^6+1/2*a^5-11/2*a^4-a^3+23/2*a^2-4*a-4)*q^110 + (1/2*a^6+1/2*a^5-3/2*a^4-7*a^3-27/2*a^2+26*a+20)*q^111 + (-a^6+2*a^5+9*a^4-16*a^3-23*a^2+26*a+24)*q^112 + (5/4*a^6+1/4*a^5-49/4*a^4-7/2*a^3+127/4*a^2+9*a-15)*q^113 + (a^6-10*a^4+a^3+26*a^2-8*a-8)*q^114 + (-2*a^5-2*a^4+17*a^3+14*a^2-31*a-22)*q^115 + (1/2*a^6+1/2*a^5-7/2*a^4-4*a^3+19/2*a^2+5*a-8)*q^116 + (a^6+1/2*a^5-17/2*a^4-7/2*a^3+15*a^2+5/2*a-5)*q^117 + (-a^6+7*a^4-a^3-5*a^2)*q^118 + (-1/2*a^6-1/2*a^5+11/2*a^4+4*a^3-31/2*a^2-6*a+4)*q^119 + (2*a^6+a^5-18*a^4-5*a^3+34*a^2-8)*q^120 + (7/4*a^6-13/4*a^5-67/4*a^4+55/2*a^3+165/4*a^2-51*a-26)*q^121 + (2*a^6+a^5-14*a^4-9*a^3+14*a^2+18*a+4)*q^122 + (-1/2*a^6+3/2*a^5+9/2*a^4-15*a^3-19/2*a^2+38*a-4)*q^123 + (-1/2*a^6-7/2*a^5+5/2*a^4+27*a^3+5/2*a^2-42*a-10)*q^124 + (-5/4*a^6-1/4*a^5+45/4*a^4+5/2*a^3-75/4*a^2-7*a-6)*q^125 + (2*a^5-a^4-15*a^3+5*a^2+18*a+6)*q^126 + (-3/2*a^6+4*a^5+15*a^4-67/2*a^3-83/2*a^2+111/2*a+31)*q^127 + (a^6-a^5-8*a^4+5*a^3+10*a^2+8)*q^128 + (-2*a^6+2*a^5+19*a^4-17*a^3-46*a^2+30*a+24)*q^129 + (3/2*a^6+3/2*a^5-27/2*a^4-12*a^3+49/2*a^2+20*a)*q^130 + (-1/4*a^6-15/4*a^5+7/4*a^4+32*a^3+9/4*a^2-113/2*a-22)*q^131 + (a^6-4*a^5-9*a^4+32*a^3+22*a^2-52*a-12)*q^132 + (2*a^6-3*a^5-20*a^4+25*a^3+56*a^2-42*a-48)*q^133 + (-3/2*a^6-3/2*a^5+29/2*a^4+11*a^3-67/2*a^2-13*a+2)*q^134 + (a^6+2*a^5-7*a^4-14*a^3+14*a+20)*q^135 + (a^6+a^5-8*a^4-6*a^3+12*a^2)*q^136 + (-a^6+1/2*a^5+15/2*a^4-11/2*a^3-11*a^2+25/2*a+3)*q^137 + (a^4-a^3-6*a^2+4*a)*q^138 + 1*q^139 + (3/2*a^6-1/2*a^5-33/2*a^4+8*a^3+91/2*a^2-18*a-32)*q^140 + (3/2*a^6-11/2*a^5-27/2*a^4+45*a^3+55/2*a^2-66*a-12)*q^141 + (-1/2*a^6-3/2*a^5+9/2*a^4+8*a^3-19/2*a^2+3*a+4)*q^142 + (-3/4*a^6+1/4*a^5+31/4*a^4-5/2*a^3-81/4*a^2+4*a+11)*q^143 + (a^6-3*a^5-9*a^4+22*a^3+18*a^2-24*a-12)*q^144 + (-7/4*a^6-7/4*a^5+67/4*a^4+25/2*a^3-149/4*a^2-21*a+10)*q^145 + (-2*a^6+15*a^4-a^3-18*a^2+2*a+4)*q^146 + (-3/2*a^6+1/2*a^5+25/2*a^4-5*a^3-35/2*a^2+10*a-10)*q^147 + (-2*a^6+17*a^4-35*a^2+18)*q^148 + (1/2*a^6-1/2*a^5-9/2*a^4+5*a^3+15/2*a^2-11*a+10)*q^149 + (4*a^6+2*a^5-33*a^4-15*a^3+48*a^2+24*a+4)*q^150 + (-2*a^6+4*a^5+20*a^4-35*a^3-52*a^2+57*a+30)*q^151 + (-a^6+8*a^4-a^3-10*a^2-8)*q^152 + (5/2*a^6+3/2*a^5-45/2*a^4-9*a^3+89/2*a^2-2*a-6)*q^153 + (-2*a^3+4*a^2+3*a-2)*q^154 + (-1/4*a^6+5/4*a^5+11/4*a^4-10*a^3-23/4*a^2+35/2*a+2)*q^155 + (-2*a^6-a^5+18*a^4+7*a^3-36*a^2-8*a+12)*q^156 + (2*a^5+2*a^4-17*a^3-15*a^2+28*a+20)*q^157 + (-1/2*a^6-1/2*a^5+9/2*a^4+8*a^3-21/2*a^2-19*a-2)*q^158 + (4*a^6-4*a^5-37*a^4+35*a^3+82*a^2-66*a-32)*q^159 + (a^6+a^5-9*a^4-8*a^3+18*a^2+12*a-8)*q^160 + (a^6-a^5-11*a^4+8*a^3+34*a^2-13*a-24)*q^161 + (-a^6+11*a^4-2*a^3-28*a^2+13*a+8)*q^162 + (-1/4*a^6-1/4*a^5+9/4*a^4+7/2*a^3-15/4*a^2-12*a-7)*q^163 + (3*a^6-a^5-29*a^4+14*a^3+71*a^2-32*a-38)*q^164 + (-3/2*a^6+1/2*a^5+27/2*a^4-6*a^3-47/2*a^2+12*a-2)*q^165 + (-a^6-4*a^5+7*a^4+30*a^3-3*a^2-46*a-18)*q^166 + (-2*a^4+2*a^3+17*a^2-12*a-25)*q^167 + (-a^4-a^3+10*a^2-8)*q^168 + (-5/4*a^6+3/4*a^5+49/4*a^4-15/2*a^3-127/4*a^2+17*a+12)*q^169 + (3*a^6+4*a^5-25*a^4-34*a^3+38*a^2+56*a+12)*q^170 + (-3*a^6+5*a^5+28*a^4-41*a^3-63*a^2+64*a+32)*q^171 + (a^6+3*a^5-6*a^4-21*a^3-3*a^2+30*a+24)*q^172 + (1/2*a^5-1/2*a^4-11/2*a^3+6*a^2+21/2*a-5)*q^173 + (-a^6+5*a^5+8*a^4-37*a^3-17*a^2+44*a+16)*q^174 + (-3/4*a^6+9/4*a^5+27/4*a^4-33/2*a^3-77/4*a^2+23*a+21)*q^175 + (2*a^4-3*a^3-12*a^2+14*a+12)*q^176 + (3*a^5-2*a^4-22*a^3+11*a^2+24*a+4)*q^177 + (-a^6+3*a^5+10*a^4-21*a^3-24*a^2+24*a+10)*q^178 + (-7/2*a^6+3/2*a^5+63/2*a^4-13*a^3-137/2*a^2+19*a+36)*q^179 + (-7/2*a^6-3/2*a^5+61/2*a^4+13*a^3-109/2*a^2-16*a+6)*q^180 + (5/4*a^6-9/4*a^5-51/4*a^4+17*a^3+135/4*a^2-41/2*a-12)*q^181 + (-a^5+8*a^3+3*a^2-15*a-10)*q^182 + (-5*a^5+40*a^3+a^2-54*a-16)*q^183 + (2*a^6-17*a^4+a^3+34*a^2-8)*q^184 + (5/4*a^6-7/4*a^5-57/4*a^4+29/2*a^3+179/4*a^2-17*a-31)*q^185 + (3*a^6-3*a^5-26*a^4+25*a^3+49*a^2-38*a-16)*q^186 + (-2*a^6+2*a^5+18*a^4-16*a^3-37*a^2+23*a+12)*q^187 + (-2*a^6+3*a^5+18*a^4-26*a^3-45*a^2+44*a+30)*q^188 + (-2*a^6+3*a^5+19*a^4-26*a^3-46*a^2+42*a+40)*q^189 + (a^4-a^3-4*a^2+4*a+8)*q^190 + (a^5+2*a^4-11*a^3-13*a^2+30*a+19)*q^191 + (-a^6-3*a^5+8*a^4+24*a^3-12*a^2-32*a)*q^192 + (-9/4*a^6+17/4*a^5+91/4*a^4-32*a^3-239/4*a^2+81/2*a+32)*q^193 + (-2*a^6+a^5+17*a^4-8*a^3-32*a^2+10*a+8)*q^194 + (-1/2*a^6-7/2*a^5+3/2*a^4+28*a^3+31/2*a^2-42*a-30)*q^195 + (2*a^6-3*a^5-20*a^4+23*a^3+53*a^2-39*a-36)*q^196 + (2*a^6+a^5-17*a^4-9*a^3+34*a^2+17*a-10)*q^197 + (7/2*a^6-9/2*a^5-61/2*a^4+36*a^3+117/2*a^2-53*a-20)*q^198 + (3/2*a^6-5/2*a^5-33/2*a^4+22*a^3+91/2*a^2-39*a-20)*q^199 + (-2*a^6+17*a^4+a^3-34*a^2+4*a+8)*q^200 +  ...

-------------------------------------------------------
Gamma_0(140)
Weight 2

-------------------------------------------------------
J_0(140), dim = 19

-------------------------------------------------------
140A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3*5
Ker(ModPolar)  = Z/2^2*3*5 + Z/2^2*3*5
= B(Z/2 + Z/2) + C(Z/3 + Z/3) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/5 + Z/5)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.5555350611637625874 + -0.80259974498037537139e-5i
Omega-         = 0.43518616462934197091e-4 + 1.0762226869865488308i
L(1)           = 1.5555350611844682072
w1             = 0.77778928989011276079 + 0.5381073304945495135i
w2             = 0.7777457712736498266 + -0.53811535649199931725i
c4             = -1535.7419397110355016 + 0.14087974837118609279i
c6             = -183176.39507181000424 + -31.676316818436846614i
j              = 168.36038180336689451 + -0.94374037339720831991e-1i

HECKE EIGENFORM:
f(q) = q + 3*q^3 + -1*q^5 + -1*q^7 + 6*q^9 + -5*q^11 + -3*q^13 + -3*q^15 + -1*q^17 + 6*q^19 + -3*q^21 + 6*q^23 + 1*q^25 + 9*q^27 + -9*q^29 + -4*q^31 + -15*q^33 + 1*q^35 + 2*q^37 + -9*q^39 + -4*q^41 + 10*q^43 + -6*q^45 + -1*q^47 + 1*q^49 + -3*q^51 + 4*q^53 + 5*q^55 + 18*q^57 + -8*q^59 + -8*q^61 + -6*q^63 + 3*q^65 + 12*q^67 + 18*q^69 + 8*q^71 + 2*q^73 + 3*q^75 + 5*q^77 + 13*q^79 + 9*q^81 + -4*q^83 + 1*q^85 + -27*q^87 + 4*q^89 + 3*q^91 + -12*q^93 + -6*q^95 + -13*q^97 + -30*q^99 + 6*q^101 + 19*q^103 + 3*q^105 + -6*q^107 + -3*q^109 + 6*q^111 + 14*q^113 + -6*q^115 + -18*q^117 + 1*q^119 + 14*q^121 + -12*q^123 + -1*q^125 + -8*q^127 + 30*q^129 + -10*q^131 + -6*q^133 + -9*q^135 + -12*q^137 + -14*q^139 + -3*q^141 + 15*q^143 + 9*q^145 + 3*q^147 + -6*q^149 + 5*q^151 + -6*q^153 + 4*q^155 + -2*q^157 + 12*q^159 + -6*q^161 + -10*q^163 + 15*q^165 + 3*q^167 + -4*q^169 + 36*q^171 + -1*q^173 + -1*q^175 + -24*q^177 + -12*q^179 + -20*q^181 + -24*q^183 + -2*q^185 + 5*q^187 + -9*q^189 + 3*q^191 + -4*q^193 + 9*q^195 + 8*q^197 + 8*q^199 +  ...

-------------------------------------------------------
140B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 3
|L(1)/Omega|   = 1
Sha Bound      = 3^2

ANALYTIC INVARIANTS:

Omega+         = 1.3442842001972888923 + 0.17718470255818934843e-4i
Omega-         = 0.4024181105796899449e-4 + -2.6666284610701038824i
L(1)           = 1.3442842003140589131
w1             = 0.67212197919311546165 + 1.3333230897701798506i
w2             = 1.3442842001972888923 + 0.17718470255818934843e-4i
c4             = 256.06414834703984903 + -0.10913865821036062162e-1i
c6             = 20095.44110743754823 + -1.6965802749534145846i
j              = -74.961396615720212782 + -0.32057603147551646614e-2i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 1*q^5 + 1*q^7 + -2*q^9 + 3*q^11 + -1*q^13 + 1*q^15 + -3*q^17 + 2*q^19 + 1*q^21 + -6*q^23 + 1*q^25 + -5*q^27 + -9*q^29 + 8*q^31 + 3*q^33 + 1*q^35 + -10*q^37 + -1*q^39 + 2*q^43 + -2*q^45 + -3*q^47 + 1*q^49 + -3*q^51 + 3*q^55 + 2*q^57 + 12*q^59 + 8*q^61 + -2*q^63 + -1*q^65 + 8*q^67 + -6*q^69 + 14*q^73 + 1*q^75 + 3*q^77 + 5*q^79 + 1*q^81 + -12*q^83 + -3*q^85 + -9*q^87 + 12*q^89 + -1*q^91 + 8*q^93 + 2*q^95 + 17*q^97 + -6*q^99 + -6*q^101 + -7*q^103 + 1*q^105 + -6*q^107 + -19*q^109 + -10*q^111 + -6*q^113 + -6*q^115 + 2*q^117 + -3*q^119 + -2*q^121 + 1*q^125 + 20*q^127 + 2*q^129 + -18*q^131 + 2*q^133 + -5*q^135 + 12*q^137 + 2*q^139 + -3*q^141 + -3*q^143 + -9*q^145 + 1*q^147 + 18*q^149 + -19*q^151 + 6*q^153 + 8*q^155 + -22*q^157 + -6*q^161 + 2*q^163 + 3*q^165 + 9*q^167 + -12*q^169 + -4*q^171 + -3*q^173 + 1*q^175 + 12*q^177 + 12*q^179 + 8*q^181 + 8*q^183 + -10*q^185 + -9*q^187 + -5*q^189 + 3*q^191 + -4*q^193 + -1*q^195 + 12*q^197 + 20*q^199 +  ...

-------------------------------------------------------
140C (old = 70A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/3 + Z/3) + E(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
140D (old = 35A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + F(Z/3) + G(Z/3 + Z/3 + Z/3)

-------------------------------------------------------
140E (old = 35B), dim = 2

CONGRUENCES:
Modular Degree = 2^9
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
140F (old = 20A), dim = 1

CONGRUENCES:
Modular Degree = 2*3*5
Ker(ModPolar)  = Z/2*3*5 + Z/2*3*5
= A(Z/5 + Z/5) + D(Z/3) + E(Z/2 + Z/2) + G(Z/3)

-------------------------------------------------------
140G (old = 14A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= B(Z/3 + Z/3) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/3 + Z/3 + Z/3) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/3)

-------------------------------------------------------
Gamma_0(141)
Weight 2

-------------------------------------------------------
J_0(141), dim = 15

-------------------------------------------------------
141A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.364782450635576183 + -0.27505610466371149243e-4i
Omega-         = 0.44681067321806438474e-6 + -2.5402193109552389909i
L(1)           =
w1             = 0.44681067321806438474e-6 + -2.5402193109552389909i
w2             = -2.364782450635576183 + 0.27505610466371149243e-4i
c4             = 64.000042032515373051 + 0.18371250394987695655e-2i
c6             = 135.96173982112313051 + 0.27342537874861372417e-1i
j              = 1859.0976292895247229 + 0.44583044329785648154e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^4 + -1*q^5 + -3*q^7 + 1*q^9 + -3*q^11 + 2*q^12 + -4*q^13 + 1*q^15 + 4*q^16 + 8*q^17 + -6*q^19 + 2*q^20 + 3*q^21 + 3*q^23 + -4*q^25 + -1*q^27 + 6*q^28 + -1*q^29 + 4*q^31 + 3*q^33 + 3*q^35 + -2*q^36 + 1*q^37 + 4*q^39 + -10*q^41 + -8*q^43 + 6*q^44 + -1*q^45 + -1*q^47 + -4*q^48 + 2*q^49 + -8*q^51 + 8*q^52 + 10*q^53 + 3*q^55 + 6*q^57 + -10*q^59 + -2*q^60 + 2*q^61 + -3*q^63 + -8*q^64 + 4*q^65 + 4*q^67 + -16*q^68 + -3*q^69 + -6*q^71 + -8*q^73 + 4*q^75 + 12*q^76 + 9*q^77 + -3*q^79 + -4*q^80 + 1*q^81 + -18*q^83 + -6*q^84 + -8*q^85 + 1*q^87 + -2*q^89 + 12*q^91 + -6*q^92 + -4*q^93 + 6*q^95 + 5*q^97 + -3*q^99 + 8*q^100 + 12*q^101 + 11*q^103 + -3*q^105 + 9*q^107 + 2*q^108 + -1*q^111 + -12*q^112 + 6*q^113 + -3*q^115 + 2*q^116 + -4*q^117 + -24*q^119 + -2*q^121 + 10*q^123 + -8*q^124 + 9*q^125 + 8*q^127 + 8*q^129 + 14*q^131 + -6*q^132 + 18*q^133 + 1*q^135 + 10*q^137 + -10*q^139 + -6*q^140 + 1*q^141 + 12*q^143 + 4*q^144 + 1*q^145 + -2*q^147 + -2*q^148 + 10*q^151 + 8*q^153 + -4*q^155 + -8*q^156 + 9*q^157 + -10*q^159 + -9*q^161 + -2*q^163 + 20*q^164 + -3*q^165 + -19*q^167 + 3*q^169 + -6*q^171 + 16*q^172 + -18*q^173 + 12*q^175 + -12*q^176 + 10*q^177 + 5*q^179 + 2*q^180 + -18*q^181 + -2*q^183 + -1*q^185 + -24*q^187 + 2*q^188 + 3*q^189 + -4*q^191 + 8*q^192 + -14*q^193 + -4*q^195 + -4*q^196 + 22*q^197 + -28*q^199 +  ...

-------------------------------------------------------
141B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= C(Z/2) + F(Z/2 + Z/2^2) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.3805567394971343511 + -0.44513261567943541857e-6i
Omega-         = 0.15082013401358215677e-4 + -3.4069538185841775174i
L(1)           = 0.69027836974860305656
w1             = 0.69027082874186649644 + 1.703476686725780919i
w2             = 1.3805567394971343511 + -0.44513261567943541857e-6i
c4             = 384.98807291480823736 + 0.21124250390121294465e-2i
c6             = 10783.589834606111264 + -0.47974914545453380618e-1i
j              = -1664.8850212937149985 + -0.82896676072212399394e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + -1*q^4 + 1*q^6 + 4*q^7 + 3*q^8 + 1*q^9 + 1*q^12 + 6*q^13 + -4*q^14 + -1*q^16 + -6*q^17 + -1*q^18 + 2*q^19 + -4*q^21 + 4*q^23 + -3*q^24 + -5*q^25 + -6*q^26 + -1*q^27 + -4*q^28 + 8*q^29 + 6*q^31 + -5*q^32 + 6*q^34 + -1*q^36 + -6*q^37 + -2*q^38 + -6*q^39 + -8*q^41 + 4*q^42 + -6*q^43 + -4*q^46 + 1*q^47 + 1*q^48 + 9*q^49 + 5*q^50 + 6*q^51 + -6*q^52 + 2*q^53 + 1*q^54 + 12*q^56 + -2*q^57 + -8*q^58 + 12*q^59 + 2*q^61 + -6*q^62 + 4*q^63 + 7*q^64 + -2*q^67 + 6*q^68 + -4*q^69 + 3*q^72 + -10*q^73 + 6*q^74 + 5*q^75 + -2*q^76 + 6*q^78 + -4*q^79 + 1*q^81 + 8*q^82 + 4*q^83 + 4*q^84 + 6*q^86 + -8*q^87 + -10*q^89 + 24*q^91 + -4*q^92 + -6*q^93 + -1*q^94 + 5*q^96 + -18*q^97 + -9*q^98 + 5*q^100 + -10*q^101 + -6*q^102 + 4*q^103 + 18*q^104 + -2*q^106 + -12*q^107 + 1*q^108 + -2*q^109 + 6*q^111 + -4*q^112 + 8*q^113 + 2*q^114 + -8*q^116 + 6*q^117 + -12*q^118 + -24*q^119 + -11*q^121 + -2*q^122 + 8*q^123 + -6*q^124 + -4*q^126 + -6*q^127 + 3*q^128 + 6*q^129 + 20*q^131 + 8*q^133 + 2*q^134 + -18*q^136 + -16*q^137 + 4*q^138 + -2*q^139 + -1*q^141 + -1*q^144 + 10*q^146 + -9*q^147 + 6*q^148 + -10*q^149 + -5*q^150 + -2*q^151 + 6*q^152 + -6*q^153 + 6*q^156 + 22*q^157 + 4*q^158 + -2*q^159 + 16*q^161 + -1*q^162 + -10*q^163 + 8*q^164 + -4*q^166 + -12*q^167 + -12*q^168 + 23*q^169 + 2*q^171 + 6*q^172 + 2*q^173 + 8*q^174 + -20*q^175 + -12*q^177 + 10*q^178 + -20*q^179 + 14*q^181 + -24*q^182 + -2*q^183 + 12*q^184 + 6*q^186 + -1*q^188 + -4*q^189 + 24*q^191 + -7*q^192 + 10*q^193 + 18*q^194 + -9*q^196 + 14*q^197 + 2*q^199 + -15*q^200 +  ...

-------------------------------------------------------
141C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= B(Z/2) + D(Z/3 + Z/3) + F(Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 3.8498816292742880221 + -0.10011278987617271987e-4i
Omega-         = 0.91068957451941474856e-5 + -1.8233508176986016346i
L(1)           = 0.96247040732182618697
w1             = 1.924936261189271414 + 0.91167040320980700868i
w2             = 0.91068957451941474856e-5 + -1.8233508176986016346i
c4             = 97.000609521425671864 + -0.41285533002649089207e-2i
c6             = -2737.0940970354204905 + 0.30868033247832768196e-1i
j              = -239.72186210736550293 + 0.28698470220653659898e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + -1*q^4 + 2*q^5 + -1*q^6 + 3*q^8 + 1*q^9 + -2*q^10 + 4*q^11 + -1*q^12 + -2*q^13 + 2*q^15 + -1*q^16 + 2*q^17 + -1*q^18 + -2*q^20 + -4*q^22 + 3*q^24 + -1*q^25 + 2*q^26 + 1*q^27 + -6*q^29 + -2*q^30 + -4*q^31 + -5*q^32 + 4*q^33 + -2*q^34 + -1*q^36 + -10*q^37 + -2*q^39 + 6*q^40 + -2*q^41 + 8*q^43 + -4*q^44 + 2*q^45 + -1*q^47 + -1*q^48 + -7*q^49 + 1*q^50 + 2*q^51 + 2*q^52 + -2*q^53 + -1*q^54 + 8*q^55 + 6*q^58 + -4*q^59 + -2*q^60 + 14*q^61 + 4*q^62 + 7*q^64 + -4*q^65 + -4*q^66 + -8*q^67 + -2*q^68 + 16*q^71 + 3*q^72 + 2*q^73 + 10*q^74 + -1*q^75 + 2*q^78 + 8*q^79 + -2*q^80 + 1*q^81 + 2*q^82 + -4*q^83 + 4*q^85 + -8*q^86 + -6*q^87 + 12*q^88 + 18*q^89 + -2*q^90 + -4*q^93 + 1*q^94 + -5*q^96 + -14*q^97 + 7*q^98 + 4*q^99 + 1*q^100 + -10*q^101 + -2*q^102 + -16*q^103 + -6*q^104 + 2*q^106 + -4*q^107 + -1*q^108 + -18*q^109 + -8*q^110 + -10*q^111 + -10*q^113 + 6*q^116 + -2*q^117 + 4*q^118 + 6*q^120 + 5*q^121 + -14*q^122 + -2*q^123 + 4*q^124 + -12*q^125 + 4*q^127 + 3*q^128 + 8*q^129 + 4*q^130 + 12*q^131 + -4*q^132 + 8*q^134 + 2*q^135 + 6*q^136 + 14*q^137 + 16*q^139 + -1*q^141 + -16*q^142 + -8*q^143 + -1*q^144 + -12*q^145 + -2*q^146 + -7*q^147 + 10*q^148 + 6*q^149 + 1*q^150 + 4*q^151 + 2*q^153 + -8*q^155 + 2*q^156 + -18*q^157 + -8*q^158 + -2*q^159 + -10*q^160 + -1*q^162 + 24*q^163 + 2*q^164 + 8*q^165 + 4*q^166 + -9*q^169 + -4*q^170 + -8*q^172 + 6*q^173 + 6*q^174 + -4*q^176 + -4*q^177 + -18*q^178 + 20*q^179 + -2*q^180 + 6*q^181 + 14*q^183 + -20*q^185 + 4*q^186 + 8*q^187 + 1*q^188 + 7*q^192 + -14*q^193 + 14*q^194 + -4*q^195 + 7*q^196 + -10*q^197 + -4*q^198 + -4*q^199 + -3*q^200 +  ...

-------------------------------------------------------
141D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + C(Z/3 + Z/3) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.0537628697044468022 + 0.42165514020698612792e-5i
Omega-         = 0.62342517276994539406e-4 + 2.7634587509652251498i
L(1)           = 1.0537628697128829059
w1             = 0.62342517276994539406e-4 + 2.7634587509652251498i
w2             = 1.0537628697044468022 + 0.42165514020698612792e-5i
c4             = 1264.0236012522656316 + -0.20222305526229891889e-1i
c6             = 44937.258969266086282 + -1.0795700256805709143i
j              = 14324764.016538331296 + -6269.0202625375745758i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 1*q^3 + 2*q^4 + -1*q^5 + 2*q^6 + -3*q^7 + 1*q^9 + -2*q^10 + 1*q^11 + 2*q^12 + -2*q^13 + -6*q^14 + -1*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 + 1*q^27 + -6*q^28 + 3*q^29 + -2*q^30 + 2*q^31 + -8*q^32 + 1*q^33 + 4*q^34 + 3*q^35 + 2*q^36 + -7*q^37 + 12*q^38 + -2*q^39 + 10*q^41 + -6*q^42 + -10*q^43 + 2*q^44 + -1*q^45 + 6*q^46 + -1*q^47 + -4*q^48 + 2*q^49 + -8*q^50 + 2*q^51 + -4*q^52 + 4*q^53 + 2*q^54 + -1*q^55 + 6*q^57 + 6*q^58 + 8*q^59 + -2*q^60 + -10*q^61 + 4*q^62 + -3*q^63 + -8*q^64 + 2*q^65 + 2*q^66 + 10*q^67 + 4*q^68 + 3*q^69 + 6*q^70 + -14*q^71 + -10*q^73 + -14*q^74 + -4*q^75 + 12*q^76 + -3*q^77 + -4*q^78 + 17*q^79 + 4*q^80 + 1*q^81 + 20*q^82 + 8*q^83 + -6*q^84 + -2*q^85 + -20*q^86 + 3*q^87 + 6*q^89 + -2*q^90 + 6*q^91 + 6*q^92 + 2*q^93 + -2*q^94 + -6*q^95 + -8*q^96 + 1*q^97 + 4*q^98 + 1*q^99 + -8*q^100 + -16*q^101 + 4*q^102 + 11*q^103 + 3*q^105 + 8*q^106 + 5*q^107 + 2*q^108 + 6*q^109 + -2*q^110 + -7*q^111 + 12*q^112 + -10*q^113 + 12*q^114 + -3*q^115 + 6*q^116 + -2*q^117 + 16*q^118 + -6*q^119 + -10*q^121 + -20*q^122 + 10*q^123 + 4*q^124 + 9*q^125 + -6*q^126 + -8*q^127 + -10*q^129 + 4*q^130 + -6*q^131 + 2*q^132 + -18*q^133 + 20*q^134 + -1*q^135 + -22*q^137 + 6*q^138 + -2*q^139 + 6*q^140 + -1*q^141 + -28*q^142 + -2*q^143 + -4*q^144 + -3*q^145 + -20*q^146 + 2*q^147 + -14*q^148 + -12*q^149 + -8*q^150 + -14*q^151 + 2*q^153 + -6*q^154 + -2*q^155 + -4*q^156 + -3*q^157 + 34*q^158 + 4*q^159 + 8*q^160 + -9*q^161 + 2*q^162 + -6*q^163 + 20*q^164 + -1*q^165 + 16*q^166 + 21*q^167 + -9*q^169 + -4*q^170 + 6*q^171 + -20*q^172 + 6*q^174 + 12*q^175 + -4*q^176 + 8*q^177 + 12*q^178 + 5*q^179 + -2*q^180 + 12*q^181 + 12*q^182 + -10*q^183 + 7*q^185 + 4*q^186 + 2*q^187 + -2*q^188 + -3*q^189 + -12*q^190 + -18*q^191 + -8*q^192 + 4*q^193 + 2*q^194 + 2*q^195 + 4*q^196 + 8*q^197 + 2*q^198 + 26*q^199 +  ...

-------------------------------------------------------
141E (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*7
Ker(ModPolar)  = Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 1.4882073882316606266 + -0.21825392469644665878e-4i
Omega-         = 0.37006920722571552233e-4 + 1.3403278330854962186i
L(1)           =
w1             = -1.4882073882316606266 + 0.21825392469644665878e-4i
w2             = 0.37006920722571552233e-4 + 1.3403278330854962186i
c4             = 592.04225565533131344 + 0.55448757922214782889e-1i
c6             = -5463.7293534993744195 + -1.3841865434950799964i
j              = 2018.3460166721241431 + 0.76545875161121668281e-1i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + 1*q^3 + 2*q^4 + -3*q^5 + -2*q^6 + -3*q^7 + 1*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 + 1*q^27 + -6*q^28 + 1*q^29 + 6*q^30 + -2*q^31 + 8*q^32 + -5*q^33 + 12*q^34 + 9*q^35 + 2*q^36 + 1*q^37 + 12*q^38 + 2*q^39 + 6*q^41 + 6*q^42 + 2*q^43 + -10*q^44 + -3*q^45 + -18*q^46 + 1*q^47 + -4*q^48 + 2*q^49 + -8*q^50 + -6*q^51 + 4*q^52 + -2*q^54 + 15*q^55 + -6*q^57 + -2*q^58 + -12*q^59 + -6*q^60 + -2*q^61 + 4*q^62 + -3*q^63 + -8*q^64 + -6*q^65 + 10*q^66 + 2*q^67 + -12*q^68 + 9*q^69 + -18*q^70 + -2*q^71 + -2*q^73 + -2*q^74 + 4*q^75 + -12*q^76 + 15*q^77 + -4*q^78 + -15*q^79 + 12*q^80 + 1*q^81 + -12*q^82 + -4*q^83 + -6*q^84 + 18*q^85 + -4*q^86 + 1*q^87 + 10*q^89 + 6*q^90 + -6*q^91 + 18*q^92 + -2*q^93 + -2*q^94 + 18*q^95 + 8*q^96 + 1*q^97 + -4*q^98 + -5*q^99 + 8*q^100 + -4*q^101 + 12*q^102 + -13*q^103 + 9*q^105 + -17*q^107 + 2*q^108 + 6*q^109 + -30*q^110 + 1*q^111 + 12*q^112 + -14*q^113 + 12*q^114 + -27*q^115 + 2*q^116 + 2*q^117 + 24*q^118 + 18*q^119 + 14*q^121 + 4*q^122 + 6*q^123 + -4*q^124 + 3*q^125 + 6*q^126 + 20*q^127 + 2*q^129 + 12*q^130 + -22*q^131 + -10*q^132 + 18*q^133 + -4*q^134 + -3*q^135 + 6*q^137 + -18*q^138 + -10*q^139 + 18*q^140 + 1*q^141 + 4*q^142 + -10*q^143 + -4*q^144 + -3*q^145 + 4*q^146 + 2*q^147 + 2*q^148 + -8*q^150 + -10*q^151 + -6*q^153 + -30*q^154 + 6*q^155 + 4*q^156 + 13*q^157 + 30*q^158 + -24*q^160 + -27*q^161 + -2*q^162 + 18*q^163 + 12*q^164 + 15*q^165 + 8*q^166 + -1*q^167 + -9*q^169 + -36*q^170 + -6*q^171 + 4*q^172 + -2*q^174 + -12*q^175 + 20*q^176 + -12*q^177 + -20*q^178 + -9*q^179 + -6*q^180 + 12*q^181 + 12*q^182 + -2*q^183 + -3*q^185 + 4*q^186 + 30*q^187 + 2*q^188 + -3*q^189 + -36*q^190 + 26*q^191 + -8*q^192 + 16*q^193 + -2*q^194 + -6*q^195 + 4*q^196 + -24*q^197 + 10*q^198 + 10*q^199 +  ...

-------------------------------------------------------
141F (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4*43
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*43 + Z/2^2*43
= A(Z/2 + Z/2) + B(Z/2 + Z/2^2) + C(Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + G(Z/43 + Z/43)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 17
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 0.65810019923342794178 + 0.13346111545942674272e-4i
Omega-         = 0.85813693357598028263 + 0.47780840905372505839e-4i
L(1)           = 0.32905009968437794272

HECKE EIGENFORM:
a^2+a-4 = 0,
f(q) = q + a*q^2 + -1*q^3 + (-a+2)*q^4 + (a+1)*q^5 + -a*q^6 + (a+1)*q^7 + (a-4)*q^8 + 1*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 + -1*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 + 6*a*q^38 + (2*a+4)*q^39 + -4*a*q^40 + (-2*a+2)*q^41 + -4*q^42 + (2*a+8)*q^43 + (-6*a+10)*q^44 + (a+1)*q^45 + -12*q^46 + 1*q^47 + 3*a*q^48 + (a-2)*q^49 + (-a+4)*q^50 + 2*a*q^51 + -2*a*q^52 + (4*a-2)*q^53 + -a*q^54 + (3*a-1)*q^55 + -4*a*q^56 + -6*q^57 + (-8*a+4)*q^58 + (-2*a+2)*q^59 + (-2*a+2)*q^60 + 2*q^61 + (2*a+8)*q^62 + (a+1)*q^63 + (a+4)*q^64 + (-4*a-12)*q^65 + (-4*a+4)*q^66 + -2*a*q^67 + (-6*a+8)*q^68 + (3*a+3)*q^69 + (4*a+4)*q^70 + (-2*a-2)*q^71 + (a-4)*q^72 + (-2*a+4)*q^73 + (6*a-4)*q^74 + -a*q^75 + (-6*a+12)*q^76 + (3*a-1)*q^77 + (2*a+8)*q^78 + (a-7)*q^79 + -12*q^80 + 1*q^81 + (4*a-8)*q^82 + (-2*a+2)*q^83 + (-2*a+2)*q^84 + -8*q^85 + (6*a+8)*q^86 + (-a+7)*q^87 + (8*a-16)*q^88 + (4*a+2)*q^89 + 4*q^90 + (-4*a-12)*q^91 + (-6*a+6)*q^92 + (-2*a-4)*q^93 + a*q^94 + (6*a+6)*q^95 + (-a+4)*q^96 + (7*a+1)*q^97 + (-3*a+4)*q^98 + (-a+3)*q^99 + (3*a-4)*q^100 + (2*a+16)*q^101 + (-2*a+8)*q^102 + (-a+7)*q^103 + (6*a+8)*q^104 + (-a-5)*q^105 + (-6*a+16)*q^106 + (-a-1)*q^107 + (a-2)*q^108 + (-2*a+4)*q^109 + (-4*a+12)*q^110 + (a-5)*q^111 + -12*q^112 + (-2*a-14)*q^113 + -6*a*q^114 + (-3*a-15)*q^115 + (10*a-18)*q^116 + (-2*a-4)*q^117 + (4*a-8)*q^118 + -8*q^119 + 4*a*q^120 + (-7*a+2)*q^121 + 2*a*q^122 + (2*a-2)*q^123 + 2*a*q^124 + (-5*a-1)*q^125 + 4*q^126 + (-2*a-4)*q^127 + (a+12)*q^128 + (-2*a-8)*q^129 + (-8*a-16)*q^130 + (2*a+6)*q^131 + (6*a-10)*q^132 + (6*a+6)*q^133 + (2*a-8)*q^134 + (-a-1)*q^135 + (10*a-8)*q^136 + (2*a-18)*q^137 + 12*q^138 + (4*a+14)*q^139 + (-2*a+6)*q^140 + -1*q^141 + -8*q^142 + (-4*a-4)*q^143 + -3*a*q^144 + (-7*a-3)*q^145 + (6*a-8)*q^146 + (-a+2)*q^147 + (-8*a+14)*q^148 + (6*a+4)*q^149 + (a-4)*q^150 + (-4*a-2)*q^151 + (6*a-24)*q^152 + -2*a*q^153 + (-4*a+12)*q^154 + (4*a+12)*q^155 + 2*a*q^156 + (-5*a-3)*q^157 + (-8*a+4)*q^158 + (-4*a+2)*q^159 + -4*a*q^160 + (-3*a-15)*q^161 + a*q^162 + (-4*a-2)*q^163 + (-8*a+12)*q^164 + (-3*a+1)*q^165 + (4*a-8)*q^166 + (3*a-5)*q^167 + 4*a*q^168 + (12*a+19)*q^169 + -8*a*q^170 + 6*q^171 + (-2*a+8)*q^172 + (-4*a+6)*q^173 + (8*a-4)*q^174 + 4*q^175 + (-12*a+12)*q^176 + (2*a-2)*q^177 + (-2*a+16)*q^178 + (-5*a-13)*q^179 + (2*a-2)*q^180 + (-4*a-6)*q^181 + (-8*a-16)*q^182 + -2*q^183 + 12*a*q^184 + (5*a+1)*q^185 + (-2*a-8)*q^186 + (-8*a+8)*q^187 + (-a+2)*q^188 + (-a-1)*q^189 + 24*q^190 + 8*a*q^191 + (-a-4)*q^192 + (8*a+2)*q^193 + (-6*a+28)*q^194 + (4*a+12)*q^195 + (5*a-8)*q^196 + -2*q^197 + (4*a-4)*q^198 + (2*a-8)*q^199 + (-5*a+4)*q^200 +  ...

-------------------------------------------------------
141G (old = 47A), dim = 4

CONGRUENCES:
Modular Degree = 3*7*43
Ker(ModPolar)  = Z/3*7*43 + Z/3*7*43
= B(Z/3 + Z/3) + E(Z/7 + Z/7) + F(Z/43 + Z/43)

-------------------------------------------------------
Gamma_0(142)
Weight 2

-------------------------------------------------------
J_0(142), dim = 17

-------------------------------------------------------
142A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.2152200580553082216 + 0.43127061552246858734e-5i
Omega-         = 0.11925606692923189889e-4 + -2.6589355627057906537i
L(1)           =
w1             = 0.11925606692923189889e-4 + -2.6589355627057906537i
w2             = -2.2152200580553082216 + -0.43127061552246858734e-5i
c4             = 73.001518643300191671 + -0.72774142747787901265e-3i
c6             = 379.029399537501462 + -0.16687133870017789488e-2i
j              = 2739.7050599820375363 + 0.33847344041273213614e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + 1*q^4 + -2*q^5 + 1*q^6 + -1*q^7 + -1*q^8 + -2*q^9 + 2*q^10 + -2*q^11 + -1*q^12 + -3*q^13 + 1*q^14 + 2*q^15 + 1*q^16 + -6*q^17 + 2*q^18 + 5*q^19 + -2*q^20 + 1*q^21 + 2*q^22 + -1*q^23 + 1*q^24 + -1*q^25 + 3*q^26 + 5*q^27 + -1*q^28 + 6*q^29 + -2*q^30 + 1*q^31 + -1*q^32 + 2*q^33 + 6*q^34 + 2*q^35 + -2*q^36 + 6*q^37 + -5*q^38 + 3*q^39 + 2*q^40 + -6*q^41 + -1*q^42 + 5*q^43 + -2*q^44 + 4*q^45 + 1*q^46 + -3*q^47 + -1*q^48 + -6*q^49 + 1*q^50 + 6*q^51 + -3*q^52 + -6*q^53 + -5*q^54 + 4*q^55 + 1*q^56 + -5*q^57 + -6*q^58 + 2*q^59 + 2*q^60 + -6*q^61 + -1*q^62 + 2*q^63 + 1*q^64 + 6*q^65 + -2*q^66 + -14*q^67 + -6*q^68 + 1*q^69 + -2*q^70 + -1*q^71 + 2*q^72 + -17*q^73 + -6*q^74 + 1*q^75 + 5*q^76 + 2*q^77 + -3*q^78 + 10*q^79 + -2*q^80 + 1*q^81 + 6*q^82 + 4*q^83 + 1*q^84 + 12*q^85 + -5*q^86 + -6*q^87 + 2*q^88 + 9*q^89 + -4*q^90 + 3*q^91 + -1*q^92 + -1*q^93 + 3*q^94 + -10*q^95 + 1*q^96 + -6*q^97 + 6*q^98 + 4*q^99 + -1*q^100 + -8*q^101 + -6*q^102 + -4*q^103 + 3*q^104 + -2*q^105 + 6*q^106 + -17*q^107 + 5*q^108 + 12*q^109 + -4*q^110 + -6*q^111 + -1*q^112 + 6*q^113 + 5*q^114 + 2*q^115 + 6*q^116 + 6*q^117 + -2*q^118 + 6*q^119 + -2*q^120 + -7*q^121 + 6*q^122 + 6*q^123 + 1*q^124 + 12*q^125 + -2*q^126 + 16*q^127 + -1*q^128 + -5*q^129 + -6*q^130 + 3*q^131 + 2*q^132 + -5*q^133 + 14*q^134 + -10*q^135 + 6*q^136 + 8*q^137 + -1*q^138 + -8*q^139 + 2*q^140 + 3*q^141 + 1*q^142 + 6*q^143 + -2*q^144 + -12*q^145 + 17*q^146 + 6*q^147 + 6*q^148 + 3*q^149 + -1*q^150 + -5*q^152 + 12*q^153 + -2*q^154 + -2*q^155 + 3*q^156 + 2*q^157 + -10*q^158 + 6*q^159 + 2*q^160 + 1*q^161 + -1*q^162 + -6*q^163 + -6*q^164 + -4*q^165 + -4*q^166 + -24*q^167 + -1*q^168 + -4*q^169 + -12*q^170 + -10*q^171 + 5*q^172 + -9*q^173 + 6*q^174 + 1*q^175 + -2*q^176 + -2*q^177 + -9*q^178 + 21*q^179 + 4*q^180 + -19*q^181 + -3*q^182 + 6*q^183 + 1*q^184 + -12*q^185 + 1*q^186 + 12*q^187 + -3*q^188 + -5*q^189 + 10*q^190 + -20*q^191 + -1*q^192 + -2*q^193 + 6*q^194 + -6*q^195 + -6*q^196 + 27*q^197 + -4*q^198 + -26*q^199 + 1*q^200 +  ...

-------------------------------------------------------
142B (new) , dim = 1

CONGRUENCES:
Modular Degree = 3^2
Ker(ModPolar)  = Z/3^2 + Z/3^2
= C(Z/3 + Z/3) + F(Z/3 + Z/3) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.8851234557605540043 + -0.16872882337570928363e-4i
Omega-         = 0.71905484201968476787e-4 + 3.6481606755620854766i
L(1)           = 0.94256172791803237532
w1             = 0.94252577513817601789 + -1.8240887742222115238i
w2             = -1.8851234557605540043 + 0.16872882337570928363e-4i
c4             = 57.007176328062302167 + -0.22128795618981684994e-2i
c6             = 2835.0937277685975439 + 0.24047327936200862073i
j              = -40.768499023846059549 + 0.11938765369547073e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^4 + 2*q^5 + -1*q^8 + -3*q^9 + -2*q^10 + 6*q^11 + 4*q^13 + 1*q^16 + 6*q^17 + 3*q^18 + -8*q^19 + 2*q^20 + -6*q^22 + -4*q^23 + -1*q^25 + -4*q^26 + -2*q^29 + -8*q^31 + -1*q^32 + -6*q^34 + -3*q^36 + 10*q^37 + 8*q^38 + -2*q^40 + -2*q^41 + -8*q^43 + 6*q^44 + -6*q^45 + 4*q^46 + -4*q^47 + -7*q^49 + 1*q^50 + 4*q^52 + 12*q^55 + 2*q^58 + 10*q^59 + -8*q^61 + 8*q^62 + 1*q^64 + 8*q^65 + 2*q^67 + 6*q^68 + 1*q^71 + 3*q^72 + -2*q^73 + -10*q^74 + -8*q^76 + 2*q^80 + 9*q^81 + 2*q^82 + -4*q^83 + 12*q^85 + 8*q^86 + -6*q^88 + 6*q^89 + 6*q^90 + -4*q^92 + 4*q^94 + -16*q^95 + 14*q^97 + 7*q^98 + -18*q^99 + -1*q^100 + -6*q^101 + 8*q^103 + -4*q^104 + -4*q^107 + -18*q^109 + -12*q^110 + 10*q^113 + -8*q^115 + -2*q^116 + -12*q^117 + -10*q^118 + 25*q^121 + 8*q^122 + -8*q^124 + -12*q^125 + -4*q^127 + -1*q^128 + -8*q^130 + 4*q^131 + -2*q^134 + -6*q^136 + -2*q^137 + 2*q^139 + -1*q^142 + 24*q^143 + -3*q^144 + -4*q^145 + 2*q^146 + 10*q^148 + -8*q^149 + 16*q^151 + 8*q^152 + -18*q^153 + -16*q^155 + 10*q^157 + -2*q^160 + -9*q^162 + -2*q^163 + -2*q^164 + 4*q^166 + -8*q^167 + 3*q^169 + -12*q^170 + 24*q^171 + -8*q^172 + 6*q^176 + -6*q^178 + 12*q^179 + -6*q^180 + -12*q^181 + 4*q^184 + 20*q^185 + 36*q^187 + -4*q^188 + 16*q^190 + -8*q^191 + 22*q^193 + -14*q^194 + -7*q^196 + -24*q^197 + 18*q^198 + -8*q^199 + 1*q^200 +  ...

-------------------------------------------------------
142C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^4
Ker(ModPolar)  = Z/2^2*3^4 + Z/2^2*3^4
= A(Z/2 + Z/2) + B(Z/3 + Z/3) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/3^2 + Z/3^2) + G(Z/3^2 + Z/3^2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 0.65040426129601865757 + 0.70064302156858313754e-4i
Omega-         = 0.71342810990727060353e-4 + -0.33360736933319567776i
L(1)           = 0.65040426506983035793
w1             = 0.65040426129601865757 + 0.70064302156858313754e-4i
w2             = 0.71342810990727060353e-4 + -0.33360736933319567776i
c4             = 125972.38252433347915 + -107.57019876999224524i
c6             = -44526228.311544889013 + 57272.354446029698263i
j              = 209676.02901986210195 + -271.61922168247522278i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 3*q^3 + 1*q^4 + 2*q^5 + -3*q^6 + -3*q^7 + -1*q^8 + 6*q^9 + -2*q^10 + -6*q^11 + 3*q^12 + -5*q^13 + 3*q^14 + 6*q^15 + 1*q^16 + 6*q^17 + -6*q^18 + 1*q^19 + 2*q^20 + -9*q^21 + 6*q^22 + 5*q^23 + -3*q^24 + -1*q^25 + 5*q^26 + 9*q^27 + -3*q^28 + -2*q^29 + -6*q^30 + -5*q^31 + -1*q^32 + -18*q^33 + -6*q^34 + -6*q^35 + 6*q^36 + -2*q^37 + -1*q^38 + -15*q^39 + -2*q^40 + 10*q^41 + 9*q^42 + 1*q^43 + -6*q^44 + 12*q^45 + -5*q^46 + -1*q^47 + 3*q^48 + 2*q^49 + 1*q^50 + 18*q^51 + -5*q^52 + 6*q^53 + -9*q^54 + -12*q^55 + 3*q^56 + 3*q^57 + 2*q^58 + -2*q^59 + 6*q^60 + -2*q^61 + 5*q^62 + -18*q^63 + 1*q^64 + -10*q^65 + 18*q^66 + 2*q^67 + 6*q^68 + 15*q^69 + 6*q^70 + 1*q^71 + -6*q^72 + 7*q^73 + 2*q^74 + -3*q^75 + 1*q^76 + 18*q^77 + 15*q^78 + -6*q^79 + 2*q^80 + 9*q^81 + -10*q^82 + -4*q^83 + -9*q^84 + 12*q^85 + -1*q^86 + -6*q^87 + 6*q^88 + 9*q^89 + -12*q^90 + 15*q^91 + 5*q^92 + -15*q^93 + 1*q^94 + 2*q^95 + -3*q^96 + 2*q^97 + -2*q^98 + -36*q^99 + -1*q^100 + -12*q^101 + -18*q^102 + -4*q^103 + 5*q^104 + -18*q^105 + -6*q^106 + 11*q^107 + 9*q^108 + 12*q^109 + 12*q^110 + -6*q^111 + -3*q^112 + -14*q^113 + -3*q^114 + 10*q^115 + -2*q^116 + -30*q^117 + 2*q^118 + -18*q^119 + -6*q^120 + 25*q^121 + 2*q^122 + 30*q^123 + -5*q^124 + -12*q^125 + 18*q^126 + 8*q^127 + -1*q^128 + 3*q^129 + 10*q^130 + -17*q^131 + -18*q^132 + -3*q^133 + -2*q^134 + 18*q^135 + -6*q^136 + 16*q^137 + -15*q^138 + -16*q^139 + -6*q^140 + -3*q^141 + -1*q^142 + 30*q^143 + 6*q^144 + -4*q^145 + -7*q^146 + 6*q^147 + -2*q^148 + -11*q^149 + 3*q^150 + 4*q^151 + -1*q^152 + 36*q^153 + -18*q^154 + -10*q^155 + -15*q^156 + 22*q^157 + 6*q^158 + 18*q^159 + -2*q^160 + -15*q^161 + -9*q^162 + 10*q^163 + 10*q^164 + -36*q^165 + 4*q^166 + 16*q^167 + 9*q^168 + 12*q^169 + -12*q^170 + 6*q^171 + 1*q^172 + 9*q^173 + 6*q^174 + 3*q^175 + -6*q^176 + -6*q^177 + -9*q^178 + 9*q^179 + 12*q^180 + -21*q^181 + -15*q^182 + -6*q^183 + -5*q^184 + -4*q^185 + 15*q^186 + -36*q^187 + -1*q^188 + -27*q^189 + -2*q^190 + -8*q^191 + 3*q^192 + -14*q^193 + -2*q^194 + -30*q^195 + 2*q^196 + 21*q^197 + 36*q^198 + -14*q^199 + 1*q^200 +  ...

-------------------------------------------------------
142D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 2.6000187528165084128 + 0.2797494273090816051e-4i
Omega-         = 0.15027424906446022282e-4 + 1.4193236186950757402i
L(1)           = 0.86667291765566894377
w1             = -2.6000187528165084128 + -0.2797494273090816051e-4i
w2             = 0.15027424906446022282e-4 + 1.4193236186950757402i
c4             = 384.9798183483921185 + 0.16077077154347122504e-1i
c6             = -7488.4003025509079033 + -0.48506534020132228984i
j              = 100452.78496519147501 + 24.498139854790518514i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^3 + 1*q^4 + 1*q^6 + -1*q^7 + 1*q^8 + -2*q^9 + 1*q^12 + -1*q^13 + -1*q^14 + 1*q^16 + -2*q^18 + -1*q^19 + -1*q^21 + 3*q^23 + 1*q^24 + -5*q^25 + -1*q^26 + -5*q^27 + -1*q^28 + 5*q^31 + 1*q^32 + -2*q^36 + -4*q^37 + -1*q^38 + -1*q^39 + -1*q^42 + -1*q^43 + 3*q^46 + 9*q^47 + 1*q^48 + -6*q^49 + -5*q^50 + -1*q^52 + 6*q^53 + -5*q^54 + -1*q^56 + -1*q^57 + 6*q^59 + 2*q^61 + 5*q^62 + 2*q^63 + 1*q^64 + 8*q^67 + 3*q^69 + -1*q^71 + -2*q^72 + -1*q^73 + -4*q^74 + -5*q^75 + -1*q^76 + -1*q^78 + 8*q^79 + 1*q^81 + 12*q^83 + -1*q^84 + -1*q^86 + -3*q^89 + 1*q^91 + 3*q^92 + 5*q^93 + 9*q^94 + 1*q^96 + -16*q^97 + -6*q^98 + -5*q^100 + 12*q^101 + 8*q^103 + -1*q^104 + 6*q^106 + -3*q^107 + -5*q^108 + -16*q^109 + -4*q^111 + -1*q^112 + 6*q^113 + -1*q^114 + 2*q^117 + 6*q^118 + -11*q^121 + 2*q^122 + 5*q^124 + 2*q^126 + -16*q^127 + 1*q^128 + -1*q^129 + -3*q^131 + 1*q^133 + 8*q^134 + -12*q^137 + 3*q^138 + -16*q^139 + 9*q^141 + -1*q^142 + -2*q^144 + -1*q^146 + -6*q^147 + -4*q^148 + -15*q^149 + -5*q^150 + -16*q^151 + -1*q^152 + -1*q^156 + 14*q^157 + 8*q^158 + 6*q^159 + -3*q^161 + 1*q^162 + -4*q^163 + 12*q^166 + -18*q^167 + -1*q^168 + -12*q^169 + 2*q^171 + -1*q^172 + 21*q^173 + 5*q^175 + 6*q^177 + -3*q^178 + -9*q^179 + 11*q^181 + 1*q^182 + 2*q^183 + 3*q^184 + 5*q^186 + 9*q^188 + 5*q^189 + 6*q^191 + 1*q^192 + -4*q^193 + -16*q^194 + -6*q^196 + 21*q^197 + 8*q^199 + -5*q^200 +  ...

-------------------------------------------------------
142E (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2^2*3^2 + Z/2^2*3^2
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/3 + Z/3) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 1.7320938100399497687 + 0.34827988979004086082e-4i
Omega-         = 0.19198412482483557506e-4 + -1.3096814536842379029i
L(1)           =
w1             = -1.7320938100399497687 + -0.34827988979004086082e-4i
w2             = -0.19198412482483557506e-4 + 1.3096814536842379029i
c4             = 561.09228732127510588 + -0.34322841998242243681e-1i
c6             = -10667.615181671324542 + 0.86865960163908157086i
j              = 4856.8850766032479684 + 0.18164928052414111446i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -3*q^3 + 1*q^4 + -4*q^5 + -3*q^6 + -3*q^7 + 1*q^8 + 6*q^9 + -4*q^10 + -3*q^12 + 1*q^13 + -3*q^14 + 12*q^15 + 1*q^16 + 6*q^18 + -5*q^19 + -4*q^20 + 9*q^21 + -7*q^23 + -3*q^24 + 11*q^25 + 1*q^26 + -9*q^27 + -3*q^28 + -8*q^29 + 12*q^30 + 7*q^31 + 1*q^32 + 12*q^35 + 6*q^36 + 4*q^37 + -5*q^38 + -3*q^39 + -4*q^40 + 4*q^41 + 9*q^42 + -5*q^43 + -24*q^45 + -7*q^46 + -13*q^47 + -3*q^48 + 2*q^49 + 11*q^50 + 1*q^52 + -6*q^53 + -9*q^54 + -3*q^56 + 15*q^57 + -8*q^58 + 10*q^59 + 12*q^60 + -2*q^61 + 7*q^62 + -18*q^63 + 1*q^64 + -4*q^65 + -4*q^67 + 21*q^69 + 12*q^70 + 1*q^71 + 6*q^72 + 7*q^73 + 4*q^74 + -33*q^75 + -5*q^76 + -3*q^78 + -4*q^80 + 9*q^81 + 4*q^82 + -4*q^83 + 9*q^84 + -5*q^86 + 24*q^87 + -3*q^89 + -24*q^90 + -3*q^91 + -7*q^92 + -21*q^93 + -13*q^94 + 20*q^95 + -3*q^96 + -4*q^97 + 2*q^98 + 11*q^100 + 8*q^103 + 1*q^104 + -36*q^105 + -6*q^106 + 17*q^107 + -9*q^108 + -12*q^111 + -3*q^112 + -14*q^113 + 15*q^114 + 28*q^115 + -8*q^116 + 6*q^117 + 10*q^118 + 12*q^120 + -11*q^121 + -2*q^122 + -12*q^123 + 7*q^124 + -24*q^125 + -18*q^126 + 8*q^127 + 1*q^128 + 15*q^129 + -4*q^130 + 1*q^131 + 15*q^133 + -4*q^134 + 36*q^135 + 4*q^137 + 21*q^138 + 8*q^139 + 12*q^140 + 39*q^141 + 1*q^142 + 6*q^144 + 32*q^145 + 7*q^146 + -6*q^147 + 4*q^148 + -17*q^149 + -33*q^150 + 4*q^151 + -5*q^152 + -28*q^155 + -3*q^156 + 10*q^157 + 18*q^159 + -4*q^160 + 21*q^161 + 9*q^162 + -8*q^163 + 4*q^164 + -4*q^166 + -2*q^167 + 9*q^168 + -12*q^169 + -30*q^171 + -5*q^172 + -21*q^173 + 24*q^174 + -33*q^175 + -30*q^177 + -3*q^178 + 3*q^179 + -24*q^180 + -3*q^181 + -3*q^182 + 6*q^183 + -7*q^184 + -16*q^185 + -21*q^186 + -13*q^188 + 27*q^189 + 20*q^190 + 10*q^191 + -3*q^192 + 4*q^193 + -4*q^194 + 12*q^195 + 2*q^196 + 27*q^197 + -20*q^199 + 11*q^200 +  ...

-------------------------------------------------------
142F (old = 71A), dim = 3

CONGRUENCES:
Modular Degree = 3^7
Ker(ModPolar)  = Z/3^3 + Z/3^3 + Z/3^4 + Z/3^4
= B(Z/3 + Z/3) + C(Z/3^2 + Z/3^2) + E(Z/3 + Z/3) + G(Z/3^2 + Z/3^2 + Z/3^2 + Z/3^2)

-------------------------------------------------------
142G (old = 71B), dim = 3

CONGRUENCES:
Modular Degree = 3^7
Ker(ModPolar)  = Z/3^3 + Z/3^3 + Z/3^4 + Z/3^4
= B(Z/3 + Z/3) + C(Z/3^2 + Z/3^2) + E(Z/3 + Z/3) + F(Z/3^2 + Z/3^2 + Z/3^2 + Z/3^2)

-------------------------------------------------------
Gamma_0(143)
Weight 2

-------------------------------------------------------
J_0(143), dim = 13

-------------------------------------------------------
143A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= C(Z/2 + Z/2) + D(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 1.9699554242458619502 + -0.19046563142132216968e-4i
Omega-         = 0.29767384998308242465e-4 + -4.0314899052501087284i
L(1)           =
w1             = -0.98496282843043182095 + -2.0157354293434832981i
w2             = -1.9699554242458619502 + 0.19046563142132216968e-4i
c4             = 63.988312190886379381 + 0.67420745953327044597e-2i
c6             = 1863.9644945761462311 + 0.24079895776234209529e-1i
j              = -140.9357080403194531 + -0.4424372261638875733e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^4 + -1*q^5 + -2*q^7 + -2*q^9 + -1*q^11 + 2*q^12 + -1*q^13 + 1*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 + 1*q^33 + 2*q^35 + 4*q^36 + -11*q^37 + 1*q^39 + 10*q^41 + -4*q^43 + 2*q^44 + 2*q^45 + -4*q^47 + -4*q^48 + -3*q^49 + 4*q^51 + 2*q^52 + 2*q^53 + 1*q^55 + -2*q^57 + -1*q^59 + -2*q^60 + -2*q^61 + 4*q^63 + -8*q^64 + 1*q^65 + -1*q^67 + 8*q^68 + -7*q^69 + -9*q^71 + -16*q^73 + 4*q^75 + -4*q^76 + 2*q^77 + 8*q^79 + -4*q^80 + 1*q^81 + -4*q^84 + 4*q^85 + 2*q^87 + -7*q^89 + 2*q^91 + -14*q^92 + 3*q^93 + -2*q^95 + -13*q^97 + 2*q^99 + 8*q^100 + 18*q^101 + 8*q^103 + -2*q^105 + 8*q^107 + -10*q^108 + 4*q^109 + 11*q^111 + -8*q^112 + 1*q^113 + -7*q^115 + 4*q^116 + 2*q^117 + 8*q^119 + 1*q^121 + -10*q^123 + 6*q^124 + 9*q^125 + -8*q^127 + 4*q^129 + 18*q^131 + -2*q^132 + -4*q^133 + -5*q^135 + -17*q^137 + 18*q^139 + -4*q^140 + 4*q^141 + 1*q^143 + -8*q^144 + 2*q^145 + 3*q^147 + 22*q^148 + 14*q^149 + 4*q^151 + 8*q^153 + 3*q^155 + -2*q^156 + 5*q^157 + -2*q^159 + -14*q^161 + -4*q^163 + -20*q^164 + -1*q^165 + 4*q^167 + 1*q^169 + -4*q^171 + 8*q^172 + -8*q^173 + 8*q^175 + -4*q^176 + 1*q^177 + -15*q^179 + -4*q^180 + 7*q^181 + 2*q^183 + 11*q^185 + 4*q^187 + 8*q^188 + -10*q^189 + -15*q^191 + 8*q^192 + -24*q^193 + -1*q^195 + 6*q^196 + -10*q^197 + -4*q^199 +  ...

-------------------------------------------------------
143B (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3^2 + Z/2*3^2
= C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + D(Z/3^2 + Z/3^2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 19*103
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 7
Torsion Bound  = 7
|L(1)/Omega|   = 1/7
Sha Bound      = 7

ANALYTIC INVARIANTS:

Omega+         = 24.169333022836019467 + -0.37758678282642772087e-4i
Omega-         = 9.364945274603284456 + -0.25455569285774421266e-3i
L(1)           = 3.4527618604093591174

HECKE EIGENFORM:
a^4-3*a^3-a^2+5*a+1 = 0,
f(q) = 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 + 1*q^11 + (a^3-4*a^2+a+6)*q^12 + -1*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 + (-2*a^3-a^2+12*a+3)*q^38 + (a^3-3*a^2+3)*q^39 + (-2*a^3-2*a^2+6*a+4)*q^40 + (a^3-3*a^2+4*a+2)*q^41 + (2*a^3-6*a^2+a+2)*q^42 + (-2*a+8)*q^43 + (a^2-2)*q^44 + (6*a^3-14*a^2-6*a+18)*q^45 + (2*a^3-a^2-7*a-1)*q^46 + (-2*a^3+2*a^2+6*a-4)*q^47 + (-a^3+4*a^2-11)*q^48 + (-a^3+3*a^2-2*a)*q^49 + (4*a^3-13*a-4)*q^50 + (-4*a^3+10*a^2+8*a-18)*q^51 + (-a^2+2)*q^52 + (-a^3+3*a^2-2*a-3)*q^53 + (2*a^3-2*a^2-7*a)*q^54 + (-2*a^2+2*a+4)*q^55 + (4*a^2-5*a+1)*q^56 + (-a^3+3*a^2-4*a+8)*q^57 + (-2*a^3+2*a^2+4*a+2)*q^58 + (2*a^3-2*a^2-4*a-6)*q^59 + (4*a^3-12*a^2-2*a+20)*q^60 + (-2*a^3+4*a^2+6*a-8)*q^61 + (6*a^3-4*a^2-18*a-4)*q^62 + (-4*a^2+2*a+15)*q^63 + (-2*a^3+8*a^2-3*a-8)*q^64 + (2*a^2-2*a-4)*q^65 + (-a^2+2*a+1)*q^66 + (-4*a^3+4*a^2+14*a)*q^67 + (-6*a^3+12*a^2+8*a-12)*q^68 + (2*a^3-6*a^2+5)*q^69 + (-2*a^3+2*a^2-2)*q^70 + (-4*a^3+14*a^2-4*a-18)*q^71 + (-3*a^3+2*a^2+5*a+5)*q^72 + (3*a^3-3*a^2-12*a+7)*q^73 + (-4*a^3+8*a^2+8*a)*q^74 + (-3*a^3+9*a^2+4*a-21)*q^75 + (-a^3-4*a^2+9*a+8)*q^76 + (a^3-a^2-4*a+2)*q^77 + (a^2-2*a-1)*q^78 + (2*a^3-8*a^2-4*a+12)*q^79 + (-8*a^2+2*a+14)*q^80 + (2*a^3-6*a^2+4*a+4)*q^81 + (5*a^2-3*a-1)*q^82 + (-a^3+5*a^2-4*a-6)*q^83 + (4*a^3-13*a^2+16)*q^84 + (4*a^3-12*a^2+24)*q^85 + (-2*a^2+8*a)*q^86 + (4*a^3-14*a^2+2*a+20)*q^87 + (a^3-4*a)*q^88 + (-2*a^3+6*a^2-2*a-2)*q^89 + (4*a^3-12*a-6)*q^90 + (-a^3+a^2+4*a-2)*q^91 + (3*a^3-3*a^2-7*a+2)*q^92 + (2*a^2-2*a-10)*q^93 + (-4*a^3+4*a^2+6*a+2)*q^94 + (-2*a^3+6*a^2+6*a-10)*q^95 + (3*a^3-9*a^2+7)*q^96 + (-6*a^3+20*a^2-18)*q^97 + (-3*a^2+5*a+1)*q^98 + (a^3-3*a^2-2*a+5)*q^99 + (4*a^3+7*a^2-16*a-18)*q^100 + (-6*a^2+8*a+6)*q^101 + (-2*a^3+4*a^2+2*a+4)*q^102 + (3*a^3-7*a^2-6*a+6)*q^103 + (-a^3+4*a)*q^104 + (-4*a^3+14*a^2+2*a-28)*q^105 + (-3*a^2+2*a+1)*q^106 + (6*a^3-12*a^2-8*a+8)*q^107 + (4*a^3-9*a^2-6*a+12)*q^108 + (-3*a^3+3*a^2+16*a-3)*q^109 + (-2*a^3+2*a^2+4*a)*q^110 + (-4*a^3+8*a^2+12*a-16)*q^111 + (2*a^3-7*a^2+7*a+12)*q^112 + (-a^3+7*a^2-10*a-11)*q^113 + (-5*a^2+13*a+1)*q^114 + (-2*a^3+4*a^2-6)*q^115 + (-6*a^2+4*a+14)*q^116 + (-a^3+3*a^2+2*a-5)*q^117 + (4*a^3-2*a^2-16*a-2)*q^118 + (8*a^3-22*a^2-6*a+18)*q^119 + (2*a^2-8)*q^120 + 1*q^121 + (-2*a^3+4*a^2+2*a+2)*q^122 + (-4*a^2+10*a-1)*q^123 + (6*a^3-18*a-10)*q^124 + (-4*a^2-4*a+8)*q^125 + (-4*a^3+2*a^2+15*a)*q^126 + (6*a^3-16*a^2+12)*q^127 + (-2*a^3-a^2+10*a+8)*q^128 + (-8*a^3+26*a^2-4*a-26)*q^129 + (2*a^3-2*a^2-4*a)*q^130 + (-4*a^3+14*a^2-2*a-20)*q^131 + (a^3-4*a^2+a+6)*q^132 + (-2*a^3+14*a^2-20*a-13)*q^133 + (-8*a^3+10*a^2+20*a+4)*q^134 + (-4*a^3+14*a^2-2*a-24)*q^135 + (2*a^3-10*a^2+2*a+6)*q^136 + (4*a^3-6*a^2-10*a+2)*q^137 + (2*a^2-5*a-2)*q^138 + (-2*a^3+8*a^2-6*a-14)*q^139 + (-8*a^3+14*a^2+8*a-18)*q^140 + (4*a^3-14*a^2+4*a+16)*q^141 + (2*a^3-8*a^2+2*a+4)*q^142 + -1*q^143 + (-a^3-10*a^2+14*a+23)*q^144 + (-4*a^3+16*a^2-24)*q^145 + (6*a^3-9*a^2-8*a-3)*q^146 + (-2*a^3+8*a^2-6*a-3)*q^147 + (-4*a^3+12*a^2+4*a-12)*q^148 + (3*a^3-5*a^2-12*a+10)*q^149 + (a^2-6*a+3)*q^150 + (-4*a^2+4*a+8)*q^151 + (-3*a^3+10*a^2-11*a-5)*q^152 + (12*a^3-30*a^2-12*a+34)*q^153 + (2*a^3-3*a^2-3*a-1)*q^154 + (-8*a^2+12)*q^155 + (-a^3+4*a^2-a-6)*q^156 + (-7*a^3+9*a^2+22*a-10)*q^157 + (-2*a^3-2*a^2+2*a-2)*q^158 + (a^3-a^2-6*a+6)*q^159 + (-4*a^3+6*a^2+2*a-8)*q^160 + (-a^3+a^2+8*a-3)*q^161 + (6*a^2-6*a-2)*q^162 + (-10*a^2+20*a+12)*q^163 + (3*a^3+3*a^2-9*a-4)*q^164 + (-2*a^3+6*a^2+2*a-10)*q^165 + (2*a^3-5*a^2-a+1)*q^166 + (5*a^3-9*a^2-14*a+9)*q^167 + (-5*a^3+16*a^2-6*a-8)*q^168 + 1*q^169 + (4*a^2+4*a-4)*q^170 + (-a^3+13*a^2-16*a-20)*q^171 + (-2*a^3+8*a^2+4*a-16)*q^172 + (6*a^3-14*a^2-2*a+4)*q^173 + (-2*a^3+6*a^2-4)*q^174 + (7*a^3-19*a^2+4*a+22)*q^175 + (3*a^3-5*a^2-5*a+3)*q^176 + (6*a^3-18*a^2+16)*q^177 + (-4*a^2+8*a+2)*q^178 + (4*a^3-8*a^2+4)*q^179 + (20*a^2-14*a-40)*q^180 + (-5*a^3+11*a^2+2*a-19)*q^181 + (-2*a^3+3*a^2+3*a+1)*q^182 + (6*a^3-22*a^2+6*a+28)*q^183 + (2*a^3-2*a^2+a-1)*q^184 + (-8*a^2+8*a+24)*q^185 + (2*a^3-2*a^2-10*a)*q^186 + (-4*a^2+6*a+8)*q^187 + (-4*a^3-2*a^2+10*a+12)*q^188 + (-5*a^3+11*a^2+12*a-16)*q^189 + (4*a^2+2)*q^190 + (3*a^3-a^2-20*a+5)*q^191 + (2*a^3-5*a^2-8*a+19)*q^192 + (-5*a^3+11*a^2+12*a-2)*q^193 + (2*a^3-6*a^2+12*a+6)*q^194 + (2*a^3-6*a^2-2*a+10)*q^195 + (-a^3-a^2+5*a)*q^196 + (-11*a^3+27*a^2+4*a-19)*q^197 + (-a^2-1)*q^198 + (a^3+a^2-4*a-13)*q^199 + (11*a^3-12*a^2-12*a+4)*q^200 +  ...

-------------------------------------------------------
143C (new) , dim = 6

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 5*7*5560463
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^2*3
Torsion Bound  = 2^4*3
|L(1)/Omega|   = 1/2^2*3
Sha Bound      = 2^6*3

ANALYTIC INVARIANTS:

Omega+         = 11.426610150585574738 + 0.24868083855249080096e-3i
Omega-         = 10.901755361372672093 + -0.24077866677024131235e-3i
L(1)           = 0.95221751277430280049

HECKE EIGENFORM:
a^6-10*a^4+2*a^3+24*a^2-7*a-12 = 0,
f(q) = 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 + -1*q^11 + (-a^3+3*a-2)*q^12 + 1*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 + (-3*a^5-4*a^4+24*a^3+25*a^2-36*a-24)*q^38 + (-a^5-a^4+8*a^3+6*a^2-11*a-5)*q^39 + (-4*a^5-4*a^4+34*a^3+26*a^2-50*a-24)*q^40 + (2*a^5+2*a^4-17*a^3-11*a^2+26*a+6)*q^41 + (3*a^5+3*a^4-23*a^3-19*a^2+28*a+24)*q^42 + (-2*a^5-2*a^4+18*a^3+14*a^2-32*a-16)*q^43 + (-a^2+2)*q^44 + (6*a^5+10*a^4-48*a^3-68*a^2+68*a+66)*q^45 + (-4*a^5-5*a^4+35*a^3+34*a^2-54*a-36)*q^46 + (2*a^5+2*a^4-16*a^3-12*a^2+24*a+12)*q^47 + (3*a^5+4*a^4-25*a^3-26*a^2+32*a+28)*q^48 + (6*a^5+7*a^4-50*a^3-48*a^2+75*a+57)*q^49 + (-4*a^5-4*a^4+32*a^3+28*a^2-41*a-36)*q^50 + (2*a^5+4*a^4-16*a^3-26*a^2+24*a+24)*q^51 + (a^2-2)*q^52 + (6*a^5+7*a^4-50*a^3-48*a^2+75*a+54)*q^53 + (-7*a^5-9*a^4+57*a^3+61*a^2-82*a-60)*q^54 + (-a^5-2*a^4+8*a^3+14*a^2-12*a-15)*q^55 + (-5*a^5-8*a^4+42*a^3+54*a^2-67*a-60)*q^56 + (-4*a^5-6*a^4+33*a^3+43*a^2-46*a-46)*q^57 + (2*a^5+4*a^4-18*a^3-26*a^2+32*a+24)*q^58 + (-5*a^5-6*a^4+42*a^3+38*a^2-66*a-33)*q^59 + (-2*a^4-2*a^3+14*a^2+4*a-18)*q^60 + (4*a^5+6*a^4-32*a^3-42*a^2+44*a+50)*q^61 + (4*a^5+4*a^4-34*a^3-28*a^2+50*a+36)*q^62 + (-a^4+a^3+9*a^2-9*a-16)*q^63 + (-2*a^3+7*a+4)*q^64 + (a^5+2*a^4-8*a^3-14*a^2+12*a+15)*q^65 + (a^5+2*a^4-8*a^3-13*a^2+12*a+12)*q^66 + (a^5+2*a^4-8*a^3-16*a^2+12*a+23)*q^67 + (-2*a^3+4*a)*q^68 + (-5*a^5-7*a^4+39*a^3+47*a^2-53*a-51)*q^69 + (-2*a^4+12*a^2-6*a)*q^70 + (-3*a^5-4*a^4+26*a^3+28*a^2-40*a-33)*q^71 + (9*a^5+12*a^4-73*a^3-80*a^2+105*a+84)*q^72 + (-a^4+8*a^2+a-4)*q^73 + (-2*a^5-2*a^4+18*a^3+14*a^2-26*a-12)*q^74 + (-8*a^5-7*a^4+66*a^3+40*a^2-93*a-32)*q^75 + (-a^3-4*a^2+a+8)*q^76 + (-2*a^5-2*a^4+17*a^3+13*a^2-26*a-14)*q^77 + (-a^5-2*a^4+8*a^3+13*a^2-12*a-12)*q^78 + (2*a^5+2*a^4-16*a^3-14*a^2+22*a+20)*q^79 + (-4*a^5-6*a^4+34*a^3+42*a^2-56*a-36)*q^80 + (-6*a^5-9*a^4+47*a^3+59*a^2-59*a-59)*q^81 + (2*a^5+3*a^4-15*a^3-22*a^2+20*a+24)*q^82 + (2*a^4+a^3-15*a^2-6*a+12)*q^83 + (-a^5+a^4+9*a^3-6*a^2-13*a+8)*q^84 + (-4*a^5-4*a^4+32*a^3+24*a^2-44*a-24)*q^85 + (-2*a^5-2*a^4+18*a^3+16*a^2-30*a-24)*q^86 + (2*a^5+4*a^4-16*a^3-30*a^2+26*a+30)*q^87 + (-a^3+4*a)*q^88 + (a^5+2*a^4-10*a^3-14*a^2+20*a+9)*q^89 + (10*a^5+12*a^4-80*a^3-76*a^2+108*a+72)*q^90 + (2*a^5+2*a^4-17*a^3-13*a^2+26*a+14)*q^91 + (a^5+3*a^4-8*a^3-16*a^2+12*a+18)*q^92 + (3*a^5+2*a^4-24*a^3-10*a^2+32*a+11)*q^93 + (2*a^5+4*a^4-16*a^3-24*a^2+26*a+24)*q^94 + (4*a^5+4*a^4-34*a^3-26*a^2+50*a+18)*q^95 + (-a^4+6*a^2+5*a-12)*q^96 + (-5*a^5-6*a^4+42*a^3+40*a^2-66*a-37)*q^97 + (7*a^5+10*a^4-60*a^3-69*a^2+99*a+72)*q^98 + (3*a^5+4*a^4-25*a^3-27*a^2+38*a+26)*q^99 + (2*a^5-16*a^3+3*a^2+24*a-8)*q^100 + (-2*a^5-2*a^4+18*a^3+12*a^2-34*a-6)*q^101 + (4*a^5+4*a^4-30*a^3-24*a^2+38*a+24)*q^102 + (6*a^5+8*a^4-51*a^3-55*a^2+86*a+56)*q^103 + (a^3-4*a)*q^104 + (-2*a^5-8*a^4+16*a^3+62*a^2-26*a-66)*q^105 + (7*a^5+10*a^4-60*a^3-69*a^2+96*a+72)*q^106 + (2*a^5+2*a^4-16*a^3-14*a^2+18*a+12)*q^107 + (a^5+a^4-7*a^3-8*a^2+9*a+10)*q^108 + (-4*a^5-7*a^4+32*a^3+48*a^2-45*a-52)*q^109 + (-2*a^5-2*a^4+16*a^3+12*a^2-22*a-12)*q^110 + (-5*a^5-8*a^4+38*a^3+54*a^2-48*a-61)*q^111 + (-6*a^5-6*a^4+48*a^3+41*a^2-67*a-52)*q^112 + (-3*a^5-5*a^4+24*a^3+34*a^2-37*a-27)*q^113 + (-6*a^5-7*a^4+51*a^3+50*a^2-74*a-48)*q^114 + (3*a^5+4*a^4-24*a^3-22*a^2+36*a+9)*q^115 + (-2*a^4+2*a^3+12*a^2-6*a-12)*q^116 + (-3*a^5-4*a^4+25*a^3+27*a^2-38*a-26)*q^117 + (-6*a^5-8*a^4+48*a^3+54*a^2-68*a-60)*q^118 + (-4*a^5-6*a^4+34*a^3+44*a^2-56*a-48)*q^119 + (-10*a^5-14*a^4+82*a^3+88*a^2-126*a-72)*q^120 + 1*q^121 + (6*a^5+8*a^4-50*a^3-52*a^2+78*a+48)*q^122 + (6*a^5+7*a^4-51*a^3-43*a^2+79*a+30)*q^123 + (-2*a^5-2*a^4+16*a^3+10*a^2-24*a-10)*q^124 + (-3*a^5+26*a^3-6*a^2-40*a+9)*q^125 + (-a^5+a^4+9*a^3-9*a^2-16*a)*q^126 + (-2*a^5-2*a^4+16*a^3+14*a^2-18*a-16)*q^127 + (-2*a^5-2*a^4+16*a^3+7*a^2-20*a)*q^128 + (2*a^5+4*a^4-16*a^3-30*a^2+20*a+32)*q^129 + (2*a^5+2*a^4-16*a^3-12*a^2+22*a+12)*q^130 + (2*a^5+4*a^4-16*a^3-26*a^2+22*a+18)*q^131 + (a^3-3*a+2)*q^132 + (-2*a^5-a^4+19*a^3+7*a^2-35*a-8)*q^133 + (2*a^5+2*a^4-18*a^3-12*a^2+30*a+12)*q^134 + (15*a^5+20*a^4-122*a^3-132*a^2+174*a+123)*q^135 + (-2*a^4+8*a^2)*q^136 + (5*a^5+8*a^4-42*a^3-56*a^2+66*a+63)*q^137 + (-7*a^5-11*a^4+57*a^3+67*a^2-86*a-60)*q^138 + (-10*a^5-14*a^4+84*a^3+94*a^2-132*a-94)*q^139 + (-2*a^5+16*a^3-6*a^2-24*a+12)*q^140 + (2*a^5+2*a^4-18*a^3-16*a^2+30*a+12)*q^141 + (-4*a^5-4*a^4+34*a^3+32*a^2-54*a-36)*q^142 + -1*q^143 + (10*a^5+15*a^4-82*a^3-101*a^2+123*a+100)*q^144 + (-2*a^5+16*a^3-4*a^2-16*a+6)*q^145 + (-a^5+8*a^3+a^2-4*a)*q^146 + (5*a^5+9*a^4-41*a^3-63*a^2+65*a+63)*q^147 + (2*a^4+2*a^3-10*a^2-6*a+14)*q^148 + (6*a^5+6*a^4-51*a^3-37*a^2+78*a+30)*q^149 + (-7*a^5-14*a^4+56*a^3+99*a^2-88*a-96)*q^150 + (4*a^2+4*a-16)*q^151 + (6*a^5+7*a^4-52*a^3-49*a^2+80*a+48)*q^152 + (8*a^5+10*a^4-66*a^3-68*a^2+94*a+72)*q^153 + (-2*a^5-3*a^4+17*a^3+22*a^2-28*a-24)*q^154 + (3*a^5-26*a^3+2*a^2+36*a+3)*q^155 + (-a^3+3*a-2)*q^156 + (-a^5+9*a^3-a^2-18*a+5)*q^157 + (2*a^5+4*a^4-18*a^3-26*a^2+34*a+24)*q^158 + (8*a^5+12*a^4-65*a^3-81*a^2+98*a+78)*q^159 + (2*a^5+2*a^4-18*a^3-12*a^2+36*a)*q^160 + (-8*a^5-9*a^4+68*a^3+60*a^2-115*a-66)*q^161 + (-9*a^5-13*a^4+71*a^3+85*a^2-101*a-72)*q^162 + (-2*a^5-2*a^4+18*a^3+12*a^2-38*a-4)*q^163 + (-a^5+a^4+8*a^3-6*a^2-14*a+12)*q^164 + (-3*a^5-4*a^4+24*a^3+28*a^2-30*a-33)*q^165 + (2*a^5+a^4-15*a^3-6*a^2+12*a)*q^166 + (-8*a^5-11*a^4+68*a^3+72*a^2-111*a-72)*q^167 + (-5*a^5-7*a^4+42*a^3+49*a^2-55*a-60)*q^168 + 1*q^169 + (-4*a^5-8*a^4+32*a^3+52*a^2-52*a-48)*q^170 + (-8*a^5-12*a^4+63*a^3+79*a^2-84*a-76)*q^171 + (2*a^5+2*a^4-16*a^3-10*a^2+26*a+8)*q^172 + (-4*a^5-4*a^4+34*a^3+30*a^2-54*a-36)*q^173 + (4*a^5+4*a^4-34*a^3-22*a^2+44*a+24)*q^174 + (-6*a^4+a^3+49*a^2-14*a-64)*q^175 + (-a^4+6*a^2-4)*q^176 + (-11*a^5-12*a^4+92*a^3+76*a^2-136*a-63)*q^177 + (2*a^5-16*a^3-4*a^2+16*a+12)*q^178 + (a^5-10*a^3-2*a^2+20*a+9)*q^179 + (4*a^2+6*a-12)*q^180 + (-5*a^5-5*a^4+40*a^3+34*a^2-49*a-37)*q^181 + (2*a^5+3*a^4-17*a^3-22*a^2+28*a+24)*q^182 + (8*a^5+14*a^4-64*a^3-100*a^2+88*a+110)*q^183 + (11*a^5+12*a^4-88*a^3-80*a^2+133*a+84)*q^184 + (7*a^5+8*a^4-58*a^3-46*a^2+92*a+27)*q^185 + (2*a^5+6*a^4-16*a^3-40*a^2+32*a+36)*q^186 + 2*a*q^187 + (4*a^3+2*a^2-10*a)*q^188 + (4*a^5+6*a^4-31*a^3-41*a^2+38*a+38)*q^189 + (4*a^5+6*a^4-34*a^3-46*a^2+46*a+48)*q^190 + (a^5-a^4-8*a^3+14*a^2+9*a-27)*q^191 + (-7*a^5-8*a^4+56*a^3+57*a^2-76*a-56)*q^192 + (4*a^5+6*a^4-31*a^3-41*a^2+38*a+56)*q^193 + (-6*a^5-8*a^4+50*a^3+54*a^2-72*a-60)*q^194 + (3*a^5+4*a^4-24*a^3-28*a^2+30*a+33)*q^195 + (-2*a^5-4*a^4+17*a^3+27*a^2-29*a-30)*q^196 + (-2*a^5-3*a^4+16*a^3+16*a^2-21*a-6)*q^197 + (4*a^5+5*a^4-33*a^3-34*a^2+47*a+36)*q^198 + (8*a^5+9*a^4-66*a^3-56*a^2+99*a+56)*q^199 + (8*a^5+12*a^4-65*a^3-80*a^2+88*a+96)*q^200 +  ...

-------------------------------------------------------
143D (old = 11A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3^2 + Z/2*3^2
= A(Z/2 + Z/2) + B(Z/3^2 + Z/3^2) + C(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(144)
Weight 2

-------------------------------------------------------
J_0(144), dim = 13

-------------------------------------------------------
144A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= C(Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 2.4900391492473164825 + 0.38891588326345625925e-4i
Omega-         = 0.15011171677005464674e-4 + 1.9465125566969817846i
L(1)           = 1.2450195747755188699
w1             = 1.245027080209496744 + 0.97327572414265406512i
w2             = 1.2450120690378197385 + -0.97323683255432771949i
c4             = -288.04597569898663645 + 0.21938990861599100282e-1i
c6             = -6048.4796058783401817 + -0.25374648941790991413i
j              = 682.79893689608317336 + -0.12902041709049506316i

HECKE EIGENFORM:
f(q) = q + 2*q^5 + 4*q^11 + -2*q^13 + -2*q^17 + 4*q^19 + -8*q^23 + -1*q^25 + -6*q^29 + -8*q^31 + 6*q^37 + 6*q^41 + -4*q^43 + -7*q^49 + 2*q^53 + 8*q^55 + 4*q^59 + -2*q^61 + -4*q^65 + 4*q^67 + 8*q^71 + 10*q^73 + 8*q^79 + -4*q^83 + -4*q^85 + 6*q^89 + 8*q^95 + 2*q^97 + 18*q^101 + -16*q^103 + -12*q^107 + -2*q^109 + -18*q^113 + -16*q^115 + 5*q^121 + -12*q^125 + 8*q^127 + -4*q^131 + 6*q^137 + 12*q^139 + -8*q^143 + -12*q^145 + -14*q^149 + 16*q^151 + -16*q^155 + -2*q^157 + -12*q^163 + 24*q^167 + -9*q^169 + -6*q^173 + 12*q^179 + 6*q^181 + 12*q^185 + -8*q^187 + 2*q^193 + 18*q^197 + -16*q^199 +  ...

-------------------------------------------------------
144B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= E(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.4286644503500312262 + -0.38683236644358706814e-41i
Omega-         = 0.10233862640017059111e-44 + -4.2065702225425950772i
L(1)           = 1.2143322251750156131
w1             = -2.4286644503500312262 + 0.38683236644358706814e-41i
w2             = 1.2143322251750156131 + 2.1032851112712975386i
c4             = -0.52570194164491696071e-10 + 0.91054247256660522701e-10i
c6             = 863.97053890081311082 + 0.41277092851146951915e-38i
j              = -0.26906338489013003736e-32 + 0.94710805579798878578e-62i

HECKE EIGENFORM:
f(q) = q + 4*q^7 + 2*q^13 + -8*q^19 + -5*q^25 + 4*q^31 + -10*q^37 + -8*q^43 + 9*q^49 + 14*q^61 + 16*q^67 + -10*q^73 + 4*q^79 + 8*q^91 + 14*q^97 + -20*q^103 + 2*q^109 + -11*q^121 + -20*q^127 + -32*q^133 + 16*q^139 + 4*q^151 + 14*q^157 + -8*q^163 + -9*q^169 + -20*q^175 + 26*q^181 + 2*q^193 + 28*q^199 +  ...

-------------------------------------------------------
144C (old = 72A), dim = 1

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2^3 + Z/2^3 + Z/2^3 + Z/2^3
= A(Z/2) + D(Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2^2 + Z/2^2)

-------------------------------------------------------
144D (old = 48A), dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + C(Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
144E (old = 36A), dim = 1

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
144F (old = 24A), dim = 1

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^3 + Z/2^3 + Z/2^3 + Z/2^3
= A(Z/2) + C(Z/2 + Z/2 + Z/2^2 + Z/2^2) + D(Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(145)
Weight 2

-------------------------------------------------------
J_0(145), dim = 13

-------------------------------------------------------
145A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.8457661327134272959 + 0.62810555546031003043e-4i
Omega-         = 0.15124992690837449921e-4 + 1.872243230845324518i
L(1)           =
w1             = -2.8457661327134272959 + -0.62810555546031003043e-4i
w2             = 0.15124992690837449921e-4 + 1.872243230845324518i
c4             = 129.01243590694609289 + 0.35441832019153217366e-2i
c6             = -1377.2127443522125201 + -0.81581707878009176183e-1i
j              = 14806.967218016380334 + 4.0411618572661716439i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^4 + -1*q^5 + -2*q^7 + 3*q^8 + -3*q^9 + 1*q^10 + -6*q^11 + 2*q^13 + 2*q^14 + -1*q^16 + -2*q^17 + 3*q^18 + -2*q^19 + 1*q^20 + 6*q^22 + 2*q^23 + 1*q^25 + -2*q^26 + 2*q^28 + -1*q^29 + 2*q^31 + -5*q^32 + 2*q^34 + 2*q^35 + 3*q^36 + 10*q^37 + 2*q^38 + -3*q^40 + 2*q^41 + 8*q^43 + 6*q^44 + 3*q^45 + -2*q^46 + -12*q^47 + -3*q^49 + -1*q^50 + -2*q^52 + -6*q^53 + 6*q^55 + -6*q^56 + 1*q^58 + -8*q^59 + -6*q^61 + -2*q^62 + 6*q^63 + 7*q^64 + -2*q^65 + 2*q^67 + 2*q^68 + -2*q^70 + -12*q^71 + -9*q^72 + -6*q^73 + -10*q^74 + 2*q^76 + 12*q^77 + -10*q^79 + 1*q^80 + 9*q^81 + -2*q^82 + -14*q^83 + 2*q^85 + -8*q^86 + -18*q^88 + 18*q^89 + -3*q^90 + -4*q^91 + -2*q^92 + 12*q^94 + 2*q^95 + 2*q^97 + 3*q^98 + 18*q^99 + -1*q^100 + 10*q^101 + -6*q^103 + 6*q^104 + 6*q^106 + 6*q^107 + -14*q^109 + -6*q^110 + 2*q^112 + 2*q^113 + -2*q^115 + 1*q^116 + -6*q^117 + 8*q^118 + 4*q^119 + 25*q^121 + 6*q^122 + -2*q^124 + -1*q^125 + -6*q^126 + -16*q^127 + 3*q^128 + 2*q^130 + 14*q^131 + 4*q^133 + -2*q^134 + -6*q^136 + 6*q^137 + -2*q^140 + 12*q^142 + -12*q^143 + 3*q^144 + 1*q^145 + 6*q^146 + -10*q^148 + -10*q^149 + -4*q^151 + -6*q^152 + 6*q^153 + -12*q^154 + -2*q^155 + 22*q^157 + 10*q^158 + 5*q^160 + -4*q^161 + -9*q^162 + 4*q^163 + -2*q^164 + 14*q^166 + 18*q^167 + -9*q^169 + -2*q^170 + 6*q^171 + -8*q^172 + -14*q^173 + -2*q^175 + 6*q^176 + -18*q^178 + -12*q^179 + -3*q^180 + 6*q^181 + 4*q^182 + 6*q^184 + -10*q^185 + 12*q^187 + 12*q^188 + -2*q^190 + -22*q^191 + -10*q^193 + -2*q^194 + 3*q^196 + 2*q^197 + -18*q^198 + -4*q^199 + 3*q^200 +  ...

-------------------------------------------------------
145B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^3*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2) + E(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 2^3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2^2
ord((0)-(oo))  = 1
Torsion Bound  = 2^2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 3.0218686047096396159 + 0.42914409200203680998e-4i
Omega-         = 1.5467668232597158475 + -0.12564156586155816787e-4i
L(1)           =

HECKE EIGENFORM:
a^2+2*a-1 = 0,
f(q) = q + a*q^2 + -2*q^3 + (-2*a-1)*q^4 + 1*q^5 + -2*a*q^6 + (-2*a-4)*q^7 + (a-2)*q^8 + 1*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 + 1*q^25 + -2*a*q^26 + 4*q^27 + (2*a+8)*q^28 + 1*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 + -2*q^38 + 4*q^39 + (a-2)*q^40 + -6*q^41 + 4*q^42 + -6*q^43 + (6*a-4)*q^44 + 1*q^45 + (-8*a+2)*q^46 + (-4*a-10)*q^47 + -6*q^48 + (8*a+13)*q^49 + a*q^50 + (-4*a-4)*q^51 + (4*a+2)*q^52 + (-4*a-2)*q^53 + 4*a*q^54 + 2*a*q^55 + (4*a+6)*q^56 + (4*a+8)*q^57 + a*q^58 + (4*a+2)*q^60 + (-4*a-2)*q^61 + (-8*a+6)*q^62 + (-2*a-4)*q^63 + (2*a-5)*q^64 + -2*q^65 + (8*a-4)*q^66 + (6*a+4)*q^67 + (2*a-6)*q^68 + (-4*a+8)*q^69 + -2*q^70 + (-8*a-12)*q^71 + (a-2)*q^72 + (6*a+6)*q^73 + (6*a-6)*q^74 + -2*q^75 + (2*a+8)*q^76 + -4*q^77 + 4*a*q^78 + -6*a*q^79 + 3*q^80 + -11*q^81 + -6*a*q^82 + (-2*a+8)*q^83 + (-4*a-16)*q^84 + (2*a+2)*q^85 + -6*a*q^86 + -2*q^87 + (-8*a+2)*q^88 + (-4*a-6)*q^89 + a*q^90 + (4*a+8)*q^91 + 14*a*q^92 + (-12*a-8)*q^93 + (-2*a-4)*q^94 + (-2*a-4)*q^95 + (-2*a-8)*q^96 + (-6*a-10)*q^97 + (-3*a+8)*q^98 + 2*a*q^99 + (-2*a-1)*q^100 + (4*a+14)*q^101 + (4*a-4)*q^102 + (10*a+12)*q^103 + (-2*a+4)*q^104 + (4*a+8)*q^105 + (6*a-4)*q^106 + (10*a+16)*q^107 + (-8*a-4)*q^108 + 2*q^109 + (-4*a+2)*q^110 + (12*a+12)*q^111 + (-6*a-12)*q^112 + (-2*a-2)*q^113 + 4*q^114 + (2*a-4)*q^115 + (-2*a-1)*q^116 + -2*q^117 + (-4*a-12)*q^119 + (-2*a+4)*q^120 + (-8*a-7)*q^121 + (6*a-4)*q^122 + 12*q^123 + (10*a-16)*q^124 + 1*q^125 + -2*q^126 + 6*q^127 + (-11*a-6)*q^128 + 12*q^129 + -2*a*q^130 + (-10*a-8)*q^131 + (-12*a+8)*q^132 + (8*a+20)*q^133 + (-8*a+6)*q^134 + 4*q^135 + (-6*a-2)*q^136 + (2*a-6)*q^137 + (16*a-4)*q^138 + (4*a+20)*q^139 + (2*a+8)*q^140 + (8*a+20)*q^141 + (4*a-8)*q^142 + -4*a*q^143 + 3*q^144 + 1*q^145 + (-6*a+6)*q^146 + (-16*a-26)*q^147 + (-6*a+18)*q^148 + (8*a+6)*q^149 + -2*a*q^150 + -12*q^151 + (4*a+6)*q^152 + (2*a+2)*q^153 + -4*a*q^154 + (6*a+4)*q^155 + (-8*a-4)*q^156 + (6*a-2)*q^157 + (12*a-6)*q^158 + (8*a+4)*q^159 + (a+4)*q^160 + (8*a+12)*q^161 + -11*a*q^162 + (4*a-10)*q^163 + (12*a+6)*q^164 + -4*a*q^165 + (12*a-2)*q^166 + -6*a*q^167 + (-8*a-12)*q^168 + -9*q^169 + (-2*a+2)*q^170 + (-2*a-4)*q^171 + (12*a+6)*q^172 + (8*a+14)*q^173 + -2*a*q^174 + (-2*a-4)*q^175 + 6*a*q^176 + (2*a-4)*q^178 + (-8*a-20)*q^179 + (-2*a-1)*q^180 + -6*q^181 + 4*q^182 + (8*a+4)*q^183 + (-12*a+10)*q^184 + (-6*a-6)*q^185 + (16*a-12)*q^186 + (-4*a+4)*q^187 + (8*a+18)*q^188 + (-8*a-16)*q^189 + -2*q^190 + (-2*a-20)*q^191 + (-4*a+10)*q^192 + (6*a+2)*q^193 + (2*a-6)*q^194 + 4*q^195 + (-2*a-29)*q^196 + (-4*a-18)*q^197 + (-4*a+2)*q^198 + 12*q^199 + (a-2)*q^200 +  ...

-------------------------------------------------------
145C (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^4*5^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*5 + Z/2*5 + Z/2^2*5 + Z/2^2*5
= A(Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + E(Z/5 + Z/5 + Z/5 + Z/5)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*37
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2^2
ord((0)-(oo))  = 1
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 0.86250944465496360892 + 0.31373426951111855522e-4i
Omega-         = 0.2519911895829474922e-3 + -5.1568732969421042379i
L(1)           = 0.43125472261278068566

HECKE EIGENFORM:
a^3-3*a^2-a+5 = 0,
f(q) = q + a*q^2 + (-a^2+2*a+1)*q^3 + (a^2-2)*q^4 + -1*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 + 1*q^25 + (2*a^2-4*a)*q^26 + (2*a^2-10)*q^27 + (-5*a^2+2*a+9)*q^28 + 1*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 + (5*a^2-4*a-15)*q^38 + (2*a^2-8*a+6)*q^39 + (-3*a^2+3*a+5)*q^40 + (-2*a^2+2*a+2)*q^41 + (2*a^2-2*a)*q^42 + (a^2-2*a-5)*q^43 + (3*a^2-7)*q^44 + (2*a-3)*q^45 + (a^2+4*a-5)*q^46 + (3*a^2-6*a+1)*q^47 + (a^2-6*a-1)*q^48 + (4*a^2-2*a-13)*q^49 + a*q^50 + (-2*a^2+6*a+4)*q^51 + (2*a^2-2*a-2)*q^52 + (2*a^2-2*a-2)*q^53 + (6*a^2-8*a-10)*q^54 + (-a^2+2*a-1)*q^55 + (-7*a^2+15)*q^56 + (2*a^2-2*a-12)*q^57 + a*q^58 + (-4*a^2+6*a+10)*q^59 + (a^2-3)*q^60 + 2*a*q^61 + (-5*a^2+8*a+15)*q^62 + (3*a^2-4*a-1)*q^63 + (3*a^2-2*a+2)*q^64 + (-2*a+4)*q^65 + (-6*a+10)*q^66 + (a^2-2*a-5)*q^67 + (-9*a^2+4*a+17)*q^68 + (-4*a^2+10*a-2)*q^69 + (3*a^2-2*a-5)*q^70 + (2*a+6)*q^71 + (-3*a^2-5*a+15)*q^72 + (a^2-8*a+3)*q^73 + (-5*a^2+6*a+5)*q^74 + (-a^2+2*a+1)*q^75 + (5*a^2-2*a-11)*q^76 + (-2*a^2-2*a+8)*q^77 + (-2*a^2+8*a-10)*q^78 + (-5*a^2+6*a+15)*q^79 + (-4*a^2+2*a+11)*q^80 + (4*a^2-6*a-9)*q^81 + (-4*a^2+10)*q^82 + (-a^2+4*a-1)*q^83 + (4*a^2-2*a-6)*q^84 + (3*a^2-2*a-9)*q^85 + (a^2-4*a-5)*q^86 + (-a^2+2*a+1)*q^87 + (7*a^2-8*a-5)*q^88 + 2*a^2*q^89 + (2*a^2-3*a)*q^90 + (-2*a^2+4*a-2)*q^91 + (5*a^2-11)*q^92 + (-6*a^2+10*a+16)*q^93 + (3*a^2+4*a-15)*q^94 + (-3*a^2+4*a+7)*q^95 + (-a^2-4*a+5)*q^96 + (3*a^2-23)*q^97 + (10*a^2-9*a-20)*q^98 + (a^2-10*a+13)*q^99 + (a^2-2)*q^100 + (6*a^2-12*a-8)*q^101 + (2*a+10)*q^102 + (a^2-6*a-1)*q^103 + (8*a-10)*q^104 + (-2*a+2)*q^105 + (4*a^2-10)*q^106 + (-7*a^2+8*a+17)*q^107 + (6*a^2-4*a-10)*q^108 + (-8*a^2+10*a+16)*q^109 + (-a^2-2*a+5)*q^110 + (-2*a^2+10*a-8)*q^111 + (-11*a^2+4*a+17)*q^112 + (-7*a^2+4*a+23)*q^113 + (4*a^2-10*a-10)*q^114 + (-a^2+2*a-3)*q^115 + (a^2-2)*q^116 + (-4*a^2+14*a-12)*q^117 + (-6*a^2+6*a+20)*q^118 + (6*a^2-2*a-8)*q^119 + (a^2-2*a+5)*q^120 + (4*a^2-10*a-5)*q^121 + 2*a^2*q^122 + (2*a^2-4*a+2)*q^123 + (-a^2+2*a+3)*q^124 + -1*q^125 + (5*a^2+2*a-15)*q^126 + (9*a^2-6*a-33)*q^127 + (-a^2+7*a+5)*q^128 + (4*a^2-6*a-10)*q^129 + (-2*a^2+4*a)*q^130 + (5*a^2-8*a-13)*q^131 + (-2*a^2-2*a+8)*q^132 + (-2*a^2-2*a+4)*q^133 + (a^2-4*a-5)*q^134 + (-2*a^2+10)*q^135 + (-9*a^2-4*a+15)*q^136 + (a^2+2*a-19)*q^137 + (-2*a^2-6*a+20)*q^138 + (-2*a^2-4*a+6)*q^139 + (5*a^2-2*a-9)*q^140 + (-4*a^2+14*a-14)*q^141 + (2*a^2+6*a)*q^142 + (-2*a^2+12*a-14)*q^143 + (-8*a^2+8*a+7)*q^144 + -1*q^145 + (-5*a^2+4*a-5)*q^146 + (3*a^2-10*a-3)*q^147 + (-7*a^2+4*a+11)*q^148 + (4*a^2-22)*q^149 + (-a^2+5)*q^150 + (-4*a^2+2*a+14)*q^151 + (3*a^2+2*a+5)*q^152 + (5*a^2-6*a-3)*q^153 + (-8*a^2+6*a+10)*q^154 + (3*a^2-4*a-11)*q^155 + (-2*a^2+4*a-2)*q^156 + (7*a^2-12*a-23)*q^157 + (-9*a^2+10*a+25)*q^158 + (-2*a^2+4*a-2)*q^159 + (-4*a^2+a+10)*q^160 + (-4*a^2-2*a+14)*q^161 + (6*a^2-5*a-20)*q^162 + (a^2+2*a-5)*q^163 + (-8*a^2+2*a+16)*q^164 + (2*a^2-6*a+4)*q^165 + (a^2-2*a+5)*q^166 + (-a^2+6*a+13)*q^167 + (6*a^2+2*a-20)*q^168 + (4*a^2-16*a+3)*q^169 + (7*a^2-6*a-15)*q^170 + (-a^2-4*a+9)*q^171 + (-3*a^2+5)*q^172 + (12*a^2-22*a-20)*q^173 + (-a^2+5)*q^174 + (-a^2+3)*q^175 + (7*a^2+2*a-21)*q^176 + (-4*a^2+4*a+20)*q^177 + (6*a^2+2*a-10)*q^178 + (-4*a^2+8*a+12)*q^179 + (3*a^2-2*a-4)*q^180 + (4*a^2-10*a)*q^181 + (-2*a^2-4*a+10)*q^182 + (-2*a^2+10)*q^183 + (13*a^2-14*a-15)*q^184 + (a^2+2*a-7)*q^185 + (-8*a^2+10*a+30)*q^186 + (-4*a^2-2*a+14)*q^187 + (7*a^2-17)*q^188 + (-4*a^2+4*a)*q^189 + (-5*a^2+4*a+15)*q^190 + (3*a^2-2*a+3)*q^191 + (-9*a^2+16*a+7)*q^192 + (-a^2+6*a+11)*q^193 + (9*a^2-20*a-15)*q^194 + (-2*a^2+8*a-6)*q^195 + (13*a^2-6*a-24)*q^196 + (-6*a^2+8*a+8)*q^197 + (-7*a^2+14*a-5)*q^198 + (4*a^2-6*a-10)*q^199 + (3*a^2-3*a-5)*q^200 +  ...

-------------------------------------------------------
145D (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^2*37
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2^2
ord((0)-(oo))  = 5
Torsion Bound  = 2^2*5
|L(1)/Omega|   = 1/2*5
Sha Bound      = 2^3*5

ANALYTIC INVARIANTS:

Omega+         = 6.267244197698374948 + -0.16403688885024746465e-3i
Omega-         = 0.45406604087149421308e-4 + -6.2164589420126578379i
L(1)           = 0.62672441998451000516

HECKE EIGENFORM:
a^3-a^2-3*a+1 = 0,
f(q) = q + a*q^2 + (-a^2+3)*q^3 + (a^2-2)*q^4 + 1*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 + 1*q^25 + -2*a^2*q^26 + (-2*a^2+4*a+6)*q^27 + (a^2+2*a+1)*q^28 + -1*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 + (-a^2-4*a+1)*q^38 + (2*a^2-2)*q^39 + (a^2-a-1)*q^40 + (-2*a^2+6*a+2)*q^41 + (-2*a^2-2*a)*q^42 + (5*a^2-11)*q^43 + (-a^2+3)*q^44 + (-2*a^2+2*a+5)*q^45 + (a^2+4*a+1)*q^46 + (-a^2+7)*q^47 + (-3*a^2+4*a+9)*q^48 + (2*a^2+2*a-7)*q^49 + a*q^50 + (8*a^2-6*a-22)*q^51 + (-2*a^2-2*a+2)*q^52 + (-2*a^2+2*a+6)*q^53 + (2*a^2+2)*q^54 + (a^2-2*a-1)*q^55 + (a^2+1)*q^56 + (2*a^2+2*a-4)*q^57 + -a*q^58 + (2*a^2-6*a)*q^59 + (a^2-2*a-5)*q^60 + -6*a*q^61 + (a^2-4*a-1)*q^62 + (a^2-5)*q^63 + (a^2-6*a-4)*q^64 + -2*a*q^65 + (2*a-2)*q^66 + (-a^2+2*a+11)*q^67 + (-5*a^2+2*a+15)*q^68 + (-8*a^2+2*a+22)*q^69 + (a^2+2*a-1)*q^70 + (-2*a^2+6*a+12)*q^71 + (a^2+a-7)*q^72 + (-7*a^2+6*a+9)*q^73 + (a^2-6*a+3)*q^74 + (-a^2+3)*q^75 + (-3*a^2-2*a+3)*q^76 + (-2*a+2)*q^77 + (2*a^2+4*a-2)*q^78 + (-5*a^2+2*a+9)*q^79 + (-2*a^2+2*a+3)*q^80 + (-2*a^2-2*a+5)*q^81 + (4*a^2-4*a+2)*q^82 + (-3*a^2+11)*q^83 + (-4*a^2-2*a+6)*q^84 + (3*a^2-4*a-7)*q^85 + (5*a^2+4*a-5)*q^86 + (a^2-3)*q^87 + (a^2-4*a+3)*q^88 + (2*a^2-8)*q^89 + (-a+2)*q^90 + (-2*a^2-4*a+2)*q^91 + (7*a^2-15)*q^92 + (6*a^2-2*a-20)*q^93 + (-a^2+4*a+1)*q^94 + (-a^2-1)*q^95 + (-a^2+4*a+9)*q^96 + (3*a^2+2*a-5)*q^97 + (4*a^2-a-2)*q^98 + (a^2+2*a-9)*q^99 + (a^2-2)*q^100 + (-6*a^2+8*a+12)*q^101 + (2*a^2+2*a-8)*q^102 + (7*a^2-2*a-13)*q^103 + (-4*a+2)*q^104 + (-2*a-2)*q^105 + 2*q^106 + (-5*a^2+8*a+9)*q^107 + (6*a^2-14)*q^108 + (6*a^2-2*a-18)*q^109 + (-a^2+2*a-1)*q^110 + (-4*a^2+6*a+10)*q^111 + (-a^2-3)*q^112 + (a^2+2*a-11)*q^113 + (4*a^2+2*a-2)*q^114 + (-a^2+2*a+7)*q^115 + (-a^2+2)*q^116 + (2*a-4)*q^117 + (-4*a^2+6*a-2)*q^118 + (-2*a^2-2*a+8)*q^119 + (a^2-2*a-3)*q^120 + (2*a^2-6*a-7)*q^121 + -6*a^2*q^122 + (-6*a^2+4*a+10)*q^123 + (-5*a^2+2*a+13)*q^124 + 1*q^125 + (a^2-2*a-1)*q^126 + (-3*a^2-8*a+9)*q^127 + (-a^2+a-9)*q^128 + (6*a^2-10*a-28)*q^129 + -2*a^2*q^130 + (5*a^2-4*a-11)*q^131 + (-2*a^2+2*a+8)*q^132 + (-4*a^2-2*a+2)*q^133 + (a^2+8*a+1)*q^134 + (-2*a^2+4*a+6)*q^135 + (-a^2-4*a+11)*q^136 + (7*a^2-4*a-3)*q^137 + (-6*a^2-2*a+8)*q^138 + (2*a^2+4*a-10)*q^139 + (a^2+2*a+1)*q^140 + (-6*a^2+2*a+20)*q^141 + (4*a^2+6*a+2)*q^142 + (2*a^2-4*a+2)*q^143 + (-4*a^2+19)*q^144 + -1*q^145 + (-a^2-12*a+7)*q^146 + (3*a^2-4*a-17)*q^147 + (a^2-2*a-7)*q^148 + (4*a^2-6)*q^149 + (-a^2+1)*q^150 + (-6*a^2-2*a+12)*q^151 + (-3*a^2+2*a+1)*q^152 + (11*a^2-4*a-43)*q^153 + (-2*a^2+2*a)*q^154 + (a^2-7)*q^155 + (2*a^2+4*a+2)*q^156 + (-a^2-2*a+3)*q^157 + (-3*a^2-6*a+5)*q^158 + (-6*a^2+4*a+18)*q^159 + (-2*a^2-a+4)*q^160 + (6*a^2+2*a-8)*q^161 + (-4*a^2-a+2)*q^162 + (-7*a^2+17)*q^163 + (4*a^2+2*a-8)*q^164 + (2*a^2-2*a-4)*q^165 + (-3*a^2+2*a+3)*q^166 + (a^2-6*a-3)*q^167 + (-2*a^2-2*a+4)*q^168 + (4*a^2-13)*q^169 + (-a^2+2*a-3)*q^170 + (3*a^2-4*a-5)*q^171 + (-a^2+10*a+17)*q^172 + (-4*a^2+2*a+4)*q^173 + (a^2-1)*q^174 + (a^2-1)*q^175 + (-a^2+6*a-7)*q^176 + (4*a^2-4*a-4)*q^177 + (2*a^2-2*a-2)*q^178 + (-8*a^2+8*a+8)*q^179 + (3*a^2-2*a-10)*q^180 + (2*a^2-6*a+2)*q^181 + (-6*a^2-4*a+2)*q^182 + (6*a^2-6)*q^183 + (5*a^2-2*a-9)*q^184 + (-3*a^2+4*a+3)*q^185 + (4*a^2-2*a-6)*q^186 + (-6*a+14)*q^187 + (5*a^2-2*a-13)*q^188 + (4*a^2+4*a-8)*q^189 + (-a^2-4*a+1)*q^190 + (7*a^2-2*a-15)*q^191 + (9*a^2-2*a-17)*q^192 + (a^2-4*a-13)*q^193 + (5*a^2+4*a-3)*q^194 + (2*a^2-2)*q^195 + (-a^2+6*a+10)*q^196 + (-2*a^2+8*a-8)*q^197 + (3*a^2-6*a-1)*q^198 + (10*a^2-10*a-20)*q^199 + (a^2-a-1)*q^200 +  ...

-------------------------------------------------------
145E (old = 29A), dim = 2

CONGRUENCES:
Modular Degree = 5^2*7
Ker(ModPolar)  = Z/5 + Z/5 + Z/5*7 + Z/5*7
= B(Z/7 + Z/7) + C(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
Gamma_0(146)
Weight 2

-------------------------------------------------------
J_0(146), dim = 17

-------------------------------------------------------
146A (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2*3^2 + Z/2^2*3^2
= B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/3^2 + Z/3^2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*101
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/2*3
Sha Bound      = 2*3

ANALYTIC INVARIANTS:

Omega+         = 1.7707164109013203158 + 0.61313376481290571002e-4i
Omega-         = 0.13325313436825266947e-3 + 4.1687818399126197843i
L(1)           = 0.29511940199380805423

HECKE EIGENFORM:
a^3-8*a+4 = 0,
f(q) = q + -1*q^2 + a*q^3 + 1*q^4 + (-1/2*a^2+2)*q^5 + -a*q^6 + 1/2*a^2*q^7 + -1*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 + 1*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 + -1*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 + (a^2+2*a-8)*q^38 + 2*q^39 + (1/2*a^2-2)*q^40 + (-a-2)*q^41 + (-4*a+2)*q^42 + (-2*a-2)*q^43 + (-a^2-2*a+6)*q^44 + (-1/2*a^2+2*a-6)*q^45 + (-a^2+4)*q^46 + (3/2*a^2-6)*q^47 + a*q^48 + (2*a^2-a-7)*q^49 + (a+1)*q^50 + (2*a^2+2*a-4)*q^51 + (-1/2*a^2+4)*q^52 + (1/2*a^2+2*a-4)*q^53 + (-2*a+4)*q^54 + (-a^2+2*a+8)*q^55 + -1/2*a^2*q^56 + (-2*a^2+4)*q^57 + (-3/2*a^2+2*a+10)*q^58 + (-a^2-2*a+6)*q^59 + (-2*a+2)*q^60 + (a^2+2*a+2)*q^61 + (-1/2*a^2-2*a+2)*q^62 + (5/2*a^2-2*a)*q^63 + 1*q^64 + (-a^2-a+8)*q^65 + (2*a^2+2*a-4)*q^66 + (2*a^2+3*a-12)*q^67 + (a^2+2*a-6)*q^68 + (4*a-4)*q^69 + (a^2-a)*q^70 + (-2*a^2-2*a+16)*q^71 + (-a^2+3)*q^72 + 1*q^73 + (2*a^2+2*a-6)*q^74 + (-a^2-a)*q^75 + (-a^2-2*a+8)*q^76 + (-a^2-6*a+4)*q^77 + -2*q^78 + (-a^2+4*a+8)*q^79 + (-1/2*a^2+2)*q^80 + (-a^2-4*a+9)*q^81 + (a+2)*q^82 + (a^2+4*a-2)*q^83 + (4*a-2)*q^84 + (a^2-2*a-8)*q^85 + (2*a+2)*q^86 + (-2*a^2+2*a-6)*q^87 + (a^2+2*a-6)*q^88 + (-a-2)*q^89 + (1/2*a^2-2*a+6)*q^90 + a*q^91 + (a^2-4)*q^92 + (2*a^2+2*a-2)*q^93 + (-3/2*a^2+6)*q^94 + (-2*a^2+2*a+12)*q^95 + -a*q^96 + (a^2-4*a-10)*q^97 + (-2*a^2+a+7)*q^98 + (a^2-6*a-10)*q^99 + (-a-1)*q^100 + (-3/2*a^2+4*a+8)*q^101 + (-2*a^2-2*a+4)*q^102 + (-1/2*a^2-2*a+12)*q^103 + (1/2*a^2-4)*q^104 + (a^2-8*a+4)*q^105 + (-1/2*a^2-2*a+4)*q^106 + (2*a^2+2*a-10)*q^107 + (2*a-4)*q^108 + 2*q^109 + (a^2-2*a-8)*q^110 + (-2*a^2-10*a+8)*q^111 + 1/2*a^2*q^112 + (2*a^2+4*a-18)*q^113 + (2*a^2-4)*q^114 + (2*a-8)*q^115 + (3/2*a^2-2*a-10)*q^116 + (3/2*a^2+2*a-12)*q^117 + (a^2+2*a-6)*q^118 + (a^2+6*a-4)*q^119 + (2*a-2)*q^120 + (4*a+9)*q^121 + (-a^2-2*a-2)*q^122 + (-a^2-2*a)*q^123 + (1/2*a^2+2*a-2)*q^124 + (3*a^2+2*a-14)*q^125 + (-5/2*a^2+2*a)*q^126 + -a^2*q^127 + -1*q^128 + (-2*a^2-2*a)*q^129 + (a^2+a-8)*q^130 + (6*a+6)*q^131 + (-2*a^2-2*a+4)*q^132 + (-6*a+4)*q^133 + (-2*a^2-3*a+12)*q^134 + (2*a^2-4*a-4)*q^135 + (-a^2-2*a+6)*q^136 + (-2*a^2-3*a+2)*q^137 + (-4*a+4)*q^138 + (-4*a^2-4*a+22)*q^139 + (-a^2+a)*q^140 + (6*a-6)*q^141 + (2*a^2+2*a-16)*q^142 + (-3*a^2-2*a+20)*q^143 + (a^2-3)*q^144 + (2*a^2+7*a-24)*q^145 + -1*q^146 + (-a^2+9*a-8)*q^147 + (-2*a^2-2*a+6)*q^148 + (-a^2+22)*q^149 + (a^2+a)*q^150 + (7/2*a^2+8*a-26)*q^151 + (a^2+2*a-8)*q^152 + (-a^2+6*a+10)*q^153 + (a^2+6*a-4)*q^154 + -3*a*q^155 + 2*q^156 + (1/2*a^2+2*a-2)*q^157 + (a^2-4*a-8)*q^158 + (2*a^2-2)*q^159 + (1/2*a^2-2)*q^160 + (2*a^2-2*a)*q^161 + (a^2+4*a-9)*q^162 + (-2*a+10)*q^163 + (-a-2)*q^164 + (2*a^2+4)*q^165 + (-a^2-4*a+2)*q^166 + (1/2*a^2+2*a+8)*q^167 + (-4*a+2)*q^168 + (-2*a^2-a+3)*q^169 + (-a^2+2*a+8)*q^170 + (3*a^2-6*a-16)*q^171 + (-2*a-2)*q^172 + (-5*a^2-6*a+26)*q^173 + (2*a^2-2*a+6)*q^174 + (-1/2*a^2-4*a+2)*q^175 + (-a^2-2*a+6)*q^176 + (-2*a^2-2*a+4)*q^177 + (a+2)*q^178 + (2*a^2-2*a-18)*q^179 + (-1/2*a^2+2*a-6)*q^180 + (a^2-4*a+2)*q^181 + -a*q^182 + (2*a^2+10*a-4)*q^183 + (-a^2+4)*q^184 + (a^2+8)*q^185 + (-2*a^2-2*a+2)*q^186 + (-4*a-20)*q^187 + (3/2*a^2-6)*q^188 + (-2*a^2+8*a-4)*q^189 + (2*a^2-2*a-12)*q^190 + (-1/2*a^2-4*a+6)*q^191 + a*q^192 + (-5*a^2-2*a+30)*q^193 + (-a^2+4*a+10)*q^194 + (-a^2+4)*q^195 + (2*a^2-a-7)*q^196 + (-7/2*a^2-8*a+16)*q^197 + (-a^2+6*a+10)*q^198 + (-1/2*a^2-4*a-10)*q^199 + (a+1)*q^200 +  ...

-------------------------------------------------------
146B (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^4*19
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*19 + Z/2*19
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/19 + Z/19)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^4*389
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 37
Torsion Bound  = 2*37
|L(1)/Omega|   = 19/2*37
Sha Bound      = 2*19*37

ANALYTIC INVARIANTS:

Omega+         = 13.029051256113462584 + 0.29384995818568513635e-3i
Omega-         = 1.7554502697172707616 + -0.61585930028011047532e-5i
L(1)           = 3.3452969449880460318

HECKE EIGENFORM:
a^4-8*a^2+4*a+4 = 0,
f(q) = q + 1*q^2 + a*q^3 + 1*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 + 1*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 + 1*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 + 1*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 + (a^2+2*a-4)*q^38 + (-3/2*a^3-a^2+5*a)*q^39 + (-1/2*a^3-1/2*a^2+2*a+1)*q^40 + (-2*a^3-2*a^2+13*a+2)*q^41 + (1/2*a^3+a^2-3*a-4)*q^42 + (-a^3+8*a+2)*q^43 + (a^2-4)*q^44 + (-1/2*a^3+1/2*a^2-2*a-1)*q^45 + (-a^3-a^2+8*a-2)*q^46 + (1/2*a^3+1/2*a^2-6*a-5)*q^47 + a*q^48 + (-a^3-4*a^2+5*a+17)*q^49 + (2*a^2+a-5)*q^50 + (-a^3-2*a^2+4*a+4)*q^51 + (-3/2*a^2-a+5)*q^52 + (3*a^3+5/2*a^2-17*a+1)*q^53 + (a^3-6*a)*q^54 + (a^2-4*a-2)*q^55 + (a^3+1/2*a^2-7*a+1)*q^56 + (a^3+2*a^2-4*a)*q^57 + (3/2*a^3+1/2*a^2-10*a+3)*q^58 + (a^3+a^2-6*a+4)*q^59 + (-1/2*a^3-2*a^2+3*a+2)*q^60 + (-a^3+a^2+10*a-4)*q^61 + (-1/2*a^3+1/2*a^2+6*a-5)*q^62 + (-2*a^3-1/2*a^2+15*a-5)*q^63 + 1*q^64 + (a^3+a^2+a)*q^65 + (a^3-4*a)*q^66 + (-a^3-2*a^2+3*a+4)*q^67 + (-a^3-a^2+6*a)*q^68 + (-a^3+2*a+4)*q^69 + (a^3+a^2-7*a-4)*q^70 + (2*a^3-14*a)*q^71 + (a^2-3)*q^72 + -1*q^73 + (a^3-8*a+6)*q^74 + (2*a^3+a^2-5*a)*q^75 + (a^2+2*a-4)*q^76 + (-3*a^3-a^2+22*a-6)*q^77 + (-3/2*a^3-a^2+5*a)*q^78 + (-a^2+2*a+14)*q^79 + (-1/2*a^3-1/2*a^2+2*a+1)*q^80 + (-a^2-4*a+5)*q^81 + (-2*a^3-2*a^2+13*a+2)*q^82 + (-a^3-a^2+4*a)*q^83 + (1/2*a^3+a^2-3*a-4)*q^84 + (a^2+4*a+2)*q^85 + (-a^3+8*a+2)*q^86 + (1/2*a^3+2*a^2-3*a-6)*q^87 + (a^2-4)*q^88 + (-a^3-2*a^2+9*a+2)*q^89 + (-1/2*a^3+1/2*a^2-2*a-1)*q^90 + (3*a^3-23*a+12)*q^91 + (-a^3-a^2+8*a-2)*q^92 + (1/2*a^3+2*a^2-3*a+2)*q^93 + (1/2*a^3+1/2*a^2-6*a-5)*q^94 + (-a^3-3*a^2+2*a+2)*q^95 + a*q^96 + (2*a^3+a^2-12*a+2)*q^97 + (-a^3-4*a^2+5*a+17)*q^98 + (a^2-4*a+8)*q^99 + (2*a^2+a-5)*q^100 + (-1/2*a^2+a-5)*q^101 + (-a^3-2*a^2+4*a+4)*q^102 + (2*a^3+9/2*a^2-11*a-15)*q^103 + (-3/2*a^2-a+5)*q^104 + (a^3+a^2-8*a-4)*q^105 + (3*a^3+5/2*a^2-17*a+1)*q^106 + (2*a^2+2*a-6)*q^107 + (a^3-6*a)*q^108 + (-3*a^3-4*a^2+14*a+14)*q^109 + (a^2-4*a-2)*q^110 + (2*a-4)*q^111 + (a^3+1/2*a^2-7*a+1)*q^112 + (-a^3+6*a+6)*q^113 + (a^3+2*a^2-4*a)*q^114 + (-2*a^2+6*a+4)*q^115 + (3/2*a^3+1/2*a^2-10*a+3)*q^116 + (-a^3-5/2*a^2+9*a-9)*q^117 + (a^3+a^2-6*a+4)*q^118 + (a^3+3*a^2-6*a-18)*q^119 + (-1/2*a^3-2*a^2+3*a+2)*q^120 + (-4*a+1)*q^121 + (-a^3+a^2+10*a-4)*q^122 + (-2*a^3-3*a^2+10*a+8)*q^123 + (-1/2*a^3+1/2*a^2+6*a-5)*q^124 + (1/2*a^3+a^2-9*a-4)*q^125 + (-2*a^3-1/2*a^2+15*a-5)*q^126 + (-2*a^3-a^2+14*a-6)*q^127 + 1*q^128 + (6*a+4)*q^129 + (a^3+a^2+a)*q^130 + (a^3+2*a^2-8*a-6)*q^131 + (a^3-4*a)*q^132 + (-2*a^3+a^2+16*a-14)*q^133 + (-a^3-2*a^2+3*a+4)*q^134 + (2*a^3-8*a-4)*q^135 + (-a^3-a^2+6*a)*q^136 + (-a-6)*q^137 + (-a^3+2*a+4)*q^138 + (-2*a^3+12*a-2)*q^139 + (a^3+a^2-7*a-4)*q^140 + (1/2*a^3-2*a^2-7*a-2)*q^141 + (2*a^3-14*a)*q^142 + (-a^3-a^2+10*a-14)*q^143 + (a^2-3)*q^144 + (a^3-7*a-4)*q^145 + -1*q^146 + (-4*a^3-3*a^2+21*a+4)*q^147 + (a^3-8*a+6)*q^148 + (2*a^3+a^2-18*a+4)*q^149 + (2*a^3+a^2-5*a)*q^150 + (5/2*a^3+5/2*a^2-22*a+3)*q^151 + (a^2+2*a-4)*q^152 + (a^3-a^2-10*a+4)*q^153 + (-3*a^3-a^2+22*a-6)*q^154 + (-a^3-4*a^2+5*a+4)*q^155 + (-3/2*a^3-a^2+5*a)*q^156 + (1/2*a^3-5/2*a^2-6*a+5)*q^157 + (-a^2+2*a+14)*q^158 + (5/2*a^3+7*a^2-11*a-12)*q^159 + (-1/2*a^3-1/2*a^2+2*a+1)*q^160 + (4*a^2+2*a-28)*q^161 + (-a^2-4*a+5)*q^162 + (-a^3-2*a^2+8*a+6)*q^163 + (-2*a^3-2*a^2+13*a+2)*q^164 + (a^3-4*a^2-2*a)*q^165 + (-a^3-a^2+4*a)*q^166 + (-1/2*a^2-a-5)*q^167 + (1/2*a^3+a^2-3*a-4)*q^168 + (3*a^3+4*a^2-19*a+3)*q^169 + (a^2+4*a+2)*q^170 + (2*a^3+a^2-10*a+8)*q^171 + (-a^3+8*a+2)*q^172 + (2*a^3+a^2-12*a+4)*q^173 + (1/2*a^3+2*a^2-3*a-6)*q^174 + (-5/2*a^3+1/2*a^2+20*a-13)*q^175 + (a^2-4)*q^176 + (a^3+2*a^2-4)*q^177 + (-a^3-2*a^2+9*a+2)*q^178 + (-2*a^3+2*a^2+18*a-18)*q^179 + (-1/2*a^3+1/2*a^2-2*a-1)*q^180 + (-a^3+a^2+4*a-8)*q^181 + (3*a^3-23*a+12)*q^182 + (a^3+2*a^2+4)*q^183 + (-a^3-a^2+8*a-2)*q^184 + (a^2-2*a-2)*q^185 + (1/2*a^3+2*a^2-3*a+2)*q^186 + (2*a^3-16*a+4)*q^187 + (1/2*a^3+1/2*a^2-6*a-5)*q^188 + (-2*a^3-4*a^2+12*a+20)*q^189 + (-a^3-3*a^2+2*a+2)*q^190 + (-3/2*a^3-11/2*a^2+6*a+19)*q^191 + a*q^192 + (a^2-8*a-12)*q^193 + (2*a^3+a^2-12*a+2)*q^194 + (a^3+9*a^2-4*a-4)*q^195 + (-a^3-4*a^2+5*a+17)*q^196 + (-2*a^3+3/2*a^2+13*a-9)*q^197 + (a^2-4*a+8)*q^198 + (-3/2*a^3-11/2*a^2+6*a+27)*q^199 + (2*a^2+a-5)*q^200 +  ...

-------------------------------------------------------
146C (old = 73A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/3 + Z/3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + E(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
146D (old = 73B), dim = 2

CONGRUENCES:
Modular Degree = 2^4*19
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*19 + Z/2*19
= B(Z/19 + Z/19) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
146E (old = 73C), dim = 2

CONGRUENCES:
Modular Degree = 2^4*3^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3^2 + Z/2*3^2
= A(Z/3^2 + Z/3^2) + C(Z/3 + Z/3 + Z/3 + Z/3) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(147)
Weight 2

-------------------------------------------------------
J_0(147), dim = 11

-------------------------------------------------------
147A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*3
Ker(ModPolar)  = Z/2^3*3 + Z/2^3*3
= B(Z/3 + Z/3) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.4445644196783426852 + -0.15259866590900219396e-4i
Omega-         = 0.24127556021043008063e-4 + -1.3640472747789022035i
L(1)           = 0.72228220987947129826
w1             = -0.72229427361718186409 + 0.68203126732274655187i
w2             = 0.72227014606116082108 + 0.68201600745615565165i
c4             = -2303.0261602940748061 + -0.94427321352925541766e-3i
c6             = -24350.178362799923458 + 12.303484144267175228i
j              = 1648.0044253289727642 + 0.77190696019928111793e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + -1*q^4 + 2*q^5 + 1*q^6 + 3*q^8 + 1*q^9 + -2*q^10 + 4*q^11 + 1*q^12 + 2*q^13 + -2*q^15 + -1*q^16 + 6*q^17 + -1*q^18 + -4*q^19 + -2*q^20 + -4*q^22 + -3*q^24 + -1*q^25 + -2*q^26 + -1*q^27 + -2*q^29 + 2*q^30 + -5*q^32 + -4*q^33 + -6*q^34 + -1*q^36 + 6*q^37 + 4*q^38 + -2*q^39 + 6*q^40 + -2*q^41 + -4*q^43 + -4*q^44 + 2*q^45 + 1*q^48 + 1*q^50 + -6*q^51 + -2*q^52 + 6*q^53 + 1*q^54 + 8*q^55 + 4*q^57 + 2*q^58 + -12*q^59 + 2*q^60 + 2*q^61 + 7*q^64 + 4*q^65 + 4*q^66 + 4*q^67 + -6*q^68 + 3*q^72 + 6*q^73 + -6*q^74 + 1*q^75 + 4*q^76 + 2*q^78 + -16*q^79 + -2*q^80 + 1*q^81 + 2*q^82 + 12*q^83 + 12*q^85 + 4*q^86 + 2*q^87 + 12*q^88 + 14*q^89 + -2*q^90 + -8*q^95 + 5*q^96 + -18*q^97 + 4*q^99 + 1*q^100 + -14*q^101 + 6*q^102 + -8*q^103 + 6*q^104 + -6*q^106 + 4*q^107 + 1*q^108 + -18*q^109 + -8*q^110 + -6*q^111 + -14*q^113 + -4*q^114 + 2*q^116 + 2*q^117 + 12*q^118 + -6*q^120 + 5*q^121 + -2*q^122 + 2*q^123 + -12*q^125 + 3*q^128 + 4*q^129 + -4*q^130 + -4*q^131 + 4*q^132 + -4*q^134 + -2*q^135 + 18*q^136 + -6*q^137 + -12*q^139 + 8*q^143 + -1*q^144 + -4*q^145 + -6*q^146 + -6*q^148 + 6*q^149 + -1*q^150 + 8*q^151 + -12*q^152 + 6*q^153 + 2*q^156 + 2*q^157 + 16*q^158 + -6*q^159 + -10*q^160 + -1*q^162 + 4*q^163 + 2*q^164 + -8*q^165 + -12*q^166 + 8*q^167 + -9*q^169 + -12*q^170 + -4*q^171 + 4*q^172 + 10*q^173 + -2*q^174 + -4*q^176 + 12*q^177 + -14*q^178 + -4*q^179 + -2*q^180 + 26*q^181 + -2*q^183 + 12*q^185 + 24*q^187 + 8*q^190 + -8*q^191 + -7*q^192 + 2*q^193 + 18*q^194 + -4*q^195 + 22*q^197 + -4*q^198 + -24*q^199 + -3*q^200 +  ...

-------------------------------------------------------
147B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= A(Z/3 + Z/3) + C(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.9200255849700411157 + -0.30840888326317068497e-4i
Omega-         = 0.72420907397786528374e-4 + -5.6460806358332457108i
L(1)           = 1.920025585217735834
w1             = 0.95997658203132166461 + 2.8230248974724596969i
w2             = 1.9200255849700411157 + -0.30840888326317068497e-4i
c4             = 112.00674934595913171 + 0.79096428786575645888e-2i
c6             = 1288.1093389958172045 + 0.10818168202727109865i
j              = -9558.0196967156772756 + -2.7394338393274403748i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + -1*q^3 + 2*q^4 + 2*q^5 + -2*q^6 + 1*q^9 + 4*q^10 + -2*q^11 + -2*q^12 + -1*q^13 + -2*q^15 + -4*q^16 + 2*q^18 + -1*q^19 + 4*q^20 + -4*q^22 + -1*q^25 + -2*q^26 + -1*q^27 + 4*q^29 + -4*q^30 + -9*q^31 + -8*q^32 + 2*q^33 + 2*q^36 + 3*q^37 + -2*q^38 + 1*q^39 + 10*q^41 + 5*q^43 + -4*q^44 + 2*q^45 + 6*q^47 + 4*q^48 + -2*q^50 + -2*q^52 + 12*q^53 + -2*q^54 + -4*q^55 + 1*q^57 + 8*q^58 + 12*q^59 + -4*q^60 + -10*q^61 + -18*q^62 + -8*q^64 + -2*q^65 + 4*q^66 + -5*q^67 + -6*q^71 + 3*q^73 + 6*q^74 + 1*q^75 + -2*q^76 + 2*q^78 + -1*q^79 + -8*q^80 + 1*q^81 + 20*q^82 + -6*q^83 + 10*q^86 + -4*q^87 + -16*q^89 + 4*q^90 + 9*q^93 + 12*q^94 + -2*q^95 + 8*q^96 + 6*q^97 + -2*q^99 + -2*q^100 + -2*q^101 + 7*q^103 + 24*q^106 + -8*q^107 + -2*q^108 + 9*q^109 + -8*q^110 + -3*q^111 + 10*q^113 + 2*q^114 + 8*q^116 + -1*q^117 + 24*q^118 + -7*q^121 + -20*q^122 + -10*q^123 + -18*q^124 + -12*q^125 + -15*q^127 + -5*q^129 + -4*q^130 + 14*q^131 + 4*q^132 + -10*q^134 + -2*q^135 + -12*q^137 + 3*q^139 + -6*q^141 + -12*q^142 + 2*q^143 + -4*q^144 + 8*q^145 + 6*q^146 + 6*q^148 + -12*q^149 + 2*q^150 + -16*q^151 + -18*q^155 + 2*q^156 + 14*q^157 + -2*q^158 + -12*q^159 + -16*q^160 + 2*q^162 + 4*q^163 + 20*q^164 + 4*q^165 + -12*q^166 + 14*q^167 + -12*q^169 + -1*q^171 + 10*q^172 + -8*q^173 + -8*q^174 + 8*q^176 + -12*q^177 + -32*q^178 + 2*q^179 + 4*q^180 + -13*q^181 + 10*q^183 + 6*q^185 + 18*q^186 + 12*q^188 + -4*q^190 + 10*q^191 + 8*q^192 + 11*q^193 + 12*q^194 + 2*q^195 + 16*q^197 + -4*q^198 +  ...

-------------------------------------------------------
147C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3*7
Ker(ModPolar)  = Z/2*3*7 + Z/2*3*7
= B(Z/2 + Z/2) + E(Z/7 + Z/7) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 2.134011926744914986 + 0.76728968872498134005e-5i
Omega-         = 0.65781896073979457473e-5 + -0.72570583294306161061i
L(1)           = 2.1340119267587090389
w1             = 1.067002674277653794 + 0.36285675291997443021i
w2             = 0.65781896073979457473e-5 + -0.72570583294306161061i
c4             = 5488.187720170847104 + -0.20560667025673922667i
c6             = -441807.19762559539027 + 22.992196836074192439i
j              = -9557.1834546098671979 + 0.51854963057785534102i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 1*q^3 + 2*q^4 + -2*q^5 + 2*q^6 + 1*q^9 + -4*q^10 + -2*q^11 + 2*q^12 + 1*q^13 + -2*q^15 + -4*q^16 + 2*q^18 + 1*q^19 + -4*q^20 + -4*q^22 + -1*q^25 + 2*q^26 + 1*q^27 + 4*q^29 + -4*q^30 + 9*q^31 + -8*q^32 + -2*q^33 + 2*q^36 + 3*q^37 + 2*q^38 + 1*q^39 + -10*q^41 + 5*q^43 + -4*q^44 + -2*q^45 + -6*q^47 + -4*q^48 + -2*q^50 + 2*q^52 + 12*q^53 + 2*q^54 + 4*q^55 + 1*q^57 + 8*q^58 + -12*q^59 + -4*q^60 + 10*q^61 + 18*q^62 + -8*q^64 + -2*q^65 + -4*q^66 + -5*q^67 + -6*q^71 + -3*q^73 + 6*q^74 + -1*q^75 + 2*q^76 + 2*q^78 + -1*q^79 + 8*q^80 + 1*q^81 + -20*q^82 + 6*q^83 + 10*q^86 + 4*q^87 + 16*q^89 + -4*q^90 + 9*q^93 + -12*q^94 + -2*q^95 + -8*q^96 + -6*q^97 + -2*q^99 + -2*q^100 + 2*q^101 + -7*q^103 + 24*q^106 + -8*q^107 + 2*q^108 + 9*q^109 + 8*q^110 + 3*q^111 + 10*q^113 + 2*q^114 + 8*q^116 + 1*q^117 + -24*q^118 + -7*q^121 + 20*q^122 + -10*q^123 + 18*q^124 + 12*q^125 + -15*q^127 + 5*q^129 + -4*q^130 + -14*q^131 + -4*q^132 + -10*q^134 + -2*q^135 + -12*q^137 + -3*q^139 + -6*q^141 + -12*q^142 + -2*q^143 + -4*q^144 + -8*q^145 + -6*q^146 + 6*q^148 + -12*q^149 + -2*q^150 + -16*q^151 + -18*q^155 + 2*q^156 + -14*q^157 + -2*q^158 + 12*q^159 + 16*q^160 + 2*q^162 + 4*q^163 + -20*q^164 + 4*q^165 + 12*q^166 + -14*q^167 + -12*q^169 + 1*q^171 + 10*q^172 + 8*q^173 + 8*q^174 + 8*q^176 + -12*q^177 + 32*q^178 + 2*q^179 + -4*q^180 + 13*q^181 + 10*q^183 + -6*q^185 + 18*q^186 + -12*q^188 + -4*q^190 + 10*q^191 + -8*q^192 + 11*q^193 + -12*q^194 + -2*q^195 + 16*q^197 + -4*q^198 +  ...

-------------------------------------------------------
147D (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 2^3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 13.616476703088982899 + 0.21534595414024542063e-3i
Omega-         = 3.5080077501538837068 + -0.32728496882030359551e-4i
L(1)           =

HECKE EIGENFORM:
a^2+2*a-1 = 0,
f(q) = q + a*q^2 + -1*q^3 + (-2*a-1)*q^4 + (-a-3)*q^5 + -a*q^6 + (a-2)*q^8 + 1*q^9 + (-a-1)*q^10 + -2*q^11 + (2*a+1)*q^12 + (a-3)*q^13 + (a+3)*q^15 + 3*q^16 + (3*a+1)*q^17 + a*q^18 + (2*a+2)*q^19 + (3*a+5)*q^20 + -2*a*q^22 + (-4*a-6)*q^23 + (-a+2)*q^24 + (4*a+5)*q^25 + (-5*a+1)*q^26 + -1*q^27 + (-2*a-6)*q^29 + (a+1)*q^30 + (-2*a+2)*q^31 + (a+4)*q^32 + 2*q^33 + (-5*a+3)*q^34 + (-2*a-1)*q^36 + -4*q^37 + (-2*a+2)*q^38 + (-a+3)*q^39 + (a+5)*q^40 + (-3*a-5)*q^41 + (4*a+4)*q^43 + (4*a+2)*q^44 + (-a-3)*q^45 + (2*a-4)*q^46 + (2*a+2)*q^47 + -3*q^48 + (-3*a+4)*q^50 + (-3*a-1)*q^51 + (9*a+1)*q^52 + -2*q^53 + -a*q^54 + (2*a+6)*q^55 + (-2*a-2)*q^57 + (-2*a-2)*q^58 + (-2*a+2)*q^59 + (-3*a-5)*q^60 + (-3*a-11)*q^61 + (6*a-2)*q^62 + (2*a-5)*q^64 + (2*a+8)*q^65 + 2*a*q^66 + (-4*a-4)*q^67 + (7*a-7)*q^68 + (4*a+6)*q^69 + (8*a+6)*q^71 + (a-2)*q^72 + (-7*a-11)*q^73 + -4*a*q^74 + (-4*a-5)*q^75 + (2*a-6)*q^76 + (5*a-1)*q^78 + (4*a+12)*q^79 + (-3*a-9)*q^80 + 1*q^81 + (a-3)*q^82 + (-8*a-4)*q^83 + (-4*a-6)*q^85 + (-4*a+4)*q^86 + (2*a+6)*q^87 + (-2*a+4)*q^88 + (3*a+13)*q^89 + (-a-1)*q^90 + 14*q^92 + (2*a-2)*q^93 + (-2*a+2)*q^94 + (-4*a-8)*q^95 + (-a-4)*q^96 + (a-3)*q^97 + -2*q^99 + (2*a-13)*q^100 + (5*a-5)*q^101 + (5*a-3)*q^102 + (-6*a-2)*q^103 + (-7*a+7)*q^104 + -2*a*q^106 + (4*a-2)*q^107 + (2*a+1)*q^108 + (-4*a-4)*q^109 + (2*a+2)*q^110 + 4*q^111 + (-8*a-2)*q^113 + (2*a-2)*q^114 + (10*a+22)*q^115 + (6*a+10)*q^116 + (a-3)*q^117 + (6*a-2)*q^118 + (-a-5)*q^120 + -7*q^121 + (-5*a-3)*q^122 + (3*a+5)*q^123 + (-10*a+2)*q^124 + (-4*a-4)*q^125 + -4*a*q^127 + (-11*a-6)*q^128 + (-4*a-4)*q^129 + (4*a+2)*q^130 + (8*a+12)*q^131 + (-4*a-2)*q^132 + (4*a-4)*q^134 + (a+3)*q^135 + (-11*a+1)*q^136 + (10*a+10)*q^137 + (-2*a+4)*q^138 + (4*a+16)*q^139 + (-2*a-2)*q^141 + (-10*a+8)*q^142 + (-2*a+6)*q^143 + 3*q^144 + (8*a+20)*q^145 + (3*a-7)*q^146 + (8*a+4)*q^148 + (8*a+14)*q^149 + (3*a-4)*q^150 + 12*q^151 + (-6*a-2)*q^152 + (3*a+1)*q^153 + -4*q^155 + (-9*a-1)*q^156 + (3*a-13)*q^157 + (4*a+4)*q^158 + 2*q^159 + (-5*a-13)*q^160 + a*q^162 + (-8*a-8)*q^163 + (a+11)*q^164 + (-2*a-6)*q^165 + (12*a-8)*q^166 + (14*a+14)*q^167 + (-8*a-3)*q^169 + (2*a-4)*q^170 + (2*a+2)*q^171 + (4*a-12)*q^172 + (-5*a-19)*q^173 + (2*a+2)*q^174 + -6*q^176 + (2*a-2)*q^177 + (7*a+3)*q^178 + (-4*a-18)*q^179 + (3*a+5)*q^180 + (-a+3)*q^181 + (3*a+11)*q^183 + (10*a+8)*q^184 + (4*a+12)*q^185 + (-6*a+2)*q^186 + (-6*a-2)*q^187 + (2*a-6)*q^188 + -4*q^190 + -18*q^191 + (-2*a+5)*q^192 + (8*a+2)*q^193 + (-5*a+1)*q^194 + (-2*a-8)*q^195 + 2*q^197 + -2*a*q^198 + (-4*a-20)*q^199 + (-11*a-6)*q^200 +  ...

-------------------------------------------------------
147E (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4*7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2) + C(Z/7 + Z/7) + D(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 7
Torsion Bound  = 2*7
|L(1)/Omega|   = 2/7
Sha Bound      = 2^3*7

ANALYTIC INVARIANTS:

Omega+         = 3.5078906400467481723 + -0.60612428194071202736e-4i
Omega-         = 1.9450922878730097374 + -0.11383769524607897709e-3i
L(1)           = 1.0022544687344016192

HECKE EIGENFORM:
a^2+2*a-1 = 0,
f(q) = q + a*q^2 + 1*q^3 + (-2*a-1)*q^4 + (a+3)*q^5 + a*q^6 + (a-2)*q^8 + 1*q^9 + (a+1)*q^10 + -2*q^11 + (-2*a-1)*q^12 + (-a+3)*q^13 + (a+3)*q^15 + 3*q^16 + (-3*a-1)*q^17 + a*q^18 + (-2*a-2)*q^19 + (-3*a-5)*q^20 + -2*a*q^22 + (-4*a-6)*q^23 + (a-2)*q^24 + (4*a+5)*q^25 + (5*a-1)*q^26 + 1*q^27 + (-2*a-6)*q^29 + (a+1)*q^30 + (2*a-2)*q^31 + (a+4)*q^32 + -2*q^33 + (5*a-3)*q^34 + (-2*a-1)*q^36 + -4*q^37 + (2*a-2)*q^38 + (-a+3)*q^39 + (-a-5)*q^40 + (3*a+5)*q^41 + (4*a+4)*q^43 + (4*a+2)*q^44 + (a+3)*q^45 + (2*a-4)*q^46 + (-2*a-2)*q^47 + 3*q^48 + (-3*a+4)*q^50 + (-3*a-1)*q^51 + (-9*a-1)*q^52 + -2*q^53 + a*q^54 + (-2*a-6)*q^55 + (-2*a-2)*q^57 + (-2*a-2)*q^58 + (2*a-2)*q^59 + (-3*a-5)*q^60 + (3*a+11)*q^61 + (-6*a+2)*q^62 + (2*a-5)*q^64 + (2*a+8)*q^65 + -2*a*q^66 + (-4*a-4)*q^67 + (-7*a+7)*q^68 + (-4*a-6)*q^69 + (8*a+6)*q^71 + (a-2)*q^72 + (7*a+11)*q^73 + -4*a*q^74 + (4*a+5)*q^75 + (-2*a+6)*q^76 + (5*a-1)*q^78 + (4*a+12)*q^79 + (3*a+9)*q^80 + 1*q^81 + (-a+3)*q^82 + (8*a+4)*q^83 + (-4*a-6)*q^85 + (-4*a+4)*q^86 + (-2*a-6)*q^87 + (-2*a+4)*q^88 + (-3*a-13)*q^89 + (a+1)*q^90 + 14*q^92 + (2*a-2)*q^93 + (2*a-2)*q^94 + (-4*a-8)*q^95 + (a+4)*q^96 + (-a+3)*q^97 + -2*q^99 + (2*a-13)*q^100 + (-5*a+5)*q^101 + (5*a-3)*q^102 + (6*a+2)*q^103 + (7*a-7)*q^104 + -2*a*q^106 + (4*a-2)*q^107 + (-2*a-1)*q^108 + (-4*a-4)*q^109 + (-2*a-2)*q^110 + -4*q^111 + (-8*a-2)*q^113 + (2*a-2)*q^114 + (-10*a-22)*q^115 + (6*a+10)*q^116 + (-a+3)*q^117 + (-6*a+2)*q^118 + (-a-5)*q^120 + -7*q^121 + (5*a+3)*q^122 + (3*a+5)*q^123 + (10*a-2)*q^124 + (4*a+4)*q^125 + -4*a*q^127 + (-11*a-6)*q^128 + (4*a+4)*q^129 + (4*a+2)*q^130 + (-8*a-12)*q^131 + (4*a+2)*q^132 + (4*a-4)*q^134 + (a+3)*q^135 + (11*a-1)*q^136 + (10*a+10)*q^137 + (2*a-4)*q^138 + (-4*a-16)*q^139 + (-2*a-2)*q^141 + (-10*a+8)*q^142 + (2*a-6)*q^143 + 3*q^144 + (-8*a-20)*q^145 + (-3*a+7)*q^146 + (8*a+4)*q^148 + (8*a+14)*q^149 + (-3*a+4)*q^150 + 12*q^151 + (6*a+2)*q^152 + (-3*a-1)*q^153 + -4*q^155 + (-9*a-1)*q^156 + (-3*a+13)*q^157 + (4*a+4)*q^158 + -2*q^159 + (5*a+13)*q^160 + a*q^162 + (-8*a-8)*q^163 + (-a-11)*q^164 + (-2*a-6)*q^165 + (-12*a+8)*q^166 + (-14*a-14)*q^167 + (-8*a-3)*q^169 + (2*a-4)*q^170 + (-2*a-2)*q^171 + (4*a-12)*q^172 + (5*a+19)*q^173 + (-2*a-2)*q^174 + -6*q^176 + (2*a-2)*q^177 + (-7*a-3)*q^178 + (-4*a-18)*q^179 + (-3*a-5)*q^180 + (a-3)*q^181 + (3*a+11)*q^183 + (10*a+8)*q^184 + (-4*a-12)*q^185 + (-6*a+2)*q^186 + (6*a+2)*q^187 + (-2*a+6)*q^188 + -4*q^190 + -18*q^191 + (2*a-5)*q^192 + (8*a+2)*q^193 + (5*a-1)*q^194 + (2*a+8)*q^195 + 2*q^197 + -2*a*q^198 + (4*a+20)*q^199 + (-11*a-6)*q^200 +  ...

-------------------------------------------------------
147F (old = 49A), dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + G(Z/2 + Z/2)

-------------------------------------------------------
147G (old = 21A), dim = 1

CONGRUENCES:
Modular Degree = 2^3*3
Ker(ModPolar)  = Z/2^3*3 + Z/2^3*3
= A(Z/2 + Z/2) + C(Z/3 + Z/3) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(148)
Weight 2

-------------------------------------------------------
J_0(148), dim = 17

-------------------------------------------------------
148A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= B(Z/2 + Z/2) + C(Z/3 + Z/3) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 1.692477966794783013 + -0.8699703984904188126e-4i
Omega-         = 0.3308163563017056197e-4 + -1.7642858816788816077i
L(1)           =
w1             = 0.3308163563017056197e-4 + -1.7642858816788816077i
w2             = -1.692477966794783013 + 0.8699703984904188126e-4i
c4             = 255.99760116432096469 + 0.21895850483810755983e-1i
c6             = 640.47471412148082345 + 1.1479045842513827696i
j              = 1771.3101579646939397 + 0.14774693550221945948i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -4*q^5 + -3*q^7 + -2*q^9 + 5*q^11 + 4*q^15 + -6*q^17 + 2*q^19 + 3*q^21 + -6*q^23 + 11*q^25 + 5*q^27 + -6*q^29 + 4*q^31 + -5*q^33 + 12*q^35 + 1*q^37 + -9*q^41 + 4*q^43 + 8*q^45 + -7*q^47 + 2*q^49 + 6*q^51 + 9*q^53 + -20*q^55 + -2*q^57 + -4*q^59 + -8*q^61 + 6*q^63 + -12*q^67 + 6*q^69 + 3*q^71 + -5*q^73 + -11*q^75 + -15*q^77 + 6*q^79 + 1*q^81 + -1*q^83 + 24*q^85 + 6*q^87 + 2*q^89 + -4*q^93 + -8*q^95 + -10*q^99 + 7*q^101 + -8*q^103 + -12*q^105 + -4*q^107 + -10*q^109 + -1*q^111 + 2*q^113 + 24*q^115 + 18*q^119 + 14*q^121 + 9*q^123 + -24*q^125 + -5*q^127 + -4*q^129 + 2*q^131 + -6*q^133 + -20*q^135 + 18*q^137 + 20*q^139 + 7*q^141 + 24*q^145 + -2*q^147 + 3*q^149 + 24*q^151 + 12*q^153 + -16*q^155 + 7*q^157 + -9*q^159 + 18*q^161 + 4*q^163 + 20*q^165 + -14*q^167 + -13*q^169 + -4*q^171 + 13*q^173 + -33*q^175 + 4*q^177 + -18*q^179 + -19*q^181 + 8*q^183 + -4*q^185 + -30*q^187 + -15*q^189 + 16*q^191 + -16*q^193 + -21*q^197 + -26*q^199 +  ...

-------------------------------------------------------
148B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/3 + Z/3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + D(Z/3 + Z/3 + Z/3 + Z/3) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 17
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.3443408973287204016 + 0.15733657524521462726e-4i
Omega-         = 1.7166376476814366492 + 0.4321739633000721174e-4i
L(1)           = 0.67217044871039539536

HECKE EIGENFORM:
a^2+a-4 = 0,
f(q) = q + a*q^3 + 2*q^5 + -a*q^7 + (-a+1)*q^9 + -a*q^11 + 2*q^13 + 2*a*q^15 + (-2*a+2)*q^17 + (2*a-2)*q^19 + (a-4)*q^21 + -2*q^23 + -1*q^25 + (-a-4)*q^27 + (4*a+2)*q^29 + (-2*a-6)*q^31 + (a-4)*q^33 + -2*a*q^35 + -1*q^37 + 2*a*q^39 + (-a+2)*q^41 + (-4*a-2)*q^43 + (-2*a+2)*q^45 + (-a+8)*q^47 + (-a-3)*q^49 + (4*a-8)*q^51 + (5*a+6)*q^53 + -2*a*q^55 + (-4*a+8)*q^57 + (-2*a-2)*q^59 + (2*a-6)*q^61 + (-2*a+4)*q^63 + 4*q^65 + (4*a-4)*q^67 + -2*a*q^69 + (a+8)*q^71 + (7*a+2)*q^73 + -a*q^75 + (-a+4)*q^77 + (6*a+6)*q^79 + -7*q^81 + (a+4)*q^83 + (-4*a+4)*q^85 + (-2*a+16)*q^87 + (2*a+10)*q^89 + -2*a*q^91 + (-4*a-8)*q^93 + (4*a-4)*q^95 + (-2*a-6)*q^97 + (-2*a+4)*q^99 + (-5*a-2)*q^101 + 2*q^103 + (2*a-8)*q^105 + (4*a-8)*q^107 + (-2*a+2)*q^109 + -a*q^111 + (-4*a-6)*q^113 + -4*q^115 + (-2*a+2)*q^117 + (-4*a+8)*q^119 + (-a-7)*q^121 + (3*a-4)*q^123 + -12*q^125 + (a+16)*q^127 + (2*a-16)*q^129 + (2*a-6)*q^131 + (4*a-8)*q^133 + (-2*a-8)*q^135 + (4*a+6)*q^137 + 12*q^139 + (9*a-4)*q^141 + -2*a*q^143 + (8*a+4)*q^145 + (-2*a-4)*q^147 + (-a-6)*q^149 + -16*q^151 + (-6*a+10)*q^153 + (-4*a-12)*q^155 + (-5*a+2)*q^157 + (a+20)*q^159 + 2*a*q^161 + (-4*a+2)*q^163 + (2*a-8)*q^165 + (6*a+6)*q^167 + -9*q^169 + (6*a-10)*q^171 + (a+18)*q^173 + a*q^175 + -8*q^177 + (-4*a-14)*q^179 + (-7*a-10)*q^181 + (-8*a+8)*q^183 + -2*q^185 + (-4*a+8)*q^187 + (3*a+4)*q^189 + (2*a-2)*q^191 + 10*q^193 + 4*a*q^195 + (-a+10)*q^197 + (-4*a+10)*q^199 +  ...

-------------------------------------------------------
148C (old = 74A), dim = 2

CONGRUENCES:
Modular Degree = 2^4*3^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= A(Z/3 + Z/3) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + F(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
148D (old = 74B), dim = 2

CONGRUENCES:
Modular Degree = 2^4*3^2*5^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3*5 + Z/2*3*5 + Z/2*3*5 + Z/2*3*5
= B(Z/3 + Z/3 + Z/3 + Z/3) + C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + E(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
148E (old = 37A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*5^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*5 + Z/2*5 + Z/2^2*5 + Z/2^2*5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/5 + Z/5 + Z/5 + Z/5) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
148F (old = 37B), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/3 + Z/3 + Z/3 + Z/3) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(149)
Weight 2

-------------------------------------------------------
J_0(149), dim = 12

-------------------------------------------------------
149A (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 7^2
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 48.851488507719155362 + 0.11138732680988959209e-2i
Omega-         = 0.5060210153611155991e-3 + 12.057746519353118745i
L(1)           =

HECKE EIGENFORM:
a^3+a^2-2*a-1 = 0,
f(q) = 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 + (a^2-7*a-2)*q^38 + (2*a^2+2*a+1)*q^39 + (4*a^2+4*a-3)*q^40 + (-a^2-5*a+2)*q^41 + (-a^2+a+1)*q^42 + (3*a^2-5*a-8)*q^43 + (-a^2+2*a-1)*q^44 + (-6*a^2-7*a+5)*q^45 + (2*a-1)*q^46 + (-7*a^2-3*a+10)*q^47 + (3*a^2+2*a+1)*q^48 + (-4*a^2-3*a+3)*q^49 + (a^2+a)*q^50 + (-4*a^2-6*a-3)*q^51 + (a^2+2*a-3)*q^52 + (2*a^2+5*a+1)*q^53 + (-4*a^2-a+1)*q^54 + (-2*a^2+3*a-1)*q^55 + (2*a^2+2*a-5)*q^56 + (7*a^2+7*a+1)*q^57 + (a^2-3*a-4)*q^58 + (4*a^2+a-6)*q^59 + (-2*a^2-a+1)*q^60 + (a^2-4*a-2)*q^61 + (-3*a^2-5*a+3)*q^62 + (-4*a^2-3*a+9)*q^63 + (3*a^2+5*a-2)*q^64 + (2*a^2+5*a-3)*q^65 + (-4*a^2+3*a+2)*q^66 + (a^2+a-9)*q^67 + (-3*a^2-4*a+7)*q^68 + (-2*a^2-a+1)*q^69 + (3*a^2-4)*q^70 + (7*a^2+7*a-11)*q^71 + (-a^2-5*a-7)*q^72 + (9*a^2+10*a-12)*q^73 + (6*a^2+3*a)*q^74 + (-a^2-3*a-1)*q^75 + (-4*a^2+2*a+7)*q^76 + (4*a^2-a-5)*q^77 + (5*a+2)*q^78 + (2*a^2+4*a-5)*q^79 + (2*a^2+7*a-4)*q^80 + (-5*a^2-a+9)*q^81 + (-4*a^2-1)*q^82 + (a^2-1)*q^83 + (-a+1)*q^84 + (-6*a^2-11*a+7)*q^85 + (-8*a^2-2*a+3)*q^86 + (3*a^2+5*a+3)*q^87 + (-3*a^2+a+3)*q^88 + (4*a^2-4*a-11)*q^89 + (-a^2-7*a-6)*q^90 + (4*a^2+a-7)*q^91 + (4*a^2+a-8)*q^92 + (5*a^2+8*a)*q^93 + (4*a^2-4*a-7)*q^94 + (-3*a^2+10*a+12)*q^95 + (-3*a^2-a-1)*q^96 + (-13*a^2-8*a+18)*q^97 + (a^2-5*a-4)*q^98 + (3*a^2-4)*q^99 + -1*q^100 + (2*a^2+8*a+3)*q^101 + (-2*a^2-11*a-4)*q^102 + (-a^2-12*a)*q^103 + (-a^2+3*a+5)*q^104 + (-2*a+1)*q^105 + (3*a^2+5*a+2)*q^106 + (-7*a^2-5*a+2)*q^107 + (a^2-a+2)*q^108 + (-4*a^2-2*a+13)*q^109 + (5*a^2-5*a-2)*q^110 + (-3*a^2-15*a-6)*q^111 + (6*a^2+a-10)*q^112 + (-7*a^2-a+17)*q^113 + (15*a+7)*q^114 + (5*a^2-11)*q^115 + (4*a^2+4*a-9)*q^116 + (a^2-4*a-8)*q^117 + (-3*a^2+2*a+4)*q^118 + (-8*a^2-3*a+15)*q^119 + (-5*a^2-9*a-4)*q^120 + (9*a^2-8*a-15)*q^121 + (-5*a^2+1)*q^122 + (9*a+5)*q^123 + (-8*a^2-3*a+19)*q^124 + (-6*a^2+3*a+13)*q^125 + (a^2+a-4)*q^126 + (4*a^2-2*a+1)*q^127 + (-6*a^2+2*a+13)*q^128 + (2*a^2+15*a+5)*q^129 + (3*a^2+a+2)*q^130 + (10*a^2+5*a-20)*q^131 + (3*a^2-2*a-2)*q^132 + (-a^2-4*a+8)*q^133 + (-7*a+1)*q^134 + (4*a^2+3*a+4)*q^135 + (a^2-7*a-11)*q^136 + (-5*a^2-5*a+12)*q^137 + (a^2-3*a-2)*q^138 + (10*a^2+15*a-18)*q^139 + (5*a^2+4*a-13)*q^140 + (4*a^2+3*a+3)*q^141 + (3*a+7)*q^142 + (3*a^2-4*a)*q^143 + (2*a^2-5*a-11)*q^144 + (7*a^2+10*a-10)*q^145 + (a^2+6*a+9)*q^146 + (5*a^2+7*a+3)*q^147 + -3*a^2*q^148 + -1*q^149 + (-2*a^2-3*a-1)*q^150 + (-13*a^2-3*a+19)*q^151 + (4*a^2+13*a)*q^152 + (-a^2+10*a+18)*q^153 + (-5*a^2+3*a+4)*q^154 + (-8*a^2+2*a+27)*q^155 + (a^2-2*a-2)*q^156 + (-9*a^2+16)*q^157 + (2*a^2-a+2)*q^158 + (-5*a^2-13*a-5)*q^159 + (-3*a^2-8*a+8)*q^160 + (5*a^2+4*a-13)*q^161 + (4*a^2-a-5)*q^162 + (10*a^2+3*a-15)*q^163 + (6*a^2+a-8)*q^164 + (5*a^2-3*a-3)*q^165 + (-a^2+a+1)*q^166 + (4*a^2+10*a-3)*q^167 + (a^2-a-2)*q^168 + (a^2-9)*q^169 + (-5*a^2-5*a-6)*q^170 + (-9*a^2-19*a+2)*q^171 + (-3*a+8)*q^172 + (-7*a^2+2*a+17)*q^173 + (2*a^2+9*a+3)*q^174 + (a^2-2)*q^175 + (6*a^2-7*a-1)*q^176 + (-2*a^2-1)*q^177 + (-8*a^2-3*a+4)*q^178 + (-5*a^2+2*a)*q^179 + (6*a^2+6*a-11)*q^180 + (-8*a^2-7*a-2)*q^181 + (-3*a^2+a+4)*q^182 + (9*a+4)*q^183 + (-3*a^2-4*a+6)*q^184 + (-9*a^2-9*a-3)*q^185 + (3*a^2+10*a+5)*q^186 + (-3*a^2+6*a-2)*q^187 + (6*a^2+7*a-16)*q^188 + (-4*a^2+a+6)*q^189 + (13*a^2+6*a-3)*q^190 + (-5*a^2+4)*q^191 + (-4*a^2-11*a-5)*q^192 + (-4*a^2-6*a+2)*q^193 + (5*a^2-8*a-13)*q^194 + (-a^2-9*a-5)*q^195 + (2*a^2+4*a-5)*q^196 + (6*a^2-2*a-24)*q^197 + (-3*a^2+2*a+3)*q^198 + (-7*a^2+6*a+8)*q^199 + (-2*a^2-3*a)*q^200 +  ...

-------------------------------------------------------
149B (new) , dim = 9

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^6*234893*1252037
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 37
Torsion Bound  = 37
|L(1)/Omega|   = 2^3/37
Sha Bound      = 2^3*37

ANALYTIC INVARIANTS:

Omega+         = 11.736376219753112514 + -0.29108608122117993893e-3i
Omega-         = 0.57263568408665477733e-3 + 522.60472508161883574i
L(1)           = 2.5375948591054869053

HECKE EIGENFORM:
a^9+a^8-15*a^7-12*a^6+75*a^5+48*a^4-137*a^3-76*a^2+68*a+39 = 0,
f(q) = 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 + (1/2*a^8-15/2*a^6+1/2*a^5+36*a^4-3*a^3-117/2*a^2+13/2*a+39/2)*q^38 + (5/2*a^8+1/2*a^7-38*a^6-1/2*a^5+377/2*a^4-45/2*a^3-326*a^2+101/2*a+133)*q^39 + (-1/2*a^8+1/4*a^7+29/4*a^6-9/2*a^5-141/4*a^4+85/4*a^3+255/4*a^2-25*a-117/4)*q^40 + (2*a^8+a^7-30*a^6-8*a^5+148*a^4+10*a^3-257*a^2+17*a+105)*q^41 + (-1/2*a^8+15/2*a^6-3/2*a^5-36*a^4+11*a^3+113/2*a^2-27/2*a-39/2)*q^42 + (-3/4*a^8-1/2*a^7+43/4*a^6+21/4*a^5-49*a^4-16*a^3+297/4*a^2+49/4*a-97/4)*q^43 + (-7/4*a^8-3/2*a^7+95/4*a^6+45/4*a^5-108*a^4-15*a^3+717/4*a^2-39/4*a-297/4)*q^44 + (-5/2*a^8-a^7+75/2*a^6+13/2*a^5-183*a^4+3*a^3+617/2*a^2-81/2*a-247/2)*q^45 + (-3/4*a^8-3/4*a^7+19/2*a^6+27/4*a^5-153/4*a^4-61/4*a^3+53*a^2+13/4*a-39/2)*q^46 + (-3/2*a^8+47/2*a^6-3/2*a^5-118*a^4+12*a^3+407/2*a^2-37/2*a-171/2)*q^47 + (-5/4*a^8-3/4*a^7+37/2*a^6+23/4*a^5-355/4*a^4-25/4*a^3+291/2*a^2-43/4*a-59)*q^48 + (-a^7-2*a^6+10*a^5+17*a^4-27*a^3-36*a^2+14*a+18)*q^49 + (3/4*a^8+3/4*a^7-10*a^6-29/4*a^5+167/4*a^4+73/4*a^3-57*a^2-27/4*a+39/2)*q^50 + (9/4*a^8+1/2*a^7-137/4*a^6-3/4*a^5+171*a^4-19*a^3-1203/4*a^2+165/4*a+515/4)*q^51 + (-a^8+1/2*a^7+35/2*a^6-6*a^5-191/2*a^4+49/2*a^3+353/2*a^2-33*a-151/2)*q^52 + (-1/2*a^8+1/4*a^7+33/4*a^6-3*a^5-171/4*a^4+47/4*a^3+307/4*a^2-14*a-151/4)*q^53 + (7/4*a^8+a^7-99/4*a^6-29/4*a^5+229/2*a^4+7*a^3-735/4*a^2+57/4*a+273/4)*q^54 + (3/2*a^8+1/4*a^7-91/4*a^6+1/2*a^5+455/4*a^4-63/4*a^3-809/4*a^2+30*a+351/4)*q^55 + (5/2*a^8+3/2*a^7-36*a^6-21/2*a^5+343/2*a^4+15/2*a^3-289*a^2+43/2*a+117)*q^56 + (-5*a^8-3/2*a^7+153/2*a^6+6*a^5-771/2*a^4+65/2*a^3+1371/2*a^2-97*a-583/2)*q^57 + (1/4*a^8+3/4*a^7-5/2*a^6-31/4*a^5+27/4*a^4+89/4*a^3-7/2*a^2-61/4*a)*q^58 + (-a^8-1/4*a^7+61/4*a^6+a^5-307/4*a^4+23/4*a^3+555/4*a^2-41/2*a-233/4)*q^59 + (9/4*a^8+3/4*a^7-69/2*a^6-15/4*a^5+699/4*a^4-43/4*a^3-623/2*a^2+155/4*a+130)*q^60 + (3/4*a^8+1/2*a^7-45/4*a^6-17/4*a^5+56*a^4+13/2*a^3-405/4*a^2+33/4*a+195/4)*q^61 + (-a^8-1/2*a^7+29/2*a^6+3*a^5-143/2*a^4+3/2*a^3+265/2*a^2-14*a-117/2)*q^62 + (4*a^8+1/2*a^7-125/2*a^6+a^5+635/2*a^4-73/2*a^3-1121/2*a^2+79*a+467/2)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (2*a^8+1/2*a^7-61/2*a^6-2*a^5+305/2*a^4-23/2*a^3-537/2*a^2+37*a+221/2)*q^65 + (1/4*a^8+1/2*a^7-13/4*a^6-19/4*a^5+14*a^4+12*a^3-79/4*a^2-31/4*a+39/4)*q^66 + (3/2*a^8-47/2*a^6+5/2*a^5+118*a^4-22*a^3-407/2*a^2+79/2*a+183/2)*q^67 + (-1/4*a^8-a^7+1/4*a^6+35/4*a^5+25/2*a^4-21*a^3-151/4*a^2+49/4*a+89/4)*q^68 + (-1/2*a^8-3/4*a^7+25/4*a^6+8*a^5-95/4*a^4-97/4*a^3+111/4*a^2+14*a-43/4)*q^69 + (-a^8-1/2*a^7+31/2*a^6+4*a^5-159/2*a^4-9/2*a^3+287/2*a^2-11*a-117/2)*q^70 + (-13/4*a^8-5/4*a^7+49*a^6+31/4*a^5-969/4*a^4+17/4*a^3+420*a^2-171/4*a-345/2)*q^71 + (-9/4*a^8-a^7+135/4*a^6+27/4*a^5-331/2*a^4-1/2*a^3+1121/4*a^2-125/4*a-429/4)*q^72 + (-3*a^8-5/4*a^7+181/4*a^6+17/2*a^5-897/4*a^4-7/4*a^3+1559/4*a^2-69/2*a-639/4)*q^73 + (-1/2*a^8+3/4*a^7+39/4*a^6-15/2*a^5-223/4*a^4+87/4*a^3+421/4*a^2-19*a-195/4)*q^74 + (a^8+5/4*a^7-53/4*a^6-13*a^5+223/4*a^4+149/4*a^3-311/4*a^2-37/2*a+113/4)*q^75 + (1/2*a^8-17/2*a^6+3/2*a^5+47*a^4-14*a^3-173/2*a^2+53/2*a+71/2)*q^76 + (a^8+a^7-14*a^6-9*a^5+66*a^4+19*a^3-117*a^2-3*a+54)*q^77 + (-2*a^8-1/2*a^7+59/2*a^6+a^5-285/2*a^4+33/2*a^3+481/2*a^2-37*a-195/2)*q^78 + (-a^8+15*a^6-a^5-71*a^4+7*a^3+109*a^2-10*a-32)*q^79 + (1/4*a^8+1/4*a^7-5/2*a^6-13/4*a^5+19/4*a^4+51/4*a^3+8*a^2-47/4*a-13/2)*q^80 + (-11/2*a^8-7/4*a^7+333/4*a^6+8*a^5-1655/4*a^4+115/4*a^3+2891/4*a^2-94*a-1211/4)*q^81 + (-a^8+16*a^6-2*a^5-86*a^4+17*a^3+169*a^2-31*a-78)*q^82 + (-3/4*a^8+1/4*a^7+13*a^6-15/4*a^5-291/4*a^4+83/4*a^3+144*a^2-149/4*a-141/2)*q^83 + (-1/2*a^8+15/2*a^6-3/2*a^5-37*a^4+12*a^3+127/2*a^2-45/2*a-43/2)*q^84 + (1/4*a^8+1/4*a^7-7/2*a^6-9/4*a^5+63/4*a^4+19/4*a^3-24*a^2+13/4*a+13/2)*q^85 + (1/4*a^8-1/2*a^7-15/4*a^6+29/4*a^5+20*a^4-57/2*a^3-179/4*a^2+107/4*a+117/4)*q^86 + (19/4*a^8+2*a^7-285/4*a^6-53/4*a^5+701/2*a^4-1/2*a^3-2419/4*a^2+243/4*a+1007/4)*q^87 + (7/4*a^8-1/2*a^7-117/4*a^6+27/4*a^5+156*a^4-61/2*a^3-1153/4*a^2+173/4*a+507/4)*q^88 + (2*a^8-32*a^6+3*a^5+166*a^4-26*a^3-300*a^2+45*a+128)*q^89 + (3/2*a^8-47/2*a^6+9/2*a^5+123*a^4-34*a^3-461/2*a^2+93/2*a+195/2)*q^90 + (-2*a^8-a^7+30*a^6+7*a^5-149*a^4-a^3+264*a^2-33*a-107)*q^91 + (-a^8-5/4*a^7+57/4*a^6+11*a^5-271/4*a^4-85/4*a^3+455/4*a^2+3/2*a-181/4)*q^92 + (-3/2*a^8+47/2*a^6-7/2*a^5-122*a^4+25*a^3+457/2*a^2-59/2*a-217/2)*q^93 + (3/2*a^8+a^7-39/2*a^6-11/2*a^5+84*a^4-2*a^3-265/2*a^2+33/2*a+117/2)*q^94 + (-2*a^8-a^7+30*a^6+6*a^5-148*a^4+7*a^3+254*a^2-44*a-104)*q^95 + (9/2*a^8+5/4*a^7-275/4*a^6-4*a^5+1381/4*a^4-133/4*a^3-2449/4*a^2+87*a+1053/4)*q^96 + (-5/2*a^8-3/2*a^7+36*a^6+23/2*a^5-341/2*a^4-33/2*a^3+282*a^2-15/2*a-107)*q^97 + (-a^8-2*a^7+10*a^6+17*a^5-27*a^4-36*a^3+14*a^2+18*a)*q^98 + (15/4*a^8+9/4*a^7-109/2*a^6-65/4*a^5+1049/4*a^4+51/4*a^3-895/2*a^2+161/4*a+183)*q^99 + (a^8+3/4*a^7-59/4*a^6-13/2*a^5+287/4*a^4+41/4*a^3-493/4*a^2+13/2*a+209/4)*q^100 + (1/2*a^8-17/2*a^6-1/2*a^5+45*a^4+4*a^3-153/2*a^2-15/2*a+47/2)*q^101 + (-7/4*a^8-1/2*a^7+105/4*a^6+9/4*a^5-127*a^4+15/2*a^3+849/4*a^2-97/4*a-351/4)*q^102 + (-3/2*a^8+47/2*a^6-5/2*a^5-119*a^4+20*a^3+417/2*a^2-55/2*a-175/2)*q^103 + (5/2*a^8+3/2*a^7-36*a^6-19/2*a^5+343/2*a^4+1/2*a^3-289*a^2+67/2*a+117)*q^104 + (2*a^8+1/2*a^7-61/2*a^6-a^5+307/2*a^4-39/2*a^3-547/2*a^2+52*a+221/2)*q^105 + (3/4*a^8+3/4*a^7-9*a^6-21/4*a^5+143/4*a^4+33/4*a^3-52*a^2-15/4*a+39/2)*q^106 + (-a^8-1/2*a^7+31/2*a^6+5*a^5-157/2*a^4-25/2*a^3+281/2*a^2-121/2)*q^107 + (11/4*a^8+3/2*a^7-163/4*a^6-37/4*a^5+200*a^4-5*a^3-1385/4*a^2+203/4*a+565/4)*q^108 + (a^8+1/2*a^7-31/2*a^6-5*a^5+157/2*a^4+27/2*a^3-281/2*a^2-11*a+125/2)*q^109 + (-5/4*a^8-1/4*a^7+37/2*a^6+5/4*a^5-351/4*a^4+13/4*a^3+144*a^2-57/4*a-117/2)*q^110 + (-15/4*a^8-5/4*a^7+113/2*a^6+29/4*a^5-1121/4*a^4+29/4*a^3+987/2*a^2-193/4*a-213)*q^111 + (a^8+1/2*a^7-31/2*a^6-4*a^5+161/2*a^4+9/2*a^3-303/2*a^2+13*a+131/2)*q^112 + (-3/2*a^8-5/4*a^7+87/4*a^6+11*a^5-421/4*a^4-91/4*a^3+725/4*a^2+2*a-305/4)*q^113 + (7/2*a^8+3/2*a^7-54*a^6-21/2*a^5+545/2*a^4+1/2*a^3-477*a^2+97/2*a+195)*q^114 + (5/4*a^8+5/4*a^7-18*a^6-51/4*a^5+333/4*a^4+131/4*a^3-127*a^2-37/4*a+91/2)*q^115 + (1/2*a^8+3/4*a^7-25/4*a^6-7*a^5+103/4*a^4+69/4*a^3-163/4*a^2-10*a+83/4)*q^116 + (6*a^8+a^7-93*a^6+470*a^4-56*a^3-828*a^2+127*a+343)*q^117 + (3/4*a^8+1/4*a^7-11*a^6-7/4*a^5+215/4*a^4+7/4*a^3-193/2*a^2+39/4*a+39)*q^118 + (-2*a^8+33*a^6-2*a^5-177*a^4+19*a^3+331*a^2-43*a-145)*q^119 + (-7/2*a^8-1/4*a^7+219/4*a^6-5*a^5-1129/4*a^4+217/4*a^3+2057/4*a^2-92*a-897/4)*q^120 + (7/4*a^8+3/4*a^7-53/2*a^6-19/4*a^5+533/4*a^4+1/4*a^3-237*a^2+71/4*a+191/2)*q^121 + (-1/4*a^8+19/4*a^6-1/4*a^5-59/2*a^4+3/2*a^3+261/4*a^2-9/4*a-117/4)*q^122 + (a^8+a^7-14*a^6-10*a^5+63*a^4+24*a^3-93*a^2+3*a+21)*q^123 + (-5/2*a^8-3/2*a^7+37*a^6+21/2*a^5-363/2*a^4-11/2*a^3+318*a^2-55/2*a-137)*q^124 + (-1/4*a^7+1/4*a^6+9/2*a^5-5/4*a^4-75/4*a^3+7/4*a^2+19/2*a-39/4)*q^125 + (-7/2*a^8-5/2*a^7+49*a^6+35/2*a^5-457/2*a^4-25/2*a^3+383*a^2-77/2*a-156)*q^126 + (-1/2*a^8-1/2*a^7+7*a^6+7/2*a^5-67/2*a^4-3/2*a^3+62*a^2-23/2*a-35)*q^127 + (a^7-12*a^5+40*a^3-32*a)*q^128 + (7/4*a^8-1/2*a^7-113/4*a^6+39/4*a^5+151*a^4-101/2*a^3-1173/4*a^2+265/4*a+563/4)*q^129 + (-3/2*a^8-1/2*a^7+22*a^6+5/2*a^5-215/2*a^4+11/2*a^3+189*a^2-51/2*a-78)*q^130 + (9/4*a^8+1/2*a^7-137/4*a^6+1/4*a^5+173*a^4-29*a^3-1259/4*a^2+261/4*a+579/4)*q^131 + (3/4*a^8+1/2*a^7-41/4*a^6-17/4*a^5+47*a^4+21/2*a^3-325/4*a^2-23/4*a+159/4)*q^132 + (6*a^8+3*a^7-88*a^6-20*a^5+426*a^4+5*a^3-730*a^2+68*a+298)*q^133 + (-3/2*a^8-a^7+41/2*a^6+11/2*a^5-94*a^4+2*a^3+307/2*a^2-21/2*a-117/2)*q^134 + (-5*a^8-2*a^7+75*a^6+12*a^5-369*a^4+13*a^3+635*a^2-90*a-260)*q^135 + (-1/4*a^8-3/2*a^7+9/4*a^6+55/4*a^5-8*a^4-33*a^3+67/4*a^2+71/4*a-39/4)*q^136 + (-11/2*a^8-1/2*a^7+86*a^6-11/2*a^5-883/2*a^4+143/2*a^3+803*a^2-271/2*a-360)*q^137 + (-1/4*a^8-5/4*a^7+2*a^6+55/4*a^5-1/4*a^4-163/4*a^3-24*a^2+93/4*a+39/2)*q^138 + (-9/2*a^8-3/4*a^7+281/4*a^6+1/2*a^5-1433/4*a^4+149/4*a^3+2567/4*a^2-85*a-1101/4)*q^139 + (-5/2*a^8-1/2*a^7+38*a^6+1/2*a^5-379/2*a^4+43/2*a^3+333*a^2-99/2*a-143)*q^140 + (5/2*a^8+1/2*a^7-39*a^6-3/2*a^5+403/2*a^4-31/2*a^3-377*a^2+93/2*a+174)*q^141 + (2*a^8+1/4*a^7-125/4*a^6+3/2*a^5+641/4*a^4-101/4*a^3-1159/4*a^2+97/2*a+507/4)*q^142 + (-3/2*a^8-1/2*a^7+22*a^6+3/2*a^5-213/2*a^4+23/2*a^3+180*a^2-57/2*a-72)*q^143 + (-5/4*a^8-a^7+69/4*a^6+35/4*a^5-153/2*a^4-17*a^3+453/4*a^2-15/4*a-155/4)*q^144 + (1/2*a^8-1/4*a^7-33/4*a^6+5*a^5+183/4*a^4-103/4*a^3-363/4*a^2+30*a+143/4)*q^145 + (7/4*a^8+1/4*a^7-55/2*a^6+3/4*a^5+569/4*a^4-85/4*a^3-525/2*a^2+177/4*a+117)*q^146 + (-7/4*a^8-5/4*a^7+51/2*a^6+45/4*a^5-493/4*a^4-87/4*a^3+429/2*a^2-49/4*a-90)*q^147 + (-5/4*a^8+3/4*a^7+45/2*a^6-31/4*a^5-507/4*a^4+113/4*a^3+242*a^2-141/4*a-225/2)*q^148 + 1*q^149 + (1/4*a^8+7/4*a^7-a^6-77/4*a^5-43/4*a^4+237/4*a^3+115/2*a^2-159/4*a-39)*q^150 + (-9/2*a^8-7/4*a^7+273/4*a^6+19/2*a^5-1377/4*a^4+65/4*a^3+2495/4*a^2-76*a-1093/4)*q^151 + (-3/2*a^8-a^7+45/2*a^6+17/2*a^5-110*a^4-12*a^3+363/2*a^2-23/2*a-117/2)*q^152 + (2*a^8+5/4*a^7-113/4*a^6-15/2*a^5+533/4*a^4-13/4*a^3-899/4*a^2+65/2*a+347/4)*q^153 + (a^7+3*a^6-9*a^5-29*a^4+20*a^3+73*a^2-14*a-39)*q^154 + (2*a^8-1/2*a^7-65/2*a^6+10*a^5+347/2*a^4-105/2*a^3-657/2*a^2+63*a+299/2)*q^155 + (-7/2*a^8-3/2*a^7+53*a^6+17/2*a^5-529/2*a^4+23/2*a^3+463*a^2-125/2*a-188)*q^156 + (2*a^8-32*a^6+3*a^5+164*a^4-28*a^3-287*a^2+55*a+117)*q^157 + (a^8-13*a^6+4*a^5+55*a^4-28*a^3-86*a^2+36*a+39)*q^158 + (11/4*a^8+1/2*a^7-171/4*a^6-5/4*a^5+218*a^4-17*a^3-1577/4*a^2+179/4*a+677/4)*q^159 + (a^8+3/4*a^7-59/4*a^6-5*a^5+285/4*a^4-1/4*a^3-481/4*a^2+53/2*a+195/4)*q^160 + (a^8+3/2*a^7-25/2*a^6-13*a^5+105/2*a^4+55/2*a^3-165/2*a^2-12*a+67/2)*q^161 + (15/4*a^8+3/4*a^7-58*a^6-5/4*a^5+1171/4*a^4-123/4*a^3-512*a^2+285/4*a+429/2)*q^162 + (a^8-3/4*a^7-73/4*a^6+8*a^5+415/4*a^4-115/4*a^3-807/4*a^2+71/2*a+373/4)*q^163 + (-3*a^8-a^7+46*a^6+5*a^5-231*a^4+12*a^3+407*a^2-44*a-171)*q^164 + (1/2*a^8-1/2*a^7-9*a^6+15/2*a^5+103/2*a^4-69/2*a^3-99*a^2+79/2*a+39)*q^165 + (a^8+7/4*a^7-51/4*a^6-33/2*a^5+227/4*a^4+165/4*a^3-377/4*a^2-39/2*a+117/4)*q^166 + (4*a^8+7/4*a^7-243/4*a^6-13*a^5+1213/4*a^4+39/4*a^3-2133/4*a^2+71/2*a+883/4)*q^167 + (3/2*a^8-45/2*a^6+7/2*a^5+108*a^4-27*a^3-347/2*a^2+79/2*a+117/2)*q^168 + (-4*a^8-a^7+62*a^6+4*a^5-314*a^4+25*a^3+558*a^2-80*a-243)*q^169 + (1/4*a^7+3/4*a^6-3*a^5-29/4*a^4+41/4*a^3+89/4*a^2-21/2*a-39/4)*q^170 + (-15/2*a^8-3/2*a^7+115*a^6+3/2*a^5-1155/2*a^4+135/2*a^3+1014*a^2-311/2*a-410)*q^171 + (3/4*a^8+a^7-45/4*a^6-37/4*a^5+115/2*a^4+43/2*a^3-411/4*a^2-49/4*a+155/4)*q^172 + (7/4*a^8-115/4*a^6+3/4*a^5+303/2*a^4-8*a^3-1091/4*a^2+73/4*a+437/4)*q^173 + (-11/4*a^8+175/4*a^6-23/4*a^5-457/2*a^4+46*a^3+1687/4*a^2-285/4*a-741/4)*q^174 + (-3/2*a^8-3/2*a^7+20*a^6+23/2*a^5-179/2*a^4-33/2*a^3+147*a^2-7/2*a-64)*q^175 + (5/4*a^8-79/4*a^6+9/4*a^5+203/2*a^4-37/2*a^3-729/4*a^2+109/4*a+321/4)*q^176 + (-3*a^8-5/4*a^7+185/4*a^6+15/2*a^5-945/4*a^4+37/4*a^3+1707/4*a^2-117/2*a-707/4)*q^177 + (-2*a^8-2*a^7+27*a^6+16*a^5-122*a^4-26*a^3+197*a^2-8*a-78)*q^178 + (7/2*a^8+5/2*a^7-50*a^6-41/2*a^5+475/2*a^4+71/2*a^3-406*a^2+13/2*a+171)*q^179 + (7/2*a^8+a^7-105/2*a^6-5/2*a^5+260*a^4-31*a^3-913/2*a^2+153/2*a+377/2)*q^180 + (7/2*a^8+3/2*a^7-53*a^6-21/2*a^5+531/2*a^4+5/2*a^3-475*a^2+93/2*a+205)*q^181 + (a^8-17*a^6+a^5+95*a^4-10*a^3-185*a^2+29*a+78)*q^182 + (-15/4*a^8-1/2*a^7+231/4*a^6-7/4*a^5-292*a^4+38*a^3+2085/4*a^2-263/4*a-897/4)*q^183 + (5/4*a^8+3/4*a^7-20*a^6-25/4*a^5+413/4*a^4+29/4*a^3-361/2*a^2+65/4*a+78)*q^184 + (a^8+3/4*a^7-63/4*a^6-13/2*a^5+327/4*a^4+41/4*a^3-597/4*a^2+13/2*a+273/4)*q^185 + (3/2*a^8+a^7-43/2*a^6-19/2*a^5+97*a^4+23*a^3-287/2*a^2-13/2*a+117/2)*q^186 + (-3*a^8-5/4*a^7+177/4*a^6+8*a^5-855/4*a^4+7/4*a^3+1463/4*a^2-69/2*a-621/4)*q^187 + (5/2*a^8+3*a^7-69/2*a^6-51/2*a^5+162*a^4+49*a^3-553/2*a^2-13/2*a+225/2)*q^188 + (15/2*a^8+5/2*a^7-114*a^6-27/2*a^5+1139/2*a^4-51/2*a^3-1000*a^2+241/2*a+409)*q^189 + (a^8-18*a^6+2*a^5+103*a^4-20*a^3-196*a^2+32*a+78)*q^190 + (-1/2*a^8-3/2*a^7+5*a^6+29/2*a^5-31/2*a^4-81/2*a^3+14*a^2+71/2*a-1)*q^191 + (-3/4*a^8+1/4*a^7+13*a^6-15/4*a^5-287/4*a^4+67/4*a^3+138*a^2-85/4*a-115/2)*q^192 + (-9/2*a^8-1/2*a^7+71*a^6-3/2*a^5-727/2*a^4+85/2*a^3+648*a^2-185/2*a-283)*q^193 + (a^8-3/2*a^7-37/2*a^6+17*a^5+207/2*a^4-121/2*a^3-395/2*a^2+63*a+195/2)*q^194 + (6*a^8+2*a^7-91*a^6-10*a^5+454*a^4-28*a^3-796*a^2+110*a+325)*q^195 + (-a^8-3*a^7+9*a^6+28*a^5-22*a^4-69*a^3+14*a^2+40*a+3)*q^196 + (4*a^8+2*a^7-60*a^6-13*a^5+299*a^4-a^3-530*a^2+54*a+225)*q^197 + (-3/2*a^8+7/4*a^7+115/4*a^6-19*a^5-669/4*a^4+265/4*a^3+1301/4*a^2-72*a-585/4)*q^198 + (1/4*a^8-1/4*a^7-9/2*a^6+17/4*a^5+111/4*a^4-75/4*a^3-131/2*a^2+59/4*a+47)*q^199 + (-7/4*a^8-5/4*a^7+51/2*a^6+45/4*a^5-485/4*a^4-91/4*a^3+393/2*a^2-9/4*a-78)*q^200 +  ...

-------------------------------------------------------
Gamma_0(150)
Weight 2

-------------------------------------------------------
J_0(150), dim = 19

-------------------------------------------------------
150A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*5
Ker(ModPolar)  = Z/2^3*5 + Z/2^3*5
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/5) + E(Z/2 + Z/2) + G(Z/5) + I(Z/2 + Z/2) + J(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 1
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 0.79123781064391926641 + 0.36104746801185132456e-4i
Omega-         = 0.7021784782964698008e-4 + -1.9905302287326326875i
L(1)           = 0.79123781146766196637
w1             = 0.3956540142458744567 + -0.99524706199291575117i
w2             = -0.79123781064391926641 + -0.36104746801185132456e-4i
c4             = 3624.9538743228257645 + -0.69030358933362904088i
c6             = 296876.24561247210129 + -77.551358887646949242i
j              = -2032.2106538745839247 + 0.21599704718769908665i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + 1*q^4 + 1*q^6 + 2*q^7 + -1*q^8 + 1*q^9 + 2*q^11 + -1*q^12 + 6*q^13 + -2*q^14 + 1*q^16 + 2*q^17 + -1*q^18 + -2*q^21 + -2*q^22 + -4*q^23 + 1*q^24 + -6*q^26 + -1*q^27 + 2*q^28 + -8*q^31 + -1*q^32 + -2*q^33 + -2*q^34 + 1*q^36 + 2*q^37 + -6*q^39 + 2*q^41 + 2*q^42 + -4*q^43 + 2*q^44 + 4*q^46 + -8*q^47 + -1*q^48 + -3*q^49 + -2*q^51 + 6*q^52 + 6*q^53 + 1*q^54 + -2*q^56 + 10*q^59 + 2*q^61 + 8*q^62 + 2*q^63 + 1*q^64 + 2*q^66 + -8*q^67 + 2*q^68 + 4*q^69 + 12*q^71 + -1*q^72 + -4*q^73 + -2*q^74 + 4*q^77 + 6*q^78 + 1*q^81 + -2*q^82 + -4*q^83 + -2*q^84 + 4*q^86 + -2*q^88 + -10*q^89 + 12*q^91 + -4*q^92 + 8*q^93 + 8*q^94 + 1*q^96 + -8*q^97 + 3*q^98 + 2*q^99 + -8*q^101 + 2*q^102 + -14*q^103 + -6*q^104 + -6*q^106 + 12*q^107 + -1*q^108 + 10*q^109 + -2*q^111 + 2*q^112 + 6*q^113 + 6*q^117 + -10*q^118 + 4*q^119 + -7*q^121 + -2*q^122 + -2*q^123 + -8*q^124 + -2*q^126 + 2*q^127 + -1*q^128 + 4*q^129 + -18*q^131 + -2*q^132 + 8*q^134 + -2*q^136 + -18*q^137 + -4*q^138 + -20*q^139 + 8*q^141 + -12*q^142 + 12*q^143 + 1*q^144 + 4*q^146 + 3*q^147 + 2*q^148 + -20*q^149 + -8*q^151 + 2*q^153 + -4*q^154 + -6*q^156 + 22*q^157 + -6*q^159 + -8*q^161 + -1*q^162 + 16*q^163 + 2*q^164 + 4*q^166 + 12*q^167 + 2*q^168 + 23*q^169 + -4*q^172 + -14*q^173 + 2*q^176 + -10*q^177 + 10*q^178 + 10*q^179 + 2*q^181 + -12*q^182 + -2*q^183 + 4*q^184 + -8*q^186 + 4*q^187 + -8*q^188 + -2*q^189 + 12*q^191 + -1*q^192 + -4*q^193 + 8*q^194 + -3*q^196 + 22*q^197 + -2*q^198 +  ...

-------------------------------------------------------
150B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^4*3 + Z/2^4*3
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + H(Z/3 + Z/3) + I(Z/2 + Z/2) + J(Z/2^2 + Z/2^2)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2^2
|L(1)/Omega|   = 1
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 1.4991931300574937028 + 0.12779195266719483471e-3i
Omega-         = 0.45185755221248486716e-4 + 1.0361298985228366589i
L(1)           = 1.4991931355040178395
w1             = 0.74961915790635747566 + 0.51812884523775192687i
w2             = 0.74957397215113622717 + -0.51800105328508473203i
c4             = -1773.8434486482859811 + 1.3410466881925373907i
c6             = -229548.57489033417164 + -1.3119688964680765613i
j              = 165.50625468475603246 + -0.34113213987498618766i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + -1*q^6 + 4*q^7 + 1*q^8 + 1*q^9 + -1*q^12 + -2*q^13 + 4*q^14 + 1*q^16 + -6*q^17 + 1*q^18 + -4*q^19 + -4*q^21 + -1*q^24 + -2*q^26 + -1*q^27 + 4*q^28 + -6*q^29 + 8*q^31 + 1*q^32 + -6*q^34 + 1*q^36 + -2*q^37 + -4*q^38 + 2*q^39 + -6*q^41 + -4*q^42 + 4*q^43 + -1*q^48 + 9*q^49 + 6*q^51 + -2*q^52 + 6*q^53 + -1*q^54 + 4*q^56 + 4*q^57 + -6*q^58 + -10*q^61 + 8*q^62 + 4*q^63 + 1*q^64 + 4*q^67 + -6*q^68 + 1*q^72 + -2*q^73 + -2*q^74 + -4*q^76 + 2*q^78 + 8*q^79 + 1*q^81 + -6*q^82 + -12*q^83 + -4*q^84 + 4*q^86 + 6*q^87 + 18*q^89 + -8*q^91 + -8*q^93 + -1*q^96 + -2*q^97 + 9*q^98 + 18*q^101 + 6*q^102 + 4*q^103 + -2*q^104 + 6*q^106 + 12*q^107 + -1*q^108 + -10*q^109 + 2*q^111 + 4*q^112 + 18*q^113 + 4*q^114 + -6*q^116 + -2*q^117 + -24*q^119 + -11*q^121 + -10*q^122 + 6*q^123 + 8*q^124 + 4*q^126 + -20*q^127 + 1*q^128 + -4*q^129 + -16*q^133 + 4*q^134 + -6*q^136 + -6*q^137 + -4*q^139 + 1*q^144 + -2*q^146 + -9*q^147 + -2*q^148 + -6*q^149 + 8*q^151 + -4*q^152 + -6*q^153 + 2*q^156 + -2*q^157 + 8*q^158 + -6*q^159 + 1*q^162 + 4*q^163 + -6*q^164 + -12*q^166 + -4*q^168 + -9*q^169 + -4*q^171 + 4*q^172 + -18*q^173 + 6*q^174 + 18*q^178 + 24*q^179 + 14*q^181 + -8*q^182 + 10*q^183 + -8*q^186 + -4*q^189 + -24*q^191 + -1*q^192 + 22*q^193 + -2*q^194 + 9*q^196 + 6*q^197 + 8*q^199 +  ...

-------------------------------------------------------
150C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + E(Z/2 + Z/2) + I(Z/2 + Z/2) + J(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2*5
|L(1)/Omega|   = 1
Sha Bound      = 2^2*5^2

ANALYTIC INVARIANTS:

Omega+         = 1.7692658692520432294 + 0.16301413526951081806e-4i
Omega-         = 0.64307871618296255828e-4 + 4.4509846860687960592i
L(1)           = 1.7692658693271410673
w1             = -0.88460078069021246658 + 2.2254841923276345541i
w2             = 1.7692658692520432294 + 0.16301413526951081806e-4i
c4             = 144.99705623440772114 + -0.79639818947552493139e-2i
c6             = 2374.966783913358982 + -0.63131618017074422644e-1i
j              = -2032.2709340825264618 + 0.49358811439447376651i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^3 + 1*q^4 + 1*q^6 + -2*q^7 + 1*q^8 + 1*q^9 + 2*q^11 + 1*q^12 + -6*q^13 + -2*q^14 + 1*q^16 + -2*q^17 + 1*q^18 + -2*q^21 + 2*q^22 + 4*q^23 + 1*q^24 + -6*q^26 + 1*q^27 + -2*q^28 + -8*q^31 + 1*q^32 + 2*q^33 + -2*q^34 + 1*q^36 + -2*q^37 + -6*q^39 + 2*q^41 + -2*q^42 + 4*q^43 + 2*q^44 + 4*q^46 + 8*q^47 + 1*q^48 + -3*q^49 + -2*q^51 + -6*q^52 + -6*q^53 + 1*q^54 + -2*q^56 + 10*q^59 + 2*q^61 + -8*q^62 + -2*q^63 + 1*q^64 + 2*q^66 + 8*q^67 + -2*q^68 + 4*q^69 + 12*q^71 + 1*q^72 + 4*q^73 + -2*q^74 + -4*q^77 + -6*q^78 + 1*q^81 + 2*q^82 + 4*q^83 + -2*q^84 + 4*q^86 + 2*q^88 + -10*q^89 + 12*q^91 + 4*q^92 + -8*q^93 + 8*q^94 + 1*q^96 + 8*q^97 + -3*q^98 + 2*q^99 + -8*q^101 + -2*q^102 + 14*q^103 + -6*q^104 + -6*q^106 + -12*q^107 + 1*q^108 + 10*q^109 + -2*q^111 + -2*q^112 + -6*q^113 + -6*q^117 + 10*q^118 + 4*q^119 + -7*q^121 + 2*q^122 + 2*q^123 + -8*q^124 + -2*q^126 + -2*q^127 + 1*q^128 + 4*q^129 + -18*q^131 + 2*q^132 + 8*q^134 + -2*q^136 + 18*q^137 + 4*q^138 + -20*q^139 + 8*q^141 + 12*q^142 + -12*q^143 + 1*q^144 + 4*q^146 + -3*q^147 + -2*q^148 + -20*q^149 + -8*q^151 + -2*q^153 + -4*q^154 + -6*q^156 + -22*q^157 + -6*q^159 + -8*q^161 + 1*q^162 + -16*q^163 + 2*q^164 + 4*q^166 + -12*q^167 + -2*q^168 + 23*q^169 + 4*q^172 + 14*q^173 + 2*q^176 + 10*q^177 + -10*q^178 + 10*q^179 + 2*q^181 + 12*q^182 + 2*q^183 + 4*q^184 + -8*q^186 + -4*q^187 + 8*q^188 + -2*q^189 + 12*q^191 + 1*q^192 + 4*q^193 + 8*q^194 + -3*q^196 + -22*q^197 + 2*q^198 +  ...

-------------------------------------------------------
150D (old = 75A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2*5
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3*5 + Z/2*3*5
= A(Z/5) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/5) + J(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
150E (old = 75B), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2^4*3 + Z/2^4*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + F(Z/3 + Z/3 + Z/3 + Z/3) + I(Z/2^2 + Z/2^2) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
150F (old = 75C), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2*5
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3*5 + Z/2*3*5
= D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/3 + Z/3 + Z/3 + Z/3) + H(Z/5 + Z/5)

-------------------------------------------------------
150G (old = 50A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3*5 + Z/2*3*5
= A(Z/5) + D(Z/5) + H(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/3 + Z/3)

-------------------------------------------------------
150H (old = 50B), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3*5 + Z/2*3*5
= B(Z/3 + Z/3) + F(Z/5 + Z/5) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
150I (old = 30A), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4*3 + Z/2^4*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2^2 + Z/2^2) + G(Z/3 + Z/3) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
150J (old = 15A), dim = 1

CONGRUENCES:
Modular Degree = 2^6*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2^4*3 + Z/2^4*3
= A(Z/2 + Z/2) + B(Z/2^2 + Z/2^2) + C(Z/2 + Z/2) + D(Z/3 + Z/3 + Z/3 + Z/3) + E(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(151)
Weight 2

-------------------------------------------------------
J_0(151), dim = 12

-------------------------------------------------------
151A (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 7^2
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 69.107950648708997706 + 0.26008934450236585231e-2i
Omega-         = 0.19631152339782081795e-4 + 6.8881054229919388027i
L(1)           =

HECKE EIGENFORM:
a^3+2*a^2-a-1 = 0,
f(q) = q + a*q^2 + (-a-1)*q^3 + (a^2-2)*q^4 + (-a^2-a-1)*q^5 + (-a^2-a)*q^6 + -1*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 + (4*a^2-5)*q^38 + (-2*a^2-5*a)*q^39 + (4*a^2+5*a)*q^40 + (2*a^2+6*a-7)*q^41 + (a^2+a)*q^42 + (5*a^2+7*a)*q^43 + (-5*a^2-6*a+6)*q^44 + (-2*a+1)*q^45 + (a+3)*q^46 + (-4*a^2-12*a+1)*q^47 + -1*q^48 + -6*q^49 + (-5*a^2+4)*q^50 + (2*a^2+8*a+3)*q^51 + (-4*a^2-8*a+5)*q^52 + (3*a^2+a-8)*q^53 + (4*a^2+3*a-1)*q^54 + (-a^2-5*a+1)*q^55 + (2*a^2+3*a-1)*q^56 + (a^2+6*a)*q^57 + (-5*a^2-4*a-1)*q^58 + (7*a^2+8*a-9)*q^59 + (-4*a^2-3*a-1)*q^60 + (5*a+3)*q^61 + (a^2-a-4)*q^62 + (-a^2-2*a+2)*q^63 + (-a^2+4*a+1)*q^64 + (-4*a^2-7*a+1)*q^65 + (a^2-a-2)*q^66 + (-8*a^2-7*a+11)*q^67 + (a^2+8*a+1)*q^68 + (-3*a^2-7*a-1)*q^69 + (-a^2+2*a+1)*q^70 + (5*a^2+13*a-6)*q^71 + (3*a^2+3*a-5)*q^72 + (4*a^2+2*a-7)*q^73 + (a^2+4*a-3)*q^74 + (a^2-3*a)*q^75 + (2*a^2+11*a-6)*q^76 + (-2*a^2-4*a+3)*q^77 + (-a^2-2*a-2)*q^78 + (5*a^2+3*a-9)*q^79 + (a^2-2)*q^80 + (-6*a^2-11*a+3)*q^81 + (2*a^2-5*a+2)*q^82 + (-4*a^2-6*a+3)*q^83 + (-a^2-a-1)*q^84 + (7*a^2+10*a+2)*q^85 + (-3*a^2+5*a+5)*q^86 + (6*a^2+11*a+4)*q^87 + (4*a^2+3*a-9)*q^88 + -12*q^89 + (-2*a^2+a)*q^90 + (-3*a^2-5*a+3)*q^91 + (-5*a^2-9*a+4)*q^92 + (3*a^2+8*a+1)*q^93 + (-4*a^2-3*a-4)*q^94 + (9*a^2+7*a-4)*q^95 + (-2*a^2-9*a-2)*q^96 + (6*a^2+9*a-6)*q^97 + -6*a*q^98 + (-5*a^2-8*a+10)*q^99 + (2*a^2-7*a+3)*q^100 + (a^2-4*a-15)*q^101 + (4*a^2+5*a+2)*q^102 + (-9*a^2-6*a+17)*q^103 + (2*a^2+a-10)*q^104 + (-3*a-2)*q^105 + (-5*a^2-5*a+3)*q^106 + (-3*a+4)*q^107 + (-3*a^2-a-4)*q^108 + (a^2+11*a+5)*q^109 + (-3*a^2-1)*q^110 + (2*a^2+a-4)*q^111 + (a^2+a-2)*q^112 + (-9*a^2-8*a+9)*q^113 + (4*a^2+a+1)*q^114 + (-4*a^2-10*a-1)*q^115 + (8*a^2+8*a+1)*q^116 + (-6*a^2-8*a+11)*q^117 + (-6*a^2-2*a+7)*q^118 + (3*a^2+5*a)*q^119 + (-a^2-9*a-4)*q^120 + (-8*a^2-12*a+6)*q^121 + (5*a^2+3*a)*q^122 + (-4*a^2-a+5)*q^123 + (5*a^2+11*a-5)*q^124 + (-4*a^2+3*a+10)*q^125 + (a-1)*q^126 + (9*a^2+20*a)*q^127 + (-4*a^2-14*a+5)*q^128 + (-2*a^2-12*a-5)*q^129 + (a^2-3*a-4)*q^130 + (-a^2-4*a+4)*q^131 + (a^2+5*a-1)*q^132 + (5*a^2+6*a-5)*q^133 + (9*a^2+3*a-8)*q^134 + (2*a^2-8*a-7)*q^135 + (4*a^2+8*a+7)*q^136 + (-3*a^2-2)*q^137 + (-a^2-4*a-3)*q^138 + (2*a+4)*q^139 + (2*a^2-2*a-3)*q^140 + (8*a^2+15*a+3)*q^141 + (3*a^2-a+5)*q^142 + (-9*a^2-11*a+19)*q^143 + (3*a^2+4*a-5)*q^144 + (17*a+9)*q^145 + (-6*a^2-3*a+4)*q^146 + (6*a+6)*q^147 + (8*a^2+8*a-13)*q^148 + (a^2-3*a)*q^149 + (-5*a^2+a+1)*q^150 + -1*q^151 + (-a^2-4*a+12)*q^152 + (3*a^2+2*a-5)*q^153 + (a-2)*q^154 + (6*a^2+11*a)*q^155 + (4*a^2+7*a-1)*q^156 + (3*a^2+12*a-1)*q^157 + (-7*a^2-4*a+5)*q^158 + (2*a^2+4*a+5)*q^159 + (-10*a^2-11*a+1)*q^160 + (-3*a^2-6*a+2)*q^161 + (a^2-3*a-6)*q^162 + (4*a^2+12*a+11)*q^163 + (-13*a^2-8*a+16)*q^164 + (4*a^2+5*a)*q^165 + (2*a^2-a-4)*q^166 + (-6*a^2-14*a-1)*q^167 + (-a^2-4*a-1)*q^168 + (-8*a^2-9*a+8)*q^169 + (-4*a^2+9*a+7)*q^170 + (10*a^2+11*a-16)*q^171 + (a^2-12*a-3)*q^172 + (6*a^2+10*a-5)*q^173 + (-a^2+10*a+6)*q^174 + (-4*a^2-3*a+4)*q^175 + (5*a^2+7*a-8)*q^176 + (-a^2-6*a+2)*q^177 + -12*a*q^178 + (-4*a^2-5*a-7)*q^179 + (5*a^2+2*a-4)*q^180 + (-10*a^2-19*a+8)*q^181 + (a^2-3)*q^182 + (-5*a^2-8*a-3)*q^183 + (a^2-3*a-11)*q^184 + (3*a-5)*q^185 + (2*a^2+4*a+3)*q^186 + (3*a^2-a-10)*q^187 + (13*a^2+16*a-6)*q^188 + (a^2-2*a-4)*q^189 + (-11*a^2+5*a+9)*q^190 + (5*a+13)*q^191 + (-5*a^2-4*a)*q^192 + (8*a^2-a-26)*q^193 + (-3*a^2+6)*q^194 + (3*a^2+10*a+3)*q^195 + (-6*a^2+12)*q^196 + (3*a^2+6*a+17)*q^197 + (2*a^2+5*a-5)*q^198 + (-4*a^2-21*a-5)*q^199 + (-a^2+5*a-6)*q^200 +  ...

-------------------------------------------------------
151B (new) , dim = 3

CONGRUENCES:
Modular Degree = 67
Ker(ModPolar)  = Z/67 + Z/67
= C(Z/67 + Z/67)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 257
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 3.2619560408448811355 + -0.72108968257355294842e-4i
Omega-         = 0.11196906149113655472e-3 + -17.975475324005819913i
L(1)           = 3.2619560416419034186

HECKE EIGENFORM:
a^3-5*a+3 = 0,
f(q) = 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 + 1*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 + (3*a^2+6*a-9)*q^38 + (-4*a^2+12)*q^39 + (a^2+6*a-12)*q^40 + -4*a*q^42 + (-a^2+3)*q^43 + (-a^2-3*a+11)*q^44 + (-a^2-2*a+5)*q^45 + 2*a^2*q^46 + (-a^2-a-1)*q^47 + (-2*a^2-6*a+8)*q^48 + -3*q^49 + (-3*a^2+3*a+3)*q^50 + (-2*a+6)*q^51 + (6*a-12)*q^52 + (-6*a^2-6*a+18)*q^53 + -4*a*q^54 + (5*a^2-20)*q^55 + (-2*a+6)*q^56 + (6*a^2+6*a-18)*q^57 + (5*a^2+6*a-9)*q^58 + (-a^2+11)*q^59 + (4*a^2-6*a-8)*q^60 + (4*a^2-16)*q^61 + (-2*a+3)*q^62 + -2*q^63 + (-a^2+1)*q^64 + (-6*a^2+2*a+18)*q^65 + (2*a^2+6*a-12)*q^66 + (-4*a^2+14)*q^67 + (3*a^2-3*a-3)*q^68 + 4*a*q^69 + (4*a^2-6)*q^70 + -2*a*q^71 + (a-3)*q^72 + (-2*a^2+10)*q^73 + (-3*a^2+a)*q^74 + (-2*a^2-6*a+16)*q^75 + 9*q^76 + (-4*a^2-2*a+14)*q^77 + (-8*a+12)*q^78 + (-2*a^2-2)*q^79 + (2*a^2-a+5)*q^80 + -11*q^81 + (-2*a^2+2*a+16)*q^83 + (-4*a^2+8)*q^84 + (-a^2-6*a+12)*q^85 + (-2*a+3)*q^86 + (6*a^2+10*a-18)*q^87 + (-5*a^2+15)*q^88 + (2*a+12)*q^89 + (-2*a^2+3)*q^90 + (4*a^2-12)*q^91 + (6*a-6)*q^92 + (-2*a^2+6)*q^93 + (-a^2-6*a+3)*q^94 + (3*a^2-3*a-18)*q^95 + (-6*a^2-6*a+18)*q^96 + (7*a^2+9*a-25)*q^97 + -3*a*q^98 + (2*a^2+a-7)*q^99 + (5*a^2-6*a-7)*q^100 + (6*a^2+4*a-18)*q^101 + (-2*a^2+6*a)*q^102 + (-6*a^2-3*a+13)*q^103 + (6*a^2-4*a-12)*q^104 + (4*a^2+8*a-20)*q^105 + (-6*a^2-12*a+18)*q^106 + (-4*a^2-6*a+14)*q^107 + (-4*a^2+8)*q^108 + 2*q^109 + (5*a-15)*q^110 + (-6*a+2)*q^111 + (2*a^2+6*a-8)*q^112 + (6*a^2+10*a-18)*q^113 + (6*a^2+12*a-18)*q^114 + (-4*a^2+6)*q^115 + (6*a+3)*q^116 + (-2*a^2+6)*q^117 + (6*a+3)*q^118 + (2*a-6)*q^119 + (2*a^2+12*a-24)*q^120 + (-7*a^2-6*a+26)*q^121 + (4*a-12)*q^122 + (3*a-6)*q^124 + (3*a^2+a)*q^125 + -2*a*q^126 + (3*a^2-13)*q^127 + (6*a^2+2*a-15)*q^128 + (-2*a^2+6)*q^129 + (2*a^2-12*a+18)*q^130 + (-4*a^2-6*a+2)*q^131 + (-2*a^2-6*a+22)*q^132 + (-6*a^2-6*a+18)*q^133 + (-6*a+12)*q^134 + (4*a^2+8*a-20)*q^135 + (-a^2+6*a-9)*q^136 + (a^2-2*a+7)*q^137 + 4*a^2*q^138 + (5*a^2-3*a-23)*q^139 + (-4*a^2+6*a+8)*q^140 + (-2*a^2-2*a-2)*q^141 + -2*a^2*q^142 + (6*a^2+8*a-36)*q^143 + (-a^2-3*a+4)*q^144 + (-a^2-3*a-12)*q^145 + 6*q^146 + -6*q^147 + (a^2-9*a+7)*q^148 + (-2*a^2-4*a+16)*q^149 + (-6*a^2+6*a+6)*q^150 + 1*q^151 + (-6*a^2-3*a+18)*q^152 + (-a+3)*q^153 + (-2*a^2-6*a+12)*q^154 + (-3*a^2+a+9)*q^155 + (12*a-24)*q^156 + (-2*a^2-6*a+14)*q^157 + (-12*a+6)*q^158 + (-12*a^2-12*a+36)*q^159 + (-3*a^2+3*a+18)*q^160 + -4*a*q^161 + -11*a*q^162 + (4*a^2-6*a-16)*q^163 + (10*a^2-40)*q^165 + (2*a^2+6*a+6)*q^166 + (-4*a^2-8*a+8)*q^167 + (-4*a+12)*q^168 + (-4*a^2-12*a+23)*q^169 + (-6*a^2+7*a+3)*q^170 + (3*a^2+3*a-9)*q^171 + (3*a-6)*q^172 + (7*a^2+13*a-29)*q^173 + (10*a^2+12*a-18)*q^174 + (2*a^2+6*a-16)*q^175 + (2*a^2-4*a-7)*q^176 + (-2*a^2+22)*q^177 + (2*a^2+12*a)*q^178 + (4*a^2+6*a-8)*q^179 + (2*a^2-3*a-4)*q^180 + (-6*a-2)*q^181 + (8*a-12)*q^182 + (8*a^2-32)*q^183 + (2*a^2-6*a)*q^184 + (5*a^2-2*a-4)*q^185 + (-4*a+6)*q^186 + (5*a^2-15)*q^187 + (-4*a^2+5)*q^188 + 8*q^189 + (-3*a^2-3*a-9)*q^190 + (a^2+5*a+1)*q^191 + (-2*a^2+2)*q^192 + (-a^2-6*a-3)*q^193 + (9*a^2+10*a-21)*q^194 + (-12*a^2+4*a+36)*q^195 + (-3*a^2+6)*q^196 + (4*a^2+4*a-14)*q^197 + (a^2+3*a-6)*q^198 + (4*a^2+12*a-16)*q^199 + (12*a-21)*q^200 +  ...

-------------------------------------------------------
151C (new) , dim = 6

CONGRUENCES:
Modular Degree = 2^3*67
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*67 + Z/2*67
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + B(Z/67 + Z/67)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 11*439867
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 5^2
Torsion Bound  = 5^2
|L(1)/Omega|   = 2^3/5^2
Sha Bound      = 2^3*5^2

ANALYTIC INVARIANTS:

Omega+         = 2.8253524509273114195 + 0.65838734027003786238e-3i
Omega-         = 108.65181540849115869 + 0.35862785862753102735e-2i
L(1)           = 0.90411280884441030261

HECKE EIGENFORM:
a^6-a^5-7*a^4+3*a^3+13*a^2+3*a-1 = 0,
f(q) = 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 + (a^5+2*a^4-4*a^3-11*a^2-5*a+2)*q^38 + (5*a^5-8*a^4-31*a^3+31*a^2+51*a-6)*q^39 + (a^5-a^4-4*a^3+4*a^2+a-3)*q^40 + (a^4-5*a^2-a+9)*q^41 + (2*a^5-2*a^4-7*a^3+3*a^2+4*a-3)*q^42 + (-3*a^5+6*a^4+14*a^3-22*a^2-16*a+5)*q^43 + (a^5-7*a^3+10*a)*q^44 + (5*a^5-5*a^4-35*a^3+14*a^2+65*a+17)*q^45 + (-a^5-a^4+3*a^3+6*a^2+4*a-1)*q^46 + (-3*a^5+5*a^4+16*a^3-18*a^2-18*a+6)*q^47 + (-4*a^5+5*a^4+24*a^3-15*a^2-39*a-5)*q^48 + (a^4-4*a^3-a^2+13*a+4)*q^49 + (a^5+a^4-5*a^3-5*a^2-a+2)*q^50 + (2*a^5-3*a^4-8*a^3+9*a^2+7*a-7)*q^51 + (-2*a^5+5*a^4+12*a^3-21*a^2-21*a+7)*q^52 + (-2*a^4+3*a^3+11*a^2-10*a-9)*q^53 + (a^5-a^4-7*a^3+8*a^2+10*a-5)*q^54 + (a^5-2*a^4-4*a^3+8*a^2+2*a-4)*q^55 + (-a^5-a^4+7*a^3+4*a^2-10*a-1)*q^56 + (a^5-4*a^4-6*a^3+20*a^2+11*a-15)*q^57 + (-2*a^5+4*a^4+10*a^3-15*a^2-12*a+3)*q^58 + (a^4+a^3-4*a^2-4*a)*q^59 + (a^5-a^4-11*a^3+28*a+19)*q^60 + (3*a^5-7*a^4-15*a^3+28*a^2+20*a-7)*q^61 + (a^5-4*a^4-3*a^3+14*a^2+3*a-2)*q^62 + (a^5+2*a^4-6*a^3-20*a^2+13*a+27)*q^63 + (a^5-3*a^4-3*a^3+11*a^2-3*a-7)*q^64 + (-a^5+a^4+9*a^3-4*a^2-20*a-1)*q^65 + (-3*a^3+3*a^2+8*a-1)*q^66 + (a^5-a^4-a^3+4*a^2-14*a-11)*q^67 + (-3*a^5+a^4+15*a^3+a^2-13*a-1)*q^68 + (-2*a^5+5*a^4+13*a^3-20*a^2-25*a+6)*q^69 + (-a^5-a^4+4*a^3+3*a^2+2*a+2)*q^70 + (-3*a^3-a^2+10*a+7)*q^71 + (-5*a^5+8*a^4+29*a^3-30*a^2-43*a+3)*q^72 + (-4*a^5+3*a^4+22*a^3-5*a^2-29*a-9)*q^73 + (a^3+3*a^2-5*a)*q^74 + (-2*a^5+13*a^3+9*a^2-24*a-25)*q^75 + (-a^5+5*a^4+10*a^3-22*a^2-31*a-1)*q^76 + (-a^4+4*a^3+a^2-13*a-1)*q^77 + (-3*a^5+4*a^4+16*a^3-14*a^2-21*a+5)*q^78 + (-2*a^5+5*a^4+17*a^3-22*a^2-41*a-2)*q^79 + (2*a^5-a^4-15*a^3+2*a^2+28*a+9)*q^80 + (-a^5+2*a^4+3*a^3-13*a^2+3*a+29)*q^81 + (a^5-5*a^3-a^2+9*a)*q^82 + (-2*a^5+5*a^4+8*a^3-21*a^2-7*a+9)*q^83 + (6*a^5-3*a^4-41*a^3+10*a^2+63*a+12)*q^84 + (-a^4-a^3+2*a^2+6*a+5)*q^85 + (3*a^5-7*a^4-13*a^3+23*a^2+14*a-3)*q^86 + (5*a^5-8*a^4-31*a^3+35*a^2+47*a-16)*q^87 + (a^5-2*a^4-3*a^3+7*a^2-3*a+1)*q^88 + (-2*a^5+6*a^4+8*a^3-24*a^2-8*a+14)*q^89 + (-a^3+2*a+5)*q^90 + (4*a^5-7*a^4-21*a^3+26*a^2+25*a-10)*q^91 + (-4*a^4-3*a^3+17*a^2+16*a-3)*q^92 + (3*a^5-3*a^4-18*a^3+5*a^2+32*a+12)*q^93 + (2*a^5-5*a^4-9*a^3+21*a^2+15*a-3)*q^94 + (a^5+a^4-7*a^3-7*a^2+12*a+12)*q^95 + (3*a^5-6*a^4-15*a^3+23*a^2+23*a-12)*q^96 + (-2*a^5+2*a^4+13*a^3-8*a^2-20*a+3)*q^97 + (a^5-4*a^4-a^3+13*a^2+4*a)*q^98 + (-7*a^5+11*a^4+39*a^3-39*a^2-55*a+4)*q^99 + (-2*a^5+4*a^4+18*a^3-16*a^2-43*a-9)*q^100 + (-5*a^5+5*a^4+30*a^3-17*a^2-40*a)*q^101 + (-a^5+6*a^4+3*a^3-19*a^2-13*a+2)*q^102 + (-a^5+2*a^4+a^3-4*a^2+6*a+1)*q^103 + (5*a^5-8*a^4-27*a^3+31*a^2+33*a-6)*q^104 + (-3*a^5+2*a^4+27*a^3-a^2-59*a-34)*q^105 + (-2*a^5+3*a^4+11*a^3-10*a^2-9*a)*q^106 + (a^5-2*a^4-7*a^3+7*a^2+19*a-4)*q^107 + (10*a^5-12*a^4-63*a^3+41*a^2+106*a+11)*q^108 + (-a^4-5*a^3+2*a^2+25*a+8)*q^109 + (-a^5+3*a^4+5*a^3-11*a^2-7*a+1)*q^110 + (5*a^5-6*a^4-37*a^3+25*a^2+65*a+2)*q^111 + (4*a^4-5*a^3-17*a^2+8*a+13)*q^112 + (-a^5+a^4+10*a^3-3*a^2-28*a-8)*q^113 + (-3*a^5+a^4+17*a^3-2*a^2-18*a+1)*q^114 + (-3*a^4-2*a^3+13*a^2+9*a-3)*q^115 + (-4*a^5+6*a^4+25*a^3-24*a^2-39*a+4)*q^116 + (6*a^5-9*a^4-42*a^3+43*a^2+75*a-25)*q^117 + (a^5+a^4-4*a^3-4*a^2)*q^118 + (2*a^5-6*a^4-9*a^3+21*a^2+24*a+1)*q^119 + (2*a^5-4*a^4-15*a^3+15*a^2+30*a+3)*q^120 + (a^5-3*a^4-3*a^3+12*a^2-3*a-10)*q^121 + (-4*a^5+6*a^4+19*a^3-19*a^2-16*a+3)*q^122 + (-9*a^5+9*a^4+61*a^3-34*a^2-102*a-9)*q^123 + (a^5-2*a^4-9*a^3+8*a^2+19*a+7)*q^124 + (-2*a^5+5*a^4+7*a^3-21*a^2-a+15)*q^125 + (3*a^5+a^4-23*a^3+24*a+1)*q^126 + (2*a^5+2*a^4-15*a^3-9*a^2+23*a-3)*q^127 + (-4*a^5+4*a^4+24*a^3-16*a^2-34*a+1)*q^128 + (-4*a^5+5*a^4+30*a^3-25*a^2-49*a+5)*q^129 + (2*a^4-a^3-7*a^2+2*a-1)*q^130 + (a^5+4*a^4-4*a^3-22*a^2-5*a+11)*q^131 + (2*a^5-5*a^4-11*a^3+20*a^2+19*a-10)*q^132 + (5*a^5-3*a^4-32*a^3+5*a^2+42*a+6)*q^133 + (6*a^4+a^3-27*a^2-14*a+1)*q^134 + (-4*a^5+3*a^4+32*a^3+a^2-69*a-47)*q^135 + (-2*a^4-2*a^3+10*a^2+8*a-3)*q^136 + (2*a^5-2*a^4-13*a^3+7*a^2+17*a+1)*q^137 + (3*a^5-a^4-14*a^3+a^2+12*a-2)*q^138 + (a^5-4*a^4-6*a^3+15*a^2+13*a+9)*q^139 + (-6*a^5+3*a^4+36*a^3-5*a^2-53*a-17)*q^140 + (-7*a^5+9*a^4+45*a^3-38*a^2-72*a+7)*q^141 + (-3*a^4-a^3+10*a^2+7*a)*q^142 + (6*a^5-11*a^4-33*a^3+44*a^2+43*a-8)*q^143 + (a^5-2*a^4-5*a^3-2*a^2+16*a+27)*q^144 + (a^3-2*a^2-4*a+8)*q^145 + (-a^5-6*a^4+7*a^3+23*a^2+3*a-4)*q^146 + (-4*a^4+8*a^3+12*a^2-18*a-18)*q^147 + (a^4+3*a^3-7*a^2-6*a+10)*q^148 + (2*a^5-6*a^4-9*a^3+31*a^2+4*a-23)*q^149 + (-2*a^5-a^4+15*a^3+2*a^2-19*a-2)*q^150 + 1*q^151 + (2*a^5-a^4-11*a^3+4*a^2+12*a-5)*q^152 + (5*a^5-2*a^4-37*a^3+10*a^2+54*a+3)*q^153 + (-a^5+4*a^4+a^3-13*a^2-a)*q^154 + (-4*a^5+4*a^4+25*a^3-12*a^2-38*a-13)*q^155 + (-9*a^5+11*a^4+57*a^3-44*a^2-88*a+9)*q^156 + (-7*a^5+13*a^4+46*a^3-53*a^2-78*a)*q^157 + (3*a^5+3*a^4-16*a^3-15*a^2+4*a-2)*q^158 + (6*a^5-7*a^4-40*a^3+19*a^2+71*a+21)*q^159 + (-a^5+a^4+4*a^3-6*a^2+a+8)*q^160 + (-a^5+4*a^4+8*a^3-14*a^2-19*a+3)*q^161 + (a^5-4*a^4-10*a^3+16*a^2+32*a-1)*q^162 + (-6*a^5+5*a^4+34*a^3-13*a^2-43*a-5)*q^163 + (a^5-4*a^3+6*a^2-a-17)*q^164 + (3*a^5-4*a^4-21*a^3+15*a^2+37*a+4)*q^165 + (3*a^5-6*a^4-15*a^3+19*a^2+15*a-2)*q^166 + (4*a^5-5*a^4-22*a^3+11*a^2+27*a+15)*q^167 + (-a^5+5*a^4+6*a^3-21*a^2-14*a+12)*q^168 + (-5*a^5+5*a^4+37*a^3-22*a^2-70*a+2)*q^169 + (-a^5-a^4+2*a^3+6*a^2+5*a)*q^170 + (10*a^5-16*a^4-67*a^3+62*a^2+124*a+5)*q^171 + (2*a^5-4*a^4-14*a^3+19*a^2+20*a-7)*q^172 + (-a^5+3*a^4-8*a^2+16*a-2)*q^173 + (-3*a^5+4*a^4+20*a^3-18*a^2-31*a+5)*q^174 + (5*a^5-2*a^4-39*a^3+3*a^2+67*a+20)*q^175 + (-3*a^5+4*a^4+18*a^3-16*a^2-22*a+1)*q^176 + (-a^5+4*a^3-a+3)*q^177 + (4*a^5-6*a^4-18*a^3+18*a^2+20*a-2)*q^178 + (5*a^5-5*a^4-31*a^3+20*a^2+46*a-11)*q^179 + (-10*a^5+9*a^4+70*a^3-26*a^2-125*a-34)*q^180 + (-3*a^5+6*a^4+19*a^3-27*a^2-35*a+10)*q^181 + (-3*a^5+7*a^4+14*a^3-27*a^2-22*a+4)*q^182 + (7*a^5-9*a^4-46*a^3+37*a^2+72*a-6)*q^183 + (-2*a^5-a^4+11*a^3+4*a^2-11*a+2)*q^184 + (-4*a^5+8*a^4+26*a^3-28*a^2-47*a-7)*q^185 + (3*a^4-4*a^3-7*a^2+3*a+3)*q^186 + (a^5-8*a^3+2*a^2+8*a-3)*q^187 + (3*a^5-5*a^4-17*a^3+25*a^2+27*a-10)*q^188 + (-17*a^5+18*a^4+104*a^3-52*a^2-165*a-27)*q^189 + (2*a^5-10*a^3-a^2+9*a+1)*q^190 + (4*a^5-3*a^4-33*a^3+17*a^2+67*a)*q^191 + (5*a^5-4*a^4-34*a^3+14*a^2+57*a+13)*q^192 + (2*a^5-8*a^4-12*a^3+38*a^2+25*a-12)*q^193 + (-a^4-2*a^3+6*a^2+9*a-2)*q^194 + (-3*a^5+5*a^4+16*a^3-23*a^2-20*a+20)*q^195 + (-3*a^5+4*a^4+18*a^3-7*a^2-29*a-7)*q^196 + (-a^5+3*a^4+10*a^3-9*a^2-36*a-8)*q^197 + (4*a^5-10*a^4-18*a^3+36*a^2+25*a-7)*q^198 + (5*a^5-5*a^4-31*a^3+16*a^2+42*a+7)*q^199 + (2*a^4-7*a^2-a-6)*q^200 +  ...

-------------------------------------------------------
Gamma_0(152)
Weight 2

-------------------------------------------------------
J_0(152), dim = 17

-------------------------------------------------------
152A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= C(Z/2 + Z/2) + D(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 3.645579681453683474 + 0.31513567541903909989e-4i
Omega-         = 0.71347062093998439869e-5 + 1.8637001359161365252i
L(1)           =
w1             = 1.8227862733737370371 + -0.93183431117429731064i
w2             = -0.71347062093998439869e-5 + -1.8637001359161365252i
c4             = 63.997736183242169579 + 0.58795145722060559514e-2i
c6             = -2944.2259850081090075 + 0.37163869919684662657e-1i
j              = -53.880307477605158758 + -0.16715730154906415223e-1i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -1*q^5 + -3*q^7 + 1*q^9 + -3*q^11 + -4*q^13 + 2*q^15 + 5*q^17 + -1*q^19 + 6*q^21 + -4*q^25 + 4*q^27 + 2*q^29 + 8*q^31 + 6*q^33 + 3*q^35 + -10*q^37 + 8*q^39 + 6*q^41 + -7*q^43 + -1*q^45 + -9*q^47 + 2*q^49 + -10*q^51 + -8*q^53 + 3*q^55 + 2*q^57 + 14*q^59 + -5*q^61 + -3*q^63 + 4*q^65 + -6*q^71 + -15*q^73 + 8*q^75 + 9*q^77 + -4*q^79 + -11*q^81 + 4*q^83 + -5*q^85 + -4*q^87 + 12*q^91 + -16*q^93 + 1*q^95 + 16*q^97 + -3*q^99 + -18*q^101 + -14*q^103 + -6*q^105 + 10*q^107 + 12*q^109 + 20*q^111 + 2*q^113 + -4*q^117 + -15*q^119 + -2*q^121 + -12*q^123 + 9*q^125 + -6*q^127 + 14*q^129 + -9*q^131 + 3*q^133 + -4*q^135 + 21*q^137 + 5*q^139 + 18*q^141 + 12*q^143 + -2*q^145 + -4*q^147 + 17*q^149 + 2*q^151 + 5*q^153 + -8*q^155 + 14*q^157 + 16*q^159 + 4*q^163 + -6*q^165 + -2*q^167 + 3*q^169 + -1*q^171 + -2*q^173 + 12*q^175 + -28*q^177 + -18*q^179 + 2*q^181 + 10*q^183 + 10*q^185 + -15*q^187 + -12*q^189 + -15*q^191 + -24*q^193 + -8*q^195 + 18*q^197 + -15*q^199 +  ...

-------------------------------------------------------
152B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= C(Z/2 + Z/2) + E(Z/2^2 + Z/2^2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.3670830429344771571 + -0.22210356173043057924e-4i
Omega-         = 0.14488940870520809811e-3 + 3.3696486176612095325i
L(1)           = 1.3670830431148977701
w1             = -0.6834690767628859745 + 1.6848354140086912878i
w2             = 1.3670830429344771571 + -0.22210356173043057924e-4i
c4             = 399.96414204669751009 + 0.16449404143216892738e-1i
c6             = 11455.754705306450321 + 1.531183874990221084i
j              = -1644.0110312988531633 + 0.46177534747675786255i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 3*q^7 + -2*q^9 + 2*q^11 + 1*q^13 + -5*q^17 + 1*q^19 + 3*q^21 + -1*q^23 + -5*q^25 + -5*q^27 + -3*q^29 + 4*q^31 + 2*q^33 + 2*q^37 + 1*q^39 + -8*q^41 + -8*q^43 + -8*q^47 + 2*q^49 + -5*q^51 + 9*q^53 + 1*q^57 + 1*q^59 + 14*q^61 + -6*q^63 + 13*q^67 + -1*q^69 + 10*q^71 + 9*q^73 + -5*q^75 + 6*q^77 + -10*q^79 + 1*q^81 + 10*q^83 + -3*q^87 + -12*q^89 + 3*q^91 + 4*q^93 + 14*q^97 + -4*q^99 + -14*q^101 + 6*q^103 + 15*q^107 + 7*q^109 + 2*q^111 + -18*q^113 + -2*q^117 + -15*q^119 + -7*q^121 + -8*q^123 + -6*q^127 + -8*q^129 + 3*q^133 + 7*q^137 + -12*q^139 + -8*q^141 + 2*q^143 + 2*q^147 + -8*q^149 + 22*q^151 + 10*q^153 + -22*q^157 + 9*q^159 + -3*q^161 + -4*q^163 + 4*q^167 + -12*q^169 + -2*q^171 + 22*q^173 + -15*q^175 + 1*q^177 + -14*q^181 + 14*q^183 + -10*q^187 + -15*q^189 + 23*q^191 + 6*q^193 + -8*q^197 + -9*q^199 +  ...

-------------------------------------------------------
152C (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2^3 + Z/2^3 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2^2 + Z/2^2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 31^2
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 3.7320492165012234226 + 0.77081473116262064298e-5i
Omega-         = 0.24016339450290343148e-4 + 1.5271389808404737011i
L(1)           = 0.93301230412729589957

HECKE EIGENFORM:
a^3-a^2-10*a+8 = 0,
f(q) = q + a*q^3 + (-1/2*a^2-1/2*a+4)*q^5 + (1/2*a^2-1/2*a-2)*q^7 + (a^2-3)*q^9 + (-1/2*a^2-1/2*a+2)*q^11 + (-a+2)*q^13 + (-a^2-a+4)*q^15 + (-1/2*a^2+1/2*a+4)*q^17 + -1*q^19 + (3*a-4)*q^21 + (a^2-2*a-8)*q^23 + (-1/2*a^2+3/2*a+5)*q^25 + (a^2+4*a-8)*q^27 + (a^2-10)*q^29 + (-a^2-3*a+4)*q^33 + (1/2*a^2-3/2*a-6)*q^35 + -2*q^37 + (-a^2+2*a)*q^39 + (2*a+2)*q^41 + (-1/2*a^2-5/2*a+10)*q^43 + (-1/2*a^2-9/2*a-4)*q^45 + (-3/2*a^2+1/2*a+10)*q^47 + (1/2*a^2-5/2*a-1)*q^49 + (-a+4)*q^51 + (2*a^2+a-14)*q^53 + (1/2*a^2+5/2*a+2)*q^55 + -a*q^57 + (a-8)*q^59 + (-1/2*a^2+3/2*a+4)*q^61 + (3/2*a^2-5/2*a+6)*q^63 + 4*q^65 + (-a^2+12)*q^67 + (-a^2+2*a-8)*q^69 + (a^2+3*a-12)*q^71 + (-1/2*a^2+5/2*a+4)*q^73 + (a^2+4)*q^75 + (-1/2*a^2-1/2*a-2)*q^77 + (2*a+8)*q^79 + (2*a^2+2*a+1)*q^81 + (-2*a^2+12)*q^83 + (-3/2*a^2+1/2*a+14)*q^85 + (a^2-8)*q^87 + (-a^2-3*a+14)*q^89 + (a^2-4*a)*q^91 + (1/2*a^2+1/2*a-4)*q^95 + (a^2+a-10)*q^97 + (-5/2*a^2-9/2*a+2)*q^99 + (4*a+6)*q^101 + (-3*a^2-a+20)*q^103 + (-a^2-a-4)*q^105 + -a*q^107 + (2*a^2-a-14)*q^109 + -2*a*q^111 + (-4*a+2)*q^113 + (4*a^2-32)*q^115 + (a^2-7*a+2)*q^117 + (1/2*a^2+3/2*a-10)*q^119 + (3/2*a^2+7/2*a-13)*q^121 + (2*a^2+2*a)*q^123 + (-1/2*a^2+3/2*a+2)*q^125 + (a^2+3*a-4)*q^127 + (-3*a^2+5*a+4)*q^129 + (1/2*a^2+5/2*a-10)*q^131 + (-1/2*a^2+1/2*a+2)*q^133 + (-2*a^2-6*a-8)*q^135 + (-1/2*a^2+9/2*a+12)*q^137 + (-5/2*a^2-1/2*a+18)*q^139 + (-a^2-5*a+12)*q^141 + 2*a*q^143 + (3*a^2-a-32)*q^145 + (-2*a^2+4*a-4)*q^147 + (-3/2*a^2-3/2*a)*q^149 + (-3*a^2-a+20)*q^151 + (1/2*a^2+5/2*a-12)*q^153 + 14*q^157 + (3*a^2+6*a-16)*q^159 + (-a^2-6*a+24)*q^161 + (4*a-4)*q^163 + (3*a^2+7*a-4)*q^165 + (a^2+a-20)*q^167 + (a^2-4*a-9)*q^169 + (-a^2+3)*q^171 + (-4*a+6)*q^173 + (a^2+4*a-16)*q^175 + (a^2-8*a)*q^177 + (3*a^2-5*a-24)*q^179 + (-2*a^2-2*a+6)*q^181 + (a^2-a+4)*q^183 + (a^2+a-8)*q^185 + (-1/2*a^2-1/2*a+6)*q^187 + (-a^2+12*a)*q^189 + (-3/2*a^2-13/2*a+14)*q^191 + (-3*a^2+a+22)*q^193 + 4*a*q^195 + (-2*a-2)*q^197 + (5/2*a^2-5/2*a-26)*q^199 +  ...

-------------------------------------------------------
152D (old = 76A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + F(Z/3 + Z/3 + Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
152E (old = 38A), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3^3
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2^3*3 + Z/2^3*3
= B(Z/2^2 + Z/2^2) + C(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + G(Z/3 + Z/3 + Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
152F (old = 38B), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2^3*3 + Z/2^3*3
= B(Z/2 + Z/2) + C(Z/2^2 + Z/2^2) + D(Z/3 + Z/3 + Z/3 + Z/3) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
152G (old = 19A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/3 + Z/3 + Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
Gamma_0(153)
Weight 2

-------------------------------------------------------
J_0(153), dim = 15

-------------------------------------------------------
153A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 5.0866620628403114498 + -0.10956155988814095115e-3i
Omega-         = 0.43808291826932633091e-4 + 1.7985049153303292475i
L(1)           =
w1             = 2.5433091272742422586 + -0.89930723844510869421i
w2             = -0.43808291826932633091e-4 + -1.7985049153303292475i
c4             = 144.01899018779340098 + 0.14155799778211529321e-1i
c6             = -1944.3134228318393996 + -0.28101158326373702228i
j              = -6507.6805022573407686 + -0.1803144725078756301i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + 2*q^4 + -1*q^5 + -2*q^7 + 2*q^10 + -3*q^11 + -5*q^13 + 4*q^14 + -4*q^16 + -1*q^17 + -1*q^19 + -2*q^20 + 6*q^22 + -7*q^23 + -4*q^25 + 10*q^26 + -4*q^28 + 6*q^29 + 4*q^31 + 8*q^32 + 2*q^34 + 2*q^35 + 10*q^37 + 2*q^38 + 9*q^41 + 1*q^43 + -6*q^44 + 14*q^46 + -12*q^47 + -3*q^49 + 8*q^50 + -10*q^52 + -12*q^53 + 3*q^55 + -12*q^58 + 6*q^59 + 2*q^61 + -8*q^62 + -8*q^64 + 5*q^65 + 4*q^67 + -2*q^68 + -4*q^70 + -8*q^71 + -20*q^74 + -2*q^76 + 6*q^77 + -6*q^79 + 4*q^80 + -18*q^82 + 4*q^83 + 1*q^85 + -2*q^86 + 2*q^89 + 10*q^91 + -14*q^92 + 24*q^94 + 1*q^95 + 8*q^97 + 6*q^98 + -8*q^100 + 4*q^101 + -19*q^103 + 24*q^106 + -11*q^107 + -6*q^110 + 8*q^112 + -1*q^113 + 7*q^115 + 12*q^116 + -12*q^118 + 2*q^119 + -2*q^121 + -4*q^122 + 8*q^124 + 9*q^125 + 11*q^127 + -10*q^130 + 11*q^131 + 2*q^133 + -8*q^134 + 18*q^137 + -14*q^139 + 4*q^140 + 16*q^142 + 15*q^143 + -6*q^145 + 20*q^148 + -2*q^149 + -16*q^151 + -12*q^154 + -4*q^155 + -5*q^157 + 12*q^158 + -8*q^160 + 14*q^161 + -24*q^163 + 18*q^164 + -8*q^166 + -23*q^167 + 12*q^169 + -2*q^170 + 2*q^172 + 23*q^173 + 8*q^175 + 12*q^176 + -4*q^178 + -12*q^179 + -14*q^181 + -20*q^182 + -10*q^185 + 3*q^187 + -24*q^188 + -2*q^190 + -14*q^191 + -4*q^193 + -16*q^194 + -6*q^196 + 3*q^197 + 16*q^199 +  ...

-------------------------------------------------------
153B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*3
Ker(ModPolar)  = Z/2^3*3 + Z/2^3*3
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.038383749404969167 + -0.9249438137217688077e-5i
Omega-         = 0.12345733751533360464e-4 + -2.9366527685449259253i
L(1)           = 2.076767498892328015
w1             = 0.51918570183560881681 + 1.4683217595533943538i
w2             = 1.038383749404969167 + -0.9249438137217688077e-5i
c4             = 1296.0646462632967873 + 0.51356482269210227914e-1i
c6             = 52493.31532099346704 + 2.410069916531058893i
j              = -6503.7728311655165319 + -0.83810286849322696423i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 2*q^4 + 1*q^5 + -2*q^7 + 2*q^10 + 3*q^11 + -5*q^13 + -4*q^14 + -4*q^16 + 1*q^17 + -1*q^19 + 2*q^20 + 6*q^22 + 7*q^23 + -4*q^25 + -10*q^26 + -4*q^28 + -6*q^29 + 4*q^31 + -8*q^32 + 2*q^34 + -2*q^35 + 10*q^37 + -2*q^38 + -9*q^41 + 1*q^43 + 6*q^44 + 14*q^46 + 12*q^47 + -3*q^49 + -8*q^50 + -10*q^52 + 12*q^53 + 3*q^55 + -12*q^58 + -6*q^59 + 2*q^61 + 8*q^62 + -8*q^64 + -5*q^65 + 4*q^67 + 2*q^68 + -4*q^70 + 8*q^71 + 20*q^74 + -2*q^76 + -6*q^77 + -6*q^79 + -4*q^80 + -18*q^82 + -4*q^83 + 1*q^85 + 2*q^86 + -2*q^89 + 10*q^91 + 14*q^92 + 24*q^94 + -1*q^95 + 8*q^97 + -6*q^98 + -8*q^100 + -4*q^101 + -19*q^103 + 24*q^106 + 11*q^107 + 6*q^110 + 8*q^112 + 1*q^113 + 7*q^115 + -12*q^116 + -12*q^118 + -2*q^119 + -2*q^121 + 4*q^122 + 8*q^124 + -9*q^125 + 11*q^127 + -10*q^130 + -11*q^131 + 2*q^133 + 8*q^134 + -18*q^137 + -14*q^139 + -4*q^140 + 16*q^142 + -15*q^143 + -6*q^145 + 20*q^148 + 2*q^149 + -16*q^151 + -12*q^154 + 4*q^155 + -5*q^157 + -12*q^158 + -8*q^160 + -14*q^161 + -24*q^163 + -18*q^164 + -8*q^166 + 23*q^167 + 12*q^169 + 2*q^170 + 2*q^172 + -23*q^173 + 8*q^175 + -12*q^176 + -4*q^178 + 12*q^179 + -14*q^181 + 20*q^182 + 10*q^185 + 3*q^187 + 24*q^188 + -2*q^190 + 14*q^191 + -4*q^193 + 16*q^194 + -6*q^196 + -3*q^197 + 16*q^199 +  ...

-------------------------------------------------------
153C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= E(Z/2^2 + Z/2^2) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.5852156310867416721 + -0.15283391287676545496e-4i
Omega-         = 0.13709383006412538584e-4 + 1.7863888632040366291i
L(1)           = 0.792607815580208419
w1             = -0.13709383006412538584e-4 + -1.7863888632040366291i
w2             = -1.5852156310867416721 + 0.15283391287676545496e-4i
c4             = 297.02468144764459672 + 0.10750139130065355168e-1i
c6             = 2187.4308797071108083 + 0.15071672214508095502i
j              = 2114.0095037975073331 + 0.13800814122654008896e-1i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^4 + 2*q^5 + 4*q^7 + -3*q^8 + 2*q^10 + -2*q^13 + 4*q^14 + -1*q^16 + -1*q^17 + -4*q^19 + -2*q^20 + -4*q^23 + -1*q^25 + -2*q^26 + -4*q^28 + -6*q^29 + 4*q^31 + 5*q^32 + -1*q^34 + 8*q^35 + -2*q^37 + -4*q^38 + -6*q^40 + 6*q^41 + 4*q^43 + -4*q^46 + 9*q^49 + -1*q^50 + 2*q^52 + -6*q^53 + -12*q^56 + -6*q^58 + 12*q^59 + -10*q^61 + 4*q^62 + 7*q^64 + -4*q^65 + 4*q^67 + 1*q^68 + 8*q^70 + 4*q^71 + -6*q^73 + -2*q^74 + 4*q^76 + 12*q^79 + -2*q^80 + 6*q^82 + 4*q^83 + -2*q^85 + 4*q^86 + -10*q^89 + -8*q^91 + 4*q^92 + -8*q^95 + 2*q^97 + 9*q^98 + 1*q^100 + 10*q^101 + 8*q^103 + 6*q^104 + -6*q^106 + -8*q^107 + 6*q^109 + -4*q^112 + 14*q^113 + -8*q^115 + 6*q^116 + 12*q^118 + -4*q^119 + -11*q^121 + -10*q^122 + -4*q^124 + -12*q^125 + 8*q^127 + -3*q^128 + -4*q^130 + -16*q^131 + -16*q^133 + 4*q^134 + 3*q^136 + 6*q^137 + -8*q^139 + -8*q^140 + 4*q^142 + -12*q^145 + -6*q^146 + 2*q^148 + 10*q^149 + -16*q^151 + 12*q^152 + 8*q^155 + -2*q^157 + 12*q^158 + 10*q^160 + -16*q^161 + 24*q^163 + -6*q^164 + 4*q^166 + 4*q^167 + -9*q^169 + -2*q^170 + -4*q^172 + -22*q^173 + -4*q^175 + -10*q^178 + -12*q^179 + -2*q^181 + -8*q^182 + 12*q^184 + -4*q^185 + -8*q^190 + 16*q^191 + 2*q^193 + 2*q^194 + -9*q^196 + 18*q^197 + -20*q^199 + 3*q^200 +  ...

-------------------------------------------------------
153D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2^2 + Z/2^2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 3
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.2550512974777530462 + 0.10217945879572922718e-3i
Omega-         = 0.65095964043355879462e-4 + -1.4896305503877347359i
L(1)           =
w1             = -1.1274931007568548451 + -0.74486636492326523256i
w2             = -1.127558196720898201 + 0.74476418546446950333i
c4             = -287.61987735905953507 + 0.54539087383974731729e-1i
c6             = -23538.701644387617524 + 6.2623174441519327437i
j              = 71.149994028026438537 + -0.25091074315774687143e-2i

HECKE EIGENFORM:
f(q) = q + -2*q^4 + -3*q^5 + -4*q^7 + 3*q^11 + -1*q^13 + 4*q^16 + 1*q^17 + -1*q^19 + 6*q^20 + -9*q^23 + 4*q^25 + 8*q^28 + -6*q^29 + 2*q^31 + 12*q^35 + -4*q^37 + 3*q^41 + -7*q^43 + -6*q^44 + 6*q^47 + 9*q^49 + 2*q^52 + 6*q^53 + -9*q^55 + -6*q^59 + 8*q^61 + -8*q^64 + 3*q^65 + -4*q^67 + -2*q^68 + -12*q^71 + 2*q^73 + 2*q^76 + -12*q^77 + -10*q^79 + -12*q^80 + 6*q^83 + -3*q^85 + 4*q^91 + 18*q^92 + 3*q^95 + -16*q^97 + -8*q^100 + 5*q^103 + -9*q^107 + 20*q^109 + -16*q^112 + 9*q^113 + 27*q^115 + 12*q^116 + -4*q^119 + -2*q^121 + -4*q^124 + 3*q^125 + -13*q^127 + -3*q^131 + 4*q^133 + 6*q^137 + 2*q^139 + -24*q^140 + -3*q^143 + 18*q^145 + 8*q^148 + 18*q^149 + 8*q^151 + -6*q^155 + 11*q^157 + 36*q^161 + 2*q^163 + -6*q^164 + -21*q^167 + -12*q^169 + 14*q^172 + -15*q^173 + -16*q^175 + 12*q^176 + 6*q^179 + 14*q^181 + 12*q^185 + 3*q^187 + -12*q^188 + -18*q^191 + -22*q^193 + -18*q^196 + -3*q^197 + -16*q^199 +  ...

-------------------------------------------------------
153E (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2^3 + Z/2^3 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2^2 + Z/2^2) + D(Z/2 + Z/2) + F(Z/2^2 + Z/2^2) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 17
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2^2
|L(1)/Omega|   = 1
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 0.81258188870011877455 + 0.19714030061970617808e-5i
Omega-         = 2.4062539662810932045 + 0.62152117362639548967e-3i
L(1)           = 0.81258188870251018264

HECKE EIGENFORM:
a^2-a-4 = 0,
f(q) = q + a*q^2 + (a+2)*q^4 + (-a-1)*q^5 + (a+4)*q^8 + (-2*a-4)*q^10 + (-a+1)*q^11 + (-a+3)*q^13 + 3*a*q^16 + -1*q^17 + (-3*a+3)*q^19 + (-4*a-6)*q^20 + -4*q^22 + (-a+5)*q^23 + 3*a*q^25 + (2*a-4)*q^26 + (4*a-2)*q^29 + (2*a-2)*q^31 + (a+4)*q^32 + -a*q^34 + -2*a*q^37 + -12*q^38 + (-6*a-8)*q^40 + (a+1)*q^41 + (3*a-3)*q^43 + (-2*a-2)*q^44 + (4*a-4)*q^46 + (2*a+6)*q^47 + -7*q^49 + (3*a+12)*q^50 + 2*q^52 + (-4*a-2)*q^53 + (a+3)*q^55 + (2*a+16)*q^58 + (-2*a-2)*q^59 + (2*a+4)*q^61 + 8*q^62 + (-a+4)*q^64 + (-a+1)*q^65 + 4*q^67 + (-a-2)*q^68 + (4*a-4)*q^71 + (-4*a-2)*q^73 + (-2*a-8)*q^74 + (-6*a-6)*q^76 + (-6*a+6)*q^79 + (-6*a-12)*q^80 + (2*a+4)*q^82 + (-2*a+6)*q^83 + (a+1)*q^85 + 12*q^86 + -4*a*q^88 + (2*a-4)*q^89 + (2*a+6)*q^92 + (8*a+8)*q^94 + (3*a+9)*q^95 + (2*a-8)*q^97 + -7*a*q^98 + (9*a+12)*q^100 + (2*a-16)*q^101 + (3*a+9)*q^103 + (-2*a+8)*q^104 + (-6*a-16)*q^106 + (3*a-3)*q^107 + (2*a-12)*q^109 + (4*a+4)*q^110 + (-a+3)*q^113 + (-3*a-1)*q^115 + (10*a+12)*q^116 + (-4*a-8)*q^118 + (-a-6)*q^121 + (6*a+8)*q^122 + (4*a+4)*q^124 + (-a-7)*q^125 + (5*a+7)*q^127 + (a-12)*q^128 + -4*q^130 + (a-17)*q^131 + 4*a*q^134 + (-a-4)*q^136 + (-4*a+10)*q^137 + (2*a-6)*q^139 + 16*q^142 + (-3*a+7)*q^143 + (-6*a-14)*q^145 + (-6*a-16)*q^146 + (-6*a-8)*q^148 + (-4*a-2)*q^149 + 8*q^151 + -12*a*q^152 + (-2*a-6)*q^155 + (3*a-1)*q^157 + -24*q^158 + (-6*a-8)*q^160 + (-2*a-10)*q^163 + (4*a+6)*q^164 + (4*a-8)*q^166 + (-5*a-7)*q^167 + -5*a*q^169 + (2*a+4)*q^170 + (6*a+6)*q^172 + (-5*a+11)*q^173 + -12*q^176 + (-2*a+8)*q^178 + (-2*a+6)*q^179 + 6*q^181 + 16*q^184 + (4*a+8)*q^185 + (a-1)*q^187 + (12*a+20)*q^188 + (12*a+12)*q^190 + (-2*a+10)*q^191 + (4*a-18)*q^193 + (-6*a+8)*q^194 + (-7*a-14)*q^196 + (7*a-9)*q^197 + 16*q^199 + (15*a+12)*q^200 +  ...

-------------------------------------------------------
153F (old = 51A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2^2 + Z/2^2) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
153G (old = 51B), dim = 2

CONGRUENCES:
Modular Degree = 2^10
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2^2 + Z/2^2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2)

-------------------------------------------------------
153H (old = 17A), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3*3 + Z/2^3*3
= B(Z/3 + Z/3) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + G(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2)

-------------------------------------------------------
Gamma_0(154)
Weight 2

-------------------------------------------------------
J_0(154), dim = 21

-------------------------------------------------------
154A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*3
Ker(ModPolar)  = Z/2^3*3 + Z/2^3*3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/3 + Z/3) + F(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 3.5423609476174857508 + -0.20421352007225001411e-4i
Omega-         = 0.20404216756032165662e-4 + 1.0257896074906724241i
L(1)           =
w1             = 1.7711702717003648593 + -0.51290501442133982456i
w2             = -0.20404216756032165662e-4 + -1.0257896074906724241i
c4             = 1401.0610672354560678 + 0.1124807508902199514i
c6             = -53328.361181158150719 + -6.2854569439539803188i
j              = -50735.617554376971476 + -7.8883241916188928047i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^4 + -4*q^5 + -1*q^7 + -1*q^8 + -3*q^9 + 4*q^10 + -1*q^11 + 2*q^13 + 1*q^14 + 1*q^16 + -4*q^17 + 3*q^18 + -6*q^19 + -4*q^20 + 1*q^22 + 4*q^23 + 11*q^25 + -2*q^26 + -1*q^28 + -2*q^29 + -2*q^31 + -1*q^32 + 4*q^34 + 4*q^35 + -3*q^36 + 10*q^37 + 6*q^38 + 4*q^40 + 4*q^41 + -8*q^43 + -1*q^44 + 12*q^45 + -4*q^46 + 2*q^47 + 1*q^49 + -11*q^50 + 2*q^52 + 6*q^53 + 4*q^55 + 1*q^56 + 2*q^58 + -12*q^59 + -14*q^61 + 2*q^62 + 3*q^63 + 1*q^64 + -8*q^65 + -12*q^67 + -4*q^68 + -4*q^70 + -8*q^71 + 3*q^72 + 4*q^73 + -10*q^74 + -6*q^76 + 1*q^77 + -4*q^80 + 9*q^81 + -4*q^82 + -6*q^83 + 16*q^85 + 8*q^86 + 1*q^88 + -6*q^89 + -12*q^90 + -2*q^91 + 4*q^92 + -2*q^94 + 24*q^95 + -14*q^97 + -1*q^98 + 3*q^99 + 11*q^100 + 6*q^101 + 18*q^103 + -2*q^104 + -6*q^106 + -16*q^107 + -14*q^109 + -4*q^110 + -1*q^112 + 14*q^113 + -16*q^115 + -2*q^116 + -6*q^117 + 12*q^118 + 4*q^119 + 1*q^121 + 14*q^122 + -2*q^124 + -24*q^125 + -3*q^126 + 8*q^127 + -1*q^128 + 8*q^130 + 6*q^131 + 6*q^133 + 12*q^134 + 4*q^136 + 6*q^137 + 14*q^139 + 4*q^140 + 8*q^142 + -2*q^143 + -3*q^144 + 8*q^145 + -4*q^146 + 10*q^148 + 2*q^149 + -24*q^151 + 6*q^152 + 12*q^153 + -1*q^154 + 8*q^155 + -8*q^157 + 4*q^160 + -4*q^161 + -9*q^162 + 4*q^163 + 4*q^164 + 6*q^166 + 4*q^167 + -9*q^169 + -16*q^170 + 18*q^171 + -8*q^172 + -14*q^173 + -11*q^175 + -1*q^176 + 6*q^178 + 4*q^179 + 12*q^180 + 20*q^181 + 2*q^182 + -4*q^184 + -40*q^185 + 4*q^187 + 2*q^188 + -24*q^190 + -4*q^191 + 2*q^193 + 14*q^194 + 1*q^196 + 6*q^197 + -3*q^198 + -14*q^199 + -11*q^200 +  ...

-------------------------------------------------------
154B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/2^2 + Z/2^2) + H(Z/2 + Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 1
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 1.2199472881883836064 + 0.16423614499584538343e-4i
Omega-         = 0.36901716020868649344e-4 + -3.9435387538817366944i
L(1)           = 1.2199472882989355605
w1             = -0.60999209495220223754 + 1.971761165133618555i
w2             = 1.2199472881883836064 + 0.16423614499584538343e-4i
c4             = 697.08611681182744332 + -0.37811697440373121912e-1i
c6             = 19030.375667212620384 + -1.5219818560933764158i
j              = -24992.015893161110367 + 1.0722541217841870221i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 2*q^3 + 1*q^4 + 2*q^5 + -2*q^6 + -1*q^7 + -1*q^8 + 1*q^9 + -2*q^10 + 1*q^11 + 2*q^12 + -4*q^13 + 1*q^14 + 4*q^15 + 1*q^16 + -1*q^18 + 4*q^19 + 2*q^20 + -2*q^21 + -1*q^22 + 4*q^23 + -2*q^24 + -1*q^25 + 4*q^26 + -4*q^27 + -1*q^28 + 2*q^29 + -4*q^30 + -10*q^31 + -1*q^32 + 2*q^33 + -2*q^35 + 1*q^36 + -6*q^37 + -4*q^38 + -8*q^39 + -2*q^40 + 2*q^42 + -4*q^43 + 1*q^44 + 2*q^45 + -4*q^46 + 10*q^47 + 2*q^48 + 1*q^49 + 1*q^50 + -4*q^52 + -14*q^53 + 4*q^54 + 2*q^55 + 1*q^56 + 8*q^57 + -2*q^58 + 10*q^59 + 4*q^60 + -8*q^61 + 10*q^62 + -1*q^63 + 1*q^64 + -8*q^65 + -2*q^66 + 8*q^67 + 8*q^69 + 2*q^70 + -4*q^71 + -1*q^72 + 4*q^73 + 6*q^74 + -2*q^75 + 4*q^76 + -1*q^77 + 8*q^78 + 16*q^79 + 2*q^80 + -11*q^81 + 4*q^83 + -2*q^84 + 4*q^86 + 4*q^87 + -1*q^88 + 10*q^89 + -2*q^90 + 4*q^91 + 4*q^92 + -20*q^93 + -10*q^94 + 8*q^95 + -2*q^96 + 6*q^97 + -1*q^98 + 1*q^99 + -1*q^100 + 12*q^101 + 2*q^103 + 4*q^104 + -4*q^105 + 14*q^106 + -12*q^107 + -4*q^108 + -14*q^109 + -2*q^110 + -12*q^111 + -1*q^112 + -14*q^113 + -8*q^114 + 8*q^115 + 2*q^116 + -4*q^117 + -10*q^118 + -4*q^120 + 1*q^121 + 8*q^122 + -10*q^124 + -12*q^125 + 1*q^126 + -16*q^127 + -1*q^128 + -8*q^129 + 8*q^130 + 8*q^131 + 2*q^132 + -4*q^133 + -8*q^134 + -8*q^135 + 6*q^137 + -8*q^138 + 20*q^139 + -2*q^140 + 20*q^141 + 4*q^142 + -4*q^143 + 1*q^144 + 4*q^145 + -4*q^146 + 2*q^147 + -6*q^148 + 22*q^149 + 2*q^150 + 16*q^151 + -4*q^152 + 1*q^154 + -20*q^155 + -8*q^156 + 10*q^157 + -16*q^158 + -28*q^159 + -2*q^160 + -4*q^161 + 11*q^162 + 24*q^163 + 4*q^165 + -4*q^166 + -8*q^167 + 2*q^168 + 3*q^169 + 4*q^171 + -4*q^172 + 4*q^173 + -4*q^174 + 1*q^175 + 1*q^176 + 20*q^177 + -10*q^178 + 12*q^179 + 2*q^180 + 14*q^181 + -4*q^182 + -16*q^183 + -4*q^184 + -12*q^185 + 20*q^186 + 10*q^188 + 4*q^189 + -8*q^190 + 8*q^191 + 2*q^192 + -6*q^193 + -6*q^194 + -16*q^195 + 1*q^196 + -18*q^197 + -1*q^198 + -14*q^199 + 1*q^200 +  ...

-------------------------------------------------------
154C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*3
Ker(ModPolar)  = Z/2^3*3 + Z/2^3*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/3 + Z/3) + F(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 3/2
Sha Bound      = 2^3*3

ANALYTIC INVARIANTS:

Omega+         = 1.1263711550205807405 + 0.17352381214261902972e-4i
Omega-         = 0.24687380560175364027e-4 + 2.0261343178915852455i
L(1)           = 1.6895567327313635056
w1             = 0.56317323382001028256 + -1.0130584827551854918i
w2             = -1.1263711550205807405 + -0.17352381214261902972e-4i
c4             = 177.32672962159229843 + -0.13030776505612319402i
c6             = 77454.633300361332889 + -0.6961694661275273715i
j              = -1.6075878046688179016 + 0.35183632535199088701e-2i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + 2*q^5 + -1*q^7 + 1*q^8 + -3*q^9 + 2*q^10 + -1*q^11 + 2*q^13 + -1*q^14 + 1*q^16 + 2*q^17 + -3*q^18 + 2*q^20 + -1*q^22 + -8*q^23 + -1*q^25 + 2*q^26 + -1*q^28 + -2*q^29 + -8*q^31 + 1*q^32 + 2*q^34 + -2*q^35 + -3*q^36 + -2*q^37 + 2*q^40 + 10*q^41 + 4*q^43 + -1*q^44 + -6*q^45 + -8*q^46 + 8*q^47 + 1*q^49 + -1*q^50 + 2*q^52 + 6*q^53 + -2*q^55 + -1*q^56 + -2*q^58 + 10*q^61 + -8*q^62 + 3*q^63 + 1*q^64 + 4*q^65 + -12*q^67 + 2*q^68 + -2*q^70 + 16*q^71 + -3*q^72 + -14*q^73 + -2*q^74 + 1*q^77 + 2*q^80 + 9*q^81 + 10*q^82 + 4*q^85 + 4*q^86 + -1*q^88 + -6*q^89 + -6*q^90 + -2*q^91 + -8*q^92 + 8*q^94 + 10*q^97 + 1*q^98 + 3*q^99 + -1*q^100 + 18*q^101 + 2*q^104 + 6*q^106 + -4*q^107 + -2*q^109 + -2*q^110 + -1*q^112 + 2*q^113 + -16*q^115 + -2*q^116 + -6*q^117 + -2*q^119 + 1*q^121 + 10*q^122 + -8*q^124 + -12*q^125 + 3*q^126 + 8*q^127 + 1*q^128 + 4*q^130 + -12*q^134 + 2*q^136 + -6*q^137 + -16*q^139 + -2*q^140 + 16*q^142 + -2*q^143 + -3*q^144 + -4*q^145 + -14*q^146 + -2*q^148 + 14*q^149 + -6*q^153 + 1*q^154 + -16*q^155 + -14*q^157 + 2*q^160 + 8*q^161 + 9*q^162 + -20*q^163 + 10*q^164 + 16*q^167 + -9*q^169 + 4*q^170 + 4*q^172 + -14*q^173 + 1*q^175 + -1*q^176 + -6*q^178 + 4*q^179 + -6*q^180 + -22*q^181 + -2*q^182 + -8*q^184 + -4*q^185 + -2*q^187 + 8*q^188 + 8*q^191 + 2*q^193 + 10*q^194 + 1*q^196 + -18*q^197 + 3*q^198 + 16*q^199 + -1*q^200 +  ...

-------------------------------------------------------
154D (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^3*5 + Z/2^3*5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2 + Z/2) + J(Z/5 + Z/5)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 2^2*5
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2*5
|L(1)/Omega|   = 1
Sha Bound      = 2^4*5^2

ANALYTIC INVARIANTS:

Omega+         = 2.2487740254561987459 + -0.5511673473293138483e-4i
Omega-         = 3.0938312407643666766 + 0.20369964833654183606e-3i
L(1)           = 2.2487740261316455477

HECKE EIGENFORM:
a^2+2*a-4 = 0,
f(q) = q + 1*q^2 + a*q^3 + 1*q^4 + -a*q^5 + a*q^6 + 1*q^7 + 1*q^8 + (-2*a+1)*q^9 + -a*q^10 + 1*q^11 + a*q^12 + (-a-2)*q^13 + 1*q^14 + (2*a-4)*q^15 + 1*q^16 + 2*a*q^17 + (-2*a+1)*q^18 + (-a-6)*q^19 + -a*q^20 + a*q^21 + 1*q^22 + 4*q^23 + a*q^24 + (-2*a-1)*q^25 + (-a-2)*q^26 + (2*a-8)*q^27 + 1*q^28 + (2*a+2)*q^29 + (2*a-4)*q^30 + 2*q^31 + 1*q^32 + a*q^33 + 2*a*q^34 + -a*q^35 + (-2*a+1)*q^36 + (4*a+2)*q^37 + (-a-6)*q^38 + -4*q^39 + -a*q^40 + -2*a*q^41 + a*q^42 + (-2*a-8)*q^43 + 1*q^44 + (-5*a+8)*q^45 + 4*q^46 + -2*q^47 + a*q^48 + 1*q^49 + (-2*a-1)*q^50 + (-4*a+8)*q^51 + (-a-2)*q^52 + (2*a+6)*q^53 + (2*a-8)*q^54 + -a*q^55 + 1*q^56 + (-4*a-4)*q^57 + (2*a+2)*q^58 + (-a+4)*q^59 + (2*a-4)*q^60 + (a-2)*q^61 + 2*q^62 + (-2*a+1)*q^63 + 1*q^64 + 4*q^65 + a*q^66 + (6*a+4)*q^67 + 2*a*q^68 + 4*a*q^69 + -a*q^70 + (2*a+4)*q^71 + (-2*a+1)*q^72 + (4*a+8)*q^73 + (4*a+2)*q^74 + (3*a-8)*q^75 + (-a-6)*q^76 + 1*q^77 + -4*q^78 + -a*q^80 + (-6*a+5)*q^81 + -2*a*q^82 + (-5*a-6)*q^83 + a*q^84 + (4*a-8)*q^85 + (-2*a-8)*q^86 + (-2*a+8)*q^87 + 1*q^88 + 10*q^89 + (-5*a+8)*q^90 + (-a-2)*q^91 + 4*q^92 + 2*a*q^93 + -2*q^94 + (4*a+4)*q^95 + a*q^96 + (2*a+10)*q^97 + 1*q^98 + (-2*a+1)*q^99 + (-2*a-1)*q^100 + (5*a+2)*q^101 + (-4*a+8)*q^102 + (-4*a-10)*q^103 + (-a-2)*q^104 + (2*a-4)*q^105 + (2*a+6)*q^106 + 2*a*q^107 + (2*a-8)*q^108 + -10*q^109 + -a*q^110 + (-6*a+16)*q^111 + 1*q^112 + (-2*a+2)*q^113 + (-4*a-4)*q^114 + -4*a*q^115 + (2*a+2)*q^116 + (-a+6)*q^117 + (-a+4)*q^118 + 2*a*q^119 + (2*a-4)*q^120 + 1*q^121 + (a-2)*q^122 + (4*a-8)*q^123 + 2*q^124 + (2*a+8)*q^125 + (-2*a+1)*q^126 + -12*q^127 + 1*q^128 + (-4*a-8)*q^129 + 4*q^130 + (-a+6)*q^131 + a*q^132 + (-a-6)*q^133 + (6*a+4)*q^134 + (12*a-8)*q^135 + 2*a*q^136 + (-8*a-10)*q^137 + 4*a*q^138 + (-3*a-18)*q^139 + -a*q^140 + -2*a*q^141 + (2*a+4)*q^142 + (-a-2)*q^143 + (-2*a+1)*q^144 + (2*a-8)*q^145 + (4*a+8)*q^146 + a*q^147 + (4*a+2)*q^148 + (-10*a-10)*q^149 + (3*a-8)*q^150 + 12*q^151 + (-a-6)*q^152 + (10*a-16)*q^153 + 1*q^154 + -2*a*q^155 + -4*q^156 + (-7*a-4)*q^157 + (2*a+8)*q^159 + -a*q^160 + 4*q^161 + (-6*a+5)*q^162 + (-6*a-12)*q^163 + -2*a*q^164 + (2*a-4)*q^165 + (-5*a-6)*q^166 + (6*a+4)*q^167 + a*q^168 + (2*a-5)*q^169 + (4*a-8)*q^170 + (7*a+2)*q^171 + (-2*a-8)*q^172 + (-a-2)*q^173 + (-2*a+8)*q^174 + (-2*a-1)*q^175 + 1*q^176 + (6*a-4)*q^177 + 10*q^178 + (-4*a-4)*q^179 + (-5*a+8)*q^180 + (a+8)*q^181 + (-a-2)*q^182 + (-4*a+4)*q^183 + 4*q^184 + (6*a-16)*q^185 + 2*a*q^186 + 2*a*q^187 + -2*q^188 + (2*a-8)*q^189 + (4*a+4)*q^190 + -2*a*q^191 + a*q^192 + (-4*a-10)*q^193 + (2*a+10)*q^194 + 4*a*q^195 + 1*q^196 + 18*q^197 + (-2*a+1)*q^198 + (4*a+14)*q^199 + (-2*a-1)*q^200 +  ...

-------------------------------------------------------
154E (old = 77A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/3 + Z/3) + C(Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
154F (old = 77B), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2^4*3 + Z/2^4*3
= A(Z/2 + Z/2) + B(Z/2^2 + Z/2^2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2) + J(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
154G (old = 77C), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3*5^2
Ker(ModPolar)  = Z/2^2*5 + Z/2^2*5 + Z/2^2*3*5 + Z/2^2*3*5
= E(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/5 + Z/5 + Z/5 + Z/5) + I(Z/3 + Z/3) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
154H (old = 77D), dim = 2

CONGRUENCES:
Modular Degree = 2^5*5^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*5 + Z/2*5 + Z/2^3*5 + Z/2^3*5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/5 + Z/5 + Z/5 + Z/5) + I(Z/2 + Z/2)

-------------------------------------------------------
154I (old = 14A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/3 + Z/3) + H(Z/2 + Z/2)

-------------------------------------------------------
154J (old = 11A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2*3*5 + Z/2*3*5
= D(Z/5 + Z/5) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/3 + Z/3 + Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(155)
Weight 2

-------------------------------------------------------
J_0(155), dim = 15

-------------------------------------------------------
155A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 5.3453259724075803004 + -0.1854667720755114363e-4i
Omega-         = 0.83400956325964137264e-4 + 2.1627997849922255675i
L(1)           =
w1             = 2.6726212857256271681 + -1.0814091658347165593i
w2             = -0.83400956325964137264e-4 + -2.1627997849922255675i
c4             = 63.998037282918789745 + 0.11834004131154869229e-1i
c6             = -727.99133649288934924 + -0.13436226742637398042i
j              = -1691.0232800127845621 + -0.62100676481848505335i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^4 + -1*q^5 + -2*q^9 + -4*q^11 + 2*q^12 + -6*q^13 + 1*q^15 + 4*q^16 + 5*q^17 + -1*q^19 + 2*q^20 + 8*q^23 + 1*q^25 + 5*q^27 + -10*q^29 + -1*q^31 + 4*q^33 + 4*q^36 + 1*q^37 + 6*q^39 + -3*q^41 + -7*q^43 + 8*q^44 + 2*q^45 + -6*q^47 + -4*q^48 + -7*q^49 + -5*q^51 + 12*q^52 + 5*q^53 + 4*q^55 + 1*q^57 + 11*q^59 + -2*q^60 + -12*q^61 + -8*q^64 + 6*q^65 + -2*q^67 + -10*q^68 + -8*q^69 + 9*q^71 + -9*q^73 + -1*q^75 + 2*q^76 + -10*q^79 + -4*q^80 + 1*q^81 + 9*q^83 + -5*q^85 + 10*q^87 + -16*q^92 + 1*q^93 + 1*q^95 + -14*q^97 + 8*q^99 + -2*q^100 + -7*q^101 + 8*q^103 + -2*q^107 + -10*q^108 + 15*q^109 + -1*q^111 + -4*q^113 + -8*q^115 + 20*q^116 + 12*q^117 + 5*q^121 + 3*q^123 + 2*q^124 + -1*q^125 + -8*q^127 + 7*q^129 + -1*q^131 + -8*q^132 + -5*q^135 + 3*q^137 + 2*q^139 + 6*q^141 + 24*q^143 + -8*q^144 + 10*q^145 + 7*q^147 + -2*q^148 + 1*q^149 + 10*q^151 + -10*q^153 + 1*q^155 + -12*q^156 + -5*q^159 + 24*q^163 + 6*q^164 + -4*q^165 + -15*q^167 + 23*q^169 + 2*q^171 + 14*q^172 + 4*q^173 + -16*q^176 + -11*q^177 + -4*q^179 + -4*q^180 + -18*q^181 + 12*q^183 + -1*q^185 + -20*q^187 + 12*q^188 + 4*q^191 + 8*q^192 + 14*q^193 + -6*q^195 + 14*q^196 + -22*q^197 + -8*q^199 +  ...

-------------------------------------------------------
155B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= D(Z/2^2 + Z/2^3) + E(Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.1141440457337078056 + 0.49270424432754736969e-5i
Omega-         = 0.19090406551432657303e-3 + 4.3442602174279883704i
L(1)           = 1.0570720228697245383
w1             = 1.0569765708340967395 + -2.1721276451927725475i
w2             = -2.1141440457337078056 + -0.49270424432754736969e-5i
c4             = 48.999445577235639641 + -0.90014745562866153639e-2i
c6             = 1206.9860899202421304 + 0.12956958070570285661i
j              = -151.80331156210488528 + 0.12646624647851006294i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 2*q^3 + -1*q^4 + -1*q^5 + -2*q^6 + 4*q^7 + 3*q^8 + 1*q^9 + 1*q^10 + 4*q^11 + -2*q^12 + -4*q^14 + -2*q^15 + -1*q^16 + -8*q^17 + -1*q^18 + 4*q^19 + 1*q^20 + 8*q^21 + -4*q^22 + 2*q^23 + 6*q^24 + 1*q^25 + -4*q^27 + -4*q^28 + -6*q^29 + 2*q^30 + 1*q^31 + -5*q^32 + 8*q^33 + 8*q^34 + -4*q^35 + -1*q^36 + -4*q^37 + -4*q^38 + -3*q^40 + -6*q^41 + -8*q^42 + -6*q^43 + -4*q^44 + -1*q^45 + -2*q^46 + 8*q^47 + -2*q^48 + 9*q^49 + -1*q^50 + -16*q^51 + -12*q^53 + 4*q^54 + -4*q^55 + 12*q^56 + 8*q^57 + 6*q^58 + -4*q^59 + 2*q^60 + 10*q^61 + -1*q^62 + 4*q^63 + 7*q^64 + -8*q^66 + 8*q^67 + 8*q^68 + 4*q^69 + 4*q^70 + 3*q^72 + -4*q^73 + 4*q^74 + 2*q^75 + -4*q^76 + 16*q^77 + 1*q^80 + -11*q^81 + 6*q^82 + 2*q^83 + -8*q^84 + 8*q^85 + 6*q^86 + -12*q^87 + 12*q^88 + 14*q^89 + 1*q^90 + -2*q^92 + 2*q^93 + -8*q^94 + -4*q^95 + -10*q^96 + -18*q^97 + -9*q^98 + 4*q^99 + -1*q^100 + 10*q^101 + 16*q^102 + 8*q^103 + -8*q^105 + 12*q^106 + -4*q^107 + 4*q^108 + 10*q^109 + 4*q^110 + -8*q^111 + -4*q^112 + -18*q^113 + -8*q^114 + -2*q^115 + 6*q^116 + 4*q^118 + -32*q^119 + -6*q^120 + 5*q^121 + -10*q^122 + -12*q^123 + -1*q^124 + -1*q^125 + -4*q^126 + 2*q^127 + 3*q^128 + -12*q^129 + -4*q^131 + -8*q^132 + 16*q^133 + -8*q^134 + 4*q^135 + -24*q^136 + 12*q^137 + -4*q^138 + 4*q^140 + 16*q^141 + -1*q^144 + 6*q^145 + 4*q^146 + 18*q^147 + 4*q^148 + 6*q^149 + -2*q^150 + 12*q^152 + -8*q^153 + -16*q^154 + -1*q^155 + 14*q^157 + -24*q^159 + 5*q^160 + 8*q^161 + 11*q^162 + -16*q^163 + 6*q^164 + -8*q^165 + -2*q^166 + 14*q^167 + 24*q^168 + -13*q^169 + -8*q^170 + 4*q^171 + 6*q^172 + 6*q^173 + 12*q^174 + 4*q^175 + -4*q^176 + -8*q^177 + -14*q^178 + 4*q^179 + 1*q^180 + -18*q^181 + 20*q^183 + 6*q^184 + 4*q^185 + -2*q^186 + -32*q^187 + -8*q^188 + -16*q^189 + 4*q^190 + 8*q^191 + 14*q^192 + -18*q^193 + 18*q^194 + -9*q^196 + -8*q^197 + -4*q^198 + -20*q^199 + 3*q^200 +  ...

-------------------------------------------------------
155C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*5
Ker(ModPolar)  = Z/2^2*5 + Z/2^2*5
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/5 + Z/5)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 5
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.2165679255395177994 + -0.2404785364277072204e-3i
Omega-         = 0.34048690279907778818e-4 + -1.8397647824259755076i
L(1)           =
w1             = -1.1083009871148988536 + 0.92000263048120160742i
w2             = 1.1082669384246189458 + 0.9197621519447739002i
c4             = -463.94943670598125676 + -0.19064987303623776471i
c6             = -8212.5993557578033776 + 2.3689856875376720352i
j              = 1031.4069281951304788 + 0.75244020825812992442i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + -1*q^3 + 2*q^4 + 1*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 + -1*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 + 1*q^25 + 12*q^26 + 5*q^27 + -4*q^28 + 2*q^30 + 1*q^31 + 8*q^32 + -2*q^33 + 14*q^34 + -2*q^35 + -4*q^36 + -7*q^37 + 10*q^38 + 6*q^39 + -3*q^41 + -4*q^42 + 9*q^43 + 4*q^44 + -2*q^45 + -8*q^46 + -2*q^47 + 4*q^48 + -3*q^49 + -2*q^50 + 7*q^51 + -12*q^52 + 9*q^53 + -10*q^54 + 2*q^55 + 5*q^57 + -5*q^59 + -2*q^60 + -8*q^61 + -2*q^62 + 4*q^63 + -8*q^64 + -6*q^65 + 4*q^66 + 8*q^67 + -14*q^68 + -4*q^69 + 4*q^70 + -3*q^71 + -1*q^73 + 14*q^74 + -1*q^75 + -10*q^76 + -4*q^77 + -12*q^78 + -4*q^80 + 1*q^81 + 6*q^82 + -11*q^83 + 4*q^84 + -7*q^85 + -18*q^86 + 10*q^89 + 4*q^90 + 12*q^91 + 8*q^92 + -1*q^93 + 4*q^94 + -5*q^95 + -8*q^96 + 18*q^97 + 6*q^98 + -4*q^99 + 2*q^100 + 17*q^101 + -14*q^102 + -16*q^103 + 2*q^105 + -18*q^106 + -2*q^107 + 10*q^108 + -5*q^109 + -4*q^110 + 7*q^111 + 8*q^112 + -6*q^113 + -10*q^114 + 4*q^115 + 12*q^117 + 10*q^118 + 14*q^119 + -7*q^121 + 16*q^122 + 3*q^123 + 2*q^124 + 1*q^125 + -8*q^126 + 8*q^127 + -9*q^129 + 12*q^130 + 7*q^131 + -4*q^132 + 10*q^133 + -16*q^134 + 5*q^135 + 3*q^137 + 8*q^138 + -4*q^140 + 2*q^141 + 6*q^142 + -12*q^143 + 8*q^144 + 2*q^146 + 3*q^147 + -14*q^148 + -15*q^149 + 2*q^150 + 12*q^151 + 14*q^153 + 8*q^154 + 1*q^155 + 12*q^156 + -22*q^157 + -9*q^159 + 8*q^160 + -8*q^161 + -2*q^162 + -16*q^163 + -6*q^164 + -2*q^165 + 22*q^166 + 13*q^167 + 23*q^169 + 14*q^170 + 10*q^171 + 18*q^172 + -6*q^173 + -2*q^175 + -8*q^176 + 5*q^177 + -20*q^178 + -10*q^179 + -4*q^180 + -18*q^181 + -24*q^182 + 8*q^183 + -7*q^185 + 2*q^186 + -14*q^187 + -4*q^188 + -10*q^189 + 10*q^190 + -8*q^191 + 8*q^192 + -6*q^193 + -36*q^194 + 6*q^195 + -6*q^196 + -22*q^197 + 8*q^198 + 10*q^199 +  ...

-------------------------------------------------------
155D (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^7*7^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2*7 + Z/2^2*7 + Z/2^3*7 + Z/2^3*7
= A(Z/2 + Z/2) + B(Z/2^2 + Z/2^3) + C(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + F(Z/7 + Z/7 + Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*5077
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2*3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/3
Sha Bound      = 2^2*3

ANALYTIC INVARIANTS:

Omega+         = 1.583179037695558268 + 0.5552967859038066749e-4i
Omega-         = 2.173600591277472854 + -0.58420062324040969049e-3i
L(1)           = 0.527726346223134762

HECKE EIGENFORM:
a^4+a^3-8*a^2-4*a+12 = 0,
f(q) = q + a*q^2 + (-1/2*a^3-1/2*a^2+3*a+1)*q^3 + (a^2-2)*q^4 + -1*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 + 1*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 + 1*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 + (3*a^2+3*a-12)*q^38 + (-3*a^3-2*a^2+19*a+2)*q^39 + (-a^3+4*a)*q^40 + (a^3+2*a^2-4*a-3)*q^41 + (-a^3+a^2+6*a-12)*q^42 + (1/2*a^3-1/2*a^2-2*a+5)*q^43 + (-2*a^3+6*a)*q^44 + (2*a^2+a-10)*q^45 + (-a^3-5*a^2+2*a+12)*q^46 + (a^3+a^2-6*a-6)*q^47 + (2*a^3-12*a+4)*q^48 + (a^3+a^2-4*a-3)*q^49 + a*q^50 + (a^3-6*a+3)*q^51 + (2*a^2-2*a-4)*q^52 + (3/2*a^3+7/2*a^2-7*a-9)*q^53 + (a^3-2*a^2-5*a+18)*q^54 + (-a^2+a+6)*q^55 + 4*a*q^56 + (-1/2*a^3+5/2*a^2+4*a-19)*q^57 + (a^3-a^2-4*a+12)*q^58 + (2*a^3+a^2-10*a+3)*q^59 + 2*q^60 + (-a^3-a^2+6*a+8)*q^61 + a*q^62 + (-a^3+a^2+6*a-16)*q^63 + (-3*a^3+8*a+4)*q^64 + (a^2+a-8)*q^65 + (a^3+5*a^2-4*a-24)*q^66 + (-a^2+a+2)*q^67 + (-2*a^3+2*a^2+6*a-6)*q^68 + (-a^3-2*a^2+7*a+12)*q^69 + (-a^3-a^2+4*a)*q^70 + (-2*a^2-a+9)*q^71 + (a^3+4*a^2-12*a-12)*q^72 + (-3/2*a^3-3/2*a^2+5*a+5)*q^73 + (-a^3+7*a-6)*q^74 + (-1/2*a^3-1/2*a^2+3*a+1)*q^75 + (a^3+a^2-2*a+2)*q^76 + (-a^3-3*a^2+2*a+12)*q^77 + (a^3-5*a^2-10*a+36)*q^78 + (-3*a^2-3*a+8)*q^79 + (a^3-2*a^2-4*a+8)*q^80 + (-a^2-a+13)*q^81 + (a^3+4*a^2+a-12)*q^82 + (-1/2*a^3-7/2*a^2+9)*q^83 + (-2*a^2-2*a+8)*q^84 + (1/2*a^3-1/2*a^2-2*a+3)*q^85 + (-a^3+2*a^2+7*a-6)*q^86 + (-5*a^2-3*a+30)*q^87 + (-8*a^2+4*a+24)*q^88 + (a^2+5*a-6)*q^89 + (2*a^3+a^2-10*a)*q^90 + (-a^3+3*a^2+8*a-20)*q^91 + (-2*a^3-2*a^2+2*a)*q^92 + (-1/2*a^3-1/2*a^2+3*a+1)*q^93 + (2*a^2-2*a-12)*q^94 + (-a^3-a^2+5*a+1)*q^95 + (-2*a^3+12*a)*q^96 + (a^3+a^2-4*a+2)*q^97 + (4*a^2+a-12)*q^98 + (3*a^3+7*a^2-12*a-36)*q^99 + (a^2-2)*q^100 + (2*a^3-11*a+9)*q^101 + (-a^3+2*a^2+7*a-12)*q^102 + (a^3-a^2-6*a-4)*q^103 + (4*a^3-20*a)*q^104 + (-a^3+7*a-2)*q^105 + (2*a^3+5*a^2-3*a-18)*q^106 + (a^3+5*a^2-2*a-18)*q^107 + (4*a^2+2*a-14)*q^108 + (-a^3+a^2+7*a-1)*q^109 + (-a^3+a^2+6*a)*q^110 + (-2*a^3+a^2+14*a-13)*q^111 + (-4*a+8)*q^112 + (-a^3-2*a^2+a)*q^113 + (3*a^3-21*a+6)*q^114 + (a^3+2*a^2-3*a-6)*q^115 + (4*a^2+2*a-12)*q^116 + (a^3-9*a^2-10*a+56)*q^117 + (-a^3+6*a^2+11*a-24)*q^118 + (-a^2-3*a+6)*q^119 + (-2*a^2+12)*q^120 + (-3*a^3-3*a^2+16*a+13)*q^121 + (-2*a^2+4*a+12)*q^122 + (-1/2*a^3+3/2*a^2+3*a-15)*q^123 + (a^2-2)*q^124 + -1*q^125 + (2*a^3-2*a^2-20*a+12)*q^126 + (-2*a^3-a^2+9*a+2)*q^127 + (a^3-8*a^2+12)*q^128 + (-2*a^3-a^2+12*a-1)*q^129 + (a^3+a^2-8*a)*q^130 + (-2*a^3-6*a^2+3*a+27)*q^131 + (-2*a^2+2*a+12)*q^132 + (-a^3+2*a^2+11*a-8)*q^133 + (-a^3+a^2+2*a)*q^134 + (3/2*a^3+1/2*a^2-10*a-1)*q^135 + (2*a^3-6*a^2-4*a+12)*q^136 + (3/2*a^3+3/2*a^2-7*a-15)*q^137 + (-a^3-a^2+8*a+12)*q^138 + (3*a^2-5*a-16)*q^139 + (-2*a^2-2*a+4)*q^140 + (2*a^3+6*a^2-10*a-30)*q^141 + (-2*a^3-a^2+9*a)*q^142 + (a^3+7*a^2-6*a-36)*q^143 + (a^3+4*a-20)*q^144 + (a^3-7*a)*q^145 + (-7*a^2-a+18)*q^146 + (1/2*a^3+5/2*a^2-3*a-15)*q^147 + (-2*a+2)*q^148 + (-2*a^3+a^2+10*a-3)*q^149 + (-a^2-a+6)*q^150 + (-a^3+13*a-4)*q^151 + 12*q^152 + (a^2+5*a-12)*q^153 + (-2*a^3-6*a^2+8*a+12)*q^154 + -1*q^155 + (2*a^2+2*a-16)*q^156 + (a^3-7*a+8)*q^157 + (-3*a^3-3*a^2+8*a)*q^158 + (a^3+5*a^2-5*a-33)*q^159 + (-a^3+4*a^2+4*a-12)*q^160 + (-a^3-3*a^2-2*a)*q^161 + (-a^3-a^2+13*a)*q^162 + (a^3-a^2-2*a+8)*q^163 + (a^3+5*a^2-6)*q^164 + (-2*a^3-3*a^2+11*a+12)*q^165 + (-3*a^3-4*a^2+7*a+6)*q^166 + (1/2*a^3+11/2*a^2-27)*q^167 + (-4*a^2-4*a+24)*q^168 + (a^3-7*a^2-12*a+39)*q^169 + (-a^3+2*a^2+5*a-6)*q^170 + (4*a^3+a^2-29*a+2)*q^171 + (2*a^3-6*a+2)*q^172 + (a^3-2*a^2-13*a+12)*q^173 + (-5*a^3-3*a^2+30*a)*q^174 + (a^2+a-4)*q^175 + (-4*a^3+4*a^2+12*a)*q^176 + (-5/2*a^3+7/2*a^2+17*a-33)*q^177 + (a^3+5*a^2-6*a)*q^178 + (a^3+2*a^2-5*a-18)*q^179 + (-a^3+2*a^2+6*a-4)*q^180 + (3*a^3+5*a^2-14*a-10)*q^181 + (4*a^3-24*a+12)*q^182 + (-3*a^3-7*a^2+16*a+32)*q^183 + (2*a^3-4*a^2-12*a)*q^184 + (-1/2*a^3+1/2*a^2+4*a-5)*q^185 + (-a^2-a+6)*q^186 + (-a^3+2*a^2+3*a)*q^187 + (-4*a^2+12)*q^188 + (4*a^3+3*a^2-23*a+2)*q^189 + (-3*a^2-3*a+12)*q^190 + (-a^3-5*a^2+4*a+24)*q^191 + (-2*a^3-4*a^2+16*a+16)*q^192 + (2*a^3-14*a+2)*q^193 + (4*a^2+6*a-12)*q^194 + (3*a^3+2*a^2-19*a-2)*q^195 + (2*a^3-a^2-4*a+6)*q^196 + (-a^2-a)*q^197 + (4*a^3+12*a^2-24*a-36)*q^198 + (3*a^3-2*a^2-19*a+14)*q^199 + (a^3-4*a)*q^200 +  ...

-------------------------------------------------------
155E (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + B(Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^2*29*73
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^4
Torsion Bound  = 2^5
|L(1)/Omega|   = 1/2^4
Sha Bound      = 2^6

ANALYTIC INVARIANTS:

Omega+         = 21.611929250189003757 + 0.11074653131791144315e-2i
Omega-         = 4.6370691999199162505 + 0.16737275056824006018e-3i
L(1)           = 1.3507455799102537545

HECKE EIGENFORM:
a^4-a^3-6*a^2+4*a+4 = 0,
f(q) = q + a*q^2 + (-1/2*a^3+1/2*a^2+2*a-1)*q^3 + (a^2-2)*q^4 + 1*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 + 1*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 + -1*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 + (-3*a^2+a+4)*q^38 + (-a^3+2*a^2+3*a-8)*q^39 + (a^3-4*a)*q^40 + (-a^3+8*a-3)*q^41 + (a^3-a^2-2*a+4)*q^42 + (3/2*a^3-1/2*a^2-7*a+5)*q^43 + (-2*a^2+2*a)*q^44 + -a*q^45 + (a^3+a^2-4*a)*q^46 + (-a^3+a^2+8*a-6)*q^47 + -4*q^48 + (3*a^3-a^2-12*a+5)*q^49 + a*q^50 + (-a^3+2*a^2+2*a-5)*q^51 + (4*a^2+2*a-8)*q^52 + (-5/2*a^3+5/2*a^2+10*a-3)*q^53 + (a^3+2*a^2-5*a-6)*q^54 + (-a^2+a+2)*q^55 + (-4*a^2-4*a+8)*q^56 + (1/2*a^3+1/2*a^2-5*a+5)*q^57 + (-a^3+a^2-4)*q^58 + (2*a^3+a^2-10*a-5)*q^59 + (-2*a+2)*q^60 + (a^3-a^2-4*a+8)*q^61 + -a*q^62 + (a^3+a^2-4*a)*q^63 + (-a^3-2*a^2+8*a+4)*q^64 + (a^3-5*a+2)*q^65 + (-a^3+3*a^2)*q^66 + (-3*a^2+3*a+6)*q^67 + (4*a^2-6)*q^68 + (a^3-2*a^2-5*a+6)*q^69 + (-a^3-a^2+4*a)*q^70 + (-a-5)*q^71 + (-a^3-2*a^2+4*a+4)*q^72 + (-3/2*a^3-1/2*a^2+8*a+7)*q^73 + (-3*a^3+11*a+2)*q^74 + (-1/2*a^3+1/2*a^2+2*a-1)*q^75 + (-a^3-a^2-2*a+6)*q^76 + (a^3-a^2-2*a+4)*q^77 + (a^3-3*a^2-4*a+4)*q^78 + (-4*a^3+3*a^2+19*a-8)*q^79 + (a^3-4*a)*q^80 + (a^2+3*a-9)*q^81 + (-a^3+2*a^2+a+4)*q^82 + (-3/2*a^3-3/2*a^2+11*a+1)*q^83 + (2*a^3-10*a+8)*q^84 + (1/2*a^3+1/2*a^2-3*a+1)*q^85 + (a^3+2*a^2-a-6)*q^86 + (a^2+3*a-10)*q^87 + -4*a*q^88 + (-a^2-5*a+2)*q^89 + -a^2*q^90 + (a^3-5*a^2-10*a+16)*q^91 + (2*a^3-6*a+4)*q^92 + (1/2*a^3-1/2*a^2-2*a+1)*q^93 + (2*a^2-2*a+4)*q^94 + (-a^3+a^2+3*a-3)*q^95 + (-4*a+8)*q^96 + (-a^3-3*a^2+10*a+10)*q^97 + (2*a^3+6*a^2-7*a-12)*q^98 + (a^3-a^2-2*a)*q^99 + (a^2-2)*q^100 + (2*a^3+2*a^2-15*a-5)*q^101 + (a^3-4*a^2-a+4)*q^102 + (a^3+a^2-4*a)*q^103 + (2*a^3-4*a+8)*q^104 + (-a^3+2*a^2+5*a-6)*q^105 + (-5*a^2+7*a+10)*q^106 + (-a^3+5*a^2-22)*q^107 + (2*a^2+4*a-6)*q^108 + (-3*a^3+a^2+19*a-3)*q^109 + (-a^3+a^2+2*a)*q^110 + (-2*a^3+a^2+14*a-5)*q^111 + (-4*a^2-4*a+8)*q^112 + (a^3-4*a^2-7*a+16)*q^113 + (a^3-2*a^2+3*a-2)*q^114 + (a^2+a-4)*q^115 + (-2*a^3-2*a^2+10*a-4)*q^116 + (-a^3-a^2+2*a+4)*q^117 + (3*a^3+2*a^2-13*a-8)*q^118 + (-3*a^2-5*a+10)*q^119 + -4*q^120 + (-a^3+3*a^2-11)*q^121 + (2*a^2+4*a-4)*q^122 + (3/2*a^3-11/2*a^2-2*a+15)*q^123 + (-a^2+2)*q^124 + 1*q^125 + (2*a^3+2*a^2-4*a-4)*q^126 + (a^3+4*a^2-5*a-16)*q^127 + (-a^3-2*a^2+12)*q^128 + (-2*a^3+3*a^2+8*a-13)*q^129 + (a^3+a^2-2*a-4)*q^130 + (2*a^3-9*a-7)*q^131 + (2*a^3-4*a^2-2*a+4)*q^132 + (-a^3+6*a^2+7*a-16)*q^133 + (-3*a^3+3*a^2+6*a)*q^134 + (3/2*a^3-1/2*a^2-7*a+1)*q^135 + (2*a^3-4*a+4)*q^136 + (-1/2*a^3+9/2*a^2-4*a-13)*q^137 + (-a^3+a^2+2*a-4)*q^138 + (-3*a^2+5*a+8)*q^139 + (-2*a^3+6*a-4)*q^140 + (2*a^3-6*a^2-6*a+18)*q^141 + (-a^2-5*a)*q^142 + (a^3-3*a^2-4*a+4)*q^143 + (-a^3-2*a^2+4*a+4)*q^144 + (a^3-2*a^2-5*a+4)*q^145 + (-2*a^3-a^2+13*a+6)*q^146 + (-3/2*a^3+3/2*a^2+8*a-17)*q^147 + (-2*a^3-2*a^2+8*a-6)*q^148 + (-2*a^3+5*a^2+6*a-19)*q^149 + (-a^2+a+2)*q^150 + (a^3+2*a^2-3*a-12)*q^151 + (-2*a^3-2*a^2+8*a-4)*q^152 + (-a^3+a+2)*q^153 + (4*a^2-4)*q^154 + -1*q^155 + (-2*a^2-6*a+12)*q^156 + (a^3+4*a^2-7*a-12)*q^157 + (-a^3-5*a^2+8*a+16)*q^158 + (-a^3+a^2-a+13)*q^159 + (-a^3+2*a^2+4*a-4)*q^160 + (-3*a^3+a^2+12*a-12)*q^161 + (a^3+3*a^2-9*a)*q^162 + (3*a^3-5*a^2-20*a+12)*q^163 + (3*a^3-5*a^2-8*a+10)*q^164 + (-a^2+3*a)*q^165 + (-3*a^3+2*a^2+7*a+6)*q^166 + (3/2*a^3-5/2*a^2-13*a+5)*q^167 + (4*a^2+4*a-16)*q^168 + (3*a^3-a^2-12*a+3)*q^169 + (a^3-a-2)*q^170 + (3*a^2-a-4)*q^171 + (6*a^2+4*a-14)*q^172 + (-3*a^3-2*a^2+11*a+16)*q^173 + (a^3+3*a^2-10*a)*q^174 + (-a^2-a+4)*q^175 + -4*a*q^176 + (3/2*a^3+1/2*a^2-10*a-7)*q^177 + (-a^3-5*a^2+2*a)*q^178 + (3*a^3+4*a^2-17*a-14)*q^179 + (-a^3+2*a)*q^180 + (-3*a^3+5*a^2+16*a-6)*q^181 + (-4*a^3-4*a^2+12*a-4)*q^182 + (-3*a^3+3*a^2+14*a-12)*q^183 + (4*a^2+4*a-8)*q^184 + (-1/2*a^3-5/2*a^2+3*a+9)*q^185 + (a^2-a-2)*q^186 + (a^3-4*a^2-a+4)*q^187 + (4*a^3-4*a^2-12*a+12)*q^188 + (2*a^3-5*a^2-13*a+14)*q^189 + (-3*a^2+a+4)*q^190 + (5*a^3-7*a^2-24*a+16)*q^191 + (-4*a^2+8*a+8)*q^192 + (6*a^2-2*a-14)*q^193 + (-4*a^3+4*a^2+14*a+4)*q^194 + (-a^3+2*a^2+3*a-8)*q^195 + (2*a^3+7*a^2+4*a-18)*q^196 + (-3*a^3+4*a^2+19*a-6)*q^197 + (4*a^2-4*a-4)*q^198 + (-a^3-2*a^2+5*a+6)*q^199 + (a^3-4*a)*q^200 +  ...

-------------------------------------------------------
155F (old = 31A), dim = 2

CONGRUENCES:
Modular Degree = 5*7^2
Ker(ModPolar)  = Z/7 + Z/7 + Z/5*7 + Z/5*7
= C(Z/5 + Z/5) + D(Z/7 + Z/7 + Z/7 + Z/7)

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Gamma_0(156)
Weight 2

-------------------------------------------------------
J_0(156), dim = 23

-------------------------------------------------------
156A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= B(Z/2) + C(Z/3 + Z/3) + D(Z/2 + Z/2) + E(Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.2691313408079002833 + -0.39733335692754669355e-4i
Omega-         = 0.40413296580768931409e-4 + -1.5821734663880136508i
L(1)           =
w1             = -2.2691313408079002833 + 0.39733335692754669355e-4i
w2             = -0.40413296580768931409e-4 + 1.5821734663880136508i
c4             = 256.00771776594419145 + -0.23324543389109884373e-1i
c6             = -3680.2144519296173803 + 0.65836655510263763132i
j              = 8963.167099936866634 + -3.1697251309710969339i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -4*q^5 + -2*q^7 + 1*q^9 + -4*q^11 + 1*q^13 + 4*q^15 + 2*q^17 + -2*q^19 + 2*q^21 + 11*q^25 + -1*q^27 + -6*q^29 + -10*q^31 + 4*q^33 + 8*q^35 + 10*q^37 + -1*q^39 + 8*q^41 + 4*q^43 + -4*q^45 + -4*q^47 + -3*q^49 + -2*q^51 + -10*q^53 + 16*q^55 + 2*q^57 + -8*q^59 + -14*q^61 + -2*q^63 + -4*q^65 + 2*q^67 + 16*q^71 + -10*q^73 + -11*q^75 + 8*q^77 + -16*q^79 + 1*q^81 + -8*q^85 + 6*q^87 + -4*q^89 + -2*q^91 + 10*q^93 + 8*q^95 + -2*q^97 + -4*q^99 + 10*q^101 + -8*q^103 + -8*q^105 + 12*q^107 + -2*q^109 + -10*q^111 + 6*q^113 + 1*q^117 + -4*q^119 + 5*q^121 + -8*q^123 + -24*q^125 + 12*q^127 + -4*q^129 + 4*q^131 + 4*q^133 + 4*q^135 + 8*q^137 + 4*q^141 + -4*q^143 + 24*q^145 + 3*q^147 + 18*q^151 + 2*q^153 + 40*q^155 + 2*q^157 + 10*q^159 + 2*q^163 + -16*q^165 + -12*q^167 + 1*q^169 + -2*q^171 + 2*q^173 + -22*q^175 + 8*q^177 + 12*q^179 + 2*q^181 + 14*q^183 + -40*q^185 + -8*q^187 + 2*q^189 + -8*q^191 + -14*q^193 + 4*q^195 + -12*q^197 + 4*q^199 +  ...

-------------------------------------------------------
156B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= A(Z/2) + D(Z/2 + Z/2) + E(Z/2) + F(Z/2 + Z/2) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/2
Sha Bound      = 2*3^2

ANALYTIC INVARIANTS:

Omega+         = 1.3760734135944485049 + -0.1564199574746958311e-4i
Omega-         = 0.87850268996667977299e-4 + -1.3682824606530517913i
L(1)           = 0.68803670684167537487
w1             = -1.3760734135944485049 + 0.1564199574746958311e-4i
w2             = -0.87850268996667977299e-4 + 1.3682824606530517913i
c4             = 640.06525247303874912 + -0.69556447720410142148e-1i
c6             = -348.4599915625721224 + 4.6935675474928002453i
j              = 1728.8003920837317985 + -0.21314359139613414771e-1i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 2*q^7 + 1*q^9 + 1*q^13 + -6*q^17 + 2*q^19 + 2*q^21 + -5*q^25 + 1*q^27 + -6*q^29 + 2*q^31 + 2*q^37 + 1*q^39 + -12*q^41 + -4*q^43 + -3*q^49 + -6*q^51 + 6*q^53 + 2*q^57 + 12*q^59 + 2*q^61 + 2*q^63 + -10*q^67 + 12*q^71 + 14*q^73 + -5*q^75 + 8*q^79 + 1*q^81 + 12*q^83 + -6*q^87 + 2*q^91 + 2*q^93 + -10*q^97 + 18*q^101 + -16*q^103 + -12*q^107 + 14*q^109 + 2*q^111 + 6*q^113 + 1*q^117 + -12*q^119 + -11*q^121 + -12*q^123 + -4*q^127 + -4*q^129 + 12*q^131 + 4*q^133 + -12*q^137 + -16*q^139 + -3*q^147 + 12*q^149 + -10*q^151 + -6*q^153 + 2*q^157 + 6*q^159 + 14*q^163 + -24*q^167 + 1*q^169 + 2*q^171 + -6*q^173 + -10*q^175 + 12*q^177 + 12*q^179 + 2*q^181 + 2*q^183 + 2*q^189 + 2*q^193 + -24*q^197 + 20*q^199 +  ...

-------------------------------------------------------
156C (old = 78A), dim = 1

CONGRUENCES:
Modular Degree = 2^6*3*5^2
Ker(ModPolar)  = Z/2^3*5 + Z/2^3*5 + Z/2^3*3*5 + Z/2^3*3*5
= A(Z/3 + Z/3) + E(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
156D (old = 52A), dim = 1

CONGRUENCES:
Modular Degree = 2^3*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2) + H(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
156E (old = 39A), dim = 1

CONGRUENCES:
Modular Degree = 2^8
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3 + Z/2^3 + Z/2^3
= A(Z/2) + B(Z/2) + C(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2) + D(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
156F (old = 39B), dim = 2

CONGRUENCES:
Modular Degree = 2^7*7^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*7 + Z/2*7 + Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + H(Z/7 + Z/7 + Z/7 + Z/7)

-------------------------------------------------------
156G (old = 26A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3*5^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*5 + Z/2*5 + Z/2*3*5 + Z/2*3*5
= B(Z/3 + Z/3) + C(Z/5 + Z/5 + Z/5 + Z/5) + H(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
156H (old = 26B), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2*7^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3*7 + Z/2*3*7 + Z/2*3*7 + Z/2*3*7
= D(Z/3 + Z/3 + Z/3 + Z/3) + F(Z/7 + Z/7 + Z/7 + Z/7) + G(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(157)
Weight 2

-------------------------------------------------------
J_0(157), dim = 12

-------------------------------------------------------
157A (new) , dim = 5

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 61*397
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 437.24564424519388641 + -0.60936416104352263072e-2i
Omega-         = 0.75395596665881784751e-3 + 28.175390012033807212i
L(1)           =

HECKE EIGENFORM:
a^5+5*a^4+5*a^3-6*a^2-7*a+1 = 0,
f(q) = 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 + (-a^4-5*a^3-3*a^2+5*a)*q^38 + (2*a^4+4*a^3-6*a^2-9*a+3)*q^39 + (-a^4+5*a^2-3*a+2)*q^40 + (-3*a^4-7*a^3+6*a^2+9*a-3)*q^41 + (a^4+a^3+6*a-1)*q^42 + (-a^4+7*a^2+a-8)*q^43 + (-4*a^4-12*a^3-3*a^2+12*a+9)*q^44 + (-3*a^4-12*a^3-6*a^2+13*a+7)*q^45 + (-a^3-3*a^2-4*a+1)*q^46 + (-a^3-2*a^2+a-1)*q^47 + (-5*a^4-9*a^3+11*a^2+11*a-4)*q^48 + (4*a^4+14*a^3-21*a+3)*q^49 + (2*a^4+2*a^3-8*a^2-a+1)*q^50 + (2*a^4+8*a^3-a^2-17*a+2)*q^51 + (-2*a^4-6*a^3-3*a^2+5*a+5)*q^52 + (-5*a^4-15*a^3+2*a^2+16*a-8)*q^53 + (a^4-a^3-4*a^2+4*a)*q^54 + (-6*a^4-25*a^3-13*a^2+35*a+13)*q^55 + (-5*a^4-14*a^3+7*a^2+27*a-5)*q^56 + (2*a^4+6*a^3+4*a^2+a-3)*q^57 + (-2*a^3-2*a^2+5*a-1)*q^58 + (2*a^4+7*a^3-a^2-19*a-3)*q^59 + (a^4+5*a^3+2*a^2-8*a-3)*q^60 + (3*a^3+10*a^2+2*a-8)*q^61 + (8*a^4+24*a^3-3*a^2-26*a+2)*q^62 + (3*a^4+9*a^3-a^2-16*a-5)*q^63 + (10*a^4+31*a^3+a^2-36*a-3)*q^64 + (-4*a^4-15*a^3-6*a^2+18*a+7)*q^65 + (-7*a^4-19*a^3+5*a^2+26*a-3)*q^66 + (5*a^4+16*a^3-3*a^2-28*a-2)*q^67 + (10*a^4+27*a^3-11*a^2-35*a+4)*q^68 + (4*a^4+14*a^3+7*a^2-9*a-1)*q^69 + (4*a^4+16*a^3+4*a^2-25*a+2)*q^70 + (3*a^4+11*a^3+3*a^2-12*a-4)*q^71 + (-12*a^4-31*a^3+8*a^2+33*a-3)*q^72 + (-6*a^3-12*a^2+12*a+9)*q^73 + (-5*a^4-14*a^3+2*a^2+14*a-1)*q^74 + (-a^3+4*a^2+11*a-5)*q^75 + (4*a^3+9*a^2-a-9)*q^76 + (5*a^4+23*a^3+13*a^2-35*a-10)*q^77 + (-6*a^4-16*a^3+3*a^2+17*a-2)*q^78 + (-3*a^4-8*a^3+3*a^2+16*a+10)*q^79 + (a^4+4*a^3+7*a^2+a-13)*q^80 + (-a^4-8*a^3-10*a^2+7*a+5)*q^81 + (8*a^4+21*a^3-9*a^2-24*a+3)*q^82 + (2*a^4+4*a^3-5*a^2-7*a-5)*q^83 + (-6*a^4-17*a^3+18*a+1)*q^84 + (-11*a^4-36*a^3+4*a^2+53*a-8)*q^85 + (5*a^4+12*a^3-5*a^2-15*a+1)*q^86 + (-3*a^3-4*a^2+7*a+1)*q^87 + (2*a^4-a^3-10*a^2+7*a+2)*q^88 + (-9*a^4-31*a^3-a^2+48*a+7)*q^89 + (3*a^4+9*a^3-5*a^2-14*a+3)*q^90 + (a^4+6*a^3+4*a^2-13*a-6)*q^91 + (a^4+7*a^3+8*a^2-5*a-6)*q^92 + (-2*a^4-9*a^3-11*a^2-2*a+7)*q^93 + (-a^4-2*a^3+a^2-a)*q^94 + (2*a^4+13*a^3+16*a^2-16*a-13)*q^95 + (8*a^4+18*a^3-13*a^2-29*a+3)*q^96 + (-a^2+5*a+12)*q^97 + (-6*a^4-20*a^3+3*a^2+31*a-4)*q^98 + (-5*a^4-15*a^3-4*a^2+15*a+12)*q^99 + (-6*a^4-12*a^3+17*a^2+19*a-14)*q^100 + (-a^4-9*a^3-16*a^2+9*a+15)*q^101 + (-2*a^4-11*a^3-5*a^2+16*a-2)*q^102 + (-2*a^4-4*a^3+9*a^2+5*a-10)*q^103 + (2*a^4+a^3-9*a^2-3*a+2)*q^104 + (3*a^4+11*a^3-4*a^2-27*a+9)*q^105 + (10*a^4+27*a^3-14*a^2-43*a+5)*q^106 + (5*a^4+15*a^3+3*a^2-11*a-17)*q^107 + (-6*a^4-11*a^3+12*a^2+15*a-9)*q^108 + (5*a^4+16*a^3-23*a)*q^109 + (5*a^4+17*a^3-a^2-29*a+6)*q^110 + (-a^4+a^3+11*a^2+7*a-5)*q^111 + (5*a^4+12*a^3-9*a^2-18*a+13)*q^112 + (7*a^4+28*a^3+14*a^2-37*a-14)*q^113 + (-4*a^4-6*a^3+13*a^2+11*a-2)*q^114 + (-3*a^4-6*a^3+13*a^2+16*a-13)*q^115 + (-4*a^4-12*a^3-a^2+15*a+4)*q^116 + (-5*a^4-13*a^3+4*a^2+18*a+5)*q^117 + (-3*a^4-11*a^3-7*a^2+11*a-2)*q^118 + (7*a^4+25*a^3-a^2-47*a+7)*q^119 + (-2*a^4-11*a^3-6*a^2+16*a-3)*q^120 + (4*a^4+7*a^3-20*a^2-21*a+20)*q^121 + (3*a^4+10*a^3+2*a^2-8*a)*q^122 + (-2*a^3-3*a^2+a+1)*q^123 + (-12*a^4-39*a^3-6*a^2+40*a+16)*q^124 + (4*a^3+9*a^2-3*a-2)*q^125 + (-6*a^4-16*a^3+2*a^2+16*a-3)*q^126 + (2*a^4+9*a^3+7*a^2-3*a-6)*q^127 + (-9*a^4-23*a^3+12*a^2+29*a-8)*q^128 + (6*a^4+13*a^3-10*a^2-16*a+7)*q^129 + (5*a^4+14*a^3-6*a^2-21*a+4)*q^130 + (6*a^4+13*a^3-21*a^2-31*a+13)*q^131 + (10*a^4+24*a^3-8*a^2-26*a-3)*q^132 + (-5*a^4-18*a^3-2*a^2+33*a+8)*q^133 + (-9*a^4-28*a^3+2*a^2+33*a-5)*q^134 + (a^4+11*a^3+15*a^2-20*a-9)*q^135 + (-15*a^4-45*a^3+7*a^2+60*a-8)*q^136 + (-2*a^4+19*a^2+4*a-20)*q^137 + (-6*a^4-13*a^3+15*a^2+27*a-4)*q^138 + (2*a^4+5*a^3-2*a^2+2*a+10)*q^139 + (-4*a^3-13*a^2-2*a+18)*q^140 + (a^4+5*a^3+4*a^2-4*a+1)*q^141 + (-4*a^4-12*a^3+6*a^2+17*a-3)*q^142 + (2*a^4+2*a^3-12*a^2-7*a+16)*q^143 + (15*a^4+38*a^3-11*a^2-47*a-4)*q^144 + (2*a^4+7*a^3-4*a^2-17*a+12)*q^145 + (-6*a^4-12*a^3+12*a^2+9*a)*q^146 + (-a^4-8*a^3-7*a^2+15*a-2)*q^147 + (9*a^4+27*a^3+2*a^2-28*a-9)*q^148 + (-5*a^4-20*a^3-6*a^2+33*a+4)*q^149 + (-a^4+4*a^3+11*a^2-5*a)*q^150 + (-a^4-3*a^3+a^2+13*a+8)*q^151 + (6*a^4+19*a^3+5*a^2-19*a)*q^152 + (a^3+6*a^2-1)*q^153 + (-2*a^4-12*a^3-5*a^2+25*a-5)*q^154 + (a^4-11*a^3-38*a^2+10*a+34)*q^155 + (10*a^4+25*a^3-7*a^2-26*a)*q^156 + -1*q^157 + (7*a^4+18*a^3-2*a^2-11*a+3)*q^158 + (5*a^4+18*a^3+10*a^2-12*a+5)*q^159 + (a^4+2*a^3-3*a^2-5)*q^160 + (a^4+6*a^3+6*a^2-2*a+9)*q^161 + (-3*a^4-5*a^3+a^2-2*a+1)*q^162 + (10*a^4+33*a^3+8*a^2-35*a-16)*q^163 + (-13*a^4-35*a^3+12*a^2+41*a-2)*q^164 + (8*a^4+30*a^3+8*a^2-45*a-5)*q^165 + (-6*a^4-15*a^3+5*a^2+9*a-2)*q^166 + (-15*a^4-50*a^3-6*a^2+60*a+6)*q^167 + (11*a^4+28*a^3-18*a^2-53*a+8)*q^168 + (a^4+a^3-4*a^2-5)*q^169 + (19*a^4+59*a^3-13*a^2-85*a+11)*q^170 + (-5*a^4-11*a^3+8*a^2+8*a-13)*q^171 + (-11*a^4-30*a^3+a^2+34*a+11)*q^172 + (-2*a^4-12*a^3-16*a^2+10*a+13)*q^173 + (-3*a^4-4*a^3+7*a^2+a)*q^174 + (-9*a^4-34*a^3-7*a^2+58*a+8)*q^175 + (-3*a^4+4*a^3+25*a^2-8*a-20)*q^176 + (-8*a^4-20*a^3+18*a^2+47*a-3)*q^177 + (14*a^4+44*a^3-6*a^2-56*a+9)*q^178 + (6*a^4+20*a^3+6*a^2-21*a-17)*q^179 + (4*a^3+16*a^2-2*a-17)*q^180 + (-5*a^4-10*a^3+13*a^2+15*a-7)*q^181 + (a^4-a^3-7*a^2+a-1)*q^182 + (-2*a^4-9*a^3-11*a^2-a+5)*q^183 + (2*a^4+5*a^3+7*a^2+9*a-3)*q^184 + (a^4+10*a^3+20*a^2-8*a-20)*q^185 + (a^4-a^3-14*a^2-7*a+2)*q^186 + (6*a^4+26*a^3+7*a^2-46*a+4)*q^187 + (3*a^4+8*a^3-3*a^2-9*a+3)*q^188 + (-10*a^4-34*a^3-4*a^2+50*a+3)*q^189 + (3*a^4+6*a^3-4*a^2+a-2)*q^190 + (-3*a^4-19*a^3-20*a^2+23*a+9)*q^191 + (-12*a^4-35*a^3-3*a^2+37*a)*q^192 + (-6*a^4-15*a^3+2*a^2+5*a-1)*q^193 + (-a^3+5*a^2+12*a)*q^194 + (3*a^4+12*a^3+7*a^2-14*a-4)*q^195 + (2*a^4+5*a^3-5*a^2-4*a)*q^196 + (-8*a^4-35*a^3-24*a^2+38*a+17)*q^197 + (10*a^4+21*a^3-15*a^2-23*a+5)*q^198 + (-a^4-9*a^3-22*a^2-8*a+21)*q^199 + (14*a^4+43*a^3-a^2-54*a+4)*q^200 +  ...

-------------------------------------------------------
157B (new) , dim = 7

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^3*48795779
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 13
Torsion Bound  = 13
|L(1)/Omega|   = 2^5/13
Sha Bound      = 2^5*13

ANALYTIC INVARIANTS:

Omega+         = 6.3790395172645483901 + -0.26591126557676979487e-3i
Omega-         = 0.10243587404154710267e-1 + 334.89202295501309644i
L(1)           = 15.702251133062953481

HECKE EIGENFORM:
a^7-5*a^6+2*a^5+21*a^4-22*a^3-21*a^2+27*a-1 = 0,
f(q) = 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 + (6*a^6-20*a^5-23*a^4+97*a^3+19*a^2-111*a+4)*q^38 + (a^6-4*a^5-4*a^4+25*a^3-a^2-33*a+4)*q^39 + (-4*a^6+13*a^5+14*a^4-61*a^3-9*a^2+70*a-3)*q^40 + (2*a^5-5*a^4-9*a^3+16*a^2+13*a-5)*q^41 + (a^5-2*a^4-4*a^3+4*a^2+3*a)*q^42 + (-2*a^6+8*a^5+a^4-30*a^3+13*a^2+29*a-8)*q^43 + (a^2-3)*q^44 + (4*a^6-15*a^5-10*a^4+69*a^3-82*a)*q^45 + (a^6-4*a^5+12*a^3-4*a^2-4*a)*q^46 + (a^6-5*a^5+a^4+21*a^3-13*a^2-20*a+11)*q^47 + (-3*a^4+11*a^3+a^2-25*a+6)*q^48 + (a^6-4*a^5-2*a^4+19*a^3-3*a^2-21*a)*q^49 + (-a^6+5*a^5+a^4-24*a^3+5*a^2+26*a-1)*q^50 + (a^6-6*a^5+6*a^4+15*a^3-16*a^2-7*a-3)*q^51 + (a^6-2*a^5-6*a^4+9*a^3+10*a^2-9*a-4)*q^52 + (a^6-4*a^5-3*a^4+20*a^3+3*a^2-26*a-1)*q^53 + (-7*a^6+24*a^5+23*a^4-110*a^3-15*a^2+126*a-5)*q^54 + (2*a^6-8*a^5-4*a^4+37*a^3-5*a^2-43*a+5)*q^55 + (-a^5+7*a^3+a^2-10*a)*q^56 + (7*a^6-26*a^5-18*a^4+115*a^3+7*a^2-129*a-2)*q^57 + (-7*a^6+24*a^5+22*a^4-105*a^3-13*a^2+109*a-4)*q^58 + (-2*a^6+7*a^5+3*a^4-20*a^3-a^2+8*a+8)*q^59 + (a^5-2*a^4-6*a^3+8*a^2+9*a-6)*q^60 + (-4*a^6+13*a^5+17*a^4-68*a^3-14*a^2+85*a-7)*q^61 + (3*a^6-11*a^5-7*a^4+46*a^3-49*a+2)*q^62 + (a^6-3*a^5-4*a^4+13*a^3+6*a^2-13*a-3)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (-a^6+4*a^5+2*a^4-18*a^3-a^2+22*a+4)*q^65 + (-3*a^6+12*a^5+5*a^4-52*a^3+8*a^2+54*a-2)*q^66 + (a^4-7*a^2-4*a+10)*q^67 + (2*a^6-6*a^5-6*a^4+23*a^3+a^2-21*a+6)*q^68 + (a^5-a^4-9*a^3+5*a^2+20*a-6)*q^69 + (-2*a^6+7*a^5+7*a^4-31*a^3-6*a^2+32*a-1)*q^70 + (2*a^6-5*a^5-14*a^4+34*a^3+17*a^2-49*a+13)*q^71 + (5*a^6-20*a^5-10*a^4+88*a^3-5*a^2-99*a+4)*q^72 + (a^6-3*a^5-5*a^4+18*a^3-a^2-21*a+13)*q^73 + (-2*a^6+5*a^5+12*a^4-31*a^3-14*a^2+43*a-2)*q^74 + (-5*a^6+19*a^5+9*a^4-77*a^3+7*a^2+78*a-3)*q^75 + (2*a^6-7*a^5-5*a^4+29*a^3-3*a^2-28*a+12)*q^76 + (-a^4+3*a^3+a^2-7*a+4)*q^77 + (a^6-6*a^5+4*a^4+21*a^3-12*a^2-23*a+1)*q^78 + (-2*a^5+5*a^4+6*a^3-9*a^2-6*a-6)*q^79 + (-5*a^6+16*a^5+17*a^4-71*a^3-16*a^2+77*a+6)*q^80 + (-3*a^6+12*a^5+9*a^4-63*a^3-a^2+83*a-6)*q^81 + (2*a^6-5*a^5-9*a^4+16*a^3+13*a^2-5*a)*q^82 + (4*a^6-13*a^5-13*a^4+55*a^3+9*a^2-56*a+8)*q^83 + (a^6-2*a^5-6*a^4+8*a^3+11*a^2-8*a-6)*q^84 + (-a^6+4*a^5+3*a^4-23*a^3+3*a^2+31*a-7)*q^85 + (-2*a^6+5*a^5+12*a^4-31*a^3-13*a^2+46*a-2)*q^86 + (-5*a^6+19*a^5+13*a^4-87*a^3-3*a^2+96*a+1)*q^87 + (2*a^6-6*a^5-12*a^4+39*a^3+16*a^2-59*a+2)*q^88 + (6*a^6-23*a^5-12*a^4+98*a^3-11*a^2-99*a+14)*q^89 + (5*a^6-18*a^5-15*a^4+88*a^3+2*a^2-108*a+4)*q^90 + (a^6-3*a^5-4*a^4+14*a^3+a^2-16*a+6)*q^91 + (a^6-4*a^5-a^4+18*a^3-7*a^2-19*a+9)*q^92 + (4*a^6-15*a^5-13*a^4+78*a^3+a^2-97*a+8)*q^93 + (-a^5+9*a^3+a^2-16*a+1)*q^94 + (-a^6+6*a^5-2*a^4-32*a^3+21*a^2+46*a-14)*q^95 + (-4*a^6+13*a^5+15*a^4-61*a^3-11*a^2+68*a-2)*q^96 + (-a^6+4*a^5+4*a^4-23*a^3+2*a^2+23*a-13)*q^97 + (a^6-4*a^5-2*a^4+19*a^3-27*a+1)*q^98 + (-5*a^6+19*a^5+12*a^4-87*a^3+3*a^2+102*a-6)*q^99 + (2*a^6-5*a^5-9*a^4+23*a^3+9*a^2-26*a+1)*q^100 + (-5*a^6+13*a^5+30*a^4-71*a^3-49*a^2+86*a+11)*q^101 + (-a^6+4*a^5-6*a^4+6*a^3+14*a^2-30*a+1)*q^102 + (5*a^6-20*a^5-6*a^4+79*a^3-14*a^2-77*a+3)*q^103 + (-a^6+6*a^5-4*a^4-20*a^3+14*a^2+17*a-1)*q^104 + (a^4-a^3-6*a^2+a+7)*q^105 + (a^6-5*a^5-a^4+25*a^3-5*a^2-28*a+1)*q^106 + (-5*a^6+16*a^5+21*a^4-80*a^3-16*a^2+93*a-6)*q^107 + (-a^6+a^5+9*a^4-5*a^3-21*a^2+4*a+11)*q^108 + (6*a^6-19*a^5-28*a^4+101*a^3+32*a^2-126*a-3)*q^109 + (2*a^6-8*a^5-5*a^4+39*a^3-a^2-49*a+2)*q^110 + (-3*a^6+13*a^5+2*a^4-55*a^3+16*a^2+64*a-15)*q^111 + (3*a^6-12*a^5-7*a^4+53*a^3-4*a^2-54*a+12)*q^112 + (-a^5+4*a^4-3*a^3-4*a^2+14*a-9)*q^113 + (9*a^6-32*a^5-32*a^4+161*a^3+18*a^2-191*a+7)*q^114 + (3*a^6-11*a^5-10*a^4+52*a^3+10*a^2-59*a-7)*q^115 + (-3*a^6+10*a^5+10*a^4-43*a^3-4*a^2+43*a-9)*q^116 + (3*a^6-10*a^5-15*a^4+60*a^3+13*a^2-80*a)*q^117 + (-3*a^6+7*a^5+22*a^4-45*a^3-34*a^2+62*a-2)*q^118 + (a^6-2*a^5-7*a^4+10*a^3+14*a^2-13*a-6)*q^119 + (-7*a^6+26*a^5+20*a^4-124*a^3-3*a^2+146*a-6)*q^120 + (-3*a^6+13*a^5-a^4-45*a^3+21*a^2+32*a-10)*q^121 + (-7*a^6+25*a^5+16*a^4-102*a^3+a^2+101*a-4)*q^122 + (-8*a^6+29*a^5+23*a^4-137*a^3-a^2+166*a-12)*q^123 + (a^5-3*a^4-4*a^3+10*a^2+5*a-7)*q^124 + (-3*a^6+12*a^5+4*a^4-49*a^3+10*a^2+47*a-13)*q^125 + (2*a^6-6*a^5-8*a^4+28*a^3+8*a^2-30*a+1)*q^126 + (-5*a^6+13*a^5+29*a^4-69*a^3-46*a^2+82*a+10)*q^127 + (5*a^6-14*a^5-21*a^4+62*a^3+21*a^2-59*a+1)*q^128 + (-3*a^6+14*a^5+2*a^4-66*a^3+17*a^2+86*a-12)*q^129 + (-a^6+4*a^5+3*a^4-23*a^3+a^2+31*a-1)*q^130 + (8*a^6-27*a^5-23*a^4+114*a^3+a^2-106*a+20)*q^131 + (a^6-3*a^5-5*a^4+16*a^3+7*a^2-21*a-3)*q^132 + (-5*a^6+18*a^5+15*a^4-83*a^3-3*a^2+89*a-17)*q^133 + (a^5-7*a^3-4*a^2+10*a)*q^134 + (5*a^6-20*a^5-11*a^4+94*a^3-2*a^2-116*a-8)*q^135 + (2*a^5-3*a^4-11*a^3+11*a^2+10*a)*q^136 + (5*a^6-19*a^5-13*a^4+88*a^3-99*a+6)*q^137 + (a^6-a^5-9*a^4+5*a^3+20*a^2-6*a)*q^138 + (-2*a^6+7*a^5+13*a^4-50*a^3-16*a^2+71*a-5)*q^139 + (-a^6+5*a^5+a^4-22*a^3+8*a^2+23*a-12)*q^140 + (4*a^6-13*a^5-16*a^4+66*a^3+8*a^2-81*a+16)*q^141 + (5*a^6-18*a^5-8*a^4+61*a^3-7*a^2-41*a+2)*q^142 + (2*a^6-7*a^5-7*a^4+35*a^3+4*a^2-46*a+5)*q^143 + (5*a^6-18*a^5-21*a^4+97*a^3+18*a^2-121*a-1)*q^144 + (-2*a^6+4*a^5+12*a^4-15*a^3-24*a^2+7*a+8)*q^145 + (2*a^6-7*a^5-3*a^4+21*a^3-14*a+1)*q^146 + (4*a^6-13*a^5-20*a^4+77*a^3+19*a^2-106*a+3)*q^147 + (-a^6+9*a^4+2*a^3-25*a^2-4*a+20)*q^148 + (-a^6+2*a^5+3*a^4-a^3-3*a^2-7*a-9)*q^149 + (-6*a^6+19*a^5+28*a^4-103*a^3-27*a^2+132*a-5)*q^150 + (2*a^6-7*a^5-6*a^4+32*a^3-a^2-32*a+5)*q^151 + (-9*a^6+31*a^5+33*a^4-153*a^3-24*a^2+180*a-6)*q^152 + (4*a^6-17*a^5-a^4+62*a^3-18*a^2-61*a+6)*q^153 + (-a^5+3*a^4+a^3-7*a^2+4*a)*q^154 + (-3*a^6+12*a^5+7*a^4-56*a^3-a^2+68*a+5)*q^155 + (-3*a^6+10*a^5+8*a^4-40*a^3+40*a-7)*q^156 + 1*q^157 + (-2*a^6+5*a^5+6*a^4-9*a^3-6*a^2-6*a)*q^158 + (6*a^6-22*a^5-13*a^4+90*a^3-2*a^2-92*a+1)*q^159 + (-a^6+a^5+6*a^4-4*a^3-10*a^2+a+1)*q^160 + (-5*a^6+17*a^5+14*a^4-72*a^3-a^2+71*a-13)*q^161 + (-3*a^6+15*a^5-67*a^3+20*a^2+75*a-3)*q^162 + (-2*a^6+8*a^5+6*a^4-37*a^3-10*a^2+37*a+14)*q^163 + (5*a^6-17*a^5-16*a^4+75*a^3+5*a^2-80*a+12)*q^164 + (7*a^6-26*a^5-20*a^4+125*a^3+a^2-151*a+10)*q^165 + (7*a^6-21*a^5-29*a^4+97*a^3+28*a^2-100*a+4)*q^166 + (-7*a^6+21*a^5+34*a^4-110*a^3-39*a^2+133*a-2)*q^167 + (3*a^6-10*a^5-9*a^4+41*a^3+5*a^2-39*a+1)*q^168 + (-2*a^6+5*a^5+14*a^4-34*a^3-18*a^2+45*a-10)*q^169 + (-a^6+5*a^5-2*a^4-19*a^3+10*a^2+20*a-1)*q^170 + (8*a^6-33*a^5-10*a^4+142*a^3-28*a^2-165*a+14)*q^171 + (-a^6+9*a^4+3*a^3-22*a^2-6*a+14)*q^172 + (-9*a^6+35*a^5+13*a^4-140*a^3+29*a^2+137*a-27)*q^173 + (-6*a^6+23*a^5+18*a^4-113*a^3-9*a^2+136*a-5)*q^174 + (2*a^6-7*a^5-6*a^4+29*a^3+3*a^2-27*a+1)*q^175 + (4*a^6-16*a^5-3*a^4+60*a^3-19*a^2-52*a+8)*q^176 + (3*a^6-10*a^5-8*a^4+43*a^3-9*a^2-39*a+12)*q^177 + (7*a^6-24*a^5-28*a^4+121*a^3+27*a^2-148*a+6)*q^178 + (a^6-3*a^5+a^4-4*a^3+a^2+30*a-9)*q^179 + (-a^6+5*a^5+3*a^4-26*a^3-3*a^2+33*a+5)*q^180 + (-7*a^6+24*a^5+19*a^4-103*a^3+4*a^2+107*a-26)*q^181 + (2*a^6-6*a^5-7*a^4+23*a^3+5*a^2-21*a+1)*q^182 + (-8*a^6+30*a^5+22*a^4-143*a^3+3*a^2+163*a-11)*q^183 + (-a^6+5*a^5-3*a^4-9*a^3+10*a^2-10*a+1)*q^184 + (3*a^6-9*a^5-14*a^4+46*a^3+23*a^2-57*a-20)*q^185 + (5*a^6-21*a^5-6*a^4+89*a^3-13*a^2-100*a+4)*q^186 + (a^6-a^5-15*a^4+24*a^3+30*a^2-51*a-2)*q^187 + (-3*a^6+10*a^5+7*a^4-41*a^3+10*a^2+41*a-22)*q^188 + (a^6-3*a^5-7*a^4+18*a^3+19*a^2-23*a-13)*q^189 + (a^6-11*a^4-a^3+25*a^2+13*a-1)*q^190 + (2*a^5-9*a^4-a^3+34*a^2-9*a-25)*q^191 + (-7*a^6+23*a^5+29*a^4-121*a^3-18*a^2+156*a-16)*q^192 + (-a^6+7*a^5-9*a^4-15*a^3+17*a^2+21)*q^193 + (-a^6+6*a^5-2*a^4-20*a^3+2*a^2+14*a-1)*q^194 + (-6*a^6+22*a^5+15*a^4-96*a^3-3*a^2+108*a+2)*q^195 + (-a^6+4*a^5+2*a^4-16*a^3+16*a+1)*q^196 + (4*a^6-13*a^5-17*a^4+70*a^3+8*a^2-95*a+24)*q^197 + (-6*a^6+22*a^5+18*a^4-107*a^3-3*a^2+129*a-5)*q^198 + (-6*a^6+25*a^5+8*a^4-108*a^3+20*a^2+113*a-12)*q^199 + (7*a^6-23*a^5-21*a^4+101*a^3+6*a^2-105*a+4)*q^200 +  ...

-------------------------------------------------------
Gamma_0(158)
Weight 2

-------------------------------------------------------
J_0(158), dim = 19

-------------------------------------------------------
158A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.6687213233468265557 + 0.13074413233062488345e-3i
Omega-         = 0.54184882276043249133e-4 + 1.7496878727716680686i
L(1)           =
w1             = -2.6687213233468265557 + -0.13074413233062488345e-3i
w2             = 0.54184882276043249133e-4 + 1.7496878727716680686i
c4             = 169.04408390978252215 + 0.18831537891379311504e-1i
c6             = -2069.8578603792657416 + -0.44188817867337870716i
j              = 15280.292221664577267 + 11.118006425042307266i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + 1*q^4 + -1*q^5 + 1*q^6 + -3*q^7 + -1*q^8 + -2*q^9 + 1*q^10 + 4*q^11 + -1*q^12 + -7*q^13 + 3*q^14 + 1*q^15 + 1*q^16 + -4*q^17 + 2*q^18 + -6*q^19 + -1*q^20 + 3*q^21 + -4*q^22 + 6*q^23 + 1*q^24 + -4*q^25 + 7*q^26 + 5*q^27 + -3*q^28 + 4*q^29 + -1*q^30 + 8*q^31 + -1*q^32 + -4*q^33 + 4*q^34 + 3*q^35 + -2*q^36 + 10*q^37 + 6*q^38 + 7*q^39 + 1*q^40 + -8*q^41 + -3*q^42 + -8*q^43 + 4*q^44 + 2*q^45 + -6*q^46 + -3*q^47 + -1*q^48 + 2*q^49 + 4*q^50 + 4*q^51 + -7*q^52 + 2*q^53 + -5*q^54 + -4*q^55 + 3*q^56 + 6*q^57 + -4*q^58 + 1*q^59 + 1*q^60 + -8*q^62 + 6*q^63 + 1*q^64 + 7*q^65 + 4*q^66 + -4*q^67 + -4*q^68 + -6*q^69 + -3*q^70 + -11*q^71 + 2*q^72 + -6*q^73 + -10*q^74 + 4*q^75 + -6*q^76 + -12*q^77 + -7*q^78 + -1*q^79 + -1*q^80 + 1*q^81 + 8*q^82 + 6*q^83 + 3*q^84 + 4*q^85 + 8*q^86 + -4*q^87 + -4*q^88 + -15*q^89 + -2*q^90 + 21*q^91 + 6*q^92 + -8*q^93 + 3*q^94 + 6*q^95 + 1*q^96 + 1*q^97 + -2*q^98 + -8*q^99 + -4*q^100 + 5*q^101 + -4*q^102 + 1*q^103 + 7*q^104 + -3*q^105 + -2*q^106 + 5*q^107 + 5*q^108 + -14*q^109 + 4*q^110 + -10*q^111 + -3*q^112 + -10*q^113 + -6*q^114 + -6*q^115 + 4*q^116 + 14*q^117 + -1*q^118 + 12*q^119 + -1*q^120 + 5*q^121 + 8*q^123 + 8*q^124 + 9*q^125 + -6*q^126 + -13*q^127 + -1*q^128 + 8*q^129 + -7*q^130 + 18*q^131 + -4*q^132 + 18*q^133 + 4*q^134 + -5*q^135 + 4*q^136 + -12*q^137 + 6*q^138 + -5*q^139 + 3*q^140 + 3*q^141 + 11*q^142 + -28*q^143 + -2*q^144 + -4*q^145 + 6*q^146 + -2*q^147 + 10*q^148 + 16*q^149 + -4*q^150 + -4*q^151 + 6*q^152 + 8*q^153 + 12*q^154 + -8*q^155 + 7*q^156 + 1*q^158 + -2*q^159 + 1*q^160 + -18*q^161 + -1*q^162 + 4*q^163 + -8*q^164 + 4*q^165 + -6*q^166 + 8*q^167 + -3*q^168 + 36*q^169 + -4*q^170 + 12*q^171 + -8*q^172 + 14*q^173 + 4*q^174 + 12*q^175 + 4*q^176 + -1*q^177 + 15*q^178 + -14*q^179 + 2*q^180 + -6*q^181 + -21*q^182 + -6*q^184 + -10*q^185 + 8*q^186 + -16*q^187 + -3*q^188 + -15*q^189 + -6*q^190 + 3*q^191 + -1*q^192 + -22*q^193 + -1*q^194 + -7*q^195 + 2*q^196 + -18*q^197 + 8*q^198 + -15*q^199 + 4*q^200 +  ...

-------------------------------------------------------
158B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*5
Ker(ModPolar)  = Z/2^3*5 + Z/2^3*5
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/5 + Z/5) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 2/3
Sha Bound      = 2*3

ANALYTIC INVARIANTS:

Omega+         = 0.84261057228243128054 + -0.17227769166509667799e-4i
Omega-         = 0.3333824932728679425e-4 + -0.91397629898967044311i
L(1)           = 0.56174038163903216254
w1             = -0.3333824932728679425e-4 + 0.91397629898967044311i
w2             = 0.84261057228243128054 + -0.17227769166509667799e-4i
c4             = 3913.7365681493030876 + -0.19236587468472030997e-2i
c6             = 73414.315866574917717 + 48.575389003790614356i
j              = 1898.7040185395042793 + 0.24848874951257655469i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + 3*q^5 + -1*q^6 + -1*q^7 + -1*q^8 + -2*q^9 + -3*q^10 + 1*q^12 + 5*q^13 + 1*q^14 + 3*q^15 + 1*q^16 + 2*q^18 + 2*q^19 + 3*q^20 + -1*q^21 + -6*q^23 + -1*q^24 + 4*q^25 + -5*q^26 + -5*q^27 + -1*q^28 + -3*q^30 + -4*q^31 + -1*q^32 + -3*q^35 + -2*q^36 + 2*q^37 + -2*q^38 + 5*q^39 + -3*q^40 + -12*q^41 + 1*q^42 + 8*q^43 + -6*q^45 + 6*q^46 + -9*q^47 + 1*q^48 + -6*q^49 + -4*q^50 + 5*q^52 + 6*q^53 + 5*q^54 + 1*q^56 + 2*q^57 + -9*q^59 + 3*q^60 + 8*q^61 + 4*q^62 + 2*q^63 + 1*q^64 + 15*q^65 + -4*q^67 + -6*q^69 + 3*q^70 + -9*q^71 + 2*q^72 + 2*q^73 + -2*q^74 + 4*q^75 + 2*q^76 + -5*q^78 + 1*q^79 + 3*q^80 + 1*q^81 + 12*q^82 + 18*q^83 + -1*q^84 + -8*q^86 + 9*q^89 + 6*q^90 + -5*q^91 + -6*q^92 + -4*q^93 + 9*q^94 + 6*q^95 + -1*q^96 + 17*q^97 + 6*q^98 + 4*q^100 + -15*q^101 + -13*q^103 + -5*q^104 + -3*q^105 + -6*q^106 + 3*q^107 + -5*q^108 + 2*q^109 + 2*q^111 + -1*q^112 + 18*q^113 + -2*q^114 + -18*q^115 + -10*q^117 + 9*q^118 + -3*q^120 + -11*q^121 + -8*q^122 + -12*q^123 + -4*q^124 + -3*q^125 + -2*q^126 + -7*q^127 + -1*q^128 + 8*q^129 + -15*q^130 + 6*q^131 + -2*q^133 + 4*q^134 + -15*q^135 + 12*q^137 + 6*q^138 + 5*q^139 + -3*q^140 + -9*q^141 + 9*q^142 + -2*q^144 + -2*q^146 + -6*q^147 + 2*q^148 + 12*q^149 + -4*q^150 + 8*q^151 + -2*q^152 + -12*q^155 + 5*q^156 + -4*q^157 + -1*q^158 + 6*q^159 + -3*q^160 + 6*q^161 + -1*q^162 + 20*q^163 + -12*q^164 + -18*q^166 + 12*q^167 + 1*q^168 + 12*q^169 + -4*q^171 + 8*q^172 + -6*q^173 + -4*q^175 + -9*q^177 + -9*q^178 + 18*q^179 + -6*q^180 + 2*q^181 + 5*q^182 + 8*q^183 + 6*q^184 + 6*q^185 + 4*q^186 + -9*q^188 + 5*q^189 + -6*q^190 + -15*q^191 + 1*q^192 + -22*q^193 + -17*q^194 + 15*q^195 + -6*q^196 + 6*q^197 + 11*q^199 + -4*q^200 +  ...

-------------------------------------------------------
158C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^4*3 + Z/2^4*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/3 + Z/3) + E(Z/2 + Z/2) + G(Z/2^2 + Z/2^2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 5
Torsion Bound  = 5
|L(1)/Omega|   = 2^2/5
Sha Bound      = 2^2*5

ANALYTIC INVARIANTS:

Omega+         = 0.96523700409782264806 + 0.35982482679321301234e-4i
Omega-         = 0.46221029131120809212e-4 + 0.52765753537271980239i
L(1)           = 0.77218960381480574512
w1             = 0.96523700409782264806 + 0.35982482679321301234e-4i
w2             = -0.46221029131120809212e-4 + -0.52765753537271980239i
c4             = 20154.505592829505587 + 6.9912582382501982929i
c6             = -2836145.7291980775532 + -1511.6568075998339465i
j              = 98846.462029375028886 + 140.79904587822469849i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + 1*q^5 + -1*q^6 + 3*q^7 + 1*q^8 + -2*q^9 + 1*q^10 + 2*q^11 + -1*q^12 + -1*q^13 + 3*q^14 + -1*q^15 + 1*q^16 + -2*q^17 + -2*q^18 + 1*q^20 + -3*q^21 + 2*q^22 + -6*q^23 + -1*q^24 + -4*q^25 + -1*q^26 + 5*q^27 + 3*q^28 + -10*q^29 + -1*q^30 + 2*q^31 + 1*q^32 + -2*q^33 + -2*q^34 + 3*q^35 + -2*q^36 + -2*q^37 + 1*q^39 + 1*q^40 + 2*q^41 + -3*q^42 + 4*q^43 + 2*q^44 + -2*q^45 + -6*q^46 + 3*q^47 + -1*q^48 + 2*q^49 + -4*q^50 + 2*q^51 + -1*q^52 + 4*q^53 + 5*q^54 + 2*q^55 + 3*q^56 + -10*q^58 + 5*q^59 + -1*q^60 + 12*q^61 + 2*q^62 + -6*q^63 + 1*q^64 + -1*q^65 + -2*q^66 + 8*q^67 + -2*q^68 + 6*q^69 + 3*q^70 + -13*q^71 + -2*q^72 + -6*q^73 + -2*q^74 + 4*q^75 + 6*q^77 + 1*q^78 + -1*q^79 + 1*q^80 + 1*q^81 + 2*q^82 + -6*q^83 + -3*q^84 + -2*q^85 + 4*q^86 + 10*q^87 + 2*q^88 + -15*q^89 + -2*q^90 + -3*q^91 + -6*q^92 + -2*q^93 + 3*q^94 + -1*q^96 + 13*q^97 + 2*q^98 + -4*q^99 + -4*q^100 + 7*q^101 + 2*q^102 + 19*q^103 + -1*q^104 + -3*q^105 + 4*q^106 + 13*q^107 + 5*q^108 + 10*q^109 + 2*q^110 + 2*q^111 + 3*q^112 + 4*q^113 + -6*q^115 + -10*q^116 + 2*q^117 + 5*q^118 + -6*q^119 + -1*q^120 + -7*q^121 + 12*q^122 + -2*q^123 + 2*q^124 + -9*q^125 + -6*q^126 + -7*q^127 + 1*q^128 + -4*q^129 + -1*q^130 + -18*q^131 + -2*q^132 + 8*q^134 + 5*q^135 + -2*q^136 + -12*q^137 + 6*q^138 + -5*q^139 + 3*q^140 + -3*q^141 + -13*q^142 + -2*q^143 + -2*q^144 + -10*q^145 + -6*q^146 + -2*q^147 + -2*q^148 + -10*q^149 + 4*q^150 + 2*q^151 + 4*q^153 + 6*q^154 + 2*q^155 + 1*q^156 + 18*q^157 + -1*q^158 + -4*q^159 + 1*q^160 + -18*q^161 + 1*q^162 + 4*q^163 + 2*q^164 + -2*q^165 + -6*q^166 + -2*q^167 + -3*q^168 + -12*q^169 + -2*q^170 + 4*q^172 + 4*q^173 + 10*q^174 + -12*q^175 + 2*q^176 + -5*q^177 + -15*q^178 + 20*q^179 + -2*q^180 + -18*q^181 + -3*q^182 + -12*q^183 + -6*q^184 + -2*q^185 + -2*q^186 + -4*q^187 + 3*q^188 + 15*q^189 + -3*q^191 + -1*q^192 + 14*q^193 + 13*q^194 + 1*q^195 + 2*q^196 + 18*q^197 + -4*q^198 + 15*q^199 + -4*q^200 +  ...

-------------------------------------------------------
158D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/3 + Z/3) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 3.8328755635799255422 + 0.34967203811527551859e-4i
Omega-         = 0.18964918148221250909e-3 + 2.7832341286397744335i
L(1)           = 1.9164377818697139476
w1             = 1.9165326063807038774 + 1.3916345479217929805i
w2             = 1.9163429571992216649 + -1.391599580717981453i
c4             = -46.995976258894519392 + 0.85627153299350134034e-2i
c6             = -665.01571533125973281 + -0.19929035127140800617i
j              = 328.47276756726658733 + -0.30486385233097393399i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 2*q^3 + 1*q^4 + -2*q^5 + 2*q^6 + 1*q^8 + 1*q^9 + -2*q^10 + -4*q^11 + 2*q^12 + 2*q^13 + -4*q^15 + 1*q^16 + -2*q^17 + 1*q^18 + -2*q^20 + -4*q^22 + 2*q^24 + -1*q^25 + 2*q^26 + -4*q^27 + 8*q^29 + -4*q^30 + 8*q^31 + 1*q^32 + -8*q^33 + -2*q^34 + 1*q^36 + 4*q^37 + 4*q^39 + -2*q^40 + -10*q^41 + -2*q^43 + -4*q^44 + -2*q^45 + 2*q^48 + -7*q^49 + -1*q^50 + -4*q^51 + 2*q^52 + -8*q^53 + -4*q^54 + 8*q^55 + 8*q^58 + 14*q^59 + -4*q^60 + 8*q^62 + 1*q^64 + -4*q^65 + -8*q^66 + 8*q^67 + -2*q^68 + 8*q^71 + 1*q^72 + 6*q^73 + 4*q^74 + -2*q^75 + 4*q^78 + -1*q^79 + -2*q^80 + -11*q^81 + -10*q^82 + 12*q^83 + 4*q^85 + -2*q^86 + 16*q^87 + -4*q^88 + 6*q^89 + -2*q^90 + 16*q^93 + 2*q^96 + 10*q^97 + -7*q^98 + -4*q^99 + -1*q^100 + -14*q^101 + -4*q^102 + -8*q^103 + 2*q^104 + -8*q^106 + -14*q^107 + -4*q^108 + 4*q^109 + 8*q^110 + 8*q^111 + -14*q^113 + 8*q^116 + 2*q^117 + 14*q^118 + -4*q^120 + 5*q^121 + -20*q^123 + 8*q^124 + 12*q^125 + 8*q^127 + 1*q^128 + -4*q^129 + -4*q^130 + -8*q^132 + 8*q^134 + 8*q^135 + -2*q^136 + -18*q^137 + 22*q^139 + 8*q^142 + -8*q^143 + 1*q^144 + -16*q^145 + 6*q^146 + -14*q^147 + 4*q^148 + -16*q^149 + -2*q^150 + -16*q^151 + -2*q^153 + -16*q^155 + 4*q^156 + 12*q^157 + -1*q^158 + -16*q^159 + -2*q^160 + -11*q^162 + -20*q^163 + -10*q^164 + 16*q^165 + 12*q^166 + 16*q^167 + -9*q^169 + 4*q^170 + -2*q^172 + -20*q^173 + 16*q^174 + -4*q^176 + 28*q^177 + 6*q^178 + -4*q^179 + -2*q^180 + -18*q^181 + -8*q^185 + 16*q^186 + 8*q^187 + -12*q^191 + 2*q^192 + 14*q^193 + 10*q^194 + -8*q^195 + -7*q^196 + 12*q^197 + -4*q^198 + -12*q^199 + -1*q^200 +  ...

-------------------------------------------------------
158E (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^5 + Z/2^5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2^3 + Z/2^3)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 1.7907221959657011547 + 0.67805448108977399382e-4i
Omega-         = 0.17047183268100876692e-4 + 1.4196351237381823343i
L(1)           =
w1             = -1.7907221959657011547 + -0.67805448108977399382e-4i
w2             = 0.17047183268100876692e-4 + 1.4196351237381823343i
c4             = 417.10686425868646398 + 0.6794252139029751573e-2i
c6             = -6131.1594486963011826 + -0.99583981636511220813i
j              = 3585.1812102559457402 + 1.0634008963781644242i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -3*q^3 + 1*q^4 + -3*q^5 + -3*q^6 + -3*q^7 + 1*q^8 + 6*q^9 + -3*q^10 + -2*q^11 + -3*q^12 + -5*q^13 + -3*q^14 + 9*q^15 + 1*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 + 1*q^32 + 6*q^33 + 6*q^34 + 9*q^35 + 6*q^36 + -10*q^37 + 15*q^39 + -3*q^40 + 2*q^41 + 9*q^42 + 4*q^43 + -2*q^44 + -18*q^45 + -2*q^46 + -3*q^47 + -3*q^48 + 2*q^49 + 4*q^50 + -18*q^51 + -5*q^52 + -12*q^53 + -9*q^54 + 6*q^55 + -3*q^56 + 6*q^58 + -1*q^59 + 9*q^60 + 12*q^61 + -10*q^62 + -18*q^63 + 1*q^64 + 15*q^65 + 6*q^66 + -8*q^67 + 6*q^68 + 6*q^69 + 9*q^70 + -3*q^71 + 6*q^72 + -6*q^73 + -10*q^74 + -12*q^75 + 6*q^77 + 15*q^78 + 1*q^79 + -3*q^80 + 9*q^81 + 2*q^82 + 14*q^83 + 9*q^84 + -18*q^85 + 4*q^86 + -18*q^87 + -2*q^88 + -7*q^89 + -18*q^90 + 15*q^91 + -2*q^92 + 30*q^93 + -3*q^94 + -3*q^96 + -11*q^97 + 2*q^98 + -12*q^99 + 4*q^100 + 3*q^101 + -18*q^102 + 13*q^103 + -5*q^104 + -27*q^105 + -12*q^106 + -1*q^107 + -9*q^108 + 2*q^109 + 6*q^110 + 30*q^111 + -3*q^112 + 12*q^113 + 6*q^115 + 6*q^116 + -30*q^117 + -1*q^118 + -18*q^119 + 9*q^120 + -7*q^121 + 12*q^122 + -6*q^123 + -10*q^124 + 3*q^125 + -18*q^126 + 7*q^127 + 1*q^128 + -12*q^129 + 15*q^130 + -6*q^131 + 6*q^132 + -8*q^134 + 27*q^135 + 6*q^136 + -4*q^137 + 6*q^138 + -7*q^139 + 9*q^140 + 9*q^141 + -3*q^142 + 10*q^143 + 6*q^144 + -18*q^145 + -6*q^146 + -6*q^147 + -10*q^148 + 14*q^149 + -12*q^150 + 14*q^151 + 36*q^153 + 6*q^154 + 30*q^155 + 15*q^156 + -14*q^157 + 1*q^158 + 36*q^159 + -3*q^160 + 6*q^161 + 9*q^162 + 4*q^163 + 2*q^164 + -18*q^165 + 14*q^166 + 18*q^167 + 9*q^168 + 12*q^169 + -18*q^170 + 4*q^172 + 4*q^173 + -18*q^174 + -12*q^175 + -2*q^176 + 3*q^177 + -7*q^178 + -4*q^179 + -18*q^180 + -18*q^181 + 15*q^182 + -36*q^183 + -2*q^184 + 30*q^185 + 30*q^186 + -12*q^187 + -3*q^188 + 27*q^189 + -21*q^191 + -3*q^192 + -26*q^193 + -11*q^194 + -45*q^195 + 2*q^196 + -6*q^197 + -12*q^198 + 9*q^199 + 4*q^200 +  ...

-------------------------------------------------------
158F (new) , dim = 2

CONGRUENCES:
Modular Degree = 2*5*53
Ker(ModPolar)  = Z/2*5*53 + Z/2*5*53
= B(Z/5 + Z/5) + D(Z/2 + Z/2) + H(Z/53 + Z/53)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^3*3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.3654847271296321472 + -0.82092227435435081794e-4i
Omega-         = 0.73548223204184807961 + -0.21914791036215406076e-4i
L(1)           = 0.68274236479865151411

HECKE EIGENFORM:
a^2-6 = 0,
f(q) = q + -1*q^2 + a*q^3 + 1*q^4 + -2*q^5 + -a*q^6 + 4*q^7 + -1*q^8 + 3*q^9 + 2*q^10 + a*q^12 + (-2*a+2)*q^13 + -4*q^14 + -2*a*q^15 + 1*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 + -1*q^25 + (2*a-2)*q^26 + 4*q^28 + (-3*a-2)*q^29 + 2*a*q^30 + (-2*a-2)*q^31 + -1*q^32 + (2*a-2)*q^34 + -8*q^35 + 3*q^36 + (-a-2)*q^37 + -2*a*q^38 + (2*a-12)*q^39 + 2*q^40 + (2*a+6)*q^41 + -4*a*q^42 + (a-8)*q^43 + -6*q^45 + (-2*a-2)*q^46 + -4*a*q^47 + a*q^48 + 9*q^49 + 1*q^50 + (2*a-12)*q^51 + (-2*a+2)*q^52 + (-a+2)*q^53 + -4*q^56 + 12*q^57 + (3*a+2)*q^58 + a*q^59 + -2*a*q^60 + (-a-6)*q^61 + (2*a+2)*q^62 + 12*q^63 + 1*q^64 + (4*a-4)*q^65 + (-2*a+8)*q^67 + (-2*a+2)*q^68 + (2*a+12)*q^69 + 8*q^70 + -4*q^71 + -3*q^72 + 12*q^73 + (a+2)*q^74 + -a*q^75 + 2*a*q^76 + (-2*a+12)*q^78 + 1*q^79 + -2*q^80 + -9*q^81 + (-2*a-6)*q^82 + (4*a+4)*q^83 + 4*a*q^84 + (4*a-4)*q^85 + (-a+8)*q^86 + (-2*a-18)*q^87 + 4*q^89 + 6*q^90 + (-8*a+8)*q^91 + (2*a+2)*q^92 + (-2*a-12)*q^93 + 4*a*q^94 + -4*a*q^95 + -a*q^96 + (4*a-2)*q^97 + -9*q^98 + -1*q^100 + (2*a-2)*q^101 + (-2*a+12)*q^102 + (4*a+8)*q^103 + (2*a-2)*q^104 + -8*a*q^105 + (a-2)*q^106 + 3*a*q^107 + (5*a+2)*q^109 + (-2*a-6)*q^111 + 4*q^112 + -2*q^113 + -12*q^114 + (-4*a-4)*q^115 + (-3*a-2)*q^116 + (-6*a+6)*q^117 + -a*q^118 + (-8*a+8)*q^119 + 2*a*q^120 + -11*q^121 + (a+6)*q^122 + (6*a+12)*q^123 + (-2*a-2)*q^124 + 12*q^125 + -12*q^126 + (4*a+4)*q^127 + -1*q^128 + (-8*a+6)*q^129 + (-4*a+4)*q^130 + (-2*a-12)*q^131 + 8*a*q^133 + (2*a-8)*q^134 + (2*a-2)*q^136 + (2*a-10)*q^137 + (-2*a-12)*q^138 + (-3*a+8)*q^139 + -8*q^140 + -24*q^141 + 4*q^142 + 3*q^144 + (6*a+4)*q^145 + -12*q^146 + 9*a*q^147 + (-a-2)*q^148 + (3*a-6)*q^149 + a*q^150 + (-4*a-8)*q^151 + -2*a*q^152 + (-6*a+6)*q^153 + (4*a+4)*q^155 + (2*a-12)*q^156 + (-a-18)*q^157 + -1*q^158 + (2*a-6)*q^159 + 2*q^160 + (8*a+8)*q^161 + 9*q^162 + (4*a-4)*q^163 + (2*a+6)*q^164 + (-4*a-4)*q^166 + (4*a+8)*q^167 + -4*a*q^168 + (-8*a+15)*q^169 + (-4*a+4)*q^170 + 6*a*q^171 + (a-8)*q^172 + (a+18)*q^173 + (2*a+18)*q^174 + -4*q^175 + 6*q^177 + -4*q^178 + (-4*a+12)*q^179 + -6*q^180 + (-4*a+6)*q^181 + (8*a-8)*q^182 + (-6*a-6)*q^183 + (-2*a-2)*q^184 + (2*a+4)*q^185 + (2*a+12)*q^186 + -4*a*q^188 + 4*a*q^190 + (2*a-12)*q^191 + a*q^192 + (-2*a-10)*q^193 + (-4*a+2)*q^194 + (-4*a+24)*q^195 + 9*q^196 + (-5*a+6)*q^197 + (-2*a-12)*q^199 + 1*q^200 +  ...

-------------------------------------------------------
158G (old = 79A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2^2 + Z/2^2) + E(Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
158H (old = 79B), dim = 5

CONGRUENCES:
Modular Degree = 2^6*53
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^5*53 + Z/2^5*53
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2^3 + Z/2^3) + F(Z/53 + Z/53) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(159)
Weight 2

-------------------------------------------------------
J_0(159), dim = 17

-------------------------------------------------------
159A (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^4*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*7 + Z/2*7
= B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + C(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 19*103
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3^2
Torsion Bound  = 3^2
|L(1)/Omega|   = 7/3^2
Sha Bound      = 3^2*7

ANALYTIC INVARIANTS:

Omega+         = 8.491469403891791783 + 0.40161222133634453865e-3i
Omega-         = 50.242598909734860088 + 0.27042851483699660884e-2i
L(1)           = 6.6044762104137523193

HECKE EIGENFORM:
a^4-3*a^3-a^2+7*a-3 = 0,
f(q) = q + a*q^2 + 1*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 + 1*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 + 1*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 + (2*a^3-4*a^2-4*a)*q^38 + (-3*a^3+5*a^2+8*a-10)*q^39 + (-2*a^3+2*a^2+a-3)*q^40 + (-a^3-3*a^2+8*a+9)*q^41 + (-a^2-2*a+3)*q^42 + (-3*a^3+3*a^2+12*a-10)*q^43 + (2*a^3+2*a^2-6*a-6)*q^44 + (-a^3+a^2+2*a)*q^45 + (-2*a^3+5*a^2+4*a-3)*q^46 + (-4*a^3+6*a^2+14*a-12)*q^47 + (3*a^3-5*a^2-7*a+7)*q^48 + (3*a^3-5*a^2-8*a+9)*q^49 + (4*a^3-3*a^2-9*a+3)*q^50 + (-4*a^3+8*a^2+10*a-12)*q^51 + (-a^3-3*a^2+3*a+8)*q^52 + -1*q^53 + a*q^54 + (2*a^3-6*a^2-10*a+12)*q^55 + (-5*a^3+6*a^2+15*a-15)*q^56 + (2*a^2-4*a-4)*q^57 + (6*a^3-8*a^2-16*a+12)*q^58 + (-2*a^3+8*a^2-12)*q^59 + (-3*a^3+3*a^2+7*a-6)*q^60 + (-2*a^3+6*a^2+6*a-10)*q^61 + (2*a^3+2*a^2-10*a)*q^62 + (a^3-3*a^2-2*a+5)*q^63 + (-4*a^3+6*a^2+9*a-8)*q^64 + (-a^3+5*a^2+4*a-9)*q^65 + (6*a^3-8*a^2-16*a+12)*q^66 + (-4*a^2+2*a+8)*q^67 + (2*a^3-4*a^2-4*a+12)*q^68 + (-a^3+a^2+6*a-3)*q^69 + (6*a^3-4*a^2-19*a+12)*q^70 + (-a^3-a^2+6*a)*q^71 + (a^3-4*a)*q^72 + (8*a^3-14*a^2-20*a+26)*q^73 + (-3*a^2-2*a+3)*q^74 + (a^3+a^2-4*a-2)*q^75 + (2*a^3-6*a^2-6*a+14)*q^76 + (-2*a^3-4*a^2+10*a+12)*q^77 + (-4*a^3+5*a^2+11*a-9)*q^78 + (-2*a^2+8)*q^79 + (2*a^3-7*a^2-3*a+6)*q^80 + 1*q^81 + (-6*a^3+7*a^2+16*a-3)*q^82 + (-a^3+3*a^2-2*a)*q^83 + (-3*a^3+4*a^2+7*a-10)*q^84 + (-8*a^3+14*a^2+18*a-18)*q^85 + (-6*a^3+9*a^2+11*a-9)*q^86 + (4*a^3-6*a^2-12*a+12)*q^87 + (-4*a^3+12*a^2+12*a-18)*q^88 + (2*a^3-8*a^2-6*a+18)*q^89 + (-2*a^3+a^2+7*a-3)*q^90 + (6*a^2-2*a-17)*q^91 + (a^3-a)*q^92 + (2*a^2+2*a-10)*q^93 + (-6*a^3+10*a^2+16*a-12)*q^94 + (2*a^3+2*a^2-14*a)*q^95 + (2*a^3-4*a^2-6*a+9)*q^96 + (-a^3-a^2+8*a+2)*q^97 + (4*a^3-5*a^2-12*a+9)*q^98 + (4*a^3-6*a^2-12*a+12)*q^99 + (7*a^3-7*a^2-17*a+16)*q^100 + (4*a^2-6)*q^101 + (-4*a^3+6*a^2+16*a-12)*q^102 + (4*a^3-8*a^2-10*a+8)*q^103 + (2*a^3-8*a^2-7*a+15)*q^104 + (4*a^3-6*a^2-8*a+9)*q^105 + -a*q^106 + (-4*a^2+10*a+6)*q^107 + (a^2-2)*q^108 + (6*a^3-8*a^2-24*a+20)*q^109 + (-8*a^2-2*a+6)*q^110 + (a^3-3*a^2-4*a+5)*q^111 + (-3*a^3+2*a^2+6*a+5)*q^112 + (-6*a^3+16*a^2+12*a-30)*q^113 + (2*a^3-4*a^2-4*a)*q^114 + (-4*a^3+2*a^2+18*a-9)*q^115 + (2*a^3+2*a^2-6*a-6)*q^116 + (-3*a^3+5*a^2+8*a-10)*q^117 + (2*a^3-2*a^2+2*a-6)*q^118 + (2*a^2-18)*q^119 + (-2*a^3+2*a^2+a-3)*q^120 + (-4*a^3+4*a^2+20*a+1)*q^121 + (4*a^2+4*a-6)*q^122 + (-a^3-3*a^2+8*a+9)*q^123 + (8*a^3-12*a^2-18*a+26)*q^124 + (-2*a-9)*q^125 + (-a^2-2*a+3)*q^126 + (-2*a^3+6*a^2+8*a-22)*q^127 + (-10*a^3+13*a^2+32*a-30)*q^128 + (-3*a^3+3*a^2+12*a-10)*q^129 + (2*a^3+3*a^2-2*a-3)*q^130 + (-2*a^2-2*a+12)*q^131 + (2*a^3+2*a^2-6*a-6)*q^132 + (-6*a^3+12*a^2+22*a-32)*q^133 + (-4*a^3+2*a^2+8*a)*q^134 + (-a^3+a^2+2*a)*q^135 + (10*a^3-14*a^2-34*a+30)*q^136 + (7*a^3-11*a^2-18*a+12)*q^137 + (-2*a^3+5*a^2+4*a-3)*q^138 + (-2*a^3+4*a^2+2*a-10)*q^139 + (6*a^3-a^2-14*a)*q^140 + (-4*a^3+6*a^2+14*a-12)*q^141 + (-4*a^3+5*a^2+7*a-3)*q^142 + (-2*a^3+6*a^2-2*a-24)*q^143 + (3*a^3-5*a^2-7*a+7)*q^144 + (2*a^3-6*a^2-10*a+12)*q^145 + (10*a^3-12*a^2-30*a+24)*q^146 + (3*a^3-5*a^2-8*a+9)*q^147 + (-5*a^3+4*a^2+11*a-10)*q^148 + (12*a^3-22*a^2-36*a+42)*q^149 + (4*a^3-3*a^2-9*a+3)*q^150 + (4*a^3-6*a^2-14*a+14)*q^151 + (-4*a^3+4*a^2+8*a+6)*q^152 + (-4*a^3+8*a^2+10*a-12)*q^153 + (-10*a^3+8*a^2+26*a-6)*q^154 + (-4*a^3+2*a^2+16*a-18)*q^155 + (-a^3-3*a^2+3*a+8)*q^156 + (4*a^3-2*a^2-22*a+8)*q^157 + (-2*a^3+8*a)*q^158 + -1*q^159 + (3*a^3-5*a^2-10*a+12)*q^160 + (a^3-a^2-10*a+6)*q^161 + a*q^162 + (-4*a^3+4*a^2+12*a-16)*q^163 + (-9*a^3+16*a^2+23*a-36)*q^164 + (2*a^3-6*a^2-10*a+12)*q^165 + (-3*a^2+7*a-3)*q^166 + (5*a^3-7*a^2-14*a+12)*q^167 + (-5*a^3+6*a^2+15*a-15)*q^168 + (5*a^3-11*a^2-8*a+18)*q^169 + (-10*a^3+10*a^2+38*a-24)*q^170 + (2*a^2-4*a-4)*q^171 + (-3*a^3-a^2+9*a+2)*q^172 + (a^3+3*a^2-12*a+3)*q^173 + (6*a^3-8*a^2-16*a+12)*q^174 + (-8*a^3+10*a^2+22*a-25)*q^175 + (-4*a^3+4*a^2+22*a)*q^176 + (-2*a^3+8*a^2-12)*q^177 + (-2*a^3-4*a^2+4*a+6)*q^178 + (-5*a^3+5*a^2+10*a-3)*q^179 + (-3*a^3+3*a^2+7*a-6)*q^180 + (-6*a^3+12*a^2+18*a-16)*q^181 + (6*a^3-2*a^2-17*a)*q^182 + (-2*a^3+6*a^2+6*a-10)*q^183 + (7*a^3-10*a^2-15*a+9)*q^184 + (8*a^3-8*a^2-22*a+15)*q^185 + (2*a^3+2*a^2-10*a)*q^186 + (12*a^3-8*a^2-48*a)*q^187 + (-2*a^2+2*a+6)*q^188 + (a^3-3*a^2-2*a+5)*q^189 + (8*a^3-12*a^2-14*a+6)*q^190 + (7*a^3-11*a^2-18*a+21)*q^191 + (-4*a^3+6*a^2+9*a-8)*q^192 + (4*a^3-6*a^2-10*a+26)*q^193 + (-4*a^3+7*a^2+9*a-3)*q^194 + (-a^3+5*a^2+4*a-9)*q^195 + (a^3+2*a^2-3*a-6)*q^196 + (-2*a^3+4*a^2+6*a-18)*q^197 + (6*a^3-8*a^2-16*a+12)*q^198 + (-a^3+5*a^2-8*a-10)*q^199 + (6*a^3-4*a^2-15*a+15)*q^200 +  ...

-------------------------------------------------------
159B (new) , dim = 5

CONGRUENCES:
Modular Degree = 2^4*107
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*107 + Z/2*107
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + D(Z/107 + Z/107)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1054013
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2^3
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 3.3430313155714796989 + 0.10000357310715347578e-3i
Omega-         = 0.44450472058265288306e-3 + 3.6802598150409836948i
L(1)           = 0.41787891463340439385

HECKE EIGENFORM:
a^5-10*a^3+22*a+5 = 0,
f(q) = q + a*q^2 + -1*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 + 1*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 + -1*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 + (-2/3*a^4-8/3*a^3+2*a^2+14*a+10/3)*q^38 + (-2/3*a^4+1/3*a^3+5*a^2-2*a-20/3)*q^39 + (-2*a^3-2*a^2+11*a+5)*q^40 + (-a^4+8*a^2-a-6)*q^41 + (-4/3*a^4-4/3*a^3+7*a^2+6*a+5/3)*q^42 + (-2/3*a^4-5/3*a^3+5*a^2+10*a-8/3)*q^43 + (-4/3*a^4-10/3*a^3+6*a^2+14*a+14/3)*q^44 + (-a^3-a^2+6*a+4)*q^45 + (4/3*a^4+10/3*a^3-7*a^2-16*a-5/3)*q^46 + (4/3*a^4+4/3*a^3-10*a^2-6*a+28/3)*q^47 + (-a^4+6*a^2-4)*q^48 + (-2/3*a^4+1/3*a^3+5*a^2-2*a+1/3)*q^49 + (-4*a^3-a^2+23*a+5)*q^50 + 2*a*q^51 + (1/3*a^4-2/3*a^3+2*a^2-35/3)*q^52 + 1*q^53 + -a*q^54 + (2/3*a^4-4/3*a^3-4*a^2+12*a+2/3)*q^55 + (a^4+2*a^3-3*a^2-12*a)*q^56 + (2/3*a^4+2/3*a^3-4*a^2-2*a+2/3)*q^57 + (2*a^3-4*a)*q^58 + (-2/3*a^4+4/3*a^3+6*a^2-10*a-38/3)*q^59 + (a^4+2*a^3-6*a^2-10*a+3)*q^60 + (-2/3*a^4-8/3*a^3+16*a+52/3)*q^61 + (2/3*a^4+8/3*a^3-4*a^2-12*a-10/3)*q^62 + (1/3*a^4+4/3*a^3-2*a^2-7*a+4/3)*q^63 + (2*a^2-5*a-8)*q^64 + (1/3*a^4+4/3*a^3-4*a^2-9*a+40/3)*q^65 + (2/3*a^4+8/3*a^3-2*a^2-14*a-10/3)*q^66 + (-2*a^4-2*a^3+14*a^2+8*a-10)*q^67 + (-2*a^3+4*a)*q^68 + (-1/3*a^4-4/3*a^3+7*a+26/3)*q^69 + (-1/3*a^4+11/3*a^3+3*a^2-28*a-25/3)*q^70 + (-4/3*a^4-7/3*a^3+5*a^2+14*a+32/3)*q^71 + (a^3-4*a)*q^72 + (2/3*a^4+2/3*a^3-2*a-40/3)*q^73 + (4/3*a^4+4/3*a^3-5*a^2-6*a-5/3)*q^74 + (a^4-6*a^2+a-1)*q^75 + (-4/3*a^4-10/3*a^3+6*a^2+14*a+14/3)*q^76 + (-4/3*a^4+2/3*a^3+8*a^2-10*a-16/3)*q^77 + (1/3*a^4-5/3*a^3-2*a^2+8*a+10/3)*q^78 + (2/3*a^4+2/3*a^3-4*a^2-6*a+2/3)*q^79 + (2*a^3-a^2-15*a+6)*q^80 + 1*q^81 + (-2*a^3-a^2+16*a+5)*q^82 + (-4/3*a^4-7/3*a^3+9*a^2+14*a-40/3)*q^83 + (-2/3*a^4-11/3*a^3+2*a^2+17*a+28/3)*q^84 + (2*a^4+2*a^3-12*a^2-8*a)*q^85 + (-5/3*a^4-5/3*a^3+10*a^2+12*a+10/3)*q^86 + (-2*a^2+4)*q^87 + (-2*a^4-2*a^3+10*a^2+6*a)*q^88 + (4/3*a^4+10/3*a^3-8*a^2-18*a+22/3)*q^89 + (-a^4-a^3+6*a^2+4*a)*q^90 + (a^4-a^3-11*a^2+11*a+20)*q^91 + (8/3*a^4+11/3*a^3-16*a^2-17*a+32/3)*q^92 + (-2/3*a^4-2/3*a^3+4*a^2+4*a-8/3)*q^93 + (4/3*a^4+10/3*a^3-6*a^2-20*a-20/3)*q^94 + (2/3*a^4-4/3*a^3-4*a^2+12*a+2/3)*q^95 + (-2*a^3+10*a+5)*q^96 + (2*a^4-a^3-15*a^2+6*a+12)*q^97 + (1/3*a^4-5/3*a^3-2*a^2+15*a+10/3)*q^98 + (-2/3*a^4-2/3*a^3+4*a^2+2*a-2/3)*q^99 + (-2*a^4-a^3+11*a^2+7*a-2)*q^100 + (4/3*a^4+4/3*a^3-8*a^2-4*a-2/3)*q^101 + 2*a^2*q^102 + (-2/3*a^4-2/3*a^3+2*a^2+10/3)*q^103 + (2*a^3-4*a^2-3*a+5)*q^104 + (-5/3*a^4+1/3*a^3+13*a^2-3*a-26/3)*q^105 + a*q^106 + (-4/3*a^4-4/3*a^3+12*a^2+2*a-58/3)*q^107 + (-a^2+2)*q^108 + (2*a^3-12*a+4)*q^109 + (-4/3*a^4+8/3*a^3+12*a^2-14*a-10/3)*q^110 + (-1/3*a^4-4/3*a^3+2*a^2+5*a-4/3)*q^111 + (2/3*a^4-1/3*a^3-8*a^2+12*a+41/3)*q^112 + (-2/3*a^4+4/3*a^3+10*a^2-6*a-68/3)*q^113 + (2/3*a^4+8/3*a^3-2*a^2-14*a-10/3)*q^114 + (-1/3*a^4+5/3*a^3+5*a^2-13*a-64/3)*q^115 + (2*a^4-8*a^2+8)*q^116 + (2/3*a^4-1/3*a^3-5*a^2+2*a+20/3)*q^117 + (4/3*a^4-2/3*a^3-10*a^2+2*a+10/3)*q^118 + (-8/3*a^4-8/3*a^3+14*a^2+12*a+10/3)*q^119 + (2*a^3+2*a^2-11*a-5)*q^120 + (4*a^3+4*a^2-20*a-15)*q^121 + (-8/3*a^4-20/3*a^3+16*a^2+32*a+10/3)*q^122 + (a^4-8*a^2+a+6)*q^123 + (4/3*a^4+4/3*a^3-4*a^2-10*a-26/3)*q^124 + (a^4-a^3-5*a^2+11*a-6)*q^125 + (4/3*a^4+4/3*a^3-7*a^2-6*a-5/3)*q^126 + (-2/3*a^4+4/3*a^3+8*a^2-6*a-44/3)*q^127 + (-2*a^3-5*a^2+12*a+10)*q^128 + (2/3*a^4+5/3*a^3-5*a^2-10*a+8/3)*q^129 + (4/3*a^4-2/3*a^3-9*a^2+6*a-5/3)*q^130 + (8/3*a^4+8/3*a^3-18*a^2-10*a+20/3)*q^131 + (4/3*a^4+10/3*a^3-6*a^2-14*a-14/3)*q^132 + (-4/3*a^4+2/3*a^3+8*a^2-10*a-16/3)*q^133 + (-2*a^4-6*a^3+8*a^2+34*a+10)*q^134 + (a^3+a^2-6*a-4)*q^135 + (-2*a^4+8*a^2)*q^136 + (-a^3-5*a^2+2*a+24)*q^137 + (-4/3*a^4-10/3*a^3+7*a^2+16*a+5/3)*q^138 + (2/3*a^4+8/3*a^3-2*a^2-12*a-28/3)*q^139 + (1/3*a^4+1/3*a^3-2*a^2-7*a-47/3)*q^140 + (-4/3*a^4-4/3*a^3+10*a^2+6*a-28/3)*q^141 + (-7/3*a^4-25/3*a^3+14*a^2+40*a+20/3)*q^142 + (2/3*a^4-4/3*a^3-4*a^2+8*a-10/3)*q^143 + (a^4-6*a^2+4)*q^144 + (-2*a^4-4*a^3+12*a^2+20*a-6)*q^145 + (2/3*a^4+20/3*a^3-2*a^2-28*a-10/3)*q^146 + (2/3*a^4-1/3*a^3-5*a^2+2*a-1/3)*q^147 + (2/3*a^4+17/3*a^3-2*a^2-21*a-28/3)*q^148 + (2*a^4+2*a^3-12*a^2-6*a-4)*q^149 + (4*a^3+a^2-23*a-5)*q^150 + (-2/3*a^4-2/3*a^3+4*a^2+4/3)*q^151 + (-2*a^4-2*a^3+10*a^2+6*a)*q^152 + -2*a*q^153 + (2/3*a^4-16/3*a^3-10*a^2+24*a+20/3)*q^154 + (4/3*a^4+4/3*a^3-10*a^2-8*a+22/3)*q^155 + (-1/3*a^4+2/3*a^3-2*a^2+35/3)*q^156 + (-2/3*a^4-2/3*a^3+8*a^2-62/3)*q^157 + (2/3*a^4+8/3*a^3-6*a^2-14*a-10/3)*q^158 + -1*q^159 + (2*a^4+3*a^3-11*a^2-16*a-10)*q^160 + (-4/3*a^4-1/3*a^3+13*a^2+6*a-58/3)*q^161 + a*q^162 + (-4*a^3-4*a^2+28*a+16)*q^163 + (-a^3+7*a+12)*q^164 + (-2/3*a^4+4/3*a^3+4*a^2-12*a-2/3)*q^165 + (-7/3*a^4-13/3*a^3+14*a^2+16*a+20/3)*q^166 + (4/3*a^4-5/3*a^3-13*a^2+10*a+52/3)*q^167 + (-a^4-2*a^3+3*a^2+12*a)*q^168 + (5/3*a^4-4/3*a^3-14*a^2+3*a+71/3)*q^169 + (2*a^4+8*a^3-8*a^2-44*a-10)*q^170 + (-2/3*a^4-2/3*a^3+4*a^2+2*a-2/3)*q^171 + (-1/3*a^4-10/3*a^3+2*a^2+20*a+41/3)*q^172 + (-5/3*a^4-8/3*a^3+8*a^2+13*a-2/3)*q^173 + (-2*a^3+4*a)*q^174 + (-1/3*a^4+17/3*a^3+5*a^2-41*a-16/3)*q^175 + (2/3*a^4-10/3*a^3-6*a^2+16*a+2/3)*q^176 + (2/3*a^4-4/3*a^3-6*a^2+10*a+38/3)*q^177 + (10/3*a^4+16/3*a^3-18*a^2-22*a-20/3)*q^178 + (1/3*a^4-8/3*a^3-4*a^2+13*a+22/3)*q^179 + (-a^4-2*a^3+6*a^2+10*a-3)*q^180 + (-2/3*a^4+4/3*a^3+6*a^2-8*a-50/3)*q^181 + (-a^4-a^3+11*a^2-2*a-5)*q^182 + (2/3*a^4+8/3*a^3-16*a-52/3)*q^183 + (a^4+4*a^3-3*a^2-16*a-10)*q^184 + (-1/3*a^4-7/3*a^3-a^2+11*a+26/3)*q^185 + (-2/3*a^4-8/3*a^3+4*a^2+12*a+10/3)*q^186 + (4/3*a^4+16/3*a^3-4*a^2-28*a-20/3)*q^187 + (2/3*a^4+14/3*a^3-24*a-76/3)*q^188 + (-1/3*a^4-4/3*a^3+2*a^2+7*a-4/3)*q^189 + (-4/3*a^4+8/3*a^3+12*a^2-14*a-10/3)*q^190 + (-a^4+8*a^2-3*a-10)*q^191 + (-2*a^2+5*a+8)*q^192 + (-4*a^3-2*a^2+18*a+2)*q^193 + (-a^4+5*a^3+6*a^2-32*a-10)*q^194 + (-1/3*a^4-4/3*a^3+4*a^2+9*a-40/3)*q^195 + (-1/3*a^4+2/3*a^3+5*a^2-7/3)*q^196 + (-4/3*a^4+2/3*a^3+8*a^2-6*a+14/3)*q^197 + (-2/3*a^4-8/3*a^3+2*a^2+14*a+10/3)*q^198 + (2/3*a^4-7/3*a^3-5*a^2+18*a+44/3)*q^199 + (-a^4-a^3+9*a^2-4*a)*q^200 +  ...

-------------------------------------------------------
159C (old = 53A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*7 + Z/2*7
= A(Z/7 + Z/7) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
159D (old = 53B), dim = 3

CONGRUENCES:
Modular Degree = 2^2*107
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*107 + Z/2*107
= B(Z/107 + Z/107) + C(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(160)
Weight 2

-------------------------------------------------------
J_0(160), dim = 17

-------------------------------------------------------
160A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2) + C(Z/2) + F(Z/2) + G(Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.725842855400511765 + -0.42005763168892654472e-43i
Omega-         = 0.15830045389556285592e-4 + -1.5057725394602820174i
L(1)           =
w1             = -2.725842855400511765 + 0.42005763168892654472e-43i
w2             = -0.15830045389556285592e-4 + 1.5057725394602820174i
c4             = 304.00298980066506382 + -0.12683849607855436692e-1i
c6             = -5248.0766896449121117 + 0.3346926007966948681i
j              = 87793.987544584173035 + -10.408549266932564399i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -1*q^5 + -2*q^7 + 1*q^9 + -4*q^11 + -6*q^13 + 2*q^15 + 2*q^17 + 8*q^19 + 4*q^21 + -6*q^23 + 1*q^25 + 4*q^27 + -2*q^29 + 4*q^31 + 8*q^33 + 2*q^35 + 2*q^37 + 12*q^39 + -10*q^41 + -2*q^43 + -1*q^45 + -2*q^47 + -3*q^49 + -4*q^51 + 2*q^53 + 4*q^55 + -16*q^57 + 2*q^61 + -2*q^63 + 6*q^65 + -6*q^67 + 12*q^69 + -12*q^71 + 10*q^73 + -2*q^75 + 8*q^77 + -8*q^79 + -11*q^81 + -10*q^83 + -2*q^85 + 4*q^87 + -6*q^89 + 12*q^91 + -8*q^93 + -8*q^95 + 10*q^97 + -4*q^99 + 14*q^101 + 2*q^103 + -4*q^105 + -6*q^107 + -14*q^109 + -4*q^111 + -6*q^113 + 6*q^115 + -6*q^117 + -4*q^119 + 5*q^121 + 20*q^123 + -1*q^125 + 6*q^127 + 4*q^129 + 4*q^131 + -16*q^133 + -4*q^135 + 2*q^137 + -16*q^139 + 4*q^141 + 24*q^143 + 2*q^145 + 6*q^147 + 10*q^149 + 20*q^151 + 2*q^153 + -4*q^155 + 10*q^157 + -4*q^159 + 12*q^161 + 6*q^163 + -8*q^165 + 14*q^167 + 23*q^169 + 8*q^171 + -6*q^173 + -2*q^175 + -18*q^181 + -4*q^183 + -2*q^185 + -8*q^187 + -8*q^189 + -4*q^191 + 2*q^193 + -12*q^195 + -22*q^197 + -16*q^199 +  ...

-------------------------------------------------------
160B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= A(Z/2) + C(Z/2) + F(Z/2) + G(Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.5057103343013793495 + 0.42956138577657027563e-4i
Omega-         = 0.43785634925755929155e-5 + 2.7259436498660115369i
L(1)           = 0.75285516745706165732
w1             = 0.43785634925755929155e-5 + 2.7259436498660115369i
w2             = 1.5057103343013793495 + 0.42956138577657027563e-4i
c4             = 304.05248337804190794 + -0.34410656988136437976e-1i
c6             = 5249.4048555213783739 + -0.90903383707076504202i
j              = 87871.531382326042174 + -29.864857907746696992i

HECKE EIGENFORM:
f(q) = q + 2*q^3 + -1*q^5 + 2*q^7 + 1*q^9 + 4*q^11 + -6*q^13 + -2*q^15 + 2*q^17 + -8*q^19 + 4*q^21 + 6*q^23 + 1*q^25 + -4*q^27 + -2*q^29 + -4*q^31 + 8*q^33 + -2*q^35 + 2*q^37 + -12*q^39 + -10*q^41 + 2*q^43 + -1*q^45 + 2*q^47 + -3*q^49 + 4*q^51 + 2*q^53 + -4*q^55 + -16*q^57 + 2*q^61 + 2*q^63 + 6*q^65 + 6*q^67 + 12*q^69 + 12*q^71 + 10*q^73 + 2*q^75 + 8*q^77 + 8*q^79 + -11*q^81 + 10*q^83 + -2*q^85 + -4*q^87 + -6*q^89 + -12*q^91 + -8*q^93 + 8*q^95 + 10*q^97 + 4*q^99 + 14*q^101 + -2*q^103 + -4*q^105 + 6*q^107 + -14*q^109 + 4*q^111 + -6*q^113 + -6*q^115 + -6*q^117 + 4*q^119 + 5*q^121 + -20*q^123 + -1*q^125 + -6*q^127 + 4*q^129 + -4*q^131 + -16*q^133 + 4*q^135 + 2*q^137 + 16*q^139 + 4*q^141 + -24*q^143 + 2*q^145 + -6*q^147 + 10*q^149 + -20*q^151 + 2*q^153 + 4*q^155 + 10*q^157 + 4*q^159 + 12*q^161 + -6*q^163 + -8*q^165 + -14*q^167 + 23*q^169 + -8*q^171 + -6*q^173 + 2*q^175 + -18*q^181 + 4*q^183 + -2*q^185 + 8*q^187 + -8*q^189 + 4*q^191 + 2*q^193 + 12*q^195 + -22*q^197 + 16*q^199 +  ...

-------------------------------------------------------
160C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2) + B(Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2^2
ord((0)-(oo))  = 2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 1.4376349724071458243 + 0.11468792331471582529e-5i
Omega-         = 1.4376907882849112314 + 0.24900404715228421128e-4i
L(1)           = 0.35940874310190082203

HECKE EIGENFORM:
a^2-8 = 0,
f(q) = q + a*q^3 + 1*q^5 + -a*q^7 + 5*q^9 + -2*a*q^11 + -2*q^13 + a*q^15 + 2*q^17 + -8*q^21 + a*q^23 + 1*q^25 + 2*a*q^27 + 6*q^29 + 2*a*q^31 + -16*q^33 + -a*q^35 + -10*q^37 + -2*a*q^39 + 2*q^41 + -3*a*q^43 + 5*q^45 + -a*q^47 + 1*q^49 + 2*a*q^51 + 6*q^53 + -2*a*q^55 + 4*a*q^59 + -2*q^61 + -5*a*q^63 + -2*q^65 + -a*q^67 + 8*q^69 + 2*a*q^71 + -6*q^73 + a*q^75 + 16*q^77 + 4*a*q^79 + 1*q^81 + a*q^83 + 2*q^85 + 6*a*q^87 + 10*q^89 + 2*a*q^91 + 16*q^93 + 2*q^97 + -10*a*q^99 + -2*q^101 + 5*a*q^103 + -8*q^105 + -5*a*q^107 + -18*q^109 + -10*a*q^111 + 2*q^113 + a*q^115 + -10*q^117 + -2*a*q^119 + 21*q^121 + 2*a*q^123 + 1*q^125 + -a*q^127 + -24*q^129 + 2*a*q^131 + 2*a*q^135 + -6*q^137 + 4*a*q^139 + -8*q^141 + 4*a*q^143 + 6*q^145 + a*q^147 + -10*q^149 + -6*a*q^151 + 10*q^153 + 2*a*q^155 + -18*q^157 + 6*a*q^159 + -8*q^161 + 5*a*q^163 + -16*q^165 + -5*a*q^167 + -9*q^169 + -2*q^173 + -a*q^175 + 32*q^177 + 4*a*q^179 + 14*q^181 + -2*a*q^183 + -10*q^185 + -4*a*q^187 + -16*q^189 + 6*a*q^191 + 18*q^193 + -2*a*q^195 + 6*q^197 + -8*a*q^199 +  ...

-------------------------------------------------------
160D (old = 80A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= C(Z/2 + Z/2) + E(Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
160E (old = 80B), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= C(Z/2 + Z/2) + D(Z/2) + F(Z/2 + Z/2) + G(Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2^2)

-------------------------------------------------------
160F (old = 40A), dim = 1

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2) + B(Z/2) + C(Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
160G (old = 32A), dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^3 + Z/2^3
= A(Z/2) + B(Z/2) + C(Z/2 + Z/2) + D(Z/2) + E(Z/2) + F(Z/2 + Z/2) + H(Z/2 + Z/2)

-------------------------------------------------------
160H (old = 20A), dim = 1

CONGRUENCES:
Modular Degree = 2^9
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2^2) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(161)
Weight 2

-------------------------------------------------------
J_0(161), dim = 15

-------------------------------------------------------
161A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*5
Ker(ModPolar)  = Z/2*5 + Z/2*5
= C(Z/2) + D(Z/5 + Z/2*5)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 1.7256716846641059791 + -0.13253451931141101568e-4i
Omega-         = 0.24345681746265527784e-4 + 1.4314811205877263998i
L(1)           = 0.43141792117875009029
w1             = 1.7256716846641059791 + -0.13253451931141101568e-4i
w2             = -0.24345681746265527784e-4 + -1.4314811205877263998i
c4             = 417.11887071007970079 + 0.25115383022803752077e-1i
c6             = -5269.2025081487399144 + -0.67286655273347099765i
j              = 2798.6952594410424632 + 0.12964457399839015426i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^4 + 2*q^5 + 1*q^7 + 3*q^8 + -3*q^9 + -2*q^10 + 4*q^11 + 6*q^13 + -1*q^14 + -1*q^16 + -2*q^17 + 3*q^18 + 4*q^19 + -2*q^20 + -4*q^22 + -1*q^23 + -1*q^25 + -6*q^26 + -1*q^28 + -2*q^29 + -4*q^31 + -5*q^32 + 2*q^34 + 2*q^35 + 3*q^36 + -2*q^37 + -4*q^38 + 6*q^40 + -6*q^41 + 12*q^43 + -4*q^44 + -6*q^45 + 1*q^46 + -12*q^47 + 1*q^49 + 1*q^50 + -6*q^52 + -10*q^53 + 8*q^55 + 3*q^56 + 2*q^58 + 2*q^61 + 4*q^62 + -3*q^63 + 7*q^64 + 12*q^65 + 12*q^67 + 2*q^68 + -2*q^70 + 8*q^71 + -9*q^72 + -14*q^73 + 2*q^74 + -4*q^76 + 4*q^77 + 8*q^79 + -2*q^80 + 9*q^81 + 6*q^82 + -4*q^83 + -4*q^85 + -12*q^86 + 12*q^88 + 6*q^89 + 6*q^90 + 6*q^91 + 1*q^92 + 12*q^94 + 8*q^95 + -10*q^97 + -1*q^98 + -12*q^99 + 1*q^100 + 14*q^101 + -8*q^103 + 18*q^104 + 10*q^106 + -4*q^107 + -10*q^109 + -8*q^110 + -1*q^112 + -14*q^113 + -2*q^115 + 2*q^116 + -18*q^117 + -2*q^119 + 5*q^121 + -2*q^122 + 4*q^124 + -12*q^125 + 3*q^126 + -8*q^127 + 3*q^128 + -12*q^130 + -8*q^131 + 4*q^133 + -12*q^134 + -6*q^136 + -14*q^137 + -16*q^139 + -2*q^140 + -8*q^142 + 24*q^143 + 3*q^144 + -4*q^145 + 14*q^146 + 2*q^148 + 6*q^149 + 16*q^151 + 12*q^152 + 6*q^153 + -4*q^154 + -8*q^155 + 18*q^157 + -8*q^158 + -10*q^160 + -1*q^161 + -9*q^162 + 4*q^163 + 6*q^164 + 4*q^166 + -12*q^167 + 23*q^169 + 4*q^170 + -12*q^171 + -12*q^172 + -2*q^173 + -1*q^175 + -4*q^176 + -6*q^178 + 12*q^179 + 6*q^180 + -14*q^181 + -6*q^182 + -3*q^184 + -4*q^185 + -8*q^187 + 12*q^188 + -8*q^190 + 2*q^193 + 10*q^194 + -1*q^196 + 6*q^197 + 12*q^198 + -8*q^199 + -3*q^200 +  ...

-------------------------------------------------------
161B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 11.870335895070815944 + -0.20753699942377244202e-2i
Omega-         = 3.4842816930747379002 + 0.23442229259710256967e-5i
L(1)           =

HECKE EIGENFORM:
a^2+a-1 = 0,
f(q) = q + a*q^2 + -1*q^3 + (-a-1)*q^4 + (-2*a-2)*q^5 + -a*q^6 + -1*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 + 1*q^21 + (-2*a+4)*q^22 + -1*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 + (-4*a-2)*q^38 + (-2*a+1)*q^39 + (2*a+6)*q^40 + (-2*a-1)*q^41 + a*q^42 + 4*a*q^43 + (-2*a-6)*q^44 + (4*a+4)*q^45 + -a*q^46 + (-4*a-1)*q^47 + -3*a*q^48 + 1*q^49 + (-a+4)*q^50 + (a-1)*q^52 + (2*a+10)*q^53 + 5*a*q^54 + (-4*a-12)*q^55 + (2*a+1)*q^56 + (2*a+6)*q^57 + (5*a-4)*q^58 + (4*a-4)*q^59 + (-2*a-4)*q^60 + (12*a+6)*q^61 + -9*a*q^62 + 2*q^63 + (-2*a+1)*q^64 + (2*a-2)*q^65 + (2*a-4)*q^66 + (-10*a-6)*q^67 + 1*q^69 + 2*q^70 + (-2*a-9)*q^71 + (4*a+2)*q^72 + (-6*a-3)*q^73 + (4*a-6)*q^74 + (-4*a-3)*q^75 + (6*a+8)*q^76 + (-4*a-2)*q^77 + (3*a-2)*q^78 + (-2*a-6)*q^79 + -6*q^80 + 1*q^81 + (a-2)*q^82 + (4*a+4)*q^83 + (-a-1)*q^84 + (-4*a+4)*q^86 + (4*a-1)*q^87 + -10*q^88 + (8*a+4)*q^89 + 4*q^90 + (-2*a+1)*q^91 + (a+1)*q^92 + 9*q^93 + (3*a-4)*q^94 + (12*a+16)*q^95 + (-a-5)*q^96 + 6*a*q^97 + a*q^98 + (-8*a-4)*q^99 + (-3*a-7)*q^100 + (-12*a-6)*q^101 + (-6*a-12)*q^103 + (4*a-3)*q^104 + (-2*a-2)*q^105 + (8*a+2)*q^106 + (2*a+10)*q^107 + (-5*a-5)*q^108 + (-12*a-8)*q^109 + (-8*a-4)*q^110 + (6*a+2)*q^111 + -3*a*q^112 + 4*a*q^113 + (4*a+2)*q^114 + (2*a+2)*q^115 + (-a+3)*q^116 + (-4*a+2)*q^117 + (-8*a+4)*q^118 + (-2*a-6)*q^120 + 9*q^121 + (-6*a+12)*q^122 + (2*a+1)*q^123 + (9*a+9)*q^124 + (4*a-4)*q^125 + 2*a*q^126 + (-6*a+1)*q^127 + (a-12)*q^128 + -4*a*q^129 + (-4*a+2)*q^130 + (8*a-1)*q^131 + (2*a+6)*q^132 + (2*a+6)*q^133 + (4*a-10)*q^134 + (-10*a-10)*q^135 + (6*a+12)*q^137 + a*q^138 + (-4*a+5)*q^139 + (-2*a-4)*q^140 + (4*a+1)*q^141 + (-7*a-2)*q^142 + (-8*a+6)*q^143 + -6*a*q^144 + (-2*a+6)*q^145 + (3*a-6)*q^146 + -1*q^147 + (2*a+8)*q^148 + (2*a+14)*q^149 + (a-4)*q^150 + (-10*a-9)*q^151 + (10*a+10)*q^152 + (2*a-4)*q^154 + (18*a+18)*q^155 + (-a+1)*q^156 + (12*a+8)*q^157 + (-4*a-2)*q^158 + (-2*a-10)*q^159 + (-10*a-12)*q^160 + 1*q^161 + a*q^162 + (10*a+13)*q^163 + (a+3)*q^164 + (4*a+12)*q^165 + 4*q^166 + (16*a+12)*q^167 + (-2*a-1)*q^168 + (-8*a-8)*q^169 + (4*a+12)*q^171 + -4*q^172 + (4*a-6)*q^173 + (-5*a+4)*q^174 + (-4*a-3)*q^175 + (-6*a+12)*q^176 + (-4*a+4)*q^177 + (-4*a+8)*q^178 + (-6*a-15)*q^179 + (-4*a-8)*q^180 + (8*a-10)*q^181 + (3*a-2)*q^182 + (-12*a-6)*q^183 + (2*a+1)*q^184 + (4*a+16)*q^185 + 9*a*q^186 + (a+5)*q^188 + -5*q^189 + (4*a+12)*q^190 + (-10*a-18)*q^191 + (2*a-1)*q^192 + (12*a-3)*q^193 + (-6*a+6)*q^194 + (-2*a+2)*q^195 + (-a-1)*q^196 + (-4*a-19)*q^197 + (4*a-8)*q^198 + (16*a+6)*q^199 + (-2*a-11)*q^200 +  ...

-------------------------------------------------------
161C (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3*19
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*19 + Z/2*19
= A(Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + E(Z/19 + Z/19)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*37
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.3476441947480875633 + 0.48239389286776700376e-3i
Omega-         = 0.38976672350613249266e-3 + -13.981010314033724483i
L(1)           = 1.1738221221546159336

HECKE EIGENFORM:
a^3+a^2-5*a-1 = 0,
f(q) = 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 + -1*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 + 1*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 + (6*a+2)*q^38 + (a^2+2*a-7)*q^39 + (1/2*a^2-2*a+3/2)*q^40 + (2*a^2-12)*q^41 + (-1/2*a^2+1/2)*q^42 + (a^2+4*a-5)*q^43 + (2*a^2-3*a-3)*q^44 + (-3/2*a^2-2*a+15/2)*q^45 + a*q^46 + (3/2*a^2+2*a+1/2)*q^47 + (-7/2*a^2+19/2)*q^48 + 1*q^49 + (-4*a-1)*q^50 + (a-1)*q^51 + (a^2-4*a+5)*q^52 + (-2*a^2-4*a+8)*q^53 + -2*a^2*q^54 + (-a^2+3)*q^55 + (a^2-a-1)*q^56 + (2*a^2+4*a-10)*q^57 + (a+1)*q^58 + (5/2*a^2+6*a-21/2)*q^59 + (3*a^2+a-12)*q^60 + (-3/2*a^2+2*a+19/2)*q^61 + (-5/2*a^2+2*a-3/2)*q^62 + (a^2+a-3)*q^63 + (3*a^2-4*a-8)*q^64 + (a^2+2*a-7)*q^65 + (a^2-2*a-1)*q^66 + (-2*a^2-5*a+11)*q^67 + (3/2*a^2-2*a+1/2)*q^68 + (-1/2*a^2+5/2)*q^69 + (-1/2*a^2+1/2)*q^70 + -4*a*q^71 + (a^2-2*a+2)*q^72 + (-3*a^2+9)*q^73 + (a^2+1)*q^74 + (-1/2*a^2-2*a+5/2)*q^75 + (2*a^2-2*a+8)*q^76 + (a-1)*q^77 + (a^2-2*a+1)*q^78 + (-2*a^2+a+13)*q^79 + (-7/2*a^2+19/2)*q^80 + (2*a^2+3*a-8)*q^81 + (-2*a^2-2*a+2)*q^82 + (-3*a^2-8*a+15)*q^83 + (-1/2*a^2-2*a+9/2)*q^84 + (a-1)*q^85 + (3*a^2+1)*q^86 + (2*a^2+2*a-10)*q^87 + (-3*a^2+5*a+2)*q^88 + (-7/2*a^2-2*a+27/2)*q^89 + (-1/2*a^2-3/2)*q^90 + (-a^2+3)*q^91 + (a^2-2)*q^92 + (-6*a^2-3*a+25)*q^93 + (1/2*a^2+8*a+3/2)*q^94 + (2*a^2+4*a-10)*q^95 + (5/2*a^2-4*a-13/2)*q^96 + (1/2*a^2-2*a-1/2)*q^97 + a*q^98 + (-a^2+a+4)*q^99 + (-2*a^2+a-2)*q^100 + (-a^2-2*a-3)*q^101 + (a^2-a)*q^102 + (2*a^2+2)*q^103 + (-3*a^2+6*a-1)*q^104 + (a^2+a-6)*q^105 + (-2*a^2-2*a-2)*q^106 + (a^2+8*a-1)*q^107 + (2*a^2-6*a-2)*q^108 + (-a^2+4*a+7)*q^109 + (a^2-2*a-1)*q^110 + (3*a^2+2*a-13)*q^111 + (4*a-3)*q^112 + (2*a^2-4*a-12)*q^113 + (2*a^2+2)*q^114 + (-1/2*a^2+5/2)*q^115 + (-a^2-a+8)*q^116 + (a^2+2*a-9)*q^117 + (7/2*a^2+2*a+5/2)*q^118 + (-1/2*a^2+1/2)*q^119 + (-2*a^2+a+5)*q^120 + (a^2-2*a-10)*q^121 + (7/2*a^2+2*a-3/2)*q^122 + (5*a^2+4*a-29)*q^123 + (15/2*a^2-6*a-43/2)*q^124 + (2*a^2-2*a-10)*q^125 + (2*a+1)*q^126 + (a^2+2*a+1)*q^127 + (-3*a^2+5*a+7)*q^128 + (4*a^2+2*a-14)*q^129 + (a^2-2*a+1)*q^130 + (-9/2*a^2-6*a+21/2)*q^131 + (-a^2+4*a-5)*q^132 + (-2*a^2-2*a+4)*q^133 + (-3*a^2+a-2)*q^134 + (-a^2+1)*q^135 + (-5/2*a^2+4*a+1/2)*q^136 + (a^2-2*a-5)*q^137 + (1/2*a^2-1/2)*q^138 + (-3/2*a^2+2*a+27/2)*q^139 + (-1/2*a^2-2*a+9/2)*q^140 + (3*a+1)*q^141 + -4*a^2*q^142 + (2*a^2-2*a-4)*q^143 + (-3*a^2+5*a+13)*q^144 + (2*a^2+2*a-10)*q^145 + (3*a^2-6*a-3)*q^146 + (-1/2*a^2+5/2)*q^147 + (-3*a^2+2*a+11)*q^148 + (-4*a-10)*q^149 + (-3/2*a^2-1/2)*q^150 + (-a^2-6*a+7)*q^151 + (-4*a^2+6*a-2)*q^152 + (-1/2*a^2-3/2)*q^153 + (a^2-a)*q^154 + (-6*a^2-3*a+25)*q^155 + (-5*a^2+2*a+15)*q^156 + (-1/2*a^2-15/2)*q^157 + (3*a^2+3*a-2)*q^158 + (-5*a^2-4*a+21)*q^159 + (5/2*a^2-4*a-13/2)*q^160 + -1*q^161 + (a^2+2*a+2)*q^162 + (6*a^2+2*a-24)*q^163 + (-4*a^2-8*a+22)*q^164 + (-a^2-2*a+7)*q^165 + (-5*a^2-3)*q^166 + (1/2*a^2-4*a-17/2)*q^167 + (-1/2*a^2+2*a-3/2)*q^168 + (-4*a-5)*q^169 + (a^2-a)*q^170 + (-2*a-14)*q^171 + (-5*a^2+8*a+13)*q^172 + (2*a^2-2*a-6)*q^173 + 2*q^174 + (a^2+a-1)*q^175 + (4*a^2-7*a+3)*q^176 + (7*a^2+5*a-28)*q^177 + (3/2*a^2-4*a-7/2)*q^178 + (-7*a^2-6*a+17)*q^179 + (7/2*a^2-31/2)*q^180 + (5/2*a^2+2*a-1/2)*q^181 + (a^2-2*a-1)*q^182 + (-3*a^2-3*a+22)*q^183 + (-a^2+a+1)*q^184 + (3*a^2+2*a-13)*q^185 + (3*a^2-5*a-6)*q^186 + (a^2-2*a-1)*q^187 + (9/2*a^2-1/2)*q^188 + 2*a*q^189 + (2*a^2+2)*q^190 + (-5*a^2-4*a+21)*q^191 + (1/2*a^2+6*a-33/2)*q^192 + (3*a^2+6*a-23)*q^193 + (-5/2*a^2+2*a+1/2)*q^194 + (4*a^2+2*a-18)*q^195 + (a^2-2)*q^196 + (-4*a^2-4*a+6)*q^197 + (2*a^2-a-1)*q^198 + (4*a+12)*q^199 + (3*a^2-4*a)*q^200 +  ...

-------------------------------------------------------
161D (new) , dim = 5

CONGRUENCES:
Modular Degree = 2^7*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2*5 + Z/2^2*5
= A(Z/5 + Z/2*5) + B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^2*536777
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2*3
Torsion Bound  = 2*3
|L(1)/Omega|   = 2/3
Sha Bound      = 2^3*3

ANALYTIC INVARIANTS:

Omega+         = 2.8490884938670804174 + 0.28023082057023754686e-3i
Omega-         = 0.46615535320770106383e-2 + -30.516535926832211178i
L(1)           = 1.8993923384323736601

HECKE EIGENFORM:
a^5-2*a^4-9*a^3+17*a^2+16*a-27 = 0,
f(q) = 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 + 1*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 + -1*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 + (-2*a^2+2*a)*q^38 + (-a^4+7*a^2+2*a-4)*q^39 + (-3/2*a^4-3/2*a^3+9*a^2+19/2*a-27/2)*q^40 + (-a^3+a^2+5*a-3)*q^41 + (1/2*a^4+1/2*a^3-6*a^2-5/2*a+27/2)*q^42 + (a^4+a^3-10*a^2-5*a+17)*q^43 + (-3*a^4+22*a^2+3*a-30)*q^44 + (1/2*a^4-3/2*a^3+a^2+19/2*a-39/2)*q^45 + -a*q^46 + (-3/2*a^4+3/2*a^3+14*a^2-19/2*a-45/2)*q^47 + (-3/2*a^4+1/2*a^3+14*a^2-13/2*a-37/2)*q^48 + 1*q^49 + (a^4-6*a^2+4*a)*q^50 + (-3*a^4+2*a^3+26*a^2-11*a-42)*q^51 + (2*a^4+a^3-18*a^2-5*a+26)*q^52 + (-2*a^2+12)*q^53 + (-a^4+a^3+7*a^2-5*a)*q^54 + (-a^4+a^3+8*a^2-a-9)*q^55 + (a^3-4*a)*q^56 + (-2*a^3+4*a^2+10*a-16)*q^57 + (-3*a^3+a^2+12*a)*q^58 + (-1/2*a^4-1/2*a^3+5*a^2+1/2*a-9/2)*q^59 + (2*a^4-a^3-14*a^2+21)*q^60 + (-3/2*a^4+1/2*a^3+13*a^2-9/2*a-47/2)*q^61 + (-1/2*a^4-1/2*a^3+6*a^2+17/2*a-27/2)*q^62 + (-a^2-a+7)*q^63 + (3*a^4+a^3-26*a^2-5*a+46)*q^64 + (a^4+a^3-10*a^2-7*a+15)*q^65 + (3*a^4-a^3-22*a^2-a+27)*q^66 + (-a^4+10*a^2+5*a-22)*q^67 + (7/2*a^4+3/2*a^3-29*a^2-11/2*a+87/2)*q^68 + (-1/2*a^4+1/2*a^3+4*a^2-5/2*a-11/2)*q^69 + (-3/2*a^4+1/2*a^3+11*a^2-5/2*a-27/2)*q^70 + (2*a^4-a^3-17*a^2+5*a+27)*q^71 + (-3*a^4+2*a^3+21*a^2-12*a-27)*q^72 + (-a^4+5*a^2+2)*q^73 + (a^4+a^3-10*a^2-5*a+27)*q^74 + (1/2*a^4-5/2*a^3+29/2*a-37/2)*q^75 + (-2*a^3+2*a^2+4*a-4)*q^76 + (-a^4+8*a^2+a-12)*q^77 + (-2*a^4-2*a^3+19*a^2+12*a-27)*q^78 + (a^4-10*a^2-a+26)*q^79 + (-3/2*a^4-3/2*a^3+9*a^2-1/2*a-3/2)*q^80 + (a^4+2*a^3-10*a^2-11*a+19)*q^81 + (-a^4+a^3+5*a^2-3*a)*q^82 + (a^4+a^3-10*a^2-5*a+21)*q^83 + (1/2*a^4-1/2*a^3-3*a^2+1/2*a+5/2)*q^84 + (a^4-14*a^2-3*a+36)*q^85 + (3*a^4-a^3-22*a^2+a+27)*q^86 + (2*a^4-a^3-21*a^2+11*a+39)*q^87 + (-2*a^4-3*a^3+18*a^2+10*a-27)*q^88 + (-3/2*a^4+1/2*a^3+13*a^2-1/2*a-51/2)*q^89 + (-1/2*a^4+11/2*a^3+a^2-55/2*a+27/2)*q^90 + (a^4-9*a^2+14)*q^91 + (-a^2+2)*q^92 + (3*a^4-3*a^3-23*a^2+16*a+23)*q^93 + (-3/2*a^4+1/2*a^3+16*a^2+3/2*a-81/2)*q^94 + (2*a^4-2*a^3-12*a^2+10*a+6)*q^95 + (-3/2*a^4-1/2*a^3+11*a^2+13/2*a-27/2)*q^96 + (-3/2*a^4-3/2*a^3+13*a^2+19/2*a-47/2)*q^97 + a*q^98 + (a^3-2*a-3)*q^99 + (2*a^4+a^3-13*a^2-4*a+19)*q^100 + (-a^4+a^3+10*a^2-7*a-21)*q^101 + (-4*a^4-a^3+40*a^2+6*a-81)*q^102 + (-2*a^2+14)*q^103 + (a^4-5*a^2-2*a)*q^104 + (a^3-8*a+3)*q^105 + (-2*a^3+12*a)*q^106 + (-a^4+a^3+10*a^2-9*a-21)*q^107 + (-a^4+10*a^2+2*a-17)*q^108 + (-a^4+a^3+12*a^2-5*a-25)*q^109 + (-a^4-a^3+16*a^2+7*a-27)*q^110 + (a^4+a^3-14*a^2-7*a+47)*q^111 + (a^4-6*a^2+4)*q^112 + (-2*a^4+18*a^2-30)*q^113 + (-2*a^4+4*a^3+10*a^2-16*a)*q^114 + (1/2*a^4+1/2*a^3-5*a^2-5/2*a+21/2)*q^115 + (-3*a^4+a^3+18*a^2-2*a-24)*q^116 + (a^4-a^3-10*a^2+7*a+17)*q^117 + (-3/2*a^4+1/2*a^3+9*a^2+7/2*a-27/2)*q^118 + (1/2*a^4+1/2*a^3-3*a^2-5/2*a-3/2)*q^119 + (a^4+4*a^3-18*a^2-17*a+54)*q^120 + (-3*a^4-a^3+30*a^2+7*a-56)*q^121 + (-5/2*a^4-1/2*a^3+21*a^2+1/2*a-81/2)*q^122 + (a^4-9*a^2-4*a+24)*q^123 + (-1/2*a^4+1/2*a^3+9*a^2-1/2*a-29/2)*q^124 + (2*a^4-2*a^3-18*a^2+12*a+24)*q^125 + (-a^3-a^2+7*a)*q^126 + (3*a^4-29*a^2-2*a+56)*q^127 + (3*a^4-a^3-22*a^2+6*a+27)*q^128 + (-2*a^4+16*a^2+6*a-28)*q^129 + (3*a^4-a^3-24*a^2-a+27)*q^130 + (1/2*a^4-1/2*a^3-6*a^2+1/2*a+15/2)*q^131 + (3*a^4+3*a^3-32*a^2-11*a+51)*q^132 + (-2*a+2)*q^133 + (-2*a^4+a^3+22*a^2-6*a-27)*q^134 + (-3*a^4+3*a^3+22*a^2-19*a-15)*q^135 + (11/2*a^4-1/2*a^3-43*a^2+13/2*a+135/2)*q^136 + (a^4+a^3-14*a^2-7*a+33)*q^137 + (-1/2*a^4-1/2*a^3+6*a^2+5/2*a-27/2)*q^138 + (7/2*a^4-3/2*a^3-28*a^2+19/2*a+73/2)*q^139 + (-3/2*a^4-3/2*a^3+13*a^2+11/2*a-39/2)*q^140 + (-a^4-a^3+17*a^2+4*a-63)*q^141 + (3*a^4+a^3-29*a^2-5*a+54)*q^142 + (4*a^4-34*a^2-6*a+48)*q^143 + (-2*a^4-4*a^3+21*a^2+17*a-53)*q^144 + (2*a^3+2*a^2-4*a-18)*q^145 + (-2*a^4-4*a^3+17*a^2+18*a-27)*q^146 + (1/2*a^4-1/2*a^3-4*a^2+5/2*a+11/2)*q^147 + (a^4+a^3-6*a^2-3*a+5)*q^148 + (2*a^4+2*a^3-18*a^2-14*a+30)*q^149 + (-3/2*a^4+9/2*a^3+6*a^2-53/2*a+27/2)*q^150 + (-3*a^4+25*a^2-2*a-28)*q^151 + (-2*a^4+2*a^3+8*a^2-8*a)*q^152 + (-5/2*a^4-1/2*a^3+25*a^2+5/2*a-129/2)*q^153 + (-2*a^4-a^3+18*a^2+4*a-27)*q^154 + (-3*a^4-4*a^3+30*a^2+23*a-66)*q^155 + (-4*a^4+a^3+32*a^2+a-46)*q^156 + (-1/2*a^4-1/2*a^3+7*a^2+5/2*a-53/2)*q^157 + (2*a^4-a^3-18*a^2+10*a+27)*q^158 + (3*a^4-3*a^3-26*a^2+19*a+39)*q^159 + (-3/2*a^4-3/2*a^3+7*a^2+7/2*a-27/2)*q^160 + -1*q^161 + (4*a^4-a^3-28*a^2+3*a+27)*q^162 + (-2*a^4-a^3+17*a^2+7*a-25)*q^163 + (-a^4-2*a^3+12*a^2+6*a-21)*q^164 + (3*a^4+a^3-30*a^2-3*a+45)*q^165 + (3*a^4-a^3-22*a^2+5*a+27)*q^166 + (-5/2*a^4+3/2*a^3+27*a^2-15/2*a-105/2)*q^167 + (-1/2*a^4+1/2*a^3+4*a^2-1/2*a-27/2)*q^168 + (-4*a^4-a^3+35*a^2+9*a-60)*q^169 + (2*a^4-5*a^3-20*a^2+20*a+27)*q^170 + (2*a^3-16*a+14)*q^171 + (3*a^4+3*a^3-30*a^2-11*a+47)*q^172 + (-2*a^4+16*a^2-2*a-18)*q^173 + (3*a^4-3*a^3-23*a^2+7*a+54)*q^174 + (a^3-6*a+4)*q^175 + (-a^4-a+6)*q^176 + (2*a^4-3*a^3-12*a^2+12*a+9)*q^177 + (-5/2*a^4-1/2*a^3+25*a^2-3/2*a-81/2)*q^178 + (-a^4+11*a^2-6*a-24)*q^179 + (7/2*a^4-1/2*a^3-21*a^2+5/2*a+51/2)*q^180 + (1/2*a^4+1/2*a^3-5*a^2-9/2*a+13/2)*q^181 + (2*a^4-17*a^2-2*a+27)*q^182 + (-2*a^4+a^3+22*a^2-6*a-55)*q^183 + (-a^3+4*a)*q^184 + (-3*a^4+3*a^3+22*a^2-21*a-21)*q^185 + (3*a^4+4*a^3-35*a^2-25*a+81)*q^186 + (3*a^4-a^3-28*a^2-a+45)*q^187 + (1/2*a^4-1/2*a^3-a^2+5/2*a+9/2)*q^188 + (-a^3+a^2+7*a-5)*q^189 + (2*a^4+6*a^3-24*a^2-26*a+54)*q^190 + (a^4-a^3-6*a^2+5*a+9)*q^191 + (-1/2*a^4-7/2*a^3+4*a^2+47/2*a-7/2)*q^192 + (-a^4+2*a^3+3*a^2-8*a+14)*q^193 + (-9/2*a^4-1/2*a^3+35*a^2+1/2*a-81/2)*q^194 + (-4*a^4+36*a^2+6*a-66)*q^195 + (a^2-2)*q^196 + (4*a^4+a^3-31*a^2-9*a+45)*q^197 + (a^4-2*a^2-3*a)*q^198 + (-2*a^3+2*a^2+14*a+2)*q^199 + (3*a^4+5*a^3-26*a^2-21*a+54)*q^200 +  ...

-------------------------------------------------------
161E (old = 23A), dim = 2

CONGRUENCES:
Modular Degree = 2^4*19
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*19 + Z/2*19
= B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/19 + Z/19) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(162)
Weight 2

-------------------------------------------------------
J_0(162), dim = 16

-------------------------------------------------------
162A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/3) + H(Z/3)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 3
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 4.3954068689522080994 + -0.21591280995459910528e-3i
Omega-         = 0.20052549638615694125e-4 + -1.5040943413020905951i
L(1)           =
w1             = -2.1976934082012847418 + -0.75193921424606799801i
w2             = -0.20052549638615694125e-4 + 1.5040943413020905951i
c4             = 297.00061043516719831 + -0.20147172658314837432e-1i
c6             = -5589.0494478545664391 + 0.28996016662265370272i
j              = -8983.6050287865905175 + 5.5546703514145375964i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^4 + -3*q^5 + -4*q^7 + -1*q^8 + 3*q^10 + -1*q^13 + 4*q^14 + 1*q^16 + -3*q^17 + -4*q^19 + -3*q^20 + 4*q^25 + 1*q^26 + -4*q^28 + 9*q^29 + -4*q^31 + -1*q^32 + 3*q^34 + 12*q^35 + -1*q^37 + 4*q^38 + 3*q^40 + 6*q^41 + 8*q^43 + -12*q^47 + 9*q^49 + -4*q^50 + -1*q^52 + -6*q^53 + 4*q^56 + -9*q^58 + -1*q^61 + 4*q^62 + 1*q^64 + 3*q^65 + -4*q^67 + -3*q^68 + -12*q^70 + -12*q^71 + 11*q^73 + 1*q^74 + -4*q^76 + -16*q^79 + -3*q^80 + -6*q^82 + -12*q^83 + 9*q^85 + -8*q^86 + -3*q^89 + 4*q^91 + 12*q^94 + 12*q^95 + 2*q^97 + -9*q^98 + 4*q^100 + -6*q^101 + -4*q^103 + 1*q^104 + 6*q^106 + 12*q^107 + 11*q^109 + -4*q^112 + -15*q^113 + 9*q^116 + 12*q^119 + -11*q^121 + 1*q^122 + -4*q^124 + 3*q^125 + -16*q^127 + -1*q^128 + -3*q^130 + -12*q^131 + 16*q^133 + 4*q^134 + 3*q^136 + 9*q^137 + 20*q^139 + 12*q^140 + 12*q^142 + -27*q^145 + -11*q^146 + -1*q^148 + 9*q^149 + 8*q^151 + 4*q^152 + 12*q^155 + -13*q^157 + 16*q^158 + 3*q^160 + 8*q^163 + 6*q^164 + 12*q^166 + 12*q^167 + -12*q^169 + -9*q^170 + 8*q^172 + -3*q^173 + -16*q^175 + 3*q^178 + 12*q^179 + -10*q^181 + -4*q^182 + 3*q^185 + -12*q^188 + -12*q^190 + 12*q^191 + -13*q^193 + -2*q^194 + 9*q^196 + -3*q^197 + -4*q^199 + -4*q^200 +  ...

-------------------------------------------------------
162B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/2 + Z/2) + E(Z/3) + F(Z/3) + H(Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 2.8006334736963629836 + -0.91880555906940018015e-4i
Omega-         = 0.78122654839455741737e-4 + 2.9168056290850827244i
L(1)           = 0.93354449173450950953
w1             = -1.4002776755207617639 + 1.4584487548204948322i
w2             = 1.4003557981756012197 + 1.4583568742645878922i
c4             = -134.99411900973049118 + -0.15790869304694908783e-1i
c6             = 243.25783877268475701 + 0.79218406079396557259e-1i
j              = 1687.4108463385624117 + -0.119061337927345708e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^4 + 2*q^7 + -1*q^8 + 3*q^11 + 2*q^13 + -2*q^14 + 1*q^16 + 3*q^17 + -1*q^19 + -3*q^22 + 6*q^23 + -5*q^25 + -2*q^26 + 2*q^28 + -6*q^29 + -4*q^31 + -1*q^32 + -3*q^34 + -4*q^37 + 1*q^38 + -9*q^41 + -1*q^43 + 3*q^44 + -6*q^46 + 6*q^47 + -3*q^49 + 5*q^50 + 2*q^52 + -12*q^53 + -2*q^56 + 6*q^58 + -3*q^59 + 8*q^61 + 4*q^62 + 1*q^64 + 5*q^67 + 3*q^68 + 12*q^71 + 11*q^73 + 4*q^74 + -1*q^76 + 6*q^77 + -4*q^79 + 9*q^82 + -12*q^83 + 1*q^86 + -3*q^88 + -6*q^89 + 4*q^91 + 6*q^92 + -6*q^94 + 5*q^97 + 3*q^98 + -5*q^100 + 14*q^103 + -2*q^104 + 12*q^106 + -3*q^107 + -16*q^109 + 2*q^112 + -6*q^113 + -6*q^116 + 3*q^118 + 6*q^119 + -2*q^121 + -8*q^122 + -4*q^124 + 2*q^127 + -1*q^128 + -2*q^133 + -5*q^134 + -3*q^136 + 3*q^137 + -19*q^139 + -12*q^142 + 6*q^143 + -11*q^146 + -4*q^148 + 6*q^149 + -10*q^151 + 1*q^152 + -6*q^154 + -4*q^157 + 4*q^158 + 12*q^161 + -4*q^163 + -9*q^164 + 12*q^166 + 12*q^167 + -9*q^169 + -1*q^172 + 6*q^173 + -10*q^175 + 3*q^176 + 6*q^178 + -12*q^179 + 14*q^181 + -4*q^182 + -6*q^184 + 9*q^187 + 6*q^188 + 18*q^191 + 5*q^193 + -5*q^194 + -3*q^196 + 12*q^197 + -10*q^199 + 5*q^200 +  ...

-------------------------------------------------------
162C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= B(Z/2 + Z/2) + D(Z/3)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 5.0519136311028646135 + 0.36364047268699157736e-5i
Omega-         = 0.3623927842580650579e-4 + 1.6169622558307042689i
L(1)           = 1.6839712103680577897
w1             = -2.5259386959122194035 + 0.80847930971298869949i
w2             = 0.3623927842580650579e-4 + 1.6169622558307042689i
c4             = 225.00566307209768513 + 0.20849006749628033401e-1i
c6             = -3537.1217389634958411 + -0.4542087329637672524i
j              = -17579.433469164468702 + -4.1554304876952861758i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + 2*q^7 + 1*q^8 + -3*q^11 + 2*q^13 + 2*q^14 + 1*q^16 + -3*q^17 + -1*q^19 + -3*q^22 + -6*q^23 + -5*q^25 + 2*q^26 + 2*q^28 + 6*q^29 + -4*q^31 + 1*q^32 + -3*q^34 + -4*q^37 + -1*q^38 + 9*q^41 + -1*q^43 + -3*q^44 + -6*q^46 + -6*q^47 + -3*q^49 + -5*q^50 + 2*q^52 + 12*q^53 + 2*q^56 + 6*q^58 + 3*q^59 + 8*q^61 + -4*q^62 + 1*q^64 + 5*q^67 + -3*q^68 + -12*q^71 + 11*q^73 + -4*q^74 + -1*q^76 + -6*q^77 + -4*q^79 + 9*q^82 + 12*q^83 + -1*q^86 + -3*q^88 + 6*q^89 + 4*q^91 + -6*q^92 + -6*q^94 + 5*q^97 + -3*q^98 + -5*q^100 + 14*q^103 + 2*q^104 + 12*q^106 + 3*q^107 + -16*q^109 + 2*q^112 + 6*q^113 + 6*q^116 + 3*q^118 + -6*q^119 + -2*q^121 + 8*q^122 + -4*q^124 + 2*q^127 + 1*q^128 + -2*q^133 + 5*q^134 + -3*q^136 + -3*q^137 + -19*q^139 + -12*q^142 + -6*q^143 + 11*q^146 + -4*q^148 + -6*q^149 + -10*q^151 + -1*q^152 + -6*q^154 + -4*q^157 + -4*q^158 + -12*q^161 + -4*q^163 + 9*q^164 + 12*q^166 + -12*q^167 + -9*q^169 + -1*q^172 + -6*q^173 + -10*q^175 + -3*q^176 + 6*q^178 + 12*q^179 + 14*q^181 + 4*q^182 + -6*q^184 + 9*q^187 + -6*q^188 + -18*q^191 + 5*q^193 + 5*q^194 + -3*q^196 + -12*q^197 + -10*q^199 + -5*q^200 +  ...

-------------------------------------------------------
162D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + C(Z/3) + E(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 2/3
Sha Bound      = 2*3

ANALYTIC INVARIANTS:

Omega+         = 2.6051629765651617581 + 0.94377776752550715596e-4i
Omega-         = 0.12630153422324013213e-3 + 2.5377084350024117339i
L(1)           = 1.7367753188497889031
w1             = 1.3026446390496924991 + 1.2689014063895821423i
w2             = 1.302518337515469259 + -1.2688070286128295916i
c4             = -207.00153262858540951 + -0.14057647864650956211e-2i
c6             = -296.9787706443693357 + -0.9819849861926246101i
j              = 1710.9873323710119431 + -0.11105789345018999637i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + 3*q^5 + -4*q^7 + 1*q^8 + 3*q^10 + -1*q^13 + -4*q^14 + 1*q^16 + 3*q^17 + -4*q^19 + 3*q^20 + 4*q^25 + -1*q^26 + -4*q^28 + -9*q^29 + -4*q^31 + 1*q^32 + 3*q^34 + -12*q^35 + -1*q^37 + -4*q^38 + 3*q^40 + -6*q^41 + 8*q^43 + 12*q^47 + 9*q^49 + 4*q^50 + -1*q^52 + 6*q^53 + -4*q^56 + -9*q^58 + -1*q^61 + -4*q^62 + 1*q^64 + -3*q^65 + -4*q^67 + 3*q^68 + -12*q^70 + 12*q^71 + 11*q^73 + -1*q^74 + -4*q^76 + -16*q^79 + 3*q^80 + -6*q^82 + 12*q^83 + 9*q^85 + 8*q^86 + 3*q^89 + 4*q^91 + 12*q^94 + -12*q^95 + 2*q^97 + 9*q^98 + 4*q^100 + 6*q^101 + -4*q^103 + -1*q^104 + 6*q^106 + -12*q^107 + 11*q^109 + -4*q^112 + 15*q^113 + -9*q^116 + -12*q^119 + -11*q^121 + -1*q^122 + -4*q^124 + -3*q^125 + -16*q^127 + 1*q^128 + -3*q^130 + 12*q^131 + 16*q^133 + -4*q^134 + 3*q^136 + -9*q^137 + 20*q^139 + -12*q^140 + 12*q^142 + -27*q^145 + 11*q^146 + -1*q^148 + -9*q^149 + 8*q^151 + -4*q^152 + -12*q^155 + -13*q^157 + -16*q^158 + 3*q^160 + 8*q^163 + -6*q^164 + 12*q^166 + -12*q^167 + -12*q^169 + 9*q^170 + 8*q^172 + 3*q^173 + -16*q^175 + 3*q^178 + -12*q^179 + -10*q^181 + 4*q^182 + -3*q^185 + 12*q^188 + -12*q^190 + -12*q^191 + -13*q^193 + 2*q^194 + 9*q^196 + 3*q^197 + -4*q^199 + 4*q^200 +  ...

-------------------------------------------------------
162E (old = 81A), dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^3
Ker(ModPolar)  = Z/3 + Z/3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= A(Z/2 + Z/2) + B(Z/3) + D(Z/2 + Z/2) + F(Z/3 + Z/3) + G(Z/3) + H(Z/3 + Z/3 + Z/3)

-------------------------------------------------------
162F (old = 54A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^3
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3^2 + Z/2*3^2
= A(Z/3) + B(Z/3) + E(Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/3 + Z/3 + Z/3)

-------------------------------------------------------
162G (old = 54B), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= E(Z/3) + F(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/3 + Z/3)

-------------------------------------------------------
162H (old = 27A), dim = 1

CONGRUENCES:
Modular Degree = 3^5
Ker(ModPolar)  = Z/3 + Z/3 + Z/3 + Z/3 + Z/3 + Z/3 + Z/3^2 + Z/3^2
= A(Z/3) + B(Z/3) + E(Z/3 + Z/3 + Z/3) + F(Z/3 + Z/3 + Z/3) + G(Z/3 + Z/3)

-------------------------------------------------------
Gamma_0(163)
Weight 2

-------------------------------------------------------
J_0(163), dim = 13

-------------------------------------------------------
163A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= B(Z/3 + Z/3) + C(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 5.517862354181293424 + 0.13924325460757515835e-3i
Omega-         = 0.57115272157647872924e-4 + 1.9872616688037479596i
L(1)           =
w1             = 2.7589026194545678881 + -0.9935612127745701922i
w2             = -0.57115272157647872924e-4 + -1.9872616688037479596i
c4             = 96.032027193480250081 + 0.12873061778493623232e-1i
c6             = -1080.487305647450076 + -0.14814589060089127215i
j              = -5430.0411547530305156 + -2.8775375143542121365i

HECKE EIGENFORM:
f(q) = 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 + 3*q^41 + 7*q^43 + 12*q^44 + 12*q^45 + 1*q^47 + -3*q^49 + -8*q^52 + -9*q^53 + 24*q^55 + -2*q^59 + 3*q^61 + -6*q^63 + -8*q^64 + -16*q^65 + -2*q^67 + -5*q^71 + -2*q^73 + 12*q^76 + -12*q^77 + -8*q^79 + -16*q^80 + 9*q^81 + 5*q^83 + -14*q^89 + 8*q^91 + -12*q^92 + 24*q^95 + -11*q^97 + 18*q^99 + -22*q^100 + -4*q^101 + 8*q^103 + 18*q^107 + -6*q^109 + 8*q^112 + -3*q^113 + -24*q^115 + 8*q^116 + -12*q^117 + 25*q^121 + 12*q^124 + -24*q^125 + 8*q^127 + 7*q^131 + -12*q^133 + 2*q^137 + 4*q^139 + 16*q^140 + -24*q^143 + -12*q^144 + 16*q^145 + 16*q^148 + 10*q^149 + 7*q^151 + 24*q^155 + 10*q^157 + 12*q^161 + -1*q^163 + -6*q^164 + -12*q^167 + 3*q^169 + 18*q^171 + -14*q^172 + -21*q^173 + 22*q^175 + -24*q^176 + 4*q^179 + -24*q^180 + -22*q^181 + 32*q^185 + -2*q^188 + -6*q^191 + 20*q^193 + 6*q^196 + 23*q^197 + -8*q^199 +  ...

-------------------------------------------------------
163B (new) , dim = 5

CONGRUENCES:
Modular Degree = 2^5*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3 + Z/2*3
= A(Z/3 + Z/3) + C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 65657
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 189.59641003541027921 + -0.17365085025186280418e-1i
Omega-         = 0.11943542569528151424e-2 + 43.039309500614108293i
L(1)           =

HECKE EIGENFORM:
a^5+5*a^4+3*a^3-15*a^2-16*a+3 = 0,
f(q) = 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 + (7*a^4+15*a^3-22*a^2-35*a+6)*q^38 + (5*a^4+13*a^3-13*a^2-32*a+6)*q^39 + (-10*a^4-25*a^3+34*a^2+71*a-12)*q^40 + (2*a^4+8*a^3-2*a^2-25*a-6)*q^41 + (-5*a^4-14*a^3+16*a^2+38*a-6)*q^42 + (3*a^4+8*a^3-10*a^2-22*a+7)*q^43 + (a^4+3*a^3-7*a-9)*q^44 + (3*a^4+6*a^3-16*a^2-25*a+6)*q^45 + (-7*a^4-14*a^3+23*a^2+32*a-6)*q^46 + (-2*a^4-4*a^3+9*a^2+12*a-8)*q^47 + (-16*a^4-36*a^3+56*a^2+103*a-21)*q^48 + (-7*a^4-21*a^3+15*a^2+58*a+6)*q^49 + (23*a^4+59*a^3-70*a^2-160*a+27)*q^50 + (10*a^4+24*a^3-32*a^2-65*a+15)*q^51 + (-3*a^4-7*a^3+8*a^2+19*a-2)*q^52 + (-3*a^4-7*a^3+10*a^2+17*a-9)*q^53 + (-3*a^4-10*a^3+4*a^2+22*a-3)*q^54 + (-a-3)*q^55 + (-18*a^4-44*a^3+57*a^2+121*a-18)*q^56 + (2*a^4+2*a^3-11*a^2-10*a+3)*q^57 + (4*a^4+10*a^3-14*a^2-33*a+6)*q^58 + (-9*a^4-22*a^3+30*a^2+65*a-11)*q^59 + (21*a^4+53*a^3-66*a^2-143*a+24)*q^60 + (3*a^4+7*a^3-9*a^2-20*a-3)*q^61 + (-9*a^4-26*a^3+26*a^2+76*a-12)*q^62 + (6*a^4+13*a^3-23*a^2-35*a+18)*q^63 + (12*a^4+30*a^3-35*a^2-83*a+7)*q^64 + (-3*a^4-7*a^3+13*a^2+25*a-4)*q^65 + (a^4+a^3-5*a^2-3*a)*q^66 + (-a^4-5*a^3+18*a+4)*q^67 + (-6*a^4-14*a^3+15*a^2+39*a+3)*q^68 + (-4*a^4-7*a^3+16*a^2+22*a-3)*q^69 + (22*a^4+55*a^3-72*a^2-152*a+27)*q^70 + (2*a^3+4*a^2-10*a-5)*q^71 + (-7*a^4-17*a^3+18*a^2+44*a-6)*q^72 + (3*a^4+8*a^3-5*a^2-16*a-8)*q^73 + (8*a^4+19*a^3-27*a^2-53*a+9)*q^74 + (-11*a^4-30*a^3+29*a^2+72*a-9)*q^75 + (-16*a^4-37*a^3+52*a^2+102*a-15)*q^76 + (2*a^4+8*a^3+2*a^2-22*a-21)*q^77 + (-12*a^4-28*a^3+43*a^2+86*a-15)*q^78 + (7*a^4+21*a^3-17*a^2-61*a-2)*q^79 + (9*a^4+24*a^3-25*a^2-60*a+8)*q^80 + (4*a^4+12*a^3-9*a^2-27*a+9)*q^81 + (-2*a^4-8*a^3+5*a^2+26*a-6)*q^82 + (-a^4-5*a^3+18*a+2)*q^83 + (7*a^4+21*a^3-21*a^2-58*a+3)*q^84 + (-7*a^4-18*a^3+23*a^2+52*a-6)*q^85 + (-7*a^4-19*a^3+23*a^2+55*a-9)*q^86 + (4*a^4+11*a^3-8*a^2-25*a+3)*q^87 + (-4*a^4-11*a^3+12*a^2+33*a-9)*q^88 + (-2*a^4-8*a^3+a^2+18*a+1)*q^89 + (-9*a^4-25*a^3+20*a^2+54*a-9)*q^90 + (-6*a^4-15*a^3+18*a^2+41*a-4)*q^91 + (17*a^4+38*a^3-57*a^2-104*a+21)*q^92 + (7*a^4+17*a^3-21*a^2-43*a+3)*q^93 + (6*a^4+15*a^3-18*a^2-40*a+6)*q^94 + (6*a^4+14*a^3-24*a^2-46*a+9)*q^95 + (18*a^4+42*a^3-55*a^2-111*a+18)*q^96 + (11*a^4+28*a^3-36*a^2-77*a+25)*q^97 + (14*a^4+36*a^3-47*a^2-106*a+21)*q^98 + (4*a^4+14*a^3-5*a^2-40*a-6)*q^99 + (-38*a^4-95*a^3+121*a^2+265*a-37)*q^100 + (2*a^4+8*a^3-a^2-25*a-13)*q^101 + (-26*a^4-62*a^3+85*a^2+175*a-30)*q^102 + (-3*a^4-5*a^3+14*a^2+12*a-13)*q^103 + (4*a^4+7*a^3-12*a^2-14*a+3)*q^104 + (-18*a^4-45*a^3+60*a^2+125*a-24)*q^105 + (8*a^4+19*a^3-28*a^2-57*a+9)*q^106 + (8*a^4+21*a^3-23*a^2-61*a)*q^107 + (3*a^4+9*a^3-9*a^2-29*a-3)*q^108 + (-6*a^4-20*a^3+11*a^2+62*a+9)*q^109 + (-a^2-3*a)*q^110 + (-3*a^4-8*a^3+11*a^2+25*a-3)*q^111 + (22*a^4+55*a^3-65*a^2-152*a+8)*q^112 + (2*a^4+a^3-14*a^2+18)*q^113 + (-8*a^4-17*a^3+20*a^2+35*a-6)*q^114 + (-5*a^4-12*a^3+19*a^2+39*a-6)*q^115 + (-6*a^4-14*a^3+19*a^2+38*a-10)*q^116 + (-a^4-2*a^3-3*a^2-8*a+3)*q^117 + (23*a^4+57*a^3-70*a^2-155*a+27)*q^118 + (-14*a^4-37*a^3+37*a^2+102*a+6)*q^119 + (-28*a^4-71*a^3+86*a^2+188*a-33)*q^120 + (4*a^4+11*a^3-18*a^2-38*a+22)*q^121 + (-8*a^4-18*a^3+25*a^2+45*a-9)*q^122 + (5*a^4+10*a^3-19*a^2-25*a+12)*q^123 + (11*a^4+31*a^3-31*a^2-88*a+3)*q^124 + (20*a^4+48*a^3-71*a^2-137*a+30)*q^125 + (-17*a^4-41*a^3+55*a^2+114*a-18)*q^126 + (-4*a^4-11*a^3+11*a^2+23*a-7)*q^127 + (-20*a^4-49*a^3+67*a^2+143*a-30)*q^128 + (12*a^4+29*a^3-40*a^2-82*a+12)*q^129 + (8*a^4+22*a^3-20*a^2-52*a+9)*q^130 + (13*a^4+33*a^3-43*a^2-93*a+25)*q^131 + (-4*a^4-10*a^3+10*a^2+26*a+3)*q^132 + (-a^4-2*a^3+a^2+6*a+6)*q^133 + (3*a^3+3*a^2-12*a+3)*q^134 + (-4*a^4-7*a^3+25*a^2+36*a-9)*q^135 + (10*a^4+19*a^3-33*a^2-49*a+12)*q^136 + (-a^4+2*a^3+11*a^2-5*a-13)*q^137 + (13*a^4+28*a^3-38*a^2-67*a+12)*q^138 + (-5*a^4-15*a^3+7*a^2+36*a+10)*q^139 + (-37*a^4-92*a^3+122*a^2+253*a-50)*q^140 + (-a^4-4*a^3+8*a+3)*q^141 + (2*a^4+4*a^3-10*a^2-5*a)*q^142 + (3*a^4+11*a^3-7*a^2-38*a+3)*q^143 + (14*a^4+33*a^3-47*a^2-106*a+9)*q^144 + (a^3+5*a^2+5*a-2)*q^145 + (-7*a^4-14*a^3+29*a^2+40*a-9)*q^146 + (-8*a^4-17*a^3+35*a^2+52*a-21)*q^147 + (-15*a^4-37*a^3+47*a^2+101*a-14)*q^148 + (4*a^4+13*a^3-5*a^2-37*a-17)*q^149 + (25*a^4+62*a^3-93*a^2-185*a+33)*q^150 + (-9*a^4-26*a^3+26*a^2+82*a+4)*q^151 + (29*a^4+70*a^3-94*a^2-201*a+36)*q^152 + (-4*a^4-9*a^3+7*a^2+18*a+9)*q^153 + (-2*a^4-4*a^3+8*a^2+11*a-6)*q^154 + (-12*a^4-29*a^3+42*a^2+81*a-18)*q^155 + (22*a^4+53*a^3-68*a^2-143*a+24)*q^156 + (9*a^4+19*a^3-31*a^2-44*a+13)*q^157 + (-14*a^4-38*a^3+44*a^2+110*a-21)*q^158 + (4*a^2+8*a+3)*q^159 + (-a^4-2*a^3+7*a^2+10*a-3)*q^160 + (3*a^4+5*a^3-12*a^2-14*a+9)*q^161 + (-8*a^4-21*a^3+33*a^2+73*a-12)*q^162 + -1*q^163 + (-2*a^4-5*a^3+12*a+18)*q^164 + (a^4+3*a^3-a^2-4*a+3)*q^165 + (3*a^3+3*a^2-14*a+3)*q^166 + (7*a^4+14*a^3-31*a^2-41*a+24)*q^167 + (-4*a^4-14*a^3+15*a^2+39*a-9)*q^168 + (5*a^4+15*a^3-10*a^2-39*a-6)*q^169 + (17*a^4+44*a^3-53*a^2-118*a+21)*q^170 + (-13*a^4-32*a^3+47*a^2+107*a-15)*q^171 + (10*a^4+28*a^3-30*a^2-77*a+7)*q^172 + (-3*a^4-8*a^3+12*a^2+27*a-21)*q^173 + (-9*a^4-20*a^3+35*a^2+67*a-12)*q^174 + (23*a^4+56*a^3-82*a^2-153*a+49)*q^175 + (7*a^4+18*a^3-27*a^2-59*a+30)*q^176 + (5*a^4+9*a^3-21*a^2-35*a+6)*q^177 + (2*a^4+7*a^3-12*a^2-31*a+6)*q^178 + (-7*a^4-18*a^3+14*a^2+41*a+16)*q^179 + (14*a^4+35*a^3-49*a^2-103*a+15)*q^180 + (10*a^4+23*a^3-31*a^2-58*a+11)*q^181 + (15*a^4+36*a^3-49*a^2-100*a+18)*q^182 + (-4*a^4-8*a^3+15*a^2+27*a)*q^183 + (-33*a^4-80*a^3+105*a^2+229*a-39)*q^184 + (11*a^4+28*a^3-34*a^2-74*a+14)*q^185 + (-18*a^4-42*a^3+62*a^2+115*a-21)*q^186 + (3*a^4+14*a^3+a^2-45*a-18)*q^187 + (-11*a^4-28*a^3+32*a^2+78*a-2)*q^188 + (-5*a^4-10*a^3+22*a^2+26*a-24)*q^189 + (-16*a^4-42*a^3+44*a^2+105*a-18)*q^190 + (6*a^4+12*a^3-22*a^2-28*a+6)*q^191 + (-16*a^4-37*a^3+47*a^2+100*a-12)*q^192 + (-12*a^4-30*a^3+31*a^2+76*a+5)*q^193 + (-27*a^4-69*a^3+88*a^2+201*a-33)*q^194 + (-9*a^4-25*a^3+18*a^2+51*a-9)*q^195 + (-20*a^4-47*a^3+74*a^2+129*a-54)*q^196 + (5*a^4+13*a^3-18*a^2-38*a+5)*q^197 + (-6*a^4-17*a^3+20*a^2+58*a-12)*q^198 + (-4*a^4-12*a^3+16*a^2+40*a-17)*q^199 + (49*a^4+117*a^3-165*a^2-325*a+60)*q^200 +  ...

-------------------------------------------------------
163C (new) , dim = 7

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^3*82536739
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 3^3
Torsion Bound  = 2*3^3
|L(1)/Omega|   = 2^6/3^3
Sha Bound      = 2^8*3^3

ANALYTIC INVARIANTS:

Omega+         = 3.3700791562250577859 + -0.62975296572840428632e-4i
Omega-         = 0.68484218365853205307e-2 + 101.84127718187206795i
L(1)           = 7.9883357791133739724

HECKE EIGENFORM:
a^7-3*a^6-5*a^5+19*a^4-23*a^2+4*a+6 = 0,
f(q) = 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 + (3*a^6-a^5-20*a^4+4*a^3+26*a^2-2*a-6)*q^38 + (2*a^5-a^4-13*a^3+5*a^2+14*a-4)*q^39 + (-a^6-a^5+7*a^4+8*a^3-10*a^2-12*a)*q^40 + (a^6-4*a^5-4*a^4+22*a^3-3*a^2-14*a+3)*q^41 + (-2*a^5+a^4+12*a^3-4*a^2-10*a)*q^42 + (-4*a^6+4*a^5+27*a^4-24*a^3-38*a^2+26*a+11)*q^43 + (-a^6+2*a^5+7*a^4-13*a^3-11*a^2+14*a+6)*q^44 + (-a^6+a^5+8*a^4-5*a^3-18*a^2+4*a+12)*q^45 + (2*a^6-2*a^5-13*a^4+12*a^3+15*a^2-10*a-6)*q^46 + (-2*a^6+3*a^5+17*a^4-17*a^3-42*a^2+16*a+27)*q^47 + (-a^6+2*a^5+6*a^4-12*a^3-5*a^2+12*a-2)*q^48 + (2*a^6-3*a^5-14*a^4+16*a^3+22*a^2-8*a-9)*q^49 + (-5*a^6+6*a^5+33*a^4-33*a^3-45*a^2+25*a+18)*q^50 + (-a^6+2*a^5+6*a^4-12*a^3-5*a^2+12*a)*q^51 + (-a^6+a^5+6*a^4-6*a^3-2*a^2+4*a-4)*q^52 + (a^6-3*a^5-8*a^4+20*a^3+18*a^2-24*a-9)*q^53 + (-2*a^6+a^5+14*a^4-5*a^3-21*a^2+2*a+6)*q^54 + (3*a^6-6*a^5-20*a^4+36*a^3+31*a^2-36*a-18)*q^55 + (-3*a^6+5*a^5+21*a^4-29*a^3-35*a^2+22*a+18)*q^56 + (-4*a^6+5*a^5+27*a^4-29*a^3-38*a^2+28*a+14)*q^57 + (3*a^6-a^5-19*a^4+3*a^3+22*a^2+2*a-6)*q^58 + (-a^5-2*a^4+7*a^3+9*a^2-7*a)*q^59 + (5*a^6-7*a^5-32*a^4+40*a^3+38*a^2-36*a-12)*q^60 + (2*a^5-3*a^4-11*a^3+17*a^2+10*a-13)*q^61 + (-2*a^6+15*a^4+2*a^3-24*a^2-6*a+6)*q^62 + (2*a^4+a^3-11*a^2-7*a+8)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (-3*a^6+3*a^5+22*a^4-18*a^3-37*a^2+16*a+18)*q^65 + (a^6-3*a^5-6*a^4+18*a^3+7*a^2-16*a-6)*q^66 + (2*a^6-4*a^5-9*a^4+23*a^3-4*a^2-20*a+2)*q^67 + (3*a^6-2*a^5-20*a^4+10*a^3+30*a^2-8*a-12)*q^68 + (-a^5-a^4+8*a^3+7*a^2-14*a-6)*q^69 + (4*a^6-5*a^5-27*a^4+28*a^3+41*a^2-24*a-18)*q^70 + (4*a^5-4*a^4-26*a^3+20*a^2+30*a-9)*q^71 + (-2*a^5-a^4+13*a^3+6*a^2-16*a)*q^72 + (-a^6+a^5+4*a^4-3*a^3+5*a^2-7*a-4)*q^73 + (3*a^6-2*a^5-24*a^4+11*a^3+48*a^2-10*a-18)*q^74 + (a^6-3*a^4-4*a^3-14*a^2+15*a+16)*q^75 + (6*a^6-5*a^5-41*a^4+28*a^3+59*a^2-24*a-22)*q^76 + (a^5-a^4-7*a^3+3*a^2+12*a+6)*q^77 + (2*a^6-a^5-13*a^4+5*a^3+14*a^2-4*a)*q^78 + (-7*a^6+11*a^5+46*a^4-64*a^3-63*a^2+54*a+26)*q^79 + (a^4-7*a^2+6)*q^80 + (5*a^6-7*a^5-33*a^4+39*a^3+47*a^2-30*a-23)*q^81 + (-a^6+a^5+3*a^4-3*a^3+9*a^2-a-6)*q^82 + (-4*a^6+5*a^5+24*a^4-28*a^3-23*a^2+22*a+9)*q^83 + (-2*a^6+a^5+16*a^4-6*a^3-34*a^2+8*a+20)*q^84 + (a^4-2*a^3-5*a^2+4*a+6)*q^85 + (-8*a^6+7*a^5+52*a^4-38*a^3-66*a^2+27*a+24)*q^86 + (-5*a^6+10*a^5+28*a^4-57*a^3-17*a^2+46*a)*q^87 + (-3*a^6+6*a^5+20*a^4-35*a^3-31*a^2+30*a+18)*q^88 + (2*a^6-3*a^5-13*a^4+15*a^3+18*a^2-4*a-6)*q^89 + (-2*a^6+3*a^5+14*a^4-18*a^3-19*a^2+16*a+6)*q^90 + (-a^6+a^5+9*a^4-4*a^3-24*a^2-2*a+10)*q^91 + (2*a^6-a^5-12*a^4+3*a^3+12*a^2+2*a)*q^92 + (7*a^6-12*a^5-43*a^4+71*a^3+44*a^2-68*a-10)*q^93 + (-3*a^6+7*a^5+21*a^4-42*a^3-30*a^2+35*a+12)*q^94 + (2*a^6+a^5-13*a^4-9*a^3+11*a^2+14*a+6)*q^95 + (-3*a^6+a^5+25*a^4-7*a^3-55*a^2+14*a+30)*q^96 + (-a^6+3*a^5+8*a^4-15*a^3-20*a^2+6*a+17)*q^97 + (3*a^6-4*a^5-22*a^4+22*a^3+38*a^2-17*a-12)*q^98 + (2*a^3-a^2-8*a)*q^99 + (-3*a^6+20*a^4+3*a^3-24*a^2-10*a+4)*q^100 + (2*a^6-3*a^5-13*a^4+19*a^3+16*a^2-23*a)*q^101 + (-a^6+a^5+7*a^4-5*a^3-11*a^2+4*a+6)*q^102 + (6*a^6-7*a^5-42*a^4+38*a^3+69*a^2-26*a-34)*q^103 + (2*a^6-5*a^5-13*a^4+30*a^3+17*a^2-24*a-6)*q^104 + (a^6-3*a^5-9*a^4+20*a^3+26*a^2-24*a-24)*q^105 + (-3*a^5+a^4+18*a^3-a^2-13*a-6)*q^106 + (a^6-5*a^5-5*a^4+32*a^3+a^2-30*a)*q^107 + (-3*a^6+2*a^5+21*a^4-11*a^3-34*a^2+10*a+16)*q^108 + (a^6+4*a^5-10*a^4-26*a^3+26*a^2+25*a-10)*q^109 + (3*a^6-5*a^5-21*a^4+31*a^3+33*a^2-30*a-18)*q^110 + (-3*a^6+4*a^5+19*a^4-26*a^3-18*a^2+36*a-10)*q^111 + (-2*a^6+2*a^5+16*a^4-11*a^3-33*a^2+6*a+14)*q^112 + (-4*a^6+7*a^5+25*a^4-40*a^3-31*a^2+36*a+15)*q^113 + (-7*a^6+7*a^5+47*a^4-38*a^3-64*a^2+30*a+24)*q^114 + (3*a^6-5*a^5-20*a^4+29*a^3+31*a^2-30*a-18)*q^115 + (6*a^6-4*a^5-42*a^4+22*a^3+65*a^2-16*a-30)*q^116 + (a^6-4*a^5-5*a^4+24*a^3-2*a^2-17*a+8)*q^117 + (-a^6-2*a^5+7*a^4+9*a^3-7*a^2)*q^118 + (-2*a^5+13*a^3-a^2-12*a)*q^119 + (4*a^6-5*a^5-29*a^4+30*a^3+51*a^2-32*a-30)*q^120 + (-2*a^6+5*a^5+13*a^4-32*a^3-19*a^2+36*a+7)*q^121 + (2*a^6-3*a^5-11*a^4+17*a^3+10*a^2-13*a)*q^122 + (2*a^6-2*a^5-13*a^4+8*a^3+19*a^2+5*a-18)*q^123 + (-4*a^6+3*a^5+30*a^4-16*a^3-56*a^2+16*a+32)*q^124 + (-3*a^6+7*a^5+19*a^4-41*a^3-23*a^2+38*a+6)*q^125 + (2*a^5+a^4-11*a^3-7*a^2+8*a)*q^126 + (a^6-2*a^5-10*a^4+13*a^3+28*a^2-18*a-16)*q^127 + (3*a^6-7*a^5-19*a^4+40*a^3+23*a^2-36*a-6)*q^128 + (3*a^6-5*a^5-13*a^4+24*a^3-14*a^2-5*a+20)*q^129 + (-6*a^6+7*a^5+39*a^4-37*a^3-53*a^2+30*a+18)*q^130 + (7*a^6-13*a^5-42*a^4+74*a^3+41*a^2-56*a-15)*q^131 + (-2*a^6+3*a^5+15*a^4-19*a^3-29*a^2+22*a+18)*q^132 + (-2*a^6+15*a^4+2*a^3-25*a^2-8*a+4)*q^133 + (2*a^6+a^5-15*a^4-4*a^3+26*a^2-6*a-12)*q^134 + (-a^5-a^4+8*a^3+8*a^2-12*a-12)*q^135 + (3*a^6-3*a^5-19*a^4+18*a^3+21*a^2-16*a-6)*q^136 + (5*a^5-4*a^4-27*a^3+24*a^2+7*a-18)*q^137 + (-a^6-a^5+8*a^4+7*a^3-14*a^2-6*a)*q^138 + (-4*a^6+2*a^5+29*a^4-9*a^3-49*a^2+14)*q^139 + (a^6+3*a^5-8*a^4-19*a^3+12*a^2+22*a)*q^140 + (-3*a^6+12*a^5+15*a^4-74*a^3-3*a^2+75*a-6)*q^141 + (4*a^6-4*a^5-26*a^4+20*a^3+30*a^2-9*a)*q^142 + (-a^5+2*a^4+6*a^3-8*a^2-10*a)*q^143 + (2*a^6-5*a^5-11*a^4+28*a^3+6*a^2-20*a+4)*q^144 + (a^6+a^5-5*a^4-8*a^3-7*a^2+12*a+18)*q^145 + (-2*a^6-a^5+16*a^4+5*a^3-30*a^2+6)*q^146 + (-a^6-2*a^5+10*a^4+11*a^3-26*a^2-3*a+12)*q^147 + (a^6+3*a^5-12*a^4-18*a^3+37*a^2+12*a-22)*q^148 + (-3*a^6+6*a^5+14*a^4-31*a^3+8*a^2+14*a-18)*q^149 + (3*a^6+2*a^5-23*a^4-14*a^3+38*a^2+12*a-6)*q^150 + (-6*a^6+11*a^5+38*a^4-63*a^3-49*a^2+46*a+23)*q^151 + (7*a^6-9*a^5-46*a^4+51*a^3+62*a^2-42*a-24)*q^152 + (-a^6+8*a^4+a^3-20*a^2-a+12)*q^153 + (a^6-a^5-7*a^4+3*a^3+12*a^2+6*a)*q^154 + (-3*a^6-a^5+17*a^4+12*a^3-4*a^2-24*a-24)*q^155 + (5*a^6-7*a^5-31*a^4+40*a^3+32*a^2-36*a-4)*q^156 + (2*a^6-3*a^5-18*a^4+18*a^3+44*a^2-18*a-22)*q^157 + (-10*a^6+11*a^5+69*a^4-63*a^3-107*a^2+54*a+42)*q^158 + (5*a^6-4*a^5-40*a^4+26*a^3+83*a^2-37*a-42)*q^159 + (2*a^6+3*a^5-14*a^4-23*a^3+20*a^2+30*a)*q^160 + (-4*a^6+7*a^5+26*a^4-40*a^3-37*a^2+34*a+18)*q^161 + (8*a^6-8*a^5-56*a^4+47*a^3+85*a^2-43*a-30)*q^162 + 1*q^163 + (-4*a^6+6*a^5+24*a^4-35*a^3-18*a^2+26*a)*q^164 + (4*a^6-9*a^5-28*a^4+56*a^3+50*a^2-60*a-36)*q^165 + (-7*a^6+4*a^5+48*a^4-23*a^3-70*a^2+25*a+24)*q^166 + (-5*a^6+7*a^5+36*a^4-45*a^3-59*a^2+54*a+24)*q^167 + (-5*a^6+10*a^5+30*a^4-58*a^3-30*a^2+48*a+12)*q^168 + (a^6-4*a^5-5*a^4+21*a^3+5*a^2-14*a-9)*q^169 + (a^5-2*a^4-5*a^3+4*a^2+6*a)*q^170 + (2*a^6-3*a^5-12*a^4+15*a^3+10*a^2-7*a+2)*q^171 + (-9*a^6+4*a^5+60*a^4-18*a^3-81*a^2+4*a+26)*q^172 + (-5*a^6+9*a^5+28*a^4-53*a^3-18*a^2+46*a+9)*q^173 + (-5*a^6+3*a^5+38*a^4-17*a^3-69*a^2+20*a+30)*q^174 + (2*a^6-3*a^5-12*a^4+19*a^3+13*a^2-23*a-16)*q^175 + (-a^6+a^5+8*a^4-5*a^3-17*a^2+2*a+6)*q^176 + (-a^6+5*a^5-28*a^3+25*a^2+18*a-12)*q^177 + (3*a^6-3*a^5-23*a^4+18*a^3+42*a^2-14*a-12)*q^178 + (a^6-5*a^5+2*a^4+27*a^3-36*a^2-18*a+18)*q^179 + (-a^6+2*a^5+4*a^4-9*a^3+6*a^2+6*a-12)*q^180 + (2*a^6-5*a^5-7*a^4+32*a^3-16*a^2-40*a+14)*q^181 + (-2*a^6+4*a^5+15*a^4-24*a^3-25*a^2+14*a+6)*q^182 + (6*a^6-10*a^5-34*a^4+58*a^3+19*a^2-51*a+14)*q^183 + (a^6+2*a^5-9*a^4-12*a^3+18*a^2+12*a)*q^184 + (6*a^6-8*a^5-37*a^4+44*a^3+36*a^2-32*a)*q^185 + (9*a^6-8*a^5-62*a^4+44*a^3+93*a^2-38*a-42)*q^186 + (a^6-3*a^5-6*a^4+17*a^3+9*a^2-16*a-6)*q^187 + (2*a^6-19*a^4+4*a^3+50*a^2-8*a-36)*q^188 + (-2*a^6+6*a^5+13*a^4-36*a^3-18*a^2+32*a+8)*q^189 + (7*a^6-3*a^5-47*a^4+11*a^3+60*a^2-2*a-12)*q^190 + (-a^6-a^5+13*a^4+3*a^3-48*a^2+9*a+30)*q^191 + (-6*a^6+6*a^5+38*a^4-31*a^3-45*a^2+18*a+22)*q^192 + (-3*a^6+2*a^5+14*a^4-6*a^3+8*a^2-17*a-16)*q^193 + (3*a^5+4*a^4-20*a^3-17*a^2+21*a+6)*q^194 + (a^6+4*a^5-9*a^4-27*a^3+19*a^2+30*a-6)*q^195 + (a^6-a^5-7*a^4+6*a^3+8*a^2-8*a)*q^196 + (-2*a^6+4*a^5+13*a^4-27*a^3-12*a^2+38*a+3)*q^197 + (2*a^4-a^3-8*a^2)*q^198 + (6*a^6-11*a^5-35*a^4+61*a^3+27*a^2-40*a-4)*q^199 + (a^6-7*a^5-6*a^4+42*a^3+11*a^2-34*a-18)*q^200 +  ...

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Gamma_0(164)
Weight 2

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J_0(164), dim = 19

-------------------------------------------------------
164A (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^3*3^3
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= B(Z/3 + Z/3) + C(Z/3 + Z/3 + Z/3 + Z/3) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^4*1613
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2*3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/2
Sha Bound      = 2*3^2

ANALYTIC INVARIANTS:

Omega+         = 5.6975327890170456402 + -0.29362271203299637041e-3i
Omega-         = 3.0628585858217480285 + -0.52380135927343028136e-3i
L(1)           = 2.8487663982914890687

HECKE EIGENFORM:
a^4-2*a^3-10*a^2+22*a-2 = 0,
f(q) = q + a*q^3 + (-2/3*a^3-1/3*a^2+16/3*a+2/3)*q^5 + (a^3-9*a+4)*q^7 + (a^2-3)*q^9 + (1/3*a^3+2/3*a^2-11/3*a-4/3)*q^11 + (2/3*a^3-2/3*a^2-22/3*a+22/3)*q^13 + (-5/3*a^3-4/3*a^2+46/3*a-4/3)*q^15 + (-2/3*a^3-4/3*a^2+16/3*a+14/3)*q^17 + (-2/3*a^3+2/3*a^2+19/3*a-16/3)*q^19 + (2*a^3+a^2-18*a+2)*q^21 + (-2/3*a^3+2/3*a^2+16/3*a-28/3)*q^23 + (-2/3*a^3+2/3*a^2+22/3*a-13/3)*q^25 + (a^3-6*a)*q^27 + (2*a-2)*q^29 + (-4/3*a^3-2/3*a^2+32/3*a-8/3)*q^31 + (4/3*a^3-1/3*a^2-26/3*a+2/3)*q^33 + (5/3*a^3-2/3*a^2-52/3*a+16/3)*q^35 + (a^2-2)*q^37 + (2/3*a^3-2/3*a^2-22/3*a+4/3)*q^39 + -1*q^41 + (4/3*a^3+2/3*a^2-38/3*a+8/3)*q^43 + (-8/3*a^3-1/3*a^2+58/3*a-16/3)*q^45 + (-2/3*a^3+2/3*a^2+25/3*a-28/3)*q^47 + (-2*a^3-a^2+20*a+1)*q^49 + (-8/3*a^3-4/3*a^2+58/3*a-4/3)*q^51 + (2/3*a^3+4/3*a^2-22/3*a-26/3)*q^53 + (1/3*a^3+2/3*a^2-20/3*a-4/3)*q^55 + (-2/3*a^3-1/3*a^2+28/3*a-4/3)*q^57 + (2/3*a^3-2/3*a^2-16/3*a+28/3)*q^59 + (2/3*a^3-2/3*a^2-22/3*a+40/3)*q^61 + (2*a^3+2*a^2-15*a-8)*q^63 + (10/3*a^3+2/3*a^2-92/3*a+32/3)*q^65 + (-1/3*a^3-2/3*a^2+11/3*a+28/3)*q^67 + (-2/3*a^3-4/3*a^2+16/3*a-4/3)*q^69 + (8/3*a^3+4/3*a^2-67/3*a+4/3)*q^71 + (-4/3*a^3-5/3*a^2+32/3*a+22/3)*q^73 + (-2/3*a^3+2/3*a^2+31/3*a-4/3)*q^75 + (-4/3*a^3+1/3*a^2+44/3*a-20/3)*q^77 + (2/3*a^3-2/3*a^2-13/3*a+4/3)*q^79 + (2*a^3+a^2-22*a+11)*q^81 + (-2*a^3+20*a-12)*q^83 + (4/3*a^3+2/3*a^2-20/3*a+20/3)*q^85 + (2*a^2-2*a)*q^87 + (-2/3*a^3+2/3*a^2+28/3*a-22/3)*q^89 + (-8/3*a^3-10/3*a^2+70/3*a+56/3)*q^91 + (-10/3*a^3-8/3*a^2+80/3*a-8/3)*q^93 + (-3*a^3+26*a-8)*q^95 + (4/3*a^3+8/3*a^2-32/3*a-22/3)*q^97 + (4/3*a^3+8/3*a^2-53/3*a+20/3)*q^99 + (-2*a^2-2*a+10)*q^101 + (-2/3*a^3-4/3*a^2+22/3*a-4/3)*q^103 + (8/3*a^3-2/3*a^2-94/3*a+10/3)*q^105 + (2/3*a^3-8/3*a^2-16/3*a+52/3)*q^107 + (4/3*a^3+2/3*a^2-26/3*a+14/3)*q^109 + (a^3-2*a)*q^111 + (-4/3*a^3+1/3*a^2+32/3*a-26/3)*q^113 + (4/3*a^3+8/3*a^2-32/3*a-28/3)*q^115 + (-4/3*a^3+4/3*a^2+26/3*a-62/3)*q^117 + (2/3*a^3-8/3*a^2-34/3*a+52/3)*q^119 + (-2/3*a^3+5/3*a^2+4/3*a-25/3)*q^121 + -a*q^123 + (-2*a^3+20*a-12)*q^125 + (8/3*a^3-2/3*a^2-76/3*a+52/3)*q^127 + (10/3*a^3+2/3*a^2-80/3*a+8/3)*q^129 + (2*a+4)*q^131 + (8/3*a^3+7/3*a^2-70/3*a-38/3)*q^133 + (-2/3*a^3-10/3*a^2+22/3*a-4/3)*q^135 + (2*a^3-20*a+6)*q^137 + (2*a^2-12)*q^139 + (-2/3*a^3+5/3*a^2+16/3*a-4/3)*q^141 + (-8/3*a^3+2/3*a^2+70/3*a-40/3)*q^143 + (-2*a^3-2*a^2+20*a-4)*q^145 + (-5*a^3+45*a-4)*q^147 + (2*a-2)*q^149 + (-4/3*a^3+4/3*a^2+41/3*a-68/3)*q^151 + (-14/3*a^3-10/3*a^2+124/3*a-58/3)*q^153 + (4/3*a^3+8/3*a^2-20/3*a-4/3)*q^155 + (8/3*a^3-2/3*a^2-70/3*a+46/3)*q^157 + (8/3*a^3-2/3*a^2-70/3*a+4/3)*q^159 + (-10/3*a^3+4/3*a^2+92/3*a-92/3)*q^161 + (-2/3*a^3-4/3*a^2+4/3*a+32/3)*q^163 + (4/3*a^3-10/3*a^2-26/3*a+2/3)*q^165 + (-1/3*a^3-2/3*a^2+11/3*a+40/3)*q^167 + (-4*a^2+31)*q^169 + (1/3*a^3+2/3*a^2-17/3*a+44/3)*q^171 + (4*a^3-36*a+14)*q^173 + (17/3*a^3+10/3*a^2-151/3*a-20/3)*q^175 + (2/3*a^3+4/3*a^2-16/3*a+4/3)*q^177 + (a^3-13*a)*q^179 + (-2*a^3+22*a-6)*q^181 + (2/3*a^3-2/3*a^2-4/3*a+4/3)*q^183 + (-10/3*a^3-2/3*a^2+74/3*a-14/3)*q^185 + (-2/3*a^3-4/3*a^2+22/3*a-28/3)*q^187 + (2*a^2+2*a-2)*q^189 + (-a^3+2*a^2+7*a-8)*q^191 + (-8/3*a^3+2/3*a^2+64/3*a-46/3)*q^193 + (22/3*a^3+8/3*a^2-188/3*a+20/3)*q^195 + (-10/3*a^3-2/3*a^2+98/3*a-56/3)*q^197 + (-5*a^3+2*a^2+43*a-32)*q^199 +  ...

-------------------------------------------------------
164B (old = 82A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/3 + Z/3) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
164C (old = 82B), dim = 2

CONGRUENCES:
Modular Degree = 2^6*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/3 + Z/3 + Z/3 + Z/3) + B(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
164D (old = 41A), dim = 3

CONGRUENCES:
Modular Degree = 2^9
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(165)
Weight 2

-------------------------------------------------------
J_0(165), dim = 21

-------------------------------------------------------
165A (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= B(Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2) + F(Z/2) + G(Z/2)

ARITHMETIC INVARIANTS:
W_q            = +++
discriminant   = 2^3
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2^2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 9.5423200902490701825 + 0.90216343475893330171e-6i
Omega-         = 5.4587115166240200363 + 0.1813813198424504752e-3i
L(1)           =

HECKE EIGENFORM:
a^2+2*a-1 = 0,
f(q) = q + a*q^2 + -1*q^3 + (-2*a-1)*q^4 + -1*q^5 + -a*q^6 + (-2*a-4)*q^7 + (a-2)*q^8 + 1*q^9 + -a*q^10 + -1*q^11 + (2*a+1)*q^12 + (4*a+4)*q^13 + -2*q^14 + 1*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 + 1*q^25 + (-4*a+4)*q^26 + -1*q^27 + (2*a+8)*q^28 + 2*a*q^29 + a*q^30 + (a+4)*q^32 + 1*q^33 + (-2*a-2)*q^34 + (2*a+4)*q^35 + (-2*a-1)*q^36 + (-4*a+2)*q^37 + (-6*a+2)*q^38 + (-4*a-4)*q^39 + (-a+2)*q^40 + -2*a*q^41 + 2*q^42 + (2*a-4)*q^43 + (2*a+1)*q^44 + -1*q^45 + -4*a*q^46 + -4*q^47 + -3*q^48 + (8*a+13)*q^49 + a*q^50 + (2*a+6)*q^51 + (4*a-12)*q^52 + (-8*a-10)*q^53 + -a*q^54 + 1*q^55 + (4*a+6)*q^56 + (-2*a+2)*q^57 + (-4*a+2)*q^58 + -4*q^59 + (-2*a-1)*q^60 + (4*a-2)*q^61 + (-2*a-4)*q^63 + (2*a-5)*q^64 + (-4*a-4)*q^65 + a*q^66 + (4*a+4)*q^67 + (6*a+10)*q^68 + 4*q^69 + 2*q^70 + (4*a+12)*q^71 + (a-2)*q^72 + (-8*a-8)*q^73 + (10*a-4)*q^74 + -1*q^75 + (10*a-2)*q^76 + (2*a+4)*q^77 + (4*a-4)*q^78 + (-6*a-6)*q^79 + -3*q^80 + 1*q^81 + (4*a-2)*q^82 + -10*q^83 + (-2*a-8)*q^84 + (2*a+6)*q^85 + (-8*a+2)*q^86 + -2*a*q^87 + (-a+2)*q^88 + (-4*a-6)*q^89 + -a*q^90 + (-8*a-24)*q^91 + (8*a+4)*q^92 + -4*a*q^94 + (-2*a+2)*q^95 + (-a-4)*q^96 + (-4*a+2)*q^97 + (-3*a+8)*q^98 + -1*q^99 + (-2*a-1)*q^100 + (2*a+4)*q^101 + (2*a+2)*q^102 + (8*a+16)*q^103 + (-12*a-4)*q^104 + (-2*a-4)*q^105 + (6*a-8)*q^106 + (-8*a-2)*q^107 + (2*a+1)*q^108 + (-8*a-2)*q^109 + a*q^110 + (4*a-2)*q^111 + (-6*a-12)*q^112 + (12*a+10)*q^113 + (6*a-2)*q^114 + 4*q^115 + (6*a-4)*q^116 + (4*a+4)*q^117 + -4*a*q^118 + (12*a+28)*q^119 + (a-2)*q^120 + 1*q^121 + (-10*a+4)*q^122 + 2*a*q^123 + -1*q^125 + -2*q^126 + 6*a*q^127 + (-11*a-6)*q^128 + (-2*a+4)*q^129 + (4*a-4)*q^130 + (-8*a-16)*q^131 + (-2*a-1)*q^132 + (4*a+4)*q^133 + (-4*a+4)*q^134 + 1*q^135 + (2*a+10)*q^136 + (8*a+6)*q^137 + 4*a*q^138 + (-6*a-14)*q^139 + (-2*a-8)*q^140 + 4*q^141 + (4*a+4)*q^142 + (-4*a-4)*q^143 + 3*q^144 + -2*a*q^145 + (8*a-8)*q^146 + (-8*a-13)*q^147 + (-16*a+6)*q^148 + (6*a+16)*q^149 + -a*q^150 + (-6*a+2)*q^151 + (-10*a+6)*q^152 + (-2*a-6)*q^153 + 2*q^154 + (-4*a+12)*q^156 + 18*q^157 + (6*a-6)*q^158 + (8*a+10)*q^159 + (-a-4)*q^160 + (8*a+16)*q^161 + a*q^162 + (8*a+12)*q^163 + (-6*a+4)*q^164 + -1*q^165 + -10*a*q^166 + (8*a+6)*q^167 + (-4*a-6)*q^168 + 19*q^169 + (2*a+2)*q^170 + (2*a-2)*q^171 + 14*a*q^172 + (-2*a-2)*q^173 + (4*a-2)*q^174 + (-2*a-4)*q^175 + -3*q^176 + 4*q^177 + (2*a-4)*q^178 + (4*a-8)*q^179 + (2*a+1)*q^180 + -14*q^181 + (-8*a-8)*q^182 + (-4*a+2)*q^183 + (-4*a+8)*q^184 + (4*a-2)*q^185 + (2*a+6)*q^187 + (8*a+4)*q^188 + (2*a+4)*q^189 + (6*a-2)*q^190 + (-4*a-4)*q^191 + (-2*a+5)*q^192 + (-4*a+4)*q^193 + (10*a-4)*q^194 + (4*a+4)*q^195 + (-2*a-29)*q^196 + (6*a+6)*q^197 + -a*q^198 + (4*a-12)*q^199 + (a-2)*q^200 +  ...

-------------------------------------------------------
165B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2) + F(Z/2) + G(Z/2)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 2^2*3
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 2^2*3
|L(1)/Omega|   = 1/3
Sha Bound      = 2^4*3

ANALYTIC INVARIANTS:

Omega+         = 4.8488133780652147393 + -0.34053265675475486925e-4i
Omega-         = 3.7199040775517922141 + -0.12185621124574811225e-3i
L(1)           = 1.6162711260615976516

HECKE EIGENFORM:
a^2-3 = 0,
f(q) = q + a*q^2 + 1*q^3 + 1*q^4 + -1*q^5 + a*q^6 + 2*q^7 + -a*q^8 + 1*q^9 + -a*q^10 + -1*q^11 + 1*q^12 + (-2*a+2)*q^13 + 2*a*q^14 + -1*q^15 + -5*q^16 + a*q^18 + (-2*a+2)*q^19 + -1*q^20 + 2*q^21 + -a*q^22 + -4*a*q^23 + -a*q^24 + 1*q^25 + (2*a-6)*q^26 + 1*q^27 + 2*q^28 + 2*a*q^29 + -a*q^30 + (4*a-4)*q^31 + -3*a*q^32 + -1*q^33 + -2*q^35 + 1*q^36 + (4*a+2)*q^37 + (2*a-6)*q^38 + (-2*a+2)*q^39 + a*q^40 + -2*a*q^41 + 2*a*q^42 + (4*a+2)*q^43 + -1*q^44 + -1*q^45 + -12*q^46 + 4*a*q^47 + -5*q^48 + -3*q^49 + a*q^50 + (-2*a+2)*q^52 + (-4*a-6)*q^53 + a*q^54 + 1*q^55 + -2*a*q^56 + (-2*a+2)*q^57 + 6*q^58 + 4*a*q^59 + -1*q^60 + 2*q^61 + (-4*a+12)*q^62 + 2*q^63 + 1*q^64 + (2*a-2)*q^65 + -a*q^66 + 8*q^67 + -4*a*q^69 + -2*a*q^70 + -8*a*q^71 + -a*q^72 + (6*a+2)*q^73 + (2*a+12)*q^74 + 1*q^75 + (-2*a+2)*q^76 + -2*q^77 + (2*a-6)*q^78 + (-2*a-10)*q^79 + 5*q^80 + 1*q^81 + -6*q^82 + (2*a+12)*q^83 + 2*q^84 + (2*a+12)*q^86 + 2*a*q^87 + a*q^88 + (-4*a-6)*q^89 + -a*q^90 + (-4*a+4)*q^91 + -4*a*q^92 + (4*a-4)*q^93 + 12*q^94 + (2*a-2)*q^95 + -3*a*q^96 + -10*q^97 + -3*a*q^98 + -1*q^99 + 1*q^100 + 6*a*q^101 + 8*q^103 + (-2*a+6)*q^104 + -2*q^105 + (-6*a-12)*q^106 + (2*a+12)*q^107 + 1*q^108 + -10*q^109 + a*q^110 + (4*a+2)*q^111 + -10*q^112 + (4*a-6)*q^113 + (2*a-6)*q^114 + 4*a*q^115 + 2*a*q^116 + (-2*a+2)*q^117 + 12*q^118 + a*q^120 + 1*q^121 + 2*a*q^122 + -2*a*q^123 + (4*a-4)*q^124 + -1*q^125 + 2*a*q^126 + (-4*a+2)*q^127 + 7*a*q^128 + (4*a+2)*q^129 + (-2*a+6)*q^130 + (-4*a+12)*q^131 + -1*q^132 + (-4*a+4)*q^133 + 8*a*q^134 + -1*q^135 + -18*q^137 + -12*q^138 + (-6*a+2)*q^139 + -2*q^140 + 4*a*q^141 + -24*q^142 + (2*a-2)*q^143 + -5*q^144 + -2*a*q^145 + (2*a+18)*q^146 + -3*q^147 + (4*a+2)*q^148 + (2*a-12)*q^149 + a*q^150 + (6*a-10)*q^151 + (-2*a+6)*q^152 + -2*a*q^154 + (-4*a+4)*q^155 + (-2*a+2)*q^156 + (-4*a-10)*q^157 + (-10*a-6)*q^158 + (-4*a-6)*q^159 + 3*a*q^160 + -8*a*q^161 + a*q^162 + (-8*a-4)*q^163 + -2*a*q^164 + 1*q^165 + (12*a+6)*q^166 + 6*a*q^167 + -2*a*q^168 + (-8*a+3)*q^169 + (-2*a+2)*q^171 + (4*a+2)*q^172 + -12*q^173 + 6*q^174 + 2*q^175 + 5*q^176 + 4*a*q^177 + (-6*a-12)*q^178 + -4*a*q^179 + -1*q^180 + (-8*a+2)*q^181 + (4*a-12)*q^182 + 2*q^183 + 12*q^184 + (-4*a-2)*q^185 + (-4*a+12)*q^186 + 4*a*q^188 + 2*q^189 + (-2*a+6)*q^190 + (4*a-12)*q^191 + 1*q^192 + (-6*a+14)*q^193 + -10*a*q^194 + (2*a-2)*q^195 + -3*q^196 + -12*q^197 + -a*q^198 + (12*a-4)*q^199 + -a*q^200 +  ...

-------------------------------------------------------
165C (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^6*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^3*5 + Z/2^3*5
= A(Z/2 + Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2) + F(Z/2) + G(Z/2 + Z/2) + H(Z/5 + Z/5)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 2^4*37
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^4*5
|L(1)/Omega|   = 1/2
Sha Bound      = 2^7*5^2

ANALYTIC INVARIANTS:

Omega+         = 1.9173833287425650282 + 0.19453879518907619902e-3i
Omega-         = 0.60731252478783727368e-4 + 3.2898920402660605852i
L(1)           = 0.95869166930578650307

HECKE EIGENFORM:
a^3+a^2-5*a-1 = 0,
f(q) = q + a*q^2 + 1*q^3 + (a^2-2)*q^4 + 1*q^5 + a*q^6 + (-a^2-2*a+3)*q^7 + (-a^2+a+1)*q^8 + 1*q^9 + a*q^10 + 1*q^11 + (a^2-2)*q^12 + (-a^2+3)*q^13 + (-a^2-2*a-1)*q^14 + 1*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 + 1*q^25 + (a^2-2*a-1)*q^26 + 1*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 + 1*q^33 + (-3*a^2+1)*q^34 + (-a^2-2*a+3)*q^35 + (a^2-2)*q^36 + -2*q^37 + (6*a+2)*q^38 + (-a^2+3)*q^39 + (-a^2+a+1)*q^40 + (2*a-4)*q^41 + (-a^2-2*a-1)*q^42 + (3*a^2+2*a-9)*q^43 + (a^2-2)*q^44 + 1*q^45 + (2*a^2+4*a+2)*q^46 + (2*a^2-10)*q^47 + (-4*a+3)*q^48 + (4*a+5)*q^49 + a*q^50 + (a^2-2*a-5)*q^51 + (-a^2+4*a-5)*q^52 + (-2*a^2-4*a+4)*q^53 + a*q^54 + 1*q^55 + (-a^2+2*a+3)*q^56 + (2*a^2+2*a-4)*q^57 + (-2*a^2-4*a)*q^58 + (-2*a^2-4*a+10)*q^59 + (a^2-2)*q^60 + (2*a^2+4*a-8)*q^61 + (2*a^2-2)*q^62 + (-a^2-2*a+3)*q^63 + (3*a^2-4*a-8)*q^64 + (-a^2+3)*q^65 + a*q^66 + (-2*a^2+6)*q^67 + (a^2-10*a+7)*q^68 + (2*a^2+4*a-6)*q^69 + (-a^2-2*a-1)*q^70 + (-2*a^2+10)*q^71 + (-a^2+a+1)*q^72 + (a^2+4*a-7)*q^73 + -2*a*q^74 + 1*q^75 + (2*a^2-2*a+8)*q^76 + (-a^2-2*a+3)*q^77 + (a^2-2*a-1)*q^78 + (-2*a^2+2*a+12)*q^79 + (-4*a+3)*q^80 + 1*q^81 + (2*a^2-4*a)*q^82 + (-3*a^2+11)*q^83 + (a^2-2*a-7)*q^84 + (a^2-2*a-5)*q^85 + (-a^2+6*a+3)*q^86 + (-2*a-4)*q^87 + (-a^2+a+1)*q^88 + (4*a-2)*q^89 + a*q^90 + (-2*a^2+10)*q^91 + (-2*a^2+4*a+14)*q^92 + (-2*a^2+10)*q^93 + (-2*a^2+2)*q^94 + (2*a^2+2*a-4)*q^95 + (-2*a^2+a-2)*q^96 + 2*a^2*q^97 + (4*a^2+5*a)*q^98 + 1*q^99 + (a^2-2)*q^100 + (2*a^2+6*a-14)*q^101 + (-3*a^2+1)*q^102 + (-4*a-4)*q^103 + (3*a^2-6*a+1)*q^104 + (-a^2-2*a+3)*q^105 + (-2*a^2-6*a-2)*q^106 + (a^2-1)*q^107 + (a^2-2)*q^108 + (-4*a^2-8*a+10)*q^109 + a*q^110 + -2*q^111 + (a^2+2*a+13)*q^112 + -6*q^113 + (6*a+2)*q^114 + (2*a^2+4*a-6)*q^115 + (-2*a^2-6*a+6)*q^116 + (-a^2+3)*q^117 + (-2*a^2-2)*q^118 + (6*a^2+8*a-14)*q^119 + (-a^2+a+1)*q^120 + 1*q^121 + (2*a^2+2*a+2)*q^122 + (2*a-4)*q^123 + (2*a^2+8*a-18)*q^124 + 1*q^125 + (-a^2-2*a-1)*q^126 + (a^2-2*a-15)*q^127 + (-3*a^2+5*a+7)*q^128 + (3*a^2+2*a-9)*q^129 + (a^2-2*a-1)*q^130 + (2*a^2-6)*q^131 + (a^2-2)*q^132 + (-8*a-16)*q^133 + (2*a^2-4*a-2)*q^134 + 1*q^135 + (-5*a^2+12*a-1)*q^136 + (-4*a^2+14)*q^137 + (2*a^2+4*a+2)*q^138 + (2*a+14)*q^139 + (a^2-2*a-7)*q^140 + (2*a^2-10)*q^141 + (2*a^2-2)*q^142 + (-a^2+3)*q^143 + (-4*a+3)*q^144 + (-2*a-4)*q^145 + (3*a^2-2*a+1)*q^146 + (4*a+5)*q^147 + (-2*a^2+4)*q^148 + (-2*a^2+2*a+2)*q^149 + a*q^150 + (2*a^2-6*a-8)*q^151 + (-4*a^2+6*a-2)*q^152 + (a^2-2*a-5)*q^153 + (-a^2-2*a-1)*q^154 + (-2*a^2+10)*q^155 + (-a^2+4*a-5)*q^156 + (2*a^2+8*a-4)*q^157 + (4*a^2+2*a-2)*q^158 + (-2*a^2-4*a+4)*q^159 + (-2*a^2+a-2)*q^160 + (-8*a-24)*q^161 + a*q^162 + (-4*a^2-4*a+12)*q^163 + (-6*a^2+6*a+10)*q^164 + 1*q^165 + (3*a^2-4*a-3)*q^166 + (-5*a^2-8*a+17)*q^167 + (-a^2+2*a+3)*q^168 + (-4*a-5)*q^169 + (-3*a^2+1)*q^170 + (2*a^2+2*a-4)*q^171 + (a^2-6*a+17)*q^172 + (a^2-2*a-9)*q^173 + (-2*a^2-4*a)*q^174 + (-a^2-2*a+3)*q^175 + (-4*a+3)*q^176 + (-2*a^2-4*a+10)*q^177 + (4*a^2-2*a)*q^178 + (-4*a^2-12*a+12)*q^179 + (a^2-2)*q^180 + (-4*a-6)*q^181 + (2*a^2-2)*q^182 + (2*a^2+4*a-8)*q^183 + (2*a^2-4*a-6)*q^184 + -2*q^185 + (2*a^2-2)*q^186 + (a^2-2*a-5)*q^187 + (-2*a^2-8*a+18)*q^188 + (-a^2-2*a+3)*q^189 + (6*a+2)*q^190 + (4*a^2+4*a-16)*q^191 + (3*a^2-4*a-8)*q^192 + (5*a^2+8*a-15)*q^193 + (-2*a^2+10*a+2)*q^194 + (-a^2+3)*q^195 + (a^2+12*a-6)*q^196 + (5*a^2-2*a-21)*q^197 + a*q^198 + (4*a^2+4*a-8)*q^199 + (-a^2+a+1)*q^200 +  ...

-------------------------------------------------------
165D (old = 55A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2) + G(Z/2 + Z/2)

-------------------------------------------------------
165E (old = 55B), dim = 2

CONGRUENCES:
Modular Degree = 2^7*7^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2*7 + Z/2^2*7 + Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2) + G(Z/2 + Z/2) + H(Z/7 + Z/7 + Z/7 + Z/7)

-------------------------------------------------------
165F (old = 33A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2^3*3 + Z/2^3*3
= A(Z/2) + B(Z/2) + C(Z/2) + D(Z/2) + E(Z/2) + G(Z/2) + H(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
165G (old = 15A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2) + B(Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2)

-------------------------------------------------------
165H (old = 11A), dim = 1

CONGRUENCES:
Modular Degree = 3^2*5*7^2
Ker(ModPolar)  = Z/3*7 + Z/3*7 + Z/3*5*7 + Z/3*5*7
= C(Z/5 + Z/5) + E(Z/7 + Z/7 + Z/7 + Z/7) + F(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
Gamma_0(166)
Weight 2

-------------------------------------------------------
J_0(166), dim = 20

-------------------------------------------------------
166A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 4.7802503818007451573 + -0.1714972157257927063e-3i
Omega-         = 0.11238424452181268189e-4 + -1.4900048563386283173i
L(1)           =
w1             = -2.390119571688146488 + -0.74491667956145126229i
w2             = -0.11238424452181268189e-4 + 1.4900048563386283173i
c4             = 313.0222107665597418 + -0.108362379099642523e-1i
c6             = -5741.5399163784060296 + 0.20794738445756962654i
j              = -23098.805789216790829 + 10.426738655072200476i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + 1*q^4 + -2*q^5 + 1*q^6 + 1*q^7 + -1*q^8 + -2*q^9 + 2*q^10 + -5*q^11 + -1*q^12 + -2*q^13 + -1*q^14 + 2*q^15 + 1*q^16 + -3*q^17 + 2*q^18 + -2*q^19 + -2*q^20 + -1*q^21 + 5*q^22 + 4*q^23 + 1*q^24 + -1*q^25 + 2*q^26 + 5*q^27 + 1*q^28 + -3*q^29 + -2*q^30 + 1*q^31 + -1*q^32 + 5*q^33 + 3*q^34 + -2*q^35 + -2*q^36 + 1*q^37 + 2*q^38 + 2*q^39 + 2*q^40 + 6*q^41 + 1*q^42 + 8*q^43 + -5*q^44 + 4*q^45 + -4*q^46 + 12*q^47 + -1*q^48 + -6*q^49 + 1*q^50 + 3*q^51 + -2*q^52 + -14*q^53 + -5*q^54 + 10*q^55 + -1*q^56 + 2*q^57 + 3*q^58 + -3*q^59 + 2*q^60 + -7*q^61 + -1*q^62 + -2*q^63 + 1*q^64 + 4*q^65 + -5*q^66 + 2*q^67 + -3*q^68 + -4*q^69 + 2*q^70 + -14*q^71 + 2*q^72 + -4*q^73 + -1*q^74 + 1*q^75 + -2*q^76 + -5*q^77 + -2*q^78 + -6*q^79 + -2*q^80 + 1*q^81 + -6*q^82 + -1*q^83 + -1*q^84 + 6*q^85 + -8*q^86 + 3*q^87 + 5*q^88 + 4*q^89 + -4*q^90 + -2*q^91 + 4*q^92 + -1*q^93 + -12*q^94 + 4*q^95 + 1*q^96 + 12*q^97 + 6*q^98 + 10*q^99 + -1*q^100 + -6*q^101 + -3*q^102 + -8*q^103 + 2*q^104 + 2*q^105 + 14*q^106 + 10*q^107 + 5*q^108 + -13*q^109 + -10*q^110 + -1*q^111 + 1*q^112 + -9*q^113 + -2*q^114 + -8*q^115 + -3*q^116 + 4*q^117 + 3*q^118 + -3*q^119 + -2*q^120 + 14*q^121 + 7*q^122 + -6*q^123 + 1*q^124 + 12*q^125 + 2*q^126 + -7*q^127 + -1*q^128 + -8*q^129 + -4*q^130 + -20*q^131 + 5*q^132 + -2*q^133 + -2*q^134 + -10*q^135 + 3*q^136 + 14*q^137 + 4*q^138 + 14*q^139 + -2*q^140 + -12*q^141 + 14*q^142 + 10*q^143 + -2*q^144 + 6*q^145 + 4*q^146 + 6*q^147 + 1*q^148 + 20*q^149 + -1*q^150 + 5*q^151 + 2*q^152 + 6*q^153 + 5*q^154 + -2*q^155 + 2*q^156 + -10*q^157 + 6*q^158 + 14*q^159 + 2*q^160 + 4*q^161 + -1*q^162 + -14*q^163 + 6*q^164 + -10*q^165 + 1*q^166 + 9*q^167 + 1*q^168 + -9*q^169 + -6*q^170 + 4*q^171 + 8*q^172 + 9*q^173 + -3*q^174 + -1*q^175 + -5*q^176 + 3*q^177 + -4*q^178 + -10*q^179 + 4*q^180 + -2*q^181 + 2*q^182 + 7*q^183 + -4*q^184 + -2*q^185 + 1*q^186 + 15*q^187 + 12*q^188 + 5*q^189 + -4*q^190 + -15*q^191 + -1*q^192 + -22*q^193 + -12*q^194 + -4*q^195 + -6*q^196 + -17*q^197 + -10*q^198 + 8*q^199 + 1*q^200 +  ...

-------------------------------------------------------
166B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*131
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*131 + Z/2*131
= C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/131 + Z/131)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 0.56973299631954610555 + 0.26047905692147112337e-4i
Omega-         = 5.6712575286176832022 + -0.20032444653582113683e-3i
L(1)           = 0.56973299691499467091

HECKE EIGENFORM:
a^2+2*a-4 = 0,
f(q) = q + -1*q^2 + a*q^3 + 1*q^4 + (1/2*a+2)*q^5 + -a*q^6 + (1/2*a-1)*q^7 + -1*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 + 1*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 + -1*q^32 + (4*a-4)*q^33 + (-1/2*a-4)*q^34 + -1*q^35 + (-2*a+1)*q^36 + (-4*a-6)*q^37 + (1/2*a+1)*q^38 + (2*a-2)*q^39 + (-1/2*a-2)*q^40 + (5/2*a+1)*q^41 + (2*a-2)*q^42 + (-5/2*a-2)*q^43 + (-a+2)*q^44 + (-3/2*a-2)*q^45 + 3/2*a*q^46 + (-3*a+2)*q^47 + a*q^48 + (-3/2*a-5)*q^49 + -3/2*a*q^50 + (3*a+2)*q^51 + (-1/2*a+1)*q^52 + (-5/2*a+1)*q^53 + (-2*a+8)*q^54 + 2*q^55 + (-1/2*a+1)*q^56 + -2*q^57 + -4*q^58 + (-5*a-2)*q^59 + (a+2)*q^60 + (4*a+8)*q^61 + (-1/2*a+4)*q^62 + (9/2*a-5)*q^63 + 1*q^64 + 1*q^65 + (-4*a+4)*q^66 + (1/2*a-10)*q^67 + (1/2*a+4)*q^68 + (3*a-6)*q^69 + 1*q^70 + (6*a+6)*q^71 + (2*a-1)*q^72 + (-a+8)*q^73 + (4*a+6)*q^74 + (-3*a+6)*q^75 + (-1/2*a-1)*q^76 + (3*a-4)*q^77 + (-2*a+2)*q^78 + (-5*a-4)*q^79 + (1/2*a+2)*q^80 + (-6*a+5)*q^81 + (-5/2*a-1)*q^82 + 1*q^83 + (-2*a+2)*q^84 + (5/2*a+9)*q^85 + (5/2*a+2)*q^86 + 4*a*q^87 + (a-2)*q^88 + (2*a+2)*q^89 + (3/2*a+2)*q^90 + (3/2*a-2)*q^91 + -3/2*a*q^92 + (-5*a+2)*q^93 + (3*a-2)*q^94 + (-a-3)*q^95 + -a*q^96 + (3*a-2)*q^97 + (3/2*a+5)*q^98 + (-9*a+10)*q^99 + 3/2*a*q^100 + (4*a+10)*q^101 + (-3*a-2)*q^102 + (2*a+8)*q^103 + (1/2*a-1)*q^104 + -a*q^105 + (5/2*a-1)*q^106 + (-1/2*a-5)*q^107 + (2*a-8)*q^108 + (2*a+12)*q^109 + -2*q^110 + (2*a-16)*q^111 + (1/2*a-1)*q^112 + (3/2*a-9)*q^113 + 2*q^114 + (-3/2*a-3)*q^115 + 4*q^116 + (-9/2*a+5)*q^117 + (5*a+2)*q^118 + (a-3)*q^119 + (-a-2)*q^120 + (-6*a-3)*q^121 + (-4*a-8)*q^122 + (-4*a+10)*q^123 + (1/2*a-4)*q^124 + (-a-7)*q^125 + (-9/2*a+5)*q^126 + (-9/2*a-7)*q^127 + -1*q^128 + (3*a-10)*q^129 + -1*q^130 + (-5*a-10)*q^131 + (4*a-4)*q^132 + 1/2*a*q^133 + (-1/2*a+10)*q^134 + (-2*a-12)*q^135 + (-1/2*a-4)*q^136 + (a+6)*q^137 + (-3*a+6)*q^138 + (13/2*a+6)*q^139 + -1*q^140 + (8*a-12)*q^141 + (-6*a-6)*q^142 + (-3*a+4)*q^143 + (-2*a+1)*q^144 + (2*a+8)*q^145 + (a-8)*q^146 + (-2*a-6)*q^147 + (-4*a-6)*q^148 + (-3/2*a+2)*q^149 + (3*a-6)*q^150 + (11/2*a+16)*q^151 + (1/2*a+1)*q^152 + -11/2*a*q^153 + (-3*a+4)*q^154 + (-3/2*a-7)*q^155 + (2*a-2)*q^156 + (13/2*a+6)*q^157 + (5*a+4)*q^158 + (6*a-10)*q^159 + (-1/2*a-2)*q^160 + (3*a-3)*q^161 + (6*a-5)*q^162 + (7/2*a+7)*q^163 + (5/2*a+1)*q^164 + 2*a*q^165 + -1*q^166 + -8*q^167 + (2*a-2)*q^168 + (-3/2*a-11)*q^169 + (-5/2*a-9)*q^170 + (-1/2*a+3)*q^171 + (-5/2*a-2)*q^172 + (6*a+12)*q^173 + -4*a*q^174 + (-3*a+3)*q^175 + (-a+2)*q^176 + (8*a-20)*q^177 + (-2*a-2)*q^178 + (9/2*a+18)*q^179 + (-3/2*a-2)*q^180 + 14*q^181 + (-3/2*a+2)*q^182 + 16*q^183 + 3/2*a*q^184 + (-7*a-20)*q^185 + (5*a-2)*q^186 + (-2*a+6)*q^187 + (-3*a+2)*q^188 + (-8*a+12)*q^189 + (a+3)*q^190 + (2*a+12)*q^191 + a*q^192 + (-3/2*a-12)*q^193 + (-3*a+2)*q^194 + a*q^195 + (-3/2*a-5)*q^196 + (-4*a-10)*q^197 + (9*a-10)*q^198 + (7/2*a+9)*q^199 + -3/2*a*q^200 +  ...

-------------------------------------------------------
166C (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2^2 + Z/2^2) + E(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 229
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 7
Torsion Bound  = 7
|L(1)/Omega|   = 2^3/7
Sha Bound      = 2^3*7

ANALYTIC INVARIANTS:

Omega+         = 4.3954396043676303088 + 0.21323218087229775138e-3i
Omega-         = 0.84920199525540791263e-3 + -12.641815381923920922i
L(1)           = 5.0233595537597771397

HECKE EIGENFORM:
a^3-a^2-6*a+4 = 0,
f(q) = q + 1*q^2 + a*q^3 + 1*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 + 1*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 + 1*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 + 1*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 + (-5/2*a^2+1/2*a+9)*q^38 + (-4*a+2)*q^39 + (-1/2*a^2-1/2*a+2)*q^40 + (-1/2*a^2+5/2*a+5)*q^41 + (-a^2+2*a-2)*q^42 + (1/2*a^2+5/2*a-2)*q^43 + (-a+2)*q^44 + (-1/2*a^2-5/2*a-2)*q^45 + (1/2*a^2+1/2*a)*q^46 + (-a^2-3*a+6)*q^47 + a*q^48 + (3/2*a^2-11/2*a-1)*q^49 + (1/2*a^2+3/2*a-4)*q^50 + (2*a^2+a-6)*q^51 + (-1/2*a^2+1/2*a-1)*q^52 + (-5/2*a^2+5/2*a+7)*q^53 + (a^2-4)*q^54 + 2*q^55 + (1/2*a^2-3/2*a-1)*q^56 + (-2*a^2-6*a+10)*q^57 + a^2*q^58 + (-2*a^2+3*a+10)*q^59 + (-a^2-a+2)*q^60 + (a^2-4*a-8)*q^61 + (3/2*a^2+1/2*a-8)*q^62 + (-1/2*a^2-7/2*a+7)*q^63 + 1*q^64 + (a^2+2*a-3)*q^65 + (-a^2+2*a)*q^66 + (-1/2*a^2+7/2*a+6)*q^67 + (3/2*a^2+1/2*a-8)*q^68 + (a^2+3*a-2)*q^69 + (a^2-3)*q^70 + 2*q^71 + (a^2-3)*q^72 + (a^2+5*a-4)*q^73 + (-a^2-2)*q^74 + (2*a^2-a-2)*q^75 + (-5/2*a^2+1/2*a+9)*q^76 + (2*a^2-5*a)*q^77 + (-4*a+2)*q^78 + (-a^2+a+8)*q^79 + (-1/2*a^2-1/2*a+2)*q^80 + (-2*a^2+2*a+5)*q^81 + (-1/2*a^2+5/2*a+5)*q^82 + -1*q^83 + (-a^2+2*a-2)*q^84 + (1/2*a^2-5/2*a-9)*q^85 + (1/2*a^2+5/2*a-2)*q^86 + (a^2+6*a-4)*q^87 + (-a+2)*q^88 + (-2*a^2+10)*q^89 + (-1/2*a^2-5/2*a-2)*q^90 + (-3/2*a^2+13/2*a-2)*q^91 + (1/2*a^2+1/2*a)*q^92 + (2*a^2+a-6)*q^93 + (-a^2-3*a+6)*q^94 + (5*a+9)*q^95 + a*q^96 + (-3*a^2-a+10)*q^97 + (3/2*a^2-11/2*a-1)*q^98 + (a^2-3*a-2)*q^99 + (1/2*a^2+3/2*a-4)*q^100 + (-4*a+6)*q^101 + (2*a^2+a-6)*q^102 + (4*a^2-16)*q^103 + (-1/2*a^2+1/2*a-1)*q^104 + (a^2+3*a-4)*q^105 + (-5/2*a^2+5/2*a+7)*q^106 + (-5/2*a^2+1/2*a+13)*q^107 + (a^2-4)*q^108 + (a^2-2*a+4)*q^109 + 2*q^110 + (-a^2-8*a+4)*q^111 + (1/2*a^2-3/2*a-1)*q^112 + (-1/2*a^2-9/2*a+7)*q^113 + (-2*a^2-6*a+10)*q^114 + (-3/2*a^2-5/2*a+3)*q^115 + a^2*q^116 + (-5/2*a^2+1/2*a+3)*q^117 + (-2*a^2+3*a+10)*q^118 + (-3*a^2+a+13)*q^119 + (-a^2-a+2)*q^120 + (a^2-4*a-7)*q^121 + (a^2-4*a-8)*q^122 + (2*a^2+2*a+2)*q^123 + (3/2*a^2+1/2*a-8)*q^124 + (2*a^2+a-13)*q^125 + (-1/2*a^2-7/2*a+7)*q^126 + (3/2*a^2+3/2*a-7)*q^127 + 1*q^128 + (3*a^2+a-2)*q^129 + (a^2+2*a-3)*q^130 + (3*a^2-3*a-2)*q^131 + (-a^2+2*a)*q^132 + (3/2*a^2+15/2*a-20)*q^133 + (-1/2*a^2+7/2*a+6)*q^134 + (-2*a-4)*q^135 + (3/2*a^2+1/2*a-8)*q^136 + (3*a^2-a-18)*q^137 + (a^2+3*a-2)*q^138 + (-5/2*a^2+3/2*a+6)*q^139 + (a^2-3)*q^140 + (-4*a^2+4)*q^141 + 2*q^142 + (-a^2+5*a-4)*q^143 + (a^2-3)*q^144 + (-2*a^2-4*a+4)*q^145 + (a^2+5*a-4)*q^146 + (-4*a^2+8*a-6)*q^147 + (-a^2-2)*q^148 + (-1/2*a^2+11/2*a+10)*q^149 + (2*a^2-a-2)*q^150 + (-3/2*a^2-5/2*a+4)*q^151 + (-5/2*a^2+1/2*a+9)*q^152 + (-3/2*a^2+9/2*a+16)*q^153 + (2*a^2-5*a)*q^154 + (1/2*a^2-5/2*a-9)*q^155 + (-4*a+2)*q^156 + (3/2*a^2+3/2*a-26)*q^157 + (-a^2+a+8)*q^158 + (-8*a+10)*q^159 + (-1/2*a^2-1/2*a+2)*q^160 + (-3*a+1)*q^161 + (-2*a^2+2*a+5)*q^162 + (-5/2*a^2-15/2*a+17)*q^163 + (-1/2*a^2+5/2*a+5)*q^164 + 2*a*q^165 + -1*q^166 + (3*a^2+2*a-28)*q^167 + (-a^2+2*a-2)*q^168 + (5/2*a^2-7/2*a-11)*q^169 + (1/2*a^2-5/2*a-9)*q^170 + (-1/2*a^2-7/2*a-19)*q^171 + (1/2*a^2+5/2*a-2)*q^172 + (a^2-4*a-8)*q^173 + (a^2+6*a-4)*q^174 + (-3*a^2+5*a+3)*q^175 + (-a+2)*q^176 + (a^2-2*a+8)*q^177 + (-2*a^2+10)*q^178 + (7/2*a^2-1/2*a-14)*q^179 + (-1/2*a^2-5/2*a-2)*q^180 + (4*a^2-22)*q^181 + (-3/2*a^2+13/2*a-2)*q^182 + (-3*a^2-2*a-4)*q^183 + (1/2*a^2+1/2*a)*q^184 + (3*a^2+5*a-8)*q^185 + (2*a^2+a-6)*q^186 + (a^2-10)*q^187 + (-a^2-3*a+6)*q^188 + (-a^2-2*a+8)*q^189 + (5*a+9)*q^190 + (-3*a^2+16)*q^191 + a*q^192 + (-11/2*a^2+1/2*a+28)*q^193 + (-3*a^2-a+10)*q^194 + (3*a^2+3*a-4)*q^195 + (3/2*a^2-11/2*a-1)*q^196 + (-a^2+6*a-6)*q^197 + (a^2-3*a-2)*q^198 + (5/2*a^2-9/2*a-11)*q^199 + (1/2*a^2+3/2*a-4)*q^200 +  ...

-------------------------------------------------------
166D (old = 83A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + C(Z/2^2 + Z/2^2) + E(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
166E (old = 83B), dim = 6

CONGRUENCES:
Modular Degree = 2^4*131
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*131 + Z/2*131
= A(Z/2 + Z/2) + B(Z/131 + Z/131) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(167)
Weight 2

-------------------------------------------------------
J_0(167), dim = 14

-------------------------------------------------------
167A (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2
= B(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 5
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 7.3327678826492898416 + -0.10675334074824919092e-2i
Omega-         = 11.552517820695263647 + -0.36098858690910633317e-3i
L(1)           =

HECKE EIGENFORM:
a^2+a-1 = 0,
f(q) = q + a*q^2 + (-a-1)*q^3 + (-a-1)*q^4 + -1*q^5 + -1*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 + 1*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 + (-2*a+4)*q^38 + (3*a+4)*q^39 + (2*a+1)*q^40 + (-8*a-3)*q^41 + (-a+2)*q^42 + (-8*a-7)*q^43 + (-a+1)*q^45 + (a-1)*q^46 + 7*q^47 + -3*q^48 + (-5*a-2)*q^49 + -4*a*q^50 + (2*a+1)*q^51 + (3*a+4)*q^52 + (2*a-4)*q^53 + (-a+4)*q^54 + 5*a*q^56 + (-2*a-6)*q^57 + (5*a-2)*q^58 + (-2*a-2)*q^59 + (-a-2)*q^60 + (2*a+1)*q^61 + (4*a-2)*q^62 + (-4*a+3)*q^63 + (-2*a+1)*q^64 + (a+3)*q^65 + (2*a-1)*q^67 + (2*a+1)*q^68 + 1*q^69 + (3*a-1)*q^70 + (5*a-3)*q^71 + (3*a-1)*q^72 + (3*a-8)*q^73 + (-7*a+2)*q^74 + (4*a+4)*q^75 + (-2*a-6)*q^76 + (a+3)*q^78 + (-4*a-1)*q^79 + -3*a*q^80 + (-6*a-4)*q^81 + (5*a-8)*q^82 + (8*a+3)*q^83 + (-a-3)*q^84 + (-a+2)*q^85 + (a-8)*q^86 + (-3*a-1)*q^87 + (10*a+4)*q^89 + (2*a-1)*q^90 + 5*q^91 + 1*q^92 + -2*a*q^93 + 7*a*q^94 + (-4*a-2)*q^95 + (-5*a-6)*q^96 + (3*a-9)*q^97 + (3*a-5)*q^98 + (4*a+4)*q^100 + (-2*a+9)*q^101 + (-a+2)*q^102 + (-15*a-9)*q^103 + (5*a+5)*q^104 + (-2*a-1)*q^105 + (-6*a+2)*q^106 + (8*a+1)*q^107 + (-3*a-7)*q^108 + 2*q^109 + (5*a+3)*q^111 + (-9*a+3)*q^112 + (-4*a-11)*q^113 + (-4*a-2)*q^114 + a*q^115 + (-3*a-1)*q^116 + (-a+2)*q^117 + -2*q^118 + (-5*a+5)*q^119 + (-a-3)*q^120 + -11*q^121 + (-a+2)*q^122 + (3*a+11)*q^123 + -2*a*q^124 + 9*q^125 + (7*a-4)*q^126 + (-6*a-1)*q^127 + (a-12)*q^128 + (7*a+15)*q^129 + (2*a+1)*q^130 + (8*a+15)*q^131 + -10*a*q^133 + (-3*a+2)*q^134 + (-4*a-3)*q^135 + 5*a*q^136 + (4*a+4)*q^137 + a*q^138 + (-7*a-1)*q^139 + (-2*a-1)*q^140 + (-7*a-7)*q^141 + (-8*a+5)*q^142 + (-6*a+3)*q^144 + (2*a-3)*q^145 + (-11*a+3)*q^146 + (2*a+7)*q^147 + (5*a+3)*q^148 + 9*a*q^149 + 4*q^150 + (13*a+16)*q^151 + -10*q^152 + (-4*a+3)*q^153 + (2*a-2)*q^155 + (-4*a-7)*q^156 + (10*a+7)*q^157 + (3*a-4)*q^158 + (4*a+2)*q^159 + (-a-5)*q^160 + (3*a-1)*q^161 + (2*a-6)*q^162 + (2*a+2)*q^163 + (3*a+11)*q^164 + (-5*a+8)*q^166 + -1*q^167 + -5*q^168 + (5*a-3)*q^169 + (3*a-1)*q^170 + (-6*a+2)*q^171 + (7*a+15)*q^172 + (16*a+11)*q^173 + (2*a-3)*q^174 + (-4*a+8)*q^175 + (2*a+4)*q^177 + (-6*a+10)*q^178 + (-3*a+10)*q^179 + -a*q^180 + (4*a-2)*q^181 + 5*a*q^182 + (-a-3)*q^183 + (-a+2)*q^184 + (-2*a+5)*q^185 + (2*a-2)*q^186 + (-7*a-7)*q^188 + (-9*a-2)*q^189 + (2*a-4)*q^190 + (-5*a-7)*q^191 + (-a+1)*q^192 + (3*a-21)*q^193 + (-12*a+3)*q^194 + (-3*a-4)*q^195 + (2*a+7)*q^196 + (-17*a-12)*q^197 + (5*a+13)*q^199 + (8*a+4)*q^200 +  ...

-------------------------------------------------------
167B (new) , dim = 12

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 8269*5103536431379173
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 83
Torsion Bound  = 83
|L(1)/Omega|   = 2^2/83
Sha Bound      = 2^2*83

ANALYTIC INVARIANTS:

Omega+         = 190.24961050008131721 + 0.71794386562519832316e-2i
Omega-         = 457.2691747966413317 + 0.16221244468143540535e-1i
L(1)           = 9.1686559342431975841

HECKE EIGENFORM:
a^12-2*a^11-17*a^10+33*a^9+103*a^8-189*a^7-277*a^6+447*a^5+363*a^4-433*a^3-205*a^2+120*a+9 = 0,
f(q) = 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 + 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(1222/311*a^11-179/311*a^10-22235/311*a^9+823/311*a^8+145277/311*a^7+13017/311*a^6-409533/311*a^5-93709/311*a^4+465437/311*a^3+148441/311*a^2-119955/311*a-8913/311)*q^146 + (2279/933*a^11-2167/933*a^10-38161/933*a^9+10122/311*a^8+222434/933*a^7-42594/311*a^6-539072/933*a^5+45614/311*a^4+177584/311*a^3+26395/933*a^2-118715/933*a+2098/311)*q^147 + (30/311*a^11+131/311*a^10-723/311*a^9-2027/311*a^8+5911/311*a^7+10805/311*a^6-19497/311*a^5-23361/311*a^4+22541/311*a^3+20313/311*a^2-4365/311*a-4131/311)*q^148 + (-1783/933*a^11+746/933*a^10+31370/933*a^9-2868/311*a^8-196816/933*a^7+6008/311*a^6+530956/933*a^5+22732/311*a^4-196266/311*a^3-167192/933*a^2+153220/933*a+2939/311)*q^149 + (2892/311*a^11-1180/311*a^10-50664/311*a^9+14149/311*a^8+314676/311*a^7-36946/311*a^6-830259/311*a^5-68656/311*a^4+880312/311*a^3+214956/311*a^2-209928/311*a-14952/311)*q^150 + (-1187/311*a^11+280/311*a^10+21236/311*a^9-2514/311*a^8-135530/311*a^7-3262/311*a^6+369526/311*a^5+70964/311*a^4-400938/311*a^3-128630/311*a^2+92004/311*a+8603/311)*q^151 + (-1262/311*a^11+1352/311*a^10+21022/311*a^9-19372/311*a^8-121540/311*a^7+85573/311*a^6+290292/311*a^5-109326/311*a^4-278932/311*a^3+5788/311*a^2+54556/311*a+3225/311)*q^152 + (-169/933*a^11+1325/933*a^10+683/933*a^9-6709/311*a^8+14585/933*a^7+33289/311*a^6-100745/933*a^5-59831/311*a^4+53423/311*a^3+107593/933*a^2-49895/933*a+3372/311)*q^153 + (-376/311*a^11+79/311*a^10+6698/311*a^9-636/311*a^8-42715/311*a^7-1589/311*a^6+117350/311*a^5+21226/311*a^4-130891/311*a^3-36081/311*a^2+33249/311*a+1953/311)*q^154 + (508/311*a^11+62/311*a^10-9506/311*a^9-1814/311*a^8+64556/311*a^7+16476/311*a^6-191070/311*a^5-59202/311*a^4+227148/311*a^3+73770/311*a^2-63340/311*a-4766/311)*q^155 + (-65/933*a^11+79/933*a^10+1411/933*a^9-523/311*a^8-11615/933*a^7+4239/311*a^6+43643/933*a^5-15213/311*a^4-24141/311*a^3+52865/933*a^2+47555/933*a-282/311)*q^156 + (-11/311*a^11+66/311*a^10-77/311*a^9-677/311*a^8+2819/311*a^7+755/311*a^6-16145/311*a^5+7415/311*a^4+28547/311*a^3-12393/311*a^2-13172/311*a+2852/311)*q^157 + (-1567/311*a^11+72/311*a^10+28528/311*a^9+1184/311*a^8-186352/311*a^7-26092/311*a^6+524432/311*a^5+129266/311*a^4-594194/311*a^3-185022/311*a^2+158490/311*a+11169/311)*q^158 + (3832/933*a^11+22/933*a^10-70208/933*a^9-2114/311*a^8+462982/933*a^7+28454/311*a^6-1320808/933*a^5-124440/311*a^4+506750/311*a^3+509330/933*a^2-410764/933*a-13298/311)*q^159 + (902/311*a^11-747/311*a^10-15145/311*a^9+10419/311*a^8+88239/311*a^7-43561/311*a^6-210895/311*a^5+44759/311*a^4+194729/311*a^3+16983/311*a^2-28611/311*a-2169/311)*q^160 + (-84/311*a^11-429/311*a^10+2211/311*a^9+6733/311*a^8-19723/311*a^7-35541/311*a^6+71199/311*a^5+73559/311*a^4-89923/311*a^3-60173/311*a^2+21863/311*a+5409/311)*q^161 + (-1531/311*a^11+478/311*a^10+27225/311*a^9-5478/311*a^8-172479/311*a^7+11443/311*a^6+465706/311*a^5+45315/311*a^4-499098/311*a^3-120092/311*a^2+118109/311*a+8451/311)*q^162 + (-2094/311*a^11+1368/311*a^10+36346/311*a^9-18556/311*a^8-222940/311*a^7+71516/311*a^6+578850/311*a^5-40654/311*a^4-604348/311*a^3-95662/311*a^2+135182/311*a+8506/311)*q^163 + (1042/933*a^11-965/933*a^10-17897/933*a^9+4743/311*a^8+109189/933*a^7-22247/311*a^6-285709/933*a^5+33731/311*a^4+104051/311*a^3-30661/933*a^2-90655/933*a+1559/311)*q^164 + (-3928/933*a^11+4286/933*a^10+63938/933*a^9-20438/311*a^8-355258/933*a^7+89604/311*a^6+792796/933*a^5-111384/311*a^4-234390/311*a^3+14578/933*a^2+126172/933*a+3896/311)*q^165 + (371/311*a^11+262/311*a^10-7044/311*a^9-4676/311*a^8+48520/311*a^7+28452/311*a^6-144734/311*a^5-69736/311*a^4+169482/311*a^3+64884/311*a^2-47916/311*a-3597/311)*q^166 + 1*q^167 + (-1777/311*a^11+1643/311*a^10+29857/311*a^9-23191/311*a^8-174859/311*a^7+98557/311*a^6+426106/311*a^5-106842/311*a^4-420455/311*a^3-27720/311*a^2+89214/311*a+6498/311)*q^168 + (2159/933*a^11-514/933*a^10-38068/933*a^9+1214/311*a^8+238598/933*a^7+6858/311*a^6-638354/933*a^5-65054/311*a^4+229426/311*a^3+309946/933*a^2-152570/933*a-6700/311)*q^169 + (496/311*a^11-177/311*a^10-8657/311*a^9+2169/311*a^8+53297/311*a^7-6195/311*a^6-137803/311*a^5-7375/311*a^4+138329/311*a^3+29009/311*a^2-25207/311*a-1683/311)*q^170 + (2540/933*a^11+2798/933*a^10-51262/933*a^9-15567/311*a^8+375650/933*a^7+89349/311*a^6-1190777/933*a^5-209386/311*a^4+492095/311*a^3+576598/933*a^2-454784/933*a-8358/311)*q^171 + (302/311*a^11-257/311*a^10-5039/311*a^9+3687/311*a^8+29109/311*a^7-16459/311*a^6-68511/311*a^5+21843/311*a^4+61129/311*a^3-2393/311*a^2-7243/311*a+835/311)*q^172 + (-432/311*a^11+1037/311*a^10+6306/311*a^9-15533/311*a^8-28703/311*a^7+74859/311*a^6+40727/311*a^5-124317/311*a^4-11289/311*a^3+61162/311*a^2-7741/311*a-1905/311)*q^173 + (-24/311*a^11-167/311*a^10+454/311*a^9+2990/311*a^8-3236/311*a^7-18596/311*a^6+11368/311*a^5+45808/311*a^4-20583/311*a^3-35097/311*a^2+10956/311*a+879/311)*q^174 + (-2493/311*a^11+652/311*a^10+44438/311*a^9-6556/311*a^8-282492/311*a^7+2605/311*a^6+768465/311*a^5+117564/311*a^4-840606/311*a^3-226528/311*a^2+208320/311*a+8619/311)*q^175 + (2635/933*a^11-2126/933*a^10-45932/933*a^9+9886/311*a^8+284326/933*a^7-41079/311*a^6-751030/933*a^5+39376/311*a^4+268626/311*a^3+76613/933*a^2-191350/933*a+1121/311)*q^176 + (-5656/933*a^11+1592/933*a^10+100358/933*a^9-5280/311*a^8-634900/933*a^7+1572/311*a^6+1721386/933*a^5+96060/311*a^4-630106/311*a^3-541910/933*a^2+465298/933*a+12552/311)*q^177 + (1572/311*a^11-724/311*a^10-27560/311*a^9+8793/311*a^8+171528/311*a^7-23474/311*a^6-455685/311*a^5-40948/311*a^4+493092/311*a^3+129784/311*a^2-121120/311*a-8592/311)*q^178 + (2822/933*a^11-2626/933*a^10-47422/933*a^9+12271/311*a^8+277766/933*a^7-51370/311*a^6-676538/933*a^5+51990/311*a^4+221515/311*a^3+64618/933*a^2-138476/933*a-2704/311)*q^179 + (-2257/933*a^11-142/933*a^10+41114/933*a^9+1940/311*a^8-267880/933*a^7-20524/311*a^6+747388/933*a^5+80892/311*a^4-276024/311*a^3-311054/933*a^2+198862/933*a+5849/311)*q^180 + (-1519/933*a^11+1028/933*a^10+25754/933*a^9-4605/311*a^8-152512/933*a^7+17384/311*a^6+373564/933*a^5-7976/311*a^4-115819/311*a^3-82484/933*a^2+30838/933*a+3759/311)*q^181 + (365/311*a^11+298/311*a^10-7086/311*a^9-5328/311*a^8+49888/311*a^7+33444/311*a^6-152466/311*a^5-88140/311*a^4+184318/311*a^3+88376/311*a^2-51708/311*a-4077/311)*q^182 + (37/311*a^11+89/311*a^10-985/311*a^9-1370/311*a^8+9291/311*a^7+6847/311*a^6-37637/311*a^5-12049/311*a^4+60694/311*a^3+6175/311*a^2-26687/311*a+1716/311)*q^183 + (799/311*a^11-1684/311*a^10-12134/311*a^9+25454/311*a^8+59164/311*a^7-124250/311*a^6-98456/311*a^5+210770/311*a^4+42522/311*a^3-107090/311*a^2+19186/311*a+2031/311)*q^184 + (959/311*a^11+777/311*a^10-18789/311*a^9-13865/311*a^8+133711/311*a^7+86907/311*a^6-413609/311*a^5-227621/311*a^4+507847/311*a^3+224855/311*a^2-151197/311*a-9738/311)*q^185 + (360/311*a^11-1538/311*a^10-4011/311*a^9+23570/311*a^8+5311/311*a^7-118207/311*a^6+54022/311*a^5+215713/311*a^4-125722/311*a^3-135664/311*a^2+57714/311*a+4542/311)*q^186 + (-2212/933*a^11+1454/933*a^10+38630/933*a^9-7004/311*a^8-238954/933*a^7+31684/311*a^6+628108/933*a^5-43526/311*a^4-223546/311*a^3+22174/933*a^2+173188/933*a-6946/311)*q^187 + (-27/311*a^11-149/311*a^10+744/311*a^9+2664/311*a^8-6906/311*a^7-16722/311*a^6+25851/311*a^5+44070/311*a^4-34002/311*a^3-46054/311*a^2+7194/311*a+8103/311)*q^188 + (1293/311*a^11+639/311*a^10-24537/311*a^9-11884/311*a^8+168275/311*a^7+78345/311*a^6-498003/311*a^5-220309/311*a^4+578382/311*a^3+240335/311*a^2-152833/311*a-18783/311)*q^189 + (1390/311*a^11-254/311*a^10-25102/311*a^9+1974/311*a^8+162642/311*a^7+6660/311*a^6-453966/311*a^5-78796/311*a^4+509376/311*a^3+136612/311*a^2-132892/311*a-9468/311)*q^190 + (-5032/933*a^11-286/933*a^10+92597/933*a^9+4157/311*a^8-613897/933*a^7-44907/311*a^6+1763875/933*a^5+179345/311*a^4-684659/311*a^3-701405/933*a^2+576034/933*a+12709/311)*q^191 + (1699/933*a^11+2557/933*a^10-35690/933*a^9-14066/311*a^8+271948/933*a^7+79488/311*a^6-891736/933*a^5-182428/311*a^4+373936/311*a^3+500123/933*a^2-333196/933*a-10777/311)*q^192 + (-100/933*a^11-955/933*a^10+3965/933*a^9+4913/311*a^8-44065/933*a^7-25033/311*a^6+189079/933*a^5+47623/311*a^4-99651/311*a^3-96011/933*a^2+141127/933*a-697/311)*q^193 + (-1381/311*a^11-111/311*a^10+25476/311*a^9+3980/311*a^8-169670/311*a^7-39650/311*a^6+489822/311*a^5+151186/311*a^4-568017/311*a^3-195486/311*a^2+156618/311*a+11121/311)*q^194 + (607/311*a^11-1776/311*a^10-8502/311*a^9+27604/311*a^8+34520/311*a^7-141776/311*a^6-27416/311*a^5+269344/311*a^4-33196/311*a^3-172032/311*a^2+22864/311*a+2843/311)*q^195 + (-407/311*a^11+265/311*a^10+7103/311*a^9-3901/311*a^8-43733/311*a^7+17983/311*a^6+114203/311*a^5-25449/311*a^4-122140/311*a^3+7648/311*a^2+32628/311*a-7058/311)*q^196 + (-347/933*a^11-2894/933*a^10+11566/933*a^9+15490/311*a^8-119924/933*a^7-83938/311*a^6+490394/933*a^5+179026/311*a^4-238410/311*a^3-447460/933*a^2+250928/933*a+11169/311)*q^197 + (1227/311*a^11-831/311*a^10-20956/311*a^9+11422/311*a^8+125477/311*a^7-45879/311*a^6-314040/311*a^5+36594/311*a^4+312709/311*a^3+42199/311*a^2-66724/311*a-4470/311)*q^198 + (-957/311*a^11-167/311*a^10+17870/311*a^9+3923/311*a^8-120483/311*a^7-31969/311*a^6+351291/311*a^5+109563/311*a^4-406845/311*a^3-136794/311*a^2+108299/311*a+7410/311)*q^199 + (2021/311*a^11-1241/311*a^10-34991/311*a^9+16325/311*a^8+214393/311*a^7-58363/311*a^6-558371/311*a^5+11321/311*a^4+592862/311*a^3+115369/311*a^2-144931/311*a-10614/311)*q^200 +  ...

-------------------------------------------------------
Gamma_0(168)
Weight 2

-------------------------------------------------------
J_0(168), dim = 25

-------------------------------------------------------
168A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*3
Ker(ModPolar)  = Z/2^3*3 + Z/2^3*3
= B(Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/3 + Z/2*3) + F(Z/2) + G(Z/2) + H(Z/2 + Z/2) + I(Z/2) + J(Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 2.3214861532880926187 + -0.41095834187043987339e-40i
Omega-         = 0.28633971923274522787e-45 + -1.198252240458768429i
L(1)           = 1.1607430766440463093
w1             = 1.1607430766440463093 + 0.5991261202293842145i
w2             = 0.28633971923306384625e-45 + -1.198252240458768429i
c4             = 351.90738537355672068 + -0.42644417587859645909e-37i
c6             = -42846.837862184036277 + -0.21906905013309938934e-35i
j              = -42.016998876899387906 + 0.2004737294254038116e-37i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + 2*q^5 + 1*q^7 + 1*q^9 + 6*q^13 + -2*q^15 + -2*q^17 + 4*q^19 + -1*q^21 + -4*q^23 + -1*q^25 + -1*q^27 + -10*q^29 + -8*q^31 + 2*q^35 + 6*q^37 + -6*q^39 + -2*q^41 + -4*q^43 + 2*q^45 + 8*q^47 + 1*q^49 + 2*q^51 + -10*q^53 + -4*q^57 + 12*q^59 + -2*q^61 + 1*q^63 + 12*q^65 + 12*q^67 + 4*q^69 + -12*q^71 + -14*q^73 + 1*q^75 + -8*q^79 + 1*q^81 + 12*q^83 + -4*q^85 + 10*q^87 + -2*q^89 + 6*q^91 + 8*q^93 + 8*q^95 + 10*q^97 + -6*q^101 + -2*q^105 + -2*q^109 + -6*q^111 + 18*q^113 + -8*q^115 + 6*q^117 + -2*q^119 + -11*q^121 + 2*q^123 + -12*q^125 + 8*q^127 + 4*q^129 + -4*q^131 + 4*q^133 + -2*q^135 + 2*q^137 + -12*q^139 + -8*q^141 + -20*q^145 + -1*q^147 + 22*q^149 + -8*q^151 + -2*q^153 + -16*q^155 + -18*q^157 + 10*q^159 + -4*q^161 + -20*q^163 + 23*q^169 + 4*q^171 + 2*q^173 + -1*q^175 + -12*q^177 + -16*q^179 + 14*q^181 + 2*q^183 + 12*q^185 + -1*q^189 + -20*q^191 + 18*q^193 + -12*q^195 + 6*q^197 + 8*q^199 +  ...

-------------------------------------------------------
168B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= A(Z/2) + C(Z/2) + D(Z/2) + E(Z/2) + F(Z/2) + G(Z/2) + H(Z/2) + I(Z/2^2) + J(Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.451317079492722446 + -0.89148251213963690754e-4i
Omega-         = 2.7181339076822553075i
L(1)           = 0.72565854111536094044
w1             = -2.7181339076822553075i
w2             = -1.451317079492722446 + 0.89148251213963690754e-4i
c4             = 351.94718045927865069 + 0.86002023772187266701e-1i
c6             = 6558.5053895099206517 + 2.4357702636074674005i
j              = 129751.44955438165169 + 93.248854880547990746i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 2*q^5 + -1*q^7 + 1*q^9 + -2*q^13 + 2*q^15 + 6*q^17 + -4*q^19 + -1*q^21 + -4*q^23 + -1*q^25 + 1*q^27 + 6*q^29 + -8*q^31 + -2*q^35 + -10*q^37 + -2*q^39 + -10*q^41 + 12*q^43 + 2*q^45 + -8*q^47 + 1*q^49 + 6*q^51 + 6*q^53 + -4*q^57 + 4*q^59 + -10*q^61 + -1*q^63 + -4*q^65 + 12*q^67 + -4*q^69 + 4*q^71 + 2*q^73 + -1*q^75 + 8*q^79 + 1*q^81 + 4*q^83 + 12*q^85 + 6*q^87 + 6*q^89 + 2*q^91 + -8*q^93 + -8*q^95 + 10*q^97 + 10*q^101 + -2*q^105 + 16*q^107 + 14*q^109 + -10*q^111 + -14*q^113 + -8*q^115 + -2*q^117 + -6*q^119 + -11*q^121 + -10*q^123 + -12*q^125 + 8*q^127 + 12*q^129 + -12*q^131 + 4*q^133 + 2*q^135 + -14*q^137 + -4*q^139 + -8*q^141 + 12*q^145 + 1*q^147 + 6*q^149 + -8*q^151 + 6*q^153 + -16*q^155 + -10*q^157 + 6*q^159 + 4*q^161 + -4*q^163 + 16*q^167 + -9*q^169 + -4*q^171 + 2*q^173 + 1*q^175 + 4*q^177 + 6*q^181 + -10*q^183 + -20*q^185 + -1*q^189 + -4*q^191 + 18*q^193 + -4*q^195 + 22*q^197 + -24*q^199 +  ...

-------------------------------------------------------
168C (old = 84A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2) + D(Z/2 + Z/2 + Z/2) + E(Z/2) + F(Z/2) + G(Z/3 + Z/3 + Z/3 + Z/2*3) + H(Z/2 + Z/2) + I(Z/2 + Z/2) + J(Z/2)

-------------------------------------------------------
168D (old = 84B), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2) + C(Z/2 + Z/2 + Z/2) + E(Z/2) + F(Z/2) + G(Z/2) + H(Z/2 + Z/2) + I(Z/2 + Z/2) + J(Z/3 + Z/3 + Z/3 + Z/2*3)

-------------------------------------------------------
168E (old = 56A), dim = 1

CONGRUENCES:
Modular Degree = 2^6*3
Ker(ModPolar)  = Z/2^3 + Z/2^3 + Z/2^3*3 + Z/2^3*3
= A(Z/3 + Z/2*3) + B(Z/2) + C(Z/2) + D(Z/2) + F(Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2) + I(Z/2 + Z/2) + J(Z/2 + Z/2^2 + Z/2^2 + Z/2^2)

-------------------------------------------------------
168F (old = 56B), dim = 1

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2^3 + Z/2^3 + Z/2^3 + Z/2^3
= A(Z/2) + B(Z/2) + C(Z/2) + D(Z/2) + E(Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2^2) + H(Z/2^2) + I(Z/2 + Z/2^2) + J(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
168G (old = 42A), dim = 1

CONGRUENCES:
Modular Degree = 2^8*3^2
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3 + Z/2^4*3 + Z/2^4*3
= A(Z/2) + B(Z/2) + C(Z/3 + Z/3 + Z/3 + Z/2*3) + D(Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2^2) + H(Z/2^2) + I(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + J(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
168H (old = 24A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2) + F(Z/2^2) + G(Z/2^2) + I(Z/2) + J(Z/2)

-------------------------------------------------------
168I (old = 21A), dim = 1

CONGRUENCES:
Modular Degree = 2^10
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^4 + Z/2^4
= A(Z/2) + B(Z/2^2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2^2) + G(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2) + J(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
168J (old = 14A), dim = 1

CONGRUENCES:
Modular Degree = 2^10*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^3*3 + Z/2^3*3 + Z/2^3*3 + Z/2^3*3
= A(Z/2) + B(Z/2) + C(Z/2) + D(Z/3 + Z/3 + Z/3 + Z/2*3) + E(Z/2 + Z/2^2 + Z/2^2 + Z/2^2) + F(Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(169)
Weight 2

-------------------------------------------------------
J_0(169), dim = 8

-------------------------------------------------------
169A (new) , dim = 2

CONGRUENCES:
Modular Degree = 13
Ker(ModPolar)  = Z/13 + Z/13
= C(Z/13 + Z/13)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^2*3
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 2.1923089253441273521 + -0.33051108700304280062e-3i
Omega-         = 9.0561800388023068711 + -0.13119502402756719088e-3i
L(1)           = 2.1923089502579469212

HECKE EIGENFORM:
a^2-3 = 0,
f(q) = q + a*q^2 + 2*q^3 + 1*q^4 + -a*q^5 + 2*a*q^6 + -a*q^8 + 1*q^9 + -3*q^10 + 2*q^12 + -2*a*q^15 + -5*q^16 + 3*q^17 + a*q^18 + -2*a*q^19 + -a*q^20 + 6*q^23 + -2*a*q^24 + -2*q^25 + -4*q^27 + 3*q^29 + -6*q^30 + 2*a*q^31 + -3*a*q^32 + 3*a*q^34 + 1*q^36 + 5*a*q^37 + -6*q^38 + 3*q^40 + 3*a*q^41 + -8*q^43 + -a*q^45 + 6*a*q^46 + 2*a*q^47 + -10*q^48 + -7*q^49 + -2*a*q^50 + 6*q^51 + -3*q^53 + -4*a*q^54 + -4*a*q^57 + 3*a*q^58 + -4*a*q^59 + -2*a*q^60 + 1*q^61 + 6*q^62 + 1*q^64 + -2*a*q^67 + 3*q^68 + 12*q^69 + 2*a*q^71 + -a*q^72 + -a*q^73 + 15*q^74 + -4*q^75 + -2*a*q^76 + 4*q^79 + 5*a*q^80 + -11*q^81 + 9*q^82 + 8*a*q^83 + -3*a*q^85 + -8*a*q^86 + 6*q^87 + -4*a*q^89 + -3*q^90 + 6*q^92 + 4*a*q^93 + 6*q^94 + 6*q^95 + -6*a*q^96 + 4*a*q^97 + -7*a*q^98 + -2*q^100 + 3*q^101 + 6*a*q^102 + 10*q^103 + -3*a*q^106 + 6*q^107 + -4*q^108 + -8*a*q^109 + 10*a*q^111 + -15*q^113 + -12*q^114 + -6*a*q^115 + 3*q^116 + -12*q^118 + 6*q^120 + -11*q^121 + a*q^122 + 6*a*q^123 + 2*a*q^124 + 7*a*q^125 + 2*q^127 + 7*a*q^128 + -16*q^129 + 18*q^131 + -6*q^134 + 4*a*q^135 + -3*a*q^136 + 9*a*q^137 + 12*a*q^138 + -4*q^139 + 4*a*q^141 + 6*q^142 + -5*q^144 + -3*a*q^145 + -3*q^146 + -14*q^147 + 5*a*q^148 + -11*a*q^149 + -4*a*q^150 + -10*a*q^151 + 6*q^152 + 3*q^153 + -6*q^155 + -13*q^157 + 4*a*q^158 + -6*q^159 + 9*q^160 + -11*a*q^162 + -12*a*q^163 + 3*a*q^164 + 24*q^166 + -8*a*q^167 + -9*q^170 + -2*a*q^171 + -8*q^172 + -6*q^173 + 6*a*q^174 + -8*a*q^177 + -12*q^178 + -a*q^180 + -11*q^181 + 2*q^183 + -6*a*q^184 + -15*q^185 + 12*q^186 + 2*a*q^188 + 6*a*q^190 + 18*q^191 + 2*q^192 + -3*a*q^193 + 12*q^194 + -7*q^196 + -8*a*q^197 + 2*q^199 + 2*a*q^200 +  ...

-------------------------------------------------------
169B (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 7^2
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 79.446910130341516322 + -0.12477357698366765462e-1i
Omega-         = 0.35326815722102469552e-3 + -5.0801698464107388859i
L(1)           =

HECKE EIGENFORM:
a^3+2*a^2-a-1 = 0,
f(q) = q + a*q^2 + (-a^2-2*a)*q^3 + (a^2-2)*q^4 + (a^2+2*a-2)*q^5 + (-a-1)*q^6 + (a^2-3)*q^7 + (-2*a^2-3*a+1)*q^8 + (a^2+3*a-1)*q^9 + (-a+1)*q^10 + (-a^2-2*a-2)*q^11 + (a^2+3*a)*q^12 + (-2*a^2-2*a+1)*q^14 + (a^2+a-2)*q^15 + (-a^2-a+2)*q^16 + (-a^2+a+2)*q^17 + (a^2+1)*q^18 + (-2*a^2-a+2)*q^19 + (-3*a^2-3*a+4)*q^20 + (2*a^2+5*a)*q^21 + (-3*a-1)*q^22 + (2*a^2+4*a-3)*q^23 + (a^2+3*a+3)*q^24 + (-3*a^2-5*a+1)*q^25 + (3*a^2+4*a-3)*q^27 + (-a+4)*q^28 + (5*a^2+8*a-5)*q^29 + (-a^2-a+1)*q^30 + (-5*a^2-8*a+3)*q^31 + (5*a^2+7*a-3)*q^32 + (3*a^2+7*a+2)*q^33 + (3*a^2+a-1)*q^34 + (-4*a^2-5*a+6)*q^35 + (-4*a^2-4*a+3)*q^36 + (2*a^2+3*a+2)*q^37 + (3*a^2-2)*q^38 + (3*a^2+3*a-5)*q^40 + (-4*a^2-10*a-1)*q^41 + (a^2+2*a+2)*q^42 + (-2*a^2-5*a+5)*q^43 + (-a^2+3*a+4)*q^44 + (-2*a^2-4*a+5)*q^45 + (-a+2)*q^46 + (a^2-8)*q^47 + (-a^2-2*a+1)*q^48 + (-a^2-a)*q^49 + (a^2-2*a-3)*q^50 + (-a^2-4*a-1)*q^51 + (-4*a^2-11*a+1)*q^53 + (-2*a^2+3)*q^54 + (-a^2-3*a+2)*q^55 + (3*a^2+8*a-2)*q^56 + (-a+1)*q^57 + (-2*a^2+5)*q^58 + (-4*a^2-4*a-1)*q^59 + (-a^2-2*a+3)*q^60 + (6*a^2+7*a-6)*q^61 + (2*a^2-2*a-5)*q^62 + (-5*a^2-7*a+4)*q^63 + (-a^2+4*a+1)*q^64 + (a^2+5*a+3)*q^66 + (6*a^2+11*a-5)*q^67 + (-3*a^2-1)*q^68 + (a^2-4)*q^69 + (3*a^2+2*a-4)*q^70 + (3*a^2+3*a-13)*q^71 + (2*a^2-a-6)*q^72 + (-6*a^2-3*a+13)*q^73 + (-a^2+4*a+2)*q^74 + (2*a^2+6*a+5)*q^75 + (-2*a^2+3*a-1)*q^76 + (5*a+6)*q^77 + (-a^2+7*a+5)*q^79 + (3*a^2+4*a-5)*q^80 + (-3*a^2-10*a-1)*q^81 + (-2*a^2-5*a-4)*q^82 + (9*a^2+11*a-13)*q^83 + (-4*a^2-7*a+1)*q^84 + (3*a^2+2*a-3)*q^85 + (-a^2+3*a-2)*q^86 + (-3*a-8)*q^87 + (5*a^2+9*a+1)*q^88 + (7*a^2+7*a-13)*q^89 + (3*a-2)*q^90 + (-5*a^2-6*a+6)*q^92 + (2*a^2+7*a+8)*q^93 + (-2*a^2-7*a+1)*q^94 + (4*a^2+3*a-5)*q^95 + (-2*a^2-6*a-7)*q^96 + (-a^2-8*a-1)*q^97 + (a^2-a-1)*q^98 + (-2*a^2-8*a-1)*q^99 + (2*a^2+8*a-1)*q^100 + (-3*a^2-13*a-1)*q^101 + (-2*a^2-2*a-1)*q^102 + (8*a^2+9*a-11)*q^103 + (-2*a^2-3*a+5)*q^105 + (-3*a^2-3*a-4)*q^106 + (-3*a^2-a+6)*q^107 + (-2*a^2-7*a+4)*q^108 + (2*a^2+8*a+8)*q^109 + (-a^2+a-1)*q^110 + (-4*a^2-9*a-3)*q^111 + (2*a^2+3*a-5)*q^112 + (a^2+3*a+9)*q^113 + (-a^2+a)*q^114 + (-5*a^2-8*a+10)*q^115 + (-6*a^2-13*a+8)*q^116 + (4*a^2-5*a-4)*q^118 + (-2*a^2-a-3)*q^119 + (2*a^2+4*a-3)*q^120 + (5*a^2+11*a-5)*q^121 + (-5*a^2+6)*q^122 + (5*a^2+16*a+10)*q^123 + (4*a^2+13*a-4)*q^124 + (-a^2-6*a+3)*q^125 + (3*a^2-a-5)*q^126 + (-9*a^2-10*a+4)*q^127 + (-4*a^2-14*a+5)*q^128 + (-3*a^2-3*a+5)*q^129 + (5*a^2+4*a-13)*q^131 + (-3*a^2-10*a-3)*q^132 + (4*a-3)*q^133 + (-a^2+a+6)*q^134 + (-6*a^2-7*a+10)*q^135 + (-6*a-1)*q^136 + (-4*a^2-4*a+12)*q^137 + (-2*a^2-3*a+1)*q^138 + (-11*a^2-17*a+6)*q^139 + (4*a^2+9*a-9)*q^140 + (7*a^2+15*a)*q^141 + (-3*a^2-10*a+3)*q^142 + (3*a^2+4*a-4)*q^144 + (-10*a^2-13*a+18)*q^145 + (9*a^2+7*a-6)*q^146 + (a^2+2*a+1)*q^147 + (2*a^2-5*a-5)*q^148 + (3*a^2+3*a)*q^149 + (2*a^2+7*a+2)*q^150 + (12*a^2+14*a-15)*q^151 + (a^2-3*a+2)*q^152 + (5*a^2+4*a-2)*q^153 + (5*a^2+6*a)*q^154 + (8*a^2+9*a-14)*q^155 + (a^2+6*a-1)*q^157 + (9*a^2+4*a-1)*q^158 + (3*a^2+13*a+11)*q^159 + (-8*a^2-8*a+13)*q^160 + (-7*a^2-10*a+9)*q^161 + (-4*a^2-4*a-3)*q^162 + (-a^2+a+16)*q^163 + (7*a^2+14*a)*q^164 + (-a^2+3)*q^165 + (-7*a^2-4*a+9)*q^166 + (2*a^2+16*a+2)*q^167 + (-a^2-7*a-8)*q^168 + (-4*a^2+3)*q^170 + (5*a^2+2*a-5)*q^171 + (9*a^2+7*a-11)*q^172 + (-16*a^2-24*a+8)*q^173 + (-3*a^2-8*a)*q^174 + (5*a^2+13*a-2)*q^175 + (a^2-3)*q^176 + (5*a^2+10*a+4)*q^177 + (-7*a^2-6*a+7)*q^178 + (5*a^2+9*a+1)*q^179 + (7*a^2+6*a-10)*q^180 + (-a^2+7*a+16)*q^181 + (-a-7)*q^183 + (4*a^2+3*a-9)*q^184 + (3*a-1)*q^185 + (3*a^2+10*a+2)*q^186 + (a^2-6*a-5)*q^187 + (-5*a^2-a+14)*q^188 + (-5*a^2-11*a+7)*q^189 + (-5*a^2-a+4)*q^190 + (4*a^2-5*a-13)*q^191 + (-5*a-4)*q^192 + (-8*a^2-18*a+6)*q^193 + (-6*a^2-2*a-1)*q^194 + (-a^2+2*a+1)*q^196 + (-8*a^2-8*a+11)*q^197 + (-4*a^2-3*a-2)*q^198 + (6*a^2+17*a-6)*q^199 + (2*a^2+5*a+8)*q^200 +  ...

-------------------------------------------------------
169C (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3*13
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*13 + Z/2*13
= A(Z/13 + Z/13) + B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 7^2
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 7
Torsion Bound  = 7
|L(1)/Omega|   = 2^3/7
Sha Bound      = 2^3*7

ANALYTIC INVARIANTS:

Omega+         = 1.6951334213651175985 + 0.10267640618573766347e-3i
Omega-         = 0.12709124692244631514e-2 + 18.314394625177182465i
L(1)           = 1.9372953422568439129

HECKE EIGENFORM:
a^3-2*a^2-a+1 = 0,
f(q) = q + a*q^2 + (-a^2+2*a)*q^3 + (a^2-2)*q^4 + (-a^2+2*a+2)*q^5 + (-a+1)*q^6 + (-a^2+3)*q^7 + (2*a^2-3*a-1)*q^8 + (a^2-3*a-1)*q^9 + (a+1)*q^10 + (a^2-2*a+2)*q^11 + (a^2-3*a)*q^12 + (-2*a^2+2*a+1)*q^14 + (-a^2+a+2)*q^15 + (-a^2+a+2)*q^16 + (-a^2-a+2)*q^17 + (-a^2-1)*q^18 + (2*a^2-a-2)*q^19 + (3*a^2-3*a-4)*q^20 + (-2*a^2+5*a)*q^21 + (3*a-1)*q^22 + (2*a^2-4*a-3)*q^23 + (-a^2+3*a-3)*q^24 + (-3*a^2+5*a+1)*q^25 + (3*a^2-4*a-3)*q^27 + (-a-4)*q^28 + (5*a^2-8*a-5)*q^29 + (-a^2+a+1)*q^30 + (5*a^2-8*a-3)*q^31 + (-5*a^2+7*a+3)*q^32 + (-3*a^2+7*a-2)*q^33 + (-3*a^2+a+1)*q^34 + (-4*a^2+5*a+6)*q^35 + (-4*a^2+4*a+3)*q^36 + (-2*a^2+3*a-2)*q^37 + (3*a^2-2)*q^38 + (3*a^2-3*a-5)*q^40 + (4*a^2-10*a+1)*q^41 + (a^2-2*a+2)*q^42 + (-2*a^2+5*a+5)*q^43 + (a^2+3*a-4)*q^44 + (2*a^2-4*a-5)*q^45 + (-a-2)*q^46 + (-a^2+8)*q^47 + (-a^2+2*a+1)*q^48 + (-a^2+a)*q^49 + (-a^2-2*a+3)*q^50 + (-a^2+4*a-1)*q^51 + (-4*a^2+11*a+1)*q^53 + (2*a^2-3)*q^54 + (-a^2+3*a+2)*q^55 + (3*a^2-8*a-2)*q^56 + (-a-1)*q^57 + (2*a^2-5)*q^58 + (4*a^2-4*a+1)*q^59 + (a^2-2*a-3)*q^60 + (6*a^2-7*a-6)*q^61 + (2*a^2+2*a-5)*q^62 + (5*a^2-7*a-4)*q^63 + (-a^2-4*a+1)*q^64 + (a^2-5*a+3)*q^66 + (-6*a^2+11*a+5)*q^67 + (-3*a^2-1)*q^68 + (a^2-4)*q^69 + (-3*a^2+2*a+4)*q^70 + (-3*a^2+3*a+13)*q^71 + (-2*a^2-a+6)*q^72 + (6*a^2-3*a-13)*q^73 + (-a^2-4*a+2)*q^74 + (2*a^2-6*a+5)*q^75 + (2*a^2+3*a+1)*q^76 + (-5*a+6)*q^77 + (-a^2-7*a+5)*q^79 + (-3*a^2+4*a+5)*q^80 + (-3*a^2+10*a-1)*q^81 + (-2*a^2+5*a-4)*q^82 + (-9*a^2+11*a+13)*q^83 + (4*a^2-7*a-1)*q^84 + (-3*a^2+2*a+3)*q^85 + (a^2+3*a+2)*q^86 + (3*a-8)*q^87 + (5*a^2-9*a+1)*q^88 + (-7*a^2+7*a+13)*q^89 + (-3*a-2)*q^90 + (-5*a^2+6*a+6)*q^92 + (-2*a^2+7*a-8)*q^93 + (-2*a^2+7*a+1)*q^94 + (4*a^2-3*a-5)*q^95 + (2*a^2-6*a+7)*q^96 + (a^2-8*a+1)*q^97 + (-a^2-a+1)*q^98 + (2*a^2-8*a+1)*q^99 + (2*a^2-8*a-1)*q^100 + (-3*a^2+13*a-1)*q^101 + (2*a^2-2*a+1)*q^102 + (8*a^2-9*a-11)*q^103 + (-2*a^2+3*a+5)*q^105 + (3*a^2-3*a+4)*q^106 + (-3*a^2+a+6)*q^107 + (-2*a^2+7*a+4)*q^108 + (-2*a^2+8*a-8)*q^109 + (a^2+a+1)*q^110 + (4*a^2-9*a+3)*q^111 + (-2*a^2+3*a+5)*q^112 + (a^2-3*a+9)*q^113 + (-a^2-a)*q^114 + (5*a^2-8*a-10)*q^115 + (-6*a^2+13*a+8)*q^116 + (4*a^2+5*a-4)*q^118 + (2*a^2-a+3)*q^119 + (2*a^2-4*a-3)*q^120 + (5*a^2-11*a-5)*q^121 + (5*a^2-6)*q^122 + (-5*a^2+16*a-10)*q^123 + (-4*a^2+13*a+4)*q^124 + (a^2-6*a-3)*q^125 + (3*a^2+a-5)*q^126 + (-9*a^2+10*a+4)*q^127 + (4*a^2-14*a-5)*q^128 + (-3*a^2+3*a+5)*q^129 + (5*a^2-4*a-13)*q^131 + (3*a^2-10*a+3)*q^132 + (-4*a-3)*q^133 + (-a^2-a+6)*q^134 + (6*a^2-7*a-10)*q^135 + (-6*a+1)*q^136 + (4*a^2-4*a-12)*q^137 + (2*a^2-3*a-1)*q^138 + (-11*a^2+17*a+6)*q^139 + (4*a^2-9*a-9)*q^140 + (-7*a^2+15*a)*q^141 + (-3*a^2+10*a+3)*q^142 + (3*a^2-4*a-4)*q^144 + (10*a^2-13*a-18)*q^145 + (9*a^2-7*a-6)*q^146 + (a^2-2*a+1)*q^147 + (-2*a^2-5*a+5)*q^148 + (-3*a^2+3*a)*q^149 + (-2*a^2+7*a-2)*q^150 + (-12*a^2+14*a+15)*q^151 + (a^2+3*a+2)*q^152 + (5*a^2-4*a-2)*q^153 + (-5*a^2+6*a)*q^154 + (8*a^2-9*a-14)*q^155 + (a^2-6*a-1)*q^157 + (-9*a^2+4*a+1)*q^158 + (3*a^2-13*a+11)*q^159 + (-8*a^2+8*a+13)*q^160 + (7*a^2-10*a-9)*q^161 + (4*a^2-4*a+3)*q^162 + (a^2+a-16)*q^163 + (-7*a^2+14*a)*q^164 + (-a^2+3)*q^165 + (-7*a^2+4*a+9)*q^166 + (-2*a^2+16*a-2)*q^167 + (-a^2+7*a-8)*q^168 + (-4*a^2+3)*q^170 + (-5*a^2+2*a+5)*q^171 + (9*a^2-7*a-11)*q^172 + (-16*a^2+24*a+8)*q^173 + (3*a^2-8*a)*q^174 + (-5*a^2+13*a+2)*q^175 + (-a^2+3)*q^176 + (-5*a^2+10*a-4)*q^177 + (-7*a^2+6*a+7)*q^178 + (5*a^2-9*a+1)*q^179 + (-7*a^2+6*a+10)*q^180 + (-a^2-7*a+16)*q^181 + (a-7)*q^183 + (-4*a^2+3*a+9)*q^184 + (-3*a-1)*q^185 + (3*a^2-10*a+2)*q^186 + (-a^2-6*a+5)*q^187 + (5*a^2-a-14)*q^188 + (5*a^2-11*a-7)*q^189 + (5*a^2-a-4)*q^190 + (4*a^2+5*a-13)*q^191 + (5*a-4)*q^192 + (8*a^2-18*a-6)*q^193 + (-6*a^2+2*a-1)*q^194 + (-a^2-2*a+1)*q^196 + (8*a^2-8*a-11)*q^197 + (-4*a^2+3*a-2)*q^198 + (6*a^2-17*a-6)*q^199 + (-2*a^2+5*a-8)*q^200 +  ...

-------------------------------------------------------
Gamma_0(170)
Weight 2

-------------------------------------------------------
J_0(170), dim = 23

-------------------------------------------------------
170A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^5*5
Ker(ModPolar)  = Z/2^5*5 + Z/2^5*5
= B(Z/5 + Z/5) + D(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2^2 + Z/2^2) + H(Z/2 + Z/2) + I(Z/2 + Z/2) + J(Z/2 + Z/2) + K(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/3
Sha Bound      = 2^2*3

ANALYTIC INVARIANTS:

Omega+         = 0.95591052879233097607 + -0.25029695195449415315e-3i
Omega-         = 0.11911499325148900383e-4 + -0.3357567519940107129i
L(1)           = 0.31863685385379422654
w1             = 0.95591052879233097607 + -0.25029695195449415315e-3i
w2             = 0.11911499325148900383e-4 + -0.3357567519940107129i
c4             = 122637.19898812001601 + -17.400325392887598092i
c6             = -42946417.493226692041 + 9143.510953468565373i
j              = 58728389.19875878792 + -312349.06229004537761i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -2*q^3 + 1*q^4 + -1*q^5 + 2*q^6 + 2*q^7 + -1*q^8 + 1*q^9 + 1*q^10 + 6*q^11 + -2*q^12 + 2*q^13 + -2*q^14 + 2*q^15 + 1*q^16 + 1*q^17 + -1*q^18 + 8*q^19 + -1*q^20 + -4*q^21 + -6*q^22 + -6*q^23 + 2*q^24 + 1*q^25 + -2*q^26 + 4*q^27 + 2*q^28 + -6*q^29 + -2*q^30 + 2*q^31 + -1*q^32 + -12*q^33 + -1*q^34 + -2*q^35 + 1*q^36 + 2*q^37 + -8*q^38 + -4*q^39 + 1*q^40 + -6*q^41 + 4*q^42 + -4*q^43 + 6*q^44 + -1*q^45 + 6*q^46 + 12*q^47 + -2*q^48 + -3*q^49 + -1*q^50 + -2*q^51 + 2*q^52 + 6*q^53 + -4*q^54 + -6*q^55 + -2*q^56 + -16*q^57 + 6*q^58 + 2*q^60 + 2*q^61 + -2*q^62 + 2*q^63 + 1*q^64 + -2*q^65 + 12*q^66 + 8*q^67 + 1*q^68 + 12*q^69 + 2*q^70 + -6*q^71 + -1*q^72 + 2*q^73 + -2*q^74 + -2*q^75 + 8*q^76 + 12*q^77 + 4*q^78 + -10*q^79 + -1*q^80 + -11*q^81 + 6*q^82 + 12*q^83 + -4*q^84 + -1*q^85 + 4*q^86 + 12*q^87 + -6*q^88 + 6*q^89 + 1*q^90 + 4*q^91 + -6*q^92 + -4*q^93 + -12*q^94 + -8*q^95 + 2*q^96 + 2*q^97 + 3*q^98 + 6*q^99 + 1*q^100 + -6*q^101 + 2*q^102 + -4*q^103 + -2*q^104 + 4*q^105 + -6*q^106 + -18*q^107 + 4*q^108 + 2*q^109 + 6*q^110 + -4*q^111 + 2*q^112 + -6*q^113 + 16*q^114 + 6*q^115 + -6*q^116 + 2*q^117 + 2*q^119 + -2*q^120 + 25*q^121 + -2*q^122 + 12*q^123 + 2*q^124 + -1*q^125 + -2*q^126 + -16*q^127 + -1*q^128 + 8*q^129 + 2*q^130 + 18*q^131 + -12*q^132 + 16*q^133 + -8*q^134 + -4*q^135 + -1*q^136 + -18*q^137 + -12*q^138 + -22*q^139 + -2*q^140 + -24*q^141 + 6*q^142 + 12*q^143 + 1*q^144 + 6*q^145 + -2*q^146 + 6*q^147 + 2*q^148 + 6*q^149 + 2*q^150 + -4*q^151 + -8*q^152 + 1*q^153 + -12*q^154 + -2*q^155 + -4*q^156 + -10*q^157 + 10*q^158 + -12*q^159 + 1*q^160 + -12*q^161 + 11*q^162 + 2*q^163 + -6*q^164 + 12*q^165 + -12*q^166 + -18*q^167 + 4*q^168 + -9*q^169 + 1*q^170 + 8*q^171 + -4*q^172 + -6*q^173 + -12*q^174 + 2*q^175 + 6*q^176 + -6*q^178 + -1*q^180 + -22*q^181 + -4*q^182 + -4*q^183 + 6*q^184 + -2*q^185 + 4*q^186 + 6*q^187 + 12*q^188 + 8*q^189 + 8*q^190 + 24*q^191 + -2*q^192 + 2*q^193 + -2*q^194 + 4*q^195 + -3*q^196 + 18*q^197 + -6*q^198 + 2*q^199 + -1*q^200 +  ...

-------------------------------------------------------
170B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*5
Ker(ModPolar)  = Z/2^2*5 + Z/2^2*5
= A(Z/5 + Z/5) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.3358949914862805169 + 0.48618806176873385748e-4i
Omega-         = 0.74465686760266003245e-4 + -5.7164165852958571864i
L(1)           = 1.3358949923710013701
w1             = -0.66798472858652039147 + 2.8581839832448401565i
w2             = 1.3358949914862805169 + 0.48618806176873385748e-4i
c4             = 489.19150154943130918 + -0.71268436647191141535e-1i
c6             = 10833.34986289027234 + -2.3631386142331658932i
j              = -688370.02341686906495 + 216.47375525425892556i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 3*q^3 + 1*q^4 + -1*q^5 + -3*q^6 + 2*q^7 + -1*q^8 + 6*q^9 + 1*q^10 + -4*q^11 + 3*q^12 + -3*q^13 + -2*q^14 + -3*q^15 + 1*q^16 + 1*q^17 + -6*q^18 + 3*q^19 + -1*q^20 + 6*q^21 + 4*q^22 + -6*q^23 + -3*q^24 + 1*q^25 + 3*q^26 + 9*q^27 + 2*q^28 + 9*q^29 + 3*q^30 + -3*q^31 + -1*q^32 + -12*q^33 + -1*q^34 + -2*q^35 + 6*q^36 + -8*q^37 + -3*q^38 + -9*q^39 + 1*q^40 + -6*q^41 + -6*q^42 + 6*q^43 + -4*q^44 + -6*q^45 + 6*q^46 + -13*q^47 + 3*q^48 + -3*q^49 + -1*q^50 + 3*q^51 + -3*q^52 + -9*q^53 + -9*q^54 + 4*q^55 + -2*q^56 + 9*q^57 + -9*q^58 + 15*q^59 + -3*q^60 + 7*q^61 + 3*q^62 + 12*q^63 + 1*q^64 + 3*q^65 + 12*q^66 + -2*q^67 + 1*q^68 + -18*q^69 + 2*q^70 + 9*q^71 + -6*q^72 + -3*q^73 + 8*q^74 + 3*q^75 + 3*q^76 + -8*q^77 + 9*q^78 + -1*q^80 + 9*q^81 + 6*q^82 + 12*q^83 + 6*q^84 + -1*q^85 + -6*q^86 + 27*q^87 + 4*q^88 + -9*q^89 + 6*q^90 + -6*q^91 + -6*q^92 + -9*q^93 + 13*q^94 + -3*q^95 + -3*q^96 + 7*q^97 + 3*q^98 + -24*q^99 + 1*q^100 + -6*q^101 + -3*q^102 + 16*q^103 + 3*q^104 + -6*q^105 + 9*q^106 + 12*q^107 + 9*q^108 + 7*q^109 + -4*q^110 + -24*q^111 + 2*q^112 + -1*q^113 + -9*q^114 + 6*q^115 + 9*q^116 + -18*q^117 + -15*q^118 + 2*q^119 + 3*q^120 + 5*q^121 + -7*q^122 + -18*q^123 + -3*q^124 + -1*q^125 + -12*q^126 + -11*q^127 + -1*q^128 + 18*q^129 + -3*q^130 + -2*q^131 + -12*q^132 + 6*q^133 + 2*q^134 + -9*q^135 + -1*q^136 + 22*q^137 + 18*q^138 + 8*q^139 + -2*q^140 + -39*q^141 + -9*q^142 + 12*q^143 + 6*q^144 + -9*q^145 + 3*q^146 + -9*q^147 + -8*q^148 + 16*q^149 + -3*q^150 + 6*q^151 + -3*q^152 + 6*q^153 + 8*q^154 + 3*q^155 + -9*q^156 + 10*q^157 + -27*q^159 + 1*q^160 + -12*q^161 + -9*q^162 + -8*q^163 + -6*q^164 + 12*q^165 + -12*q^166 + 2*q^167 + -6*q^168 + -4*q^169 + 1*q^170 + 18*q^171 + 6*q^172 + -6*q^173 + -27*q^174 + 2*q^175 + -4*q^176 + 45*q^177 + 9*q^178 + 20*q^179 + -6*q^180 + -2*q^181 + 6*q^182 + 21*q^183 + 6*q^184 + 8*q^185 + 9*q^186 + -4*q^187 + -13*q^188 + 18*q^189 + 3*q^190 + 4*q^191 + 3*q^192 + -18*q^193 + -7*q^194 + 9*q^195 + -3*q^196 + -12*q^197 + 24*q^198 + -13*q^199 + -1*q^200 +  ...

-------------------------------------------------------
170C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= B(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + I(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 3.3285861455973793541 + 0.27368824733937141268e-3i
Omega-         = 0.81139717201270348634e-4 + -1.6523384076661167708i
L(1)           = 1.1095287189497307284
w1             = -1.6643336426572903122 + 0.82603235970938869968i
w2             = -0.81139717201270348634e-4 + 1.6523384076661167708i
c4             = 120.9708206203151087 + -0.55917962395756400397e-2i
c6             = -5584.3767937528934181 + 2.1494434562643376375i
j              = -103.99604538266581744 + -0.69585468632738668234e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + 1*q^5 + -1*q^6 + 2*q^7 + -1*q^8 + -2*q^9 + -1*q^10 + 1*q^12 + 5*q^13 + -2*q^14 + 1*q^15 + 1*q^16 + -1*q^17 + 2*q^18 + -1*q^19 + 1*q^20 + 2*q^21 + 6*q^23 + -1*q^24 + 1*q^25 + -5*q^26 + -5*q^27 + 2*q^28 + -9*q^29 + -1*q^30 + -1*q^31 + -1*q^32 + 1*q^34 + 2*q^35 + -2*q^36 + -4*q^37 + 1*q^38 + 5*q^39 + -1*q^40 + -6*q^41 + -2*q^42 + 2*q^43 + -2*q^45 + -6*q^46 + -9*q^47 + 1*q^48 + -3*q^49 + -1*q^50 + -1*q^51 + 5*q^52 + -9*q^53 + 5*q^54 + -2*q^56 + -1*q^57 + 9*q^58 + 3*q^59 + 1*q^60 + -7*q^61 + 1*q^62 + -4*q^63 + 1*q^64 + 5*q^65 + 14*q^67 + -1*q^68 + 6*q^69 + -2*q^70 + 3*q^71 + 2*q^72 + 11*q^73 + 4*q^74 + 1*q^75 + -1*q^76 + -5*q^78 + 8*q^79 + 1*q^80 + 1*q^81 + 6*q^82 + 2*q^84 + -1*q^85 + -2*q^86 + -9*q^87 + -9*q^89 + 2*q^90 + 10*q^91 + 6*q^92 + -1*q^93 + 9*q^94 + -1*q^95 + -1*q^96 + -7*q^97 + 3*q^98 + 1*q^100 + 18*q^101 + 1*q^102 + -16*q^103 + -5*q^104 + 2*q^105 + 9*q^106 + 12*q^107 + -5*q^108 + -7*q^109 + -4*q^111 + 2*q^112 + 9*q^113 + 1*q^114 + 6*q^115 + -9*q^116 + -10*q^117 + -3*q^118 + -2*q^119 + -1*q^120 + -11*q^121 + 7*q^122 + -6*q^123 + -1*q^124 + 1*q^125 + 4*q^126 + -7*q^127 + -1*q^128 + 2*q^129 + -5*q^130 + 6*q^131 + -2*q^133 + -14*q^134 + -5*q^135 + 1*q^136 + -6*q^137 + -6*q^138 + 20*q^139 + 2*q^140 + -9*q^141 + -3*q^142 + -2*q^144 + -9*q^145 + -11*q^146 + -3*q^147 + -4*q^148 + -12*q^149 + -1*q^150 + 14*q^151 + 1*q^152 + 2*q^153 + -1*q^155 + 5*q^156 + 2*q^157 + -8*q^158 + -9*q^159 + -1*q^160 + 12*q^161 + -1*q^162 + -16*q^163 + -6*q^164 + 6*q^167 + -2*q^168 + 12*q^169 + 1*q^170 + 2*q^171 + 2*q^172 + 6*q^173 + 9*q^174 + 2*q^175 + 3*q^177 + 9*q^178 + 12*q^179 + -2*q^180 + 2*q^181 + -10*q^182 + -7*q^183 + -6*q^184 + -4*q^185 + 1*q^186 + -9*q^188 + -10*q^189 + 1*q^190 + 24*q^191 + 1*q^192 + 2*q^193 + 7*q^194 + 5*q^195 + -3*q^196 + 24*q^197 + -7*q^199 + -1*q^200 +  ...

-------------------------------------------------------
170D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2 + Z/2) + J(Z/2 + Z/2) + K(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +--
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.0204893888489093322 + -0.24707496327430047309e-3i
Omega-         = 0.74167503027521877139e-4 + 1.4555062677389027822i
L(1)           =
w1             = 2.0204893888489093322 + -0.24707496327430047309e-3i
w2             = -0.74167503027521877139e-4 + -1.4555062677389027822i
c4             = 360.86672717836963126 + 0.82027458837855826466e-1i
c6             = -5937.0467903754367835 + -1.4809982078642279362i
j              = 6913.8674617135904848 + -3.7974918573578836714i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -2*q^3 + 1*q^4 + 1*q^5 + 2*q^6 + -2*q^7 + -1*q^8 + 1*q^9 + -1*q^10 + -2*q^11 + -2*q^12 + -6*q^13 + 2*q^14 + -2*q^15 + 1*q^16 + 1*q^17 + -1*q^18 + -8*q^19 + 1*q^20 + 4*q^21 + 2*q^22 + -2*q^23 + 2*q^24 + 1*q^25 + 6*q^26 + 4*q^27 + -2*q^28 + 6*q^29 + 2*q^30 + -2*q^31 + -1*q^32 + 4*q^33 + -1*q^34 + -2*q^35 + 1*q^36 + 6*q^37 + 8*q^38 + 12*q^39 + -1*q^40 + 2*q^41 + -4*q^42 + -4*q^43 + -2*q^44 + 1*q^45 + 2*q^46 + 4*q^47 + -2*q^48 + -3*q^49 + -1*q^50 + -2*q^51 + -6*q^52 + -10*q^53 + -4*q^54 + -2*q^55 + 2*q^56 + 16*q^57 + -6*q^58 + -2*q^60 + -10*q^61 + 2*q^62 + -2*q^63 + 1*q^64 + -6*q^65 + -4*q^66 + 8*q^67 + 1*q^68 + 4*q^69 + 2*q^70 + 14*q^71 + -1*q^72 + 10*q^73 + -6*q^74 + -2*q^75 + -8*q^76 + 4*q^77 + -12*q^78 + -14*q^79 + 1*q^80 + -11*q^81 + -2*q^82 + -4*q^83 + 4*q^84 + 1*q^85 + 4*q^86 + -12*q^87 + 2*q^88 + 6*q^89 + -1*q^90 + 12*q^91 + -2*q^92 + 4*q^93 + -4*q^94 + -8*q^95 + 2*q^96 + -14*q^97 + 3*q^98 + -2*q^99 + 1*q^100 + -6*q^101 + 2*q^102 + 4*q^103 + 6*q^104 + 4*q^105 + 10*q^106 + -10*q^107 + 4*q^108 + -2*q^109 + 2*q^110 + -12*q^111 + -2*q^112 + 18*q^113 + -16*q^114 + -2*q^115 + 6*q^116 + -6*q^117 + -2*q^119 + 2*q^120 + -7*q^121 + 10*q^122 + -4*q^123 + -2*q^124 + 1*q^125 + 2*q^126 + 16*q^127 + -1*q^128 + 8*q^129 + 6*q^130 + -6*q^131 + 4*q^132 + 16*q^133 + -8*q^134 + 4*q^135 + -1*q^136 + -18*q^137 + -4*q^138 + 2*q^139 + -2*q^140 + -8*q^141 + -14*q^142 + 12*q^143 + 1*q^144 + 6*q^145 + -10*q^146 + 6*q^147 + 6*q^148 + -10*q^149 + 2*q^150 + 20*q^151 + 8*q^152 + 1*q^153 + -4*q^154 + -2*q^155 + 12*q^156 + -18*q^157 + 14*q^158 + 20*q^159 + -1*q^160 + 4*q^161 + 11*q^162 + 2*q^163 + 2*q^164 + 4*q^165 + 4*q^166 + 2*q^167 + -4*q^168 + 23*q^169 + -1*q^170 + -8*q^171 + -4*q^172 + -10*q^173 + 12*q^174 + -2*q^175 + -2*q^176 + -6*q^178 + -16*q^179 + 1*q^180 + 14*q^181 + -12*q^182 + 20*q^183 + 2*q^184 + 6*q^185 + -4*q^186 + -2*q^187 + 4*q^188 + -8*q^189 + 8*q^190 + -8*q^191 + -2*q^192 + -14*q^193 + 14*q^194 + 12*q^195 + -3*q^196 + 6*q^197 + 2*q^198 + -26*q^199 + -1*q^200 +  ...

-------------------------------------------------------
170E (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3*7
Ker(ModPolar)  = Z/2^2*3*7 + Z/2^2*3*7
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/7 + Z/7) + J(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 7/3
Sha Bound      = 3*7

ANALYTIC INVARIANTS:

Omega+         = 0.79159537713389966355 + 0.30311087879038983303e-4i
Omega-         = 0.17693182211424079364e-3 + 0.8573288302687387057i
L(1)           = 1.8470558813331862739
w1             = 0.39588615447800695217 + 0.42867957067830887234i
w2             = 0.39570922265589271138 + -0.42864925959042983336i
c4             = -19145.641213946969587 + -9.8401716707298674525i
c6             = 822181.52801499844478 + -2021.1376547223644818i
j              = 1576.1807990138524519 + 0.89437354500813125655i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^3 + 1*q^4 + -1*q^5 + 1*q^6 + 2*q^7 + 1*q^8 + -2*q^9 + -1*q^10 + 1*q^12 + -1*q^13 + 2*q^14 + -1*q^15 + 1*q^16 + -1*q^17 + -2*q^18 + -1*q^19 + -1*q^20 + 2*q^21 + -6*q^23 + 1*q^24 + 1*q^25 + -1*q^26 + -5*q^27 + 2*q^28 + -3*q^29 + -1*q^30 + 5*q^31 + 1*q^32 + -1*q^34 + -2*q^35 + -2*q^36 + 8*q^37 + -1*q^38 + -1*q^39 + -1*q^40 + 6*q^41 + 2*q^42 + -10*q^43 + 2*q^45 + -6*q^46 + -3*q^47 + 1*q^48 + -3*q^49 + 1*q^50 + -1*q^51 + -1*q^52 + -3*q^53 + -5*q^54 + 2*q^56 + -1*q^57 + -3*q^58 + 3*q^59 + -1*q^60 + 11*q^61 + 5*q^62 + -4*q^63 + 1*q^64 + 1*q^65 + 2*q^67 + -1*q^68 + -6*q^69 + -2*q^70 + 9*q^71 + -2*q^72 + 11*q^73 + 8*q^74 + 1*q^75 + -1*q^76 + -1*q^78 + 8*q^79 + -1*q^80 + 1*q^81 + 6*q^82 + -12*q^83 + 2*q^84 + 1*q^85 + -10*q^86 + -3*q^87 + 15*q^89 + 2*q^90 + -2*q^91 + -6*q^92 + 5*q^93 + -3*q^94 + 1*q^95 + 1*q^96 + -7*q^97 + -3*q^98 + 1*q^100 + 6*q^101 + -1*q^102 + 8*q^103 + -1*q^104 + -2*q^105 + -3*q^106 + -12*q^107 + -5*q^108 + 11*q^109 + 8*q^111 + 2*q^112 + 9*q^113 + -1*q^114 + 6*q^115 + -3*q^116 + 2*q^117 + 3*q^118 + -2*q^119 + -1*q^120 + -11*q^121 + 11*q^122 + 6*q^123 + 5*q^124 + -1*q^125 + -4*q^126 + 11*q^127 + 1*q^128 + -10*q^129 + 1*q^130 + -18*q^131 + -2*q^133 + 2*q^134 + 5*q^135 + -1*q^136 + -18*q^137 + -6*q^138 + 8*q^139 + -2*q^140 + -3*q^141 + 9*q^142 + -2*q^144 + 3*q^145 + 11*q^146 + -3*q^147 + 8*q^148 + -12*q^149 + 1*q^150 + -22*q^151 + -1*q^152 + 2*q^153 + -5*q^155 + -1*q^156 + 14*q^157 + 8*q^158 + -3*q^159 + -1*q^160 + -12*q^161 + 1*q^162 + -16*q^163 + 6*q^164 + -12*q^166 + -18*q^167 + 2*q^168 + -12*q^169 + 1*q^170 + 2*q^171 + -10*q^172 + 18*q^173 + -3*q^174 + 2*q^175 + 3*q^177 + 15*q^178 + -12*q^179 + 2*q^180 + -10*q^181 + -2*q^182 + 11*q^183 + -6*q^184 + -8*q^185 + 5*q^186 + -3*q^188 + -10*q^189 + 1*q^190 + 12*q^191 + 1*q^192 + 2*q^193 + -7*q^194 + 1*q^195 + -3*q^196 + -24*q^197 + 11*q^199 + 1*q^200 +  ...

-------------------------------------------------------
170F (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^5 + Z/2^5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2 + Z/2) + J(Z/2 + Z/2) + K(Z/2^2 + Z/2^2)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 17
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2^4
|L(1)/Omega|   = 1/2
Sha Bound      = 2^7

ANALYTIC INVARIANTS:

Omega+         = 2.641635646359620467 + 0.17262511029419027745e-3i
Omega-         = 1.1053611403840895732 + -0.74666426774988539324e-5i
L(1)           = 1.3208178259999785555

HECKE EIGENFORM:
a^2+a-4 = 0,
f(q) = q + 1*q^2 + a*q^3 + 1*q^4 + 1*q^5 + a*q^6 + -2*a*q^7 + 1*q^8 + (-a+1)*q^9 + 1*q^10 + -4*q^11 + a*q^12 + (-a+2)*q^13 + -2*a*q^14 + a*q^15 + 1*q^16 + 1*q^17 + (-a+1)*q^18 + a*q^19 + 1*q^20 + (2*a-8)*q^21 + -4*q^22 + 2*a*q^23 + a*q^24 + 1*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 + 1*q^32 + -4*a*q^33 + 1*q^34 + -2*a*q^35 + (-a+1)*q^36 + (2*a-2)*q^37 + a*q^38 + (3*a-4)*q^39 + 1*q^40 + (-4*a-6)*q^41 + (2*a-8)*q^42 + (2*a+4)*q^43 + -4*q^44 + (-a+1)*q^45 + 2*a*q^46 + (-a+4)*q^47 + a*q^48 + (-4*a+9)*q^49 + 1*q^50 + a*q^51 + (-a+2)*q^52 + (a+2)*q^53 + (-a-4)*q^54 + -4*q^55 + -2*a*q^56 + (-a+4)*q^57 + (3*a+2)*q^58 + (-3*a-8)*q^59 + a*q^60 + (a+10)*q^61 + (a-4)*q^62 + (-4*a+8)*q^63 + 1*q^64 + (-a+2)*q^65 + -4*a*q^66 + (2*a-4)*q^67 + 1*q^68 + (-2*a+8)*q^69 + -2*a*q^70 + (-3*a-12)*q^71 + (-a+1)*q^72 + (5*a+6)*q^73 + (2*a-2)*q^74 + a*q^75 + a*q^76 + 8*a*q^77 + (3*a-4)*q^78 + 1*q^80 + -7*q^81 + (-4*a-6)*q^82 + (4*a+4)*q^83 + (2*a-8)*q^84 + 1*q^85 + (2*a+4)*q^86 + (-a+12)*q^87 + -4*q^88 + (3*a-2)*q^89 + (-a+1)*q^90 + (-6*a+8)*q^91 + 2*a*q^92 + (-5*a+4)*q^93 + (-a+4)*q^94 + a*q^95 + a*q^96 + (3*a+6)*q^97 + (-4*a+9)*q^98 + (4*a-4)*q^99 + 1*q^100 + (8*a+6)*q^101 + a*q^102 + 8*q^103 + (-a+2)*q^104 + (2*a-8)*q^105 + (a+2)*q^106 + (-8*a-4)*q^107 + (-a-4)*q^108 + (a-6)*q^109 + -4*q^110 + (-4*a+8)*q^111 + -2*a*q^112 + (-5*a-10)*q^113 + (-a+4)*q^114 + 2*a*q^115 + (3*a+2)*q^116 + (-4*a+6)*q^117 + (-3*a-8)*q^118 + -2*a*q^119 + a*q^120 + 5*q^121 + (a+10)*q^122 + (-2*a-16)*q^123 + (a-4)*q^124 + 1*q^125 + (-4*a+8)*q^126 + (a+12)*q^127 + 1*q^128 + (2*a+8)*q^129 + (-a+2)*q^130 + (-2*a-4)*q^131 + -4*a*q^132 + (2*a-8)*q^133 + (2*a-4)*q^134 + (-a-4)*q^135 + 1*q^136 + 10*q^137 + (-2*a+8)*q^138 + (-8*a-4)*q^139 + -2*a*q^140 + (5*a-4)*q^141 + (-3*a-12)*q^142 + (4*a-8)*q^143 + (-a+1)*q^144 + (3*a+2)*q^145 + (5*a+6)*q^146 + (13*a-16)*q^147 + (2*a-2)*q^148 + (-2*a-2)*q^149 + a*q^150 + 6*a*q^151 + a*q^152 + (-a+1)*q^153 + 8*a*q^154 + (a-4)*q^155 + (3*a-4)*q^156 + (-8*a-2)*q^157 + (a+4)*q^159 + 1*q^160 + (4*a-16)*q^161 + -7*q^162 + (-4*a+4)*q^163 + (-4*a-6)*q^164 + -4*a*q^165 + (4*a+4)*q^166 + -2*a*q^167 + (2*a-8)*q^168 + (-5*a-5)*q^169 + 1*q^170 + (2*a-4)*q^171 + (2*a+4)*q^172 + -18*q^173 + (-a+12)*q^174 + -2*a*q^175 + -4*q^176 + (-5*a-12)*q^177 + (3*a-2)*q^178 + (-8*a-12)*q^179 + (-a+1)*q^180 + (-4*a+6)*q^181 + (-6*a+8)*q^182 + (9*a+4)*q^183 + 2*a*q^184 + (2*a-2)*q^185 + (-5*a+4)*q^186 + -4*q^187 + (-a+4)*q^188 + (6*a+8)*q^189 + a*q^190 + a*q^192 + (4*a-14)*q^193 + (3*a+6)*q^194 + (3*a-4)*q^195 + (-4*a+9)*q^196 + (-6*a-2)*q^197 + (4*a-4)*q^198 + (-a+12)*q^199 + 1*q^200 +  ...

-------------------------------------------------------
170G (old = 85A), dim = 1

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^5 + Z/2^5
= A(Z/2^2 + Z/2^2) + D(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2) + J(Z/2 + Z/2) + K(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
170H (old = 85B), dim = 2

CONGRUENCES:
Modular Degree = 2^8*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^3*7 + Z/2^3*7
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/7 + Z/7) + F(Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + J(Z/2 + Z/2) + K(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
170I (old = 85C), dim = 2

CONGRUENCES:
Modular Degree = 2^8*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3 + Z/2^3*3 + Z/2^3*3
= A(Z/2 + Z/2) + C(Z/3 + Z/3) + D(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + J(Z/2*3 + Z/2*3) + K(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
170J (old = 34A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/3 + Z/3) + F(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2*3 + Z/2*3) + K(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
170K (old = 17A), dim = 1

CONGRUENCES:
Modular Degree = 2^10
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^5 + Z/2^5
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/2^2 + Z/2^2) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(171)
Weight 2

-------------------------------------------------------
J_0(171), dim = 17

-------------------------------------------------------
171A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= B(Z/3 + Z/3) + E(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 1.7367612193651333775 + -0.11501855575368645184e-4i
Omega-         = 0.15781770693088102848e-4 + 1.2531621521815601896i
L(1)           = 0.43419030485080485201
w1             = 1.7367612193651333775 + -0.11501855575368645184e-4i
w2             = -0.15781770693088102848e-4 + -1.2531621521815601896i
c4             = 657.06620484949547905 + 0.31791941326214522185e-1i
c6             = -14556.178117778282609 + -1.1694441279602009218i
j              = 6827.567016361013245 + 0.31283588718864875028i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^4 + 2*q^5 + 3*q^8 + -2*q^10 + 6*q^13 + -1*q^16 + 6*q^17 + -1*q^19 + -2*q^20 + -4*q^23 + -1*q^25 + -6*q^26 + -2*q^29 + 8*q^31 + -5*q^32 + -6*q^34 + -10*q^37 + 1*q^38 + 6*q^40 + 2*q^41 + -4*q^43 + 4*q^46 + -12*q^47 + -7*q^49 + 1*q^50 + -6*q^52 + 6*q^53 + 2*q^58 + 12*q^59 + -2*q^61 + -8*q^62 + 7*q^64 + 12*q^65 + -4*q^67 + -6*q^68 + 10*q^73 + 10*q^74 + 1*q^76 + -2*q^80 + -2*q^82 + -16*q^83 + 12*q^85 + 4*q^86 + 2*q^89 + 4*q^92 + 12*q^94 + -2*q^95 + 10*q^97 + 7*q^98 + 1*q^100 + 10*q^101 + 8*q^103 + 18*q^104 + -6*q^106 + -4*q^107 + -10*q^109 + -6*q^113 + -8*q^115 + 2*q^116 + -12*q^118 + -11*q^121 + 2*q^122 + -8*q^124 + -12*q^125 + -8*q^127 + 3*q^128 + -12*q^130 + -8*q^131 + 4*q^134 + 18*q^136 + -18*q^137 + 4*q^139 + -4*q^145 + -10*q^146 + 10*q^148 + -6*q^149 + -8*q^151 + -3*q^152 + 16*q^155 + -2*q^157 + -10*q^160 + -4*q^163 + -2*q^164 + 16*q^166 + -24*q^167 + 23*q^169 + -12*q^170 + 4*q^172 + 22*q^173 + -2*q^178 + 4*q^179 + 14*q^181 + -12*q^184 + -20*q^185 + 12*q^188 + 2*q^190 + 12*q^191 + -14*q^193 + -10*q^194 + 7*q^196 + 2*q^197 + -8*q^199 + -3*q^200 +  ...

-------------------------------------------------------
171B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^5*3
Ker(ModPolar)  = Z/2^5*3 + Z/2^5*3
= A(Z/3 + Z/3) + C(Z/2^2 + Z/2^2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.0700946524229621235 + -0.13451082878730281224e-4i
Omega-         = 0.67374821435156257188e-4 + 0.84667443555080002578i
L(1)           = 2.1401893050150042721
w1             = -0.53508101362219863989 + -0.42333049223396064775i
w2             = -0.53501363880076348363 + 0.42334394331683937803i
c4             = -8496.2395875091580918 + -0.18949320421240989493i
c6             = -893681.56128348719273 + -431.33022339517695192i
j              = 750.57879414741677385 + -0.38141153347368695746i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 2*q^4 + -1*q^5 + 3*q^7 + -2*q^10 + 3*q^11 + -6*q^13 + 6*q^14 + -4*q^16 + -3*q^17 + -1*q^19 + -2*q^20 + 6*q^22 + -4*q^23 + -4*q^25 + -12*q^26 + 6*q^28 + 10*q^29 + 2*q^31 + -8*q^32 + -6*q^34 + -3*q^35 + 8*q^37 + -2*q^38 + 8*q^41 + -1*q^43 + 6*q^44 + -8*q^46 + -3*q^47 + 2*q^49 + -8*q^50 + -12*q^52 + 6*q^53 + -3*q^55 + 20*q^58 + 7*q^61 + 4*q^62 + -8*q^64 + 6*q^65 + 8*q^67 + -6*q^68 + -6*q^70 + -12*q^71 + -11*q^73 + 16*q^74 + -2*q^76 + 9*q^77 + 4*q^80 + 16*q^82 + -4*q^83 + 3*q^85 + -2*q^86 + -10*q^89 + -18*q^91 + -8*q^92 + -6*q^94 + 1*q^95 + -2*q^97 + 4*q^98 + -8*q^100 + -2*q^101 + 14*q^103 + 12*q^106 + 2*q^107 + 20*q^109 + -6*q^110 + -12*q^112 + 6*q^113 + 4*q^115 + 20*q^116 + -9*q^119 + -2*q^121 + 14*q^122 + 4*q^124 + 9*q^125 + -2*q^127 + 12*q^130 + 13*q^131 + -3*q^133 + 16*q^134 + -3*q^137 + -5*q^139 + -6*q^140 + -24*q^142 + -18*q^143 + -10*q^145 + -22*q^146 + 16*q^148 + -15*q^149 + -8*q^151 + 18*q^154 + -2*q^155 + -2*q^157 + 8*q^160 + -12*q^161 + -16*q^163 + 16*q^164 + -8*q^166 + -18*q^167 + 23*q^169 + 6*q^170 + -2*q^172 + -14*q^173 + -12*q^175 + -12*q^176 + -20*q^178 + 10*q^179 + 2*q^181 + -36*q^182 + -8*q^185 + -9*q^187 + -6*q^188 + 2*q^190 + 3*q^191 + 4*q^193 + -4*q^194 + 4*q^196 + 2*q^197 + -5*q^199 +  ...

-------------------------------------------------------
171C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^5 + Z/2^5
= B(Z/2^2 + Z/2^2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.1075953207506858718 + -0.27335345537176428628e-4i
Omega-         = 0.21725700156050588979e-3 + 3.207269192222631847i
L(1)           = 2.2151906421760054311
w1             = 0.55368903187456268295 + -1.6036482637840845117i
w2             = -1.1075953207506858718 + 0.27335345537176428628e-4i
c4             = 1007.8011939967187199 + 0.88608776644811917835e-1i
c6             = 35200.783753977260813 + 5.9438904914460597103i
j              = -8207.3647864067312201 + 3.4894112724341239413i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 2*q^4 + 3*q^5 + -5*q^7 + 6*q^10 + -1*q^11 + 2*q^13 + -10*q^14 + -4*q^16 + 1*q^17 + -1*q^19 + 6*q^20 + -2*q^22 + 4*q^23 + 4*q^25 + 4*q^26 + -10*q^28 + 2*q^29 + -6*q^31 + -8*q^32 + 2*q^34 + -15*q^35 + -2*q^38 + -1*q^43 + -2*q^44 + 8*q^46 + 9*q^47 + 18*q^49 + 8*q^50 + 4*q^52 + -10*q^53 + -3*q^55 + 4*q^58 + 8*q^59 + -1*q^61 + -12*q^62 + -8*q^64 + 6*q^65 + 8*q^67 + 2*q^68 + -30*q^70 + 12*q^71 + -11*q^73 + -2*q^76 + 5*q^77 + 16*q^79 + -12*q^80 + -12*q^83 + 3*q^85 + -2*q^86 + 6*q^89 + -10*q^91 + 8*q^92 + 18*q^94 + -3*q^95 + -10*q^97 + 36*q^98 + 8*q^100 + -2*q^101 + -2*q^103 + -20*q^106 + -6*q^107 + 4*q^109 + -6*q^110 + 20*q^112 + -2*q^113 + 12*q^115 + 4*q^116 + 16*q^118 + -5*q^119 + -10*q^121 + -2*q^122 + -12*q^124 + -3*q^125 + -2*q^127 + 12*q^130 + -7*q^131 + 5*q^133 + 16*q^134 + 9*q^137 + -13*q^139 + -30*q^140 + 24*q^142 + -2*q^143 + 6*q^145 + -22*q^146 + 21*q^149 + 10*q^154 + -18*q^155 + -18*q^157 + 32*q^158 + -24*q^160 + -20*q^161 + -24*q^166 + -10*q^167 + -9*q^169 + 6*q^170 + -2*q^172 + -6*q^173 + -20*q^175 + 4*q^176 + 12*q^178 + 18*q^179 + -14*q^181 + -20*q^182 + -1*q^187 + 18*q^188 + -6*q^190 + -9*q^191 + 4*q^193 + -20*q^194 + 36*q^196 + 2*q^197 + -21*q^199 +  ...

-------------------------------------------------------
171D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 3
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.3827317587418670396 + -0.83700643303308520342e-4i
Omega-         = 0.40299111727322814641e-4 + 2.3551110887443081198i
L(1)           =
w1             = 1.1913457298150698584 + -1.1775973946938057142i
w2             = -1.1913860289267971812 + -1.1775136940505024057i
c4             = -288.02607444772925759 + -0.30636224098443905958e-1i
c6             = -216.1574167229364571 + 0.29988735374884647634i
j              = 1724.6276009576610219 + 0.10413230079976938685e-1i

HECKE EIGENFORM:
f(q) = q + -2*q^4 + -3*q^5 + -1*q^7 + -3*q^11 + -4*q^13 + 4*q^16 + 3*q^17 + 1*q^19 + 6*q^20 + 4*q^25 + 2*q^28 + -6*q^29 + -4*q^31 + 3*q^35 + 2*q^37 + 6*q^41 + -1*q^43 + 6*q^44 + 3*q^47 + -6*q^49 + 8*q^52 + -12*q^53 + 9*q^55 + 6*q^59 + -1*q^61 + -8*q^64 + 12*q^65 + -4*q^67 + -6*q^68 + -6*q^71 + -7*q^73 + -2*q^76 + 3*q^77 + 8*q^79 + -12*q^80 + -12*q^83 + -9*q^85 + -12*q^89 + 4*q^91 + -3*q^95 + 8*q^97 + -8*q^100 + -6*q^101 + 14*q^103 + 18*q^107 + -16*q^109 + -4*q^112 + -6*q^113 + 12*q^116 + -3*q^119 + -2*q^121 + 8*q^124 + 3*q^125 + 2*q^127 + 15*q^131 + -1*q^133 + 3*q^137 + -13*q^139 + -6*q^140 + 12*q^143 + 18*q^145 + -4*q^148 + -21*q^149 + -10*q^151 + 12*q^155 + 14*q^157 + 20*q^163 + -12*q^164 + 18*q^167 + 3*q^169 + 2*q^172 + 18*q^173 + -4*q^175 + -12*q^176 + 18*q^179 + 2*q^181 + -6*q^185 + -9*q^187 + -6*q^188 + -3*q^191 + -4*q^193 + 12*q^196 + -18*q^197 + 11*q^199 +  ...

-------------------------------------------------------
171E (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^6*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/2*3 + Z/2*3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^4*3^3*11^2
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2*3
Torsion Bound  = 2^2*3
|L(1)/Omega|   = 1/3
Sha Bound      = 2^4*3

ANALYTIC INVARIANTS:

Omega+         = 6.0569644503352137428 + 0.47434839981578458208e-4i
Omega-         = 6.0553648120493168878 + -0.14843986648065623271e-2i
L(1)           = 2.0189881501736518774

HECKE EIGENFORM:
a^4-9*a^2+12 = 0,
f(q) = q + a*q^2 + (a^2-2)*q^4 + (-1/2*a^3+5/2*a)*q^5 + (-a^2+5)*q^7 + (a^3-4*a)*q^8 + (-2*a^2+6)*q^10 + (1/2*a^3-9/2*a)*q^11 + 2*q^13 + (-a^3+5*a)*q^14 + (3*a^2-8)*q^16 + (-1/2*a^3+5/2*a)*q^17 + 1*q^19 + (-a^3+a)*q^20 + -6*q^22 + (a^3-7*a)*q^23 + (a^2-2)*q^25 + 2*a*q^26 + (-2*a^2+2)*q^28 + (a^3-7*a)*q^29 + (2*a^2-10)*q^31 + a^3*q^32 + (-2*a^2+6)*q^34 + (-1/2*a^3+13/2*a)*q^35 + (2*a^2-4)*q^37 + a*q^38 + -4*a^2*q^40 + -2*a*q^41 + (-3*a^2+11)*q^43 + (-a^3+3*a)*q^44 + (2*a^2-12)*q^46 + (-3/2*a^3+19/2*a)*q^47 + (-a^2+6)*q^49 + (a^3-2*a)*q^50 + (2*a^2-4)*q^52 + (-a^3+11*a)*q^53 + (3*a^2-15)*q^55 + -8*a*q^56 + (2*a^2-12)*q^58 + 4*a*q^59 + (-3*a^2+17)*q^61 + (2*a^3-10*a)*q^62 + (3*a^2+4)*q^64 + (-a^3+5*a)*q^65 + -4*q^67 + (-a^3+a)*q^68 + (2*a^2+6)*q^70 + (2*a^3-14*a)*q^71 + (-3*a^2+17)*q^73 + (2*a^3-4*a)*q^74 + (a^2-2)*q^76 + (5/2*a^3-33/2*a)*q^77 + -4*q^79 + (-2*a^3-2*a)*q^80 + -2*a^2*q^82 + (-a^3+3*a)*q^83 + (a^2+3)*q^85 + (-3*a^3+11*a)*q^86 + (-6*a^2+24)*q^88 + (-a^3+11*a)*q^89 + (-2*a^2+10)*q^91 + 2*a*q^92 + (-4*a^2+18)*q^94 + (-1/2*a^3+5/2*a)*q^95 + (4*a^2-22)*q^97 + (-a^3+6*a)*q^98 + (5*a^2-8)*q^100 + (2*a^3-10*a)*q^101 + (2*a^2-22)*q^103 + (2*a^3-8*a)*q^104 + (2*a^2+12)*q^106 + (-a^3+9*a)*q^107 + (-2*a^2+20)*q^109 + (3*a^3-15*a)*q^110 + (-4*a^2-4)*q^112 + (-a^3+3*a)*q^113 + (2*a^2-18)*q^115 + 2*a*q^116 + 4*a^2*q^118 + (-1/2*a^3+13/2*a)*q^119 + (-3*a^2+16)*q^121 + (-3*a^3+17*a)*q^122 + (4*a^2-4)*q^124 + (3/2*a^3-23/2*a)*q^125 + (-2*a^2+2)*q^127 + (a^3+4*a)*q^128 + (-4*a^2+12)*q^130 + (-3/2*a^3+11/2*a)*q^131 + (-a^2+5)*q^133 + -4*a*q^134 + -4*a^2*q^136 + (-3/2*a^3+31/2*a)*q^137 + (3*a^2-19)*q^139 + (3*a^3-7*a)*q^140 + (4*a^2-24)*q^142 + (a^3-9*a)*q^143 + (2*a^2-18)*q^145 + (-3*a^3+17*a)*q^146 + (10*a^2-16)*q^148 + (3/2*a^3-7/2*a)*q^149 + -4*q^151 + (a^3-4*a)*q^152 + (6*a^2-30)*q^154 + (a^3-13*a)*q^155 + 2*q^157 + -4*a*q^158 + (-12*a^2+24)*q^160 + (3*a^3-23*a)*q^161 + (-4*a^2+8)*q^163 + (-2*a^3+4*a)*q^164 + (-6*a^2+12)*q^166 + (-a^3+5*a)*q^167 + -9*q^169 + (a^3+3*a)*q^170 + (-10*a^2+14)*q^172 + (-a^3+7*a)*q^173 + (-2*a^2+2)*q^175 + (-4*a^3+18*a)*q^176 + (2*a^2+12)*q^178 + (a^3-9*a)*q^179 + (4*a^2-10)*q^181 + (-2*a^3+10*a)*q^182 + (-2*a^2+24)*q^184 + (-2*a^3+2*a)*q^185 + (3*a^2-15)*q^187 + (-a^3-a)*q^188 + (-2*a^2+6)*q^190 + (-5/2*a^3+21/2*a)*q^191 + (6*a^2-28)*q^193 + (4*a^3-22*a)*q^194 + -a^2*q^196 + (-2*a^3+6*a)*q^197 + (-3*a^2+23)*q^199 + (3*a^3-4*a)*q^200 +  ...

-------------------------------------------------------
171F (old = 57A), dim = 1

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^5 + Z/2^5
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2^2 + Z/2^2) + I(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
171G (old = 57B), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/3 + Z/3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + E(Z/2 + Z/2) + H(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
171H (old = 57C), dim = 1

CONGRUENCES:
Modular Degree = 2^7*3^2
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^5*3 + Z/2^5*3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2^2 + Z/2^2) + G(Z/3 + Z/3 + Z/3 + Z/3) + I(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
171I (old = 19A), dim = 1

CONGRUENCES:
Modular Degree = 2^5*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^3*3 + Z/2^3*3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2*3 + Z/2*3) + F(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(172)
Weight 2

-------------------------------------------------------
J_0(172), dim = 20

-------------------------------------------------------
172A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= B(Z/2 + Z/2) + C(Z/3 + Z/3) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 3
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 4.0102150369226148255 + 0.13329186854749945345e-3i
Omega-         = 0.9049148773697795928e-4 + -1.2462300738334742669i
L(1)           =
w1             = -2.0050622727174389238 + -0.62318168285101088317i
w2             = -0.9049148773697795928e-4 + 1.2462300738334742669i
c4             = 639.83053804891870359 + -0.18834844230418770397i
c6             = -16760.877103024671594 + 7.1685157793081584894i
j              = -23833.413519517588365 + 9.7765297655503172194i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -4*q^7 + 1*q^9 + -3*q^11 + -1*q^13 + -3*q^17 + 2*q^19 + 8*q^21 + -3*q^23 + -5*q^25 + 4*q^27 + 6*q^29 + 5*q^31 + 6*q^33 + 8*q^37 + 2*q^39 + -3*q^41 + 1*q^43 + -12*q^47 + 9*q^49 + 6*q^51 + -9*q^53 + -4*q^57 + -12*q^59 + -10*q^61 + -4*q^63 + 11*q^67 + 6*q^69 + 6*q^71 + -10*q^73 + 10*q^75 + 12*q^77 + 8*q^79 + -11*q^81 + -15*q^83 + -12*q^87 + 4*q^91 + -10*q^93 + -1*q^97 + -3*q^99 + 3*q^101 + -13*q^103 + 12*q^107 + 11*q^109 + -16*q^111 + -12*q^113 + -1*q^117 + 12*q^119 + -2*q^121 + 6*q^123 + 11*q^127 + -2*q^129 + -8*q^133 + -18*q^137 + 5*q^139 + 24*q^141 + 3*q^143 + -18*q^147 + 12*q^149 + -16*q^151 + -3*q^153 + 14*q^157 + 18*q^159 + 12*q^161 + 14*q^163 + 21*q^167 + -12*q^169 + 2*q^171 + 6*q^173 + 20*q^175 + 24*q^177 + -24*q^179 + -22*q^181 + 20*q^183 + 9*q^187 + -16*q^189 + 24*q^191 + 11*q^193 + -6*q^197 + 2*q^199 +  ...

-------------------------------------------------------
172B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^3*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + D(Z/3 + Z/3 + Z/3 + Z/3) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.2088996396800871513 + -0.97027625276566288058e-4i
Omega-         = 7.1829995560039993717 + -0.10287699543459262511e-2i
L(1)           = 2.4177992871477190604

HECKE EIGENFORM:
a^2-4*a+2 = 0,
f(q) = q + a*q^3 + (-a+2)*q^5 + (-a+2)*q^7 + (4*a-5)*q^9 + (-2*a+5)*q^11 + (-2*a+1)*q^13 + (-2*a+2)*q^15 + (2*a-3)*q^17 + (-2*a+2)*q^19 + (-2*a+2)*q^21 + 3*q^23 + -3*q^25 + (8*a-8)*q^27 + (3*a-8)*q^29 + (4*a-9)*q^31 + (-3*a+4)*q^33 + 2*q^35 + (2*a-8)*q^37 + (-7*a+4)*q^39 + (-6*a+11)*q^41 + -1*q^43 + (-3*a-2)*q^45 + (4*a-2)*q^47 + -5*q^49 + (5*a-4)*q^51 + (-2*a-1)*q^53 + (-a+6)*q^55 + (-6*a+4)*q^57 + (2*a-2)*q^59 + (7*a-12)*q^61 + (-3*a-2)*q^63 + (3*a-2)*q^65 + (-6*a+11)*q^67 + 3*a*q^69 + (-2*a+14)*q^71 + (-a+4)*q^73 + -3*a*q^75 + (-a+6)*q^77 + (-2*a+2)*q^79 + (12*a-1)*q^81 + 7*q^83 + (-a-2)*q^85 + (4*a-6)*q^87 + (-3*a+10)*q^89 + (3*a-2)*q^91 + (7*a-8)*q^93 + 2*a*q^95 + (-2*a+15)*q^97 + (-2*a-9)*q^99 + (-2*a-1)*q^101 + (2*a-9)*q^103 + 2*a*q^105 + 10*q^107 + 5*q^109 + -4*q^111 + (-6*a+20)*q^113 + (-3*a+6)*q^115 + (-18*a+11)*q^117 + (-a-2)*q^119 + (-4*a+6)*q^121 + (-13*a+12)*q^123 + (8*a-16)*q^125 + (10*a-25)*q^127 + -a*q^129 + (8*a-12)*q^131 + 2*a*q^133 + -8*a*q^135 + (-2*a+10)*q^137 + (10*a-29)*q^139 + (14*a-8)*q^141 + (4*a-3)*q^143 + (2*a-10)*q^145 + -5*a*q^147 + (-2*a-16)*q^149 + (3*a-6)*q^151 + (10*a-1)*q^153 + (a-10)*q^155 + (-8*a+14)*q^157 + (-9*a+4)*q^159 + (-3*a+6)*q^161 + (-9*a+24)*q^163 + (2*a+2)*q^165 + (-4*a+23)*q^167 + (12*a-20)*q^169 + (-14*a+6)*q^171 + (-4*a+2)*q^173 + (3*a-6)*q^175 + (6*a-4)*q^177 + (9*a-26)*q^179 + (-12*a+24)*q^181 + (16*a-14)*q^183 + (4*a-12)*q^185 + -7*q^187 + -8*a*q^189 + -2*a*q^191 + (-4*a+15)*q^193 + (10*a-6)*q^195 + (14*a-36)*q^197 + (-8*a+22)*q^199 +  ...

-------------------------------------------------------
172C (old = 86A), dim = 2

CONGRUENCES:
Modular Degree = 2^4*3*7^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*7 + Z/2*7 + Z/2*3*7 + Z/2*3*7
= A(Z/3 + Z/3) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + F(Z/7 + Z/7 + Z/7 + Z/7)

-------------------------------------------------------
172D (old = 86B), dim = 2

CONGRUENCES:
Modular Degree = 2^4*3^2*5^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3*5 + Z/2*3*5 + Z/2*3*5 + Z/2*3*5
= B(Z/3 + Z/3 + Z/3 + Z/3) + C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + E(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
172E (old = 43A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*5^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*5 + Z/2*5 + Z/2^2*5 + Z/2^2*5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/5 + Z/5 + Z/5 + Z/5) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
172F (old = 43B), dim = 2

CONGRUENCES:
Modular Degree = 2^5*7^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*7 + Z/2*7 + Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/7 + Z/7 + Z/7 + Z/7) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(173)
Weight 2

-------------------------------------------------------
J_0(173), dim = 14

-------------------------------------------------------
173A (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 5^2*29
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 62.343728407446868396 + -0.33648114664913953343e-2i
Omega-         = 43.894117048976929683 + -0.1772452827421550059e-2i
L(1)           =

HECKE EIGENFORM:
a^4+a^3-3*a^2-a+1 = 0,
f(q) = 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 + (a^3+4*a^2-2*a-2)*q^38 + (2*a^3+6*a^2-2*a-5)*q^39 + (-2*a^3-2*a^2+6*a+1)*q^40 + (a^3-2*a^2-10*a+5)*q^41 + (2*a^3+3*a^2+a)*q^42 + (3*a^3+2*a^2-7*a-6)*q^43 + (4*a^3+4*a^2-10*a-3)*q^44 + (-a^3-2*a^2+5)*q^45 + (-a^3+a^2-3)*q^46 + (-a^2-a)*q^47 + (2*a^3+6*a^2-a-3)*q^48 + (-5*a^3-6*a^2+14*a+5)*q^49 + (-2*a^2-3*a+1)*q^50 + (-5*a^3-9*a^2+2*a+5)*q^51 + (7*a^3+6*a^2-17*a-5)*q^52 + (-4*a^3-6*a^2+10*a+7)*q^53 + (-3*a^3-8*a^2+4)*q^54 + (4*a^3+4*a^2-10*a-3)*q^55 + (-2*a^3-a^2+8*a+4)*q^56 + (-4*a^3-5*a^2+3*a+3)*q^57 + (-3*a^2+a+2)*q^58 + (-4*a^3-6*a^2+12*a+4)*q^59 + (2*a^3-3*a-1)*q^60 + (3*a^3+7*a^2-9*a-10)*q^61 + (2*a^3+5*a^2-a-2)*q^62 + (-6*a^3-13*a^2+6*a+11)*q^63 + (4*a^3+4*a^2-5*a-2)*q^64 + (7*a^3+6*a^2-17*a-5)*q^65 + (4*a^3+8*a^2-a-3)*q^66 + (-a^3+3*a^2+2*a-15)*q^67 + (-4*a^3-6*a^2+11*a+5)*q^68 + (-a^3+2*a^2+4*a+2)*q^69 + (-2*a^3-a^2+4*a+2)*q^70 + (7*a^3+7*a^2-14*a+1)*q^71 + (-7*a^3-11*a^2+10*a+3)*q^72 + (-9*a^3-9*a^2+19*a+5)*q^73 + (-4*a^3-a^2+4*a-3)*q^74 + (2*a^3+5*a^2+2*a-1)*q^75 + (-a^3-5*a^2+3*a+7)*q^76 + (8*a^3+13*a^2-14*a-12)*q^77 + (4*a^3+4*a^2-3*a-2)*q^78 + (-5*a^3+14*a-7)*q^79 + (2*a^3+2*a^2-3*a-4)*q^80 + (5*a^3+5*a^2-4*a+5)*q^81 + (-3*a^3-7*a^2+6*a-1)*q^82 + (4*a^3+12*a^2-4*a-17)*q^83 + (a^3+3*a^2-4*a-4)*q^84 + (-4*a^3-6*a^2+11*a+5)*q^85 + (-a^3+2*a^2-3*a-3)*q^86 + (3*a^3+2*a^2-3*a-2)*q^87 + (2*a^3+8*a^2+3*a-10)*q^88 + (a^3+3*a+4)*q^89 + (-a^3-3*a^2+4*a+1)*q^90 + (11*a^3+17*a^2-24*a-19)*q^91 + (-4*a^3-7*a^2+12*a+7)*q^92 + (-5*a^3-10*a^2+a+4)*q^93 + (-a^3-a^2)*q^94 + (-a^3-5*a^2+3*a+7)*q^95 + (2*a^3-a^2-3*a-2)*q^96 + (-a^2-10*a+1)*q^97 + (-a^3-a^2+5)*q^98 + (a^3-7*a^2-18*a+1)*q^99 + (-a^2-a+4)*q^100 + (-6*a^3-7*a^2+21*a+10)*q^101 + (-4*a^3-13*a^2+5)*q^102 + (-4*a^3+a^2+15*a-4)*q^103 + (a^3+8*a^2+4*a-15)*q^104 + (a^3+3*a^2-4*a-4)*q^105 + (-2*a^3-2*a^2+3*a+4)*q^106 + (-7*a^3-2*a^2+18*a-3)*q^107 + (3*a^3+5*a^2-7*a-5)*q^108 + (6*a^3+4*a^2-10*a-1)*q^109 + (2*a^2+a-4)*q^110 + (a^3+9*a^2+3*a-1)*q^111 + (5*a^3+10*a^2-8*a-10)*q^112 + (6*a^3+7*a^2-19*a-6)*q^113 + (-a^3-9*a^2-a+4)*q^114 + (-4*a^3-7*a^2+12*a+7)*q^115 + (a^3+5*a^2-4*a-6)*q^116 + (8*a^3+2*a^2-29*a-3)*q^117 + (-2*a^3+4)*q^118 + (-11*a^3-17*a^2+18*a+16)*q^119 + (a^2-a-2)*q^120 + (2*a^3+2*a^2+a+1)*q^121 + (4*a^3-7*a-3)*q^122 + (7*a^3+10*a^2-2*a-2)*q^123 + (-a^3-3*a^2+2*a+4)*q^124 + (-6*a^2-a+14)*q^125 + (-7*a^3-12*a^2+5*a+6)*q^126 + (-8*a^3-10*a^2+15*a+8)*q^127 + (8*a^3+11*a^2-18*a-6)*q^128 + (-2*a^3+4*a^2+7*a+2)*q^129 + (-a^3+4*a^2+2*a-7)*q^130 + (-7*a^3-10*a^2+10*a+7)*q^131 + (-2*a^3-3*a^2+3*a+4)*q^132 + (-8*a^3-12*a^2+13*a+14)*q^133 + (4*a^3-a^2-16*a+1)*q^134 + (3*a^3+5*a^2-7*a-5)*q^135 + (-4*a^3-11*a^2-a+12)*q^136 + (8*a^2+6*a-14)*q^137 + (3*a^3+a^2+a+1)*q^138 + (10*a^3+3*a^2-34*a)*q^139 + (5*a^3+6*a^2-10*a-10)*q^140 + (a^3+4*a^2+a-1)*q^141 + (7*a^2+8*a-7)*q^142 + (-a^3-6*a^2+2*a+23)*q^143 + (-2*a^3-7*a^2-4*a-3)*q^144 + (a^3+5*a^2-4*a-6)*q^145 + (-8*a^2-4*a+9)*q^146 + (a^3+4*a^2-4*a-6)*q^147 + (-3*a^3-6*a^2+13*a+2)*q^148 + (2*a^3+a^2-3*a+3)*q^149 + (3*a^3+8*a^2+a-2)*q^150 + (4*a^3+5*a^2-21*a-8)*q^151 + (-6*a^3-8*a^2+10*a+5)*q^152 + (a^3+10*a^2+20*a)*q^153 + (5*a^3+10*a^2-4*a-8)*q^154 + (-a^3-3*a^2+2*a+4)*q^155 + (-4*a^3-3*a^2+6*a+6)*q^156 + (2*a^3+2*a^2-6*a+1)*q^157 + (5*a^3-a^2-12*a+5)*q^158 + (2*a^3+5*a^2-5*a-6)*q^159 + (4*a^3+7*a^2-14*a-4)*q^160 + (-9*a^3-10*a^2+23*a+17)*q^161 + (11*a^2+10*a-5)*q^162 + (2*a^3+5*a^2-4*a-15)*q^163 + (-6*a^3+a^2+16*a-7)*q^164 + (-2*a^3-3*a^2+3*a+4)*q^165 + (8*a^3+8*a^2-13*a-4)*q^166 + (-4*a^3+3*a^2+20*a-5)*q^167 + (-2*a^3-7*a^2-5*a-1)*q^168 + (-5*a^3-15*a^2+5*a+27)*q^169 + (-2*a^3-a^2+a+4)*q^170 + (3*a^3+4*a^2+4*a+7)*q^171 + (-3*a^3-10*a^2+10*a+13)*q^172 + -1*q^173 + (-a^3+6*a^2+a-3)*q^174 + (a^2+5*a+5)*q^175 + (-2*a^3+a^2+12*a+4)*q^176 + (6*a^2-2*a-6)*q^177 + (-a^3+6*a^2+5*a-1)*q^178 + (3*a^2+a-5)*q^179 + (5*a^2-9)*q^180 + (-a^3-9*a^2-4*a+16)*q^181 + (6*a^3+9*a^2-8*a-11)*q^182 + (-5*a^2+6*a+7)*q^183 + (-a^3-2*a^2+3*a+10)*q^184 + (-3*a^3-6*a^2+13*a+2)*q^185 + (-5*a^3-14*a^2-a+5)*q^186 + (-2*a^3-3*a^2-5*a-14)*q^187 + (-a^2+a+1)*q^188 + (12*a^3+22*a^2-13*a-16)*q^189 + (-4*a^3+6*a+1)*q^190 + (4*a^3+5*a^2-7*a+10)*q^191 + (-7*a^3-9*a^2+2*a+4)*q^192 + (9*a^3+11*a^2-10*a-5)*q^193 + (-a^3-10*a^2+a)*q^194 + (-4*a^3-3*a^2+6*a+6)*q^195 + (10*a^3+9*a^2-24*a-9)*q^196 + (-4*a^3-22*a^2-5*a+31)*q^197 + (-8*a^3-15*a^2+2*a-1)*q^198 + (3*a^3-5*a^2-11*a+2)*q^199 + (-a^3+3*a^2+10*a-2)*q^200 +  ...

-------------------------------------------------------
173B (new) , dim = 10

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^6*7*5608385124289
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 43
Torsion Bound  = 43
|L(1)/Omega|   = 2^4/43
Sha Bound      = 2^4*43

ANALYTIC INVARIANTS:

Omega+         = 41.388706702012483944 + 0.4545396090001338448e-2i
Omega-         = 219.26162348516627288 + 0.72584048090206101061e-1i
L(1)           = 15.400449098271639903

HECKE EIGENFORM:
a^10-a^9-16*a^8+16*a^7+85*a^6-80*a^5-175*a^4+136*a^3+138*a^2-71*a-25 = 0,
f(q) = 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 + (13/58*a^9-99/116*a^8-331/116*a^7+1429/116*a^6+887/116*a^5-1521/29*a^4+1251/116*a^3+6949/116*a^2-2441/116*a-1175/116)*q^38 + (-9/116*a^9-9/29*a^8+49/29*a^7+273/58*a^6-1515/116*a^5-2621/116*a^4+2355/58*a^3+2057/58*a^2-2197/58*a-1495/116)*q^39 + (-39/58*a^9+38/29*a^8+270/29*a^7-557/29*a^6-2041/58*a^5+4747/58*a^4+606/29*a^3-2638/29*a^2+504/29*a+675/58)*q^40 + (41/58*a^9-165/116*a^8-1093/116*a^7+2459/116*a^6+3837/116*a^5-2709/29*a^4-1279/116*a^3+13167/116*a^2-2947/116*a-2693/116)*q^41 + (-97/116*a^9+67/58*a^8+705/58*a^7-496/29*a^6-6101/116*a^5+8459/116*a^4+1840/29*a^3-2276/29*a^2-328/29*a+675/116)*q^42 + (25/29*a^9-16/29*a^8-364/29*a^7+233/29*a^6+1608/29*a^5-891/29*a^4-2131/29*a^3+488/29*a^2+612/29*a+386/29)*q^43 + (7/116*a^9-1/116*a^8-117/116*a^7-9/116*a^6+333/58*a^5+73/116*a^4-1469/116*a^3+161/116*a^2+1133/116*a-100/29)*q^44 + (-35/58*a^9+63/58*a^8+469/58*a^7-941/58*a^6-824/29*a^5+4159/58*a^4+385/58*a^3-5097/58*a^2+1933/58*a+478/29)*q^45 + (25/58*a^9-8/29*a^8-182/29*a^7+131/29*a^6+1637/58*a^5-1181/58*a^4-1167/29*a^3+563/29*a^2+422/29*a+125/58)*q^46 + (-14/29*a^9+31/29*a^8+205/29*a^7-446/29*a^6-897/29*a^5+1884/29*a^4+1111/29*a^3-2178/29*a^2-207/29*a+365/29)*q^47 + (19/116*a^9+9/58*a^8-165/58*a^7-61/29*a^6+1903/116*a^5+1035/116*a^4-1060/29*a^3-333/29*a^2+774/29*a-137/116)*q^48 + (41/116*a^9-63/58*a^8-133/29*a^7+456/29*a^6+1643/116*a^5-7651/116*a^4+170/29*a^3+3937/58*a^2-691/29*a+147/116)*q^49 + (1/29*a^9+4/29*a^8-25/29*a^7-80/29*a^6+178/29*a^5+462/29*a^4-417/29*a^3-760/29*a^2+282/29*a+150/29)*q^50 + (-16/29*a^9+23/29*a^8+226/29*a^7-344/29*a^6-934/29*a^5+1511/29*a^4+1017/29*a^3-1760/29*a^2-75/29*a+152/29)*q^51 + (5/116*a^9-9/116*a^8-67/116*a^7+93/116*a^6+92/29*a^5-213/116*a^4-1157/116*a^3-1/116*a^2+1207/116*a+85/58)*q^52 + (33/58*a^9-13/58*a^8-477/58*a^7+231/58*a^6+1052/29*a^5-1139/58*a^4-2799/58*a^3+1571/58*a^2+635/58*a-367/29)*q^53 + (1/29*a^9+161/116*a^8-187/116*a^7-2263/116*a^6+2249/116*a^5+4781/58*a^4-8889/116*a^3-11827/116*a^2+8407/116*a+2775/116)*q^54 + (-3/58*a^9+75/58*a^8+17/58*a^7-1065/58*a^6+139/29*a^5+4501/58*a^4-1939/58*a^3-5347/58*a^2+2083/58*a+500/29)*q^55 + (109/116*a^9-115/116*a^8-1565/116*a^7+1691/116*a^6+3379/58*a^5-7033/116*a^4-8391/116*a^3+6625/116*a^2+1709/116*a+100/29)*q^56 + (-31/58*a^9+129/116*a^8+825/116*a^7-1855/116*a^6-2829/116*a^5+1916/29*a^4+479/116*a^3-7719/116*a^2+3019/116*a+357/116)*q^57 + (-53/116*a^9+5/29*a^8+179/29*a^7-171/58*a^6-2735/116*a^5+1527/116*a^4+1147/58*a^3-653/58*a^2+125/58*a+25/116)*q^58 + (-9/116*a^9-9/29*a^8+49/29*a^7+273/58*a^6-1399/116*a^5-2621/116*a^4+1775/58*a^3+2173/58*a^2-1037/58*a-1959/116)*q^59 + (8/29*a^9-23/58*a^8-197/58*a^7+373/58*a^6+557/58*a^5-857/29*a^4+375/58*a^3+1963/58*a^2-1259/58*a-239/58)*q^60 + (3/29*a^9-17/29*a^8-17/29*a^7+253/29*a^6-162/29*a^5-1108/29*a^4+1069/29*a^3+1345/29*a^2-1039/29*a-333/29)*q^61 + (-1/58*a^9-31/29*a^8+27/29*a^7+446/29*a^6-671/58*a^5-3797/58*a^4+1354/29*a^3+2265/29*a^2-1243/29*a-875/58)*q^62 + (8/29*a^9-81/58*a^8-139/58*a^7+1185/58*a^6-371/58*a^5-2568/29*a^4+4667/58*a^3+6197/58*a^2-6131/58*a-1341/58)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (-a^9+a^8+14*a^7-15*a^6-57*a^5+64*a^4+59*a^3-67*a^2-3*a+5)*q^65 + (-23/116*a^9+53/116*a^8+285/116*a^7-799/116*a^6-423/58*a^5+3671/116*a^4-327/116*a^3-4937/116*a^2+1431/116*a+225/29)*q^66 + (-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^3-888/29*a^2+63/29*a+697/58)*q^67 + (1/58*a^9-25/58*a^8-25/58*a^7+297/58*a^6+60/29*a^5-1017/58*a^4-69/58*a^3+1009/58*a^2-95/58*a-12/29)*q^68 + (7/58*a^9+57/58*a^8-175/58*a^7-821/58*a^6+768/29*a^5+3611/58*a^4-5239/58*a^3-4943/58*a^2+5019/58*a+844/29)*q^69 + (7/29*a^9-30/29*a^8-88/29*a^7+426/29*a^6+231/29*a^5-1812/29*a^4+387/29*a^3+2220/29*a^2-897/29*a-400/29)*q^70 + (3/4*a^8-1/4*a^7-43/4*a^6+17/4*a^5+93/2*a^4-75/4*a^3-225/4*a^2+59/4*a+19/4)*q^71 + (39/116*a^9-163/116*a^8-395/116*a^7+2361/116*a^6+10/29*a^5-10199/116*a^4+6821/116*a^3+12555/116*a^2-9273/116*a-1425/58)*q^72 + (-33/58*a^9+171/116*a^8+867/116*a^7-2521/116*a^6-2903/116*a^5+2730/29*a^4+233/116*a^3-12741/116*a^2+3109/116*a+2135/116)*q^73 + (-33/116*a^9-37/58*a^8+253/58*a^7+254/29*a^6-2597/116*a^5-4313/116*a^4+1287/29*a^3+1485/29*a^2-804/29*a-1325/116)*q^74 + (19/116*a^9-49/58*a^8-107/58*a^7+345/29*a^6+163/116*a^5-5693/116*a^4+883/29*a^3+1581/29*a^2-1459/29*a-717/116)*q^75 + (21/116*a^9-61/116*a^8-293/116*a^7+843/116*a^6+282/29*a^5-3493/116*a^4-869/116*a^3+4253/116*a^2-255/116*a-571/58)*q^76 + (75/116*a^9-77/116*a^8-1063/116*a^7+1105/116*a^6+2209/58*a^5-4355/116*a^4-4653/116*a^3+3175/116*a^2-397/116*a+275/29)*q^77 + (-45/116*a^9+13/29*a^8+345/58*a^7-375/58*a^6-3341/116*a^5+3135/116*a^4+2669/58*a^3-788/29*a^2-1067/58*a-225/116)*q^78 + (53/116*a^9-34/29*a^8-179/29*a^7+983/58*a^6+2619/116*a^5-8487/116*a^4-799/58*a^3+5235/58*a^2-183/58*a-1881/116)*q^79 + (11/58*a^9-36/29*a^8-65/29*a^7+517/29*a^6+189/58*a^5-4343/58*a^4+708/29*a^3+2403/29*a^2-1001/29*a-641/58)*q^80 + (159/116*a^9-59/58*a^8-595/29*a^7+445/29*a^6+11221/116*a^5-7597/116*a^4-4519/29*a^3+3757/58*a^2+2292/29*a+389/116)*q^81 + (-83/116*a^9+219/116*a^8+1147/116*a^7-3133/116*a^6-1069/29*a^5+13071/116*a^4+2015/116*a^3-14263/116*a^2+3129/116*a+1025/58)*q^82 + (-35/58*a^9+5/58*a^8+527/58*a^7-71/58*a^6-1230/29*a^5+157/58*a^4+3575/58*a^3+471/58*a^2-967/58*a-131/29)*q^83 + (-17/116*a^9+53/58*a^8+41/29*a^7-385/29*a^6+77/116*a^5+6907/116*a^4-845/29*a^3-4995/58*a^2+1136/29*a+4033/116)*q^84 + (28/29*a^9-33/29*a^8-381/29*a^7+515/29*a^6+1446/29*a^5-2318/29*a^4-1033/29*a^3+2645/29*a^2-572/29*a-353/29)*q^85 + (9/29*a^9+36/29*a^8-167/29*a^7-517/29*a^6+1109/29*a^5+2244/29*a^4-2912/29*a^3-2838/29*a^2+2161/29*a+625/29)*q^86 + (65/116*a^9-59/116*a^8-987/116*a^7+861/116*a^6+2363/58*a^5-3581/116*a^4-7791/116*a^3+3699/116*a^2+4439/116*a-158/29)*q^87 + (-25/58*a^9-55/116*a^8+757/116*a^7+781/116*a^6-3825/116*a^5-874/29*a^4+7307/116*a^3+5085/116*a^2-4269/116*a-975/116)*q^88 + 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(-5/29*a^9+67/29*a^8+67/29*a^7-934/29*a^6-78/29*a^5+3867/29*a^4-1163/29*a^3-4436/29*a^2+1635/29*a+700/29)*q^170 + (-33/116*a^9+25/29*a^8+112/29*a^7-739/58*a^6-1611/116*a^5+6591/116*a^4+283/58*a^3-4367/58*a^2+857/58*a+1981/116)*q^171 + (-5/29*a^9+9/29*a^8+67/29*a^7-122/29*a^6-252/29*a^5+445/29*a^4+200/29*a^3-57/29*a^2+40/29*a-547/29)*q^172 + 1*q^173 + (3/58*a^9+53/116*a^8-179/116*a^7-799/116*a^6+1619/116*a^5+896/29*a^4-5141/116*a^3-4531/116*a^2+3983/116*a+1625/116)*q^174 + (109/58*a^9-259/116*a^8-3159/116*a^7+3875/116*a^6+13777/116*a^5-4198/29*a^4-17565/116*a^3+18789/116*a^2+4201/116*a-2593/116)*q^175 + (-119/116*a^9-41/116*a^8+1815/116*a^7+443/116*a^6-2207/29*a^5-1589/116*a^4+14823/116*a^3+2309/116*a^2-6791/116*a-225/58)*q^176 + (-49/58*a^9+43/116*a^8+1551/116*a^7-657/116*a^6-8019/116*a^5+716/29*a^4+15085/116*a^3-3501/116*a^2-8351/116*a+1047/116)*q^177 + (57/116*a^9-89/58*a^8-379/58*a^7+629/29*a^6+2577/116*a^5-10235/116*a^4-106/29*a^3+2626/29*a^2-607/29*a-875/116)*q^178 + (-3/29*a^9-12/29*a^8+46/29*a^7+182/29*a^6-244/29*a^5-922/29*a^4+497/29*a^3+1758/29*a^2-382/29*a-740/29)*q^179 + (7/58*a^9-59/58*a^8-59/58*a^7+861/58*a^6-102/29*a^5-3755/58*a^4+2185/58*a^3+4801/58*a^2-2753/58*a-606/29)*q^180 + (22/29*a^9-85/58*a^8-607/58*a^7+1265/58*a^6+2293/58*a^5-2741/29*a^4-1209/58*a^3+6203/58*a^2-2005/58*a-969/58)*q^181 + (-83/116*a^9+33/29*a^8+559/58*a^7-943/58*a^6-4131/116*a^5+7793/116*a^4+1167/58*a^3-2065/29*a^2+1579/58*a+1325/116)*q^182 + (-11/58*a^9-22/29*a^8+123/29*a^7+324/29*a^6-1929/58*a^5-2907/58*a^4+2917/29*a^3+1947/29*a^2-2392/29*a-1447/58)*q^183 + (-55/58*a^9+35/29*a^8+412/29*a^7-497/29*a^6-3787/58*a^5+4025/58*a^4+2753/29*a^3-1923/29*a^2-1056/29*a-275/58)*q^184 + (57/58*a^9-149/58*a^8-729/58*a^7+2197/58*a^6+1129/29*a^5-9481/58*a^4+649/58*a^3+10765/58*a^2-3675/58*a-684/29)*q^185 + (14/29*a^9-60/29*a^8-176/29*a^7+852/29*a^6+404/29*a^5-3595/29*a^4+1122/29*a^3+4237/29*a^2-1968/29*a-800/29)*q^186 + (-6/29*a^9+39/58*a^8+155/58*a^7-577/58*a^6-483/58*a^5+1259/29*a^4-187/58*a^3-2915/58*a^2+1111/58*a+375/58)*q^187 + (26/29*a^9-12/29*a^8-389/29*a^7+211/29*a^6+1815/29*a^5-1067/29*a^4-2809/29*a^3+1381/29*a^2+1271/29*a-305/29)*q^188 + (17/58*a^9-53/29*a^8-53/29*a^7+770/29*a^6-1005/58*a^5-6675/58*a^4+3836/29*a^3+4212/29*a^2-4969/29*a-2641/58)*q^189 + (10/29*a^9-65/58*a^8-239/58*a^7+923/58*a^6+573/58*a^5-1876/29*a^4+911/58*a^3+3795/58*a^2-1349/58*a-625/58)*q^190 + (5/4*a^9-2*a^8-18*a^7+59/2*a^6+303/4*a^5-503/4*a^4-165/2*a^3+267/2*a^2+19/2*a-33/4)*q^191 + (35/116*a^9-23/29*a^8-110/29*a^7+717/58*a^6+1213/116*a^5-6537/116*a^4+605/58*a^3+3897/58*a^2-1677/58*a+349/116)*q^192 + (-11/29*a^9+173/58*a^8+231/58*a^7-2503/58*a^6-1/58*a^5+5445/29*a^4-4253/58*a^3-13933/58*a^2+4961/58*a+3689/58)*q^193 + (22/29*a^9-57/29*a^8-289/29*a^7+821/29*a^6+987/29*a^5-3408/29*a^4-300/29*a^3+3667/29*a^2-640/29*a-325/29)*q^194 + (-83/58*a^9+161/58*a^8+1147/58*a^7-2379/58*a^6-2196/29*a^5+10229/58*a^4+3059/58*a^3-11363/58*a^2+1737/58*a+590/29)*q^195 + (-43/116*a^9+15/29*a^8+291/58*a^7-397/58*a^6-2231/116*a^5+2725/116*a^4+889/58*a^3-240/29*a^2+259/58*a-2419/116)*q^196 + (11/58*a^9+1/116*a^8-347/116*a^7-107/116*a^6+1799/116*a^5+337/29*a^4-3345/116*a^3-4975/116*a^2+1303/116*a+3561/116)*q^197 + (-159/116*a^9+59/58*a^8+566/29*a^7-445/29*a^6-9597/116*a^5+7597/116*a^4+2808/29*a^3-3815/58*a^2-378/29*a+75/116)*q^198 + (-19/29*a^9+40/29*a^8+243/29*a^7-597/29*a^6-743/29*a^5+2590/29*a^4-284/29*a^3-2931/29*a^2+1167/29*a+398/29)*q^199 + (-8/29*a^9-32/29*a^8+113/29*a^7+437/29*a^6-554/29*a^5-1869/29*a^4+1132/29*a^3+2571/29*a^2-748/29*a-475/29)*q^200 +  ...

-------------------------------------------------------
Gamma_0(174)
Weight 2

-------------------------------------------------------
J_0(174), dim = 27

-------------------------------------------------------
174A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*13
Ker(ModPolar)  = Z/2^2*13 + Z/2^2*13
= C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + G(Z/13 + Z/13)

ARITHMETIC INVARIANTS:
W_q            = ++-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 0.86866397748909582669 + -0.54414211875574238143e-4i
Omega-         = 0.50356391304353732473e-3 + 2.8390351800767170039i
L(1)           = 0.86866397919338340386
w1             = -0.43408020678802614468 + 1.4195447971442962891i
w2             = 0.86866397748909582669 + -0.54414211875574238143e-4i
c4             = 2714.4204717618900255 + 0.6532708272215302003i
c6             = 145712.94242341480004 + 57.712915461737193494i
j              = -28047.444429127934585 + 33.90042312635089611i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + 1*q^4 + 3*q^5 + 1*q^6 + -3*q^7 + -1*q^8 + 1*q^9 + -3*q^10 + 6*q^11 + -1*q^12 + 3*q^14 + -3*q^15 + 1*q^16 + 7*q^17 + -1*q^18 + 5*q^19 + 3*q^20 + 3*q^21 + -6*q^22 + -8*q^23 + 1*q^24 + 4*q^25 + -1*q^27 + -3*q^28 + 1*q^29 + 3*q^30 + -8*q^31 + -1*q^32 + -6*q^33 + -7*q^34 + -9*q^35 + 1*q^36 + -3*q^37 + -5*q^38 + -3*q^40 + -5*q^41 + -3*q^42 + 3*q^43 + 6*q^44 + 3*q^45 + 8*q^46 + 9*q^47 + -1*q^48 + 2*q^49 + -4*q^50 + -7*q^51 + -2*q^53 + 1*q^54 + 18*q^55 + 3*q^56 + -5*q^57 + -1*q^58 + -11*q^59 + -3*q^60 + -6*q^61 + 8*q^62 + -3*q^63 + 1*q^64 + 6*q^66 + 7*q^68 + 8*q^69 + 9*q^70 + -1*q^72 + -10*q^73 + 3*q^74 + -4*q^75 + 5*q^76 + -18*q^77 + -2*q^79 + 3*q^80 + 1*q^81 + 5*q^82 + 3*q^84 + 21*q^85 + -3*q^86 + -1*q^87 + -6*q^88 + 10*q^89 + -3*q^90 + -8*q^92 + 8*q^93 + -9*q^94 + 15*q^95 + 1*q^96 + -2*q^98 + 6*q^99 + 4*q^100 + 6*q^101 + 7*q^102 + -5*q^103 + 9*q^105 + 2*q^106 + 9*q^107 + -1*q^108 + -4*q^109 + -18*q^110 + 3*q^111 + -3*q^112 + 1*q^113 + 5*q^114 + -24*q^115 + 1*q^116 + 11*q^118 + -21*q^119 + 3*q^120 + 25*q^121 + 6*q^122 + 5*q^123 + -8*q^124 + -3*q^125 + 3*q^126 + 6*q^127 + -1*q^128 + -3*q^129 + -20*q^131 + -6*q^132 + -15*q^133 + -3*q^135 + -7*q^136 + -6*q^137 + -8*q^138 + 14*q^139 + -9*q^140 + -9*q^141 + 1*q^144 + 3*q^145 + 10*q^146 + -2*q^147 + -3*q^148 + 5*q^149 + 4*q^150 + 1*q^151 + -5*q^152 + 7*q^153 + 18*q^154 + -24*q^155 + -7*q^157 + 2*q^158 + 2*q^159 + -3*q^160 + 24*q^161 + -1*q^162 + -1*q^163 + -5*q^164 + -18*q^165 + 18*q^167 + -3*q^168 + -13*q^169 + -21*q^170 + 5*q^171 + 3*q^172 + -3*q^173 + 1*q^174 + -12*q^175 + 6*q^176 + 11*q^177 + -10*q^178 + -16*q^179 + 3*q^180 + -24*q^181 + 6*q^183 + 8*q^184 + -9*q^185 + -8*q^186 + 42*q^187 + 9*q^188 + 3*q^189 + -15*q^190 + 23*q^191 + -1*q^192 + -20*q^193 + 2*q^196 + 7*q^197 + -6*q^198 + -4*q^200 +  ...

-------------------------------------------------------
174B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*5
Ker(ModPolar)  = Z/2*5 + Z/2*5
= C(Z/5 + Z/5) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 2.276166844310417884 + -0.75442610388403025576e-4i
Omega-         = 0.75114869707661574576e-3 + -3.6889403445164663334i
L(1)           = 1.1380834227803374859
w1             = -1.1384589965037472499 + 1.8445078935634273682i
w2             = 1.1377078478066706341 + 1.8444324509530389652i
c4             = -22.967374437564919431 + 0.89135382838745256035e-1i
c6             = 1547.6457309911031829 + -0.71848078212202929327i
j              = 8.6961818439000032298 + -0.92708350418859758384e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + 2*q^5 + -1*q^6 + -1*q^8 + 1*q^9 + -2*q^10 + -4*q^11 + 1*q^12 + 6*q^13 + 2*q^15 + 1*q^16 + -2*q^17 + -1*q^18 + 4*q^19 + 2*q^20 + 4*q^22 + -1*q^24 + -1*q^25 + -6*q^26 + 1*q^27 + -1*q^29 + -2*q^30 + -4*q^31 + -1*q^32 + -4*q^33 + 2*q^34 + 1*q^36 + -6*q^37 + -4*q^38 + 6*q^39 + -2*q^40 + 6*q^41 + -12*q^43 + -4*q^44 + 2*q^45 + -8*q^47 + 1*q^48 + -7*q^49 + 1*q^50 + -2*q^51 + 6*q^52 + -6*q^53 + -1*q^54 + -8*q^55 + 4*q^57 + 1*q^58 + 8*q^59 + 2*q^60 + 10*q^61 + 4*q^62 + 1*q^64 + 12*q^65 + 4*q^66 + -4*q^67 + -2*q^68 + -8*q^71 + -1*q^72 + 2*q^73 + 6*q^74 + -1*q^75 + 4*q^76 + -6*q^78 + 4*q^79 + 2*q^80 + 1*q^81 + -6*q^82 + -4*q^85 + 12*q^86 + -1*q^87 + 4*q^88 + 14*q^89 + -2*q^90 + -4*q^93 + 8*q^94 + 8*q^95 + -1*q^96 + 18*q^97 + 7*q^98 + -4*q^99 + -1*q^100 + -6*q^101 + 2*q^102 + -8*q^103 + -6*q^104 + 6*q^106 + 16*q^107 + 1*q^108 + -2*q^109 + 8*q^110 + -6*q^111 + -18*q^113 + -4*q^114 + -1*q^116 + 6*q^117 + -8*q^118 + -2*q^120 + 5*q^121 + -10*q^122 + 6*q^123 + -4*q^124 + -12*q^125 + -12*q^127 + -1*q^128 + -12*q^129 + -12*q^130 + 12*q^131 + -4*q^132 + 4*q^134 + 2*q^135 + 2*q^136 + 14*q^137 + 4*q^139 + -8*q^141 + 8*q^142 + -24*q^143 + 1*q^144 + -2*q^145 + -2*q^146 + -7*q^147 + -6*q^148 + 18*q^149 + 1*q^150 + -8*q^151 + -4*q^152 + -2*q^153 + -8*q^155 + 6*q^156 + 2*q^157 + -4*q^158 + -6*q^159 + -2*q^160 + -1*q^162 + -20*q^163 + 6*q^164 + -8*q^165 + 16*q^167 + 23*q^169 + 4*q^170 + 4*q^171 + -12*q^172 + -6*q^173 + 1*q^174 + -4*q^176 + 8*q^177 + -14*q^178 + 2*q^180 + -2*q^181 + 10*q^183 + -12*q^185 + 4*q^186 + 8*q^187 + -8*q^188 + -8*q^190 + 24*q^191 + 1*q^192 + 26*q^193 + -18*q^194 + 12*q^195 + -7*q^196 + -6*q^197 + 4*q^198 + 24*q^199 + 1*q^200 +  ...

-------------------------------------------------------
174C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*5*7*11
Ker(ModPolar)  = Z/2^2*5*7*11 + Z/2^2*5*7*11
= A(Z/2 + Z/2) + B(Z/5 + Z/5) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/11 + Z/11) + H(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 7/3
Sha Bound      = 3*7

ANALYTIC INVARIANTS:

Omega+         = 0.43625983117037117229 + -0.14346511419420571348e-4i
Omega-         = 0.31691386372016662938e-5 + -0.21912022064249647557i
L(1)           = 1.0179396066146193681
w1             = -0.21812833101586698531 + -0.1095529370655385275i
w2             = -0.31691386372016662938e-5 + 0.21912022064249647557i
c4             = 369693.49756983363683 + -110.54364747268260873i
c6             = -1060502216.8221957584 + -47592.898409972101749i
j              = -81.284739975663399379 + 0.83984813489976126402e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -3*q^5 + -1*q^6 + 5*q^7 + -1*q^8 + 1*q^9 + 3*q^10 + 6*q^11 + 1*q^12 + -4*q^13 + -5*q^14 + -3*q^15 + 1*q^16 + 3*q^17 + -1*q^18 + -1*q^19 + -3*q^20 + 5*q^21 + -6*q^22 + -1*q^24 + 4*q^25 + 4*q^26 + 1*q^27 + 5*q^28 + -1*q^29 + 3*q^30 + -4*q^31 + -1*q^32 + 6*q^33 + -3*q^34 + -15*q^35 + 1*q^36 + -1*q^37 + 1*q^38 + -4*q^39 + 3*q^40 + -9*q^41 + -5*q^42 + -7*q^43 + 6*q^44 + -3*q^45 + -3*q^47 + 1*q^48 + 18*q^49 + -4*q^50 + 3*q^51 + -4*q^52 + -6*q^53 + -1*q^54 + -18*q^55 + -5*q^56 + -1*q^57 + 1*q^58 + 3*q^59 + -3*q^60 + -10*q^61 + 4*q^62 + 5*q^63 + 1*q^64 + 12*q^65 + -6*q^66 + -4*q^67 + 3*q^68 + 15*q^70 + 12*q^71 + -1*q^72 + 2*q^73 + 1*q^74 + 4*q^75 + -1*q^76 + 30*q^77 + 4*q^78 + 14*q^79 + -3*q^80 + 1*q^81 + 9*q^82 + 5*q^84 + -9*q^85 + 7*q^86 + -1*q^87 + -6*q^88 + -6*q^89 + 3*q^90 + -20*q^91 + -4*q^93 + 3*q^94 + 3*q^95 + -1*q^96 + 8*q^97 + -18*q^98 + 6*q^99 + 4*q^100 + -6*q^101 + -3*q^102 + -13*q^103 + 4*q^104 + -15*q^105 + 6*q^106 + -9*q^107 + 1*q^108 + 8*q^109 + 18*q^110 + -1*q^111 + 5*q^112 + -3*q^113 + 1*q^114 + -1*q^116 + -4*q^117 + -3*q^118 + 15*q^119 + 3*q^120 + 25*q^121 + 10*q^122 + -9*q^123 + -4*q^124 + 3*q^125 + -5*q^126 + -22*q^127 + -1*q^128 + -7*q^129 + -12*q^130 + 12*q^131 + 6*q^132 + -5*q^133 + 4*q^134 + -3*q^135 + -3*q^136 + -6*q^137 + 14*q^139 + -15*q^140 + -3*q^141 + -12*q^142 + -24*q^143 + 1*q^144 + 3*q^145 + -2*q^146 + 18*q^147 + -1*q^148 + 3*q^149 + -4*q^150 + 17*q^151 + 1*q^152 + 3*q^153 + -30*q^154 + 12*q^155 + -4*q^156 + -13*q^157 + -14*q^158 + -6*q^159 + 3*q^160 + -1*q^162 + 5*q^163 + -9*q^164 + -18*q^165 + 6*q^167 + -5*q^168 + 3*q^169 + 9*q^170 + -1*q^171 + -7*q^172 + -21*q^173 + 1*q^174 + 20*q^175 + 6*q^176 + 3*q^177 + 6*q^178 + -3*q^180 + 8*q^181 + 20*q^182 + -10*q^183 + 3*q^185 + 4*q^186 + 18*q^187 + -3*q^188 + 5*q^189 + -3*q^190 + -21*q^191 + 1*q^192 + -4*q^193 + -8*q^194 + 12*q^195 + 18*q^196 + 9*q^197 + -6*q^198 + -16*q^199 + -4*q^200 +  ...

-------------------------------------------------------
174D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + I(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.5847206958439150601 + 0.84911913696646398146e-4i
Omega-         = 0.19165753137991969221e-3 + 4.6286067190682153268i
L(1)           = 1.5847206981187743149
w1             = 0.79226451915626757019 + -2.3142609035772593402i
w2             = -1.5847206958439150601 + -0.84911913696646398146e-4i
c4             = 240.98721509289703436 + -0.56990657027996279976e-1i
c6             = 4086.7130947284225938 + -1.1384046837923846615i
j              = -8937.3502093761978406 + 8.4033920345403730801i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + 1*q^5 + -1*q^6 + 1*q^7 + 1*q^8 + 1*q^9 + 1*q^10 + 6*q^11 + -1*q^12 + -4*q^13 + 1*q^14 + -1*q^15 + 1*q^16 + -7*q^17 + 1*q^18 + -3*q^19 + 1*q^20 + -1*q^21 + 6*q^22 + 4*q^23 + -1*q^24 + -4*q^25 + -4*q^26 + -1*q^27 + 1*q^28 + -1*q^29 + -1*q^30 + 1*q^32 + -6*q^33 + -7*q^34 + 1*q^35 + 1*q^36 + -7*q^37 + -3*q^38 + 4*q^39 + 1*q^40 + 5*q^41 + -1*q^42 + -5*q^43 + 6*q^44 + 1*q^45 + 4*q^46 + -5*q^47 + -1*q^48 + -6*q^49 + -4*q^50 + 7*q^51 + -4*q^52 + 10*q^53 + -1*q^54 + 6*q^55 + 1*q^56 + 3*q^57 + -1*q^58 + 3*q^59 + -1*q^60 + 10*q^61 + 1*q^63 + 1*q^64 + -4*q^65 + -6*q^66 + -7*q^68 + -4*q^69 + 1*q^70 + -4*q^71 + 1*q^72 + 10*q^73 + -7*q^74 + 4*q^75 + -3*q^76 + 6*q^77 + 4*q^78 + -6*q^79 + 1*q^80 + 1*q^81 + 5*q^82 + 16*q^83 + -1*q^84 + -7*q^85 + -5*q^86 + 1*q^87 + 6*q^88 + -10*q^89 + 1*q^90 + -4*q^91 + 4*q^92 + -5*q^94 + -3*q^95 + -1*q^96 + -8*q^97 + -6*q^98 + 6*q^99 + -4*q^100 + -2*q^101 + 7*q^102 + -1*q^103 + -4*q^104 + -1*q^105 + 10*q^106 + 7*q^107 + -1*q^108 + 20*q^109 + 6*q^110 + 7*q^111 + 1*q^112 + -9*q^113 + 3*q^114 + 4*q^115 + -1*q^116 + -4*q^117 + 3*q^118 + -7*q^119 + -1*q^120 + 25*q^121 + 10*q^122 + -5*q^123 + -9*q^125 + 1*q^126 + 14*q^127 + 1*q^128 + 5*q^129 + -4*q^130 + -6*q^132 + -3*q^133 + -1*q^135 + -7*q^136 + -18*q^137 + -4*q^138 + 10*q^139 + 1*q^140 + 5*q^141 + -4*q^142 + -24*q^143 + 1*q^144 + -1*q^145 + 10*q^146 + 6*q^147 + -7*q^148 + -9*q^149 + 4*q^150 + -19*q^151 + -3*q^152 + -7*q^153 + 6*q^154 + 4*q^156 + -3*q^157 + -6*q^158 + -10*q^159 + 1*q^160 + 4*q^161 + 1*q^162 + -9*q^163 + 5*q^164 + -6*q^165 + 16*q^166 + 22*q^167 + -1*q^168 + 3*q^169 + -7*q^170 + -3*q^171 + -5*q^172 + -9*q^173 + 1*q^174 + -4*q^175 + 6*q^176 + -3*q^177 + -10*q^178 + -16*q^179 + 1*q^180 + 16*q^181 + -4*q^182 + -10*q^183 + 4*q^184 + -7*q^185 + -42*q^187 + -5*q^188 + -1*q^189 + -3*q^190 + 13*q^191 + -1*q^192 + -16*q^193 + -8*q^194 + 4*q^195 + -6*q^196 + 21*q^197 + 6*q^198 + 8*q^199 + -4*q^200 +  ...

-------------------------------------------------------
174E (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*7
Ker(ModPolar)  = Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + J(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 7
|L(1)/Omega|   = 1
Sha Bound      = 7^2

ANALYTIC INVARIANTS:

Omega+         = 1.8595635597582997548 + -0.85765667682213443616e-4i
Omega-         = 0.85083926130092516707e-4 + -1.0653052646875925456i
L(1)           = 1.8595635617361159231
w1             = 0.92973923791608483113 + 0.53260974950995516608i
w2             = 0.85083926130092516707e-4 + -1.0653052646875925456i
c4             = 48.409331733804447557 + -0.78773336095800238247i
c6             = -118498.3913001434177 + 11.843059196609270739i
j              = -0.13949822778992100886e-1 + 0.67868072690060374546e-3i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^3 + 1*q^4 + -1*q^5 + 1*q^6 + 1*q^7 + 1*q^8 + 1*q^9 + -1*q^10 + -2*q^11 + 1*q^12 + 1*q^14 + -1*q^15 + 1*q^16 + -3*q^17 + 1*q^18 + -1*q^19 + -1*q^20 + 1*q^21 + -2*q^22 + -4*q^23 + 1*q^24 + -4*q^25 + 1*q^27 + 1*q^28 + 1*q^29 + -1*q^30 + 4*q^31 + 1*q^32 + -2*q^33 + -3*q^34 + -1*q^35 + 1*q^36 + 3*q^37 + -1*q^38 + -1*q^40 + -7*q^41 + 1*q^42 + 9*q^43 + -2*q^44 + -1*q^45 + -4*q^46 + -1*q^47 + 1*q^48 + -6*q^49 + -4*q^50 + -3*q^51 + -2*q^53 + 1*q^54 + 2*q^55 + 1*q^56 + -1*q^57 + 1*q^58 + -3*q^59 + -1*q^60 + 6*q^61 + 4*q^62 + 1*q^63 + 1*q^64 + -2*q^66 + 12*q^67 + -3*q^68 + -4*q^69 + -1*q^70 + 16*q^71 + 1*q^72 + -10*q^73 + 3*q^74 + -4*q^75 + -1*q^76 + -2*q^77 + 10*q^79 + -1*q^80 + 1*q^81 + -7*q^82 + 1*q^84 + 3*q^85 + 9*q^86 + 1*q^87 + -2*q^88 + 6*q^89 + -1*q^90 + -4*q^92 + 4*q^93 + -1*q^94 + 1*q^95 + 1*q^96 + -6*q^98 + -2*q^99 + -4*q^100 + 18*q^101 + -3*q^102 + -1*q^103 + -1*q^105 + -2*q^106 + 17*q^107 + 1*q^108 + -16*q^109 + 2*q^110 + 3*q^111 + 1*q^112 + -5*q^113 + -1*q^114 + 4*q^115 + 1*q^116 + -3*q^118 + -3*q^119 + -1*q^120 + -7*q^121 + 6*q^122 + -7*q^123 + 4*q^124 + 9*q^125 + 1*q^126 + 2*q^127 + 1*q^128 + 9*q^129 + -8*q^131 + -2*q^132 + -1*q^133 + 12*q^134 + -1*q^135 + -3*q^136 + -2*q^137 + -4*q^138 + -14*q^139 + -1*q^140 + -1*q^141 + 16*q^142 + 1*q^144 + -1*q^145 + -10*q^146 + -6*q^147 + 3*q^148 + 17*q^149 + -4*q^150 + 5*q^151 + -1*q^152 + -3*q^153 + -2*q^154 + -4*q^155 + -17*q^157 + 10*q^158 + -2*q^159 + -1*q^160 + -4*q^161 + 1*q^162 + -11*q^163 + -7*q^164 + 2*q^165 + -14*q^167 + 1*q^168 + -13*q^169 + 3*q^170 + -1*q^171 + 9*q^172 + -15*q^173 + 1*q^174 + -4*q^175 + -2*q^176 + -3*q^177 + 6*q^178 + -16*q^179 + -1*q^180 + 6*q^183 + -4*q^184 + -3*q^185 + 4*q^186 + 6*q^187 + -1*q^188 + 1*q^189 + 1*q^190 + 17*q^191 + 1*q^192 + -16*q^193 + -6*q^196 + -5*q^197 + -2*q^198 + -24*q^199 + -4*q^200 +  ...

-------------------------------------------------------
174F (old = 87A), dim = 2

CONGRUENCES:
Modular Degree = 2^4*5*11
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*5*11 + Z/2*5*11
= C(Z/11 + Z/11) + G(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + I(Z/5 + Z/5)

-------------------------------------------------------
174G (old = 87B), dim = 3

CONGRUENCES:
Modular Degree = 2^5*13*23^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*23 + Z/2*23 + Z/2*13*23 + Z/2*13*23
= A(Z/13 + Z/13) + B(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + J(Z/23 + Z/23 + Z/23 + Z/23)

-------------------------------------------------------
174H (old = 58A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*7 + Z/2^2*7
= C(Z/7 + Z/7) + I(Z/2 + Z/2 + Z/2 + Z/2) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
174I (old = 58B), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3*5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3*5 + Z/2^2*3*5
= D(Z/3 + Z/3) + F(Z/5 + Z/5) + H(Z/2 + Z/2 + Z/2 + Z/2) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
174J (old = 29A), dim = 2

CONGRUENCES:
Modular Degree = 2^4*7*23^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*23 + Z/2*23 + Z/2*7*23 + Z/2*7*23
= E(Z/7 + Z/7) + G(Z/23 + Z/23 + Z/23 + Z/23) + H(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(175)
Weight 2

-------------------------------------------------------
J_0(175), dim = 15

-------------------------------------------------------
175A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^4 + Z/2^4
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2^2 + Z/2^2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.8286103274986809587 + -0.48328408097838864297e-3i
Omega-         = 0.13319564586949717274e-3 + -0.98594506518296656195i
L(1)           =
w1             = 1.4142385659264057308 + 0.49273089055099408665i
w2             = 0.13319564586949717274e-3 + -0.98594506518296656195i
c4             = 1601.1679091704090201 + -0.9979084795974425005i
c6             = -71078.53206877478373 + 46.365012791812911682i
j              = -7488.8975926042985451 + 22.572901055405534978i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^4 + -1*q^7 + -2*q^9 + -3*q^11 + 2*q^12 + -5*q^13 + 4*q^16 + -3*q^17 + 2*q^19 + 1*q^21 + 6*q^23 + 5*q^27 + 2*q^28 + 3*q^29 + -4*q^31 + 3*q^33 + 4*q^36 + -2*q^37 + 5*q^39 + -12*q^41 + 10*q^43 + 6*q^44 + -9*q^47 + -4*q^48 + 1*q^49 + 3*q^51 + 10*q^52 + -12*q^53 + -2*q^57 + 8*q^61 + 2*q^63 + -8*q^64 + 4*q^67 + 6*q^68 + -6*q^69 + -2*q^73 + -4*q^76 + 3*q^77 + -1*q^79 + 1*q^81 + -12*q^83 + -2*q^84 + -3*q^87 + -12*q^89 + 5*q^91 + -12*q^92 + 4*q^93 + 1*q^97 + 6*q^99 + 6*q^101 + -5*q^103 + -6*q^107 + -10*q^108 + -7*q^109 + 2*q^111 + -4*q^112 + -6*q^113 + -6*q^116 + 10*q^117 + 3*q^119 + -2*q^121 + 12*q^123 + 8*q^124 + 16*q^127 + -10*q^129 + -6*q^131 + -6*q^132 + -2*q^133 + 12*q^137 + 14*q^139 + 9*q^141 + 15*q^143 + -8*q^144 + -1*q^147 + 4*q^148 + -6*q^149 + -1*q^151 + 6*q^153 + -10*q^156 + -14*q^157 + 12*q^159 + -6*q^161 + -2*q^163 + 24*q^164 + 3*q^167 + 12*q^169 + -4*q^171 + -20*q^172 + 9*q^173 + -12*q^176 + 12*q^179 + 20*q^181 + -8*q^183 + 9*q^187 + 18*q^188 + -5*q^189 + 9*q^191 + 8*q^192 + 4*q^193 + -2*q^196 + -16*q^199 +  ...

-------------------------------------------------------
175B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*5
Ker(ModPolar)  = Z/2^3*5 + Z/2^3*5
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/5 + Z/5) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.1737162375037153345 + -0.2744710917359474604e-4i
Omega-         = 0.14168246676476324024e-4 + -1.5286042949937828029i
L(1)           = 2.3474324756492755867
w1             = -0.5868652028751959054 + 0.76431587105147819883i
w2             = 0.58685103462851942908 + 0.76428842394230460409i
c4             = -2002.2013660119455127 + 0.13017626110173410354i
c6             = 125018.23907802742014 + 15.348775165233854243i
j              = 586.30766610610626671 + -0.17067494839758928349i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 1*q^3 + 2*q^4 + 2*q^6 + -1*q^7 + -2*q^9 + -3*q^11 + 2*q^12 + 1*q^13 + -2*q^14 + -4*q^16 + 7*q^17 + -4*q^18 + -1*q^21 + -6*q^22 + 6*q^23 + 2*q^26 + -5*q^27 + -2*q^28 + -5*q^29 + 2*q^31 + -8*q^32 + -3*q^33 + 14*q^34 + -4*q^36 + 2*q^37 + 1*q^39 + 2*q^41 + -2*q^42 + -4*q^43 + -6*q^44 + 12*q^46 + -3*q^47 + -4*q^48 + 1*q^49 + 7*q^51 + 2*q^52 + 6*q^53 + -10*q^54 + -10*q^58 + 10*q^59 + -8*q^61 + 4*q^62 + 2*q^63 + -8*q^64 + -6*q^66 + 2*q^67 + 14*q^68 + 6*q^69 + -8*q^71 + 6*q^73 + 4*q^74 + 3*q^77 + 2*q^78 + -5*q^79 + 1*q^81 + 4*q^82 + -4*q^83 + -2*q^84 + -8*q^86 + -5*q^87 + -1*q^91 + 12*q^92 + 2*q^93 + -6*q^94 + -8*q^96 + 7*q^97 + 2*q^98 + 6*q^99 + 12*q^101 + 14*q^102 + -19*q^103 + 12*q^106 + -8*q^107 + -10*q^108 + 5*q^109 + 2*q^111 + 4*q^112 + 6*q^113 + -10*q^116 + -2*q^117 + 20*q^118 + -7*q^119 + -2*q^121 + -16*q^122 + 2*q^123 + 4*q^124 + 4*q^126 + 2*q^127 + -4*q^129 + 22*q^131 + -6*q^132 + 4*q^134 + 12*q^137 + 12*q^138 + -10*q^139 + -3*q^141 + -16*q^142 + -3*q^143 + 8*q^144 + 12*q^146 + 1*q^147 + 4*q^148 + 10*q^149 + -13*q^151 + -14*q^153 + 6*q^154 + 2*q^156 + -18*q^157 + -10*q^158 + 6*q^159 + -6*q^161 + 2*q^162 + -14*q^163 + 4*q^164 + -8*q^166 + -3*q^167 + -12*q^169 + -8*q^172 + -9*q^173 + -10*q^174 + 12*q^176 + 10*q^177 + -20*q^179 + -18*q^181 + -2*q^182 + -8*q^183 + 4*q^186 + -21*q^187 + -6*q^188 + 5*q^189 + -3*q^191 + -8*q^192 + 16*q^193 + 14*q^194 + 2*q^196 + 2*q^197 + 12*q^198 + -10*q^199 +  ...

-------------------------------------------------------
175C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 5
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.6254560191357098004 + -0.58400426864895701551e-3i
Omega-         = 0.35202960613352380811e-3 + -3.4190762708508150018i
L(1)           =
w1             = -1.3129040243709216621 + 1.7098301375597319794i
w2             = 1.3125519947647881383 + 1.7092461332910830224i
c4             = -79.997613267972178917 + 0.55194955099848526456e-1i
c6             = 998.01856600511543005 + 1.157968586147430393i
j              = 586.64286136208790129 + -1.7012073233033358171i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + -1*q^3 + 2*q^4 + 2*q^6 + 1*q^7 + -2*q^9 + -3*q^11 + -2*q^12 + -1*q^13 + -2*q^14 + -4*q^16 + -7*q^17 + 4*q^18 + -1*q^21 + 6*q^22 + -6*q^23 + 2*q^26 + 5*q^27 + 2*q^28 + -5*q^29 + 2*q^31 + 8*q^32 + 3*q^33 + 14*q^34 + -4*q^36 + -2*q^37 + 1*q^39 + 2*q^41 + 2*q^42 + 4*q^43 + -6*q^44 + 12*q^46 + 3*q^47 + 4*q^48 + 1*q^49 + 7*q^51 + -2*q^52 + -6*q^53 + -10*q^54 + 10*q^58 + 10*q^59 + -8*q^61 + -4*q^62 + -2*q^63 + -8*q^64 + -6*q^66 + -2*q^67 + -14*q^68 + 6*q^69 + -8*q^71 + -6*q^73 + 4*q^74 + -3*q^77 + -2*q^78 + -5*q^79 + 1*q^81 + -4*q^82 + 4*q^83 + -2*q^84 + -8*q^86 + 5*q^87 + -1*q^91 + -12*q^92 + -2*q^93 + -6*q^94 + -8*q^96 + -7*q^97 + -2*q^98 + 6*q^99 + 12*q^101 + -14*q^102 + 19*q^103 + 12*q^106 + 8*q^107 + 10*q^108 + 5*q^109 + 2*q^111 + -4*q^112 + -6*q^113 + -10*q^116 + 2*q^117 + -20*q^118 + -7*q^119 + -2*q^121 + 16*q^122 + -2*q^123 + 4*q^124 + 4*q^126 + -2*q^127 + -4*q^129 + 22*q^131 + 6*q^132 + 4*q^134 + -12*q^137 + -12*q^138 + -10*q^139 + -3*q^141 + 16*q^142 + 3*q^143 + 8*q^144 + 12*q^146 + -1*q^147 + -4*q^148 + 10*q^149 + -13*q^151 + 14*q^153 + 6*q^154 + 2*q^156 + 18*q^157 + 10*q^158 + 6*q^159 + -6*q^161 + -2*q^162 + 14*q^163 + 4*q^164 + -8*q^166 + 3*q^167 + -12*q^169 + 8*q^172 + 9*q^173 + -10*q^174 + 12*q^176 + -10*q^177 + -20*q^179 + -18*q^181 + 2*q^182 + 8*q^183 + 4*q^186 + 21*q^187 + 6*q^188 + 5*q^189 + -3*q^191 + 8*q^192 + -16*q^193 + 14*q^194 + 2*q^196 + -2*q^197 + -12*q^198 + -10*q^199 +  ...

-------------------------------------------------------
175D (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2^4*3 + Z/2^4*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/3 + Z/3 + Z/3 + Z/3) + G(Z/2^2 + Z/2^2) + H(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 17
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 2.3853764475438199663 + -0.52979634258573630509e-5i
Omega-         = 1.2325808313735126191 + 0.19986732609889183631e-3i
L(1)           = 2.3853764475497034017

HECKE EIGENFORM:
a^2-a-4 = 0,
f(q) = q + a*q^2 + (-a+1)*q^3 + (a+2)*q^4 + -4*q^6 + 1*q^7 + (a+4)*q^8 + (-a+2)*q^9 + (-a+1)*q^11 + (-2*a-2)*q^12 + (a-3)*q^13 + a*q^14 + 3*a*q^16 + (-a+3)*q^17 + (a-4)*q^18 + (-2*a-2)*q^19 + (-a+1)*q^21 + -4*q^22 + (-2*a+2)*q^23 + -4*a*q^24 + (-2*a+4)*q^26 + (a+3)*q^27 + (a+2)*q^28 + (3*a-1)*q^29 + (a+4)*q^32 + (-a+5)*q^33 + (2*a-4)*q^34 + -a*q^36 + -6*q^37 + (-4*a-8)*q^38 + (3*a-7)*q^39 + 2*a*q^41 + -4*q^42 + (2*a-6)*q^43 + (-2*a-2)*q^44 + -8*q^46 + (3*a+1)*q^47 + -12*q^48 + 1*q^49 + (-3*a+7)*q^51 + -2*q^52 + 2*a*q^53 + (4*a+4)*q^54 + (a+4)*q^56 + (2*a+6)*q^57 + (2*a+12)*q^58 + -4*q^59 + 6*a*q^61 + (-a+2)*q^63 + (-a+4)*q^64 + (4*a-4)*q^66 + -4*a*q^67 + 2*q^68 + (-2*a+10)*q^69 + 8*q^71 + (-3*a+4)*q^72 + (4*a+2)*q^73 + -6*a*q^74 + (-8*a-12)*q^76 + (-a+1)*q^77 + (-4*a+12)*q^78 + (a-5)*q^79 + -7*q^81 + (2*a+8)*q^82 + -4*q^83 + (-2*a-2)*q^84 + (-4*a+8)*q^86 + (a-13)*q^87 + -4*a*q^88 + (-2*a+4)*q^89 + (a-3)*q^91 + (-4*a-4)*q^92 + (4*a+12)*q^94 + -4*a*q^96 + (-5*a+7)*q^97 + a*q^98 + (-2*a+6)*q^99 + (-4*a-6)*q^101 + (4*a-12)*q^102 + (-a-3)*q^103 + (2*a-8)*q^104 + (2*a+8)*q^106 + (-6*a+2)*q^107 + (6*a+10)*q^108 + (-3*a+13)*q^109 + (6*a-6)*q^111 + 3*a*q^112 + 14*q^113 + (8*a+8)*q^114 + (8*a+10)*q^116 + (4*a-10)*q^117 + -4*a*q^118 + (-a+3)*q^119 + (-a-6)*q^121 + (6*a+24)*q^122 + -8*q^123 + (a-4)*q^126 + (4*a-4)*q^127 + (a-12)*q^128 + (6*a-14)*q^129 + (2*a-6)*q^131 + (2*a+6)*q^132 + (-2*a-2)*q^133 + (-4*a-16)*q^134 + (-2*a+8)*q^136 + (2*a+12)*q^137 + (8*a-8)*q^138 + (-2*a-10)*q^139 + (-a-11)*q^141 + 8*a*q^142 + (3*a-7)*q^143 + (3*a-12)*q^144 + (6*a+16)*q^146 + (-a+1)*q^147 + (-6*a-12)*q^148 + (4*a+2)*q^149 + (-7*a+11)*q^151 + (-12*a-16)*q^152 + (-4*a+10)*q^153 + -4*q^154 + (2*a-2)*q^156 + (-4*a-10)*q^157 + (-4*a+4)*q^158 + -8*q^159 + (-2*a+2)*q^161 + -7*a*q^162 + (2*a+2)*q^163 + (6*a+8)*q^164 + -4*a*q^166 + (7*a-11)*q^167 + -4*a*q^168 + -5*a*q^169 + 4*q^171 + -4*q^172 + (-a+7)*q^173 + (-12*a+4)*q^174 + -12*q^176 + (4*a-4)*q^177 + (2*a-8)*q^178 + 20*q^179 + (-10*a+8)*q^181 + (-2*a+4)*q^182 + -24*q^183 + -8*a*q^184 + (-3*a+7)*q^187 + (10*a+14)*q^188 + (a+3)*q^189 + (-a-11)*q^191 + (-4*a+8)*q^192 + (-6*a-4)*q^193 + (2*a-20)*q^194 + (a+2)*q^196 + (-2*a+4)*q^197 + (4*a-8)*q^198 + (4*a-12)*q^199 +  ...

-------------------------------------------------------
175E (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= D(Z/3 + Z/3 + Z/3 + Z/3) + F(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 5
Torsion Bound  = 5
|L(1)/Omega|   = 1/5
Sha Bound      = 5

ANALYTIC INVARIANTS:

Omega+         = 4.8609838973019798214 + 0.82940685527781918877e-3i
Omega-         = 8.564543002329814138 + 0.21166401859749804579e-2i
L(1)           = 0.97219679361217554448

HECKE EIGENFORM:
a^2-a-1 = 0,
f(q) = q + a*q^2 + (2*a-2)*q^3 + (a-1)*q^4 + 2*q^6 + 1*q^7 + (-2*a+1)*q^8 + (-4*a+5)*q^9 + (2*a+1)*q^11 + (-2*a+4)*q^12 + -2*a*q^13 + a*q^14 + -3*a*q^16 + -4*a*q^17 + (a-4)*q^18 + (4*a-2)*q^19 + (2*a-2)*q^21 + (3*a+2)*q^22 + (-2*a+5)*q^23 + (2*a-6)*q^24 + (-2*a-2)*q^26 + (4*a-12)*q^27 + (a-1)*q^28 + 5*q^29 + -6*a*q^31 + (a-5)*q^32 + (2*a+2)*q^33 + (-4*a-4)*q^34 + (5*a-9)*q^36 + 3*q^37 + (2*a+4)*q^38 + -4*q^39 + (2*a+6)*q^41 + 2*q^42 + (2*a+3)*q^43 + (a+1)*q^44 + (3*a-2)*q^46 + -2*q^47 + -6*q^48 + 1*q^49 + -8*q^51 + -2*q^52 + (-4*a+6)*q^53 + (-8*a+4)*q^54 + (-2*a+1)*q^56 + (-4*a+12)*q^57 + 5*a*q^58 + (-6*a+8)*q^59 + (6*a-6)*q^61 + (-6*a-6)*q^62 + (-4*a+5)*q^63 + (2*a+1)*q^64 + (4*a+2)*q^66 + (2*a-3)*q^67 + -4*q^68 + (10*a-14)*q^69 + (-6*a+5)*q^71 + (-6*a+13)*q^72 + (-2*a-10)*q^73 + 3*a*q^74 + (-2*a+6)*q^76 + (2*a+1)*q^77 + -4*a*q^78 + (10*a-5)*q^79 + (-12*a+17)*q^81 + (8*a+2)*q^82 + (6*a-4)*q^83 + (-2*a+4)*q^84 + (5*a+2)*q^86 + (10*a-10)*q^87 + (-4*a-3)*q^88 + (-2*a+16)*q^89 + -2*a*q^91 + (5*a-7)*q^92 + -12*q^93 + -2*a*q^94 + (-10*a+12)*q^96 + (-2*a+4)*q^97 + a*q^98 + (-2*a-3)*q^99 + (2*a+6)*q^101 + -8*a*q^102 + (-4*a+6)*q^103 + (2*a+4)*q^104 + (2*a-4)*q^106 + 8*q^107 + (-12*a+16)*q^108 + (-12*a+1)*q^109 + (6*a-6)*q^111 + -3*a*q^112 + (12*a-7)*q^113 + (8*a-4)*q^114 + (5*a-5)*q^116 + (-2*a+8)*q^117 + (2*a-6)*q^118 + -4*a*q^119 + (8*a-6)*q^121 + 6*q^122 + (12*a-8)*q^123 + -6*q^124 + (a-4)*q^126 + (-14*a+5)*q^127 + (a+12)*q^128 + (6*a-2)*q^129 + (8*a-12)*q^131 + 2*a*q^132 + (4*a-2)*q^133 + (-a+2)*q^134 + (4*a+8)*q^136 + (8*a-6)*q^137 + (-4*a+10)*q^138 + (-14*a+2)*q^139 + (-4*a+4)*q^141 + (-a-6)*q^142 + (-6*a-4)*q^143 + (-3*a+12)*q^144 + (-12*a-2)*q^146 + (2*a-2)*q^147 + (3*a-3)*q^148 + (-8*a-1)*q^149 + (2*a-19)*q^151 + -10*q^152 + (-4*a+16)*q^153 + (3*a+2)*q^154 + (-4*a+4)*q^156 + (2*a+2)*q^157 + (5*a+10)*q^158 + (12*a-20)*q^159 + (-2*a+5)*q^161 + (5*a-12)*q^162 + (-4*a-4)*q^163 + (6*a-4)*q^164 + (2*a+6)*q^166 + (-2*a+4)*q^167 + (2*a-6)*q^168 + (4*a-9)*q^169 + (12*a-26)*q^171 + (3*a-1)*q^172 + (-4*a-14)*q^173 + 10*q^174 + (-9*a-6)*q^176 + (16*a-28)*q^177 + (14*a-2)*q^178 + (12*a-16)*q^179 + (-10*a+2)*q^181 + (-2*a-2)*q^182 + (-12*a+24)*q^183 + (-8*a+9)*q^184 + -12*a*q^186 + (-12*a-8)*q^187 + (-2*a+2)*q^188 + (4*a-12)*q^189 + (-4*a+4)*q^191 + (2*a+2)*q^192 + (-12*a+5)*q^193 + (2*a-2)*q^194 + (a-1)*q^196 + (4*a+1)*q^197 + (-5*a-2)*q^198 + (-2*a+6)*q^199 +  ...

-------------------------------------------------------
175F (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^2*5
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3*5 + Z/2*3*5
= B(Z/5 + Z/5) + E(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/3 + Z/3 + Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 0.97195408167373795673 + -0.31042931528536064258e-3i
Omega-         = 8.5656322181306342662 + -0.36769103130709502729e-2i
L(1)           = 0.97195413124725132943

HECKE EIGENFORM:
a^2+a-1 = 0,
f(q) = q + a*q^2 + (2*a+2)*q^3 + (-a-1)*q^4 + 2*q^6 + -1*q^7 + (-2*a-1)*q^8 + (4*a+5)*q^9 + (-2*a+1)*q^11 + (-2*a-4)*q^12 + -2*a*q^13 + -a*q^14 + 3*a*q^16 + -4*a*q^17 + (a+4)*q^18 + (-4*a-2)*q^19 + (-2*a-2)*q^21 + (3*a-2)*q^22 + (-2*a-5)*q^23 + (-2*a-6)*q^24 + (2*a-2)*q^26 + (4*a+12)*q^27 + (a+1)*q^28 + 5*q^29 + 6*a*q^31 + (a+5)*q^32 + (2*a-2)*q^33 + (4*a-4)*q^34 + (-5*a-9)*q^36 + -3*q^37 + (2*a-4)*q^38 + -4*q^39 + (-2*a+6)*q^41 + -2*q^42 + (2*a-3)*q^43 + (-a+1)*q^44 + (-3*a-2)*q^46 + 2*q^47 + 6*q^48 + 1*q^49 + -8*q^51 + 2*q^52 + (-4*a-6)*q^53 + (8*a+4)*q^54 + (2*a+1)*q^56 + (-4*a-12)*q^57 + 5*a*q^58 + (6*a+8)*q^59 + (-6*a-6)*q^61 + (-6*a+6)*q^62 + (-4*a-5)*q^63 + (-2*a+1)*q^64 + (-4*a+2)*q^66 + (2*a+3)*q^67 + 4*q^68 + (-10*a-14)*q^69 + (6*a+5)*q^71 + (-6*a-13)*q^72 + (-2*a+10)*q^73 + -3*a*q^74 + (2*a+6)*q^76 + (2*a-1)*q^77 + -4*a*q^78 + (-10*a-5)*q^79 + (12*a+17)*q^81 + (8*a-2)*q^82 + (6*a+4)*q^83 + (2*a+4)*q^84 + (-5*a+2)*q^86 + (10*a+10)*q^87 + (-4*a+3)*q^88 + (2*a+16)*q^89 + 2*a*q^91 + (5*a+7)*q^92 + 12*q^93 + 2*a*q^94 + (10*a+12)*q^96 + (-2*a-4)*q^97 + a*q^98 + (2*a-3)*q^99 + (-2*a+6)*q^101 + -8*a*q^102 + (-4*a-6)*q^103 + (-2*a+4)*q^104 + (-2*a-4)*q^106 + -8*q^107 + (-12*a-16)*q^108 + (12*a+1)*q^109 + (-6*a-6)*q^111 + -3*a*q^112 + (12*a+7)*q^113 + (-8*a-4)*q^114 + (-5*a-5)*q^116 + (-2*a-8)*q^117 + (2*a+6)*q^118 + 4*a*q^119 + (-8*a-6)*q^121 + -6*q^122 + (12*a+8)*q^123 + -6*q^124 + (-a-4)*q^126 + (-14*a-5)*q^127 + (a-12)*q^128 + (-6*a-2)*q^129 + (-8*a-12)*q^131 + 2*a*q^132 + (4*a+2)*q^133 + (a+2)*q^134 + (-4*a+8)*q^136 + (8*a+6)*q^137 + (-4*a-10)*q^138 + (14*a+2)*q^139 + (4*a+4)*q^141 + (-a+6)*q^142 + (-6*a+4)*q^143 + (3*a+12)*q^144 + (12*a-2)*q^146 + (2*a+2)*q^147 + (3*a+3)*q^148 + (8*a-1)*q^149 + (-2*a-19)*q^151 + 10*q^152 + (-4*a-16)*q^153 + (-3*a+2)*q^154 + (4*a+4)*q^156 + (2*a-2)*q^157 + (5*a-10)*q^158 + (-12*a-20)*q^159 + (2*a+5)*q^161 + (5*a+12)*q^162 + (-4*a+4)*q^163 + (-6*a-4)*q^164 + (-2*a+6)*q^166 + (-2*a-4)*q^167 + (2*a+6)*q^168 + (-4*a-9)*q^169 + (-12*a-26)*q^171 + (3*a+1)*q^172 + (-4*a+14)*q^173 + 10*q^174 + (9*a-6)*q^176 + (16*a+28)*q^177 + (14*a+2)*q^178 + (-12*a-16)*q^179 + (10*a+2)*q^181 + (-2*a+2)*q^182 + (-12*a-24)*q^183 + (8*a+9)*q^184 + 12*a*q^186 + (-12*a+8)*q^187 + (-2*a-2)*q^188 + (-4*a-12)*q^189 + (4*a+4)*q^191 + (2*a-2)*q^192 + (-12*a-5)*q^193 + (-2*a-2)*q^194 + (-a-1)*q^196 + (4*a-1)*q^197 + (-5*a+2)*q^198 + (2*a+6)*q^199 +  ...

-------------------------------------------------------
175G (old = 35A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2^2 + Z/2^2) + H(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
175H (old = 35B), dim = 2

CONGRUENCES:
Modular Degree = 2^6*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2^4*3 + Z/2^4*3
= A(Z/2^2 + Z/2^2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/3 + Z/3 + Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(176)
Weight 2

-------------------------------------------------------
J_0(176), dim = 19

-------------------------------------------------------
176A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^4 + Z/2^4
= D(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.6554152769418230154 + 0.18571149436819536864e-3i
Omega-         = 0.42892776622529447732e-3 + 4.2523481502317588546i
L(1)           = 1.655415287358773829
w1             = -0.82749317458779886047 + 2.1260812193686953296i
w2             = 1.6554152769418230154 + 0.18571149436819536864e-3i
c4             = 191.99917026035254088 + -0.11279325310933132139i
c6             = 3456.24399848809088 + -1.5327158691090137793i
j              = -2512.4964885083902932 + 5.3978913087240164841i

HECKE EIGENFORM:
f(q) = q + 3*q^3 + -3*q^5 + 2*q^7 + 6*q^9 + 1*q^11 + -9*q^15 + -6*q^17 + -4*q^19 + 6*q^21 + -1*q^23 + 4*q^25 + 9*q^27 + -8*q^29 + 7*q^31 + 3*q^33 + -6*q^35 + -1*q^37 + 4*q^41 + -6*q^43 + -18*q^45 + 8*q^47 + -3*q^49 + -18*q^51 + 2*q^53 + -3*q^55 + -12*q^57 + 1*q^59 + 4*q^61 + 12*q^63 + 5*q^67 + -3*q^69 + -3*q^71 + 16*q^73 + 12*q^75 + 2*q^77 + -2*q^79 + 9*q^81 + 2*q^83 + 18*q^85 + -24*q^87 + 15*q^89 + 21*q^93 + 12*q^95 + -7*q^97 + 6*q^99 + -10*q^101 + 16*q^103 + -18*q^105 + -2*q^107 + -14*q^109 + -3*q^111 + -7*q^113 + 3*q^115 + -12*q^119 + 1*q^121 + 12*q^123 + 3*q^125 + -4*q^127 + -18*q^129 + 2*q^131 + -8*q^133 + -27*q^135 + -15*q^137 + 22*q^139 + 24*q^141 + 24*q^145 + -9*q^147 + 18*q^149 + 18*q^151 + -36*q^153 + -21*q^155 + -11*q^157 + 6*q^159 + -2*q^161 + 4*q^163 + -9*q^165 + -16*q^167 + -13*q^169 + -24*q^171 + 18*q^173 + 8*q^175 + 3*q^177 + 5*q^179 + -5*q^181 + 12*q^183 + 3*q^185 + -6*q^187 + 18*q^189 + 9*q^191 + 4*q^193 + 6*q^197 + -8*q^199 +  ...

-------------------------------------------------------
176B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.4587497765259904477 + -0.71058407078324420738e-4i
Omega-         = 0.60839502221061757167e-5 + -3.1723034682413544726i
L(1)           = 1.4587497782566838451
w1             = 0.72937184628788417076 + 1.5861162049171380741i
w2             = 1.4587497765259904477 + -0.71058407078324420738e-4i
c4             = 255.93887352189209713 + 0.80097177134273818867e-1i
c6             = 9734.6648417940895312 + 1.7287602263321122499i
j              = -371.42077300678437823 + -0.26339160127083263164i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 1*q^5 + 2*q^7 + -2*q^9 + -1*q^11 + 4*q^13 + 1*q^15 + -2*q^17 + 2*q^21 + 1*q^23 + -4*q^25 + -5*q^27 + -7*q^31 + -1*q^33 + 2*q^35 + 3*q^37 + 4*q^39 + -8*q^41 + 6*q^43 + -2*q^45 + -8*q^47 + -3*q^49 + -2*q^51 + -6*q^53 + -1*q^55 + -5*q^59 + 12*q^61 + -4*q^63 + 4*q^65 + 7*q^67 + 1*q^69 + 3*q^71 + 4*q^73 + -4*q^75 + -2*q^77 + 10*q^79 + 1*q^81 + 6*q^83 + -2*q^85 + 15*q^89 + 8*q^91 + -7*q^93 + -7*q^97 + 2*q^99 + 2*q^101 + 16*q^103 + 2*q^105 + -18*q^107 + 10*q^109 + 3*q^111 + 9*q^113 + 1*q^115 + -8*q^117 + -4*q^119 + 1*q^121 + -8*q^123 + -9*q^125 + -8*q^127 + 6*q^129 + 18*q^131 + -5*q^135 + -7*q^137 + -10*q^139 + -8*q^141 + -4*q^143 + -3*q^147 + -10*q^149 + -2*q^151 + 4*q^153 + -7*q^155 + -7*q^157 + -6*q^159 + 2*q^161 + -4*q^163 + -1*q^165 + 12*q^167 + 3*q^169 + -6*q^173 + -8*q^175 + -5*q^177 + 15*q^179 + 7*q^181 + 12*q^183 + 3*q^185 + 2*q^187 + -10*q^189 + -17*q^191 + 4*q^193 + 4*q^195 + -2*q^197 +  ...

-------------------------------------------------------
176C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 3.0541071115086155484 + -0.18962559798203810825e-3i
Omega-         = 0.47999779812693075244e-4 + -2.4138538969678204173i
L(1)           =
w1             = -1.5270775556442141208 + 1.2070217612829012277i
w2             = 1.5270295558644014277 + 1.2068321356849191896i
c4             = -127.99110869800573888 + -0.36322530748802601939e-1i
c6             = -1664.3558066551207422 + 0.20582095768631324819i
j              = 744.45777629916318451 + 0.46555085643667169758i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -3*q^5 + -2*q^7 + -2*q^9 + 1*q^11 + -4*q^13 + 3*q^15 + 6*q^17 + -8*q^19 + 2*q^21 + 3*q^23 + 4*q^25 + 5*q^27 + -5*q^31 + -1*q^33 + 6*q^35 + -1*q^37 + 4*q^39 + 10*q^43 + 6*q^45 + -3*q^49 + -6*q^51 + -6*q^53 + -3*q^55 + 8*q^57 + -3*q^59 + -4*q^61 + 4*q^63 + 12*q^65 + 1*q^67 + -3*q^69 + -15*q^71 + -4*q^73 + -4*q^75 + -2*q^77 + -2*q^79 + 1*q^81 + -6*q^83 + -18*q^85 + -9*q^89 + 8*q^91 + 5*q^93 + 24*q^95 + -7*q^97 + -2*q^99 + 18*q^101 + -8*q^103 + -6*q^105 + -6*q^107 + 2*q^109 + 1*q^111 + -15*q^113 + -9*q^115 + 8*q^117 + -12*q^119 + 1*q^121 + 3*q^125 + 16*q^127 + -10*q^129 + 6*q^131 + 16*q^133 + -15*q^135 + 9*q^137 + -14*q^139 + -4*q^143 + 3*q^147 + 6*q^149 + 10*q^151 + -12*q^153 + 15*q^155 + 5*q^157 + 6*q^159 + -6*q^161 + 4*q^163 + 3*q^165 + 12*q^167 + 3*q^169 + 16*q^171 + 18*q^173 + -8*q^175 + 3*q^177 + 9*q^179 + -13*q^181 + 4*q^183 + 3*q^185 + 6*q^187 + -10*q^189 + 21*q^191 + 20*q^193 + -12*q^195 + 6*q^197 + -8*q^199 +  ...

-------------------------------------------------------
176D (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 17
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 2.8047867176166572658 + 0.18190719363306481192e-3i
Omega-         = 2.3226873163943621849 + 0.17013795474238591122e-3i
L(1)           = 0.70119668087888549813

HECKE EIGENFORM:
a^2+a-4 = 0,
f(q) = q + a*q^3 + (a+2)*q^5 + -2*a*q^7 + (-a+1)*q^9 + 1*q^11 + (-2*a-2)*q^13 + (a+4)*q^15 + 2*q^17 + 4*q^19 + (2*a-8)*q^21 + (a-4)*q^23 + (3*a+3)*q^25 + (-a-4)*q^27 + (-2*a-2)*q^29 + (a+4)*q^31 + a*q^33 + (-2*a-8)*q^35 + (-a-6)*q^37 + -8*q^39 + (-2*a+2)*q^41 + (2*a+4)*q^43 + -2*q^45 + -8*q^47 + (-4*a+9)*q^49 + 2*a*q^51 + (4*a+6)*q^53 + (a+2)*q^55 + 4*a*q^57 + -5*a*q^59 + (2*a-2)*q^61 + (-4*a+8)*q^63 + (-4*a-12)*q^65 + (-a-8)*q^67 + (-5*a+4)*q^69 + (3*a+4)*q^71 + (2*a+2)*q^73 + 12*q^75 + -2*a*q^77 + (2*a+8)*q^79 + -7*q^81 + (2*a-4)*q^83 + (2*a+4)*q^85 + -8*q^87 + (3*a-2)*q^89 + 16*q^91 + (3*a+4)*q^93 + (4*a+8)*q^95 + (a+14)*q^97 + (-a+1)*q^99 + -2*q^101 + (-6*a-8)*q^105 + (6*a+4)*q^107 + (4*a+6)*q^109 + (-5*a-4)*q^111 + (a-2)*q^113 + (-3*a-4)*q^115 + (-2*a+6)*q^117 + -4*a*q^119 + 1*q^121 + (4*a-8)*q^123 + (a+8)*q^125 + -4*a*q^127 + (2*a+8)*q^129 + (-6*a-4)*q^131 + -8*a*q^133 + (-5*a-12)*q^135 + (a-10)*q^137 + (-2*a-12)*q^139 + -8*a*q^141 + (-2*a-2)*q^143 + (-4*a-12)*q^145 + (13*a-16)*q^147 + (4*a-2)*q^149 + 6*a*q^151 + (-2*a+2)*q^153 + (5*a+12)*q^155 + (a-6)*q^157 + (2*a+16)*q^159 + (10*a-8)*q^161 + 4*q^163 + (a+4)*q^165 + -8*q^167 + (4*a+7)*q^169 + (-4*a+4)*q^171 + (4*a+6)*q^173 + -24*q^175 + (5*a-20)*q^177 + (-a+8)*q^179 + (3*a-6)*q^181 + (-4*a+8)*q^183 + (-7*a-16)*q^185 + 2*q^187 + (6*a+8)*q^189 + (-a+12)*q^191 + (-2*a-6)*q^193 + (-8*a-16)*q^195 + (-8*a-2)*q^197 + 8*a*q^199 +  ...

-------------------------------------------------------
176E (old = 88A), dim = 1

CONGRUENCES:
Modular Degree = 2^8
Ker(ModPolar)  = Z/2^4 + Z/2^4 + Z/2^4 + Z/2^4
= C(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2^2 + Z/2^2) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
176F (old = 88B), dim = 2

CONGRUENCES:
Modular Degree = 2^9
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4 + Z/2^4 + Z/2^4 + Z/2^4
= C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2^2 + Z/2^2) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
176G (old = 44A), dim = 1

CONGRUENCES:
Modular Degree = 2^9
Ker(ModPolar)  = Z/2^3 + Z/2^3 + Z/2^3 + Z/2^3 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
176H (old = 11A), dim = 1

CONGRUENCES:
Modular Degree = 2^9
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(177)
Weight 2

-------------------------------------------------------
J_0(177), dim = 19

-------------------------------------------------------
177A (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 13.742933627996464616 + 0.87024312355709621662e-3i
Omega-         = 6.5355209491431860529 + -0.16742966802090419992e-3i
L(1)           =

HECKE EIGENFORM:
a^2+a-1 = 0,
f(q) = q + a*q^2 + -1*q^3 + (-a-1)*q^4 + (-2*a-1)*q^5 + -a*q^6 + (a-3)*q^7 + (-2*a-1)*q^8 + 1*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 + -1*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 + (-5*a+5)*q^38 + (2*a+5)*q^39 + 5*q^40 + (5*a+5)*q^41 + (4*a-1)*q^42 + (-6*a-5)*q^43 + (-a-3)*q^44 + (-2*a-1)*q^45 + (-3*a-1)*q^46 + (-3*a-9)*q^47 + -3*a*q^48 + (-7*a+3)*q^49 + -3*a*q^51 + (5*a+7)*q^52 + (2*a+5)*q^53 + -a*q^54 + -5*q^55 + (7*a+1)*q^56 + -5*a*q^57 + (8*a-1)*q^58 + -1*q^59 + (-a-3)*q^60 + (3*a-5)*q^61 + (4*a-9)*q^62 + (a-3)*q^63 + (-2*a+1)*q^64 + (8*a+9)*q^65 + (a-2)*q^66 + (6*a+7)*q^67 + -3*q^68 + (a+4)*q^69 + (-6*a+7)*q^70 + (-8*a-3)*q^71 + (-2*a-1)*q^72 + (3*a-1)*q^73 + (-5*a+3)*q^74 + -5*q^76 + (-7*a-1)*q^77 + (3*a+2)*q^78 + -3*q^79 + (3*a-6)*q^80 + 1*q^81 + 5*q^82 + (-a-1)*q^83 + (-3*a-2)*q^84 + (3*a-6)*q^85 + (a-6)*q^86 + (a-7)*q^87 + -5*q^88 + (-11*a-7)*q^89 + (a-2)*q^90 + (3*a+13)*q^91 + (4*a+5)*q^92 + (9*a+5)*q^93 + (-6*a-3)*q^94 + (5*a-10)*q^95 + (-a-5)*q^96 + 3*q^97 + (10*a-7)*q^98 + (2*a+1)*q^99 + 6*a*q^101 + (3*a-3)*q^102 + (-2*a-2)*q^103 + (8*a+9)*q^104 + (-7*a-1)*q^105 + (3*a+2)*q^106 + (-5*a+4)*q^107 + (a+1)*q^108 + (3*a-6)*q^109 + -5*a*q^110 + (-3*a+2)*q^111 + (-12*a+3)*q^112 + -9*q^113 + (5*a-5)*q^114 + (7*a+6)*q^115 + (-7*a-6)*q^116 + (-2*a-5)*q^117 + -a*q^118 + (-12*a+3)*q^119 + -5*q^120 + -6*q^121 + (-8*a+3)*q^122 + (-5*a-5)*q^123 + (5*a+14)*q^124 + (10*a+5)*q^125 + (-4*a+1)*q^126 + (8*a+11)*q^127 + (a-12)*q^128 + (6*a+5)*q^129 + (a+8)*q^130 + (-14*a-12)*q^131 + (a+3)*q^132 + (-20*a+5)*q^133 + (a+6)*q^134 + (2*a+1)*q^135 + (3*a-6)*q^136 + (2*a+11)*q^137 + (3*a+1)*q^138 + (-2*a+13)*q^139 + (-a-8)*q^140 + (3*a+9)*q^141 + (5*a-8)*q^142 + (-8*a-9)*q^143 + 3*a*q^144 + (-15*a-5)*q^145 + (-4*a+3)*q^146 + (7*a-3)*q^147 + (2*a-1)*q^148 + (5*a+16)*q^149 + (9*a-3)*q^151 + (5*a-10)*q^152 + 3*a*q^153 + (6*a-7)*q^154 + (a+23)*q^155 + (-5*a-7)*q^156 + 9*q^157 + -3*a*q^158 + (-2*a-5)*q^159 + (-9*a-7)*q^160 + 11*q^161 + a*q^162 + (-9*a-13)*q^163 + (-5*a-10)*q^164 + 5*q^165 + -1*q^166 + (13*a-1)*q^167 + (-7*a-1)*q^168 + (16*a+16)*q^169 + (-9*a+3)*q^170 + 5*a*q^171 + (5*a+11)*q^172 + (-a+13)*q^173 + (-8*a+1)*q^174 + (-3*a+6)*q^176 + 1*q^177 + (4*a-11)*q^178 + (4*a-3)*q^179 + (a+3)*q^180 + (15*a+13)*q^181 + (10*a+3)*q^182 + (-3*a+5)*q^183 + (7*a+6)*q^184 + (7*a-4)*q^185 + (-4*a+9)*q^186 + (-3*a+6)*q^187 + (9*a+12)*q^188 + (-a+3)*q^189 + (-15*a+5)*q^190 + (12*a+9)*q^191 + (2*a-1)*q^192 + 8*q^193 + 3*a*q^194 + (-8*a-9)*q^195 + (-3*a+4)*q^196 + (-14*a-12)*q^197 + (-a+2)*q^198 + (-9*a-11)*q^199 +  ...

-------------------------------------------------------
177B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 5
Torsion Bound  = 5
|L(1)/Omega|   = 2^2/5
Sha Bound      = 2^2*5

ANALYTIC INVARIANTS:

Omega+         = 2.9607455109723686598 + -0.26987682691176799867e-3i
Omega-         = 10.068712217248862188 + 0.12500703772949553672e-3i
L(1)           = 2.3685964186177817108

HECKE EIGENFORM:
a^2-a-1 = 0,
f(q) = q + a*q^2 + 1*q^3 + (a-1)*q^4 + 1*q^5 + a*q^6 + (-a+1)*q^7 + (-2*a+1)*q^8 + 1*q^9 + a*q^10 + (-2*a+3)*q^11 + (a-1)*q^12 + -1*q^13 + -1*q^14 + 1*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 + 1*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 + (-a+3)*q^38 + -1*q^39 + (-2*a+1)*q^40 + (5*a-3)*q^41 + -1*q^42 + (8*a-5)*q^43 + (3*a-5)*q^44 + 1*q^45 + (3*a+3)*q^46 + (a+5)*q^47 + -3*a*q^48 + (-a-5)*q^49 + -4*a*q^50 + (-3*a+2)*q^51 + (-a+1)*q^52 + (8*a-5)*q^53 + a*q^54 + (-2*a+3)*q^55 + (-a+3)*q^56 + (3*a-4)*q^57 + (2*a-1)*q^58 + -1*q^59 + (a-1)*q^60 + (-3*a+1)*q^61 + (-2*a-3)*q^62 + (-a+1)*q^63 + (2*a+1)*q^64 + -1*q^65 + (a-2)*q^66 + (-8*a+7)*q^67 + (2*a-5)*q^68 + 3*a*q^69 + -1*q^70 + (6*a-1)*q^71 + (-2*a+1)*q^72 + (a+1)*q^73 + (-5*a-1)*q^74 + -4*q^75 + (-4*a+7)*q^76 + (-3*a+5)*q^77 + -a*q^78 + (-8*a+9)*q^79 + -3*a*q^80 + 1*q^81 + (2*a+5)*q^82 + (3*a+5)*q^83 + (a-2)*q^84 + (-3*a+2)*q^85 + (3*a+8)*q^86 + (-a+3)*q^87 + (-4*a+7)*q^88 + (5*a-5)*q^89 + a*q^90 + (a-1)*q^91 + 3*q^92 + (-3*a+1)*q^93 + (6*a+1)*q^94 + (3*a-4)*q^95 + (a-5)*q^96 + (6*a-5)*q^97 + (-6*a-1)*q^98 + (-2*a+3)*q^99 + (-4*a+4)*q^100 + (-2*a+8)*q^101 + (-a-3)*q^102 + (-2*a+10)*q^103 + (2*a-1)*q^104 + (-a+1)*q^105 + (3*a+8)*q^106 + (-11*a+6)*q^107 + (a-1)*q^108 + (11*a-8)*q^109 + (a-2)*q^110 + (-a-4)*q^111 + 3*q^112 + (-12*a+5)*q^113 + (-a+3)*q^114 + 3*a*q^115 + (3*a-4)*q^116 + -1*q^117 + -a*q^118 + (-2*a+5)*q^119 + (-2*a+1)*q^120 + (-8*a+2)*q^121 + (-2*a-3)*q^122 + (5*a-3)*q^123 + (a-4)*q^124 + -9*q^125 + -1*q^126 + (16*a-5)*q^127 + (a+12)*q^128 + (8*a-5)*q^129 + -a*q^130 + (10*a-8)*q^131 + (3*a-5)*q^132 + (4*a-7)*q^133 + (-a-8)*q^134 + 1*q^135 + (-a+8)*q^136 + (-4*a-15)*q^137 + (3*a+3)*q^138 + (10*a-15)*q^139 + (a-2)*q^140 + (a+5)*q^141 + (5*a+6)*q^142 + (2*a-3)*q^143 + -3*a*q^144 + (-a+3)*q^145 + (2*a+1)*q^146 + (-a-5)*q^147 + (-4*a+3)*q^148 + (a-8)*q^149 + -4*a*q^150 + (-5*a+7)*q^151 + (5*a-10)*q^152 + (-3*a+2)*q^153 + (2*a-3)*q^154 + (-3*a+1)*q^155 + (-a+1)*q^156 + (-14*a+5)*q^157 + (a-8)*q^158 + (8*a-5)*q^159 + (a-5)*q^160 + -3*q^161 + a*q^162 + (-3*a+3)*q^163 + (-3*a+8)*q^164 + (-2*a+3)*q^165 + (8*a+3)*q^166 + (-15*a+3)*q^167 + (-a+3)*q^168 + -12*q^169 + (-a-3)*q^170 + (3*a-4)*q^171 + (-5*a+13)*q^172 + (3*a+15)*q^173 + (2*a-1)*q^174 + (4*a-4)*q^175 + (-3*a+6)*q^176 + -1*q^177 + 5*q^178 + (-16*a+3)*q^179 + (a-1)*q^180 + (-3*a-19)*q^181 + 1*q^182 + (-3*a+1)*q^183 + (-3*a-6)*q^184 + (-a-4)*q^185 + (-2*a-3)*q^186 + (-7*a+12)*q^187 + (5*a-4)*q^188 + (-a+1)*q^189 + (-a+3)*q^190 + (4*a-5)*q^191 + (2*a+1)*q^192 + (-8*a-12)*q^193 + (a+6)*q^194 + -1*q^195 + (-5*a+4)*q^196 + (2*a-8)*q^197 + (a-2)*q^198 + (-3*a+9)*q^199 + (8*a-4)*q^200 +  ...

-------------------------------------------------------
177C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4*31
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*31 + Z/2^2*31
= A(Z/2 + Z/2 + Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/31 + Z/31)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 9.3115715054499743671 + 0.12280269763216105404e-3i
Omega-         = 1.2914314831424890934 + 0.12014792761083324757e-2i
L(1)           =

HECKE EIGENFORM:
a^2+3*a+1 = 0,
f(q) = q + a*q^2 + 1*q^3 + (-3*a-3)*q^4 + -3*q^5 + a*q^6 + (-a-5)*q^7 + (4*a+3)*q^8 + 1*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 + 1*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 + (-7*a-3)*q^38 + (6*a+9)*q^39 + (-12*a-9)*q^40 + (5*a+7)*q^41 + (-2*a+1)*q^42 + (-6*a-3)*q^43 + (-3*a+9)*q^44 + -3*q^45 + (-a+1)*q^46 + (3*a+3)*q^47 + (-3*a+2)*q^48 + (7*a+17)*q^49 + 4*a*q^50 + a*q^51 + (9*a-9)*q^52 + (-4*a-5)*q^53 + a*q^54 + (12*a+21)*q^55 + (-11*a-11)*q^56 + (3*a+2)*q^57 + (-4*a+1)*q^58 + 1*q^59 + (9*a+9)*q^60 + (-5*a-1)*q^61 + (-2*a+1)*q^62 + (-a-5)*q^63 + (-6*a-7)*q^64 + (-18*a-27)*q^65 + (5*a+4)*q^66 + (2*a+1)*q^67 + (6*a+3)*q^68 + (-a-4)*q^69 + (6*a-3)*q^70 + (-2*a-1)*q^71 + (4*a+3)*q^72 + (-5*a-5)*q^73 + (7*a+5)*q^74 + 4*q^75 + (12*a+3)*q^76 + (15*a+31)*q^77 + (-9*a-6)*q^78 + -3*q^79 + (9*a-6)*q^80 + 1*q^81 + (-8*a-5)*q^82 + (-3*a-9)*q^83 + (9*a+12)*q^84 + -3*a*q^85 + (15*a+6)*q^86 + (-a-7)*q^87 + (8*a-5)*q^88 + (-5*a-7)*q^89 + -3*a*q^90 + (-21*a-39)*q^91 + (6*a+9)*q^92 + (-a-5)*q^93 + (-6*a-3)*q^94 + (-9*a-6)*q^95 + (3*a-3)*q^96 + (4*a+1)*q^97 + (-4*a-7)*q^98 + (-4*a-7)*q^99 + (-12*a-12)*q^100 + (-2*a-12)*q^101 + (-3*a-1)*q^102 + (2*a-14)*q^103 + (-18*a+3)*q^104 + (3*a+15)*q^105 + (7*a+4)*q^106 + (13*a+24)*q^107 + (-3*a-3)*q^108 + (3*a+8)*q^109 + (-15*a-12)*q^110 + (-5*a-8)*q^111 + (4*a-13)*q^112 + (2*a+11)*q^113 + (-7*a-3)*q^114 + (3*a+12)*q^115 + (15*a+18)*q^116 + (6*a+9)*q^117 + a*q^118 + (-2*a+1)*q^119 + (-12*a-9)*q^120 + (8*a+22)*q^121 + (14*a+5)*q^122 + (5*a+7)*q^123 + (9*a+12)*q^124 + 3*q^125 + (-2*a+1)*q^126 + (-4*a-13)*q^127 + (5*a+12)*q^128 + (-6*a-3)*q^129 + (27*a+18)*q^130 + (2*a+12)*q^131 + (-3*a+9)*q^132 + (-8*a-7)*q^133 + (-5*a-2)*q^134 + -3*q^135 + (-9*a-4)*q^136 + (-4*a-15)*q^137 + (-a+1)*q^138 + (6*a-3)*q^139 + (-27*a-36)*q^140 + (3*a+3)*q^141 + (5*a+2)*q^142 + (-6*a-39)*q^143 + (-3*a+2)*q^144 + (3*a+21)*q^145 + (10*a+5)*q^146 + (7*a+17)*q^147 + (-6*a+9)*q^148 + (13*a+12)*q^149 + 4*a*q^150 + (-3*a+1)*q^151 + (-19*a-6)*q^152 + a*q^153 + (-14*a-15)*q^154 + (3*a+15)*q^155 + (9*a-9)*q^156 + (-8*a-13)*q^157 + -3*a*q^158 + (-4*a-5)*q^159 + (-9*a+9)*q^160 + (6*a+19)*q^161 + a*q^162 + (a-7)*q^163 + (9*a-6)*q^164 + (12*a+21)*q^165 + 3*q^166 + (-7*a-23)*q^167 + (-11*a-11)*q^168 + 32*q^169 + (9*a+3)*q^170 + (3*a+2)*q^171 + (-27*a-9)*q^172 + (a+17)*q^173 + (-4*a+1)*q^174 + (-4*a-20)*q^175 + (-23*a-26)*q^176 + 1*q^177 + (8*a+5)*q^178 + (10*a+13)*q^179 + (9*a+9)*q^180 + (9*a+15)*q^181 + (24*a+21)*q^182 + (-5*a-1)*q^183 + (-7*a-8)*q^184 + (15*a+24)*q^185 + (-2*a+1)*q^186 + (5*a+4)*q^187 + 9*a*q^188 + (-a-5)*q^189 + (21*a+9)*q^190 + (6*a-3)*q^191 + (-6*a-7)*q^192 + (-12*a-32)*q^193 + (-11*a-4)*q^194 + (-18*a-27)*q^195 + (-9*a-30)*q^196 + (-10*a-16)*q^197 + (5*a+4)*q^198 + (17*a+31)*q^199 + (16*a+12)*q^200 +  ...

-------------------------------------------------------
177D (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^4*229
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*229 + Z/2^2*229
= A(Z/2 + Z/2 + Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/229 + Z/229)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 229
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 0.41403824981107048589 + -0.68328693027475243279e-4i
Omega-         = 0.75484170148404238848e-3 + -1.2455554713509046339i
L(1)           = 0.41403825544920930662

HECKE EIGENFORM:
a^3-4*a-1 = 0,
f(q) = q + a*q^2 + -1*q^3 + (a^2-2)*q^4 + (-a^2+a+2)*q^5 + -a*q^6 + (a+3)*q^7 + 1*q^8 + 1*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 + -1*q^24 + (a^2-3*a-3)*q^25 + (-a^2-1)*q^26 + -1*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 + (a-1)*q^38 + (a^2+a-4)*q^39 + (-a^2+a+2)*q^40 + (-2*a^2+3*a+5)*q^41 + (-a^2-3*a)*q^42 + (-3*a^2+5*a+10)*q^43 + (-3*a-5)*q^44 + (-a^2+a+2)*q^45 + (-2*a^2-a-1)*q^46 + (4*a^2-a-7)*q^47 + (2*a^2-a-4)*q^48 + (a^2+6*a+2)*q^49 + (-3*a^2+a+1)*q^50 + (-3*a^2+2*a+7)*q^51 + (2*a^2-3*a-9)*q^52 + (a^2-5*a-2)*q^53 + -a*q^54 + (-a^2+a+4)*q^55 + (a+3)*q^56 + (a^2-5)*q^57 + (a^2-a+2)*q^58 + 1*q^59 + (-a+3)*q^60 + (4*a^2+a-11)*q^61 + (-a^2+7*a+2)*q^62 + (a+3)*q^63 + (-2*a-7)*q^64 + (-3*a^2+3*a+8)*q^65 + (a^2+2*a+1)*q^66 + (5*a^2+a-10)*q^67 + (-a^2-a+12)*q^68 + (a^2+2*a-3)*q^69 + (a^2-3*a-2)*q^70 + (a^2-3*a+6)*q^71 + 1*q^72 + (-4*a^2-3*a+13)*q^73 + (-2*a^2-3*a-1)*q^74 + (-a^2+3*a+3)*q^75 + (3*a^2-a-10)*q^76 + (-4*a^2-5*a+5)*q^77 + (a^2+1)*q^78 + (a^2-3*a-2)*q^79 + (a^2-4*a+5)*q^80 + 1*q^81 + (3*a^2-3*a-2)*q^82 + (6*a^2-5*a-17)*q^83 + (-3*a^2-2*a+5)*q^84 + (-a^2+6*a-9)*q^85 + (5*a^2-2*a-3)*q^86 + (-2*a^2-a+9)*q^87 + (-a^2-a+2)*q^88 + (-4*a^2+3*a+3)*q^89 + (a^2-2*a-1)*q^90 + (-4*a^2-3*a+11)*q^91 + (a^2-5*a-8)*q^92 + (-2*a^2+a+1)*q^93 + (-a^2+9*a+4)*q^94 + (-3*a^2+2*a+9)*q^95 + (-a^2+4*a+4)*q^96 + (a^2-5*a+2)*q^97 + (6*a^2+6*a+1)*q^98 + (-a^2-a+2)*q^99 + (-a^2-5*a+3)*q^100 + (-2*a-4)*q^101 + (2*a^2-5*a-3)*q^102 + (-4*a^2+6*a+10)*q^103 + (-a^2-a+4)*q^104 + (2*a^2-a-5)*q^105 + (-5*a^2+2*a+1)*q^106 + (-3*a^2+4*a+19)*q^107 + (-a^2+2)*q^108 + (3*a^2-2*a-19)*q^109 + (a^2-1)*q^110 + (a^2+2*a-1)*q^111 + (-5*a^2-a+10)*q^112 + (a^2+7*a-6)*q^113 + (-a+1)*q^114 + (-3*a^2+4*a+7)*q^115 + (-5*a^2+4*a+19)*q^116 + (-a^2-a+4)*q^117 + a*q^118 + (7*a^2-a-18)*q^119 + (a^2-a-2)*q^120 + (a^2+5*a-5)*q^121 + (a^2+5*a+4)*q^122 + (2*a^2-3*a-5)*q^123 + (3*a^2+1)*q^124 + (3*a^2+a-12)*q^125 + (a^2+3*a)*q^126 + (-a^2-a+6)*q^127 + (-4*a^2+a+8)*q^128 + (3*a^2-5*a-10)*q^129 + (3*a^2-4*a-3)*q^130 + (6*a^2-8*a-18)*q^131 + (3*a+5)*q^132 + (-3*a^2+a+14)*q^133 + (a^2+10*a+5)*q^134 + (a^2-a-2)*q^135 + (3*a^2-2*a-7)*q^136 + (-a^2+5*a+2)*q^137 + (2*a^2+a+1)*q^138 + (7*a^2-3*a-20)*q^139 + (a^2-9)*q^140 + (-4*a^2+a+7)*q^141 + (-3*a^2+10*a+1)*q^142 + (-a^2+3*a+10)*q^143 + (-2*a^2+a+4)*q^144 + (6*a^2-5*a-17)*q^145 + (-3*a^2-3*a-4)*q^146 + (-a^2-6*a-2)*q^147 + (-a^2-5*a-4)*q^148 + (-a^2-4*a-9)*q^149 + (3*a^2-a-1)*q^150 + (6*a^2-3*a-19)*q^151 + (-a^2+5)*q^152 + (3*a^2-2*a-7)*q^153 + (-5*a^2-11*a-4)*q^154 + (-4*a^2+7*a+1)*q^155 + (-2*a^2+3*a+9)*q^156 + (-5*a^2-3*a+10)*q^157 + (-3*a^2+2*a+1)*q^158 + (-a^2+5*a+2)*q^159 + (-2*a^2+7*a-3)*q^160 + (-5*a^2-7*a+8)*q^161 + a*q^162 + (3*a-3)*q^163 + (a^2+4*a-7)*q^164 + (a^2-a-4)*q^165 + (-5*a^2+7*a+6)*q^166 + (-2*a^2+3*a+19)*q^167 + (-a-3)*q^168 + (-3*a^2+a+5)*q^169 + (6*a^2-13*a-1)*q^170 + (-a^2+5)*q^171 + (4*a^2+7*a-15)*q^172 + (2*a^2+11*a-7)*q^173 + (-a^2+a-2)*q^174 + (-8*a-8)*q^175 + (-a^2+4*a+9)*q^176 + -1*q^177 + (3*a^2-13*a-4)*q^178 + (-3*a^2+3*a-8)*q^179 + (a-3)*q^180 + (4*a^2-a-1)*q^181 + (-3*a^2-5*a-4)*q^182 + (-4*a^2-a+11)*q^183 + (-a^2-2*a+3)*q^184 + (-a^2+2*a+3)*q^185 + (a^2-7*a-2)*q^186 + (3*a^2-4*a-15)*q^187 + (a^2+2*a+13)*q^188 + (-a-3)*q^189 + (2*a^2-3*a-3)*q^190 + (-3*a^2-5*a+4)*q^191 + (2*a+7)*q^192 + (-2*a^2+2*a+10)*q^193 + (-5*a^2+6*a+1)*q^194 + (3*a^2-3*a-8)*q^195 + (4*a^2+13*a+2)*q^196 + (4*a^2+2*a-16)*q^197 + (-a^2-2*a-1)*q^198 + (-2*a^2-7*a+5)*q^199 + (a^2-3*a-3)*q^200 +  ...

-------------------------------------------------------
177E (old = 59A), dim = 5

CONGRUENCES:
Modular Degree = 31*229
Ker(ModPolar)  = Z/31*229 + Z/31*229
= C(Z/31 + Z/31) + D(Z/229 + Z/229)

-------------------------------------------------------
Gamma_0(178)
Weight 2

-------------------------------------------------------
J_0(178), dim = 21

-------------------------------------------------------
178A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*7
Ker(ModPolar)  = Z/2^2*7 + Z/2^2*7
= D(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.2901984296210333357 + 0.13579484442421969805e-3i
Omega-         = 0.25600694645926566765e-3 + -0.93329445262053687192i
L(1)           = 0.6450992183836569108
w1             = 1.2901984296210333357 + 0.13579484442421969805e-3i
w2             = 0.25600694645926566765e-3 + -0.93329445262053687192i
c4             = 2137.6246422163160615 + -2.2227673478611567943i
c6             = -85131.870911122147424 + 151.8831661269114514i
j              = 6697.075328357206963 + -8.6410383857369534257i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 2*q^3 + 1*q^4 + 2*q^5 + -2*q^6 + -1*q^8 + 1*q^9 + -2*q^10 + 2*q^12 + -4*q^13 + 4*q^15 + 1*q^16 + 2*q^17 + -1*q^18 + -2*q^19 + 2*q^20 + 8*q^23 + -2*q^24 + -1*q^25 + 4*q^26 + -4*q^27 + -4*q^30 + -1*q^32 + -2*q^34 + 1*q^36 + 2*q^38 + -8*q^39 + -2*q^40 + -10*q^41 + -2*q^43 + 2*q^45 + -8*q^46 + -8*q^47 + 2*q^48 + -7*q^49 + 1*q^50 + 4*q^51 + -4*q^52 + 6*q^53 + 4*q^54 + -4*q^57 + 10*q^59 + 4*q^60 + -4*q^61 + 1*q^64 + -8*q^65 + -8*q^67 + 2*q^68 + 16*q^69 + 8*q^71 + -1*q^72 + -2*q^73 + -2*q^75 + -2*q^76 + 8*q^78 + 8*q^79 + 2*q^80 + -11*q^81 + 10*q^82 + 14*q^83 + 4*q^85 + 2*q^86 + 1*q^89 + -2*q^90 + 8*q^92 + 8*q^94 + -4*q^95 + -2*q^96 + -2*q^97 + 7*q^98 + -1*q^100 + -16*q^101 + -4*q^102 + 20*q^103 + 4*q^104 + -6*q^106 + 8*q^107 + -4*q^108 + -2*q^109 + 18*q^113 + 4*q^114 + 16*q^115 + -4*q^117 + -10*q^118 + -4*q^120 + -11*q^121 + 4*q^122 + -20*q^123 + -12*q^125 + -1*q^128 + -4*q^129 + 8*q^130 + -4*q^131 + 8*q^134 + -8*q^135 + -2*q^136 + -10*q^137 + -16*q^138 + -4*q^139 + -16*q^141 + -8*q^142 + 1*q^144 + 2*q^146 + -14*q^147 + -4*q^149 + 2*q^150 + 8*q^151 + 2*q^152 + 2*q^153 + -8*q^156 + 22*q^157 + -8*q^158 + 12*q^159 + -2*q^160 + 11*q^162 + -6*q^163 + -10*q^164 + -14*q^166 + 16*q^167 + 3*q^169 + -4*q^170 + -2*q^171 + -2*q^172 + 2*q^173 + 20*q^177 + -1*q^178 + -12*q^179 + 2*q^180 + 24*q^181 + -8*q^183 + -8*q^184 + -8*q^188 + 4*q^190 + -8*q^191 + 2*q^192 + 14*q^193 + 2*q^194 + -16*q^195 + -7*q^196 + 20*q^197 + 16*q^199 + 1*q^200 +  ...

-------------------------------------------------------
178B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^5 + Z/2^5
= C(Z/2 + Z/2) + D(Z/2^2 + Z/2^2) + E(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 2^2/3
Sha Bound      = 2^2*3

ANALYTIC INVARIANTS:

Omega+         = 1.4759465479706424892 + 0.35492769711855372305e-4i
Omega-         = 0.93925122170118068981e-4 + 2.243558197563928492i
L(1)           = 1.9679287311965306918
w1             = -0.73802023654640630363 + -1.1217968451668201737i
w2             = -0.73792631142423618556 + 1.1217613523971083183i
c4             = -287.19958246991197214 + -0.15107173817298981858i
c6             = 24633.885313670614034 + 0.37139743844913722903i
j              = 64.922864591577076688 + 0.9671825772851202201e-1i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^3 + 1*q^4 + 3*q^5 + 1*q^6 + -4*q^7 + 1*q^8 + -2*q^9 + 3*q^10 + -6*q^11 + 1*q^12 + 2*q^13 + -4*q^14 + 3*q^15 + 1*q^16 + 3*q^17 + -2*q^18 + 5*q^19 + 3*q^20 + -4*q^21 + -6*q^22 + -3*q^23 + 1*q^24 + 4*q^25 + 2*q^26 + -5*q^27 + -4*q^28 + 3*q^30 + 5*q^31 + 1*q^32 + -6*q^33 + 3*q^34 + -12*q^35 + -2*q^36 + -10*q^37 + 5*q^38 + 2*q^39 + 3*q^40 + -4*q^42 + -1*q^43 + -6*q^44 + -6*q^45 + -3*q^46 + 12*q^47 + 1*q^48 + 9*q^49 + 4*q^50 + 3*q^51 + 2*q^52 + 9*q^53 + -5*q^54 + -18*q^55 + -4*q^56 + 5*q^57 + 12*q^59 + 3*q^60 + -10*q^61 + 5*q^62 + 8*q^63 + 1*q^64 + 6*q^65 + -6*q^66 + -4*q^67 + 3*q^68 + -3*q^69 + -12*q^70 + -6*q^71 + -2*q^72 + -1*q^73 + -10*q^74 + 4*q^75 + 5*q^76 + 24*q^77 + 2*q^78 + -10*q^79 + 3*q^80 + 1*q^81 + -12*q^83 + -4*q^84 + 9*q^85 + -1*q^86 + -6*q^88 + -1*q^89 + -6*q^90 + -8*q^91 + -3*q^92 + 5*q^93 + 12*q^94 + 15*q^95 + 1*q^96 + 17*q^97 + 9*q^98 + 12*q^99 + 4*q^100 + 3*q^102 + 5*q^103 + 2*q^104 + -12*q^105 + 9*q^106 + 18*q^107 + -5*q^108 + -7*q^109 + -18*q^110 + -10*q^111 + -4*q^112 + -6*q^113 + 5*q^114 + -9*q^115 + -4*q^117 + 12*q^118 + -12*q^119 + 3*q^120 + 25*q^121 + -10*q^122 + 5*q^124 + -3*q^125 + 8*q^126 + -7*q^127 + 1*q^128 + -1*q^129 + 6*q^130 + -6*q^132 + -20*q^133 + -4*q^134 + -15*q^135 + 3*q^136 + 18*q^137 + -3*q^138 + 8*q^139 + -12*q^140 + 12*q^141 + -6*q^142 + -12*q^143 + -2*q^144 + -1*q^146 + 9*q^147 + -10*q^148 + -12*q^149 + 4*q^150 + -16*q^151 + 5*q^152 + -6*q^153 + 24*q^154 + 15*q^155 + 2*q^156 + 14*q^157 + -10*q^158 + 9*q^159 + 3*q^160 + 12*q^161 + 1*q^162 + -1*q^163 + -18*q^165 + -12*q^166 + -12*q^167 + -4*q^168 + -9*q^169 + 9*q^170 + -10*q^171 + -1*q^172 + 3*q^173 + -16*q^175 + -6*q^176 + 12*q^177 + -1*q^178 + 18*q^179 + -6*q^180 + -10*q^181 + -8*q^182 + -10*q^183 + -3*q^184 + -30*q^185 + 5*q^186 + -18*q^187 + 12*q^188 + 20*q^189 + 15*q^190 + -3*q^191 + 1*q^192 + -22*q^193 + 17*q^194 + 6*q^195 + 9*q^196 + 12*q^198 + -10*q^199 + 4*q^200 +  ...

-------------------------------------------------------
178C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 2^3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 11.214251115668047373 + -0.63917750463948108941e-3i
Omega-         = 2.993404459012531709 + -0.41109436556092092218e-3i
L(1)           =

HECKE EIGENFORM:
a^2+2*a-1 = 0,
f(q) = q + -1*q^2 + a*q^3 + 1*q^4 + (-2*a-3)*q^5 + -a*q^6 + -2*q^7 + -1*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 + 1*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 + -1*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 + (-a-2)*q^38 + -2*a*q^39 + (2*a+3)*q^40 + (4*a+4)*q^41 + 2*a*q^42 + (-5*a-2)*q^43 + 2*a*q^44 + (2*a+10)*q^45 + (a+8)*q^46 + a*q^48 + -3*q^49 + (-4*a-8)*q^50 + (-5*a+2)*q^51 + -2*q^52 + (4*a-1)*q^53 + (a+2)*q^54 + (2*a-4)*q^55 + 2*q^56 + 1*q^57 + (4*a+4)*q^58 + (8*a+6)*q^59 + (a-2)*q^60 + (-4*a+2)*q^61 + (a-2)*q^62 + (4*a+4)*q^63 + 1*q^64 + (4*a+6)*q^65 + (4*a-2)*q^66 + (-4*a-12)*q^67 + (2*a-1)*q^68 + (-6*a-1)*q^69 + (-4*a-6)*q^70 + (-6*a-8)*q^71 + (2*a+2)*q^72 + (-8*a-9)*q^73 + (-4*a-10)*q^74 + 4*q^75 + (a+2)*q^76 + -4*a*q^77 + 2*a*q^78 + (-2*a-8)*q^79 + (-2*a-3)*q^80 + (6*a+5)*q^81 + (-4*a-4)*q^82 + (-8*a-6)*q^83 + -2*a*q^84 + (4*a-1)*q^85 + (5*a+2)*q^86 + (4*a-4)*q^87 + -2*a*q^88 + -1*q^89 + (-2*a-10)*q^90 + 4*q^91 + (-a-8)*q^92 + (4*a-1)*q^93 + (-3*a-8)*q^95 + -a*q^96 + (10*a+9)*q^97 + 3*q^98 + (4*a-4)*q^99 + (4*a+8)*q^100 + (-4*a+4)*q^101 + (5*a-2)*q^102 + (-9*a-16)*q^103 + 2*q^104 + (-2*a+4)*q^105 + (-4*a+1)*q^106 + (6*a+4)*q^107 + (-a-2)*q^108 + (4*a+15)*q^109 + (-2*a+4)*q^110 + (2*a+4)*q^111 + -2*q^112 + (4*a-6)*q^113 + -1*q^114 + (15*a+26)*q^115 + (-4*a-4)*q^116 + (4*a+4)*q^117 + (-8*a-6)*q^118 + (-4*a+2)*q^119 + (-a+2)*q^120 + (-8*a-7)*q^121 + (4*a-2)*q^122 + (-4*a+4)*q^123 + (-a+2)*q^124 + (-2*a-17)*q^125 + (-4*a-4)*q^126 + (-a-18)*q^127 + -1*q^128 + (8*a-5)*q^129 + (-4*a-6)*q^130 + (4*a+20)*q^131 + (-4*a+2)*q^132 + (-2*a-4)*q^133 + (4*a+12)*q^134 + (3*a+8)*q^135 + (-2*a+1)*q^136 + (-12*a-10)*q^137 + (6*a+1)*q^138 + -12*q^139 + (4*a+6)*q^140 + (6*a+8)*q^142 + -4*a*q^143 + (-2*a-2)*q^144 + (4*a+20)*q^145 + (8*a+9)*q^146 + -3*a*q^147 + (4*a+10)*q^148 + (-4*a-12)*q^149 + -4*q^150 + (4*a+2)*q^151 + (-a-2)*q^152 + (6*a-2)*q^153 + 4*a*q^154 + (-5*a-4)*q^155 + -2*a*q^156 + -6*q^157 + (2*a+8)*q^158 + (-9*a+4)*q^159 + (2*a+3)*q^160 + (2*a+16)*q^161 + (-6*a-5)*q^162 + -a*q^163 + (4*a+4)*q^164 + (-8*a+2)*q^165 + (8*a+6)*q^166 + 20*q^167 + 2*a*q^168 + -9*q^169 + (-4*a+1)*q^170 + (-2*a-6)*q^171 + (-5*a-2)*q^172 + (2*a+17)*q^173 + (-4*a+4)*q^174 + (-8*a-16)*q^175 + 2*a*q^176 + (-10*a+8)*q^177 + 1*q^178 + (10*a+8)*q^179 + (2*a+10)*q^180 + (8*a+10)*q^181 + -4*q^182 + (10*a-4)*q^183 + (a+8)*q^184 + (-16*a-38)*q^185 + (-4*a+1)*q^186 + (-10*a+4)*q^187 + (2*a+4)*q^189 + (3*a+8)*q^190 + (7*a-6)*q^191 + a*q^192 + (8*a+10)*q^193 + (-10*a-9)*q^194 + (-2*a+4)*q^195 + -3*q^196 + -8*q^197 + (-4*a+4)*q^198 + (6*a-4)*q^199 + (-4*a-8)*q^200 +  ...

-------------------------------------------------------
178D (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^5 + Z/2^5
= A(Z/2 + Z/2) + B(Z/2^2 + Z/2^2) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^3*71
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 5
Torsion Bound  = 2*5
|L(1)/Omega|   = 2/5
Sha Bound      = 2^3*5

ANALYTIC INVARIANTS:

Omega+         = 6.6762486720877942311 + -0.71639567262129466074e-3i
Omega-         = 0.28388246171104983712e-3 + -1.4936856159424830736i
L(1)           = 2.6704994842097025374

HECKE EIGENFORM:
a^3-a^2-8*a+4 = 0,
f(q) = q + 1*q^2 + a*q^3 + 1*q^4 + -a*q^5 + a*q^6 + (-1/2*a^2-1/2*a+3)*q^7 + 1*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 + 1*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 + 1*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 + (a-4)*q^38 + (-a^2+a-2)*q^39 + -a*q^40 + (-a^2+a+4)*q^41 + (-a^2-a+2)*q^42 + (-a^2+2*a+2)*q^43 + 2*q^44 + (-a^2-5*a+4)*q^45 + (3/2*a^2+1/2*a-7)*q^46 + (a^2+a-2)*q^47 + a*q^48 + (2*a-1)*q^49 + (a^2-5)*q^50 + (-a^2-4*a+4)*q^51 + (1/2*a^2-3/2*a-3)*q^52 + (2*a^2-a-4)*q^53 + (a^2+2*a-4)*q^54 + -2*a*q^55 + (-1/2*a^2-1/2*a+3)*q^56 + (a^2-4*a)*q^57 + (-3/2*a^2+5/2*a+9)*q^58 + (-2*a-2)*q^59 + -a^2*q^60 + (-3/2*a^2+1/2*a+9)*q^61 + (1/2*a^2-1/2*a-9)*q^62 + (-1/2*a^2-9/2*a-5)*q^63 + 1*q^64 + (a^2-a+2)*q^65 + 2*a*q^66 + (-2*a+6)*q^67 + (-a^2+4)*q^68 + (2*a^2+5*a-6)*q^69 + (a^2+a-2)*q^70 + (-a^2-3*a+10)*q^71 + (a^2-3)*q^72 + (-a^2+4*a+4)*q^73 + (1/2*a^2-3/2*a+1)*q^74 + (a^2+3*a-4)*q^75 + (a-4)*q^76 + (-a^2-a+6)*q^77 + (-a^2+a-2)*q^78 + (-a^2+a+2)*q^79 + -a*q^80 + (4*a+5)*q^81 + (-a^2+a+4)*q^82 + (-2*a^2+4*a+10)*q^83 + (-a^2-a+2)*q^84 + (a^2+4*a-4)*q^85 + (-a^2+2*a+2)*q^86 + (a^2-3*a+6)*q^87 + 2*q^88 + -1*q^89 + (-a^2-5*a+4)*q^90 + (2*a^2-10)*q^91 + (3/2*a^2+1/2*a-7)*q^92 + (-5*a-2)*q^93 + (a^2+a-2)*q^94 + (-a^2+4*a)*q^95 + a*q^96 + (-a^2+4*a-2)*q^97 + (2*a-1)*q^98 + (2*a^2-6)*q^99 + (a^2-5)*q^100 + (5/2*a^2-3/2*a-7)*q^101 + (-a^2-4*a+4)*q^102 + (3/2*a^2-7/2*a-11)*q^103 + (1/2*a^2-3/2*a-3)*q^104 + (2*a^2+6*a-4)*q^105 + (2*a^2-a-4)*q^106 + (-2*a^2-4*a+16)*q^107 + (a^2+2*a-4)*q^108 + (-2*a^2-a+16)*q^109 + -2*a*q^110 + (-a^2+5*a-2)*q^111 + (-1/2*a^2-1/2*a+3)*q^112 + (-2*a^2+2*a+18)*q^113 + (a^2-4*a)*q^114 + (-2*a^2-5*a+6)*q^115 + (-3/2*a^2+5/2*a+9)*q^116 + (-3/2*a^2-11/2*a+13)*q^117 + (-2*a-2)*q^118 + (4*a+8)*q^119 + -a^2*q^120 + -7*q^121 + (-3/2*a^2+1/2*a+9)*q^122 + (-4*a+4)*q^123 + (1/2*a^2-1/2*a-9)*q^124 + (-a^2+2*a+4)*q^125 + (-1/2*a^2-9/2*a-5)*q^126 + (1/2*a^2+7/2*a-9)*q^127 + 1*q^128 + (a^2-6*a+4)*q^129 + (a^2-a+2)*q^130 + (2*a^2-4*a-14)*q^131 + 2*a*q^132 + (a^2+a-10)*q^133 + (-2*a+6)*q^134 + (-3*a^2-4*a+4)*q^135 + (-a^2+4)*q^136 + (-a^2+3*a+12)*q^137 + (2*a^2+5*a-6)*q^138 + (4*a+4)*q^139 + (a^2+a-2)*q^140 + (2*a^2+6*a-4)*q^141 + (-a^2-3*a+10)*q^142 + (a^2-3*a-6)*q^143 + (a^2-3)*q^144 + (-a^2+3*a-6)*q^145 + (-a^2+4*a+4)*q^146 + (2*a^2-a)*q^147 + (1/2*a^2-3/2*a+1)*q^148 + (5/2*a^2-3/2*a-19)*q^149 + (a^2+3*a-4)*q^150 + (3/2*a^2-5/2*a-17)*q^151 + (a-4)*q^152 + (-2*a^2-4*a-8)*q^153 + (-a^2-a+6)*q^154 + (5*a+2)*q^155 + (-a^2+a-2)*q^156 + (a^2-3*a+4)*q^157 + (-a^2+a+2)*q^158 + (a^2+12*a-8)*q^159 + -a*q^160 + (-6*a-14)*q^161 + (4*a+5)*q^162 + (-a^2-2*a-2)*q^163 + (-a^2+a+4)*q^164 + -2*a^2*q^165 + (-2*a^2+4*a+10)*q^166 + (4*a^2-16)*q^167 + (-a^2-a+2)*q^168 + (-2*a+1)*q^169 + (a^2+4*a-4)*q^170 + (-3*a^2+5*a+8)*q^171 + (-a^2+2*a+2)*q^172 + (2*a^2+a-12)*q^173 + (a^2-3*a+6)*q^174 + (1/2*a^2-7/2*a-11)*q^175 + 2*q^176 + (-2*a^2-2*a)*q^177 + -1*q^178 + (-2*a^2+12)*q^179 + (-a^2-5*a+4)*q^180 + (1/2*a^2-3/2*a-15)*q^181 + (2*a^2-10)*q^182 + (-a^2-3*a+6)*q^183 + (3/2*a^2+1/2*a-7)*q^184 + (a^2-5*a+2)*q^185 + (-5*a-2)*q^186 + (-2*a^2+8)*q^187 + (a^2+a-2)*q^188 + (-2*a^2-6*a-4)*q^189 + (-a^2+4*a)*q^190 + (3/2*a^2-15/2*a-7)*q^191 + a*q^192 + (a^2-3*a)*q^193 + (-a^2+4*a-2)*q^194 + (10*a-4)*q^195 + (2*a-1)*q^196 + (-3/2*a^2-3/2*a+13)*q^197 + (2*a^2-6)*q^198 + (a^2-a-22)*q^199 + (a^2-5)*q^200 +  ...

-------------------------------------------------------
178E (old = 89A), dim = 1

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^4 + Z/2^4
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
178F (old = 89B), dim = 1

CONGRUENCES:
Modular Degree = 2^2*5^2
Ker(ModPolar)  = Z/5 + Z/5 + Z/2^2*5 + Z/2^2*5
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + G(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
178G (old = 89C), dim = 5

CONGRUENCES:
Modular Degree = 2^6*5^2*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*5 + Z/2*5 + Z/2*5*7 + Z/2*5*7
= A(Z/7 + Z/7) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
Gamma_0(179)
Weight 2

-------------------------------------------------------
J_0(179), dim = 15

-------------------------------------------------------
179A (new) , dim = 1

CONGRUENCES:
Modular Degree = 3^2
Ker(ModPolar)  = Z/3^2 + Z/3^2
= C(Z/3^2 + Z/3^2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 1
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 2.2601096704584473815 + -0.18803291377114924885e-3i
Omega-         = 0.63873630928700727399e-3 + 5.1080983105424529852i
L(1)           = 2.260109678280275026
w1             = 1.1297354670745801871 + -2.5541431717281120672i
w2             = -2.2601096704584473815 + 0.18803291377114924885e-3i
c4             = 47.994597127494485787 + 0.12510528552863437456e-1i
c6             = 648.35374822996437313 + 0.37758987252492876552i
j              = -616.63483499567104066 + 0.32025515729411914166i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 2*q^4 + 3*q^5 + -4*q^7 + -3*q^9 + 6*q^10 + 4*q^11 + -1*q^13 + -8*q^14 + -4*q^16 + 1*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 + -6*q^38 + 12*q^41 + -11*q^43 + 8*q^44 + -9*q^45 + 12*q^46 + 1*q^47 + 9*q^49 + 8*q^50 + -2*q^52 + 12*q^55 + 6*q^58 + -5*q^59 + 14*q^61 + -16*q^62 + 12*q^63 + -8*q^64 + -3*q^65 + -9*q^67 + 2*q^68 + -24*q^70 + 10*q^73 + 4*q^74 + -6*q^76 + -16*q^77 + 10*q^79 + -12*q^80 + 9*q^81 + 24*q^82 + 17*q^83 + 3*q^85 + -22*q^86 + -1*q^89 + -18*q^90 + 4*q^91 + 12*q^92 + 2*q^94 + -9*q^95 + -14*q^97 + 18*q^98 + -12*q^99 + 8*q^100 + 9*q^101 + -6*q^103 + -4*q^107 + -14*q^109 + 24*q^110 + 16*q^112 + -4*q^113 + 18*q^115 + 6*q^116 + 3*q^117 + -10*q^118 + -4*q^119 + 5*q^121 + 28*q^122 + -16*q^124 + -3*q^125 + 24*q^126 + -8*q^127 + -6*q^130 + -6*q^131 + 12*q^133 + -18*q^134 + -10*q^137 + 7*q^139 + -24*q^140 + -4*q^143 + 12*q^144 + 9*q^145 + 20*q^146 + 4*q^148 + -18*q^149 + 21*q^151 + -3*q^153 + -32*q^154 + -24*q^155 + 4*q^157 + 20*q^158 + -24*q^160 + -24*q^161 + 18*q^162 + -20*q^163 + 24*q^164 + 34*q^166 + 10*q^167 + -12*q^169 + 6*q^170 + 9*q^171 + -22*q^172 + -14*q^173 + -16*q^175 + -16*q^176 + -2*q^178 + 1*q^179 + -18*q^180 + 2*q^181 + 8*q^182 + 6*q^185 + 4*q^187 + 2*q^188 + -18*q^190 + -13*q^191 + -6*q^193 + -28*q^194 + 18*q^196 + -2*q^197 + -24*q^198 + 17*q^199 +  ...

-------------------------------------------------------
179B (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 7^2
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 46.805009495470698879 + 0.81492347902690145164e-2i
Omega-         = 0.2044952866427762807e-2 + -11.549024546790233516i
L(1)           =

HECKE EIGENFORM:
a^3+a^2-2*a-1 = 0,
f(q) = 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 + 1*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 + (3*a^2-4*a-3)*q^38 + (4*a+3)*q^39 + (a^2+4*a+2)*q^40 + (2*a^2-3*a-4)*q^41 + (a^2-a-1)*q^42 + (4*a^2+a-3)*q^43 + (-3*a^2-2*a+7)*q^44 + (-3*a-2)*q^45 + (3*a^2+2*a-3)*q^46 + (-3*a^2-a+9)*q^47 + (a^2+4*a)*q^48 + (a^2-2*a-6)*q^49 + (a^2+2)*q^50 + (-2*a^2-5*a+2)*q^51 + (-3*a^2+a+5)*q^52 + (-5*a^2-3*a+4)*q^53 + (3*a^2-2)*q^54 + -1*q^55 + (a-2)*q^56 + (4*a+1)*q^57 + (5*a^2-2*a-5)*q^58 + (-6*a^2-6*a+7)*q^59 + (-a^2-a)*q^60 + (2*a^2-14)*q^61 + (-5*a^2-2*a)*q^62 + (-2*a+3)*q^63 + (3*a^2+5*a-2)*q^64 + (4*a^2+3*a)*q^65 + -1*q^66 + (8*a^2+7*a-7)*q^67 + (-4*a^2-5*a+11)*q^68 + (-2*a-5)*q^69 + (-2*a^2+a+1)*q^70 + (5*a^2+8*a-6)*q^71 + (-a-5)*q^72 + (-11*a^2-7*a+15)*q^73 + (-7*a^2-a+3)*q^74 + (-3*a^2-3*a+2)*q^75 + (-a^2+3*a-1)*q^76 + (-3*a^2-a+6)*q^77 + (4*a^2+3*a)*q^78 + (6*a^2+9*a-11)*q^79 + (3*a^2+2*a+1)*q^80 + (-4*a^2-7*a+4)*q^81 + (-5*a^2+2)*q^82 + (6*a^2+a-10)*q^83 + (a-1)*q^84 + (-3*a^2-2*a-2)*q^85 + (-3*a^2+5*a+4)*q^86 + (2*a-3)*q^87 + (3*a^2+a-7)*q^88 + (7*a^2+5*a-6)*q^89 + (-3*a^2-2*a)*q^90 + (2*a^2-4*a+1)*q^91 + (5*a^2+3*a-13)*q^92 + (5*a^2+7*a+2)*q^93 + (2*a^2+3*a-3)*q^94 + (4*a^2+a)*q^95 + (-a^2-4*a+1)*q^96 + (3*a^2+11*a-4)*q^97 + (-3*a^2-4*a+1)*q^98 + (-5*a^2-2*a+11)*q^99 + (-5*a^2-2*a+9)*q^100 + (a^2+4*a-12)*q^101 + (-3*a^2-2*a-2)*q^102 + (-7*a^2-5*a+8)*q^103 + (2*a^2+7*a-1)*q^104 + a^2*q^105 + (2*a^2-6*a-5)*q^106 + (3*a^2-5*a-5)*q^107 + (a^2+2*a-5)*q^108 + (2*a^2+a-16)*q^109 + -a*q^110 + (4*a^2+5*a+4)*q^111 + (5*a^2-2*a-6)*q^112 + (2*a^2+8*a+6)*q^113 + (4*a^2+a)*q^114 + (-2*a^2-5*a)*q^115 + (3*a^2+5*a-11)*q^116 + (-a^2-7*a+3)*q^117 + (-5*a-6)*q^118 + (-8*a^2+a+12)*q^119 + (-4*a^2-8*a-3)*q^120 + (-7*a^2-4*a+5)*q^121 + (-2*a^2-10*a+2)*q^122 + (3*a^2+3*a+2)*q^123 + (3*a^2-1)*q^124 + (5*a^2+a-3)*q^125 + (-2*a^2+3*a)*q^126 + (-10*a^2-13*a+10)*q^127 + (-6*a^2+2*a+13)*q^128 + (-a^2-6*a-1)*q^129 + (-a^2+8*a+4)*q^130 + (-4*a^2-a+8)*q^131 + (2*a^2+a-4)*q^132 + (6*a^2-4*a-5)*q^133 + (-a^2+9*a+8)*q^134 + (-4*a-1)*q^135 + (5*a^2-3*a-14)*q^136 + (-6*a^2-9*a+5)*q^137 + (-2*a^2-5*a)*q^138 + (-3*a^2+3*a+7)*q^139 + (a^2-a)*q^140 + (a^2-2*a-6)*q^141 + (3*a^2+4*a+5)*q^142 + (-5*a^2-2*a+9)*q^143 + (5*a^2-3*a-10)*q^144 + (2*a^2-3*a)*q^145 + (4*a^2-7*a-11)*q^146 + (2*a^2+6*a+5)*q^147 + (-3*a+7)*q^148 + (-6*a^2-5*a+8)*q^149 + (-4*a-3)*q^150 + (5*a^2+8*a)*q^151 + (-2*a^2+5*a+5)*q^152 + (-10*a^2+a+21)*q^153 + (2*a^2-3)*q^154 + (2*a^2+12*a+5)*q^155 + (-a^2-2)*q^156 + (-3*a+3)*q^157 + (3*a^2+a+6)*q^158 + (3*a^2+9*a+1)*q^159 + (-3*a^2-a-1)*q^160 + (6*a^2+2*a-11)*q^161 + (-3*a^2-4*a-4)*q^162 + (5*a^2+a-3)*q^163 + (a^2-2*a+3)*q^164 + (a+1)*q^165 + (-5*a^2+2*a+6)*q^166 + (a^2+6*a-2)*q^167 + (-a^2+a+2)*q^168 + (7*a^2-a-10)*q^169 + (a^2-8*a-3)*q^170 + (5*a^2-5*a-7)*q^171 + (-4*a+3)*q^172 + (4*a^2+13*a-5)*q^173 + (2*a^2-3*a)*q^174 + (-a^2-3*a+6)*q^175 + (4*a^2+3*a-11)*q^176 + (6*a^2+11*a-1)*q^177 + (-2*a^2+8*a+7)*q^178 + -1*q^179 + (a^2+1)*q^180 + (-4*a^2+6*a-2)*q^181 + (-6*a^2+5*a+2)*q^182 + (10*a+12)*q^183 + (-8*a^2-7*a+11)*q^184 + (a^2+12*a+4)*q^185 + (2*a^2+12*a+5)*q^186 + (-11*a^2-7*a+27)*q^187 + (7*a^2+3*a-16)*q^188 + (5*a^2-a-6)*q^189 + (-3*a^2+8*a+4)*q^190 + (-6*a^2-5*a+17)*q^191 + (-5*a^2-9*a-1)*q^192 + (-9*a^2+3*a+25)*q^193 + (8*a^2+2*a+3)*q^194 + (-3*a^2-11*a-4)*q^195 + (-3*a^2-a+9)*q^196 + (9*a+11)*q^197 + (3*a^2+a-5)*q^198 + (8*a^2-8*a-22)*q^199 + (a^2-a-9)*q^200 +  ...

-------------------------------------------------------
179C (new) , dim = 11

CONGRUENCES:
Modular Degree = 2^3*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3^2 + Z/2*3^2
= A(Z/3^2 + Z/3^2) + B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^6*313*137707*536747147
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 89
Torsion Bound  = 89
|L(1)/Omega|   = 2^3/89
Sha Bound      = 2^3*89

ANALYTIC INVARIANTS:

Omega+         = 9.5112347437106633602 + -0.36957349964593779582e-2i
Omega-         = 0.94554943929184180268e-1 + 244.65092114300399009i
L(1)           = 0.85494251341372337407

HECKE EIGENFORM:
a^11+3*a^10-14*a^9-45*a^8+59*a^7+225*a^6-58*a^5-427*a^4-76*a^3+240*a^2+56*a-16 = 0,
f(q) = 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 + (-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^2-719/17*a+158/17)*q^38 + (-23/17*a^10-9/4*a^9+1509/68*a^8+1073/34*a^7-499/4*a^6-9599/68*a^5+18731/68*a^4+7449/34*a^3-13341/68*a^2-1205/17*a+287/17)*q^39 + (-5/17*a^10-1/2*a^9+157/34*a^8+251/34*a^7-25*a^6-615/17*a^5+1873/34*a^4+1102/17*a^3-716/17*a^2-480/17*a+72/17)*q^40 + (41/34*a^10+2*a^9-659/34*a^8-939/34*a^7+106*a^6+2054/17*a^5-7681/34*a^4-6177/34*a^3+5283/34*a^2+914/17*a-268/17)*q^41 + (53/34*a^10+5/2*a^9-422/17*a^8-1179/34*a^7+269/2*a^6+5227/34*a^5-4847/17*a^4-8101/34*a^3+3312/17*a^2+1320/17*a-300/17)*q^42 + (-9/8*a^10-15/8*a^9+73/4*a^8+213/8*a^7-811/8*a^6-977/8*a^5+889/4*a^4+1595/8*a^3-161*a^2-145/2*a+19)*q^43 + (1/17*a^10-14/17*a^8-3/17*a^7+4*a^6+38/17*a^5-172/17*a^4-149/17*a^3+235/17*a^2+198/17*a-96/17)*q^44 + (25/34*a^10+3/4*a^9-853/68*a^8-165/17*a^7+297/4*a^6+2529/68*a^5-11983/68*a^4-647/17*a^3+9489/68*a^2-177/17*a-146/17)*q^45 + (32/17*a^10+3*a^9-516/17*a^8-708/17*a^7+167*a^6+3137/17*a^5-6116/17*a^4-4836/17*a^3+4239/17*a^2+1474/17*a-352/17)*q^46 + 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(1/4*a^10+3/4*a^9-4*a^8-43/4*a^7+89/4*a^6+201/4*a^5-101/2*a^4-349/4*a^3+44*a^2+43*a-14)*q^172 + (-11/17*a^10-7/4*a^9+667/68*a^8+865/34*a^7-195/4*a^6-8183/68*a^5+5851/68*a^4+7035/34*a^3-2299/68*a^2-3183/34*a-32/17)*q^173 + (-37/34*a^10-3/2*a^9+293/17*a^8+353/17*a^7-91*a^6-1536/17*a^5+3012/17*a^4+4391/34*a^3-3085/34*a^2-467/17*a+110/17)*q^174 + (37/68*a^10+5/4*a^9-155/17*a^8-1233/68*a^7+213/4*a^6+5775/68*a^5-2135/17*a^4-9559/68*a^3+3387/34*a^2+922/17*a-208/17)*q^175 + (-15/17*a^10-2*a^9+244/17*a^8+470/17*a^7-81*a^6-2066/17*a^5+3124/17*a^4+3170/17*a^3-2454/17*a^2-1100/17*a+352/17)*q^176 + (287/136*a^10+29/8*a^9-2281/68*a^8-6811/136*a^7+1441/8*a^6+29827/136*a^5-25141/68*a^4-44701/136*a^3+7779/34*a^2+3029/34*a-350/17)*q^177 + (-55/68*a^10-7/4*a^9+218/17*a^8+1661/68*a^7-281/4*a^6-7343/68*a^5+2654/17*a^4+11085/68*a^3-2071/17*a^2-878/17*a+198/17)*q^178 + 1*q^179 + (11/17*a^10+3/2*a^9-325/34*a^8-390/17*a^7+91/2*a^6+3981/34*a^5-2509/34*a^4-3764/17*a^3+699/34*a^2+1940/17*a-104/17)*q^180 + (31/34*a^10+3/2*a^9-251/17*a^8-705/34*a^7+163/2*a^6+3099/34*a^5-2989/17*a^4-4823/34*a^3+2087/17*a^2+961/17*a+8/17)*q^181 + (11/17*a^10+a^9-188/17*a^8-237/17*a^7+64*a^6+1047/17*a^5-2368/17*a^4-1639/17*a^3+1531/17*a^2+580/17*a-104/17)*q^182 + (-197/68*a^10-9/2*a^9+3217/68*a^8+4195/68*a^7-527/2*a^6-4498/17*a^5+38797/68*a^4+25273/68*a^3-26303/68*a^2-2197/34*a+342/17)*q^183 + (-61/17*a^10-6*a^9+990/17*a^8+1424/17*a^7-323*a^6-6330/17*a^5+11920/17*a^4+9718/17*a^3-8300/17*a^2-2864/17*a+688/17)*q^184 + (-35/17*a^10-3*a^9+575/17*a^8+700/17*a^7-191*a^6-3030/17*a^5+7278/17*a^4+4399/17*a^3-5471/17*a^2-912/17*a+470/17)*q^185 + (-27/34*a^10-3/2*a^9+223/17*a^8+727/34*a^7-147/2*a^6-3355/34*a^5+2645/17*a^4+5587/34*a^3-1583/17*a^2-1041/17*a+208/17)*q^186 + (-9/17*a^10-a^9+143/17*a^8+231/17*a^7-47*a^6-1022/17*a^5+1888/17*a^4+1749/17*a^3-1741/17*a^2-1051/17*a+320/17)*q^187 + (3/17*a^10+a^9-42/17*a^8-264/17*a^7+10*a^6+1355/17*a^5-108/17*a^4-2572/17*a^3-349/17*a^2+1376/17*a+86/17)*q^188 + (-109/68*a^10-11/4*a^9+865/34*a^8+2673/68*a^7-547/4*a^6-12421/68*a^5+9663/34*a^4+21035/68*a^3-3178/17*a^2-2412/17*a+440/17)*q^189 + (43/34*a^10+5/2*a^9-352/17*a^8-1217/34*a^7+235/2*a^6+5561/34*a^5-4565/17*a^4-8685/34*a^3+3446/17*a^2+1299/17*a-330/17)*q^190 + (123/136*a^10+15/8*a^9-473/34*a^8-3735/136*a^7+559/8*a^6+17917/136*a^5-2058/17*a^4-30873/136*a^3+2221/68*a^2+1408/17*a+207/17)*q^191 + (-101/34*a^10-11/2*a^9+1635/34*a^8+1299/17*a^7-266*a^6-11505/34*a^5+9774/17*a^4+8910/17*a^3-6742/17*a^2-2876/17*a+632/17)*q^192 + (33/34*a^10+5/4*a^9-1111/68*a^8-296/17*a^7+385/4*a^6+5313/68*a^5-15823/68*a^4-2110/17*a^3+13351/68*a^2+1247/34*a-275/17)*q^193 + (19/17*a^10+2*a^9-300/17*a^8-465/17*a^7+95*a^6+1997/17*a^5-3404/17*a^4-2916/17*a^3+2306/17*a^2+940/17*a-192/17)*q^194 + (125/34*a^10+6*a^9-1011/17*a^8-1403/17*a^7+657/2*a^6+6132/17*a^5-24135/34*a^4-9338/17*a^3+16761/34*a^2+2872/17*a-679/17)*q^195 + (-8/17*a^10-a^9+112/17*a^8+245/17*a^7-28*a^6-1171/17*a^5+526/17*a^4+2059/17*a^3+415/17*a^2-904/17*a-354/17)*q^196 + (-107/68*a^10-9/4*a^9+885/34*a^8+2123/68*a^7-597/4*a^6-9319/68*a^5+11769/34*a^4+13801/68*a^3-4769/17*a^2-970/17*a+664/17)*q^197 + (-a^10-a^9+17*a^8+14*a^7-99*a^6-62*a^5+227*a^4+93*a^3-170*a^2-26*a+8)*q^198 + (-419/136*a^10-41/8*a^9+3375/68*a^8+9723/136*a^7-2189/8*a^6-43275/136*a^5+40471/68*a^4+67021/136*a^3-14327/34*a^2-2716/17*a+489/17)*q^199 + (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^4-2423/17*a^3+2782/17*a^2+736/17*a-192/17)*q^200 +  ...

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Gamma_0(180)
Weight 2

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J_0(180), dim = 25

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180A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= D(Z/3 + Z/3) + E(Z/2) + F(Z/2) + H(Z/2 + Z/2) + I(Z/2)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/2
Sha Bound      = 2*3^2

ANALYTIC INVARIANTS:

Omega+         = 1.3129678278534108327 + -0.52945838992102755416e-4i
Omega-         = 0.16512779941596605048e-4 + -1.6307553965564221165i
L(1)           = 0.65648391446046980226
w1             = 0.16512779941596605048e-4 + -1.6307553965564221165i
w2             = -1.3129678278534108327 + 0.52945838992102755416e-4i
c4             = 576.00673950054812121 + 0.72536836138928687968e-1i
c6             = 9506.5252210301795818 + 3.2990919669762840714i
j              = 3278.2583024944329498 + 0.93018993013902121793i

HECKE EIGENFORM:
f(q) = q + 1*q^5 + 2*q^7 + 2*q^13 + 6*q^17 + -4*q^19 + -6*q^23 + 1*q^25 + -6*q^29 + -4*q^31 + 2*q^35 + 2*q^37 + -6*q^41 + -10*q^43 + 6*q^47 + -3*q^49 + 6*q^53 + -12*q^59 + 2*q^61 + 2*q^65 + 2*q^67 + 12*q^71 + 2*q^73 + 8*q^79 + -6*q^83 + 6*q^85 + 6*q^89 + 4*q^91 + -4*q^95 + 2*q^97 + -6*q^101 + 14*q^103 + 6*q^107 + 2*q^109 + 6*q^113 + -6*q^115 + 12*q^119 + -11*q^121 + 1*q^125 + 2*q^127 + -8*q^133 + -18*q^137 + -4*q^139 + -6*q^145 + 6*q^149 + 20*q^151 + -4*q^155 + -22*q^157 + -12*q^161 + -10*q^163 + -18*q^167 + -9*q^169 + 6*q^173 + 2*q^175 + 12*q^179 + -10*q^181 + 2*q^185 + 12*q^191 + 26*q^193 + -18*q^197 + 8*q^199 +  ...

-------------------------------------------------------
180B (old = 90A), dim = 1

CONGRUENCES:
Modular Degree = 2^6*3
Ker(ModPolar)  = Z/2^3 + Z/2^3 + Z/2^3*3 + Z/2^3*3
= C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
180C (old = 90B), dim = 1

CONGRUENCES:
Modular Degree = 2^6*3
Ker(ModPolar)  = Z/2^3 + Z/2^3 + Z/2^3*3 + Z/2^3*3
= B(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/3) + I(Z/2 + Z/2 + Z/2 + Z/2)

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180D (old = 90C), dim = 1

CONGRUENCES:
Modular Degree = 2^8*3
Ker(ModPolar)  = Z/2^4 + Z/2^4 + Z/2^4*3 + Z/2^4*3
= A(Z/3 + Z/3) + B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2)

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180E (old = 45A), dim = 1

CONGRUENCES:
Modular Degree = 2^10
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^4 + Z/2^4 + Z/2^4 + Z/2^4
= A(Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2) + G(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2) + H(Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
180F (old = 36A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= A(Z/2) + B(Z/3 + Z/3) + C(Z/3) + E(Z/2) + H(Z/2*3) + I(Z/2)

-------------------------------------------------------
180G (old = 30A), dim = 1

CONGRUENCES:
Modular Degree = 2^10*3^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^4*3 + Z/2^4*3 + Z/2^4*3 + Z/2^4*3
= B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2) + H(Z/3 + Z/3 + Z/3 + Z/3) + I(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
180H (old = 20A), dim = 1

CONGRUENCES:
Modular Degree = 2^3*3^3
Ker(ModPolar)  = Z/3 + Z/3 + Z/2*3 + Z/2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + C(Z/3) + E(Z/2) + F(Z/2*3) + G(Z/3 + Z/3 + Z/3 + Z/3) + I(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
180I (old = 15A), dim = 1

CONGRUENCES:
Modular Degree = 2^13
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^4 + Z/2^4 + Z/2^4 + Z/2^4
= A(Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2)

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Gamma_0(181)
Weight 2

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J_0(181), dim = 14

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181A (new) , dim = 5

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 61*397
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 597.72557321235914405 + -0.1425832820313682928i
Omega-         = 0.32965241302437504019e-2 + -14.033366990456339126i
L(1)           =

HECKE EIGENFORM:
a^5+3*a^4-a^3-7*a^2-2*a+1 = 0,
f(q) = 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 + (4*a^4+5*a^3-11*a^2-8*a+3)*q^38 + (2*a^4+4*a^3-9*a^2-16*a+5)*q^39 + (3*a^4+5*a^3-9*a^2-9*a+7)*q^40 + (a^4+a^3+a^2+4*a-5)*q^41 + (-a^4-2*a^3+6*a^2+6*a-2)*q^42 + (3*a^3+6*a^2-8*a-10)*q^43 + (2*a^4+5*a^3-7*a^2-11*a+6)*q^44 + (-3*a^4-9*a^3+a^2+16*a+8)*q^45 + (-3*a^4-4*a^3+11*a^2+6*a-2)*q^46 + (-3*a^4-5*a^3+7*a^2+8*a+1)*q^47 + (a^4+2*a^3+2*a-1)*q^48 + (a^2-2*a-2)*q^49 + (-2*a^4-6*a^3+3*a^2+11*a)*q^50 + (-a^3+5*a-1)*q^51 + (a^4+3*a^3-4*a^2-8*a+7)*q^52 + (-5*a^4-9*a^3+9*a^2+12*a+4)*q^53 + (-5*a^4-8*a^3+11*a^2+10*a-3)*q^54 + (-8*a^4-18*a^3+21*a^2+41*a-6)*q^55 + (-a^4-a^3+4*a^2+6*a-4)*q^56 + (2*a^4+4*a^3-5*a^2-11*a+3)*q^57 + (2*a^4+2*a^3-8*a^2-7*a+1)*q^58 + (3*a^4+2*a^3-13*a^2-5*a+1)*q^59 + (4*a^4+8*a^3-10*a^2-17*a+4)*q^60 + (a^4-2*a^3-11*a^2+4*a+8)*q^61 + (2*a^4-7*a^2+2*a+2)*q^62 + (-a^4+3*a^2-6*a-5)*q^63 + (4*a^3+5*a^2-7*a-5)*q^64 + (-7*a^4-20*a^3+11*a^2+44*a-2)*q^65 + (-4*a^4-4*a^3+18*a^2+15*a-5)*q^66 + (3*a^4+8*a^3-9*a^2-16*a+11)*q^67 + (-a^4-4*a^3+10*a+2)*q^68 + (2*a^4+a^3-9*a^2-2*a+1)*q^69 + (6*a^4+10*a^3-15*a^2-17*a+3)*q^70 + (2*a^4+8*a^3-2*a^2-24*a-9)*q^71 + (-3*a^3-6*a^2+2*a+3)*q^72 + (8*a^4+18*a^3-15*a^2-36*a)*q^73 + (3*a^4+4*a^3-10*a^2-5*a-1)*q^74 + (-2*a^4-5*a^3+8*a^2+16*a-6)*q^75 + (-a^4+3*a^3+4*a^2-9*a)*q^76 + (a^4+9*a^3+4*a^2-21*a+2)*q^77 + (-2*a^4-7*a^3-2*a^2+9*a-2)*q^78 + (3*a^4+6*a^3-3*a^2-6*a-6)*q^79 + (2*a^4+10*a^3+4*a^2-23*a-9)*q^80 + (-4*a^4-10*a^3+8*a^2+25*a+2)*q^81 + (-2*a^4+2*a^3+11*a^2-3*a-1)*q^82 + (-3*a^4+18*a^2+5*a-15)*q^83 + (-3*a^4-5*a^3+7*a^2+12*a-3)*q^84 + (-a^4-2*a^3+2*a+9)*q^85 + (3*a^4+6*a^3-8*a^2-10*a)*q^86 + (2*a^4+6*a^3+a^2-6*a+2)*q^87 + (-a^4-5*a^3+5*a^2+20*a-4)*q^88 + (4*a^4+8*a^3-8*a^2-17*a-2)*q^89 + (-2*a^3-5*a^2+2*a+3)*q^90 + (7*a^4+15*a^3-20*a^2-35*a+5)*q^91 + (a^4+2*a^3-3*a^2-2*a-1)*q^92 + (-a^4-3*a^3+4*a^2+7*a-3)*q^93 + (4*a^4+4*a^3-13*a^2-5*a+3)*q^94 + (-a^4-5*a^3+3*a^2+14*a-8)*q^95 + (a^4+5*a^3-a^2-13*a+3)*q^96 + (-4*a^4-13*a^3+3*a^2+25*a+6)*q^97 + (a^3-2*a^2-2*a)*q^98 + (-3*a^4-9*a^3-2*a^2+6*a+3)*q^99 + (5*a^3+9*a^2-10*a-20)*q^100 + (-2*a^4-9*a^3+4*a^2+26*a-5)*q^101 + (-a^4+5*a^2-a)*q^102 + (-5*a^4-13*a^3+10*a^2+32*a-2)*q^103 + (-6*a^4-15*a^3+11*a^2+27*a-5)*q^104 + (3*a^4+7*a^3-9*a^2-21*a+7)*q^105 + (6*a^4+4*a^3-23*a^2-6*a+5)*q^106 + (9*a^4+17*a^3-24*a^2-34*a+4)*q^107 + (a^4-2*a^3-3*a^2+7*a-3)*q^108 + (-5*a^4-17*a^3+7*a^2+39*a)*q^109 + (6*a^4+13*a^3-15*a^2-22*a+8)*q^110 + (-5*a^4-8*a^3+16*a^2+17*a-4)*q^111 + (-6*a^4-11*a^3+17*a^2+22*a+1)*q^112 + (-8*a^4-17*a^3+22*a^2+37*a-3)*q^113 + (-2*a^4-3*a^3+3*a^2+7*a-2)*q^114 + (-2*a^4-a^3+8*a^2-4*a-3)*q^115 + (-2*a^4-4*a^3+a^2+7*a+8)*q^116 + (a^4+2*a^3+2*a^2+8*a+5)*q^117 + (-7*a^4-10*a^3+16*a^2+7*a-3)*q^118 + (-4*a^4-5*a^3+15*a^2+8*a-8)*q^119 + (-4*a^4-10*a^3+7*a^2+20*a-6)*q^120 + (8*a^4+23*a^3-10*a^2-45*a+3)*q^121 + (-5*a^4-10*a^3+11*a^2+10*a-1)*q^122 + (3*a^4+5*a^3-17*a^2-21*a+7)*q^123 + (-2*a^4+3*a^3+12*a^2-8*a-14)*q^124 + (5*a^4+18*a^3+3*a^2-39*a-16)*q^125 + (3*a^4+2*a^3-13*a^2-7*a+1)*q^126 + (6*a^4+10*a^3-15*a^2-17*a+5)*q^127 + (10*a^4+19*a^3-21*a^2-33*a+2)*q^128 + (-a^4+3*a^2-3*a+2)*q^129 + (a^4+4*a^3-5*a^2-16*a+7)*q^130 + (7*a^4+17*a^3-15*a^2-37*a-5)*q^131 + (-2*a^4-8*a^3+5*a^2+21*a-6)*q^132 + (3*a^4+8*a^3-11*a^2-16*a+7)*q^133 + (-a^4-6*a^3+5*a^2+17*a-3)*q^134 + (3*a^4+12*a^3-2*a^2-27*a+4)*q^135 + (3*a^4+5*a^3-9*a^2-8*a+5)*q^136 + (-a^4-4*a^3-4*a^2+6*a+10)*q^137 + (-5*a^4-7*a^3+12*a^2+5*a-2)*q^138 + (-5*a^4-17*a^3-a^2+40*a+12)*q^139 + (-2*a^4-3*a^3-a^2+3*a+16)*q^140 + (-a^4-a^3+5*a^2+a-1)*q^141 + (2*a^4-10*a^2-5*a-2)*q^142 + (12*a^4+22*a^3-42*a^2-58*a+21)*q^143 + (-a^4+2*a^2-11*a-8)*q^144 + (-5*a^4-16*a^3+6*a^2+40*a+10)*q^145 + (-6*a^4-7*a^3+20*a^2+16*a-8)*q^146 + (-2*a^4-a^3+8*a^2+3*a-1)*q^147 + (-7*a^4-19*a^3+10*a^2+39*a+11)*q^148 + (-8*a^4-13*a^3+22*a^2+19*a-9)*q^149 + (a^4+6*a^3+2*a^2-10*a+2)*q^150 + (-2*a^4-2*a^3+10*a^2+13*a-7)*q^151 + (-2*a^4-7*a^3+6*a^2+14*a-5)*q^152 + (-3*a^4-7*a^3+4*a^2+11*a+4)*q^153 + (6*a^4+5*a^3-14*a^2+4*a-1)*q^154 + (11*a^4+28*a^3-15*a^2-59*a-16)*q^155 + (-5*a^4-12*a^3+13*a^2+26*a-8)*q^156 + (-6*a^4-12*a^3+19*a^2+23*a-6)*q^157 + (-3*a^4+15*a^2-3)*q^158 + (-2*a^4-a^3+15*a^2+8*a-4)*q^159 + (-2*a^4-4*a^3+9*a^2+13*a-16)*q^160 + (-9*a^4-13*a^3+25*a^2+17*a-4)*q^161 + (2*a^4+4*a^3-3*a^2-6*a+4)*q^162 + (3*a^4-12*a^2+6*a+3)*q^163 + (6*a^4+7*a^3-19*a^2-13*a+12)*q^164 + (7*a^4+18*a^3-22*a^2-52*a+14)*q^165 + (9*a^4+15*a^3-16*a^2-21*a+3)*q^166 + (4*a^4-2*a^3-27*a^2+a+26)*q^167 + (6*a^4+8*a^3-21*a^2-21*a+7)*q^168 + (10*a^4+26*a^3-19*a^2-51*a+7)*q^169 + (a^4-a^3-5*a^2+7*a+1)*q^170 + (3*a^4+5*a^3-6*a^2-7*a-1)*q^171 + (-3*a^4-11*a^3-a^2+22*a+17)*q^172 + (-a^4-a^3-a^2+3*a+16)*q^173 + (3*a^3+8*a^2+6*a-2)*q^174 + (-12*a^4-28*a^3+23*a^2+62*a+7)*q^175 + (-6*a^4-6*a^3+27*a^2+16*a-11)*q^176 + (5*a^4+12*a^3-4*a^2-7*a+2)*q^177 + (-4*a^4-4*a^3+11*a^2+6*a-4)*q^178 + (-6*a^3-a^2+12*a-19)*q^179 + (4*a^4+13*a^3-29*a-16)*q^180 + -1*q^181 + (-6*a^4-13*a^3+14*a^2+19*a-7)*q^182 + (5*a^4+9*a^3-6*a^2-3*a)*q^183 + (5*a^4+6*a^3-17*a^2-11*a+3)*q^184 + (-11*a^3-21*a^2+29*a+39)*q^185 + (3*a^3-5*a+1)*q^186 + (-8*a^4-15*a^3+23*a^2+31*a-6)*q^187 + (-2*a^4+a^3+9*a^2-5*a-6)*q^188 + (-6*a^4-12*a^3+22*a^2+28*a-7)*q^189 + (-2*a^4+2*a^3+7*a^2-10*a+1)*q^190 + (a^4-a^3-9*a^2+9*a+13)*q^191 + (-4*a^3-6*a^2+a+1)*q^192 + (3*a^3+3*a^2-5*a-4)*q^193 + (-a^4-a^3-3*a^2-2*a+4)*q^194 + (13*a^4+31*a^3-28*a^2-61*a+16)*q^195 + (a^4-2*a^3-4*a^2+4*a+4)*q^196 + (-2*a^3+a^2+6*a-12)*q^197 + (-5*a^3-15*a^2-3*a+3)*q^198 + (9*a^4+25*a^3-12*a^2-54*a-4)*q^199 + (9*a^4+21*a^3-16*a^2-42*a)*q^200 +  ...

-------------------------------------------------------
181B (new) , dim = 9

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^6*5^2*7*595051637
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 3*5
Torsion Bound  = 3*5
|L(1)/Omega|   = 2^5/3*5
Sha Bound      = 2^5*3*5

ANALYTIC INVARIANTS:

Omega+         = 4.1619805870644470442 + 0.37240959508953857211e-3i
Omega-         = 0.61165550465034002584 + 2517.131448087004241i
L(1)           = 8.878891954615155618

HECKE EIGENFORM:
a^9-3*a^8-9*a^7+29*a^6+23*a^5-84*a^4-23*a^3+89*a^2+8*a-27 = 0,
f(q) = 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 + (1/2*a^8-13/4*a^7+3/4*a^6+51/2*a^5-59/2*a^4-175/4*a^3+117/2*a^2+17*a-81/4)*q^38 + (-5/2*a^8+17/2*a^7+15*a^6-68*a^5+3/2*a^4+127*a^3-46*a^2-111/2*a+23)*q^39 + (1/4*a^8+1/4*a^7-4*a^6-3*a^5+81/4*a^4+11*a^3-73/2*a^2-49/4*a+27/2)*q^40 + (-a^8+5/2*a^7+15/2*a^6-19*a^5-10*a^4+61/2*a^3-3*a^2-7*a+9/2)*q^41 + (3/2*a^8-3/2*a^7-17*a^6+11*a^5+123/2*a^4-18*a^3-84*a^2+9/2*a+27)*q^42 + (a^8-1/2*a^7-27/2*a^6+6*a^5+56*a^4-47/2*a^3-73*a^2+23*a+43/2)*q^43 + (-1/2*a^8+1/2*a^7+5*a^6-3*a^5-27/2*a^4+a^3+11*a^2+7/2*a-3)*q^44 + (5/4*a^7-9/4*a^6-21/2*a^5+17*a^4+77/4*a^3-61/2*a^2-1/2*a+51/4)*q^45 + (a^8-21/4*a^7-7/4*a^6+83/2*a^5-33*a^4-297/4*a^3+149/2*a^2+65/2*a-135/4)*q^46 + (-3/4*a^8+19/4*a^7-1/2*a^6-39*a^5+161/4*a^4+155/2*a^3-175/2*a^2-169/4*a+36)*q^47 + (-3/2*a^8+6*a^7+13/2*a^6-47*a^5+39/2*a^4+163/2*a^3-58*a^2-59/2*a+53/2)*q^48 + (-3/2*a^8+9/4*a^7+65/4*a^6-37/2*a^5-113/2*a^4+151/4*a^3+155/2*a^2-15*a-123/4)*q^49 + (-7/4*a^8+7/4*a^7+39/2*a^6-13*a^5-271/4*a^4+45/2*a^3+169/2*a^2-33/4*a-27)*q^50 + (a^8-4*a^7-3*a^6+31*a^5-28*a^4-53*a^3+83*a^2+18*a-39)*q^51 + (-5/4*a^7+9/4*a^6+23/2*a^5-18*a^4-113/4*a^3+69/2*a^2+41/2*a-67/4)*q^52 + (a^8-3*a^7-7*a^6+25*a^5+5*a^4-52*a^3+17*a^2+30*a-12)*q^53 + (-2*a^8+7*a^7+11*a^6-55*a^5+10*a^4+98*a^3-56*a^2-40*a+27)*q^54 + (-1/2*a^8+2*a^7+9/2*a^6-19*a^5-25/2*a^4+93/2*a^3+16*a^2-45/2*a-9/2)*q^55 + (3/2*a^8-17/4*a^7-45/4*a^6+67/2*a^5+37/2*a^4-239/4*a^3-29/2*a^2+20*a+27/4)*q^56 + (-1/2*a^8+5/2*a^7-19*a^5+53/2*a^4+30*a^3-66*a^2-11/2*a+29)*q^57 + (3/4*a^8-11/4*a^7-9/2*a^6+22*a^5+7/4*a^4-79/2*a^3+5/2*a^2+57/4*a)*q^58 + (7/2*a^7-17/2*a^6-27*a^5+65*a^4+87/2*a^3-111*a^2-13*a+93/2)*q^59 + (a^8-3/2*a^7-17/2*a^6+10*a^5+16*a^4-23/2*a^3-a^2-15/2)*q^60 + (a^7-3*a^6-6*a^5+21*a^4+a^3-25*a^2+6*a-1)*q^61 + (-1/2*a^8+9/4*a^7+5/4*a^6-33/2*a^5+29/2*a^4+99/4*a^3-77/2*a^2-10*a+81/4)*q^62 + (5/4*a^8-23/4*a^7-2*a^6+44*a^5-183/4*a^4-74*a^3+219/2*a^2+123/4*a-95/2)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (a^8-2*a^7-9*a^6+15*a^5+23*a^4-22*a^3-26*a^2-3*a+12)*q^65 + (-3*a^8+11*a^7+13*a^6-84*a^5+43*a^4+140*a^3-133*a^2-55*a+54)*q^66 + (1/2*a^8-11/2*a^6-2*a^5+33/2*a^4+25/2*a^3-8*a^2-27/2*a-17/2)*q^67 + (1/2*a^8+1/2*a^7-8*a^6-5*a^5+77/2*a^4+11*a^3-58*a^2-9/2*a+24)*q^68 + (-1/2*a^8-1/2*a^7+9*a^6+a^5-87/2*a^4+14*a^3+56*a^2-33/2*a-18)*q^69 + (-3/2*a^8-1/2*a^7+22*a^6+4*a^5-199/2*a^4-5*a^3+149*a^2+11/2*a-54)*q^70 + (1/4*a^8-9/4*a^7+5/2*a^6+16*a^5-123/4*a^4-37/2*a^3+111/2*a^2-9/4*a-18)*q^71 + (a^8-4*a^7-5*a^6+33*a^5-10*a^4-65*a^3+45*a^2+25*a-27)*q^72 + (1/2*a^8-7/4*a^7-15/4*a^6+31/2*a^5+15/2*a^4-145/4*a^3-29/2*a^2+23*a+53/4)*q^73 + (1/4*a^8+5/4*a^7-6*a^6-11*a^5+137/4*a^4+23*a^3-101/2*a^2-53/4*a+27/2)*q^74 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(-a^8+11/2*a^7-3/2*a^6-40*a^5+60*a^4+111/2*a^3-127*a^2-10*a+111/2)*q^89 + (5/4*a^8-9/4*a^7-21/2*a^6+17*a^5+77/4*a^4-61/2*a^3-1/2*a^2+51/4*a)*q^90 + (-1/4*a^8+15/4*a^7-6*a^6-30*a^5+243/4*a^4+56*a^3-243/2*a^2-127/4*a+107/2)*q^91 + (1/4*a^8-9/4*a^7+1/2*a^6+20*a^5-63/4*a^4-93/2*a^3+69/2*a^2+127/4*a-18)*q^92 + (-a^8+9/2*a^7+5/2*a^6-33*a^5+26*a^4+89/2*a^3-57*a^2-a+55/2)*q^93 + (5/2*a^8-29/4*a^7-69/4*a^6+115/2*a^5+29/2*a^4-419/4*a^3+49/2*a^2+42*a-81/4)*q^94 + (7/4*a^8-27/4*a^7-15/2*a^6+53*a^5-101/4*a^4-193/2*a^3+157/2*a^2+185/4*a-33)*q^95 + (1/2*a^8+a^7-21/2*a^6-6*a^5+117/2*a^4-3/2*a^3-98*a^2+27/2*a+81/2)*q^96 + (-a^8+5*a^7-37*a^5+50*a^4+56*a^3-116*a^2-22*a+53)*q^97 + (-9/4*a^8+11/4*a^7+25*a^6-22*a^5-353/4*a^4+43*a^3+237/2*a^2-75/4*a-81/2)*q^98 + (1/2*a^8-9/2*a^7+4*a^6+37*a^5-119/2*a^4-71*a^3+133*a^2+61/2*a-57)*q^99 + (-3/2*a^8+5/4*a^7+65/4*a^6-17/2*a^5-105/2*a^4+47/4*a^3+113/2*a^2-4*a-59/4)*q^100 + (1/2*a^8-17/4*a^7+15/4*a^6+65/2*a^5-101/2*a^4-215/4*a^3+169/2*a^2+23*a-81/4)*q^101 + (-a^8+6*a^7+2*a^6-51*a^5+31*a^4+106*a^3-71*a^2-47*a+27)*q^102 + (a^8-3*a^7-7*a^6+22*a^5+10*a^4-31*a^3-11*a^2+4*a+5)*q^103 + (-7/4*a^8+23/4*a^7+23/2*a^6-48*a^5-19/4*a^4+197/2*a^3-65/2*a^2-193/4*a+27)*q^104 + (-1/2*a^8+7/2*a^6+2*a^5+7/2*a^4-15/2*a^3-38*a^2-7/2*a+33/2)*q^105 + (2*a^7-4*a^6-18*a^5+32*a^4+40*a^3-59*a^2-20*a+27)*q^106 + (5/4*a^8-31/4*a^7+a^6+61*a^5-259/4*a^4-108*a^3+253/2*a^2+199/4*a-81/2)*q^107 + (-a^8+3*a^7+7*a^6-24*a^5-6*a^4+46*a^3-12*a^2-23*a+10)*q^108 + (-1/2*a^8-a^7+21/2*a^6+7*a^5-119/2*a^4-11/2*a^3+99*a^2-15/2*a-77/2)*q^109 + (1/2*a^8-9/2*a^6-a^5+9/2*a^4+9/2*a^3+22*a^2-1/2*a-27/2)*q^110 + (-1/2*a^7+7/2*a^6+a^5-31*a^4+27/2*a^3+70*a^2-23*a-77/2)*q^111 + (-5/4*a^8+15/4*a^7+7*a^6-28*a^5+27/4*a^4+45*a^3-81/2*a^2-79/4*a+37/2)*q^112 + (1/2*a^8-15/2*a^6+2*a^5+63/2*a^4-33/2*a^3-31*a^2+51/2*a+3/2)*q^113 + (a^8-9/2*a^7-9/2*a^6+38*a^5-12*a^4-155/2*a^3+39*a^2+33*a-27/2)*q^114 + (9/4*a^8-27/4*a^7-13*a^6+49*a^5-19/4*a^4-68*a^3+81/2*a^2+35/4*a-27/2)*q^115 + (-1/2*a^8+3/4*a^7+23/4*a^6-13/2*a^5-41/2*a^4+65/4*a^3+53/2*a^2-11*a-33/4)*q^116 + (-3/2*a^8+27/4*a^7+15/4*a^6-105/2*a^5+87/2*a^4+357/4*a^3-211/2*a^2-28*a+131/4)*q^117 + (7/2*a^8-17/2*a^7-27*a^6+65*a^5+87/2*a^4-111*a^3-13*a^2+93/2*a)*q^118 + (2*a^8-5*a^7-18*a^6+42*a^5+46*a^4-86*a^3-46*a^2+37*a+12)*q^119 + (-7/2*a^8+27/2*a^7+19*a^6-109*a^5+27/2*a^4+206*a^3-69*a^2-181/2*a+27)*q^120 + (-a^8+15*a^6-73*a^4+128*a^2+2*a-56)*q^121 + (a^8-3*a^7-6*a^6+21*a^5+a^4-25*a^3+6*a^2-a)*q^122 + (-2*a^8+7*a^7+9*a^6-53*a^5+28*a^4+85*a^3-96*a^2-25*a+45)*q^123 + (-3/4*a^8+9/4*a^7+7*a^6-20*a^5-75/4*a^4+47*a^3+39/2*a^2-129/4*a-11/2)*q^124 + (a^8-2*a^7-8*a^6+16*a^5+10*a^4-31*a^3+20*a^2+13*a-24)*q^125 + (-2*a^8+37/4*a^7+31/4*a^6-149/2*a^5+31*a^4+553/4*a^3-161/2*a^2-115/2*a+135/4)*q^126 + (1/4*a^8-7/4*a^7-a^6+17*a^5-19/4*a^4-46*a^3+33/2*a^2+147/4*a-23/2)*q^127 + (a^7-12*a^5+40*a^3-32*a)*q^128 + (3*a^8-8*a^7-22*a^6+63*a^5+29*a^4-118*a^3-a^2+65*a-1)*q^129 + (a^8-14*a^6+62*a^4-3*a^3-92*a^2+4*a+27)*q^130 + (-a^8+13*a^6+3*a^5-55*a^4-19*a^3+88*a^2+22*a-33)*q^131 + (-2*a^8+4*a^7+17*a^6-30*a^5-36*a^4+48*a^3+24*a^2-12*a-3)*q^132 + (-1/2*a^8+2*a^7+7/2*a^6-17*a^5-11/2*a^4+69/2*a^3+7*a^2-21/2*a-13/2)*q^133 + (3/2*a^8-a^7-33/2*a^6+5*a^5+109/2*a^4+7/2*a^3-58*a^2-25/2*a+27/2)*q^134 + (-2*a^8+9*a^7+6*a^6-70*a^5+47*a^4+119*a^3-113*a^2-40*a+42)*q^135 + (2*a^8-21/2*a^7-5/2*a^6+83*a^5-77*a^4-299/2*a^3+173*a^2+68*a-135/2)*q^136 + (-2*a^8+27/4*a^7+53/4*a^6-109/2*a^5-12*a^4+411/4*a^3-1/2*a^2-81/2*a-27/4)*q^137 + (-2*a^8+9/2*a^7+31/2*a^6-32*a^5-28*a^4+89/2*a^3+28*a^2-14*a-27/2)*q^138 + (a^8-3*a^7-7*a^6+23*a^5+7*a^4-36*a^3+5*a^2+6*a-4)*q^139 + (-a^8-1/2*a^7+25/2*a^6+7*a^5-47*a^4-45/2*a^3+57*a^2+16*a-39/2)*q^140 + (-7/2*a^8+27/2*a^7+19*a^6-111*a^5+33/2*a^4+219*a^3-87*a^2-203/2*a+36)*q^141 + (-3/2*a^8+19/4*a^7+35/4*a^6-73/2*a^5+5/2*a^4+245/4*a^3-49/2*a^2-20*a+27/4)*q^142 + (-a^8+11/2*a^7-1/2*a^6-44*a^5+56*a^4+167/2*a^3-136*a^2-42*a+123/2)*q^143 + (a^8-14*a^6-a^5+63*a^4+4*a^3-100*a^2+a+37)*q^144 + (3*a^8-7*a^7-26*a^6+56*a^5+62*a^4-106*a^3-64*a^2+45*a+18)*q^145 + (-1/4*a^8+3/4*a^7+a^6-4*a^5+23/4*a^4-3*a^3-43/2*a^2+37/4*a+27/2)*q^146 + (-3/2*a^8+11/2*a^7+5*a^6-41*a^5+71/2*a^4+67*a^3-96*a^2-71/2*a+30)*q^147 + (a^8-5/4*a^7-47/4*a^6+23/2*a^5+43*a^4-117/4*a^3-117/2*a^2+47/2*a+101/4)*q^148 + (1/2*a^8-7*a^7+23/2*a^6+52*a^5-225/2*a^4-151/2*a^3+207*a^2+35/2*a-171/2)*q^149 + (-3/2*a^8-1/2*a^7+19*a^6+7*a^5-143/2*a^4-20*a^3+84*a^2+15/2*a-27)*q^150 + (a^8-4*a^7-4*a^6+32*a^5-17*a^4-59*a^3+47*a^2+25*a-19)*q^151 + (-2*a^8+33/4*a^7+27/4*a^6-127/2*a^5+41*a^4+429/4*a^3-205/2*a^2-81/2*a+135/4)*q^152 + (9/2*a^8-41/2*a^7-13*a^6+161*a^5-223/2*a^4-281*a^3+270*a^2+201/2*a-111)*q^153 + (-2*a^8+17/2*a^7+21/2*a^6-69*a^5+8*a^4+255/2*a^3-32*a^2-46*a+27/2)*q^154 + (1/2*a^7-9/2*a^6+a^5+37*a^4-51/2*a^3-68*a^2+28*a+51/2)*q^155 + (1/2*a^8-7/2*a^7+30*a^5-45/2*a^4-64*a^3+46*a^2+71/2*a-19)*q^156 + (1/2*a^8-2*a^7-5/2*a^6+17*a^5-11/2*a^4-73/2*a^3+30*a^2+33/2*a-71/2)*q^157 + (a^8-6*a^7-a^6+49*a^5-37*a^4-94*a^3+74*a^2+43*a-27)*q^158 + (4*a^8-14*a^7-23*a^6+112*a^5-10*a^4-209*a^3+86*a^2+93*a-39)*q^159 + (-3/4*a^8-5/4*a^7+23/2*a^6+13*a^5-211/4*a^4-75/2*a^3+157/2*a^2+131/4*a-27)*q^160 + (3/2*a^8-2*a^7-29/2*a^6+12*a^5+87/2*a^4-11/2*a^3-62*a^2-23/2*a+63/2)*q^161 + (5*a^7-12*a^6-40*a^5+92*a^4+73*a^3-158*a^2-33*a+54)*q^162 + (-13/4*a^8+35/4*a^7+24*a^6-70*a^5-121/4*a^4+133*a^3-27/2*a^2-263/4*a+31/2)*q^163 + (-a^8+1/2*a^7+25/2*a^6-4*a^5-48*a^4+19/2*a^3+63*a^2-9*a-45/2)*q^164 + (-a^8+14*a^7-21*a^6-109*a^5+211*a^4+186*a^3-389*a^2-83*a+144)*q^165 + (3/2*a^8-19/4*a^7-39/4*a^6+77/2*a^5+13/2*a^4-313/4*a^3+19/2*a^2+47*a-27/4)*q^166 + (a^8-5/2*a^7-19/2*a^6+23*a^5+27*a^4-119/2*a^3-33*a^2+42*a+33/2)*q^167 + (-1/2*a^8+1/2*a^7+8*a^6-5*a^5-87/2*a^4+12*a^3+84*a^2-3/2*a-27)*q^168 + (-9/4*a^7+29/4*a^6+27/2*a^5-55*a^4-1/4*a^3+171/2*a^2-57/2*a-87/4)*q^169 + (2*a^8-19/2*a^7-13/2*a^6+76*a^5-42*a^4-271/2*a^3+99*a^2+48*a-81/2)*q^170 + (-19/4*a^8+75/4*a^7+41/2*a^6-147*a^5+265/4*a^4+519/2*a^3-411/2*a^2-401/4*a+95)*q^171 + (a^8+1/2*a^7-25/2*a^6-9*a^5+48*a^4+77/2*a^3-63*a^2-39*a+49/2)*q^172 + (-3*a^8+7/2*a^7+71/2*a^6-31*a^5-134*a^4+151/2*a^3+182*a^2-49*a-129/2)*q^173 + (-3*a^8+13/2*a^7+51/2*a^6-50*a^5-58*a^4+171/2*a^3+57*a^2-29*a-27/2)*q^174 + (3/2*a^7-1/2*a^6-14*a^5-a^4+61/2*a^3+16*a^2-8*a-17/2)*q^175 + (3/2*a^8-3/2*a^7-17*a^6+10*a^5+127/2*a^4-11*a^3-94*a^2-3/2*a+33)*q^176 + (3*a^8-7*a^7-25*a^6+54*a^5+56*a^4-96*a^3-65*a^2+49*a+33)*q^177 + (5/2*a^8-21/2*a^7-11*a^6+83*a^5-57/2*a^4-150*a^3+79*a^2+127/2*a-27)*q^178 + (-1/4*a^8-5/4*a^7+8*a^6+9*a^5-213/4*a^4-13*a^3+203/2*a^2+49/4*a-87/2)*q^179 + (3/2*a^8-7/4*a^7-59/4*a^6+23/2*a^5+81/2*a^4-41/4*a^3-75/2*a^2-9*a+33/4)*q^180 + 1*q^181 + (3*a^8-33/4*a^7-91/4*a^6+133/2*a^5+35*a^4-509/4*a^3-19/2*a^2+111/2*a-27/4)*q^182 + (3*a^8-13*a^7-8*a^6+99*a^5-81*a^4-162*a^3+199*a^2+62*a-91)*q^183 + (-7/2*a^8+53/4*a^7+65/4*a^6-209/2*a^5+81/2*a^4+755/4*a^3-279/2*a^2-85*a+297/4)*q^184 + (-3/2*a^8+19/4*a^7+39/4*a^6-77/2*a^5-11/2*a^4+313/4*a^3-29/2*a^2-47*a+3/4)*q^185 + (3/2*a^8-13/2*a^7-4*a^6+49*a^5-79/2*a^4-80*a^3+88*a^2+71/2*a-27)*q^186 + (5*a^8-20*a^7-23*a^6+159*a^5-54*a^4-291*a^3+170*a^2+118*a-72)*q^187 + (7/4*a^8-17/4*a^7-14*a^6+35*a^5+99/4*a^4-73*a^3-11/2*a^2+177/4*a-9/2)*q^188 + (a^8-5*a^7-2*a^6+41*a^5-34*a^4-81*a^3+87*a^2+39*a-40)*q^189 + (-3/2*a^8+33/4*a^7+9/4*a^6-131/2*a^5+101/2*a^4+475/4*a^3-219/2*a^2-47*a+189/4)*q^190 + (-3/4*a^8-5/4*a^7+27/2*a^6+11*a^5-279/4*a^4-45/2*a^3+221/2*a^2+11/4*a-36)*q^191 + (11/2*a^8-18*a^7-67/2*a^6+141*a^5+3/2*a^4-499/2*a^3+85*a^2+191/2*a-79/2)*q^192 + (-1/2*a^8+13/4*a^7-7/4*a^6-47/2*a^5+75/2*a^4+119/4*a^3-143/2*a^2-a+65/4)*q^193 + (2*a^8-9*a^7-8*a^6+73*a^5-28*a^4-139*a^3+67*a^2+61*a-27)*q^194 + (5/2*a^8-11*a^7-9/2*a^6+82*a^5-175/2*a^4-251/2*a^3+209*a^2+75/2*a-165/2)*q^195 + (-a^8+1/4*a^7+43/4*a^6+1/2*a^5-33*a^4-35/4*a^3+53/2*a^2+15/2*a+3/4)*q^196 + (-a^8+6*a^7+3*a^6-53*a^5+20*a^4+122*a^3-38*a^2-73*a+6)*q^197 + (-3*a^8+17/2*a^7+45/2*a^6-71*a^5-29*a^4+289/2*a^3-14*a^2-61*a+27/2)*q^198 + (-1/4*a^8+19/4*a^7-8*a^6-38*a^5+299/4*a^4+67*a^3-277/2*a^2-103/4*a+121/2)*q^199 + (1/4*a^8-3/4*a^7-4*a^6+8*a^5+85/4*a^4-23*a^3-79/2*a^2+55/4*a+27/2)*q^200 +  ...

-------------------------------------------------------
Gamma_0(182)
Weight 2

-------------------------------------------------------
J_0(182), dim = 25

-------------------------------------------------------
182A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*7*11
Ker(ModPolar)  = Z/2^2*7*11 + Z/2^2*7*11
= B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + I(Z/11 + Z/11) + J(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = ++-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.2089144106840905102 + 0.33924726405602557847e-3i
Omega-         = 0.18313802888481783393e-4 + 0.28973984173963273387i
L(1)           = 1.2089144582841120198
w1             = -0.60444804844060101419 + 0.14470029723778835415i
w2             = 0.18313802888481783393e-4 + 0.28973984173963273387i
c4             = 221042.13353571687098 + 56.371611932962888684i
c6             = -104105504.65195205849 + -39002.424758728958498i
j              = -492132.43854925828388 + -2221.3664204268342997i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + 4*q^5 + -1*q^6 + -1*q^7 + -1*q^8 + -2*q^9 + -4*q^10 + -1*q^11 + 1*q^12 + 1*q^13 + 1*q^14 + 4*q^15 + 1*q^16 + 4*q^17 + 2*q^18 + 2*q^19 + 4*q^20 + -1*q^21 + 1*q^22 + -7*q^23 + -1*q^24 + 11*q^25 + -1*q^26 + -5*q^27 + -1*q^28 + -8*q^29 + -4*q^30 + 3*q^31 + -1*q^32 + -1*q^33 + -4*q^34 + -4*q^35 + -2*q^36 + 7*q^37 + -2*q^38 + 1*q^39 + -4*q^40 + -7*q^41 + 1*q^42 + -8*q^43 + -1*q^44 + -8*q^45 + 7*q^46 + 3*q^47 + 1*q^48 + 1*q^49 + -11*q^50 + 4*q^51 + 1*q^52 + 5*q^54 + -4*q^55 + 1*q^56 + 2*q^57 + 8*q^58 + -6*q^59 + 4*q^60 + -13*q^61 + -3*q^62 + 2*q^63 + 1*q^64 + 4*q^65 + 1*q^66 + 7*q^67 + 4*q^68 + -7*q^69 + 4*q^70 + 4*q^71 + 2*q^72 + 9*q^73 + -7*q^74 + 11*q^75 + 2*q^76 + 1*q^77 + -1*q^78 + -13*q^79 + 4*q^80 + 1*q^81 + 7*q^82 + -16*q^83 + -1*q^84 + 16*q^85 + 8*q^86 + -8*q^87 + 1*q^88 + -6*q^89 + 8*q^90 + -1*q^91 + -7*q^92 + 3*q^93 + -3*q^94 + 8*q^95 + -1*q^96 + 11*q^97 + -1*q^98 + 2*q^99 + 11*q^100 + 9*q^101 + -4*q^102 + 10*q^103 + -1*q^104 + -4*q^105 + 12*q^107 + -5*q^108 + 14*q^109 + 4*q^110 + 7*q^111 + -1*q^112 + 1*q^113 + -2*q^114 + -28*q^115 + -8*q^116 + -2*q^117 + 6*q^118 + -4*q^119 + -4*q^120 + -10*q^121 + 13*q^122 + -7*q^123 + 3*q^124 + 24*q^125 + -2*q^126 + 13*q^127 + -1*q^128 + -8*q^129 + -4*q^130 + -1*q^132 + -2*q^133 + -7*q^134 + -20*q^135 + -4*q^136 + -14*q^137 + 7*q^138 + -20*q^139 + -4*q^140 + 3*q^141 + -4*q^142 + -1*q^143 + -2*q^144 + -32*q^145 + -9*q^146 + 1*q^147 + 7*q^148 + 15*q^149 + -11*q^150 + -4*q^151 + -2*q^152 + -8*q^153 + -1*q^154 + 12*q^155 + 1*q^156 + 7*q^157 + 13*q^158 + -4*q^160 + 7*q^161 + -1*q^162 + 12*q^163 + -7*q^164 + -4*q^165 + 16*q^166 + 1*q^168 + 1*q^169 + -16*q^170 + -4*q^171 + -8*q^172 + 14*q^173 + 8*q^174 + -11*q^175 + -1*q^176 + -6*q^177 + 6*q^178 + -18*q^179 + -8*q^180 + 13*q^181 + 1*q^182 + -13*q^183 + 7*q^184 + 28*q^185 + -3*q^186 + -4*q^187 + 3*q^188 + 5*q^189 + -8*q^190 + 24*q^191 + 1*q^192 + -4*q^193 + -11*q^194 + 4*q^195 + 1*q^196 + 3*q^197 + -2*q^198 + 16*q^199 + -11*q^200 +  ...

-------------------------------------------------------
182B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*5*7
Ker(ModPolar)  = Z/2^2*5*7 + Z/2^2*5*7
= A(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + H(Z/7 + Z/7) + L(Z/5 + Z/5)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.3930757828645664828 + -0.11989962516649959604e-3i
Omega-         = 0.9525142407087201338e-5 + -0.76528590235129055958i
L(1)           = 1.3930757880243432392
w1             = -0.69653312886107969781 + -0.38258300136306202999i
w2             = -0.9525142407087201338e-5 + 0.76528590235129055958i
c4             = 1067.5298856458293287 + -1.9532214882554247286i
c6             = -759602.92008037480795 + -169.1823829990048696i
j              = -3.6510833142579670147 + 0.21713159952815358284e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 3*q^3 + 1*q^4 + -3*q^6 + 1*q^7 + -1*q^8 + 6*q^9 + -5*q^11 + 3*q^12 + -1*q^13 + -1*q^14 + 1*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 + 1*q^26 + 9*q^27 + 1*q^28 + 4*q^29 + 1*q^31 + -1*q^32 + -15*q^33 + 4*q^34 + 6*q^36 + 7*q^37 + -2*q^38 + -3*q^39 + -9*q^41 + -3*q^42 + -12*q^43 + -5*q^44 + -5*q^46 + -7*q^47 + 3*q^48 + 1*q^49 + 5*q^50 + -12*q^51 + -1*q^52 + -4*q^53 + -9*q^54 + -1*q^56 + 6*q^57 + -4*q^58 + -6*q^59 + 13*q^61 + -1*q^62 + 6*q^63 + 1*q^64 + 15*q^66 + 11*q^67 + -4*q^68 + 15*q^69 + -6*q^72 + 7*q^73 + -7*q^74 + -15*q^75 + 2*q^76 + -5*q^77 + 3*q^78 + -17*q^79 + 9*q^81 + 9*q^82 + 4*q^83 + 3*q^84 + 12*q^86 + 12*q^87 + 5*q^88 + 14*q^89 + -1*q^91 + 5*q^92 + 3*q^93 + 7*q^94 + -3*q^96 + 5*q^97 + -1*q^98 + -30*q^99 + -5*q^100 + 15*q^101 + 12*q^102 + 6*q^103 + 1*q^104 + 4*q^106 + -8*q^107 + 9*q^108 + -18*q^109 + 21*q^111 + 1*q^112 + 1*q^113 + -6*q^114 + 4*q^116 + -6*q^117 + 6*q^118 + -4*q^119 + 14*q^121 + -13*q^122 + -27*q^123 + 1*q^124 + -6*q^126 + 9*q^127 + -1*q^128 + -36*q^129 + 8*q^131 + -15*q^132 + 2*q^133 + -11*q^134 + 4*q^136 + 18*q^137 + -15*q^138 + 4*q^139 + -21*q^141 + 5*q^143 + 6*q^144 + -7*q^146 + 3*q^147 + 7*q^148 + 7*q^149 + 15*q^150 + -12*q^151 + -2*q^152 + -24*q^153 + 5*q^154 + -3*q^156 + 1*q^157 + 17*q^158 + -12*q^159 + 5*q^161 + -9*q^162 + 4*q^163 + -9*q^164 + -4*q^166 + 8*q^167 + -3*q^168 + 1*q^169 + 12*q^171 + -12*q^172 + 18*q^173 + -12*q^174 + -5*q^175 + -5*q^176 + -18*q^177 + -14*q^178 + -2*q^179 + -5*q^181 + 1*q^182 + 39*q^183 + -5*q^184 + -3*q^186 + 20*q^187 + -7*q^188 + 9*q^189 + -16*q^191 + 3*q^192 + 4*q^193 + -5*q^194 + 1*q^196 + 27*q^197 + 30*q^198 + -20*q^199 + 5*q^200 +  ...

-------------------------------------------------------
182C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2*5
Ker(ModPolar)  = Z/2^2*3^2*5 + Z/2^2*3^2*5
= D(Z/3 + Z/3) + F(Z/5 + Z/5) + I(Z/2 + Z/2) + K(Z/3 + Z/3) + L(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 5/2
Sha Bound      = 2^3*5

ANALYTIC INVARIANTS:

Omega+         = 0.71898338061265140791 + 0.68786533927703367811e-5i
Omega-         = 0.3235598431284217488e-3 + 0.61237879625266380204i
L(1)           = 1.797458451613890283
w1             = -0.35965347022788991483 + -0.30619283745302828619i
w2             = -0.35932991038476149308 + 0.30618595879963551585i
c4             = -41557.72991666846843 + -8.8975862557578260821i
c6             = -5753664.1308801380887 + -25630.154940218652639i
j              = 1182.5489282381252843 + -3.0858287414898839809i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + 2*q^5 + -1*q^7 + 1*q^8 + -3*q^9 + 2*q^10 + 4*q^11 + -1*q^13 + -1*q^14 + 1*q^16 + -6*q^17 + -3*q^18 + 2*q^20 + 4*q^22 + 8*q^23 + -1*q^25 + -1*q^26 + -1*q^28 + -10*q^29 + -8*q^31 + 1*q^32 + -6*q^34 + -2*q^35 + -3*q^36 + 6*q^37 + 2*q^40 + -6*q^41 + 4*q^43 + 4*q^44 + -6*q^45 + 8*q^46 + -8*q^47 + 1*q^49 + -1*q^50 + -1*q^52 + 6*q^53 + 8*q^55 + -1*q^56 + -10*q^58 + 8*q^59 + 10*q^61 + -8*q^62 + 3*q^63 + 1*q^64 + -2*q^65 + 4*q^67 + -6*q^68 + -2*q^70 + -8*q^71 + -3*q^72 + 2*q^73 + 6*q^74 + -4*q^77 + 8*q^79 + 2*q^80 + 9*q^81 + -6*q^82 + -12*q^85 + 4*q^86 + 4*q^88 + 18*q^89 + -6*q^90 + 1*q^91 + 8*q^92 + -8*q^94 + 2*q^97 + 1*q^98 + -12*q^99 + -1*q^100 + -14*q^101 + 16*q^103 + -1*q^104 + 6*q^106 + -4*q^107 + -2*q^109 + 8*q^110 + -1*q^112 + 2*q^113 + 16*q^115 + -10*q^116 + 3*q^117 + 8*q^118 + 6*q^119 + 5*q^121 + 10*q^122 + -8*q^124 + -12*q^125 + 3*q^126 + 16*q^127 + 1*q^128 + -2*q^130 + 8*q^131 + 4*q^134 + -6*q^136 + -6*q^137 + -8*q^139 + -2*q^140 + -8*q^142 + -4*q^143 + -3*q^144 + -20*q^145 + 2*q^146 + 6*q^148 + -18*q^149 + 18*q^153 + -4*q^154 + -16*q^155 + 2*q^157 + 8*q^158 + 2*q^160 + -8*q^161 + 9*q^162 + -4*q^163 + -6*q^164 + 1*q^169 + -12*q^170 + 4*q^172 + 2*q^173 + 1*q^175 + 4*q^176 + 18*q^178 + -12*q^179 + -6*q^180 + -6*q^181 + 1*q^182 + 8*q^184 + 12*q^185 + -24*q^187 + -8*q^188 + -8*q^191 + 2*q^193 + 2*q^194 + 1*q^196 + -18*q^197 + -12*q^198 + -16*q^199 + -1*q^200 +  ...

-------------------------------------------------------
182D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2^2*3^2 + Z/2^2*3^2
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/3 + Z/3) + E(Z/2 + Z/2) + K(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 2.1352558785267487058 + 0.29632068274182773684e-3i
Omega-         = 0.31372318505678264002e-3 + 2.8585718275317502515i
L(1)           = 2.1352558990877380188
w1             = -1.0677848008559027442 + -1.4294340741072460396i
w2             = -1.0674710776708459616 + 1.4291377534245042119i
c4             = -158.90528564865549947 + -0.12192205918556097299i
c6             = 3375.5372322136023122 + -1.9670467534098443169i
j              = 450.03567358304174671 + 1.1540082170121149708i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 3*q^3 + 1*q^4 + -4*q^5 + 3*q^6 + -1*q^7 + 1*q^8 + 6*q^9 + -4*q^10 + 1*q^11 + 3*q^12 + -1*q^13 + -1*q^14 + -12*q^15 + 1*q^16 + 6*q^18 + -6*q^19 + -4*q^20 + -3*q^21 + 1*q^22 + -7*q^23 + 3*q^24 + 11*q^25 + -1*q^26 + 9*q^27 + -1*q^28 + -4*q^29 + -12*q^30 + 7*q^31 + 1*q^32 + 3*q^33 + 4*q^35 + 6*q^36 + 9*q^37 + -6*q^38 + -3*q^39 + -4*q^40 + -3*q^41 + -3*q^42 + 4*q^43 + 1*q^44 + -24*q^45 + -7*q^46 + 7*q^47 + 3*q^48 + 1*q^49 + 11*q^50 + -1*q^52 + 9*q^54 + -4*q^55 + -1*q^56 + -18*q^57 + -4*q^58 + -10*q^59 + -12*q^60 + 1*q^61 + 7*q^62 + -6*q^63 + 1*q^64 + 4*q^65 + 3*q^66 + 1*q^67 + -21*q^69 + 4*q^70 + 16*q^71 + 6*q^72 + 5*q^73 + 9*q^74 + 33*q^75 + -6*q^76 + -1*q^77 + -3*q^78 + 11*q^79 + -4*q^80 + 9*q^81 + -3*q^82 + -3*q^84 + 4*q^86 + -12*q^87 + 1*q^88 + -6*q^89 + -24*q^90 + 1*q^91 + -7*q^92 + 21*q^93 + 7*q^94 + 24*q^95 + 3*q^96 + -1*q^97 + 1*q^98 + 6*q^99 + 11*q^100 + -5*q^101 + -14*q^103 + -1*q^104 + 12*q^105 + -4*q^107 + 9*q^108 + -14*q^109 + -4*q^110 + 27*q^111 + -1*q^112 + -7*q^113 + -18*q^114 + 28*q^115 + -4*q^116 + -6*q^117 + -10*q^118 + -12*q^120 + -10*q^121 + 1*q^122 + -9*q^123 + 7*q^124 + -24*q^125 + -6*q^126 + -11*q^127 + 1*q^128 + 12*q^129 + 4*q^130 + 8*q^131 + 3*q^132 + 6*q^133 + 1*q^134 + -36*q^135 + -6*q^137 + -21*q^138 + 4*q^139 + 4*q^140 + 21*q^141 + 16*q^142 + -1*q^143 + 6*q^144 + 16*q^145 + 5*q^146 + 3*q^147 + 9*q^148 + 9*q^149 + 33*q^150 + -6*q^152 + -1*q^154 + -28*q^155 + -3*q^156 + 5*q^157 + 11*q^158 + -4*q^160 + 7*q^161 + 9*q^162 + -4*q^163 + -3*q^164 + -12*q^165 + -3*q^168 + 1*q^169 + -36*q^171 + 4*q^172 + 2*q^173 + -12*q^174 + -11*q^175 + 1*q^176 + -30*q^177 + -6*q^178 + -6*q^179 + -24*q^180 + 15*q^181 + 1*q^182 + 3*q^183 + -7*q^184 + -36*q^185 + 21*q^186 + 7*q^188 + -9*q^189 + 24*q^190 + -8*q^191 + 3*q^192 + 20*q^193 + -1*q^194 + 12*q^195 + 1*q^196 + -27*q^197 + 6*q^198 + -4*q^199 + 11*q^200 +  ...

-------------------------------------------------------
182E (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 3
|L(1)/Omega|   = 1
Sha Bound      = 3^2

ANALYTIC INVARIANTS:

Omega+         = 1.9204239073060386867 + 0.28397670049074240567e-3i
Omega-         = 0.33099213870810019951e-3 + 2.404021821742569922i
L(1)           = 1.9204239283021233725
w1             = -0.96037744972237339347 + -1.2021528992215303322i
w2             = -0.96004645758366529327 + 1.2018689225210395898i
c4             = -334.68137217716860992 + -0.21194279779746799553i
c6             = 6551.0759862782324201 + -6.3789951560805869632i
j              = 805.66814222101123746 + 1.6544453937158362151i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^3 + 1*q^4 + 1*q^6 + 1*q^7 + 1*q^8 + -2*q^9 + -3*q^11 + 1*q^12 + 1*q^13 + 1*q^14 + 1*q^16 + -2*q^18 + 2*q^19 + 1*q^21 + -3*q^22 + -3*q^23 + 1*q^24 + -5*q^25 + 1*q^26 + -5*q^27 + 1*q^28 + 5*q^31 + 1*q^32 + -3*q^33 + -2*q^36 + -7*q^37 + 2*q^38 + 1*q^39 + 3*q^41 + 1*q^42 + 8*q^43 + -3*q^44 + -3*q^46 + -3*q^47 + 1*q^48 + 1*q^49 + -5*q^50 + 1*q^52 + -12*q^53 + -5*q^54 + 1*q^56 + 2*q^57 + 6*q^59 + -1*q^61 + 5*q^62 + -2*q^63 + 1*q^64 + -3*q^66 + 5*q^67 + -3*q^69 + 12*q^71 + -2*q^72 + 11*q^73 + -7*q^74 + -5*q^75 + 2*q^76 + -3*q^77 + 1*q^78 + -1*q^79 + 1*q^81 + 3*q^82 + 12*q^83 + 1*q^84 + 8*q^86 + -3*q^88 + -18*q^89 + 1*q^91 + -3*q^92 + 5*q^93 + -3*q^94 + 1*q^96 + 17*q^97 + 1*q^98 + 6*q^99 + -5*q^100 + -3*q^101 + 14*q^103 + 1*q^104 + -12*q^106 + -5*q^108 + 2*q^109 + -7*q^111 + 1*q^112 + 9*q^113 + 2*q^114 + -2*q^117 + 6*q^118 + -2*q^121 + -1*q^122 + 3*q^123 + 5*q^124 + -2*q^126 + -7*q^127 + 1*q^128 + 8*q^129 + -3*q^132 + 2*q^133 + 5*q^134 + -6*q^137 + -3*q^138 + -4*q^139 + -3*q^141 + 12*q^142 + -3*q^143 + -2*q^144 + 11*q^146 + 1*q^147 + -7*q^148 + -15*q^149 + -5*q^150 + 8*q^151 + 2*q^152 + -3*q^154 + 1*q^156 + -13*q^157 + -1*q^158 + -12*q^159 + -3*q^161 + 1*q^162 + 20*q^163 + 3*q^164 + 12*q^166 + -24*q^167 + 1*q^168 + 1*q^169 + -4*q^171 + 8*q^172 + -18*q^173 + -5*q^175 + -3*q^176 + 6*q^177 + -18*q^178 + -6*q^179 + -7*q^181 + 1*q^182 + -1*q^183 + -3*q^184 + 5*q^186 + -3*q^188 + -5*q^189 + 1*q^192 + -4*q^193 + 17*q^194 + 1*q^196 + -3*q^197 + 6*q^198 + -16*q^199 + -5*q^200 +  ...

-------------------------------------------------------
182F (old = 91A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*5 + Z/2^2*5
= C(Z/5 + Z/5) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
182G (old = 91B), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= E(Z/3 + Z/3) + F(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2) + J(Z/3) + L(Z/3)

-------------------------------------------------------
182H (old = 91C), dim = 2

CONGRUENCES:
Modular Degree = 2^6*7^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2*7 + Z/2^2*7 + Z/2^2*7 + Z/2^2*7
= B(Z/7 + Z/7) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + K(Z/7 + Z/7)

-------------------------------------------------------
182I (old = 91D), dim = 3

CONGRUENCES:
Modular Degree = 2^8*11
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2*11 + Z/2^2*11
= A(Z/11 + Z/11) + C(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + L(Z/2 + Z/2)

-------------------------------------------------------
182J (old = 26A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3*7 + Z/2*3*7
= A(Z/7 + Z/7) + G(Z/3) + K(Z/2 + Z/2 + Z/2 + Z/2) + L(Z/3)

-------------------------------------------------------
182K (old = 26B), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2*7
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3^2*7 + Z/2*3^2*7
= C(Z/3 + Z/3) + D(Z/3 + Z/3) + H(Z/7 + Z/7) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
182L (old = 14A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3*5 + Z/2*3*5
= B(Z/5 + Z/5) + C(Z/2 + Z/2) + G(Z/3) + I(Z/2 + Z/2) + J(Z/3)

-------------------------------------------------------
Gamma_0(183)
Weight 2

-------------------------------------------------------
J_0(183), dim = 19

-------------------------------------------------------
183A (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3 + Z/2^3
= C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 2^3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 9.6985900679326927605 + 0.8359821319259146558e-3i
Omega-         = 3.0316074549926126266 + 0.379601010699930519e-3i
L(1)           =

HECKE EIGENFORM:
a^2+2*a-1 = 0,
f(q) = q + a*q^2 + -1*q^3 + (-2*a-1)*q^4 + -1*q^5 + -a*q^6 + (-a-2)*q^7 + (a-2)*q^8 + 1*q^9 + -a*q^10 + (-a-2)*q^11 + (2*a+1)*q^12 + -3*q^13 + -1*q^14 + 1*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 + -1*q^22 + (3*a+2)*q^23 + (-a+2)*q^24 + -4*q^25 + -3*a*q^26 + -1*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 + (-2*a+4)*q^38 + 3*q^39 + (-a+2)*q^40 + (-2*a-5)*q^41 + 1*q^42 + (-4*a+2)*q^43 + (a+4)*q^44 + -1*q^45 + (-4*a+3)*q^46 + (-6*a-10)*q^47 + -3*q^48 + (2*a-2)*q^49 + -4*a*q^50 + 6*q^51 + (6*a+3)*q^52 + (6*a+4)*q^53 + -a*q^54 + (a+2)*q^55 + (2*a+3)*q^56 + (-4*a-6)*q^57 + (4*a-4)*q^58 + (-3*a-8)*q^59 + (-2*a-1)*q^60 + -1*q^61 + (-2*a+4)*q^62 + (-a-2)*q^63 + (2*a-5)*q^64 + 3*q^65 + 1*q^66 + (-5*a-2)*q^67 + (12*a+6)*q^68 + (-3*a-2)*q^69 + 1*q^70 + 6*q^71 + (a-2)*q^72 + (6*a+1)*q^73 + (-4*a+2)*q^74 + 4*q^75 + -14*q^76 + (2*a+5)*q^77 + 3*a*q^78 + a*q^79 + -3*q^80 + 1*q^81 + (-a-2)*q^82 + (2*a-2)*q^83 + (-a-4)*q^84 + 6*q^85 + (10*a-4)*q^86 + (4*a+4)*q^87 + (2*a+3)*q^88 + (-4*a-12)*q^89 + -a*q^90 + (3*a+6)*q^91 + (5*a-8)*q^92 + (-4*a-6)*q^93 + (2*a-6)*q^94 + (-4*a-6)*q^95 + (-a-4)*q^96 + (-4*a-10)*q^97 + (-6*a+2)*q^98 + (-a-2)*q^99 + (8*a+4)*q^100 + (-2*a+12)*q^101 + 6*a*q^102 + (-6*a-12)*q^103 + (-3*a+6)*q^104 + (-a-2)*q^105 + (-8*a+6)*q^106 + (-6*a-4)*q^107 + (2*a+1)*q^108 + (-8*a-1)*q^109 + 1*q^110 + -2*a*q^111 + (-3*a-6)*q^112 + (10*a+7)*q^113 + (2*a-4)*q^114 + (-3*a-2)*q^115 + (-4*a+12)*q^116 + -3*q^117 + (-2*a-3)*q^118 + (6*a+12)*q^119 + (a-2)*q^120 + (2*a-6)*q^121 + -a*q^122 + (2*a+5)*q^123 + -14*q^124 + 9*q^125 + -1*q^126 + (6*a+10)*q^127 + (-11*a-6)*q^128 + (4*a-2)*q^129 + 3*a*q^130 + (6*a+4)*q^131 + (-a-4)*q^132 + (-6*a-16)*q^133 + (8*a-5)*q^134 + 1*q^135 + (-6*a+12)*q^136 + (-12*a-13)*q^137 + (4*a-3)*q^138 + (3*a+14)*q^139 + (-a-4)*q^140 + (6*a+10)*q^141 + 6*a*q^142 + (3*a+6)*q^143 + 3*q^144 + (4*a+4)*q^145 + (-11*a+6)*q^146 + (-2*a+2)*q^147 + (6*a-4)*q^148 + (14*a+13)*q^149 + 4*a*q^150 + (-3*a+6)*q^151 + (-10*a-8)*q^152 + -6*q^153 + (a+2)*q^154 + (-4*a-6)*q^155 + (-6*a-3)*q^156 + (-4*a-2)*q^157 + (-2*a+1)*q^158 + (-6*a-4)*q^159 + (-a-4)*q^160 + (-2*a-7)*q^161 + a*q^162 + 16*q^163 + (4*a+9)*q^164 + (-a-2)*q^165 + (-6*a+2)*q^166 + -6*a*q^167 + (-2*a-3)*q^168 + -4*q^169 + 6*a*q^170 + (4*a+6)*q^171 + (-16*a+6)*q^172 + (12*a+10)*q^173 + (-4*a+4)*q^174 + (4*a+8)*q^175 + (-3*a-6)*q^176 + (3*a+8)*q^177 + (-4*a-4)*q^178 + (12*a+6)*q^179 + (2*a+1)*q^180 + (-6*a-2)*q^181 + 3*q^182 + 1*q^183 + (-10*a-1)*q^184 + -2*a*q^185 + (2*a-4)*q^186 + (6*a+12)*q^187 + (2*a+22)*q^188 + (a+2)*q^189 + (2*a-4)*q^190 + (7*a+4)*q^191 + (-2*a+5)*q^192 + (-2*a+10)*q^193 + (-2*a-4)*q^194 + -3*q^195 + (10*a-2)*q^196 + (-4*a-9)*q^197 + -1*q^198 + (10*a+12)*q^199 + (-4*a+8)*q^200 +  ...

-------------------------------------------------------
183B (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3*19
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*19 + Z/2*19
= C(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + E(Z/19 + Z/19)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*37
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 3.1930628399170581306 + -0.43182215096979515409e-3i
Omega-         = 0.15079464273387289076e-2 + -5.1190280626712858068i
L(1)           = 0.79826571727908834461

HECKE EIGENFORM:
a^3-a^2-3*a+1 = 0,
f(q) = q + a*q^2 + -1*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 + 1*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 + -1*q^25 + (4*a-2)*q^26 + -1*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 + (-2*a^2-2*a)*q^38 + (-2*a^2+2*a+2)*q^39 + (2*a^2-2*a-2)*q^40 + (-2*a^2+4*a+4)*q^41 + (2*a-2)*q^42 + (-6*a+2)*q^43 + (a^2-2*a-5)*q^44 + 2*q^45 + (-a^2+4*a-3)*q^46 + 4*a*q^47 + (2*a^2-2*a-3)*q^48 + (-4*a^2+13)*q^49 + -a*q^50 + (a^2+2*a-7)*q^51 + (2*a+4)*q^52 + (-3*a^2+6*a+9)*q^53 + -a*q^54 + (-2*a^2+6)*q^55 + (2*a-6)*q^56 + (2*a+2)*q^57 + (a^2+1)*q^58 + (7*a^2-4*a-13)*q^59 + (-2*a^2+4)*q^60 + 1*q^61 + (4*a^2-2*a-2)*q^62 + (-2*a^2+2*a+4)*q^63 + (a^2-6*a-4)*q^64 + (4*a^2-4*a-4)*q^65 + (a^2-1)*q^66 + (4*a^2+2*a-10)*q^67 + (3*a^2-4*a-11)*q^68 + (-3*a^2+4*a+5)*q^69 + (-4*a+4)*q^70 + (3*a^2-4*a-1)*q^71 + (a^2-a-1)*q^72 + (-4*a^2+8*a+6)*q^73 + (2*a-4)*q^74 + 1*q^75 + (-4*a^2-2*a+6)*q^76 + (-4*a^2+4*a+12)*q^77 + (-4*a+2)*q^78 + (-4*a^2-2*a+6)*q^79 + (-4*a^2+4*a+6)*q^80 + 1*q^81 + (2*a^2-2*a+2)*q^82 + (4*a^2-12)*q^83 + (-2*a^2+2*a+8)*q^84 + (-2*a^2-4*a+14)*q^85 + (-6*a^2+2*a)*q^86 + (a^2-2*a-3)*q^87 + (a^2-2*a-3)*q^88 + (5*a^2-6*a-11)*q^89 + 2*a*q^90 + (4*a-12)*q^91 + (-3*a^2+2*a+11)*q^92 + (-2*a^2-2*a+8)*q^93 + 4*a^2*q^94 + (-4*a-4)*q^95 + (2*a^2+a-4)*q^96 + (2*a^2-2*a+2)*q^97 + (-4*a^2+a+4)*q^98 + (-a^2+3)*q^99 + (-a^2+2)*q^100 + (3*a^2+2*a-1)*q^101 + (3*a^2-4*a-1)*q^102 + (-2*a+2)*q^103 + (2*a^2-4*a+4)*q^104 + (4*a^2-4*a-8)*q^105 + (3*a^2+3)*q^106 + -4*a*q^107 + (-a^2+2)*q^108 + -10*q^109 + (-2*a^2+2)*q^110 + (-4*a^2+4*a+10)*q^111 + (-2*a^2-2*a+16)*q^112 + (-6*a^2+20)*q^113 + (2*a^2+2*a)*q^114 + (6*a^2-8*a-10)*q^115 + (3*a^2-7)*q^116 + (2*a^2-2*a-2)*q^117 + (3*a^2+8*a-7)*q^118 + (-12*a^2+16*a+24)*q^119 + (-2*a^2+2*a+2)*q^120 + (-2*a^2+2*a-3)*q^121 + a*q^122 + (2*a^2-4*a-4)*q^123 + (-2*a^2+6*a+12)*q^124 + -12*q^125 + (-2*a+2)*q^126 + (10*a-2)*q^127 + (-a^2+a-9)*q^128 + (6*a-2)*q^129 + (8*a-4)*q^130 + (-4*a^2-4*a+8)*q^131 + (-a^2+2*a+5)*q^132 + (4*a^2-12)*q^133 + (6*a^2+2*a-4)*q^134 + -2*q^135 + (5*a^2-10*a-5)*q^136 + (2*a^2-8)*q^137 + (a^2-4*a+3)*q^138 + (-8*a^2+6*a+14)*q^139 + (4*a^2-4*a-16)*q^140 + -4*a*q^141 + (-a^2+8*a-3)*q^142 + (2*a^2-4*a-6)*q^143 + (-2*a^2+2*a+3)*q^144 + (-2*a^2+4*a+6)*q^145 + (4*a^2-6*a+4)*q^146 + (4*a^2-13)*q^147 + (-6*a^2+4*a+20)*q^148 + (2*a^2-4*a-12)*q^149 + a*q^150 + (4*a^2+6*a-18)*q^151 + (-2*a^2-2*a+4)*q^152 + (-a^2-2*a+7)*q^153 + 4*q^154 + (4*a^2+4*a-16)*q^155 + (-2*a-4)*q^156 + 6*q^157 + (-6*a^2-6*a+4)*q^158 + (3*a^2-6*a-9)*q^159 + (-4*a^2-2*a+8)*q^160 + (4*a^2+4*a-28)*q^161 + a*q^162 + (-6*a-6)*q^163 + (4*a^2-10)*q^164 + (2*a^2-6)*q^165 + (4*a^2-4)*q^166 + (-2*a^2+10)*q^167 + (-2*a+6)*q^168 + (4*a^2-8*a-5)*q^169 + (-6*a^2+8*a+2)*q^170 + (-2*a-2)*q^171 + (-4*a^2-6*a+2)*q^172 + (-7*a^2+6*a+13)*q^173 + (-a^2-1)*q^174 + (2*a^2-2*a-4)*q^175 + (-3*a^2+4*a+9)*q^176 + (-7*a^2+4*a+13)*q^177 + (-a^2+4*a-5)*q^178 + (2*a^2-4)*q^180 + (-2*a^2+4*a-8)*q^181 + (4*a^2-12*a)*q^182 + -1*q^183 + (a^2-6*a+9)*q^184 + (8*a^2-8*a-20)*q^185 + (-4*a^2+2*a+2)*q^186 + (-4*a^2+2*a+18)*q^187 + (4*a^2+4*a-4)*q^188 + (2*a^2-2*a-4)*q^189 + (-4*a^2-4*a)*q^190 + (5*a^2-8*a-11)*q^191 + (-a^2+6*a+4)*q^192 + (-4*a^2+8*a+14)*q^193 + (8*a-2)*q^194 + (-4*a^2+4*a+4)*q^195 + (5*a^2-8*a-22)*q^196 + (-8*a^2+18)*q^197 + (-a^2+1)*q^198 + (4*a^2-8*a-4)*q^199 + (-a^2+a+1)*q^200 +  ...

-------------------------------------------------------
183C (new) , dim = 6

CONGRUENCES:
Modular Degree = 2^8*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^3*3 + Z/2^3*3
= A(Z/2 + Z/2 + Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2*3 + Z/2*3) + E(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^7*127*5623
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2*31
Torsion Bound  = 2^2*31
|L(1)/Omega|   = 2*3/31
Sha Bound      = 2^5*3*31

ANALYTIC INVARIANTS:

Omega+         = 17.422710630114283414 + 0.25522067759330610579e-2i
Omega-         = 3.4421664714801429843 + 0.12982854666293920196e-2i
L(1)           = 3.372137577493024039

HECKE EIGENFORM:
a^6-11*a^4+2*a^3+31*a^2-10*a-17 = 0,
f(q) = q + a*q^2 + 1*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 + 1*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 + 1*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 + (a^5+3*a^4-10*a^3-20*a^2+23*a+17)*q^38 + (-1/2*a^5+5*a^3-21/2*a+1)*q^39 + (-2*a^5-7/2*a^4+19*a^3+23*a^2-38*a-51/2)*q^40 + (-3/2*a^5-2*a^4+13*a^3+16*a^2-39/2*a-23)*q^41 + (-3/2*a^5-2*a^4+13*a^3+14*a^2-43/2*a-17)*q^42 + (-a^4+8*a^2-9)*q^43 + (-3/2*a^4+7*a^2-3*a-7/2)*q^44 + (1/2*a^5+a^4-5*a^3-8*a^2+21/2*a+10)*q^45 + (-1/2*a^5+5*a^3-a^2-17/2*a)*q^46 + (a^5+a^4-10*a^3-8*a^2+19*a+9)*q^47 + (a^4-6*a^2+4)*q^48 + (1/2*a^5-5*a^3+25/2*a+2)*q^49 + (3*a^5+9/2*a^4-27*a^3-35*a^2+52*a+85/2)*q^50 + (a^5+a^4-9*a^3-6*a^2+16*a+5)*q^51 + (1/2*a^5+a^4-5*a^3-4*a^2+25/2*a-2)*q^52 + (2*a^5+2*a^4-19*a^3-16*a^2+35*a+20)*q^53 + a*q^54 + (1/2*a^4+a^3-3*a^2+1/2)*q^55 + (5/2*a^5+3*a^4-23*a^3-26*a^2+81/2*a+34)*q^56 + (a^5+a^4-8*a^3-8*a^2+11*a+13)*q^57 + (a^5+a^4-8*a^3-5*a^2+9*a)*q^58 + (-a^5-3/2*a^4+8*a^3+11*a^2-10*a-31/2)*q^59 + (-1/2*a^5+3*a^3-5/2*a-3)*q^60 + -1*q^61 + (-3*a^5-4*a^4+28*a^3+30*a^2-51*a-34)*q^62 + (-a^5-3/2*a^4+9*a^3+11*a^2-17*a-23/2)*q^63 + (a^4-2*a^3-7*a^2+10*a+9)*q^64 + (-5/2*a^5-3*a^4+23*a^3+22*a^2-93/2*a-24)*q^65 + (-1/2*a^5+3*a^3-a^2-5/2*a)*q^66 + (a^5+5/2*a^4-9*a^3-21*a^2+19*a+57/2)*q^67 + (a^4+a^3-4*a^2-5*a+7)*q^68 + (-1/2*a^4+5*a^2-a-17/2)*q^69 + (-3/2*a^5-3*a^4+17*a^3+26*a^2-83/2*a-34)*q^70 + (-a^5+9*a^3-16*a-4)*q^71 + (a^3-4*a)*q^72 + (-1/2*a^5+5*a^3-25/2*a+5)*q^73 + (-a^5-3*a^4+8*a^3+22*a^2-15*a-17)*q^74 + (5/2*a^5+3*a^4-23*a^3-22*a^2+85/2*a+27)*q^75 + (a^5-a^4-6*a^3+8*a^2+5*a-9)*q^76 + (1/2*a^5-3*a^3+2*a^2+5/2*a-1)*q^77 + (-1/2*a^4+a^3+5*a^2-4*a-17/2)*q^78 + (-1/2*a^4-a^3+5*a^2+6*a-17/2)*q^79 + (-5/2*a^5-3*a^4+21*a^3+24*a^2-81/2*a-28)*q^80 + 1*q^81 + (-2*a^5-7/2*a^4+19*a^3+27*a^2-38*a-51/2)*q^82 + (3*a^5+3*a^4-26*a^3-24*a^2+41*a+31)*q^83 + (-1/2*a^4-a^3+3*a^2+2*a-5/2)*q^84 + (a^5+2*a^4-12*a^3-16*a^2+31*a+16)*q^85 + (-a^5+8*a^3-9*a)*q^86 + (a^4+a^3-8*a^2-5*a+9)*q^87 + (-1/2*a^5+a^3-a^2+3/2*a)*q^88 + (-2*a^5-3*a^4+19*a^3+20*a^2-37*a-11)*q^89 + (a^5+1/2*a^4-9*a^3-5*a^2+15*a+17/2)*q^90 + (2*a^5+7/2*a^4-19*a^3-29*a^2+36*a+79/2)*q^91 + (1/2*a^4-3*a^2-3*a+17/2)*q^92 + (-2*a^5-3*a^4+18*a^3+24*a^2-32*a-31)*q^93 + (a^5+a^4-10*a^3-12*a^2+19*a+17)*q^94 + (a^5+2*a^4-10*a^3-20*a^2+25*a+28)*q^95 + (a^5-8*a^3+12*a)*q^96 + (-2*a^5-3*a^4+18*a^3+22*a^2-28*a-21)*q^97 + (1/2*a^4-a^3-3*a^2+7*a+17/2)*q^98 + (-1/2*a^4+3*a^2-a-5/2)*q^99 + (-1/2*a^5+5*a^3+3*a^2-25/2*a-3)*q^100 + (2*a^5+2*a^4-17*a^3-14*a^2+29*a+14)*q^101 + (a^5+2*a^4-8*a^3-15*a^2+15*a+17)*q^102 + (2*a^5+2*a^4-16*a^3-14*a^2+20*a+16)*q^103 + (a^5+3/2*a^4-7*a^3-13*a^2+11*a+51/2)*q^104 + (-2*a^5-3/2*a^4+19*a^3+13*a^2-36*a-43/2)*q^105 + (2*a^5+3*a^4-20*a^3-27*a^2+40*a+34)*q^106 + (2*a^5+3*a^4-18*a^3-22*a^2+34*a+23)*q^107 + (a^2-2)*q^108 + (-3/2*a^5-a^4+13*a^3+6*a^2-43/2*a-2)*q^109 + (1/2*a^5+a^4-3*a^3+1/2*a)*q^110 + (-a^5-a^4+8*a^3+6*a^2-9*a-5)*q^111 + (3*a^5+11/2*a^4-29*a^3-43*a^2+55*a+95/2)*q^112 + (-7/2*a^5-6*a^4+33*a^3+44*a^2-131/2*a-43)*q^113 + (a^5+3*a^4-10*a^3-20*a^2+23*a+17)*q^114 + (-2*a^5-3/2*a^4+17*a^3+13*a^2-26*a-51/2)*q^115 + (a^5+a^4-9*a^3-6*a^2+20*a-1)*q^116 + (-1/2*a^5+5*a^3-21/2*a+1)*q^117 + (-3/2*a^5-3*a^4+13*a^3+21*a^2-51/2*a-17)*q^118 + (-a^4+8*a^2-6*a-15)*q^119 + (-2*a^5-7/2*a^4+19*a^3+23*a^2-38*a-51/2)*q^120 + (1/2*a^5+a^4-3*a^3-2*a^2+5/2*a-9)*q^121 + -a*q^122 + (-3/2*a^5-2*a^4+13*a^3+16*a^2-39/2*a-23)*q^123 + (a^4-6*a^2+11)*q^124 + (9/2*a^5+5*a^4-43*a^3-38*a^2+177/2*a+50)*q^125 + (-3/2*a^5-2*a^4+13*a^3+14*a^2-43/2*a-17)*q^126 + (3*a^5+4*a^4-26*a^3-30*a^2+45*a+36)*q^127 + (-a^5-2*a^4+9*a^3+10*a^2-15*a)*q^128 + (-a^4+8*a^2-9)*q^129 + (-3*a^5-9/2*a^4+27*a^3+31*a^2-49*a-85/2)*q^130 + (-2*a^5-3*a^4+16*a^3+24*a^2-20*a-37)*q^131 + (-3/2*a^4+7*a^2-3*a-7/2)*q^132 + (-a^4+2*a^3+6*a^2-16*a-5)*q^133 + (5/2*a^5+2*a^4-23*a^3-12*a^2+77/2*a+17)*q^134 + (1/2*a^5+a^4-5*a^3-8*a^2+21/2*a+10)*q^135 + (-a^5-3*a^4+12*a^3+25*a^2-23*a-34)*q^136 + (-3/2*a^5-a^4+13*a^3+8*a^2-35/2*a-4)*q^137 + (-1/2*a^5+5*a^3-a^2-17/2*a)*q^138 + (-a^5-3/2*a^4+7*a^3+15*a^2-3*a-55/2)*q^139 + (a^5+7/2*a^4-9*a^3-21*a^2+23*a+35/2)*q^140 + (a^5+a^4-10*a^3-8*a^2+19*a+9)*q^141 + (-2*a^4+2*a^3+15*a^2-14*a-17)*q^142 + (-1/2*a^4-a^3+a^2+4*a-5/2)*q^143 + (a^4-6*a^2+4)*q^144 + (-4*a^5-6*a^4+38*a^3+44*a^2-78*a-46)*q^145 + (-1/2*a^4+a^3+3*a^2-17/2)*q^146 + (1/2*a^5-5*a^3+25/2*a+2)*q^147 + (-a^5-a^4+8*a^3+4*a^2-9*a-7)*q^148 + (3/2*a^5+4*a^4-13*a^3-28*a^2+47/2*a+25)*q^149 + (3*a^5+9/2*a^4-27*a^3-35*a^2+52*a+85/2)*q^150 + (-a^5-5/2*a^4+9*a^3+17*a^2-19*a-41/2)*q^151 + (-3*a^5-a^4+26*a^3+14*a^2-45*a-17)*q^152 + (a^5+a^4-9*a^3-6*a^2+16*a+5)*q^153 + (5/2*a^4+a^3-13*a^2+4*a+17/2)*q^154 + (-5*a^5-6*a^4+46*a^3+48*a^2-89*a-72)*q^155 + (1/2*a^5+a^4-5*a^3-4*a^2+25/2*a-2)*q^156 + (4*a^5+4*a^4-36*a^3-28*a^2+60*a+30)*q^157 + (-1/2*a^5-a^4+5*a^3+6*a^2-17/2*a)*q^158 + (2*a^5+2*a^4-19*a^3-16*a^2+35*a+20)*q^159 + (a^5+1/2*a^4-9*a^3-9*a^2+23*a+17/2)*q^160 + (5/2*a^5+2*a^4-23*a^3-14*a^2+81/2*a+17)*q^161 + a*q^162 + (2*a^5+3*a^4-18*a^3-20*a^2+28*a+17)*q^163 + (-1/2*a^5+a^4+5*a^3-8*a^2-13/2*a+12)*q^164 + (1/2*a^4+a^3-3*a^2+1/2)*q^165 + (3*a^5+7*a^4-30*a^3-52*a^2+61*a+51)*q^166 + (-2*a^5-3*a^4+18*a^3+24*a^2-26*a-37)*q^167 + (5/2*a^5+3*a^4-23*a^3-26*a^2+81/2*a+34)*q^168 + (1/2*a^5+3*a^4-3*a^3-26*a^2+1/2*a+39)*q^169 + (2*a^5-a^4-18*a^3+26*a+17)*q^170 + (a^5+a^4-8*a^3-8*a^2+11*a+13)*q^171 + (-a^4+2*a^3+6*a^2-10*a+1)*q^172 + (-5*a^5-5*a^4+45*a^3+34*a^2-84*a-33)*q^173 + (a^5+a^4-8*a^3-5*a^2+9*a)*q^174 + (-5*a^5-7*a^4+48*a^3+56*a^2-103*a-81)*q^175 + (-3/2*a^4+3*a^2+a-3/2)*q^176 + (-a^5-3/2*a^4+8*a^3+11*a^2-10*a-31/2)*q^177 + (-3*a^5-3*a^4+24*a^3+25*a^2-31*a-34)*q^178 + (a^5+4*a^4-8*a^3-34*a^2+11*a+40)*q^179 + (-1/2*a^5+3*a^3-5/2*a-3)*q^180 + (2*a^5+3*a^4-20*a^3-26*a^2+44*a+33)*q^181 + (7/2*a^5+3*a^4-33*a^3-26*a^2+119/2*a+34)*q^182 + -1*q^183 + (3/2*a^5-13*a^3-a^2+51/2*a)*q^184 + (4*a^5+3*a^4-34*a^3-22*a^2+52*a+35)*q^185 + (-3*a^5-4*a^4+28*a^3+30*a^2-51*a-34)*q^186 + (-2*a^4+10*a^2-6*a-4)*q^187 + (-a^5-a^4+6*a^3+4*a^2-11*a-1)*q^188 + (-a^5-3/2*a^4+9*a^3+11*a^2-17*a-23/2)*q^189 + (2*a^5+a^4-22*a^3-6*a^2+38*a+17)*q^190 + (a^5+3/2*a^4-8*a^3-9*a^2+10*a+3/2)*q^191 + (a^4-2*a^3-7*a^2+10*a+9)*q^192 + (-2*a^5-a^4+18*a^3+10*a^2-34*a-23)*q^193 + (-3*a^5-4*a^4+26*a^3+34*a^2-41*a-34)*q^194 + (-5/2*a^5-3*a^4+23*a^3+22*a^2-93/2*a-24)*q^195 + (-1/2*a^5-a^4+7*a^3+7*a^2-33/2*a-4)*q^196 + (1/2*a^5+3*a^4-5*a^3-20*a^2+29/2*a+12)*q^197 + (-1/2*a^5+3*a^3-a^2-5/2*a)*q^198 + (-3*a^4-2*a^3+22*a^2+4*a-23)*q^199 + (-6*a^5-19/2*a^4+58*a^3+73*a^2-112*a-187/2)*q^200 +  ...

-------------------------------------------------------
183D (old = 61A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + C(Z/2*3 + Z/2*3) + E(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
183E (old = 61B), dim = 3

CONGRUENCES:
Modular Degree = 2^6*19
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*19 + Z/2*19
= A(Z/2 + Z/2 + Z/2 + Z/2) + B(Z/19 + Z/19) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(184)
Weight 2

-------------------------------------------------------
J_0(184), dim = 21

-------------------------------------------------------
184A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= E(Z/2 + Z/2) + F(Z/2 + Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 5.3233142109193324905 + -0.87749544019585467021e-3i
Omega-         = 0.14200004171749811475e-3 + 1.6507538365114108844i
L(1)           =
w1             = -2.6617281054805249943 + -0.82493817053560751486i
w2             = 0.14200004171749811475e-3 + 1.6507538365114108844i
c4             = 207.88368567570412508 + 0.69928848403021460028e-1i
c6             = -3101.7402103227935991 + -1.6495068750823189952i
j              = -24371.706505891208564 + 20.042646976029725613i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^5 + -4*q^7 + -2*q^9 + -2*q^11 + 7*q^13 + 2*q^15 + -4*q^17 + -6*q^19 + 4*q^21 + -1*q^23 + -1*q^25 + 5*q^27 + 5*q^29 + 3*q^31 + 2*q^33 + 8*q^35 + 2*q^37 + -7*q^39 + -9*q^41 + 8*q^43 + 4*q^45 + -1*q^47 + 9*q^49 + 4*q^51 + -6*q^53 + 4*q^55 + 6*q^57 + -8*q^59 + -10*q^61 + 8*q^63 + -14*q^65 + 2*q^67 + 1*q^69 + -13*q^71 + -3*q^73 + 1*q^75 + 8*q^77 + 6*q^79 + 1*q^81 + 8*q^85 + -5*q^87 + -4*q^89 + -28*q^91 + -3*q^93 + 12*q^95 + -8*q^97 + 4*q^99 + -14*q^101 + 16*q^103 + -8*q^105 + 6*q^107 + -2*q^111 + -12*q^113 + 2*q^115 + -14*q^117 + 16*q^119 + -7*q^121 + 9*q^123 + 12*q^125 + -7*q^127 + -8*q^129 + 3*q^131 + 24*q^133 + -10*q^135 + 20*q^137 + -19*q^139 + 1*q^141 + -14*q^143 + -10*q^145 + -9*q^147 + 6*q^149 + 11*q^151 + 8*q^153 + -6*q^155 + 6*q^159 + 4*q^161 + 1*q^163 + -4*q^165 + -24*q^167 + 36*q^169 + 12*q^171 + 14*q^173 + 4*q^175 + 8*q^177 + 5*q^179 + 18*q^181 + 10*q^183 + -4*q^185 + 8*q^187 + -20*q^189 + 6*q^191 + 1*q^193 + 14*q^195 + -3*q^197 + -14*q^199 +  ...

-------------------------------------------------------
184B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= C(Z/3 + Z/3) + E(Z/2) + H(Z/2 + Z/2^2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.5979497590113208361 + 0.59478038589831811335e-4i
Omega-         = 0.23808263066813942337e-3 + 1.9948810774360081534i
L(1)           = 1.2989748798460862733
w1             = -1.2990939208209944878 + -0.99747027773729899261i
w2             = -1.2988558381903263484 + 0.9974107996987091608i
c4             = -239.98312852400699649 + 0.51164094911194780973e-1i
c6             = -5186.3252006472896853 + -3.3182171262553157051i
j              = 586.52688501402492221 + -0.74358379341221086719i

HECKE EIGENFORM:
f(q) = q + 4*q^7 + -3*q^9 + 6*q^11 + -2*q^13 + 6*q^17 + -6*q^19 + 1*q^23 + -5*q^25 + -6*q^29 + -8*q^37 + 6*q^41 + -2*q^43 + -8*q^47 + 9*q^49 + -8*q^53 + 4*q^59 + -4*q^61 + -12*q^63 + 2*q^67 + -8*q^71 + 6*q^73 + 24*q^77 + 12*q^79 + 9*q^81 + 10*q^83 + 10*q^89 + -8*q^91 + -18*q^97 + -18*q^99 + 6*q^101 + 8*q^103 + 2*q^107 + -12*q^109 + 2*q^113 + 6*q^117 + 24*q^119 + 25*q^121 + 8*q^127 + -12*q^131 + -24*q^133 + -2*q^137 + 4*q^139 + -12*q^143 + 8*q^149 + -8*q^151 + -18*q^153 + -24*q^157 + 4*q^161 + -8*q^163 + -8*q^167 + -9*q^169 + 18*q^171 + 2*q^173 + -20*q^175 + 12*q^181 + 36*q^187 + -4*q^191 + -22*q^193 + -6*q^197 + 20*q^199 +  ...

-------------------------------------------------------
184C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*3
Ker(ModPolar)  = Z/2^3*3 + Z/2^3*3
= B(Z/3 + Z/3) + D(Z/2 + Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 0.87663594490800442592 + 0.29434516612979587854e-3i
Omega-         = 0.62486379403971946526e-3 + 4.9480374900211380778i
L(1)           = 1.7532719886473137799
w1             = 0.43800554055698235323 + -2.473871572427504141i
w2             = -0.87663594490800442592 + -0.29434516612979587854e-3i
c4             = 2639.0025652505600637 + -3.5444621201735222075i
c6             = 135571.02950581978877 + -273.11064588778379922i
j              = -50233265.776998101842 + 411587.18352804411534i

HECKE EIGENFORM:
f(q) = q + 3*q^3 + -2*q^7 + 6*q^9 + -5*q^13 + -6*q^17 + 6*q^19 + -6*q^21 + 1*q^23 + -5*q^25 + 9*q^27 + 9*q^29 + 3*q^31 + -8*q^37 + -15*q^39 + 3*q^41 + -8*q^43 + 7*q^47 + -3*q^49 + -18*q^51 + -2*q^53 + 18*q^57 + 4*q^59 + -10*q^61 + -12*q^63 + 8*q^67 + 3*q^69 + 7*q^71 + 9*q^73 + -15*q^75 + -6*q^79 + 9*q^81 + -14*q^83 + 27*q^87 + 16*q^89 + 10*q^91 + 9*q^93 + 6*q^97 + 6*q^101 + 14*q^103 + 14*q^107 + -24*q^111 + 2*q^113 + -30*q^117 + 12*q^119 + -11*q^121 + 9*q^123 + 5*q^127 + -24*q^129 + -9*q^131 + -12*q^133 + 4*q^137 + -23*q^139 + 21*q^141 + -9*q^147 + 14*q^149 + 7*q^151 + -36*q^153 + 12*q^157 + -6*q^159 + -2*q^161 + -11*q^163 + 4*q^167 + 12*q^169 + 36*q^171 + -10*q^173 + 10*q^175 + 12*q^177 + -3*q^179 + -30*q^183 + -18*q^189 + -16*q^191 + -7*q^193 + -27*q^197 + 20*q^199 +  ...

-------------------------------------------------------
184D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= C(Z/2 + Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 4.4172757620920236736 + -0.7929357832427768031e-4i
Omega-         = 0.40857452852148779719e-3 + -2.3725232800419257943i
L(1)           =
w1             = 2.2084335937817510929 + 1.1862219932318007583i
w2             = 0.40857452852148779719e-3 + -2.3725232800419257943i
c4             = 16.037522709682694715 + -0.46958116510887277367e-1i
c6             = -799.50327596828296156 + 0.37136252980808772914i
j              = -11.223249272392774102 + 0.88733504449501839928e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -4*q^5 + 2*q^7 + -2*q^9 + -4*q^11 + -5*q^13 + 4*q^15 + -2*q^17 + 6*q^19 + -2*q^21 + 1*q^23 + 11*q^25 + 5*q^27 + 1*q^29 + -9*q^31 + 4*q^33 + -8*q^35 + -4*q^37 + 5*q^39 + 3*q^41 + 8*q^43 + 8*q^45 + -5*q^47 + -3*q^49 + 2*q^51 + 6*q^53 + 16*q^55 + -6*q^57 + -4*q^59 + -10*q^61 + -4*q^63 + 20*q^65 + -4*q^67 + -1*q^69 + -5*q^71 + -15*q^73 + -11*q^75 + -8*q^77 + -6*q^79 + 1*q^81 + 6*q^83 + 8*q^85 + -1*q^87 + -8*q^89 + -10*q^91 + 9*q^93 + -24*q^95 + 10*q^97 + 8*q^99 + -10*q^101 + 10*q^103 + 8*q^105 + 6*q^107 + 4*q^111 + 6*q^113 + -4*q^115 + 10*q^117 + -4*q^119 + 5*q^121 + -3*q^123 + -24*q^125 + -7*q^127 + -8*q^129 + -21*q^131 + 12*q^133 + -20*q^135 + 4*q^137 + 5*q^139 + 5*q^141 + 20*q^143 + -4*q^145 + 3*q^147 + -18*q^149 + 11*q^151 + 4*q^153 + 36*q^155 + -12*q^157 + -6*q^159 + 2*q^161 + 25*q^163 + -16*q^165 + 12*q^167 + 12*q^169 + -12*q^171 + -2*q^173 + 22*q^175 + 4*q^177 + 1*q^179 + -12*q^181 + 10*q^183 + 16*q^185 + 8*q^187 + 10*q^189 + 12*q^191 + 1*q^193 + -20*q^195 + 21*q^197 + 16*q^199 +  ...

-------------------------------------------------------
184E (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(Z/2) + F(Z/2 + Z/2) + H(Z/2) + I(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 17
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2
Sha Bound      = 2^5

ANALYTIC INVARIANTS:

Omega+         = 2.9636219536618522856 + 0.25195997013080328458e-3i
Omega-         = 5.5121734299958959203 + 0.94679509088485344464e-3i
L(1)           = 1.4818109821861829389

HECKE EIGENFORM:
a^2+a-4 = 0,
f(q) = q + a*q^3 + 2*q^5 + (-a+1)*q^9 + -2*a*q^11 + (-a+2)*q^13 + 2*a*q^15 + (2*a+2)*q^17 + -2*a*q^19 + -1*q^23 + -1*q^25 + (-a-4)*q^27 + (a+2)*q^29 + (a-4)*q^31 + (2*a-8)*q^33 + (4*a+2)*q^37 + (3*a-4)*q^39 + (-5*a-2)*q^41 + -8*q^43 + (-2*a+2)*q^45 + (-3*a+4)*q^47 + -7*q^49 + 8*q^51 + 2*q^53 + -4*a*q^55 + (2*a-8)*q^57 + (4*a+4)*q^59 + (-4*a+2)*q^61 + (-2*a+4)*q^65 + 2*a*q^67 + -a*q^69 + (a+12)*q^71 + (-3*a-10)*q^73 + -a*q^75 + 2*a*q^79 + -7*q^81 + (4*a+8)*q^83 + (4*a+4)*q^85 + (a+4)*q^87 + (6*a+2)*q^89 + (-5*a+4)*q^93 + -4*a*q^95 + (6*a+2)*q^97 + (-4*a+8)*q^99 + (4*a+6)*q^101 + (-4*a-8)*q^103 + (2*a+8)*q^107 + (2*a+10)*q^109 + (-2*a+16)*q^111 + (2*a-6)*q^113 + -2*q^115 + (-4*a+6)*q^117 + (-4*a+5)*q^121 + (3*a-20)*q^123 + -12*q^125 + (3*a-4)*q^127 + -8*a*q^129 + (-3*a+8)*q^131 + (-2*a-8)*q^135 + (-2*a+10)*q^137 + (3*a-8)*q^139 + (7*a-12)*q^141 + (-6*a+8)*q^143 + (2*a+4)*q^145 + -7*a*q^147 + (-4*a-14)*q^149 + (a-12)*q^151 + (2*a-6)*q^153 + (2*a-8)*q^155 + (2*a+18)*q^157 + 2*a*q^159 + (7*a+8)*q^163 + (4*a-16)*q^165 + -16*q^167 + (-5*a-5)*q^169 + (-4*a+8)*q^171 + -10*q^173 + 16*q^177 + (3*a-8)*q^179 + (-4*a+10)*q^181 + (6*a-16)*q^183 + (8*a+4)*q^185 + -16*q^187 + (6*a+16)*q^191 + (a-2)*q^193 + (6*a-8)*q^195 + (-7*a-6)*q^197 + (2*a+8)*q^199 +  ...

-------------------------------------------------------
184F (old = 92A), dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + E(Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
184G (old = 92B), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= H(Z/3 + Z/3 + Z/3 + Z/3) + I(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
184H (old = 46A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2*5^3
Ker(ModPolar)  = Z/5 + Z/5 + Z/3*5 + Z/3*5 + Z/2^2*3*5 + Z/2^2*3*5
= B(Z/2 + Z/2^2) + E(Z/2) + G(Z/3 + Z/3 + Z/3 + Z/3) + I(Z/5 + Z/5 + Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
184I (old = 23A), dim = 2

CONGRUENCES:
Modular Degree = 2^8*5^3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*5 + Z/2^2*5 + Z/2^2*5 + Z/2^2*5 + Z/2^2*5 + Z/2^2*5
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/5 + Z/5 + Z/5 + Z/5 + Z/5 + Z/5)

-------------------------------------------------------
Gamma_0(185)
Weight 2

-------------------------------------------------------
J_0(185), dim = 17

-------------------------------------------------------
185A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= B(Z/3 + Z/3) + D(Z/2) + E(Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 1.7469148809490184578 + -0.15859171289276287259e-3i
Omega-         = 0.16953161526647462908e-3 + 2.8190739736164962039i
L(1)           =
w1             = 0.16953161526647462908e-3 + 2.8190739736164962039i
w2             = 1.7469148809490184578 + -0.15859171289276287259e-3i
c4             = 168.93927691332941261 + 0.60854637074487824567e-1i
c6             = 2121.8084462860305859 + 1.1691806150847201438i
j              = 26074.459053885331586 + 7.866303310544514591i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -2*q^3 + -1*q^4 + -1*q^5 + -2*q^6 + -2*q^7 + -3*q^8 + 1*q^9 + -1*q^10 + 2*q^12 + -2*q^13 + -2*q^14 + 2*q^15 + -1*q^16 + 2*q^17 + 1*q^18 + 2*q^19 + 1*q^20 + 4*q^21 + -8*q^23 + 6*q^24 + 1*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 + -1*q^36 + -1*q^37 + 2*q^38 + 4*q^39 + 3*q^40 + 10*q^41 + 4*q^42 + -4*q^43 + -1*q^45 + -8*q^46 + -10*q^47 + 2*q^48 + -3*q^49 + 1*q^50 + -4*q^51 + 2*q^52 + -6*q^53 + 4*q^54 + 6*q^56 + -4*q^57 + 2*q^58 + -6*q^59 + -2*q^60 + 2*q^61 + -6*q^62 + -2*q^63 + 7*q^64 + 2*q^65 + -14*q^67 + -2*q^68 + 16*q^69 + 2*q^70 + -3*q^72 + 2*q^73 + -1*q^74 + -2*q^75 + -2*q^76 + 4*q^78 + -6*q^79 + 1*q^80 + -11*q^81 + 10*q^82 + 18*q^83 + -4*q^84 + -2*q^85 + -4*q^86 + -4*q^87 + 2*q^89 + -1*q^90 + 4*q^91 + 8*q^92 + 12*q^93 + -10*q^94 + -2*q^95 + -10*q^96 + -10*q^97 + -3*q^98 + -1*q^100 + 10*q^101 + -4*q^102 + -4*q^103 + 6*q^104 + -4*q^105 + -6*q^106 + 6*q^107 + -4*q^108 + 2*q^109 + 2*q^111 + 2*q^112 + 2*q^113 + -4*q^114 + 8*q^115 + -2*q^116 + -2*q^117 + -6*q^118 + -4*q^119 + -6*q^120 + -11*q^121 + 2*q^122 + -20*q^123 + 6*q^124 + -1*q^125 + -2*q^126 + -2*q^127 + -3*q^128 + 8*q^129 + 2*q^130 + 18*q^131 + -4*q^133 + -14*q^134 + -4*q^135 + -6*q^136 + -6*q^137 + 16*q^138 + -4*q^139 + -2*q^140 + 20*q^141 + -1*q^144 + -2*q^145 + 2*q^146 + 6*q^147 + 1*q^148 + -6*q^149 + -2*q^150 + -20*q^151 + -6*q^152 + 2*q^153 + 6*q^155 + -4*q^156 + 18*q^157 + -6*q^158 + 12*q^159 + -5*q^160 + 16*q^161 + -11*q^162 + 16*q^163 + -10*q^164 + 18*q^166 + 12*q^167 + -12*q^168 + -9*q^169 + -2*q^170 + 2*q^171 + 4*q^172 + 2*q^173 + -4*q^174 + -2*q^175 + 12*q^177 + 2*q^178 + 14*q^179 + 1*q^180 + 10*q^181 + 4*q^182 + -4*q^183 + 24*q^184 + 1*q^185 + 12*q^186 + 10*q^188 + -8*q^189 + -2*q^190 + 22*q^191 + -14*q^192 + 14*q^193 + -10*q^194 + -4*q^195 + 3*q^196 + 10*q^197 + -26*q^199 + -3*q^200 +  ...

-------------------------------------------------------
185B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^4*3 + Z/2^4*3
= A(Z/3 + Z/3) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2^2 + Z/2^2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 1.7963548538372358145 + 0.4342837046479804014e-3i
Omega-         = 0.18061044264302592163e-3 + 0.67499105398243694358i
L(1)           =
w1             = 1.7963548538372358145 + 0.4342837046479804014e-3i
w2             = -0.18061044264302592163e-3 + -0.67499105398243694358i
c4             = 7508.1474971394018179 + 8.0351208866222367812i
c6             = -650546.70760549948906 + -1044.5721578929822546i
j              = 18282484.390548656608 + 155705.40935025620572i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + 1*q^3 + 2*q^4 + -1*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 + -1*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 + 1*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 + -1*q^37 + 8*q^38 + -2*q^39 + 7*q^41 + 10*q^42 + -10*q^43 + 6*q^44 + 2*q^45 + 4*q^46 + 11*q^47 + -4*q^48 + 18*q^49 + -2*q^50 + -4*q^51 + -4*q^52 + -3*q^53 + 10*q^54 + -3*q^55 + -4*q^57 + -4*q^58 + -2*q^60 + -4*q^61 + 10*q^63 + -8*q^64 + 2*q^65 + -6*q^66 + 16*q^67 + -8*q^68 + -2*q^69 + -10*q^70 + -15*q^71 + 11*q^73 + 2*q^74 + 1*q^75 + -8*q^76 + -15*q^77 + 4*q^78 + -12*q^79 + 4*q^80 + 1*q^81 + -14*q^82 + -3*q^83 + -10*q^84 + 4*q^85 + 20*q^86 + 2*q^87 + -4*q^89 + -4*q^90 + 10*q^91 + -4*q^92 + -22*q^94 + 4*q^95 + 8*q^96 + 8*q^97 + -36*q^98 + -6*q^99 + 2*q^100 + -5*q^101 + 8*q^102 + -10*q^103 + 5*q^105 + 6*q^106 + -12*q^107 + -10*q^108 + -16*q^109 + 6*q^110 + -1*q^111 + 20*q^112 + 14*q^113 + 8*q^114 + 2*q^115 + 4*q^116 + 4*q^117 + 20*q^119 + -2*q^121 + 8*q^122 + 7*q^123 + -1*q^125 + -20*q^126 + -11*q^127 + -10*q^129 + -4*q^130 + 12*q^131 + 6*q^132 + 20*q^133 + -32*q^134 + 5*q^135 + -6*q^137 + 4*q^138 + -4*q^139 + 10*q^140 + 11*q^141 + 30*q^142 + -6*q^143 + 8*q^144 + -2*q^145 + -22*q^146 + 18*q^147 + -2*q^148 + 3*q^149 + -2*q^150 + -8*q^151 + 8*q^153 + 30*q^154 + -4*q^156 + 3*q^157 + 24*q^158 + -3*q^159 + -8*q^160 + 10*q^161 + -2*q^162 + -2*q^163 + 14*q^164 + -3*q^165 + 6*q^166 + -12*q^167 + -9*q^169 + -8*q^170 + 8*q^171 + -20*q^172 + 5*q^173 + -4*q^174 + -5*q^175 + -12*q^176 + 8*q^178 + -10*q^179 + 4*q^180 + 13*q^181 + -20*q^182 + -4*q^183 + 1*q^185 + -12*q^187 + 22*q^188 + 25*q^189 + -8*q^190 + -20*q^191 + -8*q^192 + 14*q^193 + -16*q^194 + 2*q^195 + 36*q^196 + -17*q^197 + 12*q^198 + -14*q^199 +  ...

-------------------------------------------------------
185C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.4492762386071285081 + -0.33052169805756642483e-3i
Omega-         = 0.72317033340625436491e-4 + 1.5761988699439844937i
L(1)           =
w1             = 2.4492762386071285081 + -0.33052169805756642483e-3i
w2             = -0.72317033340625436491e-4 + -1.5761988699439844937i
c4             = 255.99527526376077259 + 0.50014882472182881619e-1i
c6             = -3895.9563537941019864 + -0.97097129027060076456i
j              = 18143.1977294677236 + -15.110438323382742255i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^4 + 1*q^5 + -3*q^7 + -2*q^9 + -5*q^11 + 2*q^12 + 4*q^13 + -1*q^15 + 4*q^16 + -4*q^17 + -8*q^19 + -2*q^20 + 3*q^21 + 4*q^23 + 1*q^25 + 5*q^27 + 6*q^28 + 4*q^29 + 2*q^31 + 5*q^33 + -3*q^35 + 4*q^36 + 1*q^37 + -4*q^39 + -5*q^41 + -6*q^43 + 10*q^44 + -2*q^45 + 9*q^47 + -4*q^48 + 2*q^49 + 4*q^51 + -8*q^52 + 3*q^53 + -5*q^55 + 8*q^57 + -8*q^59 + 2*q^60 + -10*q^61 + 6*q^63 + -8*q^64 + 4*q^65 + -4*q^67 + 8*q^68 + -4*q^69 + 5*q^71 + -15*q^73 + -1*q^75 + 16*q^76 + 15*q^77 + -14*q^79 + 4*q^80 + 1*q^81 + 11*q^83 + -6*q^84 + -4*q^85 + -4*q^87 + -2*q^89 + -12*q^91 + -8*q^92 + -2*q^93 + -8*q^95 + 10*q^97 + 10*q^99 + -2*q^100 + -9*q^101 + -10*q^103 + 3*q^105 + -16*q^107 + -10*q^108 + 14*q^109 + -1*q^111 + -12*q^112 + -14*q^113 + 4*q^115 + -8*q^116 + -8*q^117 + 12*q^119 + 14*q^121 + 5*q^123 + -4*q^124 + 1*q^125 + -5*q^127 + 6*q^129 + 18*q^131 + -10*q^132 + 24*q^133 + 5*q^135 + 14*q^137 + 12*q^139 + 6*q^140 + -9*q^141 + -20*q^143 + -8*q^144 + 4*q^145 + -2*q^147 + -2*q^148 + 3*q^149 + -8*q^151 + 8*q^153 + 2*q^155 + 8*q^156 + -11*q^157 + -3*q^159 + -12*q^161 + 10*q^164 + 5*q^165 + 2*q^167 + 3*q^169 + 16*q^171 + 12*q^172 + 19*q^173 + -3*q^175 + -20*q^176 + 8*q^177 + 4*q^180 + -7*q^181 + 10*q^183 + 1*q^185 + 20*q^187 + -18*q^188 + -15*q^189 + 8*q^191 + 8*q^192 + -16*q^193 + -4*q^195 + -4*q^196 + 13*q^197 + 10*q^199 +  ...

-------------------------------------------------------
185D (new) , dim = 5

CONGRUENCES:
Modular Degree = 2^7*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^3*3 + Z/2^3*3
= A(Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2*3 + Z/2*3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^4*60869
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2^2
ord((0)-(oo))  = 3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/3
Sha Bound      = 2^2*3

ANALYTIC INVARIANTS:

Omega+         = 4.4069445023131965054 + -0.10887292067724916876e-2i
Omega-         = 0.12468412582633583849e-2 + -10.905388601296159274i
L(1)           = 1.4689815455992250491

HECKE EIGENFORM:
a^5-2*a^4-8*a^3+14*a^2+11*a-12 = 0,
f(q) = q + a*q^2 + (-1/2*a^3+5/2*a+1)*q^3 + (a^2-2)*q^4 + -1*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 + 1*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 + 1*q^37 + (-3/2*a^4+23/2*a^2+a-12)*q^38 + (1/2*a^4-1/2*a^3-7/2*a^2+11/2*a+2)*q^39 + (-a^3+4*a)*q^40 + (-a^2+3)*q^41 + (-1/2*a^4+1/2*a^3-3/2*a^2-1/2*a+6)*q^42 + (a^4-9*a^2+2*a+14)*q^43 + (-a^4+5*a^2-6)*q^44 + (-1/2*a^4+1/2*a^3+7/2*a^2-5/2*a-4)*q^45 + (-2*a^4+a^3+14*a^2-a-12)*q^46 + (3/2*a^4-21/2*a^2-a+9)*q^47 + (-a^4-3/2*a^3+6*a^2+7/2*a-2)*q^48 + (1/2*a^4-1/2*a^3-3/2*a^2+1/2*a)*q^49 + a*q^50 + (-1/2*a^4+1/2*a^3+15/2*a^2-11/2*a-18)*q^51 + (-3/2*a^4-1/2*a^3+19/2*a^2+9/2*a-10)*q^52 + (-a^3-a^2+9*a+3)*q^53 + (3/2*a^4-1/2*a^3-21/2*a^2+3/2*a+6)*q^54 + (a^2-3)*q^55 + (a^4+7/2*a^3-8*a^2-27/2*a+6)*q^56 + (-3/2*a^4+3/2*a^3+27/2*a^2-15/2*a-22)*q^57 + (-a^4+5*a^2)*q^58 + (1/2*a^4+a^3-9/2*a^2-6*a)*q^59 + (a^4+1/2*a^3-8*a^2-1/2*a+8)*q^60 + (a^4-a^3-7*a^2+7*a+2)*q^61 + (-3/2*a^3+3*a^2+15/2*a-6)*q^62 + (a^4-3/2*a^3-6*a^2+15/2*a+8)*q^63 + (2*a^4+2*a^3-15*a^2-10*a+16)*q^64 + (1/2*a^4-1/2*a^3-5/2*a^2+5/2*a-2)*q^65 + (2*a^4-12*a^2-2*a+12)*q^66 + (-a^4+3/2*a^3+6*a^2-11/2*a+2)*q^67 + (1/2*a^4-5/2*a^3-5/2*a^2+17/2*a+6)*q^68 + (-2*a^4+a^3+18*a^2-7*a-24)*q^69 + (-a^4-1/2*a^3+8*a^2+1/2*a-6)*q^70 + (-a^4+2*a^3+6*a^2-12*a-3)*q^71 + (1/2*a^4+3/2*a^3-5/2*a^2-9/2*a-6)*q^72 + (2*a^3-a^2-14*a+5)*q^73 + a*q^74 + (-1/2*a^3+5/2*a+1)*q^75 + (-a^4-3/2*a^3+6*a^2+19/2*a+2)*q^76 + (-a^4+4*a^2+2*a+3)*q^77 + (1/2*a^4+1/2*a^3-3/2*a^2-7/2*a+6)*q^78 + (1/2*a^4-a^3-9/2*a^2+2*a+14)*q^79 + (-a^4+6*a^2-4)*q^80 + (-1/2*a^4+1/2*a^3+5/2*a^2-5/2*a-5)*q^81 + (-a^3+3*a)*q^82 + (-1/2*a^3+2*a^2+9/2*a-3)*q^83 + (-3/2*a^4-5/2*a^3+27/2*a^2+1/2*a-16)*q^84 + (1/2*a^4-1/2*a^3-9/2*a^2+9/2*a+6)*q^85 + (2*a^4-a^3-12*a^2+3*a+12)*q^86 + (a^4-7*a^2+12)*q^87 + (-2*a^4-a^3+14*a^2-a-12)*q^88 + (2*a^4-16*a^2+2*a+18)*q^89 + (-1/2*a^4-1/2*a^3+9/2*a^2+3/2*a-6)*q^90 + (-1/2*a^4+3/2*a^3-1/2*a^2-17/2*a+10)*q^91 + (-a^4-2*a^3+9*a^2+10*a)*q^92 + (-1/2*a^4-1/2*a^3+5/2*a^2+13/2*a-4)*q^93 + (3*a^4+3/2*a^3-22*a^2-15/2*a+18)*q^94 + (a^4-1/2*a^3-8*a^2+5/2*a+10)*q^95 + (-1/2*a^4-2*a^3-3/2*a^2+7*a+12)*q^96 + (2*a^4-3*a^3-16*a^2+17*a+14)*q^97 + (1/2*a^4+5/2*a^3-13/2*a^2-11/2*a+6)*q^98 + (-a^3-2*a^2+7*a+6)*q^99 + (a^2-2)*q^100 + (-1/2*a^4-3/2*a^3+11/2*a^2+15/2*a-15)*q^101 + (-1/2*a^4+7/2*a^3+3/2*a^2-25/2*a-6)*q^102 + (-2*a^4+12*a^2+2*a+2)*q^103 + (-5/2*a^4+1/2*a^3+33/2*a^2-17/2*a-6)*q^104 + (-1/2*a^4+3/2*a^3+7/2*a^2-11/2*a-5)*q^105 + (-a^4-a^3+9*a^2+3*a)*q^106 + (-3/2*a^4+2*a^3+23/2*a^2-9*a-12)*q^107 + (3/2*a^4+1/2*a^3-21/2*a^2-7/2*a+4)*q^108 + (-a^4-a^3+9*a^2+5*a-10)*q^109 + (a^3-3*a)*q^110 + (-1/2*a^3+5/2*a+1)*q^111 + (5/2*a^4-25/2*a^2+a+8)*q^112 + (-1/2*a^4+1/2*a^3+9/2*a^2-5/2*a-12)*q^113 + (-3/2*a^4+3/2*a^3+27/2*a^2-11/2*a-18)*q^114 + (a^4-9*a^2+12)*q^115 + (-2*a^4-a^3+14*a^2+a-12)*q^116 + (1/2*a^4-3/2*a^3-9/2*a^2+19/2*a+2)*q^117 + (2*a^4-1/2*a^3-13*a^2-11/2*a+6)*q^118 + (-3/2*a^4+1/2*a^3+29/2*a^2-19/2*a-18)*q^119 + (3/2*a^4-19/2*a^2-a+12)*q^120 + (a^4-6*a^2-2)*q^121 + (a^4+a^3-7*a^2-9*a+12)*q^122 + (a^4-8*a^2+2*a+9)*q^123 + (-1/2*a^4+a^3+5/2*a^2+2*a-4)*q^124 + -1*q^125 + (1/2*a^4+2*a^3-13/2*a^2-3*a+12)*q^126 + (-5/2*a^3+2*a^2+29/2*a+5)*q^127 + (2*a^4+a^3-10*a^2-8*a)*q^128 + (a^4-2*a^3-13*a^2+14*a+26)*q^129 + (1/2*a^4+3/2*a^3-9/2*a^2-15/2*a+6)*q^130 + (a^4-1/2*a^3-4*a^2+1/2*a-12)*q^131 + (2*a^4+4*a^3-14*a^2-14*a+6)*q^132 + (-1/2*a^4+3/2*a^3+9/2*a^2-23/2*a-14)*q^133 + (-1/2*a^4-2*a^3+17/2*a^2+13*a-12)*q^134 + (-1/2*a^4-1/2*a^3+9/2*a^2+7/2*a-7)*q^135 + (-1/2*a^4+1/2*a^3-7/2*a^2+3/2*a+18)*q^136 + (-3*a^4+2*a^3+21*a^2-10*a-18)*q^137 + (-3*a^4+2*a^3+21*a^2-2*a-24)*q^138 + (-a^4+a^3+9*a^2-a-16)*q^139 + (-3/2*a^4+15/2*a^2+3*a-2)*q^140 + (1/2*a^4-3/2*a^3-11/2*a^2+7/2*a+9)*q^141 + (-2*a^3+2*a^2+8*a-12)*q^142 + (a^4+a^3-7*a^2-7*a+12)*q^143 + (3/2*a^4+1/2*a^3-17/2*a^2-5/2*a+10)*q^144 + (a^3-5*a)*q^145 + (2*a^4-a^3-14*a^2+5*a)*q^146 + (-1/2*a^4-2*a^3+13/2*a^2+3*a-6)*q^147 + (a^2-2)*q^148 + (3/2*a^4+5/2*a^3-29/2*a^2-29/2*a+21)*q^149 + (-1/2*a^4+5/2*a^2+a)*q^150 + (a^4-2*a^3-7*a^2+18*a+8)*q^151 + (-1/2*a^4-2*a^3+1/2*a^2+11*a+12)*q^152 + (-3/2*a^4+1/2*a^3+31/2*a^2-13/2*a-30)*q^153 + (-2*a^4-4*a^3+16*a^2+14*a-12)*q^154 + (1/2*a^4-a^3-5/2*a^2+4*a-2)*q^155 + (1/2*a^4+7/2*a^3-7/2*a^2-21/2*a+2)*q^156 + (-2*a^3+3*a^2+14*a-7)*q^157 + (-1/2*a^3-5*a^2+17/2*a+6)*q^158 + (-5*a^2+6*a+21)*q^159 + (-2*a^4+14*a^2-a-12)*q^160 + (a^4-3*a^2-8*a-12)*q^161 + (-1/2*a^4-3/2*a^3+9/2*a^2+1/2*a-6)*q^162 + (-2*a^3+2*a^2+10*a-4)*q^163 + (-a^4+5*a^2-6)*q^164 + (-a^4+8*a^2-2*a-9)*q^165 + (-1/2*a^4+2*a^3+9/2*a^2-3*a)*q^166 + (a^4-3*a^3-11*a^2+17*a+18)*q^167 + (-9/2*a^4+1/2*a^3+49/2*a^2+3/2*a-30)*q^168 + (-a^4+4*a^3+5*a^2-24*a+3)*q^169 + (1/2*a^4-1/2*a^3-5/2*a^2+1/2*a+6)*q^170 + (-3/2*a^4+2*a^3+27/2*a^2-13*a-28)*q^171 + (a^4+4*a^3-7*a^2-14*a-4)*q^172 + (2*a^4-11*a^2-2*a-9)*q^173 + (2*a^4+a^3-14*a^2+a+12)*q^174 + (1/2*a^4-7/2*a^2-a+5)*q^175 + (-3*a^4-2*a^3+17*a^2+10*a-12)*q^176 + (1/2*a^4+5/2*a^3-9/2*a^2-25/2*a-6)*q^177 + (4*a^4-26*a^2-4*a+24)*q^178 + (a^4-5/2*a^3-8*a^2+25/2*a+6)*q^179 + (-1/2*a^4-1/2*a^3+3/2*a^2+9/2*a+2)*q^180 + (1/2*a^4-1/2*a^3-7/2*a^2+1/2*a-1)*q^181 + (1/2*a^4-9/2*a^3-3/2*a^2+31/2*a-6)*q^182 + (a^3-4*a^2-5*a+14)*q^183 + (-a^3-4*a^2+13*a+12)*q^184 + -1*q^185 + (-3/2*a^4-3/2*a^3+27/2*a^2+3/2*a-6)*q^186 + (-a^4+3*a^3+7*a^2-13*a-12)*q^187 + (9/2*a^4+2*a^3-57/2*a^2-13*a+18)*q^188 + (-a^4+a^3+6*a^2-3*a+5)*q^189 + (3/2*a^4-23/2*a^2-a+12)*q^190 + (3/2*a^4+a^3-15/2*a^2-10*a)*q^191 + (-a^4-5/2*a^3+2*a^2+21/2*a-2)*q^192 + (2*a^4-12*a^2-4)*q^193 + (a^4-11*a^2-8*a+24)*q^194 + (-1/2*a^4+1/2*a^3+7/2*a^2-11/2*a-2)*q^195 + (5/2*a^4-3/2*a^3-19/2*a^2-1/2*a+6)*q^196 + (a^4-a^3-10*a^2-3*a+21)*q^197 + (-a^4-2*a^3+7*a^2+6*a)*q^198 + (a^4-1/2*a^3-8*a^2+1/2*a+8)*q^199 + (a^3-4*a)*q^200 +  ...

-------------------------------------------------------
185E (new) , dim = 5

CONGRUENCES:
Modular Degree = 2^9
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^5 + Z/2^5
= A(Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2^3 + Z/2^3) + G(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^4*23029
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2^2
ord((0)-(oo))  = 19
Torsion Bound  = 2*19
|L(1)/Omega|   = 2^2/19
Sha Bound      = 2^4*19

ANALYTIC INVARIANTS:

Omega+         = 2.5490627743351339269 + 0.33127373195409666952e-6i
Omega-         = 0.57850543608588529805e-2 + -10.072874489515842077i
L(1)           = 0.53664479459687483219

HECKE EIGENFORM:
a^5-8*a^3+2*a^2+11*a-2 = 0,
f(q) = q + a*q^2 + (-1/2*a^4+7/2*a^2-a-3)*q^3 + (a^2-2)*q^4 + 1*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 + 1*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 + -1*q^37 + (-a^4-3/2*a^3+3*a^2+15/2*a-1)*q^38 + (1/2*a^4+1/2*a^3-9/2*a^2-3/2*a+9)*q^39 + (a^3-4*a)*q^40 + (-2*a^3-a^2+10*a-1)*q^41 + (-1/2*a^4-1/2*a^3+7/2*a^2+5/2*a-3)*q^42 + (a^4-5*a^2+2*a+2)*q^43 + (a^3+4*a^2-3*a-8)*q^44 + (1/2*a^4+1/2*a^3-9/2*a^2-5/2*a+7)*q^45 + (a^3-2*a^2-5*a+2)*q^46 + (-3/2*a^3+a^2+19/2*a-6)*q^47 + (-1/2*a^4+9/2*a^2+a-12)*q^48 + (1/2*a^4-3/2*a^3-13/2*a^2+19/2*a+11)*q^49 + a*q^50 + (3/2*a^4-1/2*a^3-23/2*a^2+11/2*a+13)*q^51 + (1/2*a^4-3/2*a^3-7/2*a^2+7/2*a+5)*q^52 + (-a^3-a^2+5*a-1)*q^53 + (1/2*a^4+3/2*a^3-5/2*a^2-9/2*a-1)*q^54 + (a^4+a^3-6*a^2-3*a+5)*q^55 + (1/2*a^4+a^3-5/2*a^2-6*a-2)*q^56 + (-3/2*a^4+1/2*a^3+21/2*a^2-9/2*a-7)*q^57 + (2*a^4+3*a^3-10*a^2-9*a+2)*q^58 + (-a^4-3/2*a^3+7*a^2+19/2*a-5)*q^59 + (1/2*a^4-9/2*a^2+a+6)*q^60 + (-a^4+a^3+7*a^2-7*a-2)*q^61 + (3/2*a^4+a^3-15/2*a^2-2*a+2)*q^62 + (7/2*a^4+2*a^3-51/2*a^2-5*a+30)*q^63 + (-2*a^4-2*a^3+13*a^2+2*a-8)*q^64 + (-1/2*a^4-1/2*a^3+7/2*a^2+1/2*a-3)*q^65 + (-2*a-2)*q^66 + (-3/2*a^4+23/2*a^2+a-12)*q^67 + (1/2*a^4+1/2*a^3-11/2*a^2-1/2*a+9)*q^68 + (-a^4+9*a^2-18)*q^69 + (-1/2*a^4-a^3+5/2*a^2+4*a)*q^70 + (-3*a^4+20*a^2-2*a-11)*q^71 + (-3/2*a^4-3/2*a^3+21/2*a^2+1/2*a-5)*q^72 + (a^4+a^3-8*a^2-3*a+9)*q^73 + -a*q^74 + (-1/2*a^4+7/2*a^2-a-3)*q^75 + (-1/2*a^4-3*a^3+9/2*a^2+6*a-6)*q^76 + (3*a^4+2*a^3-22*a^2-8*a+21)*q^77 + (1/2*a^4-1/2*a^3-5/2*a^2+7/2*a+1)*q^78 + (a^4+1/2*a^3-5*a^2+3/2*a+7)*q^79 + (a^4-6*a^2+4)*q^80 + (3/2*a^4-1/2*a^3-21/2*a^2+13/2*a+12)*q^81 + (-2*a^4-a^3+10*a^2-a)*q^82 + (-1/2*a^4+11/2*a^2-3*a-11)*q^83 + (5/2*a^4+1/2*a^3-39/2*a^2+3/2*a+27)*q^84 + (-1/2*a^4-1/2*a^3+7/2*a^2+5/2*a-5)*q^85 + (3*a^3-9*a+2)*q^86 + (a^3-7*a)*q^87 + (-a^4+7*a^2+4*a-4)*q^88 + (4*a^2-2*a-16)*q^89 + (1/2*a^4-1/2*a^3-7/2*a^2+3/2*a+1)*q^90 + (-3/2*a^4-1/2*a^3+23/2*a^2+3/2*a-13)*q^91 + (-a^4-2*a^3+9*a^2+2*a-12)*q^92 + (-5/2*a^4+1/2*a^3+39/2*a^2-17/2*a-23)*q^93 + (-3/2*a^4+a^3+19/2*a^2-6*a)*q^94 + (-1/2*a^4-a^3+5/2*a^2+2*a+2)*q^95 + (-1/2*a^3+2*a^2+5/2*a-7)*q^96 + (-a^3-6*a^2+3*a+18)*q^97 + (-3/2*a^4-5/2*a^3+17/2*a^2+11/2*a+1)*q^98 + (a^4-2*a^3-13*a^2+10*a+26)*q^99 + (a^2-2)*q^100 + (-1/2*a^4+3/2*a^3+13/2*a^2-15/2*a-10)*q^101 + (-1/2*a^4+1/2*a^3+5/2*a^2-7/2*a+3)*q^102 + (-a^4-3*a^3+3*a^2+15*a+4)*q^103 + (-1/2*a^4+3/2*a^3-1/2*a^2-11/2*a+3)*q^104 + (-3/2*a^4-1/2*a^3+23/2*a^2+1/2*a-14)*q^105 + (-a^4-a^3+5*a^2-a)*q^106 + (a^4+5/2*a^3-7*a^2-25/2*a+3)*q^107 + (5/2*a^4+1/2*a^3-33/2*a^2+1/2*a+21)*q^108 + (a^4+a^3-9*a^2-a+10)*q^109 + (a^4+2*a^3-5*a^2-6*a+2)*q^110 + (1/2*a^4-7/2*a^2+a+3)*q^111 + (3*a^4+5/2*a^3-21*a^2-17/2*a+19)*q^112 + (3/2*a^4+7/2*a^3-21/2*a^2-39/2*a+13)*q^113 + (1/2*a^4-3/2*a^3-3/2*a^2+19/2*a-3)*q^114 + (a^4-7*a^2+6)*q^115 + (a^4+2*a^3-3*a^2-4*a)*q^116 + (-3/2*a^4+3/2*a^3+25/2*a^2-15/2*a-17)*q^117 + (-3/2*a^4-a^3+23/2*a^2+6*a-2)*q^118 + (-5/2*a^4-3/2*a^3+37/2*a^2+9/2*a-21)*q^119 + (1/2*a^3-9/2*a+3)*q^120 + (a^4-6*a^2+8*a+6)*q^121 + (a^4-a^3-5*a^2+9*a-2)*q^122 + (a^4-2*a^3-6*a^2+16*a-5)*q^123 + (-a^4+3/2*a^3+9*a^2-7/2*a-15)*q^124 + 1*q^125 + (2*a^4+5/2*a^3-12*a^2-17/2*a+7)*q^126 + (3/2*a^4+4*a^3-17/2*a^2-19*a+13)*q^127 + (-2*a^4-3*a^3+10*a^2+12*a-8)*q^128 + (-a^3+7*a-8)*q^129 + (-1/2*a^4-1/2*a^3+3/2*a^2+5/2*a-1)*q^130 + (-3/2*a^4-3*a^3+11/2*a^2+8*a+14)*q^131 + (2*a^4-18*a^2+2*a+26)*q^132 + (-1/2*a^4-3/2*a^3+3/2*a^2+19/2*a+9)*q^133 + (-1/2*a^3+4*a^2+9/2*a-3)*q^134 + (-1/2*a^4+1/2*a^3+11/2*a^2-7/2*a-10)*q^135 + (3/2*a^4-1/2*a^3-17/2*a^2+5/2*a+3)*q^136 + (-3*a^3-2*a^2+17*a-4)*q^137 + (a^3+2*a^2-7*a-2)*q^138 + (a^4+3*a^3-7*a^2-15*a+10)*q^139 + (-a^4-1/2*a^3+7*a^2+1/2*a-9)*q^140 + (5/2*a^4-5/2*a^3-37/2*a^2+41/2*a+10)*q^141 + (-4*a^3+4*a^2+22*a-6)*q^142 + (-a^4-a^3+7*a^2-a-12)*q^143 + (3/2*a^4-1/2*a^3-31/2*a^2+21/2*a+23)*q^144 + (a^4+2*a^3-5*a^2-8*a+2)*q^145 + (a^4-5*a^2-2*a+2)*q^146 + (-3*a^4-5/2*a^3+25*a^2+21/2*a-41)*q^147 + (-a^2+2)*q^148 + (-1/2*a^4+3/2*a^3+9/2*a^2-19/2*a-14)*q^149 + (-1/2*a^3+5/2*a-1)*q^150 + (-2*a^4-3*a^3+12*a^2+9*a-6)*q^151 + (-a^4+7/2*a^3+a^2-31/2*a+1)*q^152 + (-3/2*a^4-1/2*a^3+29/2*a^2+1/2*a-29)*q^153 + (2*a^4+2*a^3-14*a^2-12*a+6)*q^154 + (a^4+3/2*a^3-7*a^2-11/2*a+9)*q^155 + (-3/2*a^4+1/2*a^3+23/2*a^2-3/2*a-17)*q^156 + (a^4-3*a^3-8*a^2+13*a+1)*q^157 + (1/2*a^4+3*a^3-1/2*a^2-4*a+2)*q^158 + (a^4-a^3-6*a^2+9*a-1)*q^159 + (-2*a^2+a+2)*q^160 + (4*a^4+3*a^3-28*a^2-9*a+28)*q^161 + (-1/2*a^4+3/2*a^3+7/2*a^2-9/2*a+3)*q^162 + (-a^4+a^3+5*a^2-7*a+4)*q^163 + (-a^4-2*a^3+5*a^2+2*a-2)*q^164 + (-a^4+8*a^2-2*a-13)*q^165 + (3/2*a^3-2*a^2-11/2*a-1)*q^166 + (-4*a^4-2*a^3+26*a^2-2*a-24)*q^167 + (3/2*a^4+3/2*a^3-21/2*a^2-11/2*a+11)*q^168 + (a^4-5*a^2-5)*q^169 + (-1/2*a^4-1/2*a^3+7/2*a^2+1/2*a-1)*q^170 + (2*a^4+9/2*a^3-14*a^2-33/2*a+19)*q^171 + (a^4+a^2-2*a-4)*q^172 + (-3*a^4+a^3+20*a^2-13*a-17)*q^173 + (a^4-7*a^2)*q^174 + (-1/2*a^3-a^2+5/2*a+4)*q^175 + (-3*a^3-2*a^2+13*a+14)*q^176 + (1/2*a^4-5/2*a^3-11/2*a^2+29/2*a+7)*q^177 + (4*a^3-2*a^2-16*a)*q^178 + (1/2*a^4+a^3-9/2*a^2-6*a)*q^179 + (-3/2*a^4-1/2*a^3+19/2*a^2+1/2*a-13)*q^180 + (-3/2*a^4+1/2*a^3+27/2*a^2-25/2*a-22)*q^181 + (-1/2*a^4-1/2*a^3+9/2*a^2+7/2*a-3)*q^182 + (-a^4+2*a^3+5*a^2-16*a+12)*q^183 + (-2*a^4-a^3+8*a^2+9*a-6)*q^184 + -1*q^185 + (1/2*a^4-1/2*a^3-7/2*a^2+9/2*a-5)*q^186 + (-a^4+a^3+9*a^2-7*a-18)*q^187 + (a^4+1/2*a^3-5*a^2-5/2*a+9)*q^188 + (-3*a^4+a^3+26*a^2-11*a-45)*q^189 + (-a^4-3/2*a^3+3*a^2+15/2*a-1)*q^190 + (a^4-5/2*a^3-9*a^2+25/2*a+13)*q^191 + (1/2*a^4+2*a^3-13/2*a^2-9*a+24)*q^192 + (-2*a^4-2*a^3+18*a^2+14*a-22)*q^193 + (-a^4-6*a^3+3*a^2+18*a)*q^194 + (1/2*a^4+1/2*a^3-9/2*a^2-3/2*a+9)*q^195 + (-7/2*a^4-1/2*a^3+43/2*a^2-3/2*a-25)*q^196 + (2*a^4-11*a^2+6*a+3)*q^197 + (-2*a^4-5*a^3+8*a^2+15*a+2)*q^198 + (-3/2*a^4+3*a^3+31/2*a^2-18*a-16)*q^199 + (a^3-4*a)*q^200 +  ...

-------------------------------------------------------
185F (old = 37A), dim = 1

CONGRUENCES:
Modular Degree = 2^7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^5 + Z/2^5
= B(Z/2^2 + Z/2^2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2^3 + Z/2^3) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
185G (old = 37B), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3 + Z/2^2*3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2*3 + Z/2*3) + E(Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(186)
Weight 2

-------------------------------------------------------
J_0(186), dim = 29

-------------------------------------------------------
186A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*11
Ker(ModPolar)  = Z/2^2*11 + Z/2^2*11
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + H(Z/11 + Z/11)

ARITHMETIC INVARIANTS:
W_q            = ++-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 0.78233004515734287393 + 0.92202370739096071669e-4i
Omega-         = 0.33239951749234805713e-3 + -2.1888949081288179636i
L(1)           = 0.78233005059064892744
w1             = 0.39099882281992526294 + 1.0944935552497785299i
w2             = 0.78233004515734287393 + 0.92202370739096071669e-4i
c4             = 4008.8008461082810289 + -1.8445313780938609136i
c6             = 288864.53484198531265 + -210.36007845195006938i
j              = -5853.169385718577681 + -1.9542012441114301414i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + 1*q^4 + -1*q^5 + 1*q^6 + 2*q^7 + -1*q^8 + 1*q^9 + 1*q^10 + 3*q^11 + -1*q^12 + 3*q^13 + -2*q^14 + 1*q^15 + 1*q^16 + 1*q^17 + -1*q^18 + 7*q^19 + -1*q^20 + -2*q^21 + -3*q^22 + 1*q^24 + -4*q^25 + -3*q^26 + -1*q^27 + 2*q^28 + 4*q^29 + -1*q^30 + 1*q^31 + -1*q^32 + -3*q^33 + -1*q^34 + -2*q^35 + 1*q^36 + -10*q^37 + -7*q^38 + -3*q^39 + 1*q^40 + -6*q^41 + 2*q^42 + 6*q^43 + 3*q^44 + -1*q^45 + -5*q^47 + -1*q^48 + -3*q^49 + 4*q^50 + -1*q^51 + 3*q^52 + -2*q^53 + 1*q^54 + -3*q^55 + -2*q^56 + -7*q^57 + -4*q^58 + 6*q^59 + 1*q^60 + 3*q^61 + -1*q^62 + 2*q^63 + 1*q^64 + -3*q^65 + 3*q^66 + -3*q^67 + 1*q^68 + 2*q^70 + 7*q^71 + -1*q^72 + -10*q^73 + 10*q^74 + 4*q^75 + 7*q^76 + 6*q^77 + 3*q^78 + -1*q^79 + -1*q^80 + 1*q^81 + 6*q^82 + 17*q^83 + -2*q^84 + -1*q^85 + -6*q^86 + -4*q^87 + -3*q^88 + 6*q^89 + 1*q^90 + 6*q^91 + -1*q^93 + 5*q^94 + -7*q^95 + 1*q^96 + 5*q^97 + 3*q^98 + 3*q^99 + -4*q^100 + 14*q^101 + 1*q^102 + -14*q^103 + -3*q^104 + 2*q^105 + 2*q^106 + -16*q^107 + -1*q^108 + -10*q^109 + 3*q^110 + 10*q^111 + 2*q^112 + -6*q^113 + 7*q^114 + 4*q^116 + 3*q^117 + -6*q^118 + 2*q^119 + -1*q^120 + -2*q^121 + -3*q^122 + 6*q^123 + 1*q^124 + 9*q^125 + -2*q^126 + -12*q^127 + -1*q^128 + -6*q^129 + 3*q^130 + -14*q^131 + -3*q^132 + 14*q^133 + 3*q^134 + 1*q^135 + -1*q^136 + 10*q^137 + 16*q^139 + -2*q^140 + 5*q^141 + -7*q^142 + 9*q^143 + 1*q^144 + -4*q^145 + 10*q^146 + 3*q^147 + -10*q^148 + -21*q^149 + -4*q^150 + 5*q^151 + -7*q^152 + 1*q^153 + -6*q^154 + -1*q^155 + -3*q^156 + -20*q^157 + 1*q^158 + 2*q^159 + 1*q^160 + -1*q^162 + -1*q^163 + -6*q^164 + 3*q^165 + -17*q^166 + -14*q^167 + 2*q^168 + -4*q^169 + 1*q^170 + 7*q^171 + 6*q^172 + 13*q^173 + 4*q^174 + -8*q^175 + 3*q^176 + -6*q^177 + -6*q^178 + -11*q^179 + -1*q^180 + -10*q^181 + -6*q^182 + -3*q^183 + 10*q^185 + 1*q^186 + 3*q^187 + -5*q^188 + -2*q^189 + 7*q^190 + -24*q^191 + -1*q^192 + 19*q^193 + -5*q^194 + 3*q^195 + -3*q^196 + -26*q^197 + -3*q^198 + 7*q^199 + 4*q^200 +  ...

-------------------------------------------------------
186B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*7
Ker(ModPolar)  = Z/2^2*7 + Z/2^2*7
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/7 + Z/7)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.1828559319332875734 + 0.13788825579230494126e-3i
Omega-         = 0.1337330886993128812e-2 + -4.0120074490206444625i
L(1)           = 1.1828559399702642278
w1             = -0.59075930052314722229 + -2.0060726686382183837i
w2             = -1.1828559319332875734 + -0.13788825579230494126e-3i
c4             = 791.64252955280842199 + -0.35873789089754159196i
c6             = 22730.664473973104019 + -16.513936588377662014i
j              = -41691.979910394066515 + -97.993857456036890769i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + 3*q^5 + -1*q^6 + -2*q^7 + -1*q^8 + 1*q^9 + -3*q^10 + 5*q^11 + 1*q^12 + -7*q^13 + 2*q^14 + 3*q^15 + 1*q^16 + -1*q^17 + -1*q^18 + 7*q^19 + 3*q^20 + -2*q^21 + -5*q^22 + 4*q^23 + -1*q^24 + 4*q^25 + 7*q^26 + 1*q^27 + -2*q^28 + -8*q^29 + -3*q^30 + -1*q^31 + -1*q^32 + 5*q^33 + 1*q^34 + -6*q^35 + 1*q^36 + -6*q^37 + -7*q^38 + -7*q^39 + -3*q^40 + -2*q^41 + 2*q^42 + -10*q^43 + 5*q^44 + 3*q^45 + -4*q^46 + -1*q^47 + 1*q^48 + -3*q^49 + -4*q^50 + -1*q^51 + -7*q^52 + 6*q^53 + -1*q^54 + 15*q^55 + 2*q^56 + 7*q^57 + 8*q^58 + -10*q^59 + 3*q^60 + 1*q^61 + 1*q^62 + -2*q^63 + 1*q^64 + -21*q^65 + -5*q^66 + -3*q^67 + -1*q^68 + 4*q^69 + 6*q^70 + 3*q^71 + -1*q^72 + 14*q^73 + 6*q^74 + 4*q^75 + 7*q^76 + -10*q^77 + 7*q^78 + -11*q^79 + 3*q^80 + 1*q^81 + 2*q^82 + 7*q^83 + -2*q^84 + -3*q^85 + 10*q^86 + -8*q^87 + -5*q^88 + -6*q^89 + -3*q^90 + 14*q^91 + 4*q^92 + -1*q^93 + 1*q^94 + 21*q^95 + -1*q^96 + -3*q^97 + 3*q^98 + 5*q^99 + 4*q^100 + 6*q^101 + 1*q^102 + 10*q^103 + 7*q^104 + -6*q^105 + -6*q^106 + 8*q^107 + 1*q^108 + -6*q^109 + -15*q^110 + -6*q^111 + -2*q^112 + 6*q^113 + -7*q^114 + 12*q^115 + -8*q^116 + -7*q^117 + 10*q^118 + 2*q^119 + -3*q^120 + 14*q^121 + -1*q^122 + -2*q^123 + -1*q^124 + -3*q^125 + 2*q^126 + 4*q^127 + -1*q^128 + -10*q^129 + 21*q^130 + 10*q^131 + 5*q^132 + -14*q^133 + 3*q^134 + 3*q^135 + 1*q^136 + -18*q^137 + -4*q^138 + -8*q^139 + -6*q^140 + -1*q^141 + -3*q^142 + -35*q^143 + 1*q^144 + -24*q^145 + -14*q^146 + -3*q^147 + -6*q^148 + 15*q^149 + -4*q^150 + -1*q^151 + -7*q^152 + -1*q^153 + 10*q^154 + -3*q^155 + -7*q^156 + -4*q^157 + 11*q^158 + 6*q^159 + -3*q^160 + -8*q^161 + -1*q^162 + -9*q^163 + -2*q^164 + 15*q^165 + -7*q^166 + 10*q^167 + 2*q^168 + 36*q^169 + 3*q^170 + 7*q^171 + -10*q^172 + 1*q^173 + 8*q^174 + -8*q^175 + 5*q^176 + -10*q^177 + 6*q^178 + 19*q^179 + 3*q^180 + 18*q^181 + -14*q^182 + 1*q^183 + -4*q^184 + -18*q^185 + 1*q^186 + -5*q^187 + -1*q^188 + -2*q^189 + -21*q^190 + 1*q^192 + 19*q^193 + 3*q^194 + -21*q^195 + -3*q^196 + -2*q^197 + -5*q^198 + -11*q^199 + -4*q^200 +  ...

-------------------------------------------------------
186C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*5
Ker(ModPolar)  = Z/2^2*5 + Z/2^2*5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + I(Z/5 + Z/5)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 5
|L(1)/Omega|   = 1
Sha Bound      = 5^2

ANALYTIC INVARIANTS:

Omega+         = 1.9531025747546395502 + -0.51242080409112093324e-4i
Omega-         = 0.13017956634015474615e-2 + 1.7872054125342866609i
L(1)           = 1.9531025754268394741
w1             = -0.97720218520902054885 + -0.89357708522693877438i
w2             = -0.97590038954561900139 + 0.89362832730734788648i
c4             = -718.7353016465759638 + -0.67527905136327559633i
c6             = -6696.5296579031999866 + -65.899369610037538163i
j              = 1541.7869655290893033 + -2.8018145170708760412i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^3 + 1*q^4 + 1*q^5 + 1*q^6 + -2*q^7 + 1*q^8 + 1*q^9 + 1*q^10 + -3*q^11 + 1*q^12 + -1*q^13 + -2*q^14 + 1*q^15 + 1*q^16 + 3*q^17 + 1*q^18 + -5*q^19 + 1*q^20 + -2*q^21 + -3*q^22 + 4*q^23 + 1*q^24 + -4*q^25 + -1*q^26 + 1*q^27 + -2*q^28 + 1*q^30 + 1*q^31 + 1*q^32 + -3*q^33 + 3*q^34 + -2*q^35 + 1*q^36 + -2*q^37 + -5*q^38 + -1*q^39 + 1*q^40 + 2*q^41 + -2*q^42 + -6*q^43 + -3*q^44 + 1*q^45 + 4*q^46 + -7*q^47 + 1*q^48 + -3*q^49 + -4*q^50 + 3*q^51 + -1*q^52 + 14*q^53 + 1*q^54 + -3*q^55 + -2*q^56 + -5*q^57 + 10*q^59 + 1*q^60 + 7*q^61 + 1*q^62 + -2*q^63 + 1*q^64 + -1*q^65 + -3*q^66 + -7*q^67 + 3*q^68 + 4*q^69 + -2*q^70 + -3*q^71 + 1*q^72 + -6*q^73 + -2*q^74 + -4*q^75 + -5*q^76 + 6*q^77 + -1*q^78 + 15*q^79 + 1*q^80 + 1*q^81 + 2*q^82 + -1*q^83 + -2*q^84 + 3*q^85 + -6*q^86 + -3*q^88 + 10*q^89 + 1*q^90 + 2*q^91 + 4*q^92 + 1*q^93 + -7*q^94 + -5*q^95 + 1*q^96 + 13*q^97 + -3*q^98 + -3*q^99 + -4*q^100 + 2*q^101 + 3*q^102 + 14*q^103 + -1*q^104 + -2*q^105 + 14*q^106 + -12*q^107 + 1*q^108 + 10*q^109 + -3*q^110 + -2*q^111 + -2*q^112 + 14*q^113 + -5*q^114 + 4*q^115 + -1*q^117 + 10*q^118 + -6*q^119 + 1*q^120 + -2*q^121 + 7*q^122 + 2*q^123 + 1*q^124 + -9*q^125 + -2*q^126 + -12*q^127 + 1*q^128 + -6*q^129 + -1*q^130 + -18*q^131 + -3*q^132 + 10*q^133 + -7*q^134 + 1*q^135 + 3*q^136 + -2*q^137 + 4*q^138 + 20*q^139 + -2*q^140 + -7*q^141 + -3*q^142 + 3*q^143 + 1*q^144 + -6*q^146 + -3*q^147 + -2*q^148 + 5*q^149 + -4*q^150 + -3*q^151 + -5*q^152 + 3*q^153 + 6*q^154 + 1*q^155 + -1*q^156 + 8*q^157 + 15*q^158 + 14*q^159 + 1*q^160 + -8*q^161 + 1*q^162 + -21*q^163 + 2*q^164 + -3*q^165 + -1*q^166 + -2*q^167 + -2*q^168 + -12*q^169 + 3*q^170 + -5*q^171 + -6*q^172 + -21*q^173 + 8*q^175 + -3*q^176 + 10*q^177 + 10*q^178 + -5*q^179 + 1*q^180 + -18*q^181 + 2*q^182 + 7*q^183 + 4*q^184 + -2*q^185 + 1*q^186 + -9*q^187 + -7*q^188 + -2*q^189 + -5*q^190 + -8*q^191 + 1*q^192 + -21*q^193 + 13*q^194 + -1*q^195 + -3*q^196 + -22*q^197 + -3*q^198 + 15*q^199 + -4*q^200 +  ...

-------------------------------------------------------
186D (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^6*19
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^4*19 + Z/2^4*19
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/19 + Z/19) + F(Z/2 + Z/2) + G(Z/2^2 + Z/2^2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -++
discriminant   = 17
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 19/2^2
Sha Bound      = 2^4*19

ANALYTIC INVARIANTS:

Omega+         = 0.56184522172062387036 + 0.26768530047945129247e-3i
Omega-         = 1.3261329977186700776 + -0.33179564412299027873e-3i
L(1)           = 2.6687651060706413988

HECKE EIGENFORM:
a^2-3*a-2 = 0,
f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + a*q^5 + -1*q^6 + (-2*a+4)*q^7 + 1*q^8 + 1*q^9 + a*q^10 + (a-2)*q^11 + -1*q^12 + a*q^13 + (-2*a+4)*q^14 + -a*q^15 + 1*q^16 + (-3*a+4)*q^17 + 1*q^18 + (a-2)*q^19 + a*q^20 + (2*a-4)*q^21 + (a-2)*q^22 + -8*q^23 + -1*q^24 + (3*a-3)*q^25 + a*q^26 + -1*q^27 + (-2*a+4)*q^28 + (2*a-6)*q^29 + -a*q^30 + -1*q^31 + 1*q^32 + (-a+2)*q^33 + (-3*a+4)*q^34 + (-2*a-4)*q^35 + 1*q^36 + (-4*a+6)*q^37 + (a-2)*q^38 + -a*q^39 + a*q^40 + (-4*a+2)*q^41 + (2*a-4)*q^42 + (2*a-8)*q^43 + (a-2)*q^44 + a*q^45 + -8*q^46 + (3*a-2)*q^47 + -1*q^48 + (-4*a+17)*q^49 + (3*a-3)*q^50 + (3*a-4)*q^51 + a*q^52 + -2*q^53 + -1*q^54 + (a+2)*q^55 + (-2*a+4)*q^56 + (-a+2)*q^57 + (2*a-6)*q^58 + 2*a*q^59 + -a*q^60 + a*q^61 + -1*q^62 + (-2*a+4)*q^63 + 1*q^64 + (3*a+2)*q^65 + (-a+2)*q^66 + (3*a+2)*q^67 + (-3*a+4)*q^68 + 8*q^69 + (-2*a-4)*q^70 + (-a-2)*q^71 + 1*q^72 + 10*q^73 + (-4*a+6)*q^74 + (-3*a+3)*q^75 + (a-2)*q^76 + (2*a-12)*q^77 + -a*q^78 + (3*a-2)*q^79 + a*q^80 + 1*q^81 + (-4*a+2)*q^82 + (-5*a+10)*q^83 + (2*a-4)*q^84 + (-5*a-6)*q^85 + (2*a-8)*q^86 + (-2*a+6)*q^87 + (a-2)*q^88 + (4*a+2)*q^89 + a*q^90 + (-2*a-4)*q^91 + -8*q^92 + 1*q^93 + (3*a-2)*q^94 + (a+2)*q^95 + -1*q^96 + (5*a-12)*q^97 + (-4*a+17)*q^98 + (a-2)*q^99 + (3*a-3)*q^100 + (-4*a+14)*q^101 + (3*a-4)*q^102 + (2*a-4)*q^103 + a*q^104 + (2*a+4)*q^105 + -2*q^106 + -4*q^107 + -1*q^108 + 14*q^109 + (a+2)*q^110 + (4*a-6)*q^111 + (-2*a+4)*q^112 + -14*q^113 + (-a+2)*q^114 + -8*a*q^115 + (2*a-6)*q^116 + a*q^117 + 2*a*q^118 + (-2*a+28)*q^119 + -a*q^120 + (-a-5)*q^121 + a*q^122 + (4*a-2)*q^123 + -1*q^124 + (a+6)*q^125 + (-2*a+4)*q^126 + (-4*a+8)*q^127 + 1*q^128 + (-2*a+8)*q^129 + (3*a+2)*q^130 + (-2*a+16)*q^131 + (-a+2)*q^132 + (2*a-12)*q^133 + (3*a+2)*q^134 + -a*q^135 + (-3*a+4)*q^136 + -6*q^137 + 8*q^138 + -12*q^139 + (-2*a-4)*q^140 + (-3*a+2)*q^141 + (-a-2)*q^142 + (a+2)*q^143 + 1*q^144 + 4*q^145 + 10*q^146 + (4*a-17)*q^147 + (-4*a+6)*q^148 + (-3*a+8)*q^149 + (-3*a+3)*q^150 + (-7*a+2)*q^151 + (a-2)*q^152 + (-3*a+4)*q^153 + (2*a-12)*q^154 + -a*q^155 + -a*q^156 + (6*a-6)*q^157 + (3*a-2)*q^158 + 2*q^159 + a*q^160 + (16*a-32)*q^161 + 1*q^162 + (9*a-18)*q^163 + (-4*a+2)*q^164 + (-a-2)*q^165 + (-5*a+10)*q^166 + (2*a-4)*q^167 + (2*a-4)*q^168 + (3*a-11)*q^169 + (-5*a-6)*q^170 + (a-2)*q^171 + (2*a-8)*q^172 + (-a+4)*q^173 + (-2*a+6)*q^174 + -24*q^175 + (a-2)*q^176 + -2*a*q^177 + (4*a+2)*q^178 + (-9*a+18)*q^179 + a*q^180 + (4*a-10)*q^181 + (-2*a-4)*q^182 + -a*q^183 + -8*q^184 + (-6*a-8)*q^185 + 1*q^186 + (a-14)*q^187 + (3*a-2)*q^188 + (2*a-4)*q^189 + (a+2)*q^190 + 16*q^191 + -1*q^192 + (-a+24)*q^193 + (5*a-12)*q^194 + (-3*a-2)*q^195 + (-4*a+17)*q^196 + (-4*a+6)*q^197 + (a-2)*q^198 + (3*a+6)*q^199 + (3*a-3)*q^200 +  ...

-------------------------------------------------------
186E (old = 93A), dim = 2

CONGRUENCES:
Modular Degree = 2^8*19
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2*19 + Z/2^2*19
= D(Z/19 + Z/19) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
186F (old = 93B), dim = 3

CONGRUENCES:
Modular Degree = 2^12*7
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^4*7 + Z/2^4*7
= B(Z/7 + Z/7) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2^2 + Z/2^2) + H(Z/2 + Z/2) + I(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
186G (old = 62A), dim = 1

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2^3 + Z/2^3 + Z/2^3 + Z/2^3
= D(Z/2^2 + Z/2^2) + F(Z/2^2 + Z/2^2) + H(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
186H (old = 62B), dim = 2

CONGRUENCES:
Modular Degree = 2^4*11^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*11 + Z/2*11 + Z/2*11 + Z/2*11 + Z/2*11 + Z/2*11
= A(Z/11 + Z/11) + D(Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/11 + Z/11 + Z/11 + Z/11)

-------------------------------------------------------
186I (old = 31A), dim = 2

CONGRUENCES:
Modular Degree = 2^8*5*11^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*11 + Z/2*11 + Z/2*5*11 + Z/2*5*11
= C(Z/5 + Z/5) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + H(Z/11 + Z/11 + Z/11 + Z/11)

-------------------------------------------------------
Gamma_0(187)
Weight 2

-------------------------------------------------------
J_0(187), dim = 17

-------------------------------------------------------
187A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3*5
Ker(ModPolar)  = Z/2*3*5 + Z/2*3*5
= C(Z/2 + Z/2) + F(Z/5 + Z/5) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 2.3271019961199589654 + -0.38541748998971429316e-3i
Omega-         = 0.47205836712669195155e-4 + 2.2220918199809085319i
L(1)           = 2.327102028036617715
w1             = 1.1635273951416231481 + -1.1112386187354491231i
w2             = -1.1635746009783358173 + -1.1108532012454594088i
c4             = -336.16075603102993478 + -0.14585693329577454904i
c6             = -1088.1264809692319766 + 2.7532772766271767501i
j              = 1675.7692408980874658 + 0.32226448695985909133i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 2*q^4 + 4*q^5 + -5*q^7 + -3*q^9 + 8*q^10 + -1*q^11 + 4*q^13 + -10*q^14 + -4*q^16 + 1*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 + 4*q^38 + -3*q^41 + -2*q^43 + -2*q^44 + -12*q^45 + -4*q^46 + 3*q^47 + 18*q^49 + 22*q^50 + 8*q^52 + 9*q^53 + -4*q^55 + -6*q^58 + -3*q^59 + -10*q^61 + 8*q^62 + 15*q^63 + -8*q^64 + 16*q^65 + 7*q^67 + 2*q^68 + -40*q^70 + 2*q^71 + -3*q^73 + -4*q^74 + 4*q^76 + 5*q^77 + -16*q^80 + 9*q^81 + -6*q^82 + 14*q^83 + 4*q^85 + -4*q^86 + 1*q^89 + -24*q^90 + -20*q^91 + -4*q^92 + 6*q^94 + 8*q^95 + -10*q^97 + 36*q^98 + 3*q^99 + 22*q^100 + -16*q^101 + 17*q^103 + 18*q^106 + -13*q^107 + -9*q^109 + -8*q^110 + 20*q^112 + 10*q^113 + -8*q^115 + -6*q^116 + -12*q^117 + -6*q^118 + -5*q^119 + 1*q^121 + -20*q^122 + 8*q^124 + 24*q^125 + 30*q^126 + -4*q^127 + 32*q^130 + 1*q^131 + -10*q^133 + 14*q^134 + -21*q^137 + 13*q^139 + -40*q^140 + 4*q^142 + -4*q^143 + 12*q^144 + -12*q^145 + -6*q^146 + -4*q^148 + 14*q^149 + -22*q^151 + -3*q^153 + 10*q^154 + 16*q^155 + -11*q^157 + -32*q^160 + 10*q^161 + 18*q^162 + 6*q^163 + -6*q^164 + 28*q^166 + 8*q^167 + 3*q^169 + 8*q^170 + -6*q^171 + -4*q^172 + 7*q^173 + -55*q^175 + 4*q^176 + 2*q^178 + -21*q^179 + -24*q^180 + 10*q^181 + -40*q^182 + -8*q^185 + -1*q^187 + 6*q^188 + 16*q^190 + 8*q^191 + -10*q^193 + -20*q^194 + 36*q^196 + 6*q^197 + 6*q^198 + -2*q^199 +  ...

-------------------------------------------------------
187B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^4 + Z/2^4
= C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 2/3
Sha Bound      = 2*3

ANALYTIC INVARIANTS:

Omega+         = 2.1144877315362047593 + -0.10792333062212827097e-3i
Omega-         = 0.8124038356934417763e-4 + 1.5430355961123092872i
L(1)           = 1.409658489526936674
w1             = 1.0572844859598870517 + 0.77146383639084357948i
w2             = 1.0572032455763177076 + -0.77157175972146570775i
c4             = -512.00051029795187545 + -0.10306345867471021531i
c6             = -23058.724496355736787 + -7.2342366969800179666i
j              = 348.28193896361828734 + -0.65558918416143789289e-2i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + -2*q^4 + 3*q^5 + 2*q^7 + -2*q^9 + 1*q^11 + -2*q^12 + 2*q^13 + 3*q^15 + 4*q^16 + -1*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 + 1*q^33 + 6*q^35 + 4*q^36 + -7*q^37 + 2*q^39 + 12*q^41 + -10*q^43 + -2*q^44 + -6*q^45 + 4*q^48 + -3*q^49 + -1*q^51 + -4*q^52 + 6*q^53 + 3*q^55 + 2*q^57 + -3*q^59 + -6*q^60 + 8*q^61 + -4*q^63 + -8*q^64 + 6*q^65 + -7*q^67 + 2*q^68 + -3*q^69 + -9*q^71 + 2*q^73 + 4*q^75 + -4*q^76 + 2*q^77 + 8*q^79 + 12*q^80 + 1*q^81 + 6*q^83 + -4*q^84 + -3*q^85 + -6*q^87 + 15*q^89 + 4*q^91 + 6*q^92 + -7*q^93 + 6*q^95 + 11*q^97 + -2*q^99 + -8*q^100 + 12*q^101 + 8*q^103 + 6*q^105 + 12*q^107 + 10*q^108 + -16*q^109 + -7*q^111 + 8*q^112 + -9*q^113 + -9*q^115 + 12*q^116 + -4*q^117 + -2*q^119 + 1*q^121 + 12*q^123 + 14*q^124 + -3*q^125 + -4*q^127 + -10*q^129 + 6*q^131 + -2*q^132 + 4*q^133 + -15*q^135 + -3*q^137 + -16*q^139 + -12*q^140 + 2*q^143 + -8*q^144 + -18*q^145 + -3*q^147 + 14*q^148 + -16*q^151 + 2*q^153 + -21*q^155 + -4*q^156 + 17*q^157 + 6*q^159 + -6*q^161 + -16*q^163 + -24*q^164 + 3*q^165 + 18*q^167 + -9*q^169 + -4*q^171 + 20*q^172 + 6*q^173 + 8*q^175 + 4*q^176 + -3*q^177 + 9*q^179 + 12*q^180 + 17*q^181 + 8*q^183 + -21*q^185 + -1*q^187 + -10*q^189 + -3*q^191 + -8*q^192 + 14*q^193 + 6*q^195 + 6*q^196 + 12*q^197 + -16*q^199 +  ...

-------------------------------------------------------
187C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^5 + Z/2^5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2) + H(Z/2^2 + Z/2^2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 17
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 2.2827832718367225161 + 0.16597102744065716287e-3i
Omega-         = 4.7554225511829010715 + 0.40332873625340355066e-2i
L(1)           = 4.5655665557404608779

HECKE EIGENFORM:
a^2-3*a-2 = 0,
f(q) = q + 2*q^2 + (a-2)*q^3 + 2*q^4 + (-a+2)*q^5 + (2*a-4)*q^6 + (-a+3)*q^7 + (-a+3)*q^9 + (-2*a+4)*q^10 + 1*q^11 + (2*a-4)*q^12 + (-2*a+6)*q^14 + (a-6)*q^15 + -4*q^16 + -1*q^17 + (-2*a+6)*q^18 + (2*a-6)*q^19 + (-2*a+4)*q^20 + (2*a-8)*q^21 + 2*q^22 + (3*a-4)*q^23 + (-a+1)*q^25 + (-a-2)*q^27 + (-2*a+6)*q^28 + (-a+9)*q^29 + (2*a-12)*q^30 + (a-2)*q^31 + -8*q^32 + (a-2)*q^33 + -2*q^34 + (-2*a+8)*q^35 + (-2*a+6)*q^36 + (-a+4)*q^37 + (4*a-12)*q^38 + (3*a-7)*q^41 + (4*a-16)*q^42 + 2*q^43 + 2*q^44 + (-2*a+8)*q^45 + (6*a-8)*q^46 + (3*a-7)*q^47 + (-4*a+8)*q^48 + (-3*a+4)*q^49 + (-2*a+2)*q^50 + (-a+2)*q^51 + (-a+7)*q^53 + (-2*a-4)*q^54 + (-a+2)*q^55 + (-4*a+16)*q^57 + (-2*a+18)*q^58 + -3*q^59 + (2*a-12)*q^60 + (-2*a-2)*q^61 + (2*a-4)*q^62 + (-3*a+11)*q^63 + -8*q^64 + (2*a-4)*q^66 + (-2*a+3)*q^67 + -2*q^68 + (-a+14)*q^69 + (-4*a+16)*q^70 + (-3*a+8)*q^71 + (3*a+1)*q^73 + (-2*a+8)*q^74 + -4*q^75 + (4*a-12)*q^76 + (-a+3)*q^77 + (6*a-12)*q^79 + (4*a-8)*q^80 + -7*q^81 + (6*a-14)*q^82 + (-4*a+6)*q^83 + (4*a-16)*q^84 + (a-2)*q^85 + 4*q^86 + (8*a-20)*q^87 + (-6*a+13)*q^89 + (-4*a+16)*q^90 + (6*a-8)*q^92 + (-a+6)*q^93 + (6*a-14)*q^94 + (4*a-16)*q^95 + (-8*a+16)*q^96 + (-3*a-4)*q^97 + (-6*a+8)*q^98 + (-a+3)*q^99 + (-2*a+2)*q^100 + (6*a-8)*q^101 + (-2*a+4)*q^102 + (a-5)*q^103 + (6*a-20)*q^105 + (-2*a+14)*q^106 + (-a+11)*q^107 + (-2*a-4)*q^108 + (3*a+7)*q^109 + (-2*a+4)*q^110 + (3*a-10)*q^111 + (4*a-12)*q^112 + (a+8)*q^113 + (-8*a+32)*q^114 + (a-14)*q^115 + (-2*a+18)*q^116 + -6*q^118 + (a-3)*q^119 + 1*q^121 + (-4*a-4)*q^122 + (-4*a+20)*q^123 + (2*a-4)*q^124 + (5*a-6)*q^125 + (-6*a+22)*q^126 + (-8*a+8)*q^127 + (2*a-4)*q^129 + (-7*a+9)*q^131 + (2*a-4)*q^132 + (6*a-22)*q^133 + (-4*a+6)*q^134 + (3*a-2)*q^135 + (2*a+7)*q^137 + (-2*a+28)*q^138 + (-3*a+5)*q^139 + (-4*a+16)*q^140 + (-4*a+20)*q^141 + (-6*a+16)*q^142 + (4*a-12)*q^144 + (-8*a+20)*q^145 + (6*a+2)*q^146 + (a-14)*q^147 + (-2*a+8)*q^148 + (8*a-14)*q^149 + -8*q^150 + (4*a-6)*q^151 + (a-3)*q^153 + (-2*a+6)*q^154 + (a-6)*q^155 + (-4*a-3)*q^157 + (12*a-24)*q^158 + (6*a-16)*q^159 + (8*a-16)*q^160 + (4*a-18)*q^161 + -14*q^162 + (2*a-14)*q^163 + (6*a-14)*q^164 + (a-6)*q^165 + (-8*a+12)*q^166 + (-8*a+16)*q^167 + -13*q^169 + (2*a-4)*q^170 + (6*a-22)*q^171 + 4*q^172 + (-a+15)*q^173 + (16*a-40)*q^174 + (-a+5)*q^175 + -4*q^176 + (-3*a+6)*q^177 + (-12*a+26)*q^178 + (-6*a-1)*q^179 + (-4*a+16)*q^180 + (3*a-20)*q^181 + -4*a*q^183 + (-3*a+10)*q^185 + (-2*a+12)*q^186 + -1*q^187 + (6*a-14)*q^188 + (2*a-4)*q^189 + (8*a-32)*q^190 + (-a+6)*q^191 + (-8*a+16)*q^192 + (-6*a+14)*q^193 + (-6*a-8)*q^194 + (-6*a+8)*q^196 + (-8*a+10)*q^197 + (-2*a+6)*q^198 + (-6*a-2)*q^199 +  ...

-------------------------------------------------------
187D (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5*3
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3*3 + Z/2^3*3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/3 + Z/3) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 2^2*3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 5.4681739415989619625 + -0.148562560602409905e-2i
Omega-         = 3.5781341360396719135 + -0.13749578099179702426e-3i
L(1)           =

HECKE EIGENFORM:
a^2+2*a-2 = 0,
f(q) = 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 + 1*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 + 1*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 + (-4*a+6)*q^38 + (5*a+8)*q^39 + (-10*a+8)*q^40 + (-2*a+4)*q^41 + (-2*a+4)*q^42 + -2*q^43 + -2*a*q^44 + (-3*a+2)*q^46 + (-4*a-10)*q^47 + (-8*a+4)*q^48 + -3*q^49 + (6*a-8)*q^50 + (-a-1)*q^51 + (8*a+4)*q^52 + (-2*a-8)*q^53 + (-3*a+6)*q^54 + (a-1)*q^55 + (-4*a+8)*q^56 + (a-8)*q^57 + (-2*a-2)*q^58 + 3*q^59 + (10*a-8)*q^60 + (-4*a-8)*q^61 + (3*a+2)*q^62 + (-8*a+8)*q^64 + (-3*a+4)*q^65 + (a-2)*q^66 + 1*q^67 + -2*a*q^68 + (2*a-1)*q^69 + (6*a-4)*q^70 + (a+3)*q^71 + (3*a+12)*q^73 + (-3*a+2)*q^74 + (-2*a+10)*q^75 + (8*a-12)*q^76 + -2*q^77 + (-2*a+10)*q^78 + (-3*a-6)*q^79 + (16*a-12)*q^80 + -9*q^81 + (8*a-4)*q^82 + (-8*a-6)*q^83 + (4*a-8)*q^84 + (a-1)*q^85 + -2*a*q^86 + (3*a+6)*q^87 + (2*a-4)*q^88 + (4*a-1)*q^89 + (2*a+12)*q^91 + (6*a-4)*q^92 + (-4*a-7)*q^93 + (-2*a-8)*q^94 + (-7*a+4)*q^95 + (8*a-16)*q^96 + (-a+13)*q^97 + -3*a*q^98 + (-12*a+16)*q^100 + (-5*a-12)*q^101 + (a-2)*q^102 + (8*a+10)*q^103 + (-4*a+20)*q^104 + (-4*a+2)*q^105 + (-4*a-4)*q^106 + (-a-14)*q^107 + (6*a-12)*q^108 + (3*a+6)*q^109 + (-3*a+2)*q^110 + (2*a-1)*q^111 + (8*a-8)*q^112 + (-a-9)*q^113 + (-10*a+2)*q^114 + (-4*a+3)*q^115 + (4*a+4)*q^116 + 3*a*q^118 + -2*q^119 + (-18*a+12)*q^120 + 1*q^121 + -8*q^122 + -6*a*q^123 + (-6*a-4)*q^124 + (5*a-1)*q^125 + -4*q^127 + (8*a-16)*q^128 + (2*a+2)*q^129 + (10*a-6)*q^130 + (4*a+2)*q^131 + (-2*a+4)*q^132 + (-6*a-4)*q^133 + a*q^134 + (-6*a+3)*q^135 + (2*a-4)*q^136 + (6*a-3)*q^137 + (-5*a+4)*q^138 + (-5*a+2)*q^139 + (-12*a+8)*q^140 + (6*a+18)*q^141 + (a+2)*q^142 + (-a-6)*q^143 + (-a+2)*q^145 + (6*a+6)*q^146 + (3*a+3)*q^147 + (6*a-4)*q^148 + 7*a*q^149 + (14*a-4)*q^150 + (3*a-4)*q^151 + (-20*a+4)*q^152 + -2*a*q^154 + (2*a-3)*q^155 + (4*a-20)*q^156 + (12*a+13)*q^157 + -6*q^158 + (6*a+12)*q^159 + (-24*a+16)*q^160 + (-2*a+2)*q^161 + -9*a*q^162 + (-2*a-8)*q^163 + (-16*a+8)*q^164 + (2*a-1)*q^165 + (10*a-16)*q^166 + (-a+16)*q^167 + -12*a*q^168 + (10*a+25)*q^169 + (-3*a+2)*q^170 + 4*a*q^172 + -14*q^173 + 6*q^174 + (8*a+4)*q^175 + (-4*a+4)*q^176 + (-3*a-3)*q^177 + (-9*a+8)*q^178 + -3*q^179 + (-5*a-1)*q^181 + (8*a+4)*q^182 + (4*a+16)*q^183 + (-10*a+8)*q^184 + (-4*a+3)*q^185 + (a-8)*q^186 + 1*q^187 + (4*a+16)*q^188 + (-6*a-6)*q^189 + (18*a-14)*q^190 + (-2*a+21)*q^191 + (-16*a+8)*q^192 + (3*a-16)*q^193 + (15*a-2)*q^194 + (-7*a+2)*q^195 + 6*a*q^196 + (7*a-2)*q^197 + (12*a+16)*q^199 + (28*a-8)*q^200 +  ...

-------------------------------------------------------
187E (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 2^2*37
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 18.030899967579524419 + 0.48876908211358665629e-2i
Omega-         = 0.11236509887059568446e-2 + -10.853631653635080102i
L(1)           =

HECKE EIGENFORM:
a^3+2*a^2-2*a-2 = 0,
f(q) = 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 + -1*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 + -1*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 + (-a^2-4)*q^38 + (a^2-5*a-4)*q^39 + (4*a^2+8*a-2)*q^40 + (2*a^2+2*a-4)*q^41 + (2*a^2-4*a)*q^42 + (-4*a^2-8*a+8)*q^43 + (-a^2+2)*q^44 + (-a^2+4)*q^45 + (a^2-5*a-2)*q^46 + (3*a^2+4*a)*q^47 + (-2*a^2+2*a+4)*q^48 + (-4*a^2-8*a+9)*q^49 + (4*a^2+6*a+2)*q^50 + (a^2+a-1)*q^51 + (-4*a^2+2)*q^52 + (a^2+4*a-10)*q^53 + (a^2+a+4)*q^54 + (a+3)*q^55 + (4*a-8)*q^56 + (-3*a^2+a+10)*q^57 + (-a^2-6*a-2)*q^58 + (-a^2+4*a+5)*q^59 + (-a^2-4*a+2)*q^60 + (-2*a^2-2*a+2)*q^61 + (a^2-a+4)*q^62 + (-4*a+4)*q^63 + (4*a+4)*q^64 + (-3*a^2-11*a-6)*q^65 + (-a^2+a+2)*q^66 + (4*a^2+6*a-11)*q^67 + (-a^2+2)*q^68 + (5*a^2+4*a-3)*q^69 + (2*a^2-8)*q^70 + (3*a+1)*q^71 + (-2*a^2+4*a)*q^72 + (-a^2-a-2)*q^73 + (3*a^2-5*a-10)*q^74 + (-a^2-10*a-6)*q^75 + (6*a^2+4*a-10)*q^76 + (-2*a^2-2*a+4)*q^77 + (-7*a^2-2*a+2)*q^78 + (-a^2+a+8)*q^79 + (2*a^2+6*a)*q^80 + (-a^2-2*a-3)*q^81 + (-2*a^2+4)*q^82 + -4*a*q^83 + (-8*a^2+12)*q^84 + (a+3)*q^85 + -8*q^86 + (4*a^2+7*a)*q^87 + (2*a^2+2*a-2)*q^88 + (4*a^2+2*a-9)*q^89 + (2*a^2+2*a-2)*q^90 + (-2*a^2+4*a+4)*q^91 + (-5*a^2+2*a+8)*q^92 + (4*a^2-11)*q^93 + (-2*a^2+6*a+6)*q^94 + (7*a^2+15*a-8)*q^95 + (2*a^2-8)*q^96 + (a^2-a-9)*q^97 + (a-8)*q^98 + (-a^2+2)*q^99 + (-4*a^2-2*a)*q^100 + (2*a^2-a-6)*q^101 + (-a^2+a+2)*q^102 + (5*a^2-2*a-16)*q^103 + (2*a^2-10*a-8)*q^104 + (-2*a^2-2*a+12)*q^105 + (2*a^2-8*a+2)*q^106 + (3*a^2+5*a-10)*q^107 + (-5*a^2-4*a+8)*q^108 + (3*a^2+11*a-8)*q^109 + (a^2+3*a)*q^110 + (3*a^2+2*a+9)*q^111 + (4*a^2-8)*q^112 + (-5*a+1)*q^113 + (7*a^2+4*a-6)*q^114 + (2*a^2+8*a+11)*q^115 + (-2*a^2+2*a+6)*q^116 + (-4*a^2+2)*q^117 + (6*a^2+3*a-2)*q^118 + (-2*a^2-2*a+4)*q^119 + (-2*a^2-6*a-10)*q^120 + 1*q^121 + (2*a^2-2*a-4)*q^122 + (2*a-4)*q^123 + (-7*a^2-4*a+12)*q^124 + (-7*a^2-19*a+1)*q^125 + (-4*a^2+4*a)*q^126 + (-4*a^2-8*a+10)*q^127 + (-4*a+8)*q^128 + (-4*a^2+16)*q^129 + (-5*a^2-12*a-6)*q^130 + (-8*a^2-4*a+22)*q^131 + (a^2-2*a)*q^132 + (10*a^2+8*a-28)*q^133 + (-2*a^2-3*a+8)*q^134 + (-7*a^2-16*a+5)*q^135 + (2*a^2+2*a-2)*q^136 + (4*a^2+6*a-15)*q^137 + (-6*a^2+7*a+10)*q^138 + (-a^2-5*a+4)*q^139 + (4*a^2+8*a-12)*q^140 + (-5*a^2-4*a-2)*q^141 + (3*a^2+a)*q^142 + (-3*a-2)*q^143 + (4*a^2-4)*q^144 + (4*a^2+15*a+14)*q^145 + (a^2-4*a-2)*q^146 + (-5*a^2-a+17)*q^147 + (-a^2+10*a-4)*q^148 + (2*a^2-a-14)*q^149 + (-8*a^2-8*a-2)*q^150 + (-2*a^2-5*a+12)*q^151 + (-6*a^2+2*a+20)*q^152 + (-a^2+2)*q^153 + (2*a^2-4)*q^154 + (-7*a^2-14*a+11)*q^155 + (10*a^2-2*a-6)*q^156 + (-6*a^2-6*a+13)*q^157 + (3*a^2+6*a-2)*q^158 + (11*a^2+6*a-16)*q^159 + (-6*a^2-12*a+8)*q^160 + (-8*a^2-6*a+12)*q^161 + (-5*a-2)*q^162 + (-2*a^2+4*a+12)*q^163 + (-4*a+4)*q^164 + (-2*a^2-4*a+1)*q^165 + -4*a^2*q^166 + (5*a^2+11*a-6)*q^167 + (12*a^2+4*a-16)*q^168 + (9*a^2+12*a-9)*q^169 + (a^2+3*a)*q^170 + (6*a^2+4*a-10)*q^171 + (8*a^2+8*a-16)*q^172 + (8*a^2+10*a-16)*q^173 + (-a^2+8*a+8)*q^174 + (8*a+4)*q^175 + 2*a*q^176 + (2*a^2-9*a-5)*q^177 + (-6*a^2-a+8)*q^178 + (-6*a^2-8*a+21)*q^179 + (2*a-4)*q^180 + (a^2+a-3)*q^181 + (8*a^2-4)*q^182 + (2*a^2+2)*q^183 + (10*a^2+8*a-6)*q^184 + (12*a^2+26*a-5)*q^185 + (-8*a^2-3*a+8)*q^186 + 1*q^187 + (4*a^2-6*a-4)*q^188 + (-8*a^2-6*a+24)*q^189 + (a^2+6*a+14)*q^190 + (-4*a^2-8*a+9)*q^191 + (-8*a-4)*q^192 + (a^2+5*a+8)*q^193 + (-3*a^2-7*a+2)*q^194 + (4*a^2+17*a+10)*q^195 + (9*a^2+8*a-18)*q^196 + (3*a^2-a-24)*q^197 + (2*a^2-2)*q^198 + (-6*a^2+2*a+20)*q^199 + (-2*a^2-20*a-12)*q^200 +  ...

-------------------------------------------------------
187F (new) , dim = 4

CONGRUENCES:
Modular Degree = 2^8*5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2*5 + Z/2^2*5
= A(Z/5 + Z/5) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2^2 + Z/2^2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*8461
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^2
Torsion Bound  = 2^3
|L(1)/Omega|   = 1
Sha Bound      = 2^6

ANALYTIC INVARIANTS:

Omega+         = 1.43525357603652663 + 0.42171067523235665547e-3i
Omega-         = 2.4109338064383208656 + -0.19404372080623329215e-3i
L(1)           = 1.4352536379906972156

HECKE EIGENFORM:
a^4-a^3-6*a^2+2*a+2 = 0,
f(q) = 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 + -1*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 + 1*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 + (a^3-a^2-4*a-2)*q^38 + (-2*a^3+3*a^2+13*a-12)*q^39 + (-2*a^2-2*a+2)*q^40 + (2*a^3-2*a^2-10*a+4)*q^41 + (2*a^3-4*a^2-10*a+8)*q^43 + (-a^2+2)*q^44 + (a^3-a^2-6*a+6)*q^45 + (-a^2+a-2)*q^46 + (a^3-a^2-4*a+2)*q^47 + (-2*a^3+10*a-4)*q^48 + -7*q^49 + (a^3-2*a^2-4*a)*q^50 + (-a^3+a^2+5*a-1)*q^51 + (-2*a^3+10*a-6)*q^52 + (a^3-a^2-4*a+8)*q^53 + (a^2+a+4)*q^54 + (a-1)*q^55 + (2*a^3+a^2-15*a-10)*q^57 + (a^3-a^2)*q^58 + (2*a^3-3*a^2-8*a+9)*q^59 + (a^3+a^2-8*a+4)*q^60 + (4*a+2)*q^61 + (-2*a^3+a^2+3*a+4)*q^62 + (a^3+2*a^2+4*a-2)*q^64 + (2*a^3-3*a^2-7*a+6)*q^65 + (a^2-a-2)*q^66 + (a^3-10*a-1)*q^67 + (a^2-2)*q^68 + (-2*a^3+5*a^2+8*a-15)*q^69 + (-2*a^3+7*a+9)*q^71 + (3*a^3-4*a^2-20*a+2)*q^72 + (3*a^2-5*a-10)*q^73 + (a^2+5*a+2)*q^74 + (3*a^3-a^2-20*a)*q^75 + (-2*a^3+2*a^2+10*a+2)*q^76 + (a^3+a^2-8*a+4)*q^78 + (-2*a^3+3*a^2+13*a-12)*q^79 + (-4*a^2-2*a+4)*q^80 + (a^3-3*a^2-2*a+7)*q^81 + (2*a^2-4)*q^82 + (-2*a^3+18*a+4)*q^83 + (-a+1)*q^85 + (-2*a^3+2*a^2+4*a-4)*q^86 + (-a^3+2*a^2+a-2)*q^87 + (-a^3+4*a)*q^88 + (-3*a^3+22*a+1)*q^89 + (4*a-2)*q^90 + (-3*a^3+3*a^2+12*a-6)*q^92 + (a^3-6*a^2+4*a+23)*q^93 + (2*a^2-2)*q^94 + (a^2-3*a)*q^95 + (-2*a^3-2*a^2+4*a+16)*q^96 + (-3*a^3+3*a^2+13*a+1)*q^97 + -7*a*q^98 + (a^2-6)*q^99 + (-a^3+2*a+6)*q^100 + (-3*a^3+17*a+4)*q^101 + (-a^2+a+2)*q^102 + (3*a^3-5*a^2-14*a+6)*q^103 + (-4*a^2-6*a+8)*q^104 + (2*a^2+6*a-2)*q^106 + (a^2-a-10)*q^107 + (5*a^3-3*a^2-22*a+6)*q^108 + (2*a^3-a^2-13*a)*q^109 + (a^2-a)*q^110 + (-4*a^3+a^2+22*a+9)*q^111 + (2*a^3-2*a^2-13*a+13)*q^113 + (3*a^3-3*a^2-14*a-4)*q^114 + (a^3-8*a+5)*q^115 + (4*a^2-2)*q^116 + (6*a^3-8*a^2-30*a+22)*q^117 + (-a^3+4*a^2+5*a-4)*q^118 + (2*a^2+4*a-6)*q^120 + 1*q^121 + (4*a^2+2*a)*q^122 + (-2*a^3+4*a^2+10*a-20)*q^123 + (3*a^3-9*a^2-18*a+6)*q^124 + (-a^3+3*a^2+7*a-9)*q^125 + (4*a^2-6*a-18)*q^127 + (5*a^3+2*a^2-20*a+2)*q^128 + (-4*a^3+6*a^2+26*a-24)*q^129 + (-a^3+5*a^2+2*a-4)*q^130 + (-2*a^3+12*a-2)*q^131 + (-a^3+a^2+8*a-2)*q^132 + (a^3-4*a^2-3*a-2)*q^134 + (-2*a^3+a^2+12*a-7)*q^135 + (a^3-4*a)*q^136 + (a^3-2*a^2-6*a+11)*q^137 + (3*a^3-4*a^2-11*a+4)*q^138 + (-a^2+3*a-4)*q^139 + (-a^3+a^2+6*a-8)*q^141 + (-2*a^3-5*a^2+13*a+4)*q^142 + (-a^3+2*a^2+5*a-4)*q^143 + (a^3-6*a^2-8*a+14)*q^144 + (-a^3+2*a^2-a)*q^145 + (3*a^3-5*a^2-10*a)*q^146 + (7*a^3-7*a^2-35*a+7)*q^147 + (3*a^3+3*a^2-12*a-6)*q^148 + (-3*a^3+4*a^2+13*a-4)*q^149 + (2*a^3-2*a^2-6*a-6)*q^150 + (-a^3-4*a^2+7*a+18)*q^151 + (-2*a^3+14*a+8)*q^152 + (-a^2+6)*q^153 + (-a^2+10*a-5)*q^155 + (6*a^3-8*a^2-24*a+22)*q^156 + (-3*a^3+2*a^2+18*a-1)*q^157 + (a^3+a^2-8*a+4)*q^158 + (-7*a^3+7*a^2+36*a-14)*q^159 + (-4*a^3+2*a^2+8*a-4)*q^160 + (-2*a^3+4*a^2+5*a-2)*q^162 + (4*a^3-4*a^2-20*a)*q^163 + (-2*a^3+4*a^2+16*a-8)*q^164 + (a^3-2*a^2-4*a+3)*q^165 + (-2*a^3+6*a^2+8*a+4)*q^166 + (5*a^2-5*a-22)*q^167 + (5*a^3-5*a^2-28*a+9)*q^169 + (-a^2+a)*q^170 + (6*a^3-2*a^2-38*a-10)*q^171 + (-4*a^3+20*a-12)*q^172 + (2*a^2-4*a-8)*q^173 + (a^3-5*a^2+2)*q^174 + (-a^3+2*a-2)*q^176 + (-6*a^3+6*a^2+35*a-21)*q^177 + (-3*a^3+4*a^2+7*a+6)*q^178 + (3*a^3-4*a^2-20*a+11)*q^179 + (-2*a^3+6*a^2+10*a-12)*q^180 + (-a^3+5*a^2-a-25)*q^181 + (-2*a^3-2*a^2+14*a+6)*q^183 + (-4*a^2-2*a+10)*q^184 + (-a^3+2*a+1)*q^185 + (-5*a^3+10*a^2+21*a-2)*q^186 + -1*q^187 + (2*a^2+6*a-4)*q^188 + (a^3-3*a^2)*q^190 + (3*a^3-16*a-9)*q^191 + (-8*a^2+12)*q^192 + (-6*a^3+7*a^2+27*a-4)*q^193 + (-5*a^2+7*a+6)*q^194 + (-3*a^3+2*a^2+21*a-16)*q^195 + (-7*a^2+14)*q^196 + (2*a^3-a^2-9*a+12)*q^197 + (a^3-6*a)*q^198 + (-2*a^3+8*a^2+6*a-20)*q^199 + (-3*a^3+16*a+2)*q^200 +  ...

-------------------------------------------------------
187G (old = 17A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/3 + Z/3 + Z/2^2*3 + Z/2^2*3
= A(Z/3 + Z/3) + D(Z/3 + Z/3) + F(Z/2^2 + Z/2^2)

-------------------------------------------------------
187H (old = 11A), dim = 1

CONGRUENCES:
Modular Degree = 2^6
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^5 + Z/2^5
= B(Z/2 + Z/2) + C(Z/2^2 + Z/2^2) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(188)
Weight 2

-------------------------------------------------------
J_0(188), dim = 22

-------------------------------------------------------
188A (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3
= C(Z/3 + Z/3) + E(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 13
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 5.4832921226170090081 + 0.87456675614477690378e-4i
Omega-         = 4.0155854571516788341 + 0.56953750227689079283e-3i
L(1)           = 1.8277640411048204574

HECKE EIGENFORM:
a^2-a-3 = 0,
f(q) = q + a*q^3 + (-a+3)*q^7 + a*q^9 + (-2*a+2)*q^11 + 2*q^13 + (-a-2)*q^17 + (-2*a+4)*q^19 + (2*a-3)*q^21 + (2*a-2)*q^23 + -5*q^25 + (-2*a+3)*q^27 + (2*a-2)*q^29 + (4*a-2)*q^31 + -6*q^33 + (-3*a+2)*q^37 + 2*a*q^39 + -6*q^41 + 2*a*q^43 + -1*q^47 + (-5*a+5)*q^49 + (-3*a-3)*q^51 + (-5*a-1)*q^53 + (2*a-6)*q^57 + (3*a-9)*q^59 + (3*a-1)*q^61 + (2*a-3)*q^63 + 8*q^67 + 6*q^69 + (-5*a+8)*q^71 + (4*a-2)*q^73 + -5*a*q^75 + (-6*a+12)*q^77 + (3*a+8)*q^79 + (-2*a-6)*q^81 + (4*a-4)*q^83 + 6*q^87 + (7*a-1)*q^89 + (-2*a+6)*q^91 + (2*a+12)*q^93 + (a+1)*q^97 + -6*q^99 + (3*a-6)*q^101 + (a+4)*q^103 + (6*a+6)*q^107 + (4*a+4)*q^109 + (-a-9)*q^111 + (-6*a+6)*q^113 + 2*a*q^117 + -3*q^119 + (-4*a+5)*q^121 + -6*a*q^123 + (-10*a+6)*q^127 + (2*a+6)*q^129 + (a-19)*q^131 + (-8*a+18)*q^133 + (2*a-8)*q^137 + 8*q^139 + -a*q^141 + (-4*a+4)*q^143 + -15*q^147 + (7*a+2)*q^149 + (4*a-14)*q^151 + (-3*a-3)*q^153 + (7*a-5)*q^157 + (-6*a-15)*q^159 + (6*a-12)*q^161 + (8*a+6)*q^163 + (-8*a+2)*q^167 + -9*q^169 + (2*a-6)*q^171 + (3*a+3)*q^173 + (5*a-15)*q^175 + (-6*a+9)*q^177 + -6*q^179 + -4*a*q^181 + (2*a+9)*q^183 + (4*a+2)*q^187 + (-7*a+15)*q^189 + (4*a-16)*q^191 + (-2*a-20)*q^193 + 18*q^197 + (2*a-6)*q^199 +  ...

-------------------------------------------------------
188B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= D(Z/3 + Z/3 + Z/3 + Z/3) + E(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 11.519989937101391319 + 0.16497238648859288149e-2i
Omega-         = 4.366833466835416333 + -0.11526122388813855164e-3i
L(1)           =

HECKE EIGENFORM:
a^2+3*a+1 = 0,
f(q) = q + a*q^3 + (-2*a-4)*q^5 + (-a-5)*q^7 + (-3*a-4)*q^9 + (4*a+4)*q^11 + (4*a+4)*q^13 + (2*a+2)*q^15 + (3*a+6)*q^17 + (-6*a-10)*q^19 + (-2*a+1)*q^21 + (-4*a-6)*q^23 + (4*a+7)*q^25 + (2*a+3)*q^27 + (-8*a-4)*q^33 + (8*a+18)*q^35 + (-3*a-10)*q^37 + (-8*a-4)*q^39 + (2*a+12)*q^41 + -10*q^43 + (2*a+10)*q^45 + 1*q^47 + (7*a+17)*q^49 + (-3*a-3)*q^51 + (-5*a-13)*q^53 + -8*q^55 + (8*a+6)*q^57 + (-a-1)*q^59 + (3*a+7)*q^61 + (10*a+17)*q^63 + -8*q^65 + (2*a-4)*q^67 + (6*a+4)*q^69 + -5*a*q^71 + (-6*a-6)*q^73 + (-5*a-4)*q^75 + (-12*a-16)*q^77 + 3*a*q^79 + (6*a+10)*q^81 + (-8*a-12)*q^83 + (-6*a-18)*q^85 + (3*a+3)*q^89 + (-12*a-16)*q^91 + (8*a+28)*q^95 + (-3*a-15)*q^97 + (8*a-4)*q^99 + (-a-10)*q^101 + (9*a+12)*q^103 + (-6*a-8)*q^105 + (10*a+10)*q^107 + (2*a-2)*q^109 + (-a+3)*q^111 + (-2*a+8)*q^113 + (4*a+16)*q^115 + (8*a-4)*q^117 + (-12*a-27)*q^119 + (-16*a-11)*q^121 + (6*a-2)*q^123 + 4*a*q^125 + (4*a-2)*q^127 + -10*a*q^129 + (-3*a-3)*q^131 + (22*a+44)*q^133 + (-2*a-8)*q^135 + (-2*a-14)*q^137 + (8*a+22)*q^139 + a*q^141 + -16*a*q^143 + (-4*a-7)*q^147 + (11*a+6)*q^149 + -12*q^151 + (-3*a-15)*q^153 + (-5*a-13)*q^157 + (2*a+5)*q^159 + (14*a+26)*q^161 + (-6*a-4)*q^163 + -8*a*q^165 + (14*a+14)*q^167 + (-16*a-13)*q^169 + 22*q^171 + (-a+11)*q^173 + (-15*a-31)*q^175 + (2*a+1)*q^177 + (-4*a+6)*q^179 + (12*a+18)*q^181 + (-2*a-3)*q^183 + (14*a+34)*q^185 + 12*q^187 + (-7*a-13)*q^189 + (8*a+16)*q^191 + (10*a+16)*q^193 + -8*a*q^195 + (-4*a-2)*q^197 + (-12*a-4)*q^199 +  ...

-------------------------------------------------------
188C (old = 94A), dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3
= A(Z/3 + Z/3) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
188D (old = 94B), dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^2*47^2
Ker(ModPolar)  = Z/2*3*47 + Z/2*3*47 + Z/2*3*47 + Z/2*3*47
= B(Z/3 + Z/3 + Z/3 + Z/3) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/47 + Z/47 + Z/47 + Z/47)

-------------------------------------------------------
188E (old = 47A), dim = 4

CONGRUENCES:
Modular Degree = 2^4*47^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2*47 + Z/2*47 + Z/2*47 + Z/2*47
= A(Z/2 + Z/2 + Z/2 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/47 + Z/47 + Z/47 + Z/47)

-------------------------------------------------------
Gamma_0(189)
Weight 2

-------------------------------------------------------
J_0(189), dim = 19

-------------------------------------------------------
189A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + G(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = ++
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.0275867390464027432 + 0.20769573336977537843e-3i
Omega-         = 0.50492485896827312627e-3 + 1.9617746058323672789i
L(1)           =
w1             = -2.0275867390464027432 + -0.20769573336977537843e-3i
w2             = 0.50492485896827312627e-3 + 1.9617746058323672789i
c4             = 143.9462399600458061 + 0.56494647134770585973e-1i
c6             = -215.02098780177697765 + -2.4499426779473316604i
j              = 1755.2044604994737981 + 0.59722849393830528877i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + 2*q^4 + -1*q^5 + -1*q^7 + 2*q^10 + -4*q^11 + -2*q^13 + 2*q^14 + -4*q^16 + 3*q^17 + -8*q^19 + -2*q^20 + 8*q^22 + -6*q^23 + -4*q^25 + 4*q^26 + -2*q^28 + -4*q^29 + 6*q^31 + 8*q^32 + -6*q^34 + 1*q^35 + -3*q^37 + 16*q^38 + 1*q^41 + 11*q^43 + -8*q^44 + 12*q^46 + 9*q^47 + 1*q^49 + 8*q^50 + -4*q^52 + 6*q^53 + 4*q^55 + 8*q^58 + -15*q^59 + 4*q^61 + -12*q^62 + -8*q^64 + 2*q^65 + -8*q^67 + 6*q^68 + -2*q^70 + -12*q^71 + 6*q^73 + 6*q^74 + -16*q^76 + 4*q^77 + -1*q^79 + 4*q^80 + -2*q^82 + -9*q^83 + -3*q^85 + -22*q^86 + 2*q^89 + 2*q^91 + -12*q^92 + -18*q^94 + 8*q^95 + 12*q^97 + -2*q^98 + -8*q^100 + 10*q^101 + 2*q^103 + -12*q^106 + 2*q^107 + -9*q^109 + -8*q^110 + 4*q^112 + 2*q^113 + 6*q^115 + -8*q^116 + 30*q^118 + -3*q^119 + 5*q^121 + -8*q^122 + 12*q^124 + 9*q^125 + -15*q^127 + -4*q^130 + -4*q^131 + 8*q^133 + 16*q^134 + -18*q^137 + 2*q^140 + 24*q^142 + 8*q^143 + 4*q^145 + -12*q^146 + -6*q^148 + 12*q^149 + 5*q^151 + -8*q^154 + -6*q^155 + -8*q^157 + 2*q^158 + -8*q^160 + 6*q^161 + -11*q^163 + 2*q^164 + 18*q^166 + 17*q^167 + -9*q^169 + 6*q^170 + 22*q^172 + 22*q^173 + 4*q^175 + 16*q^176 + -4*q^178 + -2*q^179 + 16*q^181 + -4*q^182 + 3*q^185 + -12*q^187 + 18*q^188 + -16*q^190 + 2*q^191 + -25*q^193 + -24*q^194 + 2*q^196 + -4*q^197 + -12*q^199 +  ...

-------------------------------------------------------
189B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/3) + H(Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 1.8680399548243075606 + -0.8496864289672240205e-4i
Omega-         = 0.16756987101794616831e-4 + -1.5762625254160279285i
L(1)           = 0.6226799855855753836
w1             = 1.8680399548243075606 + -0.8496864289672240205e-4i
w2             = 0.16756987101794616831e-4 + -1.5762625254160279285i
c4             = 288.01671911848784518 + 0.26849644908787263773e-2i
c6             = -2808.7072847895466045 + 0.6913300881146051467i
j              = 2579.8239435827255409 + -0.66161086380502289993i

HECKE EIGENFORM:
f(q) = q + -2*q^4 + 3*q^5 + 1*q^7 + 6*q^11 + -4*q^13 + 4*q^16 + 3*q^17 + 2*q^19 + -6*q^20 + -6*q^23 + 4*q^25 + -2*q^28 + -6*q^29 + -4*q^31 + 3*q^35 + -7*q^37 + -3*q^41 + -1*q^43 + -12*q^44 + 9*q^47 + 1*q^49 + 8*q^52 + -6*q^53 + 18*q^55 + 9*q^59 + -10*q^61 + -8*q^64 + -12*q^65 + -4*q^67 + -6*q^68 + 2*q^73 + -4*q^76 + 6*q^77 + -1*q^79 + 12*q^80 + 3*q^83 + 9*q^85 + 6*q^89 + -4*q^91 + 12*q^92 + 6*q^95 + -10*q^97 + -8*q^100 + 6*q^101 + 14*q^103 + 6*q^107 + 11*q^109 + 4*q^112 + -12*q^113 + -18*q^115 + 12*q^116 + 3*q^119 + 25*q^121 + 8*q^124 + -3*q^125 + -7*q^127 + 12*q^131 + 2*q^133 + -12*q^137 + -22*q^139 + -6*q^140 + -24*q^143 + -18*q^145 + 14*q^148 + -6*q^149 + -19*q^151 + -12*q^155 + 14*q^157 + -6*q^161 + -7*q^163 + 6*q^164 + -3*q^167 + 3*q^169 + 2*q^172 + -18*q^173 + 4*q^175 + 24*q^176 + 12*q^179 + 20*q^181 + -21*q^185 + 18*q^187 + -18*q^188 + 18*q^191 + -13*q^193 + -2*q^196 + -18*q^197 + 20*q^199 +  ...

-------------------------------------------------------
189C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2^2*3^2 + Z/2^2*3^2
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/3 + Z/3) + J(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.1325775292840860322 + -0.12187761819900508231e-3i
Omega-         = 0.2983144593150227891e-3 + 1.1703831252866333719i
L(1)           = 1.1325775358417623902
w1             = 0.2983144593150227891e-3 + 1.1703831252866333719i
w2             = 1.1325775292840860322 + -0.12187761819900508231e-3i
c4             = 1296.1326827103867616 + 0.89609314267601702787i
c6             = 5781.5640653316334209 + -19.702152403326320155i
j              = 1754.93962313552887 + -0.24322164015125899025i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 2*q^4 + 1*q^5 + -1*q^7 + 2*q^10 + 4*q^11 + -2*q^13 + -2*q^14 + -4*q^16 + -3*q^17 + -8*q^19 + 2*q^20 + 8*q^22 + 6*q^23 + -4*q^25 + -4*q^26 + -2*q^28 + 4*q^29 + 6*q^31 + -8*q^32 + -6*q^34 + -1*q^35 + -3*q^37 + -16*q^38 + -1*q^41 + 11*q^43 + 8*q^44 + 12*q^46 + -9*q^47 + 1*q^49 + -8*q^50 + -4*q^52 + -6*q^53 + 4*q^55 + 8*q^58 + 15*q^59 + 4*q^61 + 12*q^62 + -8*q^64 + -2*q^65 + -8*q^67 + -6*q^68 + -2*q^70 + 12*q^71 + 6*q^73 + -6*q^74 + -16*q^76 + -4*q^77 + -1*q^79 + -4*q^80 + -2*q^82 + 9*q^83 + -3*q^85 + 22*q^86 + -2*q^89 + 2*q^91 + 12*q^92 + -18*q^94 + -8*q^95 + 12*q^97 + 2*q^98 + -8*q^100 + -10*q^101 + 2*q^103 + -12*q^106 + -2*q^107 + -9*q^109 + 8*q^110 + 4*q^112 + -2*q^113 + 6*q^115 + 8*q^116 + 30*q^118 + 3*q^119 + 5*q^121 + 8*q^122 + 12*q^124 + -9*q^125 + -15*q^127 + -4*q^130 + 4*q^131 + 8*q^133 + -16*q^134 + 18*q^137 + -2*q^140 + 24*q^142 + -8*q^143 + 4*q^145 + 12*q^146 + -6*q^148 + -12*q^149 + 5*q^151 + -8*q^154 + 6*q^155 + -8*q^157 + -2*q^158 + -8*q^160 + -6*q^161 + -11*q^163 + -2*q^164 + 18*q^166 + -17*q^167 + -9*q^169 + -6*q^170 + 22*q^172 + -22*q^173 + 4*q^175 + -16*q^176 + -4*q^178 + 2*q^179 + 16*q^181 + 4*q^182 + -3*q^185 + -12*q^187 + -18*q^188 + -16*q^190 + -2*q^191 + -25*q^193 + 24*q^194 + 2*q^196 + 4*q^197 + -12*q^199 +  ...

-------------------------------------------------------
189D (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + H(Z/3) + I(Z/3)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 3
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.7303685142238418561 + 0.21460995538063609534e-3i
Omega-         = 0.57185564876699721954e-3 + -1.0781813332626665365i
L(1)           =
w1             = -2.7303685142238418561 + -0.21460995538063609534e-3i
w2             = -0.57185564876699721954e-3 + 1.0781813332626665365i
c4             = 1153.3572053366911968 + -2.4466712376792913873i
c6             = -39165.067466895514646 + 124.65421161093286403i
j              = 8133452.2532696404797 + -58463.739643192964437i

HECKE EIGENFORM:
f(q) = q + -2*q^4 + -3*q^5 + 1*q^7 + -6*q^11 + -4*q^13 + 4*q^16 + -3*q^17 + 2*q^19 + 6*q^20 + 6*q^23 + 4*q^25 + -2*q^28 + 6*q^29 + -4*q^31 + -3*q^35 + -7*q^37 + 3*q^41 + -1*q^43 + 12*q^44 + -9*q^47 + 1*q^49 + 8*q^52 + 6*q^53 + 18*q^55 + -9*q^59 + -10*q^61 + -8*q^64 + 12*q^65 + -4*q^67 + 6*q^68 + 2*q^73 + -4*q^76 + -6*q^77 + -1*q^79 + -12*q^80 + -3*q^83 + 9*q^85 + -6*q^89 + -4*q^91 + -12*q^92 + -6*q^95 + -10*q^97 + -8*q^100 + -6*q^101 + 14*q^103 + -6*q^107 + 11*q^109 + 4*q^112 + 12*q^113 + -18*q^115 + -12*q^116 + -3*q^119 + 25*q^121 + 8*q^124 + 3*q^125 + -7*q^127 + -12*q^131 + 2*q^133 + 12*q^137 + -22*q^139 + 6*q^140 + 24*q^143 + -18*q^145 + 14*q^148 + 6*q^149 + -19*q^151 + 12*q^155 + 14*q^157 + 6*q^161 + -7*q^163 + -6*q^164 + 3*q^167 + 3*q^169 + 2*q^172 + 18*q^173 + 4*q^175 + -24*q^176 + -12*q^179 + 20*q^181 + 21*q^185 + 18*q^187 + 18*q^188 + -18*q^191 + -13*q^193 + -2*q^196 + 18*q^197 + 20*q^199 +  ...

-------------------------------------------------------
189E (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^2
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= B(Z/3) + F(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/3 + Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*3
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 3.8944860309811432556 + 0.16660461352382725778e-3i
Omega-         = 3.8941306086880383239 + -0.98311633754887114656e-4i
L(1)           = 1.2981620115149279588

HECKE EIGENFORM:
a^2-3 = 0,
f(q) = q + a*q^2 + 1*q^4 + a*q^5 + 1*q^7 + -a*q^8 + 3*q^10 + -a*q^11 + 2*q^13 + a*q^14 + -5*q^16 + -4*a*q^17 + 5*q^19 + a*q^20 + -3*q^22 + a*q^23 + -2*q^25 + 2*a*q^26 + 1*q^28 + -6*a*q^29 + 5*q^31 + -3*a*q^32 + -12*q^34 + a*q^35 + -7*q^37 + 5*a*q^38 + -3*q^40 + 3*a*q^41 + -4*q^43 + -a*q^44 + 3*q^46 + 4*a*q^47 + 1*q^49 + -2*a*q^50 + 2*q^52 + 8*a*q^53 + -3*q^55 + -a*q^56 + -18*q^58 + -4*a*q^59 + 8*q^61 + 5*a*q^62 + 1*q^64 + 2*a*q^65 + 14*q^67 + -4*a*q^68 + 3*q^70 + 3*a*q^71 + -4*q^73 + -7*a*q^74 + 5*q^76 + -a*q^77 + 8*q^79 + -5*a*q^80 + 9*q^82 + -6*a*q^83 + -12*q^85 + -4*a*q^86 + 3*q^88 + -5*a*q^89 + 2*q^91 + a*q^92 + 12*q^94 + 5*a*q^95 + -4*q^97 + a*q^98 + -2*q^100 + 8*a*q^101 + 5*q^103 + -2*a*q^104 + 24*q^106 + -2*a*q^107 + -7*q^109 + -3*a*q^110 + -5*q^112 + 6*a*q^113 + 3*q^115 + -6*a*q^116 + -12*q^118 + -4*a*q^119 + -8*q^121 + 8*a*q^122 + 5*q^124 + -7*a*q^125 + -10*q^127 + 7*a*q^128 + 6*q^130 + 4*a*q^131 + 5*q^133 + 14*a*q^134 + 12*q^136 + 2*a*q^137 + 20*q^139 + a*q^140 + 9*q^142 + -2*a*q^143 + -18*q^145 + -4*a*q^146 + -7*q^148 + -2*a*q^149 + -10*q^151 + -5*a*q^152 + -3*q^154 + 5*a*q^155 + -10*q^157 + 8*a*q^158 + -9*q^160 + a*q^161 + 2*q^163 + 3*a*q^164 + -18*q^166 + -6*a*q^167 + -9*q^169 + -12*a*q^170 + -4*q^172 + a*q^173 + -2*q^175 + 5*a*q^176 + -15*q^178 + 2*a*q^179 + 2*q^181 + 2*a*q^182 + -3*q^184 + -7*a*q^185 + 12*q^187 + 4*a*q^188 + 15*q^190 + -5*a*q^191 + -22*q^193 + -4*a*q^194 + 1*q^196 + -6*a*q^197 + -25*q^199 + 2*a*q^200 +  ...

-------------------------------------------------------
189F (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3^3*7
Ker(ModPolar)  = Z/2*3 + Z/2*3 + Z/2*3^2*7 + Z/2*3^2*7
= C(Z/3 + Z/3) + E(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/3 + Z/3) + I(Z/7 + Z/7) + J(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^2*7
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.6959248216109690016 + -0.25694959920515642784e-3i
Omega-         = 1.6951206909305682099 + 0.10887822087066310112e-2i
L(1)           = 1.6959248410761880111

HECKE EIGENFORM:
a^2-7 = 0,
f(q) = q + a*q^2 + 5*q^4 + -a*q^5 + -1*q^7 + 3*a*q^8 + -7*q^10 + -a*q^11 + -2*q^13 + -a*q^14 + 11*q^16 + 7*q^19 + -5*a*q^20 + -7*q^22 + -3*a*q^23 + 2*q^25 + -2*a*q^26 + -5*q^28 + 2*a*q^29 + 3*q^31 + 5*a*q^32 + a*q^35 + -3*q^37 + 7*a*q^38 + -21*q^40 + a*q^41 + 8*q^43 + -5*a*q^44 + -21*q^46 + 1*q^49 + 2*a*q^50 + -10*q^52 + 7*q^55 + -3*a*q^56 + 14*q^58 + -8*q^61 + 3*a*q^62 + 13*q^64 + 2*a*q^65 + -2*q^67 + 7*q^70 + 3*a*q^71 + -3*a*q^74 + 35*q^76 + a*q^77 + -4*q^79 + -11*a*q^80 + 7*q^82 + 6*a*q^83 + 8*a*q^86 + -21*q^88 + -7*a*q^89 + 2*q^91 + -15*a*q^92 + -7*a*q^95 + -12*q^97 + a*q^98 + 10*q^100 + 4*a*q^101 + -13*q^103 + -6*a*q^104 + 2*a*q^107 + 9*q^109 + 7*a*q^110 + -11*q^112 + 2*a*q^113 + 21*q^115 + 10*a*q^116 + -4*q^121 + -8*a*q^122 + 15*q^124 + 3*a*q^125 + 6*q^127 + 3*a*q^128 + 14*q^130 + 8*a*q^131 + -7*q^133 + -2*a*q^134 + -6*a*q^137 + -12*q^139 + 5*a*q^140 + 21*q^142 + 2*a*q^143 + -14*q^145 + -15*q^148 + -6*a*q^149 + 2*q^151 + 21*a*q^152 + 7*q^154 + -3*a*q^155 + -14*q^157 + -4*a*q^158 + -35*q^160 + 3*a*q^161 + 10*q^163 + 5*a*q^164 + 42*q^166 + 2*a*q^167 + -9*q^169 + 40*q^172 + -5*a*q^173 + -2*q^175 + -11*a*q^176 + -49*q^178 + -2*a*q^179 + -14*q^181 + 2*a*q^182 + -63*q^184 + 3*a*q^185 + -49*q^190 + -a*q^191 + 2*q^193 + -12*a*q^194 + 5*q^196 + -10*a*q^197 + -3*q^199 + 6*a*q^200 +  ...

-------------------------------------------------------
189G (old = 63A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^2*3 + Z/2^2*3
= A(Z/3 + Z/3) + F(Z/3 + Z/3) + H(Z/2 + Z/2 + Z/2 + Z/2) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
189H (old = 63B), dim = 2

CONGRUENCES:
Modular Degree = 2^4*3^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3 + Z/2*3
= B(Z/3) + D(Z/3) + E(Z/3 + Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/3) + J(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
189I (old = 27A), dim = 1

CONGRUENCES:
Modular Degree = 3*7
Ker(ModPolar)  = Z/3*7 + Z/3*7
= D(Z/3) + F(Z/7 + Z/7) + H(Z/3)

-------------------------------------------------------
189J (old = 21A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^2
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*3^2 + Z/2^2*3^2
= C(Z/3 + Z/3) + F(Z/3 + Z/3) + G(Z/2 + Z/2 + Z/2 + Z/2) + H(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(190)
Weight 2

-------------------------------------------------------
J_0(190), dim = 27

-------------------------------------------------------
190A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +++
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 3.4754402367059866304 + -0.52390739592679486942e-3i
Omega-         = 0.38391285241632793462e-3 + -2.5535739336314714825i
L(1)           =
w1             = 1.7379120747792014792 + -1.2770489205136991387i
w2             = -1.7375281619267851512 + -1.2765250131177723438i
c4             = -70.977481095762796042 + -0.77794881755063148218e-1i
c6             = -1132.5464066490100274 + 0.59496645053592258232i
j              = 376.70288200929569065 + 1.2781415955993391105i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^3 + 1*q^4 + -1*q^5 + 1*q^6 + -1*q^7 + -1*q^8 + -2*q^9 + 1*q^10 + -1*q^12 + -3*q^13 + 1*q^14 + 1*q^15 + 1*q^16 + -7*q^17 + 2*q^18 + -1*q^19 + -1*q^20 + 1*q^21 + -5*q^23 + 1*q^24 + 1*q^25 + 3*q^26 + 5*q^27 + -1*q^28 + -5*q^29 + -1*q^30 + 10*q^31 + -1*q^32 + 7*q^34 + 1*q^35 + -2*q^36 + 2*q^37 + 1*q^38 + 3*q^39 + 1*q^40 + 2*q^41 + -1*q^42 + 6*q^43 + 2*q^45 + 5*q^46 + -1*q^48 + -6*q^49 + -1*q^50 + 7*q^51 + -3*q^52 + 9*q^53 + -5*q^54 + 1*q^56 + 1*q^57 + 5*q^58 + -7*q^59 + 1*q^60 + -4*q^61 + -10*q^62 + 2*q^63 + 1*q^64 + 3*q^65 + 7*q^67 + -7*q^68 + 5*q^69 + -1*q^70 + 2*q^72 + -9*q^73 + -2*q^74 + -1*q^75 + -1*q^76 + -3*q^78 + -10*q^79 + -1*q^80 + 1*q^81 + -2*q^82 + -2*q^83 + 1*q^84 + 7*q^85 + -6*q^86 + 5*q^87 + -10*q^89 + -2*q^90 + 3*q^91 + -5*q^92 + -10*q^93 + 1*q^95 + 1*q^96 + -18*q^97 + 6*q^98 + 1*q^100 + -4*q^101 + -7*q^102 + 3*q^104 + -1*q^105 + -9*q^106 + 9*q^107 + 5*q^108 + 13*q^109 + -2*q^111 + -1*q^112 + 8*q^113 + -1*q^114 + 5*q^115 + -5*q^116 + 6*q^117 + 7*q^118 + 7*q^119 + -1*q^120 + -11*q^121 + 4*q^122 + -2*q^123 + 10*q^124 + -1*q^125 + -2*q^126 + -6*q^127 + -1*q^128 + -6*q^129 + -3*q^130 + -20*q^131 + 1*q^133 + -7*q^134 + -5*q^135 + 7*q^136 + -3*q^137 + -5*q^138 + 12*q^139 + 1*q^140 + -2*q^144 + 5*q^145 + 9*q^146 + 6*q^147 + 2*q^148 + 4*q^149 + 1*q^150 + -6*q^151 + 1*q^152 + 14*q^153 + -10*q^155 + 3*q^156 + 18*q^157 + 10*q^158 + -9*q^159 + 1*q^160 + 5*q^161 + -1*q^162 + -18*q^163 + 2*q^164 + 2*q^166 + 14*q^167 + -1*q^168 + -4*q^169 + -7*q^170 + 2*q^171 + 6*q^172 + 6*q^173 + -5*q^174 + -1*q^175 + 7*q^177 + 10*q^178 + 24*q^179 + 2*q^180 + -10*q^181 + -3*q^182 + 4*q^183 + 5*q^184 + -2*q^185 + 10*q^186 + -5*q^189 + -1*q^190 + -7*q^191 + -1*q^192 + -2*q^193 + 18*q^194 + -3*q^195 + -6*q^196 + -10*q^197 + 17*q^199 + -1*q^200 +  ...

-------------------------------------------------------
190B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*11
Ker(ModPolar)  = Z/2^3*11 + Z/2^3*11
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/11 + Z/11) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -+-
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.7273996381951714503 + -0.36346991937032734199e-3i
Omega-         = 0.29440664584525017168e-3 + -0.90448058086891210917i
L(1)           =
w1             = 1.3635526157746631001 + 0.45205855547477089091i
w2             = 0.29440664584525017168e-3 + -0.90448058086891210917i
c4             = 2285.8069022036462623 + -3.1625860973076296803i
c6             = -116721.74903348273325 + 209.12815526855264936i
j              = -12278.075292514560393 + 56.464260339398617106i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -3*q^3 + 1*q^4 + -1*q^5 + -3*q^6 + -5*q^7 + 1*q^8 + 6*q^9 + -1*q^10 + -4*q^11 + -3*q^12 + -1*q^13 + -5*q^14 + 3*q^15 + 1*q^16 + -3*q^17 + 6*q^18 + 1*q^19 + -1*q^20 + 15*q^21 + -4*q^22 + 7*q^23 + -3*q^24 + 1*q^25 + -1*q^26 + -9*q^27 + -5*q^28 + -3*q^29 + 3*q^30 + -2*q^31 + 1*q^32 + 12*q^33 + -3*q^34 + 5*q^35 + 6*q^36 + -2*q^37 + 1*q^38 + 3*q^39 + -1*q^40 + -6*q^41 + 15*q^42 + 6*q^43 + -4*q^44 + -6*q^45 + 7*q^46 + -3*q^48 + 18*q^49 + 1*q^50 + 9*q^51 + -1*q^52 + -13*q^53 + -9*q^54 + 4*q^55 + -5*q^56 + -3*q^57 + -3*q^58 + -9*q^59 + 3*q^60 + -12*q^61 + -2*q^62 + -30*q^63 + 1*q^64 + 1*q^65 + 12*q^66 + -3*q^67 + -3*q^68 + -21*q^69 + 5*q^70 + 6*q^72 + 11*q^73 + -2*q^74 + -3*q^75 + 1*q^76 + 20*q^77 + 3*q^78 + -2*q^79 + -1*q^80 + 9*q^81 + -6*q^82 + -10*q^83 + 15*q^84 + 3*q^85 + 6*q^86 + 9*q^87 + -4*q^88 + 2*q^89 + -6*q^90 + 5*q^91 + 7*q^92 + 6*q^93 + -1*q^95 + -3*q^96 + -2*q^97 + 18*q^98 + -24*q^99 + 1*q^100 + -8*q^101 + 9*q^102 + 4*q^103 + -1*q^104 + -15*q^105 + -13*q^106 + -13*q^107 + -9*q^108 + 19*q^109 + 4*q^110 + 6*q^111 + -5*q^112 + -3*q^114 + -7*q^115 + -3*q^116 + -6*q^117 + -9*q^118 + 15*q^119 + 3*q^120 + 5*q^121 + -12*q^122 + 18*q^123 + -2*q^124 + -1*q^125 + -30*q^126 + -6*q^127 + 1*q^128 + -18*q^129 + 1*q^130 + 16*q^131 + 12*q^132 + -5*q^133 + -3*q^134 + 9*q^135 + -3*q^136 + 9*q^137 + -21*q^138 + 16*q^139 + 5*q^140 + 4*q^143 + 6*q^144 + 3*q^145 + 11*q^146 + -54*q^147 + -2*q^148 + -4*q^149 + -3*q^150 + -10*q^151 + 1*q^152 + -18*q^153 + 20*q^154 + 2*q^155 + 3*q^156 + 6*q^157 + -2*q^158 + 39*q^159 + -1*q^160 + -35*q^161 + 9*q^162 + 22*q^163 + -6*q^164 + -12*q^165 + -10*q^166 + -2*q^167 + 15*q^168 + -12*q^169 + 3*q^170 + 6*q^171 + 6*q^172 + -14*q^173 + 9*q^174 + -5*q^175 + -4*q^176 + 27*q^177 + 2*q^178 + -8*q^179 + -6*q^180 + 26*q^181 + 5*q^182 + 36*q^183 + 7*q^184 + 2*q^185 + 6*q^186 + 12*q^187 + 45*q^189 + -1*q^190 + 9*q^191 + -3*q^192 + 10*q^193 + -2*q^194 + -3*q^195 + 18*q^196 + -22*q^197 + -24*q^198 + -15*q^199 + 1*q^200 +  ...

-------------------------------------------------------
190C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3*3
Ker(ModPolar)  = Z/2^3*3 + Z/2^3*3
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2) + I(Z/3 + Z/3)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 3
|L(1)/Omega|   = 2
Sha Bound      = 2*3^2

ANALYTIC INVARIANTS:

Omega+         = 0.98625549264688379609 + -0.14948622855692905805e-4i
Omega-         = 0.30750259311817931774e-3 + -2.3715348169912913981i
L(1)           = 1.972510985520343086
w1             = 0.49297399502688280839 + 1.1857599341842178526i
w2             = 0.98625549264688379609 + -0.14948622855692905805e-4i
c4             = 1441.1170577790096229 + 0.31182758153684625993i
c6             = 84205.166534235956742 + -10.990728737274973712i
j              = -1262.1594640212761542 + -1.987899584598725409i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^3 + 1*q^4 + 1*q^5 + 1*q^6 + -1*q^7 + 1*q^8 + -2*q^9 + 1*q^10 + 1*q^12 + -1*q^13 + -1*q^14 + 1*q^15 + 1*q^16 + -3*q^17 + -2*q^18 + 1*q^19 + 1*q^20 + -1*q^21 + 3*q^23 + 1*q^24 + 1*q^25 + -1*q^26 + -5*q^27 + -1*q^28 + -3*q^29 + 1*q^30 + 2*q^31 + 1*q^32 + -3*q^34 + -1*q^35 + -2*q^36 + -10*q^37 + 1*q^38 + -1*q^39 + 1*q^40 + 6*q^41 + -1*q^42 + 2*q^43 + -2*q^45 + 3*q^46 + 1*q^48 + -6*q^49 + 1*q^50 + -3*q^51 + -1*q^52 + 3*q^53 + -5*q^54 + -1*q^56 + 1*q^57 + -3*q^58 + 3*q^59 + 1*q^60 + 8*q^61 + 2*q^62 + 2*q^63 + 1*q^64 + -1*q^65 + -7*q^67 + -3*q^68 + 3*q^69 + -1*q^70 + 12*q^71 + -2*q^72 + -13*q^73 + -10*q^74 + 1*q^75 + 1*q^76 + -1*q^78 + 14*q^79 + 1*q^80 + 1*q^81 + 6*q^82 + 6*q^83 + -1*q^84 + -3*q^85 + 2*q^86 + -3*q^87 + 6*q^89 + -2*q^90 + 1*q^91 + 3*q^92 + 2*q^93 + 1*q^95 + 1*q^96 + -10*q^97 + -6*q^98 + 1*q^100 + 12*q^101 + -3*q^102 + 8*q^103 + -1*q^104 + -1*q^105 + 3*q^106 + 15*q^107 + -5*q^108 + 11*q^109 + -10*q^111 + -1*q^112 + -12*q^113 + 1*q^114 + 3*q^115 + -3*q^116 + 2*q^117 + 3*q^118 + 3*q^119 + 1*q^120 + -11*q^121 + 8*q^122 + 6*q^123 + 2*q^124 + 1*q^125 + 2*q^126 + 2*q^127 + 1*q^128 + 2*q^129 + -1*q^130 + -1*q^133 + -7*q^134 + -5*q^135 + -3*q^136 + 9*q^137 + 3*q^138 + 8*q^139 + -1*q^140 + 12*q^142 + -2*q^144 + -3*q^145 + -13*q^146 + -6*q^147 + -10*q^148 + -12*q^149 + 1*q^150 + -10*q^151 + 1*q^152 + 6*q^153 + 2*q^155 + -1*q^156 + -10*q^157 + 14*q^158 + 3*q^159 + 1*q^160 + -3*q^161 + 1*q^162 + -22*q^163 + 6*q^164 + 6*q^166 + 18*q^167 + -1*q^168 + -12*q^169 + -3*q^170 + -2*q^171 + 2*q^172 + -6*q^173 + -3*q^174 + -1*q^175 + 3*q^177 + 6*q^178 + -2*q^180 + 2*q^181 + 1*q^182 + 8*q^183 + 3*q^184 + -10*q^185 + 2*q^186 + 5*q^189 + 1*q^190 + -27*q^191 + 1*q^192 + -22*q^193 + -10*q^194 + -1*q^195 + -6*q^196 + 6*q^197 + -19*q^199 + 1*q^200 +  ...

-------------------------------------------------------
190D (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^5*13
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^3*13 + Z/2^3*13
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2*13 + Z/2*13) + F(Z/2 + Z/2) + G(Z/2 + Z/2) + H(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 17
#CompGroup(Fpbar) = ???
c_p            = ???
c_inf          = 1
ord((0)-(oo))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 0.72369925174963329104 + 0.43720338063172892904e-4i
Omega-         = 3.0290814826586898891 + 0.13353944636343723746e-2i
L(1)           = 0.72369925307025643249

HECKE EIGENFORM:
a^2+a-4 = 0,
f(q) = q + -1*q^2 + a*q^3 + 1*q^4 + 1*q^5 + -a*q^6 + a*q^7 + -1*q^8 + (-a+1)*q^9 + -1*q^10 + 4*q^11 + a*q^12 + (-3*a-2)*q^13 + -a*q^14 + a*q^15 + 1*q^16 + (a+6)*q^17 + (a-1)*q^18 + -1*q^19 + 1*q^20 + (-a+4)*q^21 + -4*q^22 + -3*a*q^23 + -a*q^24 + 1*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 + -1*q^32 + 4*a*q^33 + (-a-6)*q^34 + a*q^35 + (-a+1)*q^36 + -6*q^37 + 1*q^38 + (a-12)*q^39 + -1*q^40 + (-4*a+2)*q^41 + (a-4)*q^42 + (-2*a-8)*q^43 + 4*q^44 + (-a+1)*q^45 + 3*a*q^46 + (-4*a-4)*q^47 + a*q^48 + (-a-3)*q^49 + -1*q^50 + (5*a+4)*q^51 + (-3*a-2)*q^52 + (a-2)*q^53 + (a+4)*q^54 + 4*q^55 + -a*q^56 + -a*q^57 + (-3*a-2)*q^58 + -a*q^59 + a*q^60 + (-2*a+6)*q^61 + -2*a*q^62 + (2*a-4)*q^63 + 1*q^64 + (-3*a-2)*q^65 + -4*a*q^66 + a*q^67 + (a+6)*q^68 + (3*a-12)*q^69 + -a*q^70 + -4*a*q^71 + (a-1)*q^72 + (3*a+6)*q^73 + 6*q^74 + a*q^75 + -1*q^76 + 4*a*q^77 + (-a+12)*q^78 + 2*a*q^79 + 1*q^80 + -7*q^81 + (4*a-2)*q^82 + (2*a+8)*q^83 + (-a+4)*q^84 + (a+6)*q^85 + (2*a+8)*q^86 + (-a+12)*q^87 + -4*q^88 + 2*q^89 + (a-1)*q^90 + (a-12)*q^91 + -3*a*q^92 + (-2*a+8)*q^93 + (4*a+4)*q^94 + -1*q^95 + -a*q^96 + 6*q^97 + (a+3)*q^98 + (-4*a+4)*q^99 + 1*q^100 + (6*a-2)*q^101 + (-5*a-4)*q^102 + (-4*a-8)*q^103 + (3*a+2)*q^104 + (-a+4)*q^105 + (-a+2)*q^106 + (-a-8)*q^107 + (-a-4)*q^108 + (a+2)*q^109 + -4*q^110 + -6*a*q^111 + a*q^112 + (2*a+14)*q^113 + a*q^114 + -3*a*q^115 + (3*a+2)*q^116 + (-4*a+10)*q^117 + a*q^118 + (5*a+4)*q^119 + -a*q^120 + 5*q^121 + (2*a-6)*q^122 + (6*a-16)*q^123 + 2*a*q^124 + 1*q^125 + (-2*a+4)*q^126 + (-2*a+8)*q^127 + -1*q^128 + (-6*a-8)*q^129 + (3*a+2)*q^130 + (8*a+4)*q^131 + 4*a*q^132 + -a*q^133 + -a*q^134 + (-a-4)*q^135 + (-a-6)*q^136 + (5*a-2)*q^137 + (-3*a+12)*q^138 + (-8*a-4)*q^139 + a*q^140 + -16*q^141 + 4*a*q^142 + (-12*a-8)*q^143 + (-a+1)*q^144 + (3*a+2)*q^145 + (-3*a-6)*q^146 + (-2*a-4)*q^147 + -6*q^148 + (-6*a-2)*q^149 + -a*q^150 + -2*a*q^151 + 1*q^152 + (-4*a+2)*q^153 + -4*a*q^154 + 2*a*q^155 + (a-12)*q^156 + (4*a-10)*q^157 + -2*a*q^158 + (-3*a+4)*q^159 + -1*q^160 + (3*a-12)*q^161 + 7*q^162 + 6*a*q^163 + (-4*a+2)*q^164 + 4*a*q^165 + (-2*a-8)*q^166 + (6*a+8)*q^167 + (a-4)*q^168 + (3*a+27)*q^169 + (-a-6)*q^170 + (a-1)*q^171 + (-2*a-8)*q^172 + (-4*a+10)*q^173 + (a-12)*q^174 + a*q^175 + 4*q^176 + (a-4)*q^177 + -2*q^178 + (4*a-12)*q^179 + (-a+1)*q^180 + -18*q^181 + (-a+12)*q^182 + (8*a-8)*q^183 + 3*a*q^184 + -6*q^185 + (2*a-8)*q^186 + (4*a+24)*q^187 + (-4*a-4)*q^188 + (-3*a-4)*q^189 + 1*q^190 + (3*a+4)*q^191 + a*q^192 + (8*a+6)*q^193 + -6*q^194 + (a-12)*q^195 + (-a-3)*q^196 + (4*a-10)*q^197 + (4*a-4)*q^198 + (-5*a+4)*q^199 + -1*q^200 +  ...

-------------------------------------------------------
190E (old = 95A), dim = 3

CONGRUENCES:
Modular Degree = 2^7*5*13
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2*5*13 + Z/2^2*5*13
= D(Z/2*13 + Z/2*13) + F(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + H(Z/5 + Z/5)

-------------------------------------------------------
190F (old = 95B), dim = 4

CONGRUENCES:
Modular Degree = 2^7*3^5*11
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*3^2 + Z/2*3^2 + Z/2*3^3*11 + Z/2*3^3*11
= B(Z/11 + Z/11) + D(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + G(Z/3 + Z/3) + I(Z/3^2 + Z/3^2 + Z/3^2 + Z/3^2)

-------------------------------------------------------
190G (old = 38A), dim = 1

CONGRUENCES:
Modular Degree = 2^4*3^3
Ker(ModPolar)  = Z/2^2*3 + Z/2^2*3 + Z/2^2*3^2 + Z/2^2*3^2
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + F(Z/3 + Z/3) + H(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
190H (old = 38B), dim = 1

CONGRUENCES:
Modular Degree = 2^4*5
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2*5 + Z/2^2*5
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/5 + Z/5) + G(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
190I (old = 19A), dim = 1

CONGRUENCES:
Modular Degree = 3^7
Ker(ModPolar)  = Z/3 + Z/3 + Z/3 + Z/3 + Z/3^2 + Z/3^2 + Z/3^3 + Z/3^3
= C(Z/3 + Z/3) + F(Z/3^2 + Z/3^2 + Z/3^2 + Z/3^2) + G(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
Gamma_0(191)
Weight 2

-------------------------------------------------------
J_0(191), dim = 16

-------------------------------------------------------
191A (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2
= B(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +
discriminant   = 5
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 17.355877316239955294 + -0.1349410517301341526e-2i
Omega-         = 4.8466484157570279694 + -0.3042969921058230051e-3i
L(1)           =

HECKE EIGENFORM:
a^2+a-1 = 0,
f(q) = q + a*q^2 + -1*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 + -1*q^10 + a*q^11 + (a+1)*q^12 + (3*a-2)*q^13 + -1*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 + 1*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 + -3*a*q^38 + (-3*a+2)*q^39 + (a+3)*q^40 + (2*a-3)*q^41 + 1*q^42 + (-4*a+2)*q^43 + -1*q^44 + (2*a+2)*q^45 + (-a+1)*q^46 + (-7*a-2)*q^47 + -3*a*q^48 + (a-5)*q^49 + (-4*a+1)*q^50 + (2*a-1)*q^52 + (5*a+3)*q^53 + 5*a*q^54 + -1*q^55 + (a+3)*q^56 + 3*q^57 + (a-2)*q^58 + (-6*a+3)*q^59 + (-a-2)*q^60 + (-4*a-10)*q^61 + (-5*a+5)*q^62 + (2*a+2)*q^63 + (-2*a+1)*q^64 + (2*a-1)*q^65 + (a-1)*q^66 + (6*a+3)*q^67 + -a*q^69 + (a+1)*q^70 + (5*a+4)*q^71 + (4*a+2)*q^72 + -10*q^73 + (3*a-4)*q^74 + (-a+3)*q^75 + (3*a+3)*q^76 + -1*q^77 + (5*a-3)*q^78 + (-6*a-5)*q^79 + -3*q^80 + 1*q^81 + (-5*a+2)*q^82 + (-4*a+1)*q^83 + (-a-2)*q^84 + (6*a-4)*q^86 + (2*a+1)*q^87 + (a-2)*q^88 + (4*a-7)*q^89 + 2*q^90 + (2*a-1)*q^91 + -1*q^92 + -5*a*q^93 + (5*a-7)*q^94 + (3*a+3)*q^95 + (-a-5)*q^96 + (-12*a-10)*q^97 + (-6*a+1)*q^98 + -2*a*q^99 + (3*a+2)*q^100 + (6*a+3)*q^101 + (8*a+6)*q^103 + (7*a-4)*q^104 + (-a-2)*q^105 + (-2*a+5)*q^106 + (3*a+9)*q^107 + (-5*a-5)*q^108 + (-3*a-5)*q^109 + -a*q^110 + (4*a+1)*q^111 + -3*q^112 + (-10*a+2)*q^113 + 3*a*q^114 + -1*q^115 + (a+3)*q^116 + (-6*a+4)*q^117 + (9*a-6)*q^118 + (-a-3)*q^120 + (-a-10)*q^121 + (-6*a-4)*q^122 + (-2*a+3)*q^123 + -5*q^124 + (8*a+7)*q^125 + 2*q^126 + (-3*a-1)*q^127 + (a-12)*q^128 + (4*a-2)*q^129 + (-3*a+2)*q^130 + (-7*a-7)*q^131 + 1*q^132 + (3*a+3)*q^133 + (-3*a+6)*q^134 + (-5*a-5)*q^135 + (9*a+12)*q^137 + (a-1)*q^138 + (-5*a+1)*q^139 + (-2*a-3)*q^140 + (7*a+2)*q^141 + (-a+5)*q^142 + (-5*a+3)*q^143 + -6*a*q^144 + (a+3)*q^145 + -10*a*q^146 + (-a+5)*q^147 + (a+5)*q^148 + (6*a+3)*q^149 + (4*a-1)*q^150 + 3*q^151 + (6*a+3)*q^152 + -a*q^154 + -5*q^155 + (-2*a+1)*q^156 + (-12*a+3)*q^157 + (a-6)*q^158 + (-5*a-3)*q^159 + (-5*a-6)*q^160 + -1*q^161 + a*q^162 + (5*a+6)*q^163 + (3*a+1)*q^164 + 1*q^165 + (5*a-4)*q^166 + (14*a+16)*q^167 + (-a-3)*q^168 + -21*a*q^169 + 6*q^171 + (-2*a+2)*q^172 + (-5*a-4)*q^173 + (-a+2)*q^174 + (3*a+2)*q^175 + (-3*a+3)*q^176 + (6*a-3)*q^177 + (-11*a+4)*q^178 + (14*a+7)*q^179 + (-2*a-4)*q^180 + (12*a+11)*q^181 + (-3*a+2)*q^182 + (4*a+10)*q^183 + (a-2)*q^184 + (a+5)*q^185 + (5*a-5)*q^186 + (2*a+9)*q^188 + (-5*a-5)*q^189 + 3*q^190 + -1*q^191 + (2*a-1)*q^192 + (4*a+1)*q^193 + (2*a-12)*q^194 + (-2*a+1)*q^195 + (5*a+4)*q^196 + (13*a+17)*q^197 + (2*a-2)*q^198 + (-6*a-5)*q^199 + (7*a+1)*q^200 +  ...

-------------------------------------------------------
191B (new) , dim = 14

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2
= A(Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 3^3*382146223*319500117632677
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 5*19
Torsion Bound  = 5*19
|L(1)/Omega|   = 2^2/5*19
Sha Bound      = 2^2*5*19

ANALYTIC INVARIANTS:

Omega+         = 52.858848167831144949 + -0.95428253985153215006e-2i
Omega-         = 5062.7404491557082084 + -1.547498413755247925i
L(1)           = 2.225635748599322489

HECKE EIGENFORM:
a^14-23*a^12+a^11+205*a^10-13*a^9-895*a^8+35*a^7+1993*a^6+103*a^5-2135*a^4-465*a^3+853*a^2+374*a+41 = 0,
f(q) = 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 + 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