CoCalc Public Fileswww / Tables / MotiveDecomp_N1-125_k2
Author: William A. Stein

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

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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 +  ...

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Gamma_0(19)
Weight 2

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

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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

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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

-------------------------------------------------------
J_0(43), dim = 3

-------------------------------------------------------
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 +  ...

-------------------------------------------------------
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(44)
Weight 2

-------------------------------------------------------
J_0(44), dim = 4

-------------------------------------------------------
44A (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+         = 2.4139388627239761447 + -0.27237226084048045666e-13i
Omega-         = 0.10690031880778565423e-13 + -3.0540697209358646069i
L(1)           = 0.80464628757465871489
w1             = -1.2069694313619934173 + 1.5270348604679459221i
w2             = 1.2069694313619827273 + 1.5270348604679186848i
c4             = -128.00000000000462565 + 0.19861601802058593025e-11i
c6             = 1664.0000000000109575 + -0.23787120809699730358e-8i
j              = 744.72727272731308838 + 0.11918365403142769722e-8i

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 +  ...

-------------------------------------------------------
44B (old = 11A), dim = 1

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

-------------------------------------------------------

Gamma_0(45)
Weight 2

-------------------------------------------------------
J_0(45), dim = 3

-------------------------------------------------------
45A (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
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.843181753279314291 + -0.67157963678560778001e-13i
Omega-         = 0.63466824256547273178e-13 + -3.2345541740741462519i
L(1)           = 0.92159087663965714552
w1             = 0.92159087663962541211 + 1.617277087037039547i
w2             = 1.843181753279314291 + -0.67157963678560778001e-13i
c4             = 9.000000000172382152 + 0.38832523329697040126e-10i
c6             = 4346.9999997705467652 + 0.21543359707285154956e-9i
j              = -0.6666666667753570354e-1 + -0.8563701148922397039e-12i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^4 + -1*q^5 + -3*q^8 + -1*q^10 + 4*q^11 + -2*q^13 + -1*q^16 + -2*q^17 + 4*q^19 + 1*q^20 + 4*q^22 + 1*q^25 + -2*q^26 + 2*q^29 + 5*q^32 + -2*q^34 + -10*q^37 + 4*q^38 + 3*q^40 + -10*q^41 + 4*q^43 + -4*q^44 + -8*q^47 + -7*q^49 + 1*q^50 + 2*q^52 + 10*q^53 + -4*q^55 + 2*q^58 + 4*q^59 + -2*q^61 + 7*q^64 + 2*q^65 + 12*q^67 + 2*q^68 + 8*q^71 + 10*q^73 + -10*q^74 + -4*q^76 + 1*q^80 + -10*q^82 + -12*q^83 + 2*q^85 + 4*q^86 + -12*q^88 + 6*q^89 + -8*q^94 + -4*q^95 + 2*q^97 + -7*q^98 + -1*q^100 + -6*q^101 + -16*q^103 + 6*q^104 + 10*q^106 + 12*q^107 + 14*q^109 + -4*q^110 + -2*q^113 + -2*q^116 + 4*q^118 + 5*q^121 + -2*q^122 + -1*q^125 + -8*q^127 + -3*q^128 + 2*q^130 + 12*q^131 + 12*q^134 + 6*q^136 + 6*q^137 + -4*q^139 + 8*q^142 + -8*q^143 + -2*q^145 + 10*q^146 + 10*q^148 + -22*q^149 + -8*q^151 + -12*q^152 + 14*q^157 + -5*q^160 + -4*q^163 + 10*q^164 + -12*q^166 + -9*q^169 + 2*q^170 + -4*q^172 + 18*q^173 + -4*q^176 + 6*q^178 + -20*q^179 + -10*q^181 + 10*q^185 + -8*q^187 + 8*q^188 + -4*q^190 + -16*q^191 + 2*q^193 + 2*q^194 + 7*q^196 + -6*q^197 + -8*q^199 + -3*q^200 +  ...

-------------------------------------------------------
45B (old = 15A), dim = 1

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

-------------------------------------------------------
Gamma_0(46)
Weight 2

-------------------------------------------------------
J_0(46), dim = 5

-------------------------------------------------------
46A (new) , dim = 1

CONGRUENCES:
Modular Degree = 5
Ker(ModPolar)  = Z/5 + Z/5
= B(Z/5 + Z/5)

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+         = 1.3218082226480421038 + 0.21868456344929778986e-12i
Omega-         = 0.32680346263286859375e-12 + 3.6368235333081729652i
L(1)           = 0.66090411132402105188
w1             = 0.66090411132385765015 + -1.8184117666539771403i
w2             = -1.3218082226480421038 + -0.21868456344929778986e-12i
c4             = 488.99999999983443349 + -0.37110734207082758289e-9i
c6             = 12554.999999992367085 + -0.10228037924480642808e-7i
j              = -4964.766007137001296 + 0.1244925904468536394e-7i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^4 + 4*q^5 + -4*q^7 + -1*q^8 + -3*q^9 + -4*q^10 + 2*q^11 + -2*q^13 + 4*q^14 + 1*q^16 + -2*q^17 + 3*q^18 + -2*q^19 + 4*q^20 + -2*q^22 + 1*q^23 + 11*q^25 + 2*q^26 + -4*q^28 + 2*q^29 + -1*q^32 + 2*q^34 + -16*q^35 + -3*q^36 + -4*q^37 + 2*q^38 + -4*q^40 + 6*q^41 + 10*q^43 + 2*q^44 + -12*q^45 + -1*q^46 + 9*q^49 + -11*q^50 + -2*q^52 + -4*q^53 + 8*q^55 + 4*q^56 + -2*q^58 + 12*q^59 + -8*q^61 + 12*q^63 + 1*q^64 + -8*q^65 + -10*q^67 + -2*q^68 + 16*q^70 + 3*q^72 + 6*q^73 + 4*q^74 + -2*q^76 + -8*q^77 + -12*q^79 + 4*q^80 + 9*q^81 + -6*q^82 + 14*q^83 + -8*q^85 + -10*q^86 + -2*q^88 + -6*q^89 + 12*q^90 + 8*q^91 + 1*q^92 + -8*q^95 + 6*q^97 + -9*q^98 + -6*q^99 + 11*q^100 + -10*q^101 + -8*q^103 + 2*q^104 + 4*q^106 + -10*q^107 + -8*q^110 + -4*q^112 + -14*q^113 + 4*q^115 + 2*q^116 + 6*q^117 + -12*q^118 + 8*q^119 + -7*q^121 + 8*q^122 + 24*q^125 + -12*q^126 + 16*q^127 + -1*q^128 + 8*q^130 + 12*q^131 + 8*q^133 + 10*q^134 + 2*q^136 + 6*q^137 + -4*q^139 + -16*q^140 + -4*q^143 + -3*q^144 + 8*q^145 + -6*q^146 + -4*q^148 + -4*q^149 + -8*q^151 + 2*q^152 + 6*q^153 + 8*q^154 + 12*q^157 + 12*q^158 + -4*q^160 + -4*q^161 + -9*q^162 + -8*q^163 + 6*q^164 + -14*q^166 + 16*q^167 + -9*q^169 + 8*q^170 + 6*q^171 + 10*q^172 + -6*q^173 + -44*q^175 + 2*q^176 + 6*q^178 + -16*q^179 + -12*q^180 + -24*q^181 + -8*q^182 + -1*q^184 + -16*q^185 + -4*q^187 + 8*q^190 + 20*q^191 + 26*q^193 + -6*q^194 + 9*q^196 + 18*q^197 + 6*q^198 + -4*q^199 + -11*q^200 +  ...

-------------------------------------------------------
46B (old = 23A), dim = 2

CONGRUENCES:
Modular Degree = 5
Ker(ModPolar)  = Z/5 + Z/5
= A(Z/5 + Z/5)

-------------------------------------------------------
Gamma_0(47)
Weight 2

-------------------------------------------------------
J_0(47), dim = 4

-------------------------------------------------------
47A (new) , dim = 4

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 19*103
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 23
Torsion Bound  = 23
|L(1)/Omega|   = 1/23
Sha Bound      = 23

ANALYTIC INVARIANTS:

Omega+         = 10.221061625636338339 + -0.5130408686162000692e-12i
Omega-         = 22.557493156153663639 + -0.38344457575559500693e-11i
L(1)           = 0.44439398372331905821

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

-------------------------------------------------------
Gamma_0(48)
Weight 2

-------------------------------------------------------
J_0(48), dim = 3

-------------------------------------------------------
48A (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  = 2^3
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 1.6857503548126045883 + -0.99125282273795768619e-41i
Omega-         = 2.1565156474997666435i
L(1)           = 0.42143758870315114708
w1             = 2.1565156474997666435i
w2             = 1.6857503548126045883 + -0.99125282273795768619e-41i
c4             = 207.99999999996910483 + 0.418106793594213999e-38i
c6             = 2240.0000000149783626 + 0.10010075317058168738e-36i
j              = 3905.7777778458011906 + 0.14310321664900083096e-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 +  ...

-------------------------------------------------------
48B (old = 24A), dim = 1

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

-------------------------------------------------------
Gamma_0(49)
Weight 2

-------------------------------------------------------
J_0(49), dim = 1

-------------------------------------------------------
49A (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
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.9333117056167290171 + 0.28774604696549251387e-12i
Omega-         = 0.32927673660477893476e-12 + -5.1150619798331913969i
L(1)           = 0.96665585280836450853
w1             = -0.9666558528085291469 + 2.5575309899164518254i
w2             = 1.9333117056167290171 + 0.28774604696549251387e-12i
c4             = 105.00000000003379759 + -0.67106840300624147883e-10i
c6             = 1322.9999999983997019 + -0.10807238675668079684e-8i
j              = -3375.0000000337360249 + 0.282649340465540423e-8i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^4 + -3*q^8 + -3*q^9 + 4*q^11 + -1*q^16 + -3*q^18 + 4*q^22 + 8*q^23 + -5*q^25 + 2*q^29 + 5*q^32 + 3*q^36 + -6*q^37 + -12*q^43 + -4*q^44 + 8*q^46 + -5*q^50 + -10*q^53 + 2*q^58 + 7*q^64 + 4*q^67 + 16*q^71 + 9*q^72 + -6*q^74 + 8*q^79 + 9*q^81 + -12*q^86 + -12*q^88 + -8*q^92 + -12*q^99 + 5*q^100 + -10*q^106 + -20*q^107 + 18*q^109 + 2*q^113 + -2*q^116 + 5*q^121 + 16*q^127 + -3*q^128 + 4*q^134 + -10*q^137 + 16*q^142 + 3*q^144 + 6*q^148 + 22*q^149 + -24*q^151 + 8*q^158 + 9*q^162 + -20*q^163 + -13*q^169 + 12*q^172 + -4*q^176 + 4*q^179 + -24*q^184 + 8*q^191 + 18*q^193 + -26*q^197 + -12*q^198 + 15*q^200 +  ...

-------------------------------------------------------
Gamma_0(50)
Weight 2

-------------------------------------------------------
J_0(50), dim = 2

-------------------------------------------------------
50A (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+         = 2.1394949442871262789 + 0.48260832932000089625e-12i
Omega-         = 0.34154978527787931749e-11 + 3.993933476564393161i
L(1)           = 0.71316498142904209298
w1             = 1.0697474721418553905 + -1.9969667382819552763i
w2             = -2.1394949442871262789 + -0.48260832932000089625e-12i
c4             = 24.999999999799961965 + -0.32749484676594779916e-9i
c6             = 1474.9999999843674027 + 0.27641116813628485083e-8i
j              = -12.499999999964648334 + 0.54198406585615746782e-9i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -1*q^6 + 2*q^7 + -1*q^8 + -2*q^9 + -3*q^11 + 1*q^12 + -4*q^13 + -2*q^14 + 1*q^16 + -3*q^17 + 2*q^18 + 5*q^19 + 2*q^21 + 3*q^22 + 6*q^23 + -1*q^24 + 4*q^26 + -5*q^27 + 2*q^28 + 2*q^31 + -1*q^32 + -3*q^33 + 3*q^34 + -2*q^36 + 2*q^37 + -5*q^38 + -4*q^39 + -3*q^41 + -2*q^42 + -4*q^43 + -3*q^44 + -6*q^46 + 12*q^47 + 1*q^48 + -3*q^49 + -3*q^51 + -4*q^52 + 6*q^53 + 5*q^54 + -2*q^56 + 5*q^57 + 2*q^61 + -2*q^62 + -4*q^63 + 1*q^64 + 3*q^66 + -13*q^67 + -3*q^68 + 6*q^69 + 12*q^71 + 2*q^72 + 11*q^73 + -2*q^74 + 5*q^76 + -6*q^77 + 4*q^78 + -10*q^79 + 1*q^81 + 3*q^82 + -9*q^83 + 2*q^84 + 4*q^86 + 3*q^88 + 15*q^89 + -8*q^91 + 6*q^92 + 2*q^93 + -12*q^94 + -1*q^96 + 2*q^97 + 3*q^98 + 6*q^99 + -18*q^101 + 3*q^102 + -4*q^103 + 4*q^104 + -6*q^106 + -3*q^107 + -5*q^108 + -10*q^109 + 2*q^111 + 2*q^112 + -9*q^113 + -5*q^114 + 8*q^117 + -6*q^119 + -2*q^121 + -2*q^122 + -3*q^123 + 2*q^124 + 4*q^126 + 2*q^127 + -1*q^128 + -4*q^129 + 12*q^131 + -3*q^132 + 10*q^133 + 13*q^134 + 3*q^136 + -3*q^137 + -6*q^138 + 5*q^139 + 12*q^141 + -12*q^142 + 12*q^143 + -2*q^144 + -11*q^146 + -3*q^147 + 2*q^148 + 2*q^151 + -5*q^152 + 6*q^153 + 6*q^154 + -4*q^156 + 2*q^157 + 10*q^158 + 6*q^159 + 12*q^161 + -1*q^162 + 11*q^163 + -3*q^164 + 9*q^166 + 12*q^167 + -2*q^168 + 3*q^169 + -10*q^171 + -4*q^172 + -24*q^173 + -3*q^176 + -15*q^178 + -15*q^179 + 2*q^181 + 8*q^182 + 2*q^183 + -6*q^184 + -2*q^186 + 9*q^187 + 12*q^188 + -10*q^189 + -18*q^191 + 1*q^192 + -19*q^193 + -2*q^194 + -3*q^196 + -18*q^197 + -6*q^198 + 20*q^199 +  ...

-------------------------------------------------------
50B (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+         = 4.7840561329431396944 + 0.10791450308671268601e-11i
Omega-         = 0.15274570751635901036e-11 + 1.7861413502420092651i
L(1)           = 0.95681122658862793887
w1             = 2.3920280664708061186 + -0.89307067512046506003i
w2             = -0.15274570751635901036e-11 + -1.7861413502420092651i
c4             = 144.99999999963654503 + 0.5697725481299604929e-9i
c6             = -2104.9999999892359423 + -0.89041264193120328264e-8i
j              = -3810.7812500330699062 + -0.40655809394326913281e-7i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + -1*q^6 + -2*q^7 + 1*q^8 + -2*q^9 + -3*q^11 + -1*q^12 + 4*q^13 + -2*q^14 + 1*q^16 + 3*q^17 + -2*q^18 + 5*q^19 + 2*q^21 + -3*q^22 + -6*q^23 + -1*q^24 + 4*q^26 + 5*q^27 + -2*q^28 + 2*q^31 + 1*q^32 + 3*q^33 + 3*q^34 + -2*q^36 + -2*q^37 + 5*q^38 + -4*q^39 + -3*q^41 + 2*q^42 + 4*q^43 + -3*q^44 + -6*q^46 + -12*q^47 + -1*q^48 + -3*q^49 + -3*q^51 + 4*q^52 + -6*q^53 + 5*q^54 + -2*q^56 + -5*q^57 + 2*q^61 + 2*q^62 + 4*q^63 + 1*q^64 + 3*q^66 + 13*q^67 + 3*q^68 + 6*q^69 + 12*q^71 + -2*q^72 + -11*q^73 + -2*q^74 + 5*q^76 + 6*q^77 + -4*q^78 + -10*q^79 + 1*q^81 + -3*q^82 + 9*q^83 + 2*q^84 + 4*q^86 + -3*q^88 + 15*q^89 + -8*q^91 + -6*q^92 + -2*q^93 + -12*q^94 + -1*q^96 + -2*q^97 + -3*q^98 + 6*q^99 + -18*q^101 + -3*q^102 + 4*q^103 + 4*q^104 + -6*q^106 + 3*q^107 + 5*q^108 + -10*q^109 + 2*q^111 + -2*q^112 + 9*q^113 + -5*q^114 + -8*q^117 + -6*q^119 + -2*q^121 + 2*q^122 + 3*q^123 + 2*q^124 + 4*q^126 + -2*q^127 + 1*q^128 + -4*q^129 + 12*q^131 + 3*q^132 + -10*q^133 + 13*q^134 + 3*q^136 + 3*q^137 + 6*q^138 + 5*q^139 + 12*q^141 + 12*q^142 + -12*q^143 + -2*q^144 + -11*q^146 + 3*q^147 + -2*q^148 + 2*q^151 + 5*q^152 + -6*q^153 + 6*q^154 + -4*q^156 + -2*q^157 + -10*q^158 + 6*q^159 + 12*q^161 + 1*q^162 + -11*q^163 + -3*q^164 + 9*q^166 + -12*q^167 + 2*q^168 + 3*q^169 + -10*q^171 + 4*q^172 + 24*q^173 + -3*q^176 + 15*q^178 + -15*q^179 + 2*q^181 + -8*q^182 + -2*q^183 + -6*q^184 + -2*q^186 + -9*q^187 + -12*q^188 + -10*q^189 + -18*q^191 + -1*q^192 + 19*q^193 + -2*q^194 + -3*q^196 + 18*q^197 + 6*q^198 + 20*q^199 +  ...

-------------------------------------------------------
Gamma_0(51)
Weight 2

-------------------------------------------------------
J_0(51), dim = 5

-------------------------------------------------------
51A (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+         = 2.5801770483855944422 + 0.91285341939843292657e-12i
Omega-         = 0.74207954424703401266e-12 + -3.9053546347514513137i
L(1)           = 0.86005901612853148072
w1             = 1.2900885241924261813 + 1.9526773173761820836i
w2             = 1.2900885241931682609 + -1.9526773173752692301i
c4             = -32.000000000543706266 + 0.48802481535949926268e-11i
c6             = 871.99999999960948657 + 0.64965233980320135215e-8i
j              = 71.389978217057511477 + -0.10510974465026924464e-8i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + -2*q^4 + 3*q^5 + -4*q^7 + 1*q^9 + -3*q^11 + -2*q^12 + -1*q^13 + 3*q^15 + 4*q^16 + -1*q^17 + -1*q^19 + -6*q^20 + -4*q^21 + 9*q^23 + 4*q^25 + 1*q^27 + 8*q^28 + 6*q^29 + 2*q^31 + -3*q^33 + -12*q^35 + -2*q^36 + -4*q^37 + -1*q^39 + -3*q^41 + -7*q^43 + 6*q^44 + 3*q^45 + -6*q^47 + 4*q^48 + 9*q^49 + -1*q^51 + 2*q^52 + -6*q^53 + -9*q^55 + -1*q^57 + 6*q^59 + -6*q^60 + 8*q^61 + -4*q^63 + -8*q^64 + -3*q^65 + -4*q^67 + 2*q^68 + 9*q^69 + 12*q^71 + 2*q^73 + 4*q^75 + 2*q^76 + 12*q^77 + -10*q^79 + 12*q^80 + 1*q^81 + -6*q^83 + 8*q^84 + -3*q^85 + 6*q^87 + 4*q^91 + -18*q^92 + 2*q^93 + -3*q^95 + -16*q^97 + -3*q^99 + -8*q^100 + 5*q^103 + -12*q^105 + 9*q^107 + -2*q^108 + 20*q^109 + -4*q^111 + -16*q^112 + -9*q^113 + 27*q^115 + -12*q^116 + -1*q^117 + 4*q^119 + -2*q^121 + -3*q^123 + -4*q^124 + -3*q^125 + -13*q^127 + -7*q^129 + 3*q^131 + 6*q^132 + 4*q^133 + 3*q^135 + -6*q^137 + 2*q^139 + 24*q^140 + -6*q^141 + 3*q^143 + 4*q^144 + 18*q^145 + 9*q^147 + 8*q^148 + -18*q^149 + 8*q^151 + -1*q^153 + 6*q^155 + 2*q^156 + 11*q^157 + -6*q^159 + -36*q^161 + 2*q^163 + 6*q^164 + -9*q^165 + 21*q^167 + -12*q^169 + -1*q^171 + 14*q^172 + 15*q^173 + -16*q^175 + -12*q^176 + 6*q^177 + -6*q^179 + -6*q^180 + 14*q^181 + 8*q^183 + -12*q^185 + 3*q^187 + 12*q^188 + -4*q^189 + 18*q^191 + -8*q^192 + -22*q^193 + -3*q^195 + -18*q^196 + 3*q^197 + -16*q^199 +  ...

-------------------------------------------------------
51B (new) , dim = 2

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

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 17
#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+         = 1.804428599557572703 + -0.21781595956460547839e-11i
Omega-         = 2.4377710478606711244 + 0.54706633807116629692e-11i
L(1)           = 0.22555357494469658787

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

-------------------------------------------------------
51C (old = 17A), dim = 1

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

-------------------------------------------------------
Gamma_0(52)
Weight 2

-------------------------------------------------------
J_0(52), dim = 5

-------------------------------------------------------
52A (new) , dim = 1

CONGRUENCES:
Modular Degree = 3
Ker(ModPolar)  = Z/3 + Z/3
= C(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+         = 1.690966417291821379 + 0.9529667958010773441e-12i
Omega-         = 0.95354123294140990805e-12 + -2.8023148362626574491i
L(1)           = 0.84548320864591068951
w1             = -0.84548320864543391889 + -1.401157418131805208i
w2             = -0.84548320864638746013 + 1.4011574181308522412i
c4             = -48.000000004027310653 + -0.29720767253575937312e-9i
c6             = 8640.0000000064995211 + -0.35681109341584885707e-6i
j              = 2.556213018390103804 + 0.25823114250569746199e-9i

HECKE EIGENFORM:
f(q) = q + 2*q^5 + -2*q^7 + -3*q^9 + -2*q^11 + -1*q^13 + 6*q^17 + -6*q^19 + 8*q^23 + -1*q^25 + 2*q^29 + 10*q^31 + -4*q^35 + -6*q^37 + -6*q^41 + 4*q^43 + -6*q^45 + -2*q^47 + -3*q^49 + 6*q^53 + -4*q^55 + -10*q^59 + -2*q^61 + 6*q^63 + -2*q^65 + 10*q^67 + 10*q^71 + 2*q^73 + 4*q^77 + -4*q^79 + 9*q^81 + -6*q^83 + 12*q^85 + -6*q^89 + 2*q^91 + -12*q^95 + 2*q^97 + 6*q^99 + -2*q^101 + -8*q^103 + -16*q^107 + -14*q^109 + 14*q^113 + 16*q^115 + 3*q^117 + -12*q^119 + -7*q^121 + -12*q^125 + -8*q^127 + -16*q^131 + 12*q^133 + 18*q^137 + 16*q^139 + 2*q^143 + 4*q^145 + 18*q^149 + 6*q^151 + -18*q^153 + 20*q^155 + 2*q^157 + -16*q^161 + -10*q^163 + 6*q^167 + 1*q^169 + 18*q^171 + -10*q^173 + 2*q^175 + 12*q^179 + -6*q^181 + -12*q^185 + -12*q^187 + 4*q^191 + 2*q^193 + -6*q^197 + -16*q^199 +  ...

-------------------------------------------------------
52B (old = 26A), dim = 1

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

-------------------------------------------------------
52C (old = 26B), 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) + B(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(53)
Weight 2

-------------------------------------------------------
J_0(53), dim = 4

-------------------------------------------------------
53A (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+         = 4.6876410488565271208 + -0.48168680901967596905e-11i
Omega-         = 0.21472984590632507544e-11 + -3.0811813402838080833i
L(1)           =
w1             = -2.3438205244293372096 + 1.5405906701443124757i
w2             = 2.3438205244271899111 + 1.5405906701394956076i
c4             = -15.000000000900455138 + -0.19891484707449980639e-9i
c6             = -297.00000000216029806 + -0.27047006883900401884e-8i
j              = 63.679245293172081097 + 0.13229127777817996054e-8i

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

-------------------------------------------------------
53B (new) , dim = 3

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^2*37
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 13
Torsion Bound  = 13
|L(1)/Omega|   = 2/13
Sha Bound      = 2*13

ANALYTIC INVARIANTS:

Omega+         = 3.3415343014964929662 + 0.99125939515556958004e-12i
Omega-         = 0.18093847764884716842e-10 + -11.443904371146073371i
L(1)           = 0.5140822002302296871

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

-------------------------------------------------------
Gamma_0(54)
Weight 2

-------------------------------------------------------
J_0(54), dim = 4

-------------------------------------------------------
54A (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+         = 2.1047244759626368404 + -0.22416211913948226307e-44i
Omega-         = -1.7849162019780213849i
L(1)           = 0.7015748253208789468
w1             = -1.0523622379813184202 + -0.89245810098901069243i
w2             = -1.0523622379813184202 + 0.89245810098901069243i
c4             = -567.00000001092421705 + 0.27570867024903825679e-11i
c6             = -9477.0000005110583053 + -0.99138327750225395165e-8i
j              = 1157.6249999808747012 + -0.8050131060920818169e-9i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^4 + 3*q^5 + -1*q^7 + -1*q^8 + -3*q^10 + -3*q^11 + -4*q^13 + 1*q^14 + 1*q^16 + 2*q^19 + 3*q^20 + 3*q^22 + -6*q^23 + 4*q^25 + 4*q^26 + -1*q^28 + 6*q^29 + 5*q^31 + -1*q^32 + -3*q^35 + 2*q^37 + -2*q^38 + -3*q^40 + -6*q^41 + -10*q^43 + -3*q^44 + 6*q^46 + 6*q^47 + -6*q^49 + -4*q^50 + -4*q^52 + 9*q^53 + -9*q^55 + 1*q^56 + -6*q^58 + 12*q^59 + 8*q^61 + -5*q^62 + 1*q^64 + -12*q^65 + 14*q^67 + 3*q^70 + -7*q^73 + -2*q^74 + 2*q^76 + 3*q^77 + 8*q^79 + 3*q^80 + 6*q^82 + -3*q^83 + 10*q^86 + 3*q^88 + -18*q^89 + 4*q^91 + -6*q^92 + -6*q^94 + 6*q^95 + -1*q^97 + 6*q^98 + 4*q^100 + -3*q^101 + -4*q^103 + 4*q^104 + -9*q^106 + 9*q^107 + 2*q^109 + 9*q^110 + -1*q^112 + -6*q^113 + -18*q^115 + 6*q^116 + -12*q^118 + -2*q^121 + -8*q^122 + 5*q^124 + -3*q^125 + -7*q^127 + -1*q^128 + 12*q^130 + -15*q^131 + -2*q^133 + -14*q^134 + 6*q^137 + -4*q^139 + -3*q^140 + 12*q^143 + 18*q^145 + 7*q^146 + 2*q^148 + 3*q^149 + 17*q^151 + -2*q^152 + -3*q^154 + 15*q^155 + -4*q^157 + -8*q^158 + -3*q^160 + 6*q^161 + 20*q^163 + -6*q^164 + 3*q^166 + -6*q^167 + 3*q^169 + -10*q^172 + 15*q^173 + -4*q^175 + -3*q^176 + 18*q^178 + -9*q^179 + -16*q^181 + -4*q^182 + 6*q^184 + 6*q^185 + 6*q^188 + -6*q^190 + -12*q^191 + 5*q^193 + 1*q^194 + -6*q^196 + 9*q^197 + -7*q^199 + -4*q^200 +  ...

-------------------------------------------------------
54B (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))  = 3
Torsion Bound  = 3^2
|L(1)/Omega|   = 1/3
Sha Bound      = 3^3

ANALYTIC INVARIANTS:

Omega+         = 3.0915655490965189096 + -0.17603505466398667993e-44i
Omega-         = -3.6454897283146206309i
L(1)           = 1.0305218496988396365
w1             = 1.5457827745482594548 + -1.8227448641573103155i
w2             = -1.5457827745482594548 + -1.8227448641573103155i
c4             = -63.000000000223374461 + 0.30634296689459912883e-12i
c6             = 351.00000000530603916 + 0.36717899166510147726e-9i
j              = 1157.6249999925118696 + -0.80501310610875027826e-9i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + -3*q^5 + -1*q^7 + 1*q^8 + -3*q^10 + 3*q^11 + -4*q^13 + -1*q^14 + 1*q^16 + 2*q^19 + -3*q^20 + 3*q^22 + 6*q^23 + 4*q^25 + -4*q^26 + -1*q^28 + -6*q^29 + 5*q^31 + 1*q^32 + 3*q^35 + 2*q^37 + 2*q^38 + -3*q^40 + 6*q^41 + -10*q^43 + 3*q^44 + 6*q^46 + -6*q^47 + -6*q^49 + 4*q^50 + -4*q^52 + -9*q^53 + -9*q^55 + -1*q^56 + -6*q^58 + -12*q^59 + 8*q^61 + 5*q^62 + 1*q^64 + 12*q^65 + 14*q^67 + 3*q^70 + -7*q^73 + 2*q^74 + 2*q^76 + -3*q^77 + 8*q^79 + -3*q^80 + 6*q^82 + 3*q^83 + -10*q^86 + 3*q^88 + 18*q^89 + 4*q^91 + 6*q^92 + -6*q^94 + -6*q^95 + -1*q^97 + -6*q^98 + 4*q^100 + 3*q^101 + -4*q^103 + -4*q^104 + -9*q^106 + -9*q^107 + 2*q^109 + -9*q^110 + -1*q^112 + 6*q^113 + -18*q^115 + -6*q^116 + -12*q^118 + -2*q^121 + 8*q^122 + 5*q^124 + 3*q^125 + -7*q^127 + 1*q^128 + 12*q^130 + 15*q^131 + -2*q^133 + 14*q^134 + -6*q^137 + -4*q^139 + 3*q^140 + -12*q^143 + 18*q^145 + -7*q^146 + 2*q^148 + -3*q^149 + 17*q^151 + 2*q^152 + -3*q^154 + -15*q^155 + -4*q^157 + 8*q^158 + -3*q^160 + -6*q^161 + 20*q^163 + 6*q^164 + 3*q^166 + 6*q^167 + 3*q^169 + -10*q^172 + -15*q^173 + -4*q^175 + 3*q^176 + 18*q^178 + 9*q^179 + -16*q^181 + 4*q^182 + 6*q^184 + -6*q^185 + -6*q^188 + -6*q^190 + 12*q^191 + 5*q^193 + -1*q^194 + -6*q^196 + -9*q^197 + -7*q^199 + 4*q^200 +  ...

-------------------------------------------------------
54C (old = 27A), dim = 1

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

-------------------------------------------------------
Gamma_0(55)
Weight 2

-------------------------------------------------------
J_0(55), dim = 5

-------------------------------------------------------
55A (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+         = 2.0573397123474407342 + -0.22887710813904991819e-11i
Omega-         = 0.18998585092049589636e-10 + -1.7212734487292059443i
L(1)           = 0.51433492808686018355
w1             = -2.0573397123474407342 + 0.22887710813904991819e-11i
w2             = -0.18998585092049589636e-10 + 1.7212734487292059443i
c4             = 201.0000000036695419 + -0.67238960185068206844e-8i
c6             = -1701.0000002388062928 + 0.17439548446004489577e-6i
j              = 2684.4961986829516722 + -0.15556919774597640913e-6i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^4 + 1*q^5 + -3*q^8 + -3*q^9 + 1*q^10 + -1*q^11 + 2*q^13 + -1*q^16 + 6*q^17 + -3*q^18 + -4*q^19 + -1*q^20 + -1*q^22 + 4*q^23 + 1*q^25 + 2*q^26 + 6*q^29 + -8*q^31 + 5*q^32 + 6*q^34 + 3*q^36 + -2*q^37 + -4*q^38 + -3*q^40 + 2*q^41 + 4*q^43 + 1*q^44 + -3*q^45 + 4*q^46 + -12*q^47 + -7*q^49 + 1*q^50 + -2*q^52 + -2*q^53 + -1*q^55 + 6*q^58 + 4*q^59 + -10*q^61 + -8*q^62 + 7*q^64 + 2*q^65 + -16*q^67 + -6*q^68 + 8*q^71 + 9*q^72 + 14*q^73 + -2*q^74 + 4*q^76 + 8*q^79 + -1*q^80 + 9*q^81 + 2*q^82 + -4*q^83 + 6*q^85 + 4*q^86 + 3*q^88 + 10*q^89 + -3*q^90 + -4*q^92 + -12*q^94 + -4*q^95 + 10*q^97 + -7*q^98 + 3*q^99 + -1*q^100 + -10*q^101 + -4*q^103 + -6*q^104 + -2*q^106 + 12*q^107 + -18*q^109 + -1*q^110 + -6*q^113 + 4*q^115 + -6*q^116 + -6*q^117 + 4*q^118 + 1*q^121 + -10*q^122 + 8*q^124 + 1*q^125 + 16*q^127 + -3*q^128 + 2*q^130 + -12*q^131 + -16*q^134 + -18*q^136 + 18*q^137 + 12*q^139 + 8*q^142 + -2*q^143 + 3*q^144 + 6*q^145 + 14*q^146 + 2*q^148 + -10*q^149 + 8*q^151 + 12*q^152 + -18*q^153 + -8*q^155 + -2*q^157 + 8*q^158 + 5*q^160 + 9*q^162 + 16*q^163 + -2*q^164 + -4*q^166 + -8*q^167 + -9*q^169 + 6*q^170 + 12*q^171 + -4*q^172 + -6*q^173 + 1*q^176 + 10*q^178 + 4*q^179 + 3*q^180 + -10*q^181 + -12*q^184 + -2*q^185 + -6*q^187 + 12*q^188 + -4*q^190 + 8*q^191 + -26*q^193 + 10*q^194 + 7*q^196 + 2*q^197 + 3*q^198 + -3*q^200 +  ...

-------------------------------------------------------
55B (new) , dim = 2

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

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^3
#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+         = 2.1307121597966613612 + -0.48527422493907993007e-10i
Omega-         = 3.8791547561636360726 + -0.28160883368904250752e-10i
L(1)           = 0.53267803994916534029

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

-------------------------------------------------------
55C (old = 11A), dim = 1

CONGRUENCES:
Modular Degree = 7
Ker(ModPolar)  = Z/7 + Z/7
= B(Z/7 + Z/7)

-------------------------------------------------------
Gamma_0(56)
Weight 2

-------------------------------------------------------
J_0(56), dim = 5

-------------------------------------------------------
56A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= B(Z/2) + C(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+         = 1.8960382312546867737 + 0.85996552361832194157e-11i
Omega-         = 0.72758999959042540445e-10 + 3.373212196636362475i
L(1)           = 0.94801911562734338685
w1             = -0.94801911559096388687 + 1.6866060983138814099i
w2             = 1.8960382312546867737 + 0.85996552361832194157e-11i
c4             = 15.999999989697495112 + -0.15032496619331078192e-7i
c6             = 3519.9999997651472429 + 0.18208435174186213128e-6i
j              = -0.57142857040064270207 + 0.16702950955098788135e-8i

HECKE EIGENFORM:
f(q) = q + 2*q^3 + -4*q^5 + 1*q^7 + 1*q^9 + -8*q^15 + -2*q^17 + -2*q^19 + 2*q^21 + 8*q^23 + 11*q^25 + -4*q^27 + 2*q^29 + 4*q^31 + -4*q^35 + -6*q^37 + -2*q^41 + 8*q^43 + -4*q^45 + -4*q^47 + 1*q^49 + -4*q^51 + -10*q^53 + -4*q^57 + 6*q^59 + 4*q^61 + 1*q^63 + -12*q^67 + 16*q^69 + -14*q^73 + 22*q^75 + -8*q^79 + -11*q^81 + 6*q^83 + 8*q^85 + 4*q^87 + 10*q^89 + 8*q^93 + 8*q^95 + -2*q^97 + 12*q^101 + -12*q^103 + -8*q^105 + -12*q^107 + 10*q^109 + -12*q^111 + 6*q^113 + -32*q^115 + -2*q^119 + -11*q^121 + -4*q^123 + -24*q^125 + 8*q^127 + 16*q^129 + 14*q^131 + -2*q^133 + 16*q^135 + 2*q^137 + 18*q^139 + -8*q^141 + -8*q^145 + 2*q^147 + -2*q^149 + 16*q^151 + -2*q^153 + -16*q^155 + -20*q^159 + 8*q^161 + 16*q^163 + 12*q^167 + -13*q^169 + -2*q^171 + 8*q^173 + 11*q^175 + 12*q^177 + -4*q^179 + 8*q^181 + 8*q^183 + 24*q^185 + -4*q^189 + -8*q^191 + -18*q^193 + -18*q^197 + -4*q^199 +  ...

-------------------------------------------------------
56B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= A(Z/2) + C(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+         = 3.4981932567238892322 + 0.15315345041164481573e-10i
Omega-         = 2.2962114574845680677i
L(1)           = 0.87454831418097230805
w1             = 1.7490966283619446161 + 1.1481057287499417064i
w2             = 1.7490966283619446161 + -1.1481057287346263613i
c4             = -48.000000004633590111 + 0.19962634506848183007e-8i
c6             = -1728.0000000279748808 + 0.34019729004423665993e-7i
j              = 61.71428572959299133 + -0.50816822147671473703e-8i

HECKE EIGENFORM:
f(q) = q + 2*q^5 + -1*q^7 + -3*q^9 + -4*q^11 + 2*q^13 + -6*q^17 + 8*q^19 + -1*q^25 + 6*q^29 + 8*q^31 + -2*q^35 + -2*q^37 + 2*q^41 + -4*q^43 + -6*q^45 + -8*q^47 + 1*q^49 + 6*q^53 + -8*q^55 + -6*q^61 + 3*q^63 + 4*q^65 + -4*q^67 + -8*q^71 + 10*q^73 + 4*q^77 + 16*q^79 + 9*q^81 + 8*q^83 + -12*q^85 + -6*q^89 + -2*q^91 + 16*q^95 + -6*q^97 + 12*q^99 + 2*q^101 + -16*q^103 + -12*q^107 + -10*q^109 + 2*q^113 + -6*q^117 + 6*q^119 + 5*q^121 + -12*q^125 + -8*q^127 + 8*q^131 + -8*q^133 + -6*q^137 + -8*q^139 + -8*q^143 + 12*q^145 + 6*q^149 + 18*q^153 + 16*q^155 + 18*q^157 + -12*q^163 + 16*q^167 + -9*q^169 + -24*q^171 + 18*q^173 + 1*q^175 + -4*q^179 + 10*q^181 + -4*q^185 + 24*q^187 + -16*q^191 + -14*q^193 + 6*q^197 +  ...

-------------------------------------------------------
56C (old = 14A), dim = 1

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

-------------------------------------------------------
Gamma_0(57)
Weight 2

-------------------------------------------------------
J_0(57), dim = 5

-------------------------------------------------------
57A (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+         = 5.555504521378475352 + -0.39902972420958046923e-10i
Omega-         = 0.30930654733762111097e-11 + 1.9183295038005525604i
L(1)           =
w1             = 2.7777522606907842087 + 0.95916475188032479397i
w2             = -0.30930654733762111097e-11 + -1.9183295038005525604i
c4             = 111.9999999989679948 + 0.5660519725221141585e-9i
c6             = -1303.9999999832354451 + -0.1611732163935362093e-7i
j              = -8215.9532162829963703 + 0.45188428096630219472e-6i

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

-------------------------------------------------------
57B (new) , dim = 1

CONGRUENCES:
Modular Degree = 3
Ker(ModPolar)  = Z/3 + Z/3
= C(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+         = 2.1706045445455874831 + 0.10566983171898167067e-10i
Omega-         = 0.32979681388279313241e-10 + 1.504045961042228478i
L(1)           = 0.54265113613639687076
w1             = 2.1706045445455874831 + 0.10566983171898167067e-10i
w2             = -0.32979681388279313241e-10 + -1.504045961042228478i
c4             = 312.99999999570560926 + 0.25400525222618950839e-7i
c6             = -5004.9999999035657074 + -0.73411320033423096338e-6i
j              = 9438.0723300582229586 + 0.21011998333853183727e-5i

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 + 6*q^13 + -2*q^15 + -1*q^16 + -6*q^17 + 1*q^18 + -1*q^19 + 2*q^20 + 4*q^23 + -3*q^24 + -1*q^25 + 6*q^26 + 1*q^27 + 2*q^29 + -2*q^30 + 8*q^31 + 5*q^32 + -6*q^34 + -1*q^36 + -10*q^37 + -1*q^38 + 6*q^39 + 6*q^40 + -2*q^41 + -4*q^43 + -2*q^45 + 4*q^46 + 12*q^47 + -1*q^48 + -7*q^49 + -1*q^50 + -6*q^51 + -6*q^52 + -6*q^53 + 1*q^54 + -1*q^57 + 2*q^58 + -12*q^59 + 2*q^60 + -2*q^61 + 8*q^62 + 7*q^64 + -12*q^65 + -4*q^67 + 6*q^68 + 4*q^69 + -3*q^72 + 10*q^73 + -10*q^74 + -1*q^75 + 1*q^76 + 6*q^78 + 2*q^80 + 1*q^81 + -2*q^82 + 16*q^83 + 12*q^85 + -4*q^86 + 2*q^87 + -2*q^89 + -2*q^90 + -4*q^92 + 8*q^93 + 12*q^94 + 2*q^95 + 5*q^96 + 10*q^97 + -7*q^98 + 1*q^100 + -10*q^101 + -6*q^102 + 8*q^103 + -18*q^104 + -6*q^106 + 4*q^107 + -1*q^108 + -10*q^109 + -10*q^111 + 6*q^113 + -1*q^114 + -8*q^115 + -2*q^116 + 6*q^117 + -12*q^118 + 6*q^120 + -11*q^121 + -2*q^122 + -2*q^123 + -8*q^124 + 12*q^125 + -8*q^127 + -3*q^128 + -4*q^129 + -12*q^130 + 8*q^131 + -4*q^134 + -2*q^135 + 18*q^136 + 18*q^137 + 4*q^138 + 4*q^139 + 12*q^141 + -1*q^144 + -4*q^145 + 10*q^146 + -7*q^147 + 10*q^148 + 6*q^149 + -1*q^150 + -8*q^151 + 3*q^152 + -6*q^153 + -16*q^155 + -6*q^156 + -2*q^157 + -6*q^159 + -10*q^160 + 1*q^162 + -4*q^163 + 2*q^164 + 16*q^166 + 24*q^167 + 23*q^169 + 12*q^170 + -1*q^171 + 4*q^172 + -22*q^173 + 2*q^174 + -12*q^177 + -2*q^178 + -4*q^179 + 2*q^180 + 14*q^181 + -2*q^183 + -12*q^184 + 20*q^185 + 8*q^186 + -12*q^188 + 2*q^190 + -12*q^191 + 7*q^192 + -14*q^193 + 10*q^194 + -12*q^195 + 7*q^196 + -2*q^197 + -8*q^199 + 3*q^200 +  ...

-------------------------------------------------------
57C (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/3 + Z/3) + D(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|   = 2/5
Sha Bound      = 2*5

ANALYTIC INVARIANTS:

Omega+         = 1.466273979146027319 + -0.18903047271735755164e-10i
Omega-         = 0.15537142117703164034e-10 + 1.853445085276995769i
L(1)           = 0.58650959165841092758
w1             = 0.73313698956524508842 + -0.92672254264794940815i
w2             = -0.73313698958078223054 + -0.92672254262904636087i
c4             = -944.00000015500413795 + -0.29872476697467776376e-7i
c6             = 33127.999999277104876 + 0.25242108229060886143e-5i
j              = 749.80759445577481751 + -0.24388120575279660539e-7i

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

-------------------------------------------------------
57D (old = 19A), dim = 1

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

-------------------------------------------------------
Gamma_0(58)
Weight 2

-------------------------------------------------------
J_0(58), dim = 6

-------------------------------------------------------
58A (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))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 5.4655916988262027361 + -0.38457739510468408566e-10i
Omega-         = 0.46589069215917380676e-10 + 2.2236096300072203224i
L(1)           =
w1             = 2.7327958493898068334 + -1.111804815022839031i
w2             = -0.46589069215917380676e-10 + -2.2236096300072203224i
c4             = 56.999999992291783531 + 0.54995717537198426766e-8i
c6             = -620.99999992211325542 + -0.66210660890152458917e-7i
j              = -1596.4913788347176909 + -0.2340847532181865188e-6i

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

-------------------------------------------------------
58B (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)

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

ANALYTIC INVARIANTS:

Omega+         = 2.5830187734080324896 + 0.19863983720748685779e-10i
Omega-         = 0.70781223057780266591e-10 + 1.9334353047678953501i
L(1)           = 1.0332075093632129958
w1             = 1.2915093867394068563 + 0.96671765239387966691i
w2             = 1.2915093866686256333 + -0.96671765237401568319i
c4             = -238.9999999957611322 + 0.20932497913150711276e-7i
c6             = -6137.000000681381254 + -0.10907365478144568069e-5i
j              = 459.72248778427644736 + -0.20859542067358660776e-6i

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

-------------------------------------------------------
58C (old = 29A), dim = 2

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(59)
Weight 2

-------------------------------------------------------
J_0(59), dim = 5

-------------------------------------------------------
59A (new) , dim = 5

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^3*31*557
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 29
Torsion Bound  = 29
|L(1)/Omega|   = 1/29
Sha Bound      = 29

ANALYTIC INVARIANTS:

Omega+         = 10.385947849157551383 + 0.5630217614514291573e-9i
Omega-         = 0.12699064299689248573e-8 + 62.190071360782479596i
L(1)           = 0.35813613272957073736

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

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Gamma_0(60)
Weight 2

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J_0(60), dim = 7

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60A (old = 30A), dim = 1

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

-------------------------------------------------------
60B (old = 20A), 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)

-------------------------------------------------------
60C (old = 15A), dim = 1

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) + B(Z/2 + Z/2)

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Gamma_0(61)
Weight 2

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J_0(61), dim = 4

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61A (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+         = 6.1331931482905676136 + 0.30819509613653515028e-9i
Omega-         = 0.67587033128578131853e-10 + 1.9944109567882465787i
L(1)           =
w1             = -3.0665965741114902903 + 0.99720547824002574127i
w2             = 0.67587033128578131853e-10 + 1.9944109567882465787i
c4             = 96.999999995831769546 + 0.14371762288877208932e-7i
c6             = -1008.9999999577543909 + -0.17974410722213354926e-6i
j              = -14961.852452487955998 + -0.12746511426514406649e-4i

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

-------------------------------------------------------
61B (new) , dim = 3

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

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

ANALYTIC INVARIANTS:

Omega+         = 2.2673088571007449156 + 0.98274839629067325926e-10i
Omega-         = 0.30689770089604747982e-9 + -40.766587315589209934i
L(1)           = 0.90692354284029796623

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

-------------------------------------------------------
Gamma_0(62)
Weight 2

-------------------------------------------------------
J_0(62), dim = 7

-------------------------------------------------------
62A (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))  = 2^2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 4.4349626410884023345 + -0.1687357754684364388e-9i
Omega-         = 0.17349746079364425465e-9 + 2.239108332107688926i
L(1)           = 1.1087406602721005836
w1             = -2.2174813204574524369 + 1.1195541661382123507i
w2             = 0.17349746079364425465e-9 + 2.239108332107688926i
c4             = 32.999999976835035379 + 0.17217910057315764332e-7i
c6             = -945.00000024613599472 + -0.33486680292366560992e-6i
j              = -72.453628833954699612 + -0.64662418898889314748e-7i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + -2*q^5 + 1*q^8 + -3*q^9 + -2*q^10 + 2*q^13 + 1*q^16 + -6*q^17 + -3*q^18 + 4*q^19 + -2*q^20 + 8*q^23 + -1*q^25 + 2*q^26 + 2*q^29 + -1*q^31 + 1*q^32 + -6*q^34 + -3*q^36 + 10*q^37 + 4*q^38 + -2*q^40 + -6*q^41 + 8*q^43 + 6*q^45 + 8*q^46 + -8*q^47 + -7*q^49 + -1*q^50 + 2*q^52 + -6*q^53 + 2*q^58 + -12*q^59 + -6*q^61 + -1*q^62 + 1*q^64 + -4*q^65 + -12*q^67 + -6*q^68 + 8*q^71 + -3*q^72 + 10*q^73 + 10*q^74 + 4*q^76 + -8*q^79 + -2*q^80 + 9*q^81 + -6*q^82 + 8*q^83 + 12*q^85 + 8*q^86 + -6*q^89 + 6*q^90 + 8*q^92 + -8*q^94 + -8*q^95 + 2*q^97 + -7*q^98 + -1*q^100 + 14*q^101 + 8*q^103 + 2*q^104 + -6*q^106 + 20*q^107 + -2*q^109 + 2*q^113 + -16*q^115 + 2*q^116 + -6*q^117 + -12*q^118 + -11*q^121 + -6*q^122 + -1*q^124 + 12*q^125 + -8*q^127 + 1*q^128 + -4*q^130 + -12*q^131 + -12*q^134 + -6*q^136 + 2*q^137 + 8*q^142 + -3*q^144 + -4*q^145 + 10*q^146 + 10*q^148 + -2*q^149 + -16*q^151 + 4*q^152 + 18*q^153 + 2*q^155 + 14*q^157 + -8*q^158 + -2*q^160 + 9*q^162 + -4*q^163 + -6*q^164 + 8*q^166 + 8*q^167 + -9*q^169 + 12*q^170 + -12*q^171 + 8*q^172 + -2*q^173 + -6*q^178 + 16*q^179 + 6*q^180 + 2*q^181 + 8*q^184 + -20*q^185 + -8*q^188 + -8*q^190 + 24*q^191 + -14*q^193 + 2*q^194 + -7*q^196 + -6*q^197 + 24*q^199 + -1*q^200 +  ...

-------------------------------------------------------
62B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2*11
Ker(ModPolar)  = Z/2*11 + Z/2*11
= A(Z/2 + Z/2) + C(Z/11 + Z/11)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*3
#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+         = 3.5990155098019787419 + -0.32823876259261922922e-9i
Omega-         = 1.5911444078014982306 + -0.2046872496358431729e-9i
L(1)           = 0.59983591830032979032

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

-------------------------------------------------------
62C (old = 31A), dim = 2

CONGRUENCES:
Modular Degree = 11
Ker(ModPolar)  = Z/11 + Z/11
= B(Z/11 + Z/11)

-------------------------------------------------------
Gamma_0(63)
Weight 2

-------------------------------------------------------
J_0(63), dim = 5

-------------------------------------------------------
63A (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
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 2.2066209285594657705 + -0.62184166266389432371e-10i
Omega-         = 0.14968164435537681178e-9 + -2.0836128058674101847i
L(1)           = 1.1033104642797328852
w1             = -1.1033104643545737074 + 1.0418064029647971755i
w2             = 1.1033104642048920631 + 1.0418064029026130092i
c4             = -423.00000006207175096 + 0.14365473542502749416e-7i
c6             = -1916.9999982842662485 + 0.31709834310440401276e-5i
j              = 1647.9841271543185208 + 0.24468217865524996356e-6i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^4 + 2*q^5 + -1*q^7 + -3*q^8 + 2*q^10 + -4*q^11 + -2*q^13 + -1*q^14 + -1*q^16 + 6*q^17 + 4*q^19 + -2*q^20 + -4*q^22 + -1*q^25 + -2*q^26 + 1*q^28 + 2*q^29 + 5*q^32 + 6*q^34 + -2*q^35 + 6*q^37 + 4*q^38 + -6*q^40 + -2*q^41 + -4*q^43 + 4*q^44 + 1*q^49 + -1*q^50 + 2*q^52 + -6*q^53 + -8*q^55 + 3*q^56 + 2*q^58 + -12*q^59 + -2*q^61 + 7*q^64 + -4*q^65 + 4*q^67 + -6*q^68 + -2*q^70 + -6*q^73 + 6*q^74 + -4*q^76 + 4*q^77 + -16*q^79 + -2*q^80 + -2*q^82 + 12*q^83 + 12*q^85 + -4*q^86 + 12*q^88 + 14*q^89 + 2*q^91 + 8*q^95 + 18*q^97 + 1*q^98 + 1*q^100 + -14*q^101 + 8*q^103 + 6*q^104 + -6*q^106 + -4*q^107 + -18*q^109 + -8*q^110 + 1*q^112 + 14*q^113 + -2*q^116 + -12*q^118 + -6*q^119 + 5*q^121 + -2*q^122 + -12*q^125 + -3*q^128 + -4*q^130 + -4*q^131 + -4*q^133 + 4*q^134 + -18*q^136 + 6*q^137 + 12*q^139 + 2*q^140 + 8*q^143 + 4*q^145 + -6*q^146 + -6*q^148 + -6*q^149 + 8*q^151 + -12*q^152 + 4*q^154 + -2*q^157 + -16*q^158 + 10*q^160 + 4*q^163 + 2*q^164 + 12*q^166 + 8*q^167 + -9*q^169 + 12*q^170 + 4*q^172 + 10*q^173 + 1*q^175 + 4*q^176 + 14*q^178 + 4*q^179 + -26*q^181 + 2*q^182 + 12*q^185 + -24*q^187 + 8*q^190 + 8*q^191 + 2*q^193 + 18*q^194 + -1*q^196 + -22*q^197 + 24*q^199 + 3*q^200 +  ...

-------------------------------------------------------
63B (new) , dim = 2

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

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*3
#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+         = 4.5196832485402409651 + -0.64111827011074345191e-9i
Omega-         = 4.5196832498709063207 + -0.72154877468509774623e-9i
L(1)           = 0.75328054142337349419

HECKE EIGENFORM:
a^2-3 = 0,
f(q) = q + a*q^2 + 1*q^4 + -2*a*q^5 + 1*q^7 + -a*q^8 + -6*q^10 + 2*a*q^11 + 2*q^13 + a*q^14 + -5*q^16 + 2*a*q^17 + -4*q^19 + -2*a*q^20 + 6*q^22 + -2*a*q^23 + 7*q^25 + 2*a*q^26 + 1*q^28 + -4*q^31 + -3*a*q^32 + 6*q^34 + -2*a*q^35 + 2*q^37 + -4*a*q^38 + 6*q^40 + 6*a*q^41 + -4*q^43 + 2*a*q^44 + -6*q^46 + 4*a*q^47 + 1*q^49 + 7*a*q^50 + 2*q^52 + -4*a*q^53 + -12*q^55 + -a*q^56 + -4*a*q^59 + -10*q^61 + -4*a*q^62 + 1*q^64 + -4*a*q^65 + -4*q^67 + 2*a*q^68 + -6*q^70 + -6*a*q^71 + 14*q^73 + 2*a*q^74 + -4*q^76 + 2*a*q^77 + 8*q^79 + 10*a*q^80 + 18*q^82 + -12*q^85 + -4*a*q^86 + -6*q^88 + -2*a*q^89 + 2*q^91 + -2*a*q^92 + 12*q^94 + 8*a*q^95 + 14*q^97 + a*q^98 + 7*q^100 + 2*a*q^101 + -4*q^103 + -2*a*q^104 + -12*q^106 + 10*a*q^107 + 2*q^109 + -12*a*q^110 + -5*q^112 + 12*q^115 + -12*q^118 + 2*a*q^119 + 1*q^121 + -10*a*q^122 + -4*q^124 + -4*a*q^125 + 8*q^127 + 7*a*q^128 + -12*q^130 + -8*a*q^131 + -4*q^133 + -4*a*q^134 + -6*q^136 + -4*a*q^137 + -16*q^139 + -2*a*q^140 + -18*q^142 + 4*a*q^143 + 14*a*q^146 + 2*q^148 + 4*a*q^149 + 8*q^151 + 4*a*q^152 + 6*q^154 + 8*a*q^155 + -10*q^157 + 8*a*q^158 + 18*q^160 + -2*a*q^161 + 20*q^163 + 6*a*q^164 + -12*a*q^167 + -9*q^169 + -12*a*q^170 + -4*q^172 + 10*a*q^173 + 7*q^175 + -10*a*q^176 + -6*q^178 + -10*a*q^179 + 2*q^181 + 2*a*q^182 + 6*q^184 + -4*a*q^185 + 12*q^187 + 4*a*q^188 + 24*q^190 + -14*a*q^191 + 14*q^193 + 14*a*q^194 + 1*q^196 + 12*a*q^197 + -16*q^199 + -7*a*q^200 +  ...

-------------------------------------------------------
63C (old = 21A), dim = 1

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

-------------------------------------------------------
Gamma_0(64)
Weight 2

-------------------------------------------------------
J_0(64), dim = 3

-------------------------------------------------------
64A (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+         = 1.8540746773844523679 + -0.27941750873291166573e-9i
Omega-         = 0.27941750873291166573e-9 + 1.8540746773844523679i
L(1)           = 0.46351866934611309199
w1             = -0.27941750873291166573e-9 + -1.8540746773844523679i
w2             = -1.8540746773844523679 + 0.27941750873291166573e-9i
c4             = 191.99999996529534725 + 0.11574110217114564909e-6i
c6             = 0.25277970436158731359e-6 + 0.22857032495777165025e-15i
j              = 1728 + 0.17406367172643701994e-49i

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 +  ...

-------------------------------------------------------
64B (old = 32A), dim = 1

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

-------------------------------------------------------
Gamma_0(65)
Weight 2

-------------------------------------------------------
J_0(65), dim = 5

-------------------------------------------------------
65A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = Z/2 + Z/2
= B(Z/2) + C(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+         = 2.6914267354693143519 + -0.28838557963679606069e-9i
Omega-         = 0.21454246952657445327e-9 + 2.5425284454021509133i
L(1)           =
w1             = -2.6914267354693143519 + 0.28838557963679606069e-9i
w2             = 0.21454246952657445327e-9 + 2.5425284454021509133i
c4             = 48.999999979009763559 + 0.18331794986916310346e-7i
c6             = -72.999999876118375035 + -0.12545724000218443284e-7i
j              = 1809.9846152035148966 + -0.66864895601214970389e-7i

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

-------------------------------------------------------
65B (new) , dim = 2

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

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*3
#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+         = 2.7367526342583074292 + 0.1217056978967460175e-8i
Omega-         = 4.0858898554961122005 + 0.27121680176901230996e-8i
L(1)           = 0.45612543904305123824

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

-------------------------------------------------------
65C (new) , dim = 2

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

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

ANALYTIC INVARIANTS:

Omega+         = 3.164474823650066382 + -0.13216529676971745495e-8i
Omega-         = 5.162087278120552215 + -0.2543695637377267875e-8i
L(1)           = 0.22603391597500474159

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

-------------------------------------------------------
Gamma_0(66)
Weight 2

-------------------------------------------------------
J_0(66), dim = 9

-------------------------------------------------------
66A (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))  = 3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/2*3
Sha Bound      = 2*3

ANALYTIC INVARIANTS:

Omega+         = 2.3912743718576139661 + -0.67298006998167240566e-11i
Omega-         = 0.665026396405270352e-9 + 1.5635201774196933879i
L(1)           = 0.39854572864293566101
w1             = -2.3912743718576139661 + 0.67298006998167240566e-11i
w2             = 0.665026396405270352e-9 + 1.5635201774196933879i
c4             = 264.99999996236556722 + 0.43379092243818186951e-6i
c6             = -4068.9999989094710216 + -0.10964949762840754184e-4i
j              = 15664.667494524295974 + 0.6047394530972749936e-4i

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^11 + 1*q^12 + -4*q^13 + -2*q^14 + 1*q^16 + -6*q^17 + -1*q^18 + -4*q^19 + 2*q^21 + 1*q^22 + 6*q^23 + -1*q^24 + -5*q^25 + 4*q^26 + 1*q^27 + 2*q^28 + 6*q^29 + 8*q^31 + -1*q^32 + -1*q^33 + 6*q^34 + 1*q^36 + -10*q^37 + 4*q^38 + -4*q^39 + 6*q^41 + -2*q^42 + 8*q^43 + -1*q^44 + -6*q^46 + -6*q^47 + 1*q^48 + -3*q^49 + 5*q^50 + -6*q^51 + -4*q^52 + -1*q^54 + -2*q^56 + -4*q^57 + -6*q^58 + 8*q^61 + -8*q^62 + 2*q^63 + 1*q^64 + 1*q^66 + -4*q^67 + -6*q^68 + 6*q^69 + 6*q^71 + -1*q^72 + 2*q^73 + 10*q^74 + -5*q^75 + -4*q^76 + -2*q^77 + 4*q^78 + 14*q^79 + 1*q^81 + -6*q^82 + -12*q^83 + 2*q^84 + -8*q^86 + 6*q^87 + 1*q^88 + -6*q^89 + -8*q^91 + 6*q^92 + 8*q^93 + 6*q^94 + -1*q^96 + 14*q^97 + 3*q^98 + -1*q^99 + -5*q^100 + 6*q^101 + 6*q^102 + -4*q^103 + 4*q^104 + -12*q^107 + 1*q^108 + -4*q^109 + -10*q^111 + 2*q^112 + 18*q^113 + 4*q^114 + 6*q^116 + -4*q^117 + -12*q^119 + 1*q^121 + -8*q^122 + 6*q^123 + 8*q^124 + -2*q^126 + 14*q^127 + -1*q^128 + 8*q^129 + -12*q^131 + -1*q^132 + -8*q^133 + 4*q^134 + 6*q^136 + -18*q^137 + -6*q^138 + -4*q^139 + -6*q^141 + -6*q^142 + 4*q^143 + 1*q^144 + -2*q^146 + -3*q^147 + -10*q^148 + -6*q^149 + 5*q^150 + -10*q^151 + 4*q^152 + -6*q^153 + 2*q^154 + -4*q^156 + 2*q^157 + -14*q^158 + 12*q^161 + -1*q^162 + -4*q^163 + 6*q^164 + 12*q^166 + 12*q^167 + -2*q^168 + 3*q^169 + -4*q^171 + 8*q^172 + 6*q^173 + -6*q^174 + -10*q^175 + -1*q^176 + 6*q^178 + 24*q^179 + -22*q^181 + 8*q^182 + 8*q^183 + -6*q^184 + -8*q^186 + 6*q^187 + -6*q^188 + 2*q^189 + 18*q^191 + 1*q^192 + 14*q^193 + -14*q^194 + -3*q^196 + 6*q^197 + 1*q^198 + -4*q^199 + 5*q^200 +  ...

-------------------------------------------------------
66B (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) + D(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+         = 2.2043850601472195202 + -0.28532351535700727968e-9i
Omega-         = 0.17090520839979567942e-9 + -2.1940597101071264137i
L(1)           = 0.55109626503680488005
w1             = -2.2043850601472195202 + 0.28532351535700727968e-9i
w2             = -0.17090520839979567942e-9 + 2.1940597101071264137i
c4             = 97.000000086581661649 + 0.93395552773698754778e-8i
c6             = -17.000001381551882691 + 0.74811626654743117867e-6i
j              = 1728.5473485723740899 + -0.48347569540298217699e-7i

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

-------------------------------------------------------
66C (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) + E(Z/5 + Z/5)

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

ANALYTIC INVARIANTS:

Omega+         = 1.1916148153409306216 + -0.25026300925262263202e-9i
Omega-         = 0.13075794346946897219e-9 + 0.94027960493103684151i
L(1)           = 0.59580740767046531082
w1             = 1.1916148153409306216 + -0.25026300925262263202e-9i
w2             = -0.13075794346946897219e-9 + -0.94027960493103684151i
c4             = 2161.0000030653409911 + 0.12967988536086093799e-5i
c6             = -73225.000185794971683 + -0.52065229049917852329e-4i
j              = 3686.9341893953198424 + -0.15808099516741156692e-5i

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

-------------------------------------------------------
66D (old = 33A), 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) + C(Z/2 + Z/2) + E(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
66E (old = 11A), dim = 1

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

-------------------------------------------------------
Gamma_0(67)
Weight 2

-------------------------------------------------------
J_0(67), dim = 5

-------------------------------------------------------
67A (new) , dim = 1

CONGRUENCES:
Modular Degree = 5
Ker(ModPolar)  = Z/5 + Z/5
= C(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+         = 1.2737700376707416422 + -0.62991890907543819433e-9i
Omega-         = 0.60200156739615370514e-8 + 6.0599368025367942551i
L(1)           = 1.2737700376707416424
w1             = -0.63688501582536298412 + 3.0299684015833565821i
w2             = 1.2737700376707416422 + -0.62991890907543819433e-9i
c4             = 591.99999790665368193 + 0.11707076084036625856e-5i
c6             = 14407.999923635434052 + 0.42768702744609992225e-4i
j              = -3096637.0906131182146 + 0.23095038056143180282e-1i

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

-------------------------------------------------------
67B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2
= C(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+         = 20.465112920203923849 + -0.10765565475137382492e-7i
Omega-         = 6.3256501797141559617 + 0.26663283659398999294e-8i
L(1)           =

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

-------------------------------------------------------
67C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*5
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*5 + Z/2*5
= A(Z/5 + Z/5) + 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))  = 11
Torsion Bound  = 11
|L(1)/Omega|   = 2^2/11
Sha Bound      = 2^2*11

ANALYTIC INVARIANTS:

Omega+         = 1.8497601705508605148 + -0.16627577198876880946e-9i
Omega-         = 2.4286661635428506694 + -0.1268870279826250742e-8i
L(1)           = 0.67264006201849473265

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

-------------------------------------------------------
Gamma_0(68)
Weight 2

-------------------------------------------------------
J_0(68), dim = 7

-------------------------------------------------------
68A (new) , dim = 2

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   = 2^2*3
#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+         = 5.9568973377717562602 + 0.3257642418328049383e-9i
Omega-         = 2.3196986231124585824 + -0.37516688739722987706e-9i
L(1)           = 0.99281622296195937669

HECKE EIGENFORM:
a^2-2*a-2 = 0,
f(q) = q + a*q^3 + (-2*a+2)*q^5 + -a*q^7 + (2*a-1)*q^9 + (a-4)*q^11 + 2*a*q^13 + (-2*a-4)*q^15 + -1*q^17 + (-2*a+4)*q^19 + (-2*a-2)*q^21 + (a-4)*q^23 + 7*q^25 + 4*q^27 + (2*a-2)*q^29 + (3*a-4)*q^31 + (-2*a+2)*q^33 + (2*a+4)*q^35 + (-2*a+10)*q^37 + (4*a+4)*q^39 + -6*q^41 + (-6*a+8)*q^43 + (-2*a-10)*q^45 + (-4*a+4)*q^47 + (2*a-5)*q^49 + -a*q^51 + (4*a+2)*q^53 + (6*a-12)*q^55 + -4*q^57 + (-2*a+8)*q^59 + (2*a-6)*q^61 + (-3*a-4)*q^63 + (-4*a-8)*q^65 + (4*a+4)*q^67 + (-2*a+2)*q^69 + -3*a*q^71 + 2*q^73 + 7*a*q^75 + (2*a-2)*q^77 + (-3*a-4)*q^79 + (-2*a+3)*q^81 + (2*a-8)*q^83 + (2*a-2)*q^85 + (2*a+4)*q^87 + (-2*a+8)*q^89 + (-4*a-4)*q^91 + (2*a+6)*q^93 + (-4*a+16)*q^95 + (-4*a+6)*q^97 + (-5*a+8)*q^99 + (2*a-8)*q^101 + -4*a*q^103 + (8*a+4)*q^105 + (a+8)*q^107 + (-6*a+2)*q^109 + (6*a-4)*q^111 + (8*a-2)*q^113 + (6*a-12)*q^115 + (6*a+8)*q^117 + a*q^119 + (-6*a+7)*q^121 + -6*a*q^123 + (-4*a+4)*q^125 + (6*a-16)*q^127 + (-4*a-12)*q^129 + (5*a-8)*q^131 + 4*q^133 + (-8*a+8)*q^135 + (-2*a+8)*q^137 + (-a-12)*q^139 + (-4*a-8)*q^141 + (-4*a+4)*q^143 + -12*q^145 + (-a+4)*q^147 + 6*q^149 + (-2*a-8)*q^151 + (-2*a+1)*q^153 + (2*a-20)*q^155 + 2*q^157 + (10*a+8)*q^159 + (2*a-2)*q^161 + (9*a-4)*q^163 + 12*q^165 + (5*a-8)*q^167 + (8*a-5)*q^169 + (2*a-12)*q^171 + (-2*a-10)*q^173 + -7*a*q^175 + (4*a-4)*q^177 + (-2*a+20)*q^179 + (-2*a+10)*q^181 + (-2*a+4)*q^183 + (-16*a+28)*q^185 + (-a+4)*q^187 + -4*a*q^189 + 12*q^191 + (4*a+10)*q^193 + (-16*a-8)*q^195 + (2*a-2)*q^197 + (3*a-4)*q^199 +  ...

-------------------------------------------------------
68B (old = 34A), 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) + C(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
68C (old = 17A), dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = 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)

-------------------------------------------------------
Gamma_0(69)
Weight 2

-------------------------------------------------------
J_0(69), dim = 7

-------------------------------------------------------
69A (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
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.4058638651171369867 + 0.64418791126326863566e-9i
Omega-         = 0.457799610788105439e-8 + -4.7739422043360152902i
L(1)           = 1.2029319325585684934
w1             = 1.2029319302695704394 + 2.3869711024901016007i
w2             = 2.4058638651171369867 + 0.64418791126326863566e-9i
c4             = 25.000000155433262768 + 0.64301707325691775755e-7i
c6             = 611.00000309466070384 + -0.2162139952919242667e-5i
j              = -75.483092458819254038 + -0.11654441915614984841e-5i

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

-------------------------------------------------------
69B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2*11
Ker(ModPolar)  = Z/2*11 + Z/2*11
= A(Z/2 + Z/2) + C(Z/11 + Z/11)

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|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 1.3201793907241489305 + -0.84066449107115509177e-9i
Omega-         = 2.6477889068969884421 + 0.27705270691201512876e-8i
L(1)           = 0.3300448476810372327

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

-------------------------------------------------------
69C (old = 23A), dim = 2

CONGRUENCES:
Modular Degree = 11
Ker(ModPolar)  = Z/11 + Z/11
= B(Z/11 + Z/11)

-------------------------------------------------------
Gamma_0(70)
Weight 2

-------------------------------------------------------
J_0(70), dim = 9

-------------------------------------------------------
70A (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))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 2.360608692724313824 + 0.84227656981467702252e-9i
Omega-         = 0.21755233226345652679e-8 + -3.1347414301549619229i
L(1)           = 1.1803043463621569121
w1             = -1.1803043474499185733 + 1.5673707146563426766i
w2             = 1.1803043452743952507 + 1.5673707154986192464i
c4             = -110.99999974476004061 + 0.35217001913031018171e-6i
c6             = 1863.0000009216896398 + -0.45372971687892943054e-5i
j              = 488.43964009342795794 + -0.16282519846991516664e-5i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + -1*q^5 + -1*q^7 + 1*q^8 + -3*q^9 + -1*q^10 + 4*q^11 + -6*q^13 + -1*q^14 + 1*q^16 + 2*q^17 + -3*q^18 + -1*q^20 + 4*q^22 + 1*q^25 + -6*q^26 + -1*q^28 + 6*q^29 + 8*q^31 + 1*q^32 + 2*q^34 + 1*q^35 + -3*q^36 + -10*q^37 + -1*q^40 + 2*q^41 + 4*q^43 + 4*q^44 + 3*q^45 + 8*q^47 + 1*q^49 + 1*q^50 + -6*q^52 + -2*q^53 + -4*q^55 + -1*q^56 + 6*q^58 + -8*q^59 + -14*q^61 + 8*q^62 + 3*q^63 + 1*q^64 + 6*q^65 + -12*q^67 + 2*q^68 + 1*q^70 + -16*q^71 + -3*q^72 + 2*q^73 + -10*q^74 + -4*q^77 + -8*q^79 + -1*q^80 + 9*q^81 + 2*q^82 + 8*q^83 + -2*q^85 + 4*q^86 + 4*q^88 + 10*q^89 + 3*q^90 + 6*q^91 + 8*q^94 + 2*q^97 + 1*q^98 + -12*q^99 + 1*q^100 + -6*q^101 + 16*q^103 + -6*q^104 + -2*q^106 + 12*q^107 + 6*q^109 + -4*q^110 + -1*q^112 + 2*q^113 + 6*q^116 + 18*q^117 + -8*q^118 + -2*q^119 + 5*q^121 + -14*q^122 + 8*q^124 + -1*q^125 + 3*q^126 + -8*q^127 + 1*q^128 + 6*q^130 + -16*q^131 + -12*q^134 + 2*q^136 + -6*q^137 + 16*q^139 + 1*q^140 + -16*q^142 + -24*q^143 + -3*q^144 + -6*q^145 + 2*q^146 + -10*q^148 + 6*q^149 + 8*q^151 + -6*q^153 + -4*q^154 + -8*q^155 + 10*q^157 + -8*q^158 + -1*q^160 + 9*q^162 + -4*q^163 + 2*q^164 + 8*q^166 + 23*q^169 + -2*q^170 + 4*q^172 + -22*q^173 + -1*q^175 + 4*q^176 + 10*q^178 + -12*q^179 + 3*q^180 + -14*q^181 + 6*q^182 + 10*q^185 + 8*q^187 + 8*q^188 + 24*q^191 + 2*q^193 + 2*q^194 + 1*q^196 + 14*q^197 + -12*q^198 + -16*q^199 + 1*q^200 +  ...

-------------------------------------------------------
70B (old = 35A), dim = 1

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

-------------------------------------------------------
70C (old = 35B), dim = 2

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 + Z/2) + D(Z/2 + Z/2)

-------------------------------------------------------
70D (old = 14A), 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/3 + Z/3) + C(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(71)
Weight 2

-------------------------------------------------------
J_0(71), dim = 6

-------------------------------------------------------
71A (new) , dim = 3

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 257
#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+         = 2.5606400484418549486 + -0.91332366654231932e-8i
Omega-         = 0.15917461063834160998e-7 + -23.437870135491681557i
L(1)           = 0.51212800968837099299

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

-------------------------------------------------------
71B (new) , dim = 3

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 257
#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+         = 4.9554476886069234236 + -0.29167203610054182986e-7i
Omega-         = 0.2258841951006204375e-8 + -6.6645036490166339758i
L(1)           = 0.70792109837241764421

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

-------------------------------------------------------
Gamma_0(72)
Weight 2

-------------------------------------------------------
J_0(72), dim = 5

-------------------------------------------------------
72A (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
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 1.9465368388667893918 + -0.24478664029106893469e-42i
Omega-         = 2.4901297746059939989i
L(1)           = 0.9732684194333946959
w1             = 0.9732684194333946959 + -1.2450648873029969994i
w2             = -0.9732684194333946959 + -1.2450648873029969994i
c4             = -288.00000213648104364 + -0.38974099029920473552e-11i
c6             = 6048.0000636450376035 + -0.8695689984298735625e-8i
j              = 682.66666716568927903 + 0.12042887733928975617e-8i

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 +  ...

-------------------------------------------------------
72B (old = 36A), dim = 1

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

-------------------------------------------------------
72C (old = 24A), dim = 1

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

-------------------------------------------------------
Gamma_0(73)
Weight 2

-------------------------------------------------------
J_0(73), dim = 5

-------------------------------------------------------
73A (new) , dim = 1

CONGRUENCES:
Modular Degree = 3
Ker(ModPolar)  = Z/3 + Z/3
= C(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+         = 2.3653209323135984289 + 0.38560788227309058626e-8i
Omega-         = 0.1316964402880257116e-7 + 2.7927843131493701415i
L(1)           = 1.182660466156799216
w1             = 1.1826604727416212289 + 1.3963921585027244821i
w2             = 1.1826604595719772001 + -1.3963921546466456594i
c4             = -182.99999766573034709 + -0.29779978019719729163e-5i
c6             = 1755.000026893035962 + -0.41092332903996397827e-4i
j              = 1150.0256818798736068 + 0.36791757177404196907e-4i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^4 + 2*q^5 + 2*q^7 + -3*q^8 + -3*q^9 + 2*q^10 + -2*q^11 + -6*q^13 + 2*q^14 + -1*q^16 + 2*q^17 + -3*q^18 + 8*q^19 + -2*q^20 + -2*q^22 + 4*q^23 + -1*q^25 + -6*q^26 + -2*q^28 + 2*q^29 + -2*q^31 + 5*q^32 + 2*q^34 + 4*q^35 + 3*q^36 + -6*q^37 + 8*q^38 + -6*q^40 + 6*q^41 + -2*q^43 + 2*q^44 + -6*q^45 + 4*q^46 + 6*q^47 + -3*q^49 + -1*q^50 + 6*q^52 + 10*q^53 + -4*q^55 + -6*q^56 + 2*q^58 + -6*q^59 + -14*q^61 + -2*q^62 + -6*q^63 + 7*q^64 + -12*q^65 + 8*q^67 + -2*q^68 + 4*q^70 + 9*q^72 + 1*q^73 + -6*q^74 + -8*q^76 + -4*q^77 + -4*q^79 + -2*q^80 + 9*q^81 + 6*q^82 + -14*q^83 + 4*q^85 + -2*q^86 + 6*q^88 + -6*q^89 + -6*q^90 + -12*q^91 + -4*q^92 + 6*q^94 + 16*q^95 + -10*q^97 + -3*q^98 + 6*q^99 + 1*q^100 + 10*q^101 + 6*q^103 + 18*q^104 + 10*q^106 + 18*q^107 + -2*q^109 + -4*q^110 + -2*q^112 + 2*q^113 + 8*q^115 + -2*q^116 + 18*q^117 + -6*q^118 + 4*q^119 + -7*q^121 + -14*q^122 + 2*q^124 + -12*q^125 + -6*q^126 + 12*q^127 + -3*q^128 + -12*q^130 + -18*q^131 + 16*q^133 + 8*q^134 + -6*q^136 + -6*q^137 + -14*q^139 + -4*q^140 + 12*q^143 + 3*q^144 + 4*q^145 + 1*q^146 + 6*q^148 + -22*q^149 + 10*q^151 + -24*q^152 + -6*q^153 + -4*q^154 + -4*q^155 + 2*q^157 + -4*q^158 + 10*q^160 + 8*q^161 + 9*q^162 + -14*q^163 + -6*q^164 + -14*q^166 + 14*q^167 + 23*q^169 + 4*q^170 + -24*q^171 + 2*q^172 + 6*q^173 + -2*q^175 + 2*q^176 + -6*q^178 + -6*q^179 + 6*q^180 + 10*q^181 + -12*q^182 + -12*q^184 + -12*q^185 + -4*q^187 + -6*q^188 + 16*q^190 + 26*q^191 + 10*q^193 + -10*q^194 + 3*q^196 + 18*q^197 + 6*q^198 + 10*q^199 + 3*q^200 +  ...

-------------------------------------------------------
73B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2
= C(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+         = 24.093313896458979391 + 0.10413982662855055844e-6i
Omega-         = 4.7035510076830743497 + -0.23272382059087557466e-7i
L(1)           =

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

-------------------------------------------------------
73C (new) , dim = 2

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

ANALYTIC INVARIANTS:

Omega+         = 0.89025993270019304925 + 0.73367589740035208971e-9i
Omega-         = 9.7813974422411457353 + 0.79098312171543619076e-8i
L(1)           = 1.1870132436002573994

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

-------------------------------------------------------
Gamma_0(74)
Weight 2

-------------------------------------------------------
J_0(74), dim = 8

-------------------------------------------------------
74A (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*3 + Z/2*3
= B(Z/2 + Z/2 + Z/2 + Z/2) + D(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+         = 2.1889045025501513148 + 0.4177044503744995344e-8i
Omega-         = 6.502485077408060534 + -0.26800353829016225367e-7i
L(1)           = 0.72963483418338377293

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

-------------------------------------------------------
74B (new) , dim = 2

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

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 5
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 19
Torsion Bound  = 19
|L(1)/Omega|   = 5/19
Sha Bound      = 5*19

ANALYTIC INVARIANTS:

Omega+         = 5.3391952137916328013 + 0.33779097265165537501e-7i
Omega-         = 2.6231085233822682354 + 0.14318308238775450319e-7i
L(1)           = 1.4050513720504297127

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

-------------------------------------------------------
74C (old = 37A), dim = 1

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

-------------------------------------------------------
74D (old = 37B), 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) + C(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(75)
Weight 2

-------------------------------------------------------
J_0(75), dim = 5

-------------------------------------------------------
75A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/2 + Z/2) + D(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+         = 1.4025399283998501959 + 0.56526549385403475386e-8i
Omega-         = 0.66997628907387406699e-7 + -4.6695327643023998488i
L(1)           = 1.4025399283998502073
w1             = 0.70126993070111064425 + 2.3347663849775273937i
w2             = 1.4025399283998501959 + 0.56526549385403475386e-8i
c4             = 400.00001382082112405 + -0.61494887690197091075e-5i
c6             = 8200.0004001661158553 + -0.21087434575960795244e-3i
j              = -34133.337622290156251 + -0.3762590132314860737e-2i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + -1*q^3 + 2*q^4 + -2*q^6 + -3*q^7 + 1*q^9 + 2*q^11 + -2*q^12 + 1*q^13 + -6*q^14 + -4*q^16 + 2*q^17 + 2*q^18 + -5*q^19 + 3*q^21 + 4*q^22 + 6*q^23 + 2*q^26 + -1*q^27 + -6*q^28 + 10*q^29 + -3*q^31 + -8*q^32 + -2*q^33 + 4*q^34 + 2*q^36 + 2*q^37 + -10*q^38 + -1*q^39 + -8*q^41 + 6*q^42 + 1*q^43 + 4*q^44 + 12*q^46 + 2*q^47 + 4*q^48 + 2*q^49 + -2*q^51 + 2*q^52 + -4*q^53 + -2*q^54 + 5*q^57 + 20*q^58 + -10*q^59 + 7*q^61 + -6*q^62 + -3*q^63 + -8*q^64 + -4*q^66 + -3*q^67 + 4*q^68 + -6*q^69 + -8*q^71 + -14*q^73 + 4*q^74 + -10*q^76 + -6*q^77 + -2*q^78 + 1*q^81 + -16*q^82 + 6*q^83 + 6*q^84 + 2*q^86 + -10*q^87 + -3*q^91 + 12*q^92 + 3*q^93 + 4*q^94 + 8*q^96 + 17*q^97 + 4*q^98 + 2*q^99 + 12*q^101 + -4*q^102 + -4*q^103 + -8*q^106 + 12*q^107 + -2*q^108 + 5*q^109 + -2*q^111 + 12*q^112 + -4*q^113 + 10*q^114 + 20*q^116 + 1*q^117 + -20*q^118 + -6*q^119 + -7*q^121 + 14*q^122 + 8*q^123 + -6*q^124 + -6*q^126 + -8*q^127 + -1*q^129 + 12*q^131 + -4*q^132 + 15*q^133 + -6*q^134 + -18*q^137 + -12*q^138 + 20*q^139 + -2*q^141 + -16*q^142 + 2*q^143 + -4*q^144 + -28*q^146 + -2*q^147 + 4*q^148 + 10*q^149 + 7*q^151 + 2*q^153 + -12*q^154 + -2*q^156 + -13*q^157 + 4*q^159 + -18*q^161 + 2*q^162 + 11*q^163 + -16*q^164 + 12*q^166 + 12*q^167 + -12*q^169 + -5*q^171 + 2*q^172 + 6*q^173 + -20*q^174 + -8*q^176 + 10*q^177 + -10*q^179 + 17*q^181 + -6*q^182 + -7*q^183 + 6*q^186 + 4*q^187 + 4*q^188 + 3*q^189 + 22*q^191 + 8*q^192 + 11*q^193 + 34*q^194 + 4*q^196 + -18*q^197 + 4*q^198 + -5*q^199 +  ...

-------------------------------------------------------
75B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/3 + Z/3) + D(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+         = 2.505474884185016485 + 0.50675840499231059702e-8i
Omega-         = 0.94885660728963242685e-9 + 1.4277224416646443387i
L(1)           = 1.252737442092508245
w1             = -1.2527374416180799388 + 0.71386121829853014437i
w2             = 0.94885660728963242685e-9 + 1.4277224416646443387i
c4             = 25.00000307395059953 + 0.50626253408768180311e-5i
c6             = -20125.000353085536386 + 0.82842649780190821494e-4i
j              = -0.66666688919840589151e-1 + -0.41051449148685223584e-7i

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

-------------------------------------------------------
75C (new) , dim = 1

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

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+         = 3.1361746481869598557 + -0.79633820186235429366e-8i
Omega-         = 0.17077294206905537046e-7 + 2.0882785485829207682i
L(1)           = 0.62723492963739197316
w1             = -1.5680873326321270313 + -1.0441392703097693748i
w2             = -1.5680873155548328244 + 1.0441392782731513934i
c4             = -80.000003258835826542 + 0.13359202140084785647e-5i
c6             = -3159.999894188764433 + -0.11362050769226260498e-3i
j              = 84.279850557003521517 + -0.97813494795460430621e-5i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + 1*q^3 + 2*q^4 + -2*q^6 + 3*q^7 + 1*q^9 + 2*q^11 + 2*q^12 + -1*q^13 + -6*q^14 + -4*q^16 + -2*q^17 + -2*q^18 + -5*q^19 + 3*q^21 + -4*q^22 + -6*q^23 + 2*q^26 + 1*q^27 + 6*q^28 + 10*q^29 + -3*q^31 + 8*q^32 + 2*q^33 + 4*q^34 + 2*q^36 + -2*q^37 + 10*q^38 + -1*q^39 + -8*q^41 + -6*q^42 + -1*q^43 + 4*q^44 + 12*q^46 + -2*q^47 + -4*q^48 + 2*q^49 + -2*q^51 + -2*q^52 + 4*q^53 + -2*q^54 + -5*q^57 + -20*q^58 + -10*q^59 + 7*q^61 + 6*q^62 + 3*q^63 + -8*q^64 + -4*q^66 + 3*q^67 + -4*q^68 + -6*q^69 + -8*q^71 + 14*q^73 + 4*q^74 + -10*q^76 + 6*q^77 + 2*q^78 + 1*q^81 + 16*q^82 + -6*q^83 + 6*q^84 + 2*q^86 + 10*q^87 + -3*q^91 + -12*q^92 + -3*q^93 + 4*q^94 + 8*q^96 + -17*q^97 + -4*q^98 + 2*q^99 + 12*q^101 + 4*q^102 + 4*q^103 + -8*q^106 + -12*q^107 + 2*q^108 + 5*q^109 + -2*q^111 + -12*q^112 + 4*q^113 + 10*q^114 + 20*q^116 + -1*q^117 + 20*q^118 + -6*q^119 + -7*q^121 + -14*q^122 + -8*q^123 + -6*q^124 + -6*q^126 + 8*q^127 + -1*q^129 + 12*q^131 + 4*q^132 + -15*q^133 + -6*q^134 + 18*q^137 + 12*q^138 + 20*q^139 + -2*q^141 + 16*q^142 + -2*q^143 + -4*q^144 + -28*q^146 + 2*q^147 + -4*q^148 + 10*q^149 + 7*q^151 + -2*q^153 + -12*q^154 + -2*q^156 + 13*q^157 + 4*q^159 + -18*q^161 + -2*q^162 + -11*q^163 + -16*q^164 + 12*q^166 + -12*q^167 + -12*q^169 + -5*q^171 + -2*q^172 + -6*q^173 + -20*q^174 + -8*q^176 + -10*q^177 + -10*q^179 + 17*q^181 + 6*q^182 + 7*q^183 + 6*q^186 + -4*q^187 + -4*q^188 + 3*q^189 + 22*q^191 + -8*q^192 + -11*q^193 + 34*q^194 + 4*q^196 + 18*q^197 + -4*q^198 + -5*q^199 +  ...

-------------------------------------------------------
75D (old = 15A), dim = 1

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

-------------------------------------------------------
Gamma_0(76)
Weight 2

-------------------------------------------------------
J_0(76), dim = 8

-------------------------------------------------------
76A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/3 + Z/3) + 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|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.1104197507347356728 + 0.86537421842257502067e-8i
Omega-         = 0.31279514212266147737e-7 + 4.3504123761432226801i
L(1)           = 1.1104197507347357065
w1             = 0.55520985972761073028 + -2.1752061837447402479i
w2             = -1.1104197507347356728 + -0.86537421842257502067e-8i
c4             = 1023.9999844701722574 + -0.32125840064504508109e-4i
c6             = 32895.99924640448633 + -0.15244253763922209801e-2i
j              = -220752.85118055870595 + 0.40847228441316054724e-1i

HECKE EIGENFORM:
f(q) = q + 2*q^3 + -1*q^5 + -3*q^7 + 1*q^9 + 5*q^11 + -4*q^13 + -2*q^15 + -3*q^17 + -1*q^19 + -6*q^21 + 8*q^23 + -4*q^25 + -4*q^27 + -2*q^29 + 4*q^31 + 10*q^33 + 3*q^35 + 10*q^37 + -8*q^39 + 10*q^41 + 1*q^43 + -1*q^45 + -1*q^47 + 2*q^49 + -6*q^51 + -4*q^53 + -5*q^55 + -2*q^57 + 6*q^59 + -13*q^61 + -3*q^63 + 4*q^65 + -12*q^67 + 16*q^69 + 2*q^71 + 9*q^73 + -8*q^75 + -15*q^77 + 8*q^79 + -11*q^81 + -12*q^83 + 3*q^85 + -4*q^87 + 12*q^89 + 12*q^91 + 8*q^93 + 1*q^95 + -8*q^97 + 5*q^99 + -10*q^101 + -6*q^103 + 6*q^105 + 2*q^107 + 20*q^111 + -10*q^113 + -8*q^115 + -4*q^117 + 9*q^119 + 14*q^121 + 20*q^123 + 9*q^125 + 6*q^127 + 2*q^129 + -9*q^131 + 3*q^133 + 4*q^135 + -11*q^137 + -3*q^139 + -2*q^141 + -20*q^143 + 2*q^145 + 4*q^147 + -15*q^149 + 2*q^151 + -3*q^153 + -4*q^155 + -2*q^157 + -8*q^159 + -24*q^161 + -4*q^163 + -10*q^165 + -6*q^167 + 3*q^169 + -1*q^171 + 6*q^173 + 12*q^175 + 12*q^177 + 18*q^179 + 10*q^181 + -26*q^183 + -10*q^185 + -15*q^187 + 12*q^189 + 25*q^191 + 12*q^193 + 8*q^195 + 2*q^197 + -7*q^199 +  ...

-------------------------------------------------------
76B (old = 38A), dim = 1

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) + D(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
76C (old = 38B), 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) + B(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
76D (old = 19A), dim = 1

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

-------------------------------------------------------
Gamma_0(77)
Weight 2

-------------------------------------------------------
J_0(77), dim = 7

-------------------------------------------------------
77A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= C(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+         = 3.1997813627921974006 + -0.16678819553303405683e-7i
Omega-         = 0.11720500180318591729e-7 + -3.0143146352509871894i
L(1)           =
w1             = 1.5998906872563487905 + -1.5071573259649033713i
w2             = -1.5998906755358486101 + -1.507157309286083818i
c4             = -95.999999144069364493 + -0.72663781290204740356e-6i
c6             = -215.99997809572884653 + 0.31386432436528678735e-4i
j              = 1641.4397176311728843 + 0.25762710495519223528e-4i

HECKE EIGENFORM:
f(q) = q + -3*q^3 + -2*q^4 + -1*q^5 + -1*q^7 + 6*q^9 + -1*q^11 + 6*q^12 + -4*q^13 + 3*q^15 + 4*q^16 + 2*q^17 + -6*q^19 + 2*q^20 + 3*q^21 + -5*q^23 + -4*q^25 + -9*q^27 + 2*q^28 + 10*q^29 + 1*q^31 + 3*q^33 + 1*q^35 + -12*q^36 + -5*q^37 + 12*q^39 + -2*q^41 + -8*q^43 + 2*q^44 + -6*q^45 + 8*q^47 + -12*q^48 + 1*q^49 + -6*q^51 + 8*q^52 + -6*q^53 + 1*q^55 + 18*q^57 + 3*q^59 + -6*q^60 + -2*q^61 + -6*q^63 + -8*q^64 + 4*q^65 + -3*q^67 + -4*q^68 + 15*q^69 + 1*q^71 + 10*q^73 + 12*q^75 + 12*q^76 + 1*q^77 + 6*q^79 + -4*q^80 + 9*q^81 + 12*q^83 + -6*q^84 + -2*q^85 + -30*q^87 + -15*q^89 + 4*q^91 + 10*q^92 + -3*q^93 + 6*q^95 + -5*q^97 + -6*q^99 + 8*q^100 + -12*q^101 + -12*q^103 + -3*q^105 + -10*q^107 + 18*q^108 + 4*q^109 + 15*q^111 + -4*q^112 + -19*q^113 + 5*q^115 + -20*q^116 + -24*q^117 + -2*q^119 + 1*q^121 + 6*q^123 + -2*q^124 + 9*q^125 + 2*q^127 + 24*q^129 + 18*q^131 + -6*q^132 + 6*q^133 + 9*q^135 + -3*q^137 + -10*q^139 + -2*q^140 + -24*q^141 + 4*q^143 + 24*q^144 + -10*q^145 + -3*q^147 + 10*q^148 + -22*q^149 + 6*q^151 + 12*q^153 + -1*q^155 + -24*q^156 + 7*q^157 + 18*q^159 + 5*q^161 + 4*q^163 + 4*q^164 + -3*q^165 + -2*q^167 + 3*q^169 + -36*q^171 + 16*q^172 + 16*q^173 + 4*q^175 + -4*q^176 + -9*q^177 + 1*q^179 + 12*q^180 + 5*q^181 + 6*q^183 + 5*q^185 + -2*q^187 + -16*q^188 + 9*q^189 + 5*q^191 + 24*q^192 + 14*q^193 + -12*q^195 + -2*q^196 + 18*q^197 + -8*q^199 +  ...

-------------------------------------------------------
77B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= D(Z/2 + Z/2) + E(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+         = 2.6516148430476227099 + 0.63842790021559054589e-8i
Omega-         = 0.10517256541454162733e-7 + 1.7916996020430765859i
L(1)           = 1.3258074215238113588
w1             = -1.3258074267824396257 + -0.89584980421367779401i
w2             = -1.3258074162651830842 + 0.89584979782939879186i
c4             = -167.00002090181395409 + 0.72417215331381135636e-5i
c6             = -8188.9995082167202232 + -0.13926255953154040473e-3i
j              = 112.21996381691485781 + -0.17219671753081545992e-4i

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

-------------------------------------------------------
77C (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/5 + Z/5) + 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+         = 1.5489100712420961782 + -0.18070954202161598287e-8i
Omega-         = 0.31397121723326429794e-8 + 0.77645447077036919506i
L(1)           = 1.0326067141613974528
w1             = -0.77445503405119200292 + 0.38822723628873230764i
w2             = 0.31397121723326429794e-8 + 0.77645447077036919506i
c4             = 2368.0000973849706232 + 0.72324639522630321731e-4i
c6             = -532791.9991130481664 + -0.86778800739464868241e-2i
j              = -84.796681451723374342 + -0.52531721464036892975e-5i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + -2*q^4 + 3*q^5 + 1*q^7 + -2*q^9 + -1*q^11 + -2*q^12 + -4*q^13 + 3*q^15 + 4*q^16 + -6*q^17 + 2*q^19 + -6*q^20 + 1*q^21 + 3*q^23 + 4*q^25 + -5*q^27 + -2*q^28 + -6*q^29 + 5*q^31 + -1*q^33 + 3*q^35 + 4*q^36 + 11*q^37 + -4*q^39 + 6*q^41 + 8*q^43 + 2*q^44 + -6*q^45 + 4*q^48 + 1*q^49 + -6*q^51 + 8*q^52 + -6*q^53 + -3*q^55 + 2*q^57 + -9*q^59 + -6*q^60 + -10*q^61 + -2*q^63 + -8*q^64 + -12*q^65 + 5*q^67 + 12*q^68 + 3*q^69 + 9*q^71 + 2*q^73 + 4*q^75 + -4*q^76 + -1*q^77 + -10*q^79 + 12*q^80 + 1*q^81 + 12*q^83 + -2*q^84 + -18*q^85 + -6*q^87 + -3*q^89 + -4*q^91 + -6*q^92 + 5*q^93 + 6*q^95 + -1*q^97 + 2*q^99 + -8*q^100 + -12*q^101 + -4*q^103 + 3*q^105 + 6*q^107 + 10*q^108 + 20*q^109 + 11*q^111 + 4*q^112 + -3*q^113 + 9*q^115 + 12*q^116 + 8*q^117 + -6*q^119 + 1*q^121 + 6*q^123 + -10*q^124 + -3*q^125 + 2*q^127 + 8*q^129 + -6*q^131 + 2*q^132 + 2*q^133 + -15*q^135 + -3*q^137 + 14*q^139 + -6*q^140 + 4*q^143 + -8*q^144 + -18*q^145 + 1*q^147 + -22*q^148 + -6*q^149 + -10*q^151 + 12*q^153 + 15*q^155 + 8*q^156 + -13*q^157 + -6*q^159 + 3*q^161 + 20*q^163 + -12*q^164 + -3*q^165 + 6*q^167 + 3*q^169 + -4*q^171 + -16*q^172 + 4*q^175 + -4*q^176 + -9*q^177 + -15*q^179 + 12*q^180 + -7*q^181 + -10*q^183 + 33*q^185 + 6*q^187 + -5*q^189 + -27*q^191 + -8*q^192 + 14*q^193 + -12*q^195 + -2*q^196 + 18*q^197 + -16*q^199 +  ...

-------------------------------------------------------
77D (new) , dim = 2

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

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|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 2.1411728447098126266 + 0.43829345681872080065e-8i
Omega-         = 5.6240220516620567214 + -0.73073370901031162217e-7i
L(1)           = 0.53529321117745315777

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

-------------------------------------------------------
77E (old = 11A), 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/3 + Z/3) + C(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(78)
Weight 2

-------------------------------------------------------
J_0(78), dim = 11

-------------------------------------------------------
78A (new) , dim = 1

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

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+         = 1.4504359769074514833 + 0.62142526819053790156e-8i
Omega-         = 0.31897283918583857624e-7 + 0.79566430031931709606i
L(1)           = 0.7252179884537257483
w1             = -0.72521797250508378236 + 0.39783214705253220708i
w2             = 0.31897283918583857624e-7 + 0.79566430031931709606i
c4             = 937.00062234697823155 + 0.87813853692098468662e-3i
c6             = -598804.94109495063324 + -0.63847169854798500425e-1i
j              = -3.9736551002660101304 + -0.10348459847631936252e-4i

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

-------------------------------------------------------
78B (old = 39A), dim = 1

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

-------------------------------------------------------
78C (old = 39B), dim = 2

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

-------------------------------------------------------
78D (old = 26A), dim = 1

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

-------------------------------------------------------
78E (old = 26B), dim = 1

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

-------------------------------------------------------
Gamma_0(79)
Weight 2

-------------------------------------------------------
J_0(79), dim = 6

-------------------------------------------------------
79A (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+         = 2.9754001628123375083 + 0.55646653272550958937e-7i
Omega-         = 0.11890240040618198775e-7 + -2.0131555677160680437i
L(1)           =
w1             = -2.9754001628123375083 + -0.55646653272550958937e-7i
w2             = -0.11890240040618198775e-7 + 2.0131555677160680437i
c4             = 97.000000484462560288 + -0.2542838456497951499e-5i
c6             = -881.00000427853331498 + 0.26058985313828353304e-4i
j              = 11552.822438616438298 + 0.12799953802181603158e-2i

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

-------------------------------------------------------
79B (new) , dim = 5

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 83*983
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 2
ord((0)-(oo))  = 13
Torsion Bound  = 13
|L(1)/Omega|   = 1/13
Sha Bound      = 13

ANALYTIC INVARIANTS:

Omega+         = 4.7976166327098250404 + 0.22610169073107546886e-7i
Omega-         = 0.11686234379151203972e-5 + -104.73183967969688115i
L(1)           = 0.36904743328537116105

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

-------------------------------------------------------
Gamma_0(80)
Weight 2

-------------------------------------------------------
J_0(80), dim = 7

-------------------------------------------------------
80A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= B(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))  = 2
Torsion Bound  = 2^2
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 2.0189058148637293149 + -0.17840083925530415172e-7i
Omega-         = 0.96183644832373220601e-8 + 1.4844124570798571178i
L(1)           = 0.50472645371593234844
w1             = 2.0189058148637293149 + -0.17840083925530415172e-7i
w2             = -0.96183644832373220601e-8 + -1.4844124570798571178i
c4             = 336.00001370806698385 + 0.90112590282246095699e-5i
c6             = -5184.0003837794893279 + -0.19004539243973756861e-3i
j              = 5927.0403697119982678 + -0.10280208022412127224e-3i

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 +  ...

-------------------------------------------------------
80B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= A(Z/2) + C(Z/2) + D(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+         = 2.2741651898926992671 + 0.29064502288389672224e-7i
Omega-         = -2.8243751518349623073i
L(1)           = 1.1370825949463497264
w1             = 1.1370825949463496336 + 1.4121875904497322978i
w2             = 1.1370825949463496336 + -1.4121875613852300094i
c4             = -175.99999729163405107 + -0.41935050520965482745e-6i
c6             = 2368.0000660912793071 + -0.19677166420576804769e-3i
j              = 851.83995595091641514 + 0.7486817644156688164e-4i

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 +  ...

-------------------------------------------------------
80C (old = 40A), dim = 1

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

-------------------------------------------------------
80D (old = 20A), 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 + Z/2) + B(Z/2 + Z/2^2) + C(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(81)
Weight 2

-------------------------------------------------------
J_0(81), dim = 4

-------------------------------------------------------
81A (new) , dim = 2

CONGRUENCES:
Modular Degree = 3
Ker(ModPolar)  = Z/3 + Z/3
= B(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+         = 2.6851071472476092617 + 0.14305815168260531415e-7i
Omega-         = 8.0553214581770860172 + -0.33207448684928358497e-7i
L(1)           = 0.89503571574920309995

HECKE EIGENFORM:
a^2-3 = 0,
f(q) = q + a*q^2 + 1*q^4 + -a*q^5 + 2*q^7 + -a*q^8 + -3*q^10 + -2*a*q^11 + -1*q^13 + 2*a*q^14 + -5*q^16 + 3*a*q^17 + 2*q^19 + -a*q^20 + -6*q^22 + 2*a*q^23 + -2*q^25 + -a*q^26 + 2*q^28 + a*q^29 + 8*q^31 + -3*a*q^32 + 9*q^34 + -2*a*q^35 + -7*q^37 + 2*a*q^38 + 3*q^40 + -4*a*q^41 + 2*q^43 + -2*a*q^44 + 6*q^46 + 4*a*q^47 + -3*q^49 + -2*a*q^50 + -1*q^52 + 6*q^55 + -2*a*q^56 + 3*q^58 + 8*a*q^59 + -7*q^61 + 8*a*q^62 + 1*q^64 + a*q^65 + -10*q^67 + 3*a*q^68 + -6*q^70 + -6*a*q^71 + -7*q^73 + -7*a*q^74 + 2*q^76 + -4*a*q^77 + 2*q^79 + 5*a*q^80 + -12*q^82 + -8*a*q^83 + -9*q^85 + 2*a*q^86 + 6*q^88 + -3*a*q^89 + -2*q^91 + 2*a*q^92 + 12*q^94 + -2*a*q^95 + 2*q^97 + -3*a*q^98 + -2*q^100 + 4*a*q^101 + 8*q^103 + a*q^104 + 11*q^109 + 6*a*q^110 + -10*q^112 + -a*q^113 + -6*q^115 + a*q^116 + 24*q^118 + 6*a*q^119 + 1*q^121 + -7*a*q^122 + 8*q^124 + 7*a*q^125 + 2*q^127 + 7*a*q^128 + 3*q^130 + 2*a*q^131 + 4*q^133 + -10*a*q^134 + -9*q^136 + a*q^137 + 8*q^139 + -2*a*q^140 + -18*q^142 + 2*a*q^143 + -3*q^145 + -7*a*q^146 + -7*q^148 + 5*a*q^149 + 20*q^151 + -2*a*q^152 + -12*q^154 + -8*a*q^155 + 17*q^157 + 2*a*q^158 + 9*q^160 + 4*a*q^161 + -16*q^163 + -4*a*q^164 + -24*q^166 + -10*a*q^167 + -12*q^169 + -9*a*q^170 + 2*q^172 + -11*a*q^173 + -4*q^175 + 10*a*q^176 + -9*q^178 + 12*a*q^179 + 2*q^181 + -2*a*q^182 + -6*q^184 + 7*a*q^185 + -18*q^187 + 4*a*q^188 + -6*q^190 + 10*a*q^191 + -1*q^193 + 2*a*q^194 + -3*q^196 + -3*a*q^197 + 20*q^199 + 2*a*q^200 +  ...

-------------------------------------------------------
81B (old = 27A), dim = 1

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

-------------------------------------------------------
Gamma_0(82)
Weight 2

-------------------------------------------------------
J_0(82), dim = 9

-------------------------------------------------------
82A (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          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.5944974993964862429 + 0.34769476929079398865e-7i
Omega-         = 0.3253533699242214192e-7 + -2.2320363601497100878i
L(1)           =
w1             = -2.5944974993964862429 + -0.34769476929079398865e-7i
w2             = -0.3253533699242214192e-7 + 2.2320363601497100878i
c4             = 73.00000136560983519 + -0.41682056997553249746e-5i
c6             = -325.00000108900454525 + 0.29938207379125032591e-4i
j              = 2372.0548343568577317 + -0.11439434412485706975e-4i

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

-------------------------------------------------------
82B (new) , dim = 2

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

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

ANALYTIC INVARIANTS:

Omega+         = 5.6738618176736990532 + -0.89299769345101816803e-7i
Omega-         = 2.1997475613345965259 + -0.24571759910111332213e-7i
L(1)           = 0.81055168823909996514

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

-------------------------------------------------------
82C (old = 41A), dim = 3

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = 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)

-------------------------------------------------------
Gamma_0(83)
Weight 2

-------------------------------------------------------
J_0(83), dim = 7

-------------------------------------------------------
83A (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+         = 3.3744688903593837546 + 0.25725220596454439734e-7i
Omega-         = 0.37070245831548955195e-7 + -3.9143287060093718982i
L(1)           =
w1             = -1.6872344637148147931 + 1.9571643401420756509i
w2             = 1.6872344266445689615 + 1.9571643658672962473i
c4             = -46.999996516321339092 + 0.17284774498275915656e-5i
c6             = 199.00001829773587223 + -0.79959407979441374603e-5i
j              = 1250.8793777575899465 + -0.10350118340606903039e-4i

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

-------------------------------------------------------
83B (new) , dim = 6

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^2*197*11497
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 41
Torsion Bound  = 41
|L(1)/Omega|   = 2/41
Sha Bound      = 2*41

ANALYTIC INVARIANTS:

Omega+         = 21.737382998403254292 + 0.62467280983047449512e-6i
Omega-         = 40.711524855482950974 + -0.1957199371852723148e-5i
L(1)           = 1.060360146263573818

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

-------------------------------------------------------
Gamma_0(84)
Weight 2

-------------------------------------------------------
J_0(84), dim = 11

-------------------------------------------------------
84A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= B(Z/2) + C(Z/3 + Z/3) + D(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+         = 1.944923987789871479 + 0.17908303343310002392e-8i
Omega-         = 0.27142216685446192753e-7 + 3.9315932099388130585i
L(1)           = 0.9724619938949357399
w1             = -0.97246198032382739677 + 1.9657966040739913621i
w2             = 1.944923987789871479 + 0.17908303343310002392e-8i
c4             = 63.999990238013022608 + -0.24325543251205522836e-5i
c6             = 2079.9998585457703694 + 0.32588979911979048519e-4i
j              = -111.45574415923994748 + 0.17246367640570825564e-4i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + 4*q^5 + -1*q^7 + 1*q^9 + 2*q^11 + -6*q^13 + -4*q^15 + -4*q^17 + -4*q^19 + 1*q^21 + 2*q^23 + 11*q^25 + -1*q^27 + -2*q^29 + -2*q^33 + -4*q^35 + 2*q^37 + 6*q^39 + -4*q^43 + 4*q^45 + 12*q^47 + 1*q^49 + 4*q^51 + -6*q^53 + 8*q^55 + 4*q^57 + -8*q^59 + 6*q^61 + -1*q^63 + -24*q^65 + -8*q^67 + -2*q^69 + 14*q^71 + -2*q^73 + -11*q^75 + -2*q^77 + 12*q^79 + 1*q^81 + -4*q^83 + -16*q^85 + 2*q^87 + 6*q^91 + -16*q^95 + -2*q^97 + 2*q^99 + 16*q^101 + -16*q^103 + 4*q^105 + 18*q^107 + -2*q^109 + -2*q^111 + 10*q^113 + 8*q^115 + -6*q^117 + 4*q^119 + -7*q^121 + 24*q^125 + 12*q^127 + 4*q^129 + 4*q^131 + 4*q^133 + -4*q^135 + -2*q^137 + 4*q^139 + -12*q^141 + -12*q^143 + -8*q^145 + -1*q^147 + -6*q^149 + -8*q^151 + -4*q^153 + 14*q^157 + 6*q^159 + -2*q^161 + -16*q^163 + -8*q^165 + 4*q^167 + 23*q^169 + -4*q^171 + 16*q^173 + -11*q^175 + 8*q^177 + -18*q^179 + -6*q^181 + -6*q^183 + 8*q^185 + -8*q^187 + 1*q^189 + -18*q^191 + -10*q^193 + 24*q^195 + -22*q^197 + -16*q^199 +  ...

-------------------------------------------------------
84B (new) , dim = 1

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

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

ANALYTIC INVARIANTS:

Omega+         = 2.1903171168856140865 + -0.27516594202681626479e-7i
Omega-         = 2.3898781114274760204i
L(1)           = 1.0951585584428071297
w1             = 1.0951585584428070433 + -1.1949390694720351116i
w2             = -1.0951585584428070433 + -1.1949390419554409089i
c4             = -320.0000233363694952 + -0.48379890137689507008e-5i
c6             = 1951.9994725981936358 + 0.34271131871968406397e-3i
j              = 1547.9970989830001709 + -0.49308146102187968645e-4i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 1*q^7 + 1*q^9 + -6*q^11 + 2*q^13 + -4*q^19 + 1*q^21 + -6*q^23 + -5*q^25 + 1*q^27 + 6*q^29 + 8*q^31 + -6*q^33 + 2*q^37 + 2*q^39 + 12*q^41 + -4*q^43 + 12*q^47 + 1*q^49 + -6*q^53 + -4*q^57 + -10*q^61 + 1*q^63 + 8*q^67 + -6*q^69 + 6*q^71 + -10*q^73 + -5*q^75 + -6*q^77 + -4*q^79 + 1*q^81 + -12*q^83 + 6*q^87 + 12*q^89 + 2*q^91 + 8*q^93 + -10*q^97 + -6*q^99 + -12*q^101 + 8*q^103 + -6*q^107 + 14*q^109 + 2*q^111 + -6*q^113 + 2*q^117 + 25*q^121 + 12*q^123 + -4*q^127 + -4*q^129 + 12*q^131 + -4*q^133 + 6*q^137 + -4*q^139 + 12*q^141 + -12*q^143 + 1*q^147 + -6*q^149 + 8*q^151 + 14*q^157 + -6*q^159 + -6*q^161 + -16*q^163 + -12*q^167 + -9*q^169 + -4*q^171 + -12*q^173 + -5*q^175 + 6*q^179 + 2*q^181 + -10*q^183 + 1*q^189 + 6*q^191 + -10*q^193 + -6*q^197 + -16*q^199 +  ...

-------------------------------------------------------
84C (old = 42A), 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) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
84D (old = 21A), dim = 1

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

-------------------------------------------------------
84E (old = 14A), dim = 1

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
= B(Z/3 + Z/3) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(85)
Weight 2

-------------------------------------------------------
J_0(85), dim = 7

-------------------------------------------------------
85A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= B(Z/2) + C(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|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 1.3976921916701589205 + -0.24558841293826796351e-7i
Omega-         = 0.38859733880327535563e-7 + 2.6659289563028220611i
L(1)           = 0.69884609583507956812
w1             = -0.38859733880327535563e-7 + -2.6659289563028220611i
w2             = -1.3976921916701589205 + 0.24558841293826796351e-7i
c4             = 409.00003090141882664 + 0.28724194375880790799e-4i
c6             = 8227.0009495019969282 + 0.86827148557059029885e-3i
j              = 160983.4241475886256 + 0.57505958077998276043e-2i

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

-------------------------------------------------------
85B (new) , dim = 2

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

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

ANALYTIC INVARIANTS:

Omega+         = 9.172799921521473359 + -0.46684376737713239064e-6i
Omega-         = 3.5341481683158189452 + 0.14566350101657152437e-6i
L(1)           =

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

-------------------------------------------------------
85C (new) , dim = 2

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

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^2*3
#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+         = 1.7615966450062692622 + 0.74928686142766881355e-7i
Omega-         = 5.5016453058800420477 + -0.80043252792990961598e-7i
L(1)           = 0.58719888166875695192

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

-------------------------------------------------------
85D (old = 17A), dim = 1

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

-------------------------------------------------------
Gamma_0(86)
Weight 2

-------------------------------------------------------
J_0(86), dim = 10

-------------------------------------------------------
86A (new) , dim = 2

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

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 3*7
#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+         = 1.7306087996371219596 + -0.24560834849528397516e-7i
Omega-         = 2.4506392456563807397 + 0.2250317571530593515e-6i
L(1)           = 0.5768695998790407113

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

-------------------------------------------------------
86B (new) , dim = 2

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

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

ANALYTIC INVARIANTS:

Omega+         = 3.8955613636236507195 + -0.1792193905680176961e-6i
Omega-         = 5.2183452272284128703 + -0.2331870866736184466e-6i
L(1)           = 1.7707097107380249282

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

-------------------------------------------------------
86C (old = 43A), dim = 1

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

-------------------------------------------------------
86D (old = 43B), dim = 2

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

-------------------------------------------------------
Gamma_0(87)
Weight 2

-------------------------------------------------------
J_0(87), dim = 9

-------------------------------------------------------
87A (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))  = 5
Torsion Bound  = 5
|L(1)/Omega|   = 1/5
Sha Bound      = 5

ANALYTIC INVARIANTS:

Omega+         = 7.1617180426029034675 + -0.12590962333369740047e-7i
Omega-         = 10.611938296320621067 + -0.11994386788310415267e-6i
L(1)           = 1.4323436085205806957

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

-------------------------------------------------------
87B (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^2*23
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*23 + Z/2*23
= A(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/23 + Z/23)

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|   = 1/2^3
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 4.6025098679259147966 + 0.30391969643585064662e-6i
Omega-         = 0.12812275677584557495e-7 + -1.4049255444052443279i
L(1)           = 0.57531373349074060388

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

-------------------------------------------------------
87C (old = 29A), dim = 2

CONGRUENCES:
Modular Degree = 23
Ker(ModPolar)  = Z/23 + Z/23
= B(Z/23 + Z/23)

-------------------------------------------------------
Gamma_0(88)
Weight 2

-------------------------------------------------------
J_0(88), dim = 9

-------------------------------------------------------
88A (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)

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+         = 4.2525297538883908241 + 0.1428191804959661397e-6i
Omega-         = 0.87868549911852753563e-7 + -1.6554235701342178709i
L(1)           =
w1             = 2.1262648330099204561 + 0.82771185647669918345i
w2             = 0.87868549911852753563e-7 + -1.6554235701342178709i
c4             = 192.00005127548002532 + -0.43201388556030256685e-4i
c6             = -3456.0006598876438333 + 0.10280465065189862582e-2i
j              = -2513.4571322803473745 + 0.4940905249703958173e-3i

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 +  ...

-------------------------------------------------------
88B (new) , dim = 2

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)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 17
#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+         = 2.3224770953857348161 + 0.55744759523109788646e-7i
Omega-         = 2.8047736015628346693 + -0.47667352710968701477e-7i
L(1)           = 0.58061927384643387129

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 +  ...

-------------------------------------------------------
88C (old = 44A), 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) + B(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
88D (old = 11A), dim = 1

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) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(89)
Weight 2

-------------------------------------------------------
J_0(89), dim = 7

-------------------------------------------------------
89A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = 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))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 5.5526264528749013185 + 0.11195689292950407542e-7i
Omega-         = 0.34602742926410553208e-7 + 2.2993520214485766087i
L(1)           =
w1             = 2.776313209136079196 + -1.1496760051264436579i
w2             = -0.34602742926410553208e-7 + -2.2993520214485766087i
c4             = 49.000001417274073947 + 0.38203562387863256148e-5i
c6             = -521.00003888320989726 + -0.33721752384604993813e-4i
j              = -1321.8987306024815999 + -0.24369422148729809455e-3i

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

-------------------------------------------------------
89B (new) , dim = 1

CONGRUENCES:
Modular Degree = 5
Ker(ModPolar)  = Z/5 + Z/5
= C(Z/5 + Z/5)

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+         = 2.8446094991290743626 + -0.20621594456207532047e-6i
Omega-         = 0.23487125802544257885e-6 + -2.1848938560258621989i
L(1)           = 1.4223047495645409186
w1             = -1.422304867000166194 + 1.0924470311209033805i
w2             = 1.4223046321289081686 + 1.0924468249049588184i
c4             = -167.00004018641118725 + -0.73995473763257172484e-4i
c6             = -3005.0006891779488377 + 0.16509307715789179782e-2i
j              = 587.98937113942059895 + 0.94187228877223004892e-3i

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

-------------------------------------------------------
89C (new) , dim = 5

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^4*5*6689
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 11
Torsion Bound  = 11
|L(1)/Omega|   = 2/11
Sha Bound      = 2*11

ANALYTIC INVARIANTS:

Omega+         = 2.2910867618438222407 + 0.20037821729405955001e-6i
Omega-         = 0.83258018815660735416e-5 + -95.271913535000932756i
L(1)           = 0.41656122942615109149

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

-------------------------------------------------------
Gamma_0(90)
Weight 2

-------------------------------------------------------
J_0(90), dim = 11

-------------------------------------------------------
90A (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)

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+         = 2.4599352876681328026 + -0.47180280474585636975e-7i
Omega-         = 0.10980065181578604953e-7 + -2.2927122976272909083i
L(1)           = 0.81997842922271108503
w1             = 1.2299676493240989921 + -1.1463561724037856914i
w2             = -1.2299676383440338105 + -1.1463561252235052169i
c4             = -279.0000318720693647 + -0.12305175216428765585e-4i
c6             = -1268.9999199679590079 + 0.36539521456549260447e-3i
j              = 1608.7140520659004509 + 0.7864585874880782435e-4i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 1*q^4 + 1*q^5 + 2*q^7 + -1*q^8 + -1*q^10 + 6*q^11 + -4*q^13 + -2*q^14 + 1*q^16 + -6*q^17 + -4*q^19 + 1*q^20 + -6*q^22 + 1*q^25 + 4*q^26 + 2*q^28 + -6*q^29 + -4*q^31 + -1*q^32 + 6*q^34 + 2*q^35 + 8*q^37 + 4*q^38 + -1*q^40 + 8*q^43 + 6*q^44 + -3*q^49 + -1*q^50 + -4*q^52 + -6*q^53 + 6*q^55 + -2*q^56 + 6*q^58 + 6*q^59 + 2*q^61 + 4*q^62 + 1*q^64 + -4*q^65 + -4*q^67 + -6*q^68 + -2*q^70 + -12*q^71 + -10*q^73 + -8*q^74 + -4*q^76 + 12*q^77 + -4*q^79 + 1*q^80 + 12*q^83 + -6*q^85 + -8*q^86 + -6*q^88 + 12*q^89 + -8*q^91 + -4*q^95 + 2*q^97 + 3*q^98 + 1*q^100 + -6*q^101 + 2*q^103 + 4*q^104 + 6*q^106 + 12*q^107 + 2*q^109 + -6*q^110 + 2*q^112 + 6*q^113 + -6*q^116 + -6*q^118 + -12*q^119 + 25*q^121 + -2*q^122 + -4*q^124 + 1*q^125 + 2*q^127 + -1*q^128 + 4*q^130 + -6*q^131 + -8*q^133 + 4*q^134 + 6*q^136 + 6*q^137 + 20*q^139 + 2*q^140 + 12*q^142 + -24*q^143 + -6*q^145 + 10*q^146 + 8*q^148 + 6*q^149 + -16*q^151 + 4*q^152 + -12*q^154 + -4*q^155 + -4*q^157 + 4*q^158 + -1*q^160 + 20*q^163 + -12*q^166 + -24*q^167 + 3*q^169 + 6*q^170 + 8*q^172 + 18*q^173 + 2*q^175 + 6*q^176 + -12*q^178 + 6*q^179 + 2*q^181 + 8*q^182 + 8*q^185 + -36*q^187 + 4*q^190 + 12*q^191 + -10*q^193 + -2*q^194 + -3*q^196 + -18*q^197 + -16*q^199 + -1*q^200 +  ...

-------------------------------------------------------
90B (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)

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+         = 3.9710942878902952892 + -0.20495150292043107267e-7i
Omega-         = 0.19543207022179119038e-7 + 1.4202442863684492622i
L(1)           = 1.3236980959634317807
w1             = 1.9855471341735441335 + -0.7101221534317997771i
w2             = -0.19543207022179119038e-7 + -1.4202442863684492622i
c4             = 369.00007114404491273 + 0.21371055945706665188e-4i
c6             = -8073.001868919564853 + -0.62325709335744428444e-3i
j              = -5815.2123044825134373 + -0.49102571955794076771e-3i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + -1*q^5 + 2*q^7 + 1*q^8 + -1*q^10 + -6*q^11 + -4*q^13 + 2*q^14 + 1*q^16 + 6*q^17 + -4*q^19 + -1*q^20 + -6*q^22 + 1*q^25 + -4*q^26 + 2*q^28 + 6*q^29 + -4*q^31 + 1*q^32 + 6*q^34 + -2*q^35 + 8*q^37 + -4*q^38 + -1*q^40 + 8*q^43 + -6*q^44 + -3*q^49 + 1*q^50 + -4*q^52 + 6*q^53 + 6*q^55 + 2*q^56 + 6*q^58 + -6*q^59 + 2*q^61 + -4*q^62 + 1*q^64 + 4*q^65 + -4*q^67 + 6*q^68 + -2*q^70 + 12*q^71 + -10*q^73 + 8*q^74 + -4*q^76 + -12*q^77 + -4*q^79 + -1*q^80 + -12*q^83 + -6*q^85 + 8*q^86 + -6*q^88 + -12*q^89 + -8*q^91 + 4*q^95 + 2*q^97 + -3*q^98 + 1*q^100 + 6*q^101 + 2*q^103 + -4*q^104 + 6*q^106 + -12*q^107 + 2*q^109 + 6*q^110 + 2*q^112 + -6*q^113 + 6*q^116 + -6*q^118 + 12*q^119 + 25*q^121 + 2*q^122 + -4*q^124 + -1*q^125 + 2*q^127 + 1*q^128 + 4*q^130 + 6*q^131 + -8*q^133 + -4*q^134 + 6*q^136 + -6*q^137 + 20*q^139 + -2*q^140 + 12*q^142 + 24*q^143 + -6*q^145 + -10*q^146 + 8*q^148 + -6*q^149 + -16*q^151 + -4*q^152 + -12*q^154 + 4*q^155 + -4*q^157 + -4*q^158 + -1*q^160 + 20*q^163 + -12*q^166 + 24*q^167 + 3*q^169 + -6*q^170 + 8*q^172 + -18*q^173 + 2*q^175 + -6*q^176 + -12*q^178 + -6*q^179 + 2*q^181 + -8*q^182 + -8*q^185 + -36*q^187 + 4*q^190 + -12*q^191 + -10*q^193 + 2*q^194 + -3*q^196 + 18*q^197 + -16*q^199 + 1*q^200 +  ...

-------------------------------------------------------
90C (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) + D(Z/2 + Z/2) + E(Z/2 + Z/2) + F(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*3
|L(1)/Omega|   = 1
Sha Bound      = 2^4*3^2

ANALYTIC INVARIANTS:

Omega+         = 1.3375960815519764481 + 0.87040889539819281318e-47i
Omega-         = 0.25489470578119236432e-56 + 1.9352482235262253433i
L(1)           = 1.3375960815519764481
w1             = 0.66879804077598822405 + 0.96762411176311267165i
w2             = 0.66879804077598822405 + -0.96762411176311267165i
c4             = -639.00014863295366801 + -0.69884389377188435209e-10i
c6             = 49598.987373190416236 + 0.85597088996443823225e-7i
j              = 165.6997178528130703 + -0.46792896452983186891e-9i

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

-------------------------------------------------------
90D (old = 45A), 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) + E(Z/2^2 + Z/2^2) + F(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
90E (old = 30A), 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) + F(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
90F (old = 15A), dim = 1

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) + C(Z/2^2 + Z/2^2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(91)
Weight 2

-------------------------------------------------------
J_0(91), dim = 7

-------------------------------------------------------
91A (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          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 3.8972602878343825061 + -0.10014949392452581358e-6i
Omega-         = 0.64786840918646705998e-7 + -3.3385348540260465714i
L(1)           =
w1             = -1.9486301763106117124 + 1.6692674770877702479i
w2             = 1.9486301115237707937 + 1.6692673769382763234i
c4             = -48.000027519567471012 + -0.37852022427671631613e-5i
c6             = -215.99988846687329039 + 0.5094403314447037393e-4i
j              = 1215.2976958669891839 + 0.25539284711499401317e-3i

HECKE EIGENFORM:
f(q) = q + -2*q^2 + 2*q^4 + -3*q^5 + -1*q^7 + -3*q^9 + 6*q^10 + -6*q^11 + -1*q^13 + 2*q^14 + -4*q^16 + 4*q^17 + 6*q^18 + 5*q^19 + -6*q^20 + 12*q^22 + 3*q^23 + 4*q^25 + 2*q^26 + -2*q^28 + -5*q^29 + -3*q^31 + 8*q^32 + -8*q^34 + 3*q^35 + -6*q^36 + -4*q^37 + -10*q^38 + -6*q^41 + -1*q^43 + -12*q^44 + 9*q^45 + -6*q^46 + 7*q^47 + 1*q^49 + -8*q^50 + -2*q^52 + -9*q^53 + 18*q^55 + 10*q^58 + 8*q^59 + -10*q^61 + 6*q^62 + 3*q^63 + -8*q^64 + 3*q^65 + -6*q^67 + 8*q^68 + -6*q^70 + -8*q^71 + -13*q^73 + 8*q^74 + 10*q^76 + 6*q^77 + 3*q^79 + 12*q^80 + 9*q^81 + 12*q^82 + 15*q^83 + -12*q^85 + 2*q^86 + 3*q^89 + -18*q^90 + 1*q^91 + 6*q^92 + -14*q^94 + -15*q^95 + 7*q^97 + -2*q^98 + 18*q^99 + 8*q^100 + -14*q^101 + -4*q^103 + 18*q^106 + -4*q^107 + -2*q^109 + -36*q^110 + 4*q^112 + -3*q^113 + -9*q^115 + -10*q^116 + 3*q^117 + -16*q^118 + -4*q^119 + 25*q^121 + 20*q^122 + -6*q^124 + 3*q^125 + -6*q^126 + -4*q^127 + -6*q^130 + 8*q^131 + -5*q^133 + 12*q^134 + 4*q^137 + -18*q^139 + 6*q^140 + 16*q^142 + 6*q^143 + 12*q^144 + 15*q^145 + 26*q^146 + -8*q^148 + -18*q^149 + -12*q^153 + -12*q^154 + 9*q^155 + -8*q^157 + -6*q^158 + -24*q^160 + -3*q^161 + -18*q^162 + -4*q^163 + -12*q^164 + -30*q^166 + 5*q^167 + 1*q^169 + 24*q^170 + -15*q^171 + -2*q^172 + -8*q^173 + -4*q^175 + 24*q^176 + -6*q^178 + 23*q^179 + 18*q^180 + 14*q^181 + -2*q^182 + 12*q^185 + -24*q^187 + 14*q^188 + 30*q^190 + -8*q^191 + 22*q^193 + -14*q^194 + 2*q^196 + 2*q^197 + -36*q^198 + 4*q^199 +  ...

-------------------------------------------------------
91B (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) + D(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+         = 6.0394915561050794028 + 0.24752083083479746952e-6i
Omega-         = 0.36917166096903576805e-6 + -1.4504074573030941961i
L(1)           =
w1             = 3.0197455934667092169 + 0.72520385241196251544i
w2             = 0.36917166096903576805e-6 + -1.4504074573030941961i
c4             = 351.99961494784144406 + -0.35886918162985700436e-3i
c6             = -6615.9891861607405681 + 0.10084409138748052168e-1i
j              = -479275.31689885578506 + 1.3409402909267753207i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -2*q^4 + -3*q^5 + 1*q^7 + 1*q^9 + 4*q^12 + 1*q^13 + 6*q^15 + 4*q^16 + -6*q^17 + -7*q^19 + 6*q^20 + -2*q^21 + 3*q^23 + 4*q^25 + 4*q^27 + -2*q^28 + -9*q^29 + 5*q^31 + -3*q^35 + -2*q^36 + 2*q^37 + -2*q^39 + -6*q^41 + -1*q^43 + -3*q^45 + 3*q^47 + -8*q^48 + 1*q^49 + 12*q^51 + -2*q^52 + -9*q^53 + 14*q^57 + -12*q^60 + -10*q^61 + 1*q^63 + -8*q^64 + -3*q^65 + 14*q^67 + 12*q^68 + -6*q^69 + -6*q^71 + 11*q^73 + -8*q^75 + 14*q^76 + -1*q^79 + -12*q^80 + -11*q^81 + 3*q^83 + 4*q^84 + 18*q^85 + 18*q^87 + 15*q^89 + 1*q^91 + -6*q^92 + -10*q^93 + 21*q^95 + -1*q^97 + -8*q^100 + -4*q^103 + 6*q^105 + -12*q^107 + -8*q^108 + -16*q^109 + -4*q^111 + 4*q^112 + 9*q^113 + -9*q^115 + 18*q^116 + 1*q^117 + -6*q^119 + -11*q^121 + 12*q^123 + -10*q^124 + 3*q^125 + -16*q^127 + 2*q^129 + -12*q^131 + -7*q^133 + -12*q^135 + 6*q^137 + -4*q^139 + 6*q^140 + -6*q^141 + 4*q^144 + 27*q^145 + -2*q^147 + -4*q^148 + -10*q^151 + -6*q^153 + -15*q^155 + 4*q^156 + 14*q^157 + 18*q^159 + 3*q^161 + -16*q^163 + 12*q^164 + -15*q^167 + 1*q^169 + -7*q^171 + 2*q^172 + 6*q^173 + 4*q^175 + 15*q^179 + 6*q^180 + -16*q^181 + 20*q^183 + -6*q^185 + -6*q^188 + 4*q^189 + 24*q^191 + 16*q^192 + -22*q^193 + 6*q^195 + -2*q^196 + 6*q^197 + 2*q^199 +  ...

-------------------------------------------------------
91C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(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))  = 7
Torsion Bound  = 7
|L(1)/Omega|   = 2/7
Sha Bound      = 2*7

ANALYTIC INVARIANTS:

Omega+         = 3.7562285084362939393 + 0.10775368531125944152e-6i
Omega-         = 7.1018837887441466378 + 0.87971826424950660338e-6i
L(1)           = 1.0732081452675129957

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

-------------------------------------------------------
91D (new) , dim = 3

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

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*79
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^3
Torsion Bound  = 2^4
|L(1)/Omega|   = 1/2^3
Sha Bound      = 2^5

ANALYTIC INVARIANTS:

Omega+         = 3.3583066125608473615 + -0.1132459089085317099e-6i
Omega-         = 0.36088305604717439373e-6 + -8.5769827763496540226i
L(1)           = 0.41978832657010615886

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

-------------------------------------------------------
Gamma_0(92)
Weight 2

-------------------------------------------------------
J_0(92), dim = 10

-------------------------------------------------------
92A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2
Ker(ModPolar)  = 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))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 3.4103925449775886921 + -0.74893970504851144057e-45i
Omega-         = -3.0187970799904691357i
L(1)           = 1.136797514992529564
w1             = -1.705196272488794346 + -1.5093985399952345679i
w2             = -1.705196272488794346 + 1.5093985399952345679i
c4             = -79.999993240575131029 + -0.15681899839989281301e-9i
c6             = -352.00012550911950813 + 0.46510356956064015627e-7i
j              = 1391.3040857894158588 + 0.73233790221849255888e-7i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 2*q^7 + -2*q^9 + -1*q^13 + -6*q^17 + 2*q^19 + 2*q^21 + -1*q^23 + -5*q^25 + -5*q^27 + -3*q^29 + 5*q^31 + 8*q^37 + -1*q^39 + 3*q^41 + 8*q^43 + 9*q^47 + -3*q^49 + -6*q^51 + 6*q^53 + 2*q^57 + -12*q^59 + 14*q^61 + -4*q^63 + 8*q^67 + -1*q^69 + -15*q^71 + -7*q^73 + -5*q^75 + -10*q^79 + 1*q^81 + 6*q^83 + -3*q^87 + -2*q^91 + 5*q^93 + -10*q^97 + 6*q^101 + 2*q^103 + -6*q^107 + -16*q^109 + 8*q^111 + 18*q^113 + 2*q^117 + -12*q^119 + -11*q^121 + 3*q^123 + 11*q^127 + 8*q^129 + 21*q^131 + 4*q^133 + -12*q^137 + 11*q^139 + 9*q^141 + -3*q^147 + 6*q^149 + -7*q^151 + 12*q^153 + -4*q^157 + 6*q^159 + -2*q^161 + -1*q^163 + 12*q^167 + -12*q^169 + -4*q^171 + 6*q^173 + -10*q^175 + -12*q^177 + -9*q^179 + -16*q^181 + 14*q^183 + -10*q^189 + -7*q^193 + -15*q^197 + -4*q^199 +  ...

-------------------------------------------------------
92B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/3 + Z/3) + 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+         = 4.7070869005338762801 + 0.40266205653213463425e-6i
Omega-         = 0.43911371027781832949e-6 + 2.1965831504332267014i
L(1)           =
w1             = -2.3535432307100830011 + 1.0982913738855850847i
w2             = 0.43911371027781832949e-6 + 2.1965831504332267014i
c4             = 47.99996239769240897 + 0.74400283223201586029e-4i
c6             = -864.00023020811244705 + -0.45304722679406284731e-3i
j              = -300.52072203526770539 + -0.12704851075470168172e-2i

HECKE EIGENFORM:
f(q) = q + -3*q^3 + -2*q^5 + -4*q^7 + 6*q^9 + 2*q^11 + -5*q^13 + 6*q^15 + 4*q^17 + -2*q^19 + 12*q^21 + 1*q^23 + -1*q^25 + -9*q^27 + -7*q^29 + -3*q^31 + -6*q^33 + 8*q^35 + 2*q^37 + 15*q^39 + -9*q^41 + -8*q^43 + -12*q^45 + 9*q^47 + 9*q^49 + -12*q^51 + 2*q^53 + -4*q^55 + 6*q^57 + -2*q^61 + -24*q^63 + 10*q^65 + 14*q^67 + -3*q^69 + -3*q^71 + -3*q^73 + 3*q^75 + -8*q^77 + -6*q^79 + 9*q^81 + 8*q^83 + -8*q^85 + 21*q^87 + 12*q^89 + 20*q^91 + 9*q^93 + 4*q^95 + 12*q^99 + 2*q^101 + -8*q^103 + -24*q^105 + 2*q^107 + -6*q^111 + -20*q^113 + -2*q^115 + -30*q^117 + -16*q^119 + -7*q^121 + 27*q^123 + 12*q^125 + -17*q^127 + 24*q^129 + -15*q^131 + 8*q^133 + 18*q^135 + -12*q^137 + -1*q^139 + -27*q^141 + -10*q^143 + 14*q^145 + -27*q^147 + 14*q^149 + 13*q^151 + 24*q^153 + 6*q^155 + -6*q^159 + -4*q^161 + -5*q^163 + 12*q^165 + -8*q^167 + 12*q^169 + -12*q^171 + -18*q^173 + 4*q^175 + -25*q^179 + 18*q^181 + 6*q^183 + -4*q^185 + 8*q^187 + 36*q^189 + 2*q^191 + 17*q^193 + -30*q^195 + 9*q^197 + -10*q^199 +  ...

-------------------------------------------------------
92C (old = 46A), dim = 1

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

-------------------------------------------------------
92D (old = 23A), dim = 2

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

-------------------------------------------------------
Gamma_0(93)
Weight 2

-------------------------------------------------------
J_0(93), dim = 9

-------------------------------------------------------
93A (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)

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+         = 18.142294204508512133 + -0.51289275343542554346e-5i
Omega-         = 3.7785484100995385891 + 0.41463229399364552799e-6i
L(1)           =

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

-------------------------------------------------------
93B (new) , dim = 3

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)

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 229
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^4
Torsion Bound  = 2^6
|L(1)/Omega|   = 1/2^3
Sha Bound      = 2^9

ANALYTIC INVARIANTS:

Omega+         = 4.9446317081102490276 + 0.4151494276648056036e-6i
Omega-         = 0.54623686269992002132e-6 + -3.0023076957981422183i
L(1)           = 0.61807896351378330693

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

-------------------------------------------------------
93C (old = 31A), dim = 2

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) + B(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(94)
Weight 2

-------------------------------------------------------
J_0(94), dim = 11

-------------------------------------------------------
94A (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
Torsion Bound  = 2
|L(1)/Omega|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 2.7134688813031726793 + 0.71697351403123958338e-7i
Omega-         = 0.28510948189016432838e-6 + -4.3181982755772873672i
L(1)           = 1.3567344406515868132
w1             = -1.3567345832063272847 + 2.1590991019399679821i
w2             = 1.3567342980968453946 + 2.1590991736373193852i
c4             = -14.999988348192241235 + 0.97113821698132617522e-5i
c6             = 567.00005621797776155 + -0.15076108653245895924e-3i
j              = 17.952082736361789821 + -0.25058223257919110672e-4i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + 1*q^4 + 1*q^8 + -3*q^9 + 2*q^11 + -4*q^13 + 1*q^16 + -2*q^17 + -3*q^18 + -2*q^19 + 2*q^22 + 4*q^23 + -5*q^25 + -4*q^26 + 4*q^29 + 4*q^31 + 1*q^32 + -2*q^34 + -3*q^36 + 2*q^37 + -2*q^38 + 6*q^41 + 6*q^43 + 2*q^44 + 4*q^46 + -1*q^47 + -7*q^49 + -5*q^50 + -4*q^52 + 2*q^53 + 4*q^58 + 12*q^59 + 2*q^61 + 4*q^62 + 1*q^64 + 2*q^67 + -2*q^68 + 8*q^71 + -3*q^72 + -14*q^73 + 2*q^74 + -2*q^76 + -16*q^79 + 9*q^81 + 6*q^82 + -16*q^83 + 6*q^86 + 2*q^88 + -10*q^89 + 4*q^92 + -1*q^94 + -14*q^97 + -7*q^98 + -6*q^99 + -5*q^100 + 6*q^101 + -8*q^103 + -4*q^104 + 2*q^106 + -6*q^107 + 16*q^109 + -6*q^113 + 4*q^116 + 12*q^117 + 12*q^118 + -7*q^121 + 2*q^122 + 4*q^124 + 12*q^127 + 1*q^128 + 8*q^131 + 2*q^134 + -2*q^136 + 22*q^137 + -10*q^139 + 8*q^142 + -8*q^143 + -3*q^144 + -14*q^146 + 2*q^148 + 14*q^149 + 16*q^151 + -2*q^152 + 6*q^153 + 10*q^157 + -16*q^158 + 9*q^162 + 6*q^163 + 6*q^164 + -16*q^166 + -16*q^167 + 3*q^169 + 6*q^171 + 6*q^172 + -6*q^173 + 2*q^176 + -10*q^178 + -18*q^179 + 4*q^184 + -4*q^187 + -1*q^188 + -16*q^191 + -2*q^193 + -14*q^194 + -7*q^196 + -18*q^197 + -6*q^198 + 24*q^199 + -5*q^200 +  ...

-------------------------------------------------------
94B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2*47
Ker(ModPolar)  = Z/2*47 + Z/2*47
= A(Z/2 + Z/2) + C(Z/47 + Z/47)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^3
#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+         = 1.3038604840476503228 + 0.53068615405396248988e-6i
Omega-         = 6.3957255028242809021 + -0.89587746628031928942e-6i
L(1)           = 0.65193024202387916022

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

-------------------------------------------------------
94C (old = 47A), dim = 4

CONGRUENCES:
Modular Degree = 47
Ker(ModPolar)  = Z/47 + Z/47
= B(Z/47 + Z/47)

-------------------------------------------------------
Gamma_0(95)
Weight 2

-------------------------------------------------------
J_0(95), dim = 9

-------------------------------------------------------
95A (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   = 2^2*37
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2*5
Torsion Bound  = 2^2*5
|L(1)/Omega|   = 1/2^2*5
Sha Bound      = 2^2*5

ANALYTIC INVARIANTS:

Omega+         = 15.968744449725315112 + 0.75974785540514066126e-6i
Omega-         = 0.62418117817667168148e-6 + -3.6844080762932483855i
L(1)           = 0.79843722248626665927

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

-------------------------------------------------------
95B (new) , dim = 4

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/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + C(Z/3^2 + Z/3^2)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^4*709
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2*3
Torsion Bound  = 2^2*3
|L(1)/Omega|   = 1/2^2*3
Sha Bound      = 2^2*3

ANALYTIC INVARIANTS:

Omega+         = 3.1779923534385600318 + 0.17412939562023668403e-6i
Omega-         = 7.9800153865722096677 + 0.40771577135460420279e-7i
L(1)           = 0.26483269611988040019

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

-------------------------------------------------------
95C (old = 19A), dim = 1

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

-------------------------------------------------------
Gamma_0(96)
Weight 2

-------------------------------------------------------
J_0(96), dim = 9

-------------------------------------------------------
96A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= B(Z/2) + C(Z/2) + D(Z/2) + E(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+         = 2.3428402843569044356 + -0.5510699850829922922e-41i
Omega-         = 0.10064130801465986072e-6 + 2.002154830653711566i
L(1)           = 0.5857100710892261089
w1             = -2.3428402843569044356 + 0.5510699850829922922e-41i
w2             = 0.10064130801465986072e-6 + 2.002154830653711566i
c4             = 111.99998276244208226 + 0.16940265775230531419e-4i
c6             = -639.99990103451116884 + -0.31194893255361636708e-3i
j              = 2439.1112641358605746 + 0.52303728635526557847e-3i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 2*q^5 + -4*q^7 + 1*q^9 + 4*q^11 + -2*q^13 + 2*q^15 + -6*q^17 + -4*q^19 + -4*q^21 + -1*q^25 + 1*q^27 + 2*q^29 + 4*q^31 + 4*q^33 + -8*q^35 + -2*q^37 + -2*q^39 + 2*q^41 + 4*q^43 + 2*q^45 + 8*q^47 + 9*q^49 + -6*q^51 + 10*q^53 + 8*q^55 + -4*q^57 + -4*q^59 + 6*q^61 + -4*q^63 + -4*q^65 + 4*q^67 + -16*q^71 + -6*q^73 + -1*q^75 + -16*q^77 + 4*q^79 + 1*q^81 + 12*q^83 + -12*q^85 + 2*q^87 + 10*q^89 + 8*q^91 + 4*q^93 + -8*q^95 + -14*q^97 + 4*q^99 + -6*q^101 + -12*q^103 + -8*q^105 + -4*q^107 + 14*q^109 + -2*q^111 + 2*q^113 + -2*q^117 + 24*q^119 + 5*q^121 + 2*q^123 + -12*q^125 + -20*q^127 + 4*q^129 + 4*q^131 + 16*q^133 + 2*q^135 + 18*q^137 + -20*q^139 + 8*q^141 + -8*q^143 + 4*q^145 + 9*q^147 + 18*q^149 + 12*q^151 + -6*q^153 + 8*q^155 + -10*q^157 + 10*q^159 + -4*q^163 + 8*q^165 + 8*q^167 + -9*q^169 + -4*q^171 + -6*q^173 + 4*q^175 + -4*q^177 + -12*q^179 + -10*q^181 + 6*q^183 + -4*q^185 + -24*q^187 + -4*q^189 + 18*q^193 + -4*q^195 + -22*q^197 + 4*q^199 +  ...

-------------------------------------------------------
96B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= A(Z/2) + D(Z/2) + E(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+         = 2.002154830653711566 + 0.10064130801465986072e-6i
Omega-         = 2.3428402843569044356i
L(1)           = 0.50053870766342852387
w1             = 2.3428402843569044356i
w2             = 2.002154830653711566 + 0.10064130801465986072e-6i
c4             = 111.99998276244208226 + -0.16940265775230531419e-4i
c6             = 639.99990103451116884 + -0.31194893255361636708e-3i
j              = 2439.1112641358605746 + -0.52303728635526557847e-3i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + 2*q^5 + 4*q^7 + 1*q^9 + -4*q^11 + -2*q^13 + -2*q^15 + -6*q^17 + 4*q^19 + -4*q^21 + -1*q^25 + -1*q^27 + 2*q^29 + -4*q^31 + 4*q^33 + 8*q^35 + -2*q^37 + 2*q^39 + 2*q^41 + -4*q^43 + 2*q^45 + -8*q^47 + 9*q^49 + 6*q^51 + 10*q^53 + -8*q^55 + -4*q^57 + 4*q^59 + 6*q^61 + 4*q^63 + -4*q^65 + -4*q^67 + 16*q^71 + -6*q^73 + 1*q^75 + -16*q^77 + -4*q^79 + 1*q^81 + -12*q^83 + -12*q^85 + -2*q^87 + 10*q^89 + -8*q^91 + 4*q^93 + 8*q^95 + -14*q^97 + -4*q^99 + -6*q^101 + 12*q^103 + -8*q^105 + 4*q^107 + 14*q^109 + 2*q^111 + 2*q^113 + -2*q^117 + -24*q^119 + 5*q^121 + -2*q^123 + -12*q^125 + 20*q^127 + 4*q^129 + -4*q^131 + 16*q^133 + -2*q^135 + 18*q^137 + 20*q^139 + 8*q^141 + 8*q^143 + 4*q^145 + -9*q^147 + 18*q^149 + -12*q^151 + -6*q^153 + -8*q^155 + -10*q^157 + -10*q^159 + 4*q^163 + 8*q^165 + -8*q^167 + -9*q^169 + 4*q^171 + -6*q^173 + -4*q^175 + -4*q^177 + 12*q^179 + -10*q^181 + -6*q^183 + -4*q^185 + 24*q^187 + -4*q^189 + 18*q^193 + 4*q^195 + -22*q^197 + -4*q^199 +  ...

-------------------------------------------------------
96C (old = 48A), dim = 1

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

-------------------------------------------------------
96D (old = 32A), 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) + E(Z/2 + Z/2)

-------------------------------------------------------
96E (old = 24A), 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) + C(Z/2 + Z/2 + Z/2) + D(Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(97)
Weight 2

-------------------------------------------------------
J_0(97), dim = 7

-------------------------------------------------------
97A (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+         = 84.742865338139180307 + 0.16429653805847479298e-4i
Omega-         = 0.38087014936662009207e-6 + 8.3274922893515862275i
L(1)           =

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

-------------------------------------------------------
97B (new) , dim = 4

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   = 2777
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 2^3
Torsion Bound  = 2^3
|L(1)/Omega|   = 1
Sha Bound      = 2^6

ANALYTIC INVARIANTS:

Omega+         = 2.1468847868666854204 + -0.18833927288149238257e-6i
Omega-         = 63.164803378035040307 + -0.18816359698349090202e-5i
L(1)           = 2.1468847868666936816

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

-------------------------------------------------------
Gamma_0(98)
Weight 2

-------------------------------------------------------
J_0(98), dim = 7

-------------------------------------------------------
98A (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/2^2 + Z/2^2)

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+         = 1.001977022331840034 + -0.42615816147554144295e-7i
Omega-         = 0.38550722015878314843e-6 + -2.2466304438031794787i
L(1)           = 1.0019770223318409403
w1             = 0.50098831841230993761 + 1.1233152005936816655i
w2             = 1.001977022331840034 + -0.42615816147554144295e-7i
c4             = 1225.0010758932051168 + 0.68918171664841967257e-3i
c6             = 86779.072112475052932 + -0.15886808717442191962e-1i
j              = -558.03643249445972432 + -0.15163117529339765176e-2i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + 2*q^3 + 1*q^4 + -2*q^6 + -1*q^8 + 1*q^9 + 2*q^12 + 4*q^13 + 1*q^16 + -6*q^17 + -1*q^18 + -2*q^19 + -2*q^24 + -5*q^25 + -4*q^26 + -4*q^27 + -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 + 8*q^43 + 12*q^47 + 2*q^48 + 5*q^50 + -12*q^51 + 4*q^52 + 6*q^53 + 4*q^54 + -4*q^57 + 6*q^58 + 6*q^59 + -8*q^61 + -4*q^62 + 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 + -8*q^86 + -12*q^87 + 6*q^89 + 8*q^93 + -12*q^94 + -2*q^96 + 10*q^97 + -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 + 6*q^113 + 4*q^114 + -6*q^116 + 4*q^117 + -6*q^118 + -11*q^121 + 8*q^122 + -12*q^123 + 4*q^124 + -16*q^127 + -1*q^128 + 16*q^129 + -18*q^131 + 4*q^134 + 6*q^136 + 18*q^137 + -14*q^139 + 24*q^141 + 1*q^144 + 2*q^146 + 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 + 3*q^169 + -2*q^171 + 8*q^172 + 12*q^173 + 12*q^174 + 12*q^177 + -6*q^178 + -12*q^179 + -20*q^181 + -16*q^183 + -8*q^186 + 12*q^188 + 24*q^191 + 2*q^192 + 14*q^193 + -10*q^194 + -18*q^197 + -20*q^199 + 5*q^200 +  ...

-------------------------------------------------------
98B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + C(Z/2 + Z/2) + D(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|   = 1/7
Sha Bound      = 2^2*7

ANALYTIC INVARIANTS:

Omega+         = 13.27875008554808161 + -0.24461141821585627705e-6i
Omega-         = 1.8969642648661581308 + 0.19613239582430392846e-6i
L(1)           = 1.8969642979354405519

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

-------------------------------------------------------
98C (old = 49A), 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)

-------------------------------------------------------
98D (old = 14A), dim = 1

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

-------------------------------------------------------
Gamma_0(99)
Weight 2

-------------------------------------------------------
J_0(99), dim = 9

-------------------------------------------------------
99A (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) + E(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+         = 2.2492255815690473586 + -0.58114155414883897377e-7i
Omega-         = 0.76836217000345007914e-6 + 2.3630240797939221123i
L(1)           =
w1             = -0.76836217000345007914e-6 + -2.3630240797939221123i
w2             = -2.2492255815690473586 + 0.58114155414883897377e-7i
c4             = 81.000043831126759016 + 0.4857839464700461897e-4i
c6             = 135.00171157935884424 + -0.68068638857905373044e-3i
j              = 1789.3651444519397417 + -0.75511754418167292447e-3i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^4 + -4*q^5 + -2*q^7 + 3*q^8 + 4*q^10 + -1*q^11 + -2*q^13 + 2*q^14 + -1*q^16 + 2*q^17 + -6*q^19 + 4*q^20 + 1*q^22 + 4*q^23 + 11*q^25 + 2*q^26 + 2*q^28 + -6*q^29 + 4*q^31 + -5*q^32 + -2*q^34 + 8*q^35 + -6*q^37 + 6*q^38 + -12*q^40 + -10*q^41 + 6*q^43 + 1*q^44 + -4*q^46 + -8*q^47 + -3*q^49 + -11*q^50 + 2*q^52 + 4*q^55 + -6*q^56 + 6*q^58 + 4*q^59 + -6*q^61 + -4*q^62 + 7*q^64 + 8*q^65 + 8*q^67 + -2*q^68 + -8*q^70 + -2*q^73 + 6*q^74 + 6*q^76 + 2*q^77 + -10*q^79 + 4*q^80 + 10*q^82 + 12*q^83 + -8*q^85 + -6*q^86 + -3*q^88 + 4*q^91 + -4*q^92 + 8*q^94 + 24*q^95 + 2*q^97 + 3*q^98 + -11*q^100 + -14*q^101 + 8*q^103 + -6*q^104 + 12*q^107 + -2*q^109 + -4*q^110 + 2*q^112 + 12*q^113 + -16*q^115 + 6*q^116 + -4*q^118 + -4*q^119 + 1*q^121 + 6*q^122 + -4*q^124 + -24*q^125 + -10*q^127 + 3*q^128 + -8*q^130 + -12*q^131 + 12*q^133 + -8*q^134 + 6*q^136 + 4*q^137 + 10*q^139 + -8*q^140 + 2*q^143 + 24*q^145 + 2*q^146 + 6*q^148 + -2*q^149 + 14*q^151 + -18*q^152 + -2*q^154 + -16*q^155 + -10*q^157 + 10*q^158 + 20*q^160 + -8*q^161 + -20*q^163 + 10*q^164 + -12*q^166 + -9*q^169 + 8*q^170 + -6*q^172 + -6*q^173 + -22*q^175 + 1*q^176 + -24*q^179 + 10*q^181 + -4*q^182 + 12*q^184 + 24*q^185 + -2*q^187 + 8*q^188 + -24*q^190 + 16*q^191 + -14*q^193 + -2*q^194 + 3*q^196 + 2*q^197 + 12*q^199 + 33*q^200 +  ...

-------------------------------------------------------
99B (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) + F(Z/3 + Z/3)

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+         = 1.3642920047435854537 + 0.84328610522144733371e-7i
Omega-         = 0.41141734382086721846e-6 + -1.298591517402010504i
L(1)           = 0.68214600237179402994
w1             = -1.3642920047435854537 + -0.84328610522144733371e-7i
w2             = -0.41141734382086721846e-6 + 1.298591517402010504i
c4             = 729.00022508815488779 + -0.61555303811005158778e-3i
c6             = -3644.9848707649519656 + 0.23067738000687573095e-1i
j              = 1789.3630500141047199 + -0.64330725198453101823e-3i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^4 + 4*q^5 + -2*q^7 + -3*q^8 + 4*q^10 + 1*q^11 + -2*q^13 + -2*q^14 + -1*q^16 + -2*q^17 + -6*q^19 + -4*q^20 + 1*q^22 + -4*q^23 + 11*q^25 + -2*q^26 + 2*q^28 + 6*q^29 + 4*q^31 + 5*q^32 + -2*q^34 + -8*q^35 + -6*q^37 + -6*q^38 + -12*q^40 + 10*q^41 + 6*q^43 + -1*q^44 + -4*q^46 + 8*q^47 + -3*q^49 + 11*q^50 + 2*q^52 + 4*q^55 + 6*q^56 + 6*q^58 + -4*q^59 + -6*q^61 + 4*q^62 + 7*q^64 + -8*q^65 + 8*q^67 + 2*q^68 + -8*q^70 + -2*q^73 + -6*q^74 + 6*q^76 + -2*q^77 + -10*q^79 + -4*q^80 + 10*q^82 + -12*q^83 + -8*q^85 + 6*q^86 + -3*q^88 + 4*q^91 + 4*q^92 + 8*q^94 + -24*q^95 + 2*q^97 + -3*q^98 + -11*q^100 + 14*q^101 + 8*q^103 + 6*q^104 + -12*q^107 + -2*q^109 + 4*q^110 + 2*q^112 + -12*q^113 + -16*q^115 + -6*q^116 + -4*q^118 + 4*q^119 + 1*q^121 + -6*q^122 + -4*q^124 + 24*q^125 + -10*q^127 + -3*q^128 + -8*q^130 + 12*q^131 + 12*q^133 + 8*q^134 + 6*q^136 + -4*q^137 + 10*q^139 + 8*q^140 + -2*q^143 + 24*q^145 + -2*q^146 + 6*q^148 + 2*q^149 + 14*q^151 + 18*q^152 + -2*q^154 + 16*q^155 + -10*q^157 + -10*q^158 + 20*q^160 + 8*q^161 + -20*q^163 + -10*q^164 + -12*q^166 + -9*q^169 + -8*q^170 + -6*q^172 + 6*q^173 + -22*q^175 + -1*q^176 + 24*q^179 + 10*q^181 + 4*q^182 + 12*q^184 + -24*q^185 + -2*q^187 + -8*q^188 + -24*q^190 + -16*q^191 + -14*q^193 + 2*q^194 + 3*q^196 + -2*q^197 + 12*q^199 + -33*q^200 +  ...

-------------------------------------------------------
99C (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/3 + Z/3) + E(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+         = 1.5846144787056176859 + 0.70064869837981079004e-7i
Omega-         = 0.15182693515706835887e-6 + 0.86295247080798089693i
L(1)           = 0.39615361967640480873
w1             = -1.5846144787056176859 + -0.70064869837981079004e-7i
w2             = 0.15182693515706835887e-6 + 0.86295247080798089693i
c4             = 2817.0057929391044793 + 0.19657663148607044956e-2i
c6             = -148257.46177751413361 + -0.1583675721541776094i
j              = 103247.15611026405803 + 0.26035469329129472972i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^4 + 2*q^5 + 4*q^7 + 3*q^8 + -2*q^10 + -1*q^11 + -2*q^13 + -4*q^14 + -1*q^16 + 2*q^17 + -2*q^20 + 1*q^22 + -8*q^23 + -1*q^25 + 2*q^26 + -4*q^28 + 6*q^29 + -8*q^31 + -5*q^32 + -2*q^34 + 8*q^35 + 6*q^37 + 6*q^40 + 2*q^41 + 1*q^44 + 8*q^46 + -8*q^47 + 9*q^49 + 1*q^50 + 2*q^52 + -6*q^53 + -2*q^55 + 12*q^56 + -6*q^58 + 4*q^59 + 6*q^61 + 8*q^62 + 7*q^64 + -4*q^65 + -4*q^67 + -2*q^68 + -8*q^70 + -14*q^73 + -6*q^74 + -4*q^77 + -4*q^79 + -2*q^80 + -2*q^82 + -12*q^83 + 4*q^85 + -3*q^88 + 6*q^89 + -8*q^91 + 8*q^92 + 8*q^94 + 2*q^97 + -9*q^98 + 1*q^100 + -2*q^101 + 8*q^103 + -6*q^104 + 6*q^106 + 12*q^107 + -2*q^109 + 2*q^110 + -4*q^112 + 6*q^113 + -16*q^115 + -6*q^116 + -4*q^118 + 8*q^119 + 1*q^121 + -6*q^122 + 8*q^124 + -12*q^125 + -4*q^127 + 3*q^128 + 4*q^130 + 12*q^131 + 4*q^134 + 6*q^136 + -2*q^137 + -8*q^139 + -8*q^140 + 2*q^143 + 12*q^145 + 14*q^146 + -6*q^148 + 22*q^149 + 20*q^151 + 4*q^154 + -16*q^155 + 14*q^157 + 4*q^158 + -10*q^160 + -32*q^161 + 4*q^163 + -2*q^164 + 12*q^166 + -9*q^169 + -4*q^170 + 6*q^173 + -4*q^175 + 1*q^176 + -6*q^178 + -12*q^179 + 22*q^181 + 8*q^182 + -24*q^184 + 12*q^185 + -2*q^187 + 8*q^188 + -8*q^191 + -14*q^193 + -2*q^194 + -9*q^196 + 14*q^197 + -3*q^200 +  ...

-------------------------------------------------------
99D (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))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.6844960669074509361 + -0.62322542394674147924e-6i
Omega-         = 0.11567931612423565066e-5 + 3.6638903538103081025i
L(1)           = 1.6844960669075662258
w1             = -0.84224861185030608924 + -1.8319448652924420779i
w2             = -1.6844960669074509361 + 0.62322542394674147924e-6i
c4             = 144.0000237000531389 + 0.23130382986538290683e-3i
c6             = 4104.0057529547897288 + 0.86063062911074480871e-2i
j              = -372.36259092706679702 + -0.28275343884192806632e-3i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 2*q^4 + -1*q^5 + -2*q^7 + -2*q^10 + -1*q^11 + 4*q^13 + -4*q^14 + -4*q^16 + 2*q^17 + -2*q^20 + -2*q^22 + 1*q^23 + -4*q^25 + 8*q^26 + -4*q^28 + 7*q^31 + -8*q^32 + 4*q^34 + 2*q^35 + 3*q^37 + 8*q^41 + -6*q^43 + -2*q^44 + 2*q^46 + -8*q^47 + -3*q^49 + -8*q^50 + 8*q^52 + 6*q^53 + 1*q^55 + -5*q^59 + 12*q^61 + 14*q^62 + -8*q^64 + -4*q^65 + -7*q^67 + 4*q^68 + 4*q^70 + 3*q^71 + 4*q^73 + 6*q^74 + 2*q^77 + -10*q^79 + 4*q^80 + 16*q^82 + 6*q^83 + -2*q^85 + -12*q^86 + -15*q^89 + -8*q^91 + 2*q^92 + -16*q^94 + -7*q^97 + -6*q^98 + -8*q^100 + -2*q^101 + -16*q^103 + 12*q^106 + -18*q^107 + 10*q^109 + 2*q^110 + 8*q^112 + -9*q^113 + -1*q^115 + -10*q^118 + -4*q^119 + 1*q^121 + 24*q^122 + 14*q^124 + 9*q^125 + 8*q^127 + -8*q^130 + 18*q^131 + -14*q^134 + 7*q^137 + 10*q^139 + 4*q^140 + 6*q^142 + -4*q^143 + 8*q^146 + 6*q^148 + 10*q^149 + 2*q^151 + 4*q^154 + -7*q^155 + -7*q^157 + -20*q^158 + 8*q^160 + -2*q^161 + 4*q^163 + 16*q^164 + 12*q^166 + 12*q^167 + 3*q^169 + -4*q^170 + -12*q^172 + 6*q^173 + 8*q^175 + 4*q^176 + -30*q^178 + 15*q^179 + 7*q^181 + -16*q^182 + -3*q^185 + -2*q^187 + -16*q^188 + -17*q^191 + 4*q^193 + -14*q^194 + -6*q^196 + 2*q^197 +  ...

-------------------------------------------------------
99E (old = 33A), 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) + C(Z/2 + Z/2) + F(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
99F (old = 11A), dim = 1

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

-------------------------------------------------------
Gamma_0(100)
Weight 2

-------------------------------------------------------
J_0(100), dim = 7

-------------------------------------------------------
100A (new) , dim = 1

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

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+         = 1.2630987937083136592 + -0.19840491551509445547e-6i
Omega-         = 0.28177167518558851265e-6 + -1.0170373603236384364i
L(1)           = 0.63154939685416462088
w1             = -1.2630987937083136592 + 0.19840491551509445547e-6i
w2             = -0.28177167518558851265e-6 + 1.0170373603236384364i
c4             = 1600.0013697809799084 + -0.12859123911956265608e-2i
c6             = -44000.06998852940057 + 0.11295647336701937288i
j              = 3276.801800229487744 + -0.79982817825576448394e-2i

HECKE EIGENFORM:
f(q) = q + 2*q^3 + -2*q^7 + 1*q^9 + -2*q^13 + 6*q^17 + -4*q^19 + -4*q^21 + -6*q^23 + -4*q^27 + 6*q^29 + -4*q^31 + -2*q^37 + -4*q^39 + 6*q^41 + 10*q^43 + 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^67 + -12*q^69 + -12*q^71 + -2*q^73 + 8*q^79 + -11*q^81 + -6*q^83 + 12*q^87 + -6*q^89 + 4*q^91 + -8*q^93 + -2*q^97 + 6*q^101 + -14*q^103 + 6*q^107 + 2*q^109 + -4*q^111 + 6*q^113 + -2*q^117 + -12*q^119 + -11*q^121 + 12*q^123 + -2*q^127 + 20*q^129 + 8*q^133 + -18*q^137 + -4*q^139 + 12*q^141 + -6*q^147 + -6*q^149 + 20*q^151 + 6*q^153 + 22*q^157 + 12*q^159 + 12*q^161 + 10*q^163 + -18*q^167 + -9*q^169 + -4*q^171 + 6*q^173 + 24*q^177 + -12*q^179 + -10*q^181 + 4*q^183 + 8*q^189 + -12*q^191 + -26*q^193 + -18*q^197 + 8*q^199 +  ...

-------------------------------------------------------
100B (old = 50A), dim = 1

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

-------------------------------------------------------
100C (old = 50B), 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) + B(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
100D (old = 20A), dim = 1

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

-------------------------------------------------------
Gamma_0(101)
Weight 2

-------------------------------------------------------
J_0(101), dim = 8

-------------------------------------------------------
101A (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+         = 2.2951233347219711398 + 0.25316752381442347475e-6i
Omega-         = 0.29585403980189730283e-6 + -2.7235595527163724145i
L(1)           =
w1             = -0.29585403980189730283e-6 + 2.7235595527163724145i
w2             = 2.2951233347219711398 + 0.25316752381442347475e-6i
c4             = 64.000023676316405458 + -0.28139983972207928976e-4i
c6             = 296.0003162075751804 + -0.19749884103936543051e-3i
j              = 2595.4864862955019377 + -0.20051484240970021509e-4i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -2*q^4 + -1*q^5 + -2*q^7 + 1*q^9 + -2*q^11 + 4*q^12 + 1*q^13 + 2*q^15 + 4*q^16 + 3*q^17 + -5*q^19 + 2*q^20 + 4*q^21 + 1*q^23 + -4*q^25 + 4*q^27 + 4*q^28 + -4*q^29 + -9*q^31 + 4*q^33 + 2*q^35 + -2*q^36 + -2*q^37 + -2*q^39 + 8*q^41 + -8*q^43 + 4*q^44 + -1*q^45 + 7*q^47 + -8*q^48 + -3*q^49 + -6*q^51 + -2*q^52 + -2*q^53 + 2*q^55 + 10*q^57 + -14*q^59 + -4*q^60 + 4*q^61 + -2*q^63 + -8*q^64 + -1*q^65 + 2*q^67 + -6*q^68 + -2*q^69 + 13*q^71 + 8*q^73 + 8*q^75 + 10*q^76 + 4*q^77 + -9*q^79 + -4*q^80 + -11*q^81 + -4*q^83 + -8*q^84 + -3*q^85 + 8*q^87 + 14*q^89 + -2*q^91 + -2*q^92 + 18*q^93 + 5*q^95 + 2*q^97 + -2*q^99 + 8*q^100 + -1*q^101 + 16*q^103 + -4*q^105 + 13*q^107 + -8*q^108 + 4*q^111 + -8*q^112 + -12*q^113 + -1*q^115 + 8*q^116 + 1*q^117 + -6*q^119 + -7*q^121 + -16*q^123 + 18*q^124 + 9*q^125 + -16*q^127 + 16*q^129 + -21*q^131 + -8*q^132 + 10*q^133 + -4*q^135 + -15*q^137 + 4*q^139 + -4*q^140 + -14*q^141 + -2*q^143 + 4*q^144 + 4*q^145 + 6*q^147 + 4*q^148 + -24*q^149 + -6*q^151 + 3*q^153 + 9*q^155 + 4*q^156 + -9*q^157 + 4*q^159 + -2*q^161 + 4*q^163 + -16*q^164 + -4*q^165 + 22*q^167 + -12*q^169 + -5*q^171 + 16*q^172 + -12*q^173 + 8*q^175 + -8*q^176 + 28*q^177 + 12*q^179 + 2*q^180 + -11*q^181 + -8*q^183 + 2*q^185 + -6*q^187 + -14*q^188 + -8*q^189 + -8*q^191 + 16*q^192 + 13*q^193 + 2*q^195 + 6*q^196 + -1*q^197 + 12*q^199 +  ...

-------------------------------------------------------
101B (new) , dim = 7

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^6*17568767
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 2
ord((0)-(oo))  = 5^2
Torsion Bound  = 5^2
|L(1)/Omega|   = 1/5^2
Sha Bound      = 5^2

ANALYTIC INVARIANTS:

Omega+         = 16.410995573440634387 + -0.10695001690327166069e-5i
Omega-         = 0.39317680271591208091e-4 + 131.29023054625426749i
L(1)           = 0.65643982293762676944

HECKE EIGENFORM:
a^7-13*a^5+2*a^4+47*a^3-16*a^2-43*a+14 = 0,
f(q) = q + a*q^2 + (1/4*a^6+1/4*a^5-5/2*a^4-5/2*a^3+19/4*a^2+17/4*a+1/2)*q^3 + (a^2-2)*q^4 + (-1/2*a^6-3/4*a^5+11/2*a^4+7*a^3-29/2*a^2-45/4*a+15/2)*q^5 + (1/4*a^6+3/4*a^5-3*a^4-7*a^3+33/4*a^2+45/4*a-7/2)*q^6 + (-1/4*a^5-1/2*a^4+5/2*a^3+4*a^2-21/4*a-7/2)*q^7 + (a^3-4*a)*q^8 + (1/4*a^6+1/2*a^5-5/2*a^4-5*a^3+21/4*a^2+17/2*a-1)*q^9 + (-3/4*a^6-a^5+8*a^4+9*a^3-77/4*a^2-14*a+7)*q^10 + (-1/4*a^6+3*a^4-35/4*a^2+5)*q^11 + (1/4*a^6-1/4*a^5-5/2*a^4+3/2*a^3+23/4*a^2-5/4*a-9/2)*q^12 + (3/4*a^6+a^5-17/2*a^4-9*a^3+91/4*a^2+12*a-10)*q^13 + (-1/4*a^6-1/2*a^5+5/2*a^4+4*a^3-21/4*a^2-7/2*a)*q^14 + (-3/4*a^6-3/4*a^5+17/2*a^4+15/2*a^3-93/4*a^2-55/4*a+25/2)*q^15 + (a^4-6*a^2+4)*q^16 + (3/4*a^6+3/4*a^5-8*a^4-7*a^3+79/4*a^2+45/4*a-21/2)*q^17 + (1/2*a^6+3/4*a^5-11/2*a^4-13/2*a^3+25/2*a^2+39/4*a-7/2)*q^18 + (1/2*a^5-5*a^3+21/2*a+2)*q^19 + (-1/4*a^5-1/2*a^4+2*a^3+3*a^2-11/4*a-9/2)*q^20 + (3/4*a^6+1/2*a^5-17/2*a^4-4*a^3+95/4*a^2+7/2*a-14)*q^21 + (-1/4*a^5+1/2*a^4+3*a^3-4*a^2-23/4*a+7/2)*q^22 + (-1/2*a^6-1/2*a^5+5*a^4+4*a^3-21/2*a^2-7/2*a+2)*q^23 + (-3/4*a^6-3/4*a^5+7*a^4+8*a^3-55/4*a^2-65/4*a+7/2)*q^24 + (3/4*a^6+5/4*a^5-8*a^4-12*a^3+75/4*a^2+87/4*a-13/2)*q^25 + (a^6+5/4*a^5-21/2*a^4-25/2*a^3+24*a^2+89/4*a-21/2)*q^26 + (-1/2*a^6-3/4*a^5+11/2*a^4+13/2*a^3-25/2*a^2-31/4*a+3/2)*q^27 + (-1/2*a^6-1/4*a^5+11/2*a^4+3/2*a^3-31/2*a^2-1/4*a+21/2)*q^28 + (-1/2*a^6-1/2*a^5+5*a^4+4*a^3-19/2*a^2-7/2*a-1)*q^29 + (-3/4*a^6-5/4*a^5+9*a^4+12*a^3-103/4*a^2-79/4*a+21/2)*q^30 + (-a^6-3/2*a^5+11*a^4+15*a^3-28*a^2-55/2*a+14)*q^31 + (a^5-8*a^3+12*a)*q^32 + (-3/4*a^6-5/4*a^5+9*a^4+11*a^3-111/4*a^2-59/4*a+33/2)*q^33 + (3/4*a^6+7/4*a^5-17/2*a^4-31/2*a^3+93/4*a^2+87/4*a-21/2)*q^34 + (-1/4*a^6-a^5+2*a^4+10*a^3+1/4*a^2-18*a-7)*q^35 + (1/4*a^6-5/2*a^4-a^3+29/4*a^2+a-5)*q^36 + (-5/4*a^6-9/4*a^5+13*a^4+21*a^3-113/4*a^2-135/4*a+13/2)*q^37 + (1/2*a^6-5*a^4+21/2*a^2+2*a)*q^38 + (a^6+3/4*a^5-23/2*a^4-13/2*a^3+32*a^2+39/4*a-31/2)*q^39 + (5/4*a^6+3/2*a^5-14*a^4-15*a^3+143/4*a^2+47/2*a-14)*q^40 + (1/2*a^6+3/2*a^5-5*a^4-14*a^3+19/2*a^2+41/2*a-1)*q^41 + (1/2*a^6+5/4*a^5-11/2*a^4-23/2*a^3+31/2*a^2+73/4*a-21/2)*q^42 + (a^6+3/2*a^5-11*a^4-13*a^3+27*a^2+35/2*a-3)*q^43 + (1/4*a^6+1/2*a^5-3*a^4-4*a^3+47/4*a^2+7/2*a-10)*q^44 + (-1/2*a^6-1/2*a^5+6*a^4+5*a^3-37/2*a^2-17/2*a+10)*q^45 + (-1/2*a^6-3/2*a^5+5*a^4+13*a^3-23/2*a^2-39/2*a+7)*q^46 + (-1/2*a^6-1/2*a^5+6*a^4+5*a^3-39/2*a^2-17/2*a+14)*q^47 + (-5/4*a^6-9/4*a^5+29/2*a^4+37/2*a^3-159/4*a^2-105/4*a+39/2)*q^48 + (-a^6-5/4*a^5+23/2*a^4+12*a^3-34*a^2-79/4*a+49/2)*q^49 + (5/4*a^6+7/4*a^5-27/2*a^4-33/2*a^3+135/4*a^2+103/4*a-21/2)*q^50 + (1/2*a^6+3/4*a^5-13/2*a^4-15/2*a^3+47/2*a^2+47/4*a-35/2)*q^51 + (-1/4*a^6+1/2*a^5+5/2*a^4-5*a^3-29/4*a^2+17/2*a+6)*q^52 + (a^6+5/2*a^5-11*a^4-24*a^3+27*a^2+83/2*a-11)*q^53 + (-3/4*a^6-a^5+15/2*a^4+11*a^3-63/4*a^2-20*a+7)*q^54 + (3/4*a^6+5/4*a^5-15/2*a^4-25/2*a^3+53/4*a^2+93/4*a+5/2)*q^55 + (1/4*a^6-5/2*a^4+9/4*a^2-4*a+7)*q^56 + (a^6+3/2*a^5-10*a^4-15*a^3+18*a^2+59/2*a+1)*q^57 + (-1/2*a^6-3/2*a^5+5*a^4+14*a^3-23/2*a^2-45/2*a+7)*q^58 + (-3/4*a^5+1/2*a^4+15/2*a^3-4*a^2-63/4*a+15/2)*q^59 + (1/4*a^6+3/4*a^5-7/2*a^4-11/2*a^3+59/4*a^2+23/4*a-29/2)*q^60 + (-a^6-2*a^5+11*a^4+19*a^3-28*a^2-29*a+12)*q^61 + (-3/2*a^6-2*a^5+17*a^4+19*a^3-87/2*a^2-29*a+14)*q^62 + (3/4*a^6+5/4*a^5-17/2*a^4-23/2*a^3+97/4*a^2+69/4*a-35/2)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (-1/2*a^6-5/4*a^5+11/2*a^4+13*a^3-25/2*a^2-107/4*a-3/2)*q^65 + (-5/4*a^6-3/4*a^5+25/2*a^4+15/2*a^3-107/4*a^2-63/4*a+21/2)*q^66 + (1/4*a^6+3/4*a^5-5/2*a^4-17/2*a^3+23/4*a^2+79/4*a-1/2)*q^67 + (1/4*a^6-1/4*a^5-a^4+2*a^3-23/4*a^2-3/4*a+21/2)*q^68 + (1/2*a^6+a^5-5*a^4-9*a^3+21/2*a^2+16*a-6)*q^69 + (-a^6-5/4*a^5+21/2*a^4+12*a^3-22*a^2-71/4*a+7/2)*q^70 + (-a^6-2*a^5+10*a^4+18*a^3-20*a^2-28*a+5)*q^71 + (-a^6-3/4*a^5+19/2*a^4+17/2*a^3-20*a^2-55/4*a+7/2)*q^72 + (-1/2*a^6-1/2*a^5+5*a^4+4*a^3-19/2*a^2-11/2*a-1)*q^73 + (-9/4*a^6-13/4*a^5+47/2*a^4+61/2*a^3-215/4*a^2-189/4*a+35/2)*q^74 + (5/4*a^6+5/2*a^5-14*a^4-24*a^3+143/4*a^2+85/2*a-12)*q^75 + (1/2*a^5-a^4-3*a^3+10*a^2+1/2*a-11)*q^76 + (1/2*a^6+3/4*a^5-13/2*a^4-7*a^3+47/2*a^2+37/4*a-49/2)*q^77 + (3/4*a^6+3/2*a^5-17/2*a^4-15*a^3+103/4*a^2+55/2*a-14)*q^78 + (1/2*a^6+a^5-5*a^4-11*a^3+23/2*a^2+26*a-7)*q^79 + (3/2*a^6+11/4*a^5-33/2*a^4-27*a^3+75/2*a^2+181/4*a-17/2)*q^80 + (-3/4*a^6-7/4*a^5+8*a^4+16*a^3-71/4*a^2-101/4*a-3/2)*q^81 + (3/2*a^6+3/2*a^5-15*a^4-14*a^3+57/2*a^2+41/2*a-7)*q^82 + (9/4*a^6+5/2*a^5-25*a^4-22*a^3+255/4*a^2+55/2*a-26)*q^83 + (-1/4*a^6+9/2*a^4-85/4*a^2+4*a+21)*q^84 + (-1/4*a^6-1/4*a^5+2*a^4+3*a^3-1/4*a^2-39/4*a-21/2)*q^85 + (3/2*a^6+2*a^5-15*a^4-20*a^3+67/2*a^2+40*a-14)*q^86 + (1/2*a^6+1/2*a^5-5*a^4-5*a^3+23/2*a^2+21/2*a-11)*q^87 + (1/2*a^6+3/4*a^5-11/2*a^4-6*a^3+31/2*a^2+49/4*a-21/2)*q^88 + (-1/2*a^6-a^5+6*a^4+10*a^3-35/2*a^2-19*a+6)*q^89 + (-1/2*a^6-1/2*a^5+6*a^4+5*a^3-33/2*a^2-23/2*a+7)*q^90 + (3/4*a^6+3/2*a^5-7*a^4-13*a^3+37/4*a^2+31/2*a+14)*q^91 + (-1/2*a^6-1/2*a^5+4*a^4+4*a^3-13/2*a^2-15/2*a+3)*q^92 + (-2*a^6-3*a^5+22*a^4+29*a^3-58*a^2-52*a+28)*q^93 + (-1/2*a^6-1/2*a^5+6*a^4+4*a^3-33/2*a^2-15/2*a+7)*q^94 + (-5/2*a^6-7/2*a^5+28*a^4+32*a^3-151/2*a^2-97/2*a+36)*q^95 + (-3/4*a^6-1/4*a^5+7*a^4+3*a^3-75/4*a^2-7/4*a+21/2)*q^96 + (3/2*a^6+7/4*a^5-33/2*a^4-17*a^3+83/2*a^2+129/4*a-41/2)*q^97 + (-5/4*a^6-3/2*a^5+14*a^4+13*a^3-143/4*a^2-37/2*a+14)*q^98 + (-a^6-a^5+11*a^4+9*a^3-28*a^2-15*a+16)*q^99 + (1/4*a^6+1/4*a^5-3*a^4-a^3+33/4*a^2-1/4*a-9/2)*q^100 + 1*q^101 + (3/4*a^6-17/2*a^4+79/4*a^2+4*a-7)*q^102 + (1/4*a^6-3*a^4+2*a^3+35/4*a^2-14*a-1)*q^103 + (-3/2*a^6-13/4*a^5+33/2*a^4+59/2*a^3-87/2*a^2-197/4*a+49/2)*q^104 + (1/2*a^6-7*a^4+a^3+55/2*a^2-9*a-28)*q^105 + (5/2*a^6+2*a^5-26*a^4-20*a^3+115/2*a^2+32*a-14)*q^106 + (a^6+3/2*a^5-10*a^4-14*a^3+23*a^2+41/2*a-16)*q^107 + (-3/4*a^5+3/2*a^4+13/2*a^3-7*a^2-39/4*a+15/2)*q^108 + (-a^6-3/2*a^5+10*a^4+13*a^3-18*a^2-27/2*a-5)*q^109 + (5/4*a^6+9/4*a^5-14*a^4-22*a^3+141/4*a^2+139/4*a-21/2)*q^110 + (-1/2*a^6-5/4*a^5+11/2*a^4+25/2*a^3-23/2*a^2-105/4*a-11/2)*q^111 + (a^6+5/4*a^5-23/2*a^4-25/2*a^3+31*a^2+73/4*a-49/2)*q^112 + (-a^6-a^5+11*a^4+9*a^3-30*a^2-16*a+20)*q^113 + (3/2*a^6+3*a^5-17*a^4-29*a^3+91/2*a^2+44*a-14)*q^114 + (-a^6-3/2*a^5+11*a^4+14*a^3-26*a^2-37/2*a+8)*q^115 + (-1/2*a^6-1/2*a^5+5*a^4+4*a^3-23/2*a^2-15/2*a+9)*q^116 + (1/4*a^6+3/4*a^5-4*a^4-7*a^3+69/4*a^2+53/4*a-29/2)*q^117 + (-3/4*a^6+1/2*a^5+15/2*a^4-4*a^3-63/4*a^2+15/2*a)*q^118 + (1/2*a^6+5/4*a^5-7/2*a^4-25/2*a^3-9/2*a^2+93/4*a+35/2)*q^119 + (9/4*a^6+9/4*a^5-24*a^4-21*a^3+245/4*a^2+143/4*a-49/2)*q^120 + (-1/4*a^6+3/4*a^5+3*a^4-7*a^3-37/4*a^2+45/4*a+7/2)*q^121 + (-2*a^6-2*a^5+21*a^4+19*a^3-45*a^2-31*a+14)*q^122 + (-a^6-2*a^5+12*a^4+18*a^3-37*a^2-22*a+24)*q^123 + (1/2*a^5-3*a^3+3*a^2+9/2*a-7)*q^124 + (-1/4*a^6+1/4*a^5+3*a^4-2*a^3-25/4*a^2+3/4*a-15/2)*q^125 + (5/4*a^6+5/4*a^5-13*a^4-11*a^3+117/4*a^2+59/4*a-21/2)*q^126 + (1/4*a^6+3/2*a^5-a^4-14*a^3-25/4*a^2+41/2*a+10)*q^127 + (a^5-2*a^4-7*a^3+16*a^2+11*a-14)*q^128 + (2*a^6+5/2*a^5-22*a^4-23*a^3+51*a^2+73/2*a-5)*q^129 + (-5/4*a^6-a^5+14*a^4+11*a^3-139/4*a^2-23*a+7)*q^130 + (1/2*a^6+1/2*a^5-7*a^4-4*a^3+53/2*a^2+3/2*a-22)*q^131 + (3/4*a^6-5/4*a^5-8*a^4+10*a^3+79/4*a^2-55/4*a-31/2)*q^132 + (-2*a^4-a^3+18*a^2+5*a-28)*q^133 + (3/4*a^6+3/4*a^5-9*a^4-6*a^3+95/4*a^2+41/4*a-7/2)*q^134 + (-a^4-a^3+7*a^2+6*a-8)*q^135 + (-7/4*a^6-5/4*a^5+37/2*a^4+27/2*a^3-173/4*a^2-89/4*a+35/2)*q^136 + (a^6+a^5-11*a^4-8*a^3+29*a^2+7*a-9)*q^137 + (a^6+3/2*a^5-10*a^4-13*a^3+24*a^2+31/2*a-7)*q^138 + (-3/2*a^6-11/4*a^5+33/2*a^4+49/2*a^3-89/2*a^2-139/4*a+67/2)*q^139 + (-3/4*a^6-1/2*a^5+10*a^4+5*a^3-137/4*a^2-7/2*a+28)*q^140 + (-2*a^6-3/2*a^5+22*a^4+15*a^3-59*a^2-51/2*a+35)*q^141 + (-2*a^6-3*a^5+20*a^4+27*a^3-44*a^2-38*a+14)*q^142 + (-5/4*a^6-3/2*a^5+12*a^4+14*a^3-79/4*a^2-47/2*a-8)*q^143 + (-5/4*a^6-7/2*a^5+31/2*a^4+29*a^3-177/4*a^2-83/2*a+24)*q^144 + (-1/2*a^6-a^5+5*a^4+9*a^3-17/2*a^2-10*a-4)*q^145 + (-1/2*a^6-3/2*a^5+5*a^4+14*a^3-27/2*a^2-45/2*a+7)*q^146 + (-2*a^6-3/2*a^5+23*a^4+15*a^3-68*a^2-53/2*a+49)*q^147 + (-3/4*a^6-5/4*a^5+9*a^4+10*a^3-107/4*a^2-47/4*a+37/2)*q^148 + (3*a^6+4*a^5-33*a^4-35*a^3+84*a^2+45*a-32)*q^149 + (5/2*a^6+9/4*a^5-53/2*a^4-23*a^3+125/2*a^2+167/4*a-35/2)*q^150 + (-1/4*a^6-5/4*a^5+5/2*a^4+21/2*a^3-19/4*a^2-45/4*a+7/2)*q^151 + (-1/2*a^6-a^5+7*a^4+10*a^3-41/2*a^2-15*a)*q^152 + (1/2*a^6-3/4*a^5-11/2*a^4+6*a^3+31/2*a^2-25/4*a-21/2)*q^153 + (3/4*a^6-8*a^4+69/4*a^2-3*a-7)*q^154 + (3*a^6+4*a^5-33*a^4-39*a^3+81*a^2+67*a-21)*q^155 + (-1/2*a^6-1/4*a^5+13/2*a^4+7/2*a^3-49/2*a^2-5/4*a+41/2)*q^156 + (-7/4*a^6-9/4*a^5+20*a^4+22*a^3-231/4*a^2-171/4*a+79/2)*q^157 + (a^6+3/2*a^5-12*a^4-12*a^3+34*a^2+29/2*a-7)*q^158 + (3/2*a^6+5/2*a^5-16*a^4-24*a^3+71/2*a^2+99/2*a-9)*q^159 + (1/4*a^6-2*a^4-3*a^3-9/4*a^2+9*a+7)*q^160 + (-3/2*a^6-3/2*a^5+16*a^4+13*a^3-71/2*a^2-23/2*a+7)*q^161 + (-7/4*a^6-7/4*a^5+35/2*a^4+35/2*a^3-149/4*a^2-135/4*a+21/2)*q^162 + (-a^6-2*a^5+10*a^4+19*a^3-17*a^2-29*a-4)*q^163 + (1/2*a^6+3/2*a^5-7*a^4-14*a^3+51/2*a^2+33/2*a-19)*q^164 + (3/4*a^6+5/2*a^5-15/2*a^4-24*a^3+55/4*a^2+87/2*a+10)*q^165 + (5/2*a^6+17/4*a^5-53/2*a^4-42*a^3+127/2*a^2+283/4*a-63/2)*q^166 + (5/4*a^6+3/4*a^5-25/2*a^4-13/2*a^3+99/4*a^2+23/4*a-5/2)*q^167 + (-a^6-5/4*a^5+23/2*a^4+27/2*a^3-31*a^2-105/4*a+49/2)*q^168 + (1/2*a^6+3/4*a^5-11/2*a^4-7*a^3+25/2*a^2+45/4*a-1/2)*q^169 + (-1/4*a^6-5/4*a^5+7/2*a^4+23/2*a^3-55/4*a^2-85/4*a+7/2)*q^170 + (a^6+5/2*a^5-11*a^4-23*a^3+26*a^2+69/2*a-2)*q^171 + (3/2*a^5-a^4-11*a^3+10*a^2+31/2*a-15)*q^172 + (1/2*a^6+1/2*a^5-4*a^4-7*a^3+9/2*a^2+45/2*a-7)*q^173 + (1/2*a^6+3/2*a^5-6*a^4-12*a^3+37/2*a^2+21/2*a-7)*q^174 + (a^6+3/2*a^5-11*a^4-15*a^3+29*a^2+57/2*a-21)*q^175 + (1/4*a^6-a^4-13/4*a^2+4*a+13)*q^176 + (-3/4*a^6-3/2*a^5+17/2*a^4+14*a^3-87/4*a^2-57/2*a+16)*q^177 + (-a^6-1/2*a^5+11*a^4+6*a^3-27*a^2-31/2*a+7)*q^178 + (-1/2*a^5-a^4+6*a^3+6*a^2-27/2*a+7)*q^179 + (1/2*a^6+1/2*a^5-6*a^4-3*a^3+35/2*a^2+5/2*a-13)*q^180 + (9/4*a^6+5/2*a^5-47/2*a^4-21*a^3+213/4*a^2+45/2*a-17)*q^181 + (3/2*a^6+11/4*a^5-29/2*a^4-26*a^3+55/2*a^2+185/4*a-21/2)*q^182 + (-a^6+10*a^4+a^3-21*a^2-9*a+6)*q^183 + (1/2*a^6+1/2*a^5-5*a^4-9*a^3+15/2*a^2+41/2*a-7)*q^184 + (7/4*a^6+7/4*a^5-21*a^4-17*a^3+255/4*a^2+129/4*a-67/2)*q^185 + (-3*a^6-4*a^5+33*a^4+36*a^3-84*a^2-58*a+28)*q^186 + (-1/4*a^6-9/4*a^5+5/2*a^4+43/2*a^3-11/4*a^2-137/4*a-21/2)*q^187 + (1/2*a^6+1/2*a^5-7*a^4-3*a^3+47/2*a^2+5/2*a-21)*q^188 + (-7/4*a^6-7/4*a^5+19*a^4+14*a^3-191/4*a^2-45/4*a+35/2)*q^189 + (-7/2*a^6-9/2*a^5+37*a^4+42*a^3-177/2*a^2-143/2*a+35)*q^190 + (-3/4*a^6-3/4*a^5+15/2*a^4+15/2*a^3-57/4*a^2-51/4*a+5/2)*q^191 + (9/4*a^6+7/4*a^5-49/2*a^4-41/2*a^3+263/4*a^2+123/4*a-57/2)*q^192 + (7/4*a^6+5/2*a^5-37/2*a^4-21*a^3+179/4*a^2+45/2*a-19)*q^193 + (7/4*a^6+3*a^5-20*a^4-29*a^3+225/4*a^2+44*a-21)*q^194 + (-3*a^6-5*a^5+31*a^4+48*a^3-66*a^2-86*a+8)*q^195 + (1/2*a^6+1/4*a^5-15/2*a^4-a^3+59/2*a^2-1/4*a-63/2)*q^196 + (-13/4*a^6-11/2*a^5+71/2*a^4+51*a^3-345/4*a^2-147/2*a+23)*q^197 + (-a^6-2*a^5+11*a^4+19*a^3-31*a^2-27*a+14)*q^198 + (7/2*a^6+13/4*a^5-75/2*a^4-59/2*a^3+185/2*a^2+165/4*a-77/2)*q^199 + (-9/4*a^6-13/4*a^5+51/2*a^4+59/2*a^3-255/4*a^2-181/4*a+35/2)*q^200 +  ...

-------------------------------------------------------
Gamma_0(102)
Weight 2

-------------------------------------------------------
J_0(102), dim = 15

-------------------------------------------------------
102A (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) + G(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+         = 2.3639306388645945774 + 0.5023575064180533975e-6i
Omega-         = 0.17186350807172653743e-6 + -1.9478571713123440702i
L(1)           =
w1             = -2.3639306388645945774 + -0.5023575064180533975e-6i
w2             = -0.17186350807172653743e-6 + 1.9478571713123440702i
c4             = 121.00013069353014487 + -0.5482508814955385421e-4i
c6             = -845.00029244785460248 + 0.17630163304184473688e-3i
j              = 2894.7025361398818778 + 0.18411060877599331491e-2i

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

-------------------------------------------------------
102B (new) , 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/2 + Z/2) + D(Z/3 + Z/3) + 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))  = 3
Torsion Bound  = 2*3
|L(1)/Omega|   = 1/3
Sha Bound      = 2^2*3

ANALYTIC INVARIANTS:

Omega+         = 1.3930337809008413119 + 0.47823586903224788105e-6i
Omega-         = 0.48148642998448485527e-6 + 0.59706849290366886096i
L(1)           = 0.46434459363364113411
w1             = -1.3930337809008413119 + -0.47823586903224788105e-6i
w2             = 0.48148642998448485527e-6 + 0.59706849290366886096i
c4             = 12265.003471266374857 + 0.39541517390939431114e-1i
c6             = -1357813.5837998412218 + -6.5747481674191524483i
j              = 2326229.5832922410764 + 39.194406317755169325i

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^17 + -1*q^18 + -4*q^19 + 2*q^21 + -6*q^23 + -1*q^24 + -5*q^25 + -2*q^26 + 1*q^27 + 2*q^28 + -10*q^31 + -1*q^32 + 1*q^34 + 1*q^36 + 8*q^37 + 4*q^38 + 2*q^39 + 6*q^41 + -2*q^42 + -4*q^43 + 6*q^46 + 12*q^47 + 1*q^48 + -3*q^49 + 5*q^50 + -1*q^51 + 2*q^52 + 6*q^53 + -1*q^54 + -2*q^56 + -4*q^57 + -12*q^59 + 8*q^61 + 10*q^62 + 2*q^63 + 1*q^64 + -4*q^67 + -1*q^68 + -6*q^69 + 6*q^71 + -1*q^72 + 2*q^73 + -8*q^74 + -5*q^75 + -4*q^76 + -2*q^78 + -10*q^79 + 1*q^81 + -6*q^82 + 12*q^83 + 2*q^84 + 4*q^86 + -18*q^89 + 4*q^91 + -6*q^92 + -10*q^93 + -12*q^94 + -1*q^96 + 14*q^97 + 3*q^98 + -5*q^100 + 6*q^101 + 1*q^102 + -4*q^103 + -2*q^104 + -6*q^106 + 1*q^108 + 20*q^109 + 8*q^111 + 2*q^112 + -6*q^113 + 4*q^114 + 2*q^117 + 12*q^118 + -2*q^119 + -11*q^121 + -8*q^122 + 6*q^123 + -10*q^124 + -2*q^126 + 8*q^127 + -1*q^128 + -4*q^129 + -8*q^133 + 4*q^134 + 1*q^136 + -6*q^137 + 6*q^138 + 8*q^139 + 12*q^141 + -6*q^142 + 1*q^144 + -2*q^146 + -3*q^147 + 8*q^148 + -6*q^149 + 5*q^150 + 8*q^151 + 4*q^152 + -1*q^153 + 2*q^156 + -10*q^157 + 10*q^158 + 6*q^159 + -12*q^161 + -1*q^162 + 20*q^163 + 6*q^164 + -12*q^166 + 18*q^167 + -2*q^168 + -9*q^169 + -4*q^171 + -4*q^172 + -10*q^175 + -12*q^177 + 18*q^178 + -12*q^179 + 8*q^181 + -4*q^182 + 8*q^183 + 6*q^184 + 10*q^186 + 12*q^188 + 2*q^189 + -12*q^191 + 1*q^192 + 14*q^193 + -14*q^194 + -3*q^196 + -12*q^197 + 2*q^199 + 5*q^200 +  ...

-------------------------------------------------------
102C (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          = 2
ord((0)-(oo))  = 1
Torsion Bound  = 2^3
|L(1)/Omega|   = 1/2
Sha Bound      = 2^5

ANALYTIC INVARIANTS:

Omega+         = 1.4796783595015211903 + -0.11765462413483015153e-5i
Omega-         = 0.66258482610509697502e-6 + 0.99347975863241495971i
L(1)           = 0.73983917975099447386
w1             = -1.4796783595015211903 + 0.11765462413483015153e-5i
w2             = 0.66258482610509697502e-6 + 0.99347975863241495971i
c4             = 1633.0130596826662627 + 0.43962434457391532862e-2i
c6             = -61201.839134294708452 + -0.24154843185626423017i
j              = 12353.607779719664672 + -0.13887164561132607164e-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 + -2*q^13 + -2*q^15 + 1*q^16 + 1*q^17 + 1*q^18 + 4*q^19 + -2*q^20 + -4*q^22 + 1*q^24 + -1*q^25 + -2*q^26 + 1*q^27 + -10*q^29 + -2*q^30 + 8*q^31 + 1*q^32 + -4*q^33 + 1*q^34 + 1*q^36 + -2*q^37 + 4*q^38 + -2*q^39 + -2*q^40 + 10*q^41 + 12*q^43 + -4*q^44 + -2*q^45 + 1*q^48 + -7*q^49 + -1*q^50 + 1*q^51 + -2*q^52 + 6*q^53 + 1*q^54 + 8*q^55 + 4*q^57 + -10*q^58 + 12*q^59 + -2*q^60 + -10*q^61 + 8*q^62 + 1*q^64 + 4*q^65 + -4*q^66 + -12*q^67 + 1*q^68 + 1*q^72 + 10*q^73 + -2*q^74 + -1*q^75 + 4*q^76 + -2*q^78 + -8*q^79 + -2*q^80 + 1*q^81 + 10*q^82 + 4*q^83 + -2*q^85 + 12*q^86 + -10*q^87 + -4*q^88 + -6*q^89 + -2*q^90 + 8*q^93 + -8*q^95 + 1*q^96 + -14*q^97 + -7*q^98 + -4*q^99 + -1*q^100 + -10*q^101 + 1*q^102 + -8*q^103 + -2*q^104 + 6*q^106 + -4*q^107 + 1*q^108 + -10*q^109 + 8*q^110 + -2*q^111 + 2*q^113 + 4*q^114 + -10*q^116 + -2*q^117 + 12*q^118 + -2*q^120 + 5*q^121 + -10*q^122 + 10*q^123 + 8*q^124 + 12*q^125 + 1*q^128 + 12*q^129 + 4*q^130 + -12*q^131 + -4*q^132 + -12*q^134 + -2*q^135 + 1*q^136 + 10*q^137 + -4*q^139 + 8*q^143 + 1*q^144 + 20*q^145 + 10*q^146 + -7*q^147 + -2*q^148 + -10*q^149 + -1*q^150 + 24*q^151 + 4*q^152 + 1*q^153 + -16*q^155 + -2*q^156 + -2*q^157 + -8*q^158 + 6*q^159 + -2*q^160 + 1*q^162 + 4*q^163 + 10*q^164 + 8*q^165 + 4*q^166 + 16*q^167 + -9*q^169 + -2*q^170 + 4*q^171 + 12*q^172 + 6*q^173 + -10*q^174 + -4*q^176 + 12*q^177 + -6*q^178 + -12*q^179 + -2*q^180 + 14*q^181 + -10*q^183 + 4*q^185 + 8*q^186 + -4*q^187 + -8*q^190 + -16*q^191 + 1*q^192 + 18*q^193 + -14*q^194 + 4*q^195 + -7*q^196 + 14*q^197 + -4*q^198 + -1*q^200 +  ...

-------------------------------------------------------
102D (old = 51A), dim = 1

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

-------------------------------------------------------
102E (old = 51B), dim = 2

CONGRUENCES:
Modular Degree = 2^8
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2 + Z/2^2 + Z/2^4 + Z/2^4
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2) + G(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2)

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102F (old = 34A), 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/3 + Z/3) + E(Z/2 + Z/2) + G(Z/2 + Z/2 + Z/2 + Z/2)

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102G (old = 17A), 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 + Z/2) + B(Z/2 + Z/2) + C(Z/2^2 + Z/2^2) + E(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2) + F(Z/2 + Z/2 + Z/2 + Z/2)

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Gamma_0(103)
Weight 2

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J_0(103), dim = 8

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103A (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+         = 16.854911030968144024 + -0.38300636059471944568e-5i
Omega-         = 6.4767628147155182793 + -0.15929746471610142669e-6i
L(1)           =

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

-------------------------------------------------------
103B (new) , dim = 6

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   = 17*411721
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 17
Torsion Bound  = 17
|L(1)/Omega|   = 2^2/17
Sha Bound      = 2^2*17

ANALYTIC INVARIANTS:

Omega+         = 12.993918297898561257 + -0.23954686609746228273e-5i
Omega-         = 153.34668315311180994 + -0.46488877925228758335e-4i
L(1)           = 3.0573925406820663677

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

-------------------------------------------------------
Gamma_0(104)
Weight 2

-------------------------------------------------------
J_0(104), dim = 11

-------------------------------------------------------
104A (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/2^2 + 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|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.1836111010346531411 + -0.25311816065107616132e-6i
Omega-         = 0.31472941608619697177e-6 + -3.7085477760628479713i
L(1)           = 1.1836111010346802061
w1             = 0.59180539315261852747 + 1.8542737614723436601i
w2             = 1.1836111010346531411 + -0.25311816065107616132e-6i
c4             = 784.00012941085114515 + 0.70036879508392573484e-3i
c6             = 22976.004972422125452 + 0.27726130809503477675e-1i
j              = -18099.859104590329299 + -0.55347578177176201067e-1i

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

-------------------------------------------------------
104B (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) + C(Z/2 + Z/2) + D(Z/2^2 + Z/2^2) + E(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|   = 1/2^2
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 2.6290902124468387748 + 0.60617526957009839925e-6i
Omega-         = 1.4791786863707357294 + -0.13688645093063462687e-6i
L(1)           = 0.65727255311172716401

HECKE EIGENFORM:
a^2-a-4 = 0,
f(q) = q + a*q^3 + (-a+2)*q^5 + -a*q^7 + (a+1)*q^9 + -2*a*q^11 + 1*q^13 + (a-4)*q^15 + (3*a-2)*q^17 + 2*a*q^19 + (-a-4)*q^21 + -8*q^23 + (-3*a+3)*q^25 + (-a+4)*q^27 + -2*q^29 + 4*q^31 + (-2*a-8)*q^33 + (-a+4)*q^35 + (3*a+2)*q^37 + a*q^39 + (-2*a+2)*q^41 + (-a+8)*q^43 + -2*q^45 + (3*a-8)*q^47 + (a-3)*q^49 + (a+12)*q^51 + (2*a-2)*q^53 + (-2*a+8)*q^55 + (2*a+8)*q^57 + 2*a*q^59 + (2*a+6)*q^61 + (-2*a-4)*q^63 + (-a+2)*q^65 + -2*a*q^67 + -8*a*q^69 + -3*a*q^71 + -6*q^73 + -12*q^75 + (2*a+8)*q^77 + 8*q^79 + -7*q^81 + (4*a-8)*q^83 + (5*a-16)*q^85 + -2*a*q^87 + 10*q^89 + -a*q^91 + 4*a*q^93 + (2*a-8)*q^95 + (-4*a+2)*q^97 + (-4*a-8)*q^99 + (-2*a-2)*q^101 + (4*a-8)*q^103 + (3*a-4)*q^105 + 4*q^107 + (-5*a+10)*q^109 + (5*a+12)*q^111 + (-8*a+2)*q^113 + (8*a-16)*q^115 + (a+1)*q^117 + (-a-12)*q^119 + (4*a+5)*q^121 + -8*q^123 + (-a+8)*q^125 + -4*a*q^127 + (7*a-4)*q^129 + (-5*a+8)*q^131 + (-2*a-8)*q^133 + (-5*a+12)*q^135 + (-2*a+2)*q^137 + 3*a*q^139 + (-5*a+12)*q^141 + -2*a*q^143 + (2*a-4)*q^145 + (-2*a+4)*q^147 + (4*a+6)*q^149 + (a+8)*q^151 + (4*a+10)*q^153 + (-4*a+8)*q^155 + (-8*a-2)*q^157 + 8*q^159 + 8*a*q^161 + -8*a*q^163 + (6*a-8)*q^165 + (4*a+4)*q^167 + 1*q^169 + (4*a+8)*q^171 + (2*a-10)*q^173 + 12*q^175 + (2*a+8)*q^177 + 3*a*q^179 + (-2*a-18)*q^181 + (8*a+8)*q^183 + (a-8)*q^185 + (-2*a-24)*q^187 + (-3*a+4)*q^189 + 6*a*q^191 + (-6*a-6)*q^193 + (a-4)*q^195 + (-3*a+10)*q^197 + 2*a*q^199 +  ...

-------------------------------------------------------
104C (old = 52A), dim = 1

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

-------------------------------------------------------
104D (old = 26A), dim = 1

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

-------------------------------------------------------
104E (old = 26B), 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/2^2 + Z/2^2) + B(Z/2 + Z/2) + C(Z/3 + Z/3 + Z/3 + Z/3) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(105)
Weight 2

-------------------------------------------------------
J_0(105), dim = 13

-------------------------------------------------------
105A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= B(Z/2) + D(Z/2) + E(Z/2) + F(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+         = 2.9317275510183537865 + -0.28739451799715567843e-6i
Omega-         = 0.13008967536064441574e-5 + -1.9014694698516810031i
L(1)           = 0.73293188775459196824
w1             = 2.9317275510183537865 + -0.28739451799715567843e-6i
w2             = 0.13008967536064441574e-5 + -1.9014694698516810031i
c4             = 121.00004721868156614 + -0.31766154923172974085e-3i
c6             = -1261.0009993326034285 + 0.54860653562632782182e-2i
j              = 16872.07078062493424 + -0.12202236521212928782i

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

-------------------------------------------------------
105B (new) , dim = 2

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

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

ANALYTIC INVARIANTS:

Omega+         = 1.5707450907681039146 + 0.13932324006377474441e-6i
Omega-         = 3.2018642376324040336 + 0.105218235076480397e-5i
L(1)           = 0.39268627269202752339

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

-------------------------------------------------------
105C (old = 35A), dim = 1

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

-------------------------------------------------------
105D (old = 35B), dim = 2

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) + B(Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2^2) + F(Z/2 + Z/2^2)

-------------------------------------------------------
105E (old = 21A), 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 + Z/2) + D(Z/2 + Z/2^2) + F(Z/2)

-------------------------------------------------------
105F (old = 15A), 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) + D(Z/2 + Z/2^2) + E(Z/2)

-------------------------------------------------------
Gamma_0(106)
Weight 2

-------------------------------------------------------
J_0(106), dim = 12

-------------------------------------------------------
106A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= 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|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 5.012883526394776163 + 0.95953038912720265304e-6i
Omega-         = 0.8767267496317430719e-8 + 1.4399212073451028075i
L(1)           =
w1             = -2.5064417588137543333 + 0.71996012390735684017i
w2             = 0.8767267496317430719e-8 + 1.4399212073451028075i
c4             = 360.99973717893676874 + 0.12134210329616846147e-4i
c6             = -6964.9922605984062474 + -0.12092532555632567238e-3i
j              = -55478.703527534441497 + -0.12143030923959645655i

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

-------------------------------------------------------
106B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*5
Ker(ModPolar)  = Z/2*5 + Z/2*5
= D(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+         = 1.0421605959864394203 + -0.28300987079922823003e-5i
Omega-         = 0.35680389050003533905e-5 + 4.6850130294921132408i
L(1)           = 1.0421605959902821384
w1             = 0.52108208201267221032 + 2.3425050996967026243i
w2             = 1.0421605959864394203 + -0.28300987079922823003e-5i
c4             = 1321.0042990747393307 + 0.14355749072585862996e-1i
c6             = 48043.233992214033816 + 0.78230813907583641399i
j              = -1359221.3806938582525 + -37.530392248186705399i

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

-------------------------------------------------------
106C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^4*3
Ker(ModPolar)  = Z/2^4*3 + Z/2^4*3
= A(Z/2 + Z/2) + D(Z/3 + Z/3) + 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))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 2^3/3
Sha Bound      = 2^3*3

ANALYTIC INVARIANTS:

Omega+         = 0.57179918344942778689 + 0.33435604470515565952e-6i
Omega-         = 0.91766628200850811047e-6 + -1.4857711097495409381i
L(1)           = 1.5247978225320681152
w1             = 0.28589913289157288919 + 0.7428857220527928216i
w2             = 0.57179918344942778689 + 0.33435604470515565952e-6i
c4             = 13585.039375540063522 + -0.31508713032618288983e-1i
c6             = 2010887.4138295056531 + -7.1217387305181030176i
j              = -2819.6332974045290189 + -0.92811658146543472793e-3i

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

-------------------------------------------------------
106D (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+         = 3.7857835528613840914 + 0.52028974392809891173e-7i
Omega-         = 0.15866968688305135942e-5 + 2.6867174932381960866i
L(1)           = 1.2619278509537948163
w1             = 1.892892569779126461 + 1.3433587726335852397i
w2             = 1.8928909830822576305 + -1.3433587206046108469i
c4             = -46.999851248271648474 + 0.71778088492831734195e-4i
c6             = -793.00307903740387168 + -0.19959468150527091763e-2i
j              = 244.86193850041281148 + -0.20208333212745072892e-2i

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

-------------------------------------------------------
106E (old = 53A), 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) + F(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
106F (old = 53B), dim = 3

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

-------------------------------------------------------
Gamma_0(107)
Weight 2

-------------------------------------------------------
J_0(107), dim = 9

-------------------------------------------------------
107A (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+         = 11.882999353383721519 + 0.33328460304454545584e-5i
Omega-         = 9.0502098092521051131 + 0.11339906328759601086e-5i
L(1)           =

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

-------------------------------------------------------
107B (new) , dim = 7

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   = 2^2*7*1667*19079
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 53
Torsion Bound  = 53
|L(1)/Omega|   = 2^2/53
Sha Bound      = 2^2*53

ANALYTIC INVARIANTS:

Omega+         = 16.522852560380561105 + 0.55296926958159726788e-5i
Omega-         = 0.41893369630077585394e-4 + -67.391134206442778979i
L(1)           = 1.2470077404061499181

HECKE EIGENFORM:
a^7+a^6-10*a^5-7*a^4+29*a^3+12*a^2-20*a-8 = 0,
f(q) = q + a*q^2 + (-1/4*a^6-1/4*a^5+5/2*a^4+3/4*a^3-29/4*a^2+2*a+4)*q^3 + (a^2-2)*q^4 + (1/2*a^6+1/2*a^5-4*a^4-5/2*a^3+15/2*a^2+a)*q^5 + (-a^4+5*a^2-a-2)*q^6 + (-1/2*a^6-1/2*a^5+4*a^4+7/2*a^3-15/2*a^2-6*a+2)*q^7 + (a^3-4*a)*q^8 + (1/4*a^6-1/4*a^5-2*a^4+9/4*a^3+15/4*a^2-9/2*a-1)*q^9 + (a^5+a^4-7*a^3-5*a^2+10*a+4)*q^10 + (1/2*a^5-1/2*a^4-4*a^3+5/2*a^2+11/2*a)*q^11 + (1/2*a^6-1/2*a^5-5*a^4+7/2*a^3+27/2*a^2-6*a-8)*q^12 + (1/2*a^6-11/2*a^4+1/2*a^3+17*a^2-7/2*a-8)*q^13 + (-a^5+7*a^3-8*a-4)*q^14 + (-1/2*a^6+1/2*a^5+6*a^4-11/2*a^3-39/2*a^2+14*a+10)*q^15 + (a^4-6*a^2+4)*q^16 + (a^5+a^4-7*a^3-5*a^2+10*a+4)*q^17 + (-1/2*a^6+1/2*a^5+4*a^4-7/2*a^3-15/2*a^2+4*a+2)*q^18 + (-3/4*a^6-5/4*a^5+6*a^4+33/4*a^3-45/4*a^2-19/2*a)*q^19 + (a^4-5*a^2+2*a)*q^20 + (-a^6-a^5+9*a^4+6*a^3-22*a^2-5*a+8)*q^21 + (1/2*a^6-1/2*a^5-4*a^4+5/2*a^3+11/2*a^2)*q^22 + (3/4*a^6-3/4*a^5-9*a^4+23/4*a^3+113/4*a^2-21/2*a-16)*q^23 + (-a^6+9*a^4-a^3-22*a^2+4*a+8)*q^24 + (a^6-11*a^4+2*a^3+32*a^2-10*a-13)*q^25 + (-1/2*a^6-1/2*a^5+4*a^4+5/2*a^3-19/2*a^2+2*a+4)*q^26 + (1/4*a^6+1/4*a^5-3/2*a^4-3/4*a^3+13/4*a^2-2*a-5)*q^27 + (a^5-a^4-7*a^3+7*a^2+8*a-4)*q^28 + (a^5+a^4-7*a^3-4*a^2+12*a+1)*q^29 + (a^6+a^5-9*a^4-5*a^3+20*a^2-4)*q^30 + (a^4-7*a^2+2*a+8)*q^31 + (a^5-8*a^3+12*a)*q^32 + (1/2*a^6+a^5-9/2*a^4-11/2*a^3+11*a^2+11/2*a-3)*q^33 + (a^6+a^5-7*a^4-5*a^3+10*a^2+4*a)*q^34 + (-a^5+9*a^3-18*a-4)*q^35 + (1/2*a^6-1/2*a^5-3*a^4+5/2*a^3+5/2*a^2+a-2)*q^36 + (-1/4*a^6+3/4*a^5+7/2*a^4-21/4*a^3-49/4*a^2+7*a+12)*q^37 + (-1/2*a^6-3/2*a^5+3*a^4+21/2*a^3-1/2*a^2-15*a-6)*q^38 + (-1/2*a^5+1/2*a^4+a^3-3/2*a^2+15/2*a-5)*q^39 + (-a^5-2*a^4+9*a^3+12*a^2-20*a-8)*q^40 + (-3/4*a^6-3/4*a^5+13/2*a^4+21/4*a^3-51/4*a^2-7*a)*q^41 + (-a^5-a^4+7*a^3+7*a^2-12*a-8)*q^42 + (1/2*a^6+3/2*a^5-3*a^4-17/2*a^3+5/2*a^2+8*a+6)*q^43 + (-a^6+7*a^4-a^3-11*a^2-a+4)*q^44 + (1/2*a^6-1/2*a^5-6*a^4+11/2*a^3+39/2*a^2-16*a-8)*q^45 + (-3/2*a^6-3/2*a^5+11*a^4+13/2*a^3-39/2*a^2-a+6)*q^46 + (a^5-9*a^3-a^2+18*a+3)*q^47 + (2*a^4-11*a^2+8)*q^48 + (2*a^5+a^4-16*a^3-7*a^2+26*a+13)*q^49 + (-a^6-a^5+9*a^4+3*a^3-22*a^2+7*a+8)*q^50 + (a^6+a^5-9*a^4-5*a^3+20*a^2-4)*q^51 + (-a^6-a^5+10*a^4+4*a^3-26*a^2+a+12)*q^52 + (-5/4*a^6-7/4*a^5+12*a^4+39/4*a^3-131/4*a^2-11/2*a+16)*q^53 + (a^5+a^4-4*a^3-5*a^2+2)*q^54 + (1/2*a^6+1/2*a^5-4*a^4-9/2*a^3+11/2*a^2+11*a+2)*q^55 + (a^6+a^5-7*a^4-7*a^3+8*a^2+12*a+8)*q^56 + (-3/4*a^6-7/4*a^5+9/2*a^4+49/4*a^3-15/4*a^2-19*a-3)*q^57 + (a^6+a^5-7*a^4-4*a^3+12*a^2+a)*q^58 + (-a^5-2*a^4+7*a^3+12*a^2-10*a-14)*q^59 + (a^6-10*a^4+2*a^3+27*a^2-12*a-12)*q^60 + (-3/4*a^6-5/4*a^5+5*a^4+29/4*a^3-33/4*a^2-13/2*a+8)*q^61 + (a^5-7*a^3+2*a^2+8*a)*q^62 + (1/2*a^6+1/2*a^5-4*a^4-5/2*a^3+11/2*a^2+3*a+4)*q^63 + (a^6-10*a^4+24*a^2-8)*q^64 + (5/2*a^6+3/2*a^5-22*a^4-11/2*a^3+99/2*a^2-7*a-14)*q^65 + (1/2*a^6+1/2*a^5-2*a^4-7/2*a^3-1/2*a^2+7*a+4)*q^66 + (-a^6-a^5+10*a^4+7*a^3-29*a^2-10*a+14)*q^67 + (a^5-5*a^3+2*a^2)*q^68 + (-1/4*a^6-1/4*a^5+3/2*a^4-1/4*a^3+11/4*a^2+9*a-13)*q^69 + (-a^6+9*a^4-18*a^2-4*a)*q^70 + (3*a^4-a^3-19*a^2+5*a+12)*q^71 + (a^5-2*a^4-5*a^3+10*a^2)*q^72 + (-1/2*a^6-3/2*a^5+5*a^4+19/2*a^3-25/2*a^2-5*a+4)*q^73 + (a^6+a^5-7*a^4-5*a^3+10*a^2+7*a-2)*q^74 + (-7/4*a^6+1/4*a^5+33/2*a^4-27/4*a^3-159/4*a^2+28*a+8)*q^75 + (1/2*a^6+1/2*a^5-5*a^4-5/2*a^3+27/2*a^2+3*a-4)*q^76 + (-a^6-a^5+7*a^4+7*a^3-6*a^2-16*a-10)*q^77 + (-1/2*a^6+1/2*a^5+a^4-3/2*a^3+15/2*a^2-5*a)*q^78 + (-a^6-1/2*a^5+19/2*a^4+2*a^3-49/2*a^2+1/2*a+8)*q^79 + (-a^6-2*a^5+7*a^4+12*a^3-10*a^2-12*a)*q^80 + (1/4*a^6+1/4*a^5-5/2*a^4-11/4*a^3+33/4*a^2+4*a-11)*q^81 + (-a^5+9*a^3+2*a^2-15*a-6)*q^82 + (2*a^6+2*a^5-18*a^4-10*a^3+47*a^2-25)*q^83 + (a^6+a^5-11*a^4-5*a^3+32*a^2+2*a-16)*q^84 + (-a^6-a^5+9*a^4+3*a^3-22*a^2+12*a+8)*q^85 + (a^6+2*a^5-5*a^4-12*a^3+2*a^2+16*a+4)*q^86 + (7/4*a^6+3/4*a^5-37/2*a^4-9/4*a^3+203/4*a^2-10*a-20)*q^87 + (-2*a^5+13*a^3-16*a-8)*q^88 + (1/2*a^6-9/2*a^4-3/2*a^3+6*a^2+13/2*a+4)*q^89 + (-a^6-a^5+9*a^4+5*a^3-22*a^2+2*a+4)*q^90 + (-4*a^4+2*a^3+26*a^2-14*a-22)*q^91 + (-3/2*a^6-5/2*a^5+14*a^4+25/2*a^3-79/2*a^2-3*a+20)*q^92 + (-a^6+10*a^4-2*a^3-29*a^2+8*a+20)*q^93 + (a^6-9*a^4-a^3+18*a^2+3*a)*q^94 + (-a^6+11*a^4+a^3-30*a^2-5*a+4)*q^95 + (2*a^6+2*a^5-18*a^4-9*a^3+44*a^2-16)*q^96 + (1/2*a^6+1/2*a^5-2*a^4-3/2*a^3-5/2*a^2-2*a+2)*q^97 + (2*a^6+a^5-16*a^4-7*a^3+26*a^2+13*a)*q^98 + (-1/4*a^6-1/4*a^5+3/2*a^4+11/4*a^3-9/4*a^2-4*a-3)*q^99 + (-2*a^6-a^5+18*a^4+3*a^3-45*a^2+8*a+18)*q^100 + (-7/4*a^6-7/4*a^5+31/2*a^4+33/4*a^3-155/4*a^2-3*a+20)*q^101 + (a^5+2*a^4-9*a^3-12*a^2+16*a+8)*q^102 + (1/2*a^6+3/2*a^5-4*a^4-21/2*a^3+23/2*a^2+16*a-10)*q^103 + (a^6+a^5-11*a^4-2*a^3+32*a^2-12*a-16)*q^104 + (-2*a^6-a^5+19*a^4+5*a^3-47*a^2-2*a+12)*q^105 + (-1/2*a^6-1/2*a^5+a^4+7/2*a^3+19/2*a^2-9*a-10)*q^106 + 1*q^107 + (1/2*a^6+1/2*a^5-a^4-7/2*a^3-13/2*a^2+6*a+10)*q^108 + (1/2*a^6-1/2*a^5-5*a^4+9/2*a^3+29/2*a^2-7*a-12)*q^109 + (a^5-a^4-9*a^3+5*a^2+12*a+4)*q^110 + (-3/4*a^6-1/4*a^5+9*a^4-3/4*a^3-129/4*a^2+17/2*a+24)*q^111 + (a^5+2*a^4-7*a^3-14*a^2+12*a+16)*q^112 + (-1/2*a^6+1/2*a^5+9*a^4-11/2*a^3-77/2*a^2+16*a+22)*q^113 + (-a^6-3*a^5+7*a^4+18*a^3-10*a^2-18*a-6)*q^114 + (3*a^6+3*a^5-27*a^4-14*a^3+64*a^2-7*a-20)*q^115 + (a^5+a^4-3*a^3-3*a^2-4*a+6)*q^116 + (9/4*a^6-3/4*a^5-39/2*a^4+33/4*a^3+177/4*a^2-20*a-19)*q^117 + (-a^6-2*a^5+7*a^4+12*a^3-10*a^2-14*a)*q^118 + (-a^6+9*a^4-18*a^2-4*a)*q^119 + (-3*a^6-2*a^5+27*a^4+8*a^3-64*a^2+8*a+16)*q^120 + (1/4*a^6+9/4*a^5-1/2*a^4-63/4*a^3-3/4*a^2+21*a-1)*q^121 + (-1/2*a^6-5/2*a^5+2*a^4+27/2*a^3+5/2*a^2-7*a-6)*q^122 + (-1/4*a^6-7/4*a^5+51/4*a^3+25/4*a^2-45/2*a-8)*q^123 + (a^6-9*a^4+2*a^3+22*a^2-4*a-16)*q^124 + (2*a^6-23*a^4+6*a^3+71*a^2-34*a-32)*q^125 + (a^5+a^4-9*a^3-3*a^2+14*a+4)*q^126 + (3/2*a^6-1/2*a^5-14*a^4+11/2*a^3+77/2*a^2-6*a-28)*q^127 + (-a^6-2*a^5+7*a^4+11*a^3-12*a^2-12*a+8)*q^128 + (-a^6+a^5+10*a^4-10*a^3-31*a^2+21*a+20)*q^129 + (-a^6+3*a^5+12*a^4-23*a^3-37*a^2+36*a+20)*q^130 + (1/2*a^6-3/2*a^5-10*a^4+21/2*a^3+83/2*a^2-18*a-32)*q^131 + (-a^6+a^5+9*a^4-4*a^3-21*a^2+3*a+10)*q^132 + (a^6+2*a^5-7*a^4-17*a^3+6*a^2+37*a+18)*q^133 + (2*a^2-6*a-8)*q^134 + (-a^6-3*a^5+7*a^4+20*a^3-8*a^2-23*a-10)*q^135 + (-a^6-2*a^5+9*a^4+12*a^3-20*a^2-8*a)*q^136 + (a^6+a^5-8*a^4-3*a^3+14*a^2-8*a+5)*q^137 + (-a^5-2*a^4+10*a^3+12*a^2-18*a-2)*q^138 + (3/2*a^6-1/2*a^5-15*a^4+21/2*a^3+87/2*a^2-35*a-28)*q^139 + (a^6+a^5-7*a^4-7*a^3+8*a^2+16*a)*q^140 + (9/4*a^6+9/4*a^5-43/2*a^4-43/4*a^3+221/4*a^2+2*a-16)*q^141 + (3*a^5-a^4-19*a^3+5*a^2+12*a)*q^142 + (-5/4*a^6+7/4*a^5+21/2*a^4-53/4*a^3-89/4*a^2+18*a+16)*q^143 + (-a^5+a^4+5*a^3-5*a^2-2*a+4)*q^144 + (-3/2*a^6+1/2*a^5+16*a^4-17/2*a^3-89/2*a^2+33*a+16)*q^145 + (-a^6+6*a^4+2*a^3+a^2-6*a-4)*q^146 + (7/4*a^6+11/4*a^5-27/2*a^4-65/4*a^3+91/4*a^2+18*a+8)*q^147 + (1/2*a^6+3/2*a^5-5*a^4-17/2*a^3+39/2*a^2+4*a-16)*q^148 + (-1/2*a^6+2*a^5+17/2*a^4-31/2*a^3-32*a^2+53/2*a+20)*q^149 + (2*a^6-a^5-19*a^4+11*a^3+49*a^2-27*a-14)*q^150 + (-3/4*a^6-11/4*a^5+13/2*a^4+73/4*a^3-59/4*a^2-24*a-4)*q^151 + (a^6+3*a^5-5*a^4-22*a^3-2*a^2+36*a+16)*q^152 + (-a^6-a^5+9*a^4+5*a^3-22*a^2+2*a+4)*q^153 + (-3*a^5+23*a^3-4*a^2-30*a-8)*q^154 + (a^5-7*a^3+8*a+8)*q^155 + (a^6-3*a^5-6*a^4+20*a^3+4*a^2-25*a+6)*q^156 + (-a^6+8*a^4-2*a^3-19*a^2+4*a+28)*q^157 + (1/2*a^6-1/2*a^5-5*a^4+9/2*a^3+25/2*a^2-12*a-8)*q^158 + (-5/4*a^6-9/4*a^5+25/2*a^4+59/4*a^3-141/4*a^2-18*a+25)*q^159 + (-a^6-a^5+9*a^4+a^3-24*a^2+20*a+8)*q^160 + (2*a^6-a^5-22*a^4+10*a^3+66*a^2-21*a-42)*q^161 + (-a^4+a^3+a^2-6*a+2)*q^162 + (-1/2*a^5+1/2*a^4+2*a^3-13/2*a^2+17/2*a+12)*q^163 + (1/2*a^6+3/2*a^5-4*a^4-17/2*a^3+21/2*a^2+8*a)*q^164 + (a^6+2*a^5-9*a^4-12*a^3+22*a^2+12*a-2)*q^165 + (2*a^5+4*a^4-11*a^3-24*a^2+15*a+16)*q^166 + (-3*a^6-a^5+29*a^4+a^3-78*a^2+14*a+34)*q^167 + (a^5+4*a^4-11*a^3-24*a^2+28*a+24)*q^168 + (1/4*a^6-7/4*a^5-7/2*a^4+49/4*a^3+49/4*a^2-23*a-7)*q^169 + (-a^5-4*a^4+7*a^3+24*a^2-12*a-8)*q^170 + (-1/4*a^6+7/4*a^5+7/2*a^4-53/4*a^3-53/4*a^2+22*a+12)*q^171 + (2*a^5+a^4-10*a^3-a^2+8*a-4)*q^172 + (-2*a^6-2*a^5+18*a^4+11*a^3-44*a^2-3*a+26)*q^173 + (-a^6-a^5+10*a^4-31*a^2+15*a+14)*q^174 + (3/2*a^6-3/2*a^5-17*a^4+29/2*a^3+107/2*a^2-34*a-34)*q^175 + (-a^4+2*a^3+6*a^2-6*a-8)*q^176 + (1/2*a^6-1/2*a^5-8*a^4+11/2*a^3+67/2*a^2-14*a-28)*q^177 + (-1/2*a^6+1/2*a^5+2*a^4-17/2*a^3+1/2*a^2+14*a+4)*q^178 + (-1/2*a^6-1/2*a^5+6*a^4+5/2*a^3-39/2*a^2+5*a+8)*q^179 + (-a^6+10*a^4-4*a^3-25*a^2+16*a+8)*q^180 + (3/2*a^6+3/2*a^5-14*a^4-13/2*a^3+73/2*a^2-6*a-12)*q^181 + (-4*a^5+2*a^4+26*a^3-14*a^2-22*a)*q^182 + (-11/4*a^6-7/4*a^5+49/2*a^4+29/4*a^3-239/4*a^2+8*a+31)*q^183 + (2*a^6+2*a^5-20*a^4-9*a^3+54*a^2-8*a-24)*q^184 + (1/2*a^6-1/2*a^5-4*a^4+7/2*a^3+11/2*a^2+6)*q^185 + (a^6-9*a^4+20*a^2-8)*q^186 + (a^5-a^4-9*a^3+5*a^2+12*a+4)*q^187 + (-a^6-a^5+6*a^4+7*a^3-7*a^2-16*a+2)*q^188 + (3/2*a^6+9/2*a^5-13*a^4-61/2*a^3+59/2*a^2+39*a-2)*q^189 + (a^6+a^5-6*a^4-a^3+7*a^2-16*a-8)*q^190 + (-2*a^6-2*a^5+18*a^4+11*a^3-40*a^2-3*a+8)*q^191 + (2*a^5+a^4-14*a^3-2*a^2+24*a)*q^192 + (-5/4*a^6-15/4*a^5+7*a^4+87/4*a^3-23/4*a^2-39/2*a-8)*q^193 + (3*a^5+2*a^4-17*a^3-8*a^2+12*a+4)*q^194 + (-2*a^6+2*a^5+24*a^4-22*a^3-74*a^2+58*a+26)*q^195 + (-a^6+5*a^4+3*a^2-12*a-10)*q^196 + (1/4*a^6-7/4*a^5-13/2*a^4+41/4*a^3+133/4*a^2-9*a-32)*q^197 + (-a^5+a^4+5*a^3-a^2-8*a-2)*q^198 + (-5/4*a^6+7/4*a^5+31/2*a^4-61/4*a^3-213/4*a^2+32*a+40)*q^199 + (3*a^6-29*a^4+7*a^3+76*a^2-36*a-32)*q^200 +  ...

-------------------------------------------------------
Gamma_0(108)
Weight 2

-------------------------------------------------------
J_0(108), dim = 10

-------------------------------------------------------
108A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/3) + D(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|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 3.3387398707388393033 + -0.96751550999626062959e-6i
Omega-         = 0.55859534014147913175e-6 + 1.927622363125205201i
L(1)           = 1.1129132902463264963
w1             = -1.6693702146670897224 + -0.96381069780484760236i
w2             = -1.6693696560717495809 + 0.96381166532035759862i
c4             = -0.13247157264675124722e-9 + 0.22944688017233964905e-9i
c6             = -3455.9885274411795301 + -0.60089542140912209623e-2i
j              = -0.26906338489013003736e-32 + -0.77066052562031728546e-62i

HECKE EIGENFORM:
f(q) = q + 5*q^7 + -7*q^13 + -1*q^19 + -5*q^25 + -4*q^31 + -1*q^37 + 8*q^43 + 18*q^49 + -13*q^61 + 11*q^67 + 17*q^73 + -13*q^79 + -35*q^91 + 5*q^97 + -7*q^103 + 2*q^109 + -11*q^121 + 20*q^127 + -5*q^133 + -7*q^139 + 23*q^151 + 14*q^157 + 17*q^163 + 36*q^169 + -25*q^175 + -19*q^181 + -25*q^193 + 17*q^199 +  ...

-------------------------------------------------------
108B (old = 54A), dim = 1

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) + D(Z/3) + E(Z/3 + Z/3 + Z/3)

-------------------------------------------------------
108C (old = 54B), dim = 1

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

-------------------------------------------------------
108D (old = 36A), dim = 1

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

-------------------------------------------------------
108E (old = 27A), dim = 1

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

-------------------------------------------------------
Gamma_0(109)
Weight 2

-------------------------------------------------------
J_0(109), dim = 8

-------------------------------------------------------
109A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= C(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|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.4110263682167413753 + 0.13952041826282227077e-6i
Omega-         = 0.32682216092863162283e-5 + 5.942804120282169042i
L(1)           = 1.4110263682167482731
w1             = -0.70551154999756604451 + 2.9714019903808753896i
w2             = 1.4110263682167413753 + 0.13952041826282227077e-6i
c4             = 392.99949567420591348 + -0.15688979505617466803e-3i
c6             = 7802.9850344147283756 + -0.45688072989908976072e-2i
j              = -556864.0649888284271 + 4.7869847333913974165i

HECKE EIGENFORM:
f(q) = q + 1*q^2 + -1*q^4 + 3*q^5 + 2*q^7 + -3*q^8 + -3*q^9 + 3*q^10 + 1*q^11 + 2*q^14 + -1*q^16 + -8*q^17 + -3*q^18 + -5*q^19 + -3*q^20 + 1*q^22 + 7*q^23 + 4*q^25 + -2*q^28 + -5*q^29 + 6*q^31 + 5*q^32 + -8*q^34 + 6*q^35 + 3*q^36 + 2*q^37 + -5*q^38 + -9*q^40 + 2*q^41 + -4*q^43 + -1*q^44 + -9*q^45 + 7*q^46 + 9*q^47 + -3*q^49 + 4*q^50 + 12*q^53 + 3*q^55 + -6*q^56 + -5*q^58 + 12*q^59 + -5*q^61 + 6*q^62 + -6*q^63 + 7*q^64 + -12*q^67 + 8*q^68 + 6*q^70 + -6*q^71 + 9*q^72 + -5*q^73 + 2*q^74 + 5*q^76 + 2*q^77 + 8*q^79 + -3*q^80 + 9*q^81 + 2*q^82 + -2*q^83 + -24*q^85 + -4*q^86 + -3*q^88 + 1*q^89 + -9*q^90 + -7*q^92 + 9*q^94 + -15*q^95 + 1*q^97 + -3*q^98 + -3*q^99 + -4*q^100 + 12*q^101 + -11*q^103 + 12*q^106 + 3*q^107 + 1*q^109 + 3*q^110 + -2*q^112 + -18*q^113 + 21*q^115 + 5*q^116 + 12*q^118 + -16*q^119 + -10*q^121 + -5*q^122 + -6*q^124 + -3*q^125 + -6*q^126 + -7*q^127 + -3*q^128 + -10*q^133 + -12*q^134 + 24*q^136 + 1*q^137 + 16*q^139 + -6*q^140 + -6*q^142 + 3*q^144 + -15*q^145 + -5*q^146 + -2*q^148 + 6*q^149 + 1*q^151 + 15*q^152 + 24*q^153 + 2*q^154 + 18*q^155 + 17*q^157 + 8*q^158 + 15*q^160 + 14*q^161 + 9*q^162 + -13*q^163 + -2*q^164 + -2*q^166 + 8*q^167 + -13*q^169 + -24*q^170 + 15*q^171 + 4*q^172 + 6*q^173 + 8*q^175 + -1*q^176 + 1*q^178 + 11*q^179 + 9*q^180 + -10*q^181 + -21*q^184 + 6*q^185 + -8*q^187 + -9*q^188 + -15*q^190 + 12*q^191 + -13*q^193 + 1*q^194 + 3*q^196 + -17*q^197 + -3*q^198 + 16*q^199 + -12*q^200 +  ...

-------------------------------------------------------
109B (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+         = 92.89275647652801019 + 0.68455791412511956031e-4i
Omega-         = 0.89166602919176795142e-6 + 5.8765457547921628262i
L(1)           =

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

-------------------------------------------------------
109C (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/2^2 + Z/2^2) + B(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 7537
#CompGroup(Fpbar) = ?
c_p            = ?
c_inf          = 1
ord((0)-(oo))  = 3^2
Torsion Bound  = 3^2
|L(1)/Omega|   = 2^3/3^2
Sha Bound      = 2^3*3^2

ANALYTIC INVARIANTS:

Omega+         = 1.3389440470038420979 + 0.27178050632086781211e-6i
Omega-         = 33.928909407695456802 + 0.56270170658224334284e-4i
L(1)           = 1.1901724862256619387

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

-------------------------------------------------------
Gamma_0(110)
Weight 2

-------------------------------------------------------
J_0(110), dim = 15

-------------------------------------------------------
110A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*7
Ker(ModPolar)  = Z/2^2*7 + Z/2^2*7
= B(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))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 2.8261745238442562233 + -0.17473163256460317271e-5i
Omega-         = 0.10079461921447086311e-6 + 0.77771597130706759803i
L(1)           = 0.94205817461493212433
w1             = -1.4130873123194377189 + -0.388857111995370976i
w2             = 0.10079461921447086311e-6 + 0.77771597130706759803i
c4             = 4248.9930842695786681 + 0.21399253341871595678e-2i
c6             = -279612.32293992480666 + -0.22603694134414430033i
j              = -90053.633613527330168 + 0.50650906526503053397i

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

-------------------------------------------------------
110B (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) + D(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+         = 4.6222415180973794611 + 0.35813594460762678196e-5i
Omega-         = 0.18453149037838832027e-5 + 2.173804059057541149i
L(1)           = 1.540747172699588966
w1             = 2.3111198363912378386 + -1.0869002388490475364i
w2             = -0.18453149037838832027e-5 + -2.173804059057541149i
c4             = 48.999848195622315176 + 0.38940023837524034327e-3i
c6             = -936.998876779654957 + -0.10969012506173031111e-2i
j              = -267.38196144950849741 + -0.66381144132697209258e-2i

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

-------------------------------------------------------
110C (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) + G(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+         = 1.359543339533560371 + 0.11339879975053370537e-5i
Omega-         = 0.89264484339824122944e-5 + 2.0244280537365269172i
L(1)           = 1.3595433395340332978
w1             = -0.67977613299099717673 + -1.0122145938622622113i
w2             = -0.67976720654256319432 + 1.0122134598742647059i
c4             = -478.99822256745835853 + -0.19368158809496624577e-1i
c6             = 42318.724081788374282 + 0.28810554241131909573i
j              = 99.911305696908698708 + 0.1013717567219708934e-1i

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

-------------------------------------------------------
110D (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) + C(Z/2 + Z/2) + E(Z/2^2 + Z/2^2) + F(Z/2 + Z/2)

ARITHMETIC INVARIANTS:
W_q            = +-+
discriminant   = 3*11
#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+         = 3.5437090185296829935 + 0.16952459626285473113e-5i
Omega-         = 2.358404162908380397 + -0.2871622416332562404e-5i
L(1)           = 0.59061816975501474681

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

-------------------------------------------------------
110E (old = 55A), dim = 1

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

-------------------------------------------------------
110F (old = 55B), dim = 2

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

-------------------------------------------------------
110G (old = 11A), dim = 1

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

-------------------------------------------------------
Gamma_0(111)
Weight 2

-------------------------------------------------------
J_0(111), dim = 11

-------------------------------------------------------
111A (new) , dim = 3

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

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+         = 4.0688342437234428396 + 0.5964803962112560685e-6i
Omega-         = 0.34368015985537664487e-5 + -13.835535638355665939i
L(1)           = 1.0172085609308716402

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

-------------------------------------------------------
111B (new) , dim = 4

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

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 2^4*389
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2*19
Torsion Bound  = 2^2*19
|L(1)/Omega|   = 7/2^2*19
Sha Bound      = 2^2*7*19

ANALYTIC INVARIANTS:

Omega+         = 9.3058911608499307137 + -0.21373285794973019298e-5i
Omega-         = 3.4465446094767608057 + -0.21274592803241243108e-5i
L(1)           = 0.85712155428883201464

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

-------------------------------------------------------
111C (old = 37A), dim = 1

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

-------------------------------------------------------
111D (old = 37B), dim = 1

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

-------------------------------------------------------
Gamma_0(112)
Weight 2

-------------------------------------------------------
J_0(112), dim = 11

-------------------------------------------------------
112A (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) + F(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+         = 3.3732121350202120456 + 0.27269935760477381578e-5i
Omega-         = 0.27896442504588801258e-6 + -1.8960366241385379781i
L(1)           =
w1             = 1.6866062069923185458 + -0.9480169485724809652i
w2             = 0.27896442504588801258e-6 + -1.8960366241385379781i
c4             = 16.000522592894968028 + 0.36403214463542597199e-3i
c6             = -3520.0090734578523588 + 0.10146554593613158166e-1i
j              = -0.57148163556405379637 + -0.42314414945161984042e-4i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -4*q^5 + -1*q^7 + 1*q^9 + 8*q^15 + -2*q^17 + 2*q^19 + 2*q^21 + -8*q^23 + 11*q^25 + 4*q^27 + 2*q^29 + -4*q^31 + 4*q^35 + -6*q^37 + -2*q^41 + -8*q^43 + -4*q^45 + 4*q^47 + 1*q^49 + 4*q^51 + -10*q^53 + -4*q^57 + -6*q^59 + 4*q^61 + -1*q^63 + 12*q^67 + 16*q^69 + -14*q^73 + -22*q^75 + 8*q^79 + -11*q^81 + -6*q^83 + 8*q^85 + -4*q^87 + 10*q^89 + 8*q^93 + -8*q^95 + -2*q^97 + 12*q^101 + 12*q^103 + -8*q^105 + 12*q^107 + 10*q^109 + 12*q^111 + 6*q^113 + 32*q^115 + 2*q^119 + -11*q^121 + 4*q^123 + -24*q^125 + -8*q^127 + 16*q^129 + -14*q^131 + -2*q^133 + -16*q^135 + 2*q^137 + -18*q^139 + -8*q^141 + -8*q^145 + -2*q^147 + -2*q^149 + -16*q^151 + -2*q^153 + 16*q^155 + 20*q^159 + 8*q^161 + -16*q^163 + -12*q^167 + -13*q^169 + 2*q^171 + 8*q^173 + -11*q^175 + 12*q^177 + 4*q^179 + 8*q^181 + -8*q^183 + 24*q^185 + -4*q^189 + 8*q^191 + -18*q^193 + -18*q^197 + 4*q^199 +  ...

-------------------------------------------------------
112B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= A(Z/2) + C(Z/2) + D(Z/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  = 2^2
|L(1)/Omega|   = 1/2
Sha Bound      = 2^3

ANALYTIC INVARIANTS:

Omega+         = 2.2962096817556563718 + 0.12902367602485060924e-5i
Omega-         = 0.46945580476052274189e-5 + 3.4981936244427329417i
L(1)           = 1.1481048408780094314
w1             = -1.1481071881568519885 + -1.7490974573397465951i
w2             = -1.1481024935988043833 + 1.7490961671029863466i
c4             = -47.999744641489331763 + -0.76737731919525274947e-3i
c6             = 1728.0043227451831199 + 0.21830071690312858454e-2i
j              = 61.71303817253825454 + 0.27037765456035895777e-2i

HECKE EIGENFORM:
f(q) = q + 2*q^5 + 1*q^7 + -3*q^9 + 4*q^11 + 2*q^13 + -6*q^17 + -8*q^19 + -1*q^25 + 6*q^29 + -8*q^31 + 2*q^35 + -2*q^37 + 2*q^41 + 4*q^43 + -6*q^45 + 8*q^47 + 1*q^49 + 6*q^53 + 8*q^55 + -6*q^61 + -3*q^63 + 4*q^65 + 4*q^67 + 8*q^71 + 10*q^73 + 4*q^77 + -16*q^79 + 9*q^81 + -8*q^83 + -12*q^85 + -6*q^89 + 2*q^91 + -16*q^95 + -6*q^97 + -12*q^99 + 2*q^101 + 16*q^103 + 12*q^107 + -10*q^109 + 2*q^113 + -6*q^117 + -6*q^119 + 5*q^121 + -12*q^125 + 8*q^127 + -8*q^131 + -8*q^133 + -6*q^137 + 8*q^139 + 8*q^143 + 12*q^145 + 6*q^149 + 18*q^153 + -16*q^155 + 18*q^157 + 12*q^163 + -16*q^167 + -9*q^169 + 24*q^171 + 18*q^173 + -1*q^175 + 4*q^179 + 10*q^181 + -4*q^185 + -24*q^187 + 16*q^191 + -14*q^193 + 6*q^197 +  ...

-------------------------------------------------------
112C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= A(Z/2 + Z/2) + B(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          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 2
|L(1)/Omega|   = 1
Sha Bound      = 2^2

ANALYTIC INVARIANTS:

Omega+         = 1.3254917683070845385 + -0.34917854027833917606e-6i
Omega-         = 0.28709503012444003455e-5 + 2.9720119571516044214i
L(1)           = 1.3254917683071305311
w1             = -0.66274444867839164703 + 1.4860061531650723499i
w2             = 1.3254917683070845385 + -0.34917854027833917606e-6i
c4             = 399.99882850327280339 + -0.93600182943876584772e-4i
c6             = 16191.985365506384323 + 0.48876764309212255162e-1i
j              = -558.03056234282031118 + 0.49751016454227409064e-2i

HECKE EIGENFORM:
f(q) = q + 2*q^3 + -1*q^7 + 1*q^9 + -4*q^13 + 6*q^17 + -2*q^19 + -2*q^21 + -5*q^25 + -4*q^27 + -6*q^29 + 4*q^31 + 2*q^37 + -8*q^39 + 6*q^41 + -8*q^43 + 12*q^47 + 1*q^49 + 12*q^51 + 6*q^53 + -4*q^57 + 6*q^59 + 8*q^61 + -1*q^63 + 4*q^67 + 2*q^73 + -10*q^75 + -8*q^79 + -11*q^81 + 6*q^83 + -12*q^87 + -6*q^89 + 4*q^91 + 8*q^93 + -10*q^97 + 4*q^103 + -12*q^107 + 2*q^109 + 4*q^111 + 6*q^113 + -4*q^117 + -6*q^119 + -11*q^121 + 12*q^123 + 16*q^127 + -16*q^129 + -18*q^131 + 2*q^133 + 18*q^137 + -14*q^139 + 24*q^141 + 2*q^147 + -18*q^149 + -8*q^151 + 6*q^153 + -4*q^157 + 12*q^159 + 16*q^163 + 12*q^167 + 3*q^169 + -2*q^171 + -12*q^173 + 5*q^175 + 12*q^177 + 12*q^179 + 20*q^181 + 16*q^183 + 4*q^189 + -24*q^191 + 14*q^193 + -18*q^197 + -20*q^199 +  ...

-------------------------------------------------------
112D (old = 56A), dim = 1

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) + C(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2^2 + Z/2^2 + Z/2^2)

-------------------------------------------------------
112E (old = 56B), 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) + B(Z/2) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
112F (old = 14A), dim = 1

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) + C(Z/2 + Z/2) + D(Z/2 + Z/2^2 + Z/2^2 + Z/2^2) + E(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(113)
Weight 2

-------------------------------------------------------
J_0(113), dim = 9

-------------------------------------------------------
113A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= B(Z/2 + Z/2) + D(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+         = 2.0183688791662388543 + 0.95600518227676296451e-6i
Omega-         = 0.1151609101947010642e-5 + -2.8578101537042237536i
L(1)           = 1.0091844395832326307
w1             = 1.0091838637785684536 + 1.4289055548547030152i
w2             = 1.0091850153876704007 + -1.4289045988495207384i
c4             = -143.00043507697671076 + 0.20456507575493521122e-3i
c6             = 4375.0143952853319499 + -0.11890924648765950758e-1i
j              = 229.00880729416353549 + 0.22731944136460666418e-3i

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

-------------------------------------------------------
113B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2*11
Ker(ModPolar)  = Z/2*11 + Z/2*11
= A(Z/2 + Z/2) + D(Z/11 + Z/11)

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^2*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+         = 4.4705711056603940094 + -0.15277608550284426093e-5i
Omega-         = 3.2118105426462683129 + 0.17193392691980347372e-6i
L(1)           = 2.2352855528303275279

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

-------------------------------------------------------
113C (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
= D(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+         = 57.611896495337549398 + 0.15911448982435207198e-3i
Omega-         = 0.11101798574420157994e-4 + 12.585522868101328221i
L(1)           =

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

-------------------------------------------------------
113D (new) , dim = 3

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 3*107
#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+         = 0.44243675818860204654 + -0.13671847274443437995e-5i
Omega-         = 0.76773853848195444261e-4 + -8.8161009055456179704i
L(1)           = 0.50564200936081649388

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

-------------------------------------------------------
Gamma_0(114)
Weight 2

-------------------------------------------------------
J_0(114), dim = 17

-------------------------------------------------------
114A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*5
Ker(ModPolar)  = Z/2^2*5 + Z/2^2*5
= B(Z/2 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2) + G(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|   = 1/2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 0.76356955551474832545 + -0.24157781283501172127e-6i
Omega-         = 0.2764430246764974235e-6 + 1.8797306446983730196i
L(1)           = 0.3817847777573932703
w1             = -0.2764430246764974235e-6 + -1.8797306446983730196i
w2             = -0.76356955551474832545 + 0.24157781283501172127e-6i
c4             = 4585.0600623933869425 + 0.58019252390605699827e-2i
c6             = 310417.10164223659919 + 0.58933630921921929908i
j              = 5219349.6546733189853 + 13.66706036477559518i

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 + 4*q^11 + -1*q^12 + -4*q^14 + 1*q^16 + -2*q^17 + -1*q^18 + 1*q^19 + -4*q^21 + -4*q^22 + -2*q^23 + 1*q^24 + -5*q^25 + -1*q^27 + 4*q^28 + -6*q^29 + 6*q^31 + -1*q^32 + -4*q^33 + 2*q^34 + 1*q^36 + -8*q^37 + -1*q^38 + 10*q^41 + 4*q^42 + -12*q^43 + 4*q^44 + 2*q^46 + 10*q^47 + -1*q^48 + 9*q^49 + 5*q^50 + 2*q^51 + 2*q^53 + 1*q^54 + -4*q^56 + -1*q^57 + 6*q^58 + 4*q^59 + -10*q^61 + -6*q^62 + 4*q^63 + 1*q^64 + 4*q^66 + -2*q^68 + 2*q^69 + -16*q^71 + -1*q^72 + -2*q^73 + 8*q^74 + 5*q^75 + 1*q^76 + 16*q^77 + 10*q^79 + 1*q^81 + -10*q^82 + -16*q^83 + -4*q^84 + 12*q^86 + 6*q^87 + -4*q^88 + -2*q^89 + -2*q^92 + -6*q^93 + -10*q^94 + 1*q^96 + -10*q^97 + -9*q^98 + 4*q^99 + -5*q^100 + 8*q^101 + -2*q^102 + -6*q^103 + -2*q^106 + -4*q^107 + -1*q^108 + -4*q^109 + 8*q^111 + 4*q^112 + -14*q^113 + 1*q^114 + -6*q^116 + -4*q^118 + -8*q^119 + 5*q^121 + 10*q^122 + -10*q^123 + 6*q^124 + -4*q^126 + 22*q^127 + -1*q^128 + 12*q^129 + -4*q^132 + 4*q^133 + 2*q^136 + 6*q^137 + -2*q^138 + -4*q^139 + -10*q^141 + 16*q^142 + 1*q^144 + 2*q^146 + -9*q^147 + -8*q^148 + 20*q^149 + -5*q^150 + 10*q^151 + -1*q^152 + -2*q^153 + -16*q^154 + 18*q^157 + -10*q^158 + -2*q^159 + -8*q^161 + -1*q^162 + 20*q^163 + 10*q^164 + 16*q^166 + 12*q^167 + 4*q^168 + -13*q^169 + 1*q^171 + -12*q^172 + 6*q^173 + -6*q^174 + -20*q^175 + 4*q^176 + -4*q^177 + 2*q^178 + -20*q^179 + 12*q^181 + 10*q^183 + 2*q^184 + 6*q^186 + -8*q^187 + 10*q^188 + -4*q^189 + -2*q^191 + -1*q^192 + 14*q^193 + 10*q^194 + 9*q^196 + -20*q^197 + -4*q^198 + -4*q^199 + 5*q^200 +  ...

-------------------------------------------------------
114B (new) , dim = 1

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

ANALYTIC INVARIANTS:

Omega+         = 0.55509037505088283935 + 0.36567282339086755031e-6i
Omega-         = 0.19816389888769415178e-5 + 0.79615703625731828026i
L(1)           = 0.69386296881375410645
w1             = 0.19816389888769415178e-5 + 0.79615703625731828026i
w2             = 0.55509037505088283935 + 0.36567282339086755031e-6i
c4             = 16896.90187454268302 + -0.30864497040418579588e-1i
c6             = 1973481.66012823388 + -11.49713807530181786i
j              = 8968.1710397876294286 + -0.23190769465857892496i

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

-------------------------------------------------------
114C (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) + E(Z/2 + Z/2) + I(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+         = 1.5744324555162438845 + -0.19470516612048311841e-5i
Omega-         = 0.27499942216347087495e-5 + -1.5429686405170042207i
L(1)           = 0.78721622775872390681
w1             = -1.5744324555162438845 + 0.19470516612048311841e-5i
w2             = -0.27499942216347087495e-5 + 1.5429686405170042207i
c4             = 385.00399185382950624 + -0.58370483963693446797e-3i
c6             = -577.04887091952165054 + 0.87315631637603287716e-1i
j              = 1738.1417916926604723 + -0.30408069804112186591e-2i

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

-------------------------------------------------------
114D (old = 57A), dim = 1

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

-------------------------------------------------------
114E (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) + B(Z/2 + Z/2) + C(Z/2 + Z/2) + F(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
114F (old = 57C), dim = 1

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

-------------------------------------------------------
114G (old = 38A), 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 + Z/5) + H(Z/2 + Z/2 + Z/2 + Z/2) + I(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
114H (old = 38B), 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)

-------------------------------------------------------
114I (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
= C(Z/3 + Z/3) + D(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/3 + Z/3 + Z/3 + Z/3)

-------------------------------------------------------
Gamma_0(115)
Weight 2

-------------------------------------------------------
J_0(115), dim = 11

-------------------------------------------------------
115A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*5
Ker(ModPolar)  = Z/2*5 + Z/2*5
= C(Z/2 + Z/2) + D(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+         = 1.8080357444222154856 + 0.21090321080203273168e-5i
Omega-         = 0.65743719334783977223e-6 + -2.3818262778588733764i
L(1)           = 1.8080357444234455544
w1             = 0.90401754349251106889 + 1.1909141934454906984i
w2             = 0.90401820092970441673 + -1.190912084413382678i
c4             = -336.00004883436807557 + 0.59681249394043427963e-4i
c6             = 9288.0873954350847964 + -0.58874396366244213546e-1i
j              = 527.75751868301285649 + 0.44518491107883110836e-2i

HECKE EIGENFORM:
f(q) = q + 2*q^2 + 2*q^4 + -1*q^5 + 1*q^7 + -3*q^9 + -2*q^10 + 2*q^11 + -2*q^13 + 2*q^14 + -4*q^16 + 3*q^17 + -6*q^18 + -2*q^19 + -2*q^20 + 4*q^22 + 1*q^23 + 1*q^25 + -4*q^26 + 2*q^28 + 7*q^29 + -5*q^31 + -8*q^32 + 6*q^34 + -1*q^35 + -6*q^36 + 11*q^37 + -4*q^38 + 1*q^41 + 4*q^44 + 3*q^45 + 2*q^46 + -6*q^49 + 2*q^50 + -4*q^52 + 11*q^53 + -2*q^55 + 14*q^58 + -13*q^59 + -8*q^61 + -10*q^62 + -3*q^63 + -8*q^64 + 2*q^65 + 5*q^67 + 6*q^68 + -2*q^70 + 5*q^71 + 6*q^73 + 22*q^74 + -4*q^76 + 2*q^77 + -12*q^79 + 4*q^80 + 9*q^81 + 2*q^82 + 9*q^83 + -3*q^85 + 4*q^89 + 6*q^90 + -2*q^91 + 2*q^92 + 2*q^95 + -14*q^97 + -12*q^98 + -6*q^99 + 2*q^100 + -5*q^101 + -8*q^103 + 22*q^106 + -15*q^107 + -10*q^109 + -4*q^110 + -4*q^112 + -9*q^113 + -1*q^115 + 14*q^116 + 6*q^117 + -26*q^118 + 3*q^119 + -7*q^121 + -16*q^122 + -10*q^124 + -1*q^125 + -6*q^126 + -4*q^127 + 4*q^130 + 12*q^131 + -2*q^133 + 10*q^134 + 6*q^137 + -19*q^139 + -2*q^140 + 10*q^142 + -4*q^143 + 12*q^144 + -7*q^145 + 12*q^146 + 22*q^148 + 16*q^149 + 12*q^151 + -9*q^153 + 4*q^154 + 5*q^155 + 17*q^157 + -24*q^158 + 8*q^160 + 1*q^161 + 18*q^162 + -18*q^163 + 2*q^164 + 18*q^166 + -24*q^167 + -9*q^169 + -6*q^170 + 6*q^171 + 24*q^173 + 1*q^175 + -8*q^176 + 8*q^178 + 24*q^179 + 6*q^180 + 16*q^181 + -4*q^182 + -11*q^185 + 6*q^187 + 4*q^190 + 16*q^193 + -28*q^194 + -12*q^196 + -2*q^197 + -12*q^198 + 26*q^199 +  ...

-------------------------------------------------------
115B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^4
Ker(ModPolar)  = Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2
= 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+         = 10.67766379691002069 + -0.5457992742997439593e-5i
Omega-         = 5.3099401599940079011 + -0.23595125411027521621e-5i
L(1)           =

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

-------------------------------------------------------
115C (new) , dim = 4

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

ARITHMETIC INVARIANTS:
W_q            = -+
discriminant   = 17^2*53
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 2
ord((0)-(oo))  = 2^3
Torsion Bound  = 2^6
|L(1)/Omega|   = 1/2^2
Sha Bound      = 2^10

ANALYTIC INVARIANTS:

Omega+         = 2.9467773418741933427 + 0.57290299861511811606e-5i
Omega-         = 11.846742740470627939 + 0.20684436067044921303e-4i
L(1)           = 0.73669433546994061021

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

-------------------------------------------------------
115D (old = 23A), dim = 2

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

-------------------------------------------------------
Gamma_0(116)
Weight 2

-------------------------------------------------------
J_0(116), dim = 13

-------------------------------------------------------
116A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= C(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))  = 3
Torsion Bound  = 3
|L(1)/Omega|   = 1/3
Sha Bound      = 3

ANALYTIC INVARIANTS:

Omega+         = 3.8294743248793478983 + 0.16210169931271728177e-5i
Omega-         = 0.34666481649398130744e-5 + 1.598484694486496401i
L(1)           = 1.2764914416265636622
w1             = -1.9147354291155914792 + 0.79924153673475163692i
w2             = 0.34666481649398130744e-5 + 1.598484694486496401i
c4             = 208.00209585863180265 + 0.2400690220909048592e-2i
c6             = -4672.0486773958423517 + -0.41947641434951987734e-1i
j              = -1212.1572984529092661 + -0.3437739297977380544e-1i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 3*q^5 + -4*q^7 + -2*q^9 + 3*q^11 + 5*q^13 + 3*q^15 + -6*q^17 + -4*q^19 + -4*q^21 + -6*q^23 + 4*q^25 + -5*q^27 + -1*q^29 + 5*q^31 + 3*q^33 + -12*q^35 + 8*q^37 + 5*q^39 + -1*q^43 + -6*q^45 + -3*q^47 + 9*q^49 + -6*q^51 + 3*q^53 + 9*q^55 + -4*q^57 + 6*q^59 + 2*q^61 + 8*q^63 + 15*q^65 + 8*q^67 + -6*q^69 + 6*q^71 + -16*q^73 + 4*q^75 + -12*q^77 + 11*q^79 + 1*q^81 + 6*q^83 + -18*q^85 + -1*q^87 + -12*q^89 + -20*q^91 + 5*q^93 + -12*q^95 + 8*q^97 + -6*q^99 + 12*q^101 + 14*q^103 + -12*q^105 + 11*q^109 + 8*q^111 + -6*q^113 + -18*q^115 + -10*q^117 + 24*q^119 + -2*q^121 + -3*q^125 + -16*q^127 + -1*q^129 + -12*q^131 + 16*q^133 + -15*q^135 + -12*q^137 + 14*q^139 + -3*q^141 + 15*q^143 + -3*q^145 + 9*q^147 + -15*q^149 + -4*q^151 + 12*q^153 + 15*q^155 + -4*q^157 + 3*q^159 + 24*q^161 + -13*q^163 + 9*q^165 + -6*q^167 + 12*q^169 + 8*q^171 + -18*q^173 + -16*q^175 + 6*q^177 + 18*q^179 + 17*q^181 + 2*q^183 + 24*q^185 + -18*q^187 + 20*q^189 + -24*q^191 + -16*q^193 + 15*q^195 + -6*q^197 + 20*q^199 +  ...

-------------------------------------------------------
116B (new) , dim = 1

CONGRUENCES:
Modular Degree = 3*5
Ker(ModPolar)  = Z/3*5 + Z/3*5
= C(Z/5 + Z/5) + E(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+         = 2.6462315895479682403 + -0.42324955247656124958e-5i
Omega-         = 0.34177927594502951745e-5 + -1.3661387737826790238i
L(1)           = 1.3231157947756765286
w1             = -1.323114085877604395 + -0.68306727064357712911i
w2             = -0.34177927594502951745e-5 + 1.3661387737826790238i
c4             = 207.99881220834872509 + -0.7934216735797571438e-2i
c6             = -19520.204699196903987 + 0.61733999790644221081e-1i
j              = -41.796228328769532345 + 0.46279413320963134823e-2i

HECKE EIGENFORM:
f(q) = q + 2*q^3 + -2*q^5 + 4*q^7 + 1*q^9 + -6*q^11 + 2*q^13 + -4*q^15 + 2*q^17 + -6*q^19 + 8*q^21 + 4*q^23 + -1*q^25 + -4*q^27 + -1*q^29 + -6*q^31 + -12*q^33 + -8*q^35 + 2*q^37 + 4*q^39 + 2*q^41 + 10*q^43 + -2*q^45 + -2*q^47 + 9*q^49 + 4*q^51 + 10*q^53 + 12*q^55 + -12*q^57 + 10*q^61 + 4*q^63 + -4*q^65 + -12*q^67 + 8*q^69 + 8*q^71 + 10*q^73 + -2*q^75 + -24*q^77 + -6*q^79 + -11*q^81 + 16*q^83 + -4*q^85 + -2*q^87 + 2*q^89 + 8*q^91 + -12*q^93 + 12*q^95 + 10*q^97 + -6*q^99 + -14*q^101 + -4*q^103 + -16*q^105 + -8*q^107 + -10*q^109 + 4*q^111 + -6*q^113 + -8*q^115 + 2*q^117 + 8*q^119 + 25*q^121 + 4*q^123 + 12*q^125 + 2*q^127 + 20*q^129 + -18*q^131 + -24*q^133 + 8*q^135 + -6*q^137 + -8*q^139 + -4*q^141 + -12*q^143 + 2*q^145 + 18*q^147 + -6*q^149 + -16*q^151 + 2*q^153 + 12*q^155 + -6*q^157 + 20*q^159 + 16*q^161 + -18*q^163 + 24*q^165 + -8*q^167 + -9*q^169 + -6*q^171 + 18*q^173 + -4*q^175 + 20*q^179 + 22*q^181 + 20*q^183 + -4*q^185 + -12*q^187 + -16*q^189 + 10*q^191 + 2*q^193 + -8*q^195 + 6*q^197 + 20*q^199 +  ...

-------------------------------------------------------
116C (new) , dim = 1

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

ANALYTIC INVARIANTS:

Omega+         = 0.28632505355259197376 + 0.2167787962455827619e-6i
Omega-         = 0.12516612617212691574e-4 + -2.5655761420735898327i
L(1)           = 0.85897516065802210851
w1             = -0.14315626846998738054 + -1.2827881794261930391i
w2             = -0.28632505355259197376 + -0.2167787962455827619e-6i
c4             = 231890.02686832233935 + -0.70226255072240872711i
c6             = 111666552.05287819488 + -507.26139302605655228i
j              = -1679987659126.6507772 + -194914423.04365916878i

HECKE EIGENFORM:
f(q) = q + -3*q^3 + 3*q^5 + 4*q^7 + 6*q^9 + -1*q^11 + -3*q^13 + -9*q^15 + 2*q^17 + 4*q^19 + -12*q^21 + -6*q^23 + 4*q^25 + -9*q^27 + -1*q^29 + 9*q^31 + 3*q^33 + 12*q^35 + -8*q^37 + 9*q^39 + -8*q^41 + -5*q^43 + 18*q^45 + -7*q^47 + 9*q^49 + -6*q^51 + -5*q^53 + -3*q^55 + -12*q^57 + -10*q^59 + 10*q^61 + 24*q^63 + -9*q^65 + 8*q^67 + 18*q^69 + -2*q^71 + -12*q^75 + -4*q^77 + -1*q^79 + 9*q^81 + 6*q^83 + 6*q^85 + 3*q^87 + 12*q^89 + -12*q^91 + -27*q^93 + 12*q^95 + -6*q^99 + -4*q^101 + 6*q^103 + -36*q^105 + -8*q^107 + -5*q^109 + 24*q^111 + -6*q^113 + -18*q^115 + -18*q^117 + 8*q^119 + -10*q^121 + 24*q^123 + -3*q^125 + -8*q^127 + 15*q^129 + 12*q^131 + 16*q^133 + -27*q^135 + 4*q^137 + -18*q^139 + 21*q^141 + 3*q^143 + -3*q^145 + -27*q^147 + 9*q^149 + 4*q^151 + 12*q^153 + 27*q^155 + 4*q^157 + 15*q^159 + -24*q^161 + 7*q^163 + 9*q^165 + 2*q^167 + -4*q^169 + 24*q^171 + -2*q^173 + 16*q^175 + 30*q^177 + 10*q^179 + 17*q^181 + -30*q^183 + -24*q^185 + -2*q^187 + -36*q^189 + -8*q^193 + 27*q^195 + 26*q^197 + -20*q^199 +  ...

-------------------------------------------------------
116D (old = 58A), dim = 1

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

-------------------------------------------------------
116E (old = 58B), 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/3 + Z/3) + D(Z/2 + Z/2 + Z/2 + Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
116F (old = 29A), dim = 2

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) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(117)
Weight 2

-------------------------------------------------------
J_0(117), dim = 11

-------------------------------------------------------
117A (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)

ARITHMETIC INVARIANTS:
W_q            = --
discriminant   = 1
#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+         = 2.6403268645882993477 + 0.17473402698283358821e-4i
Omega-         = 0.30890383710063442523e-5 + 1.9091590442544068472i
L(1)           =
w1             = -1.320164976813335177 + -0.95458825882855256526i
w2             = -1.3201618877749641707 + 0.95457078542585428191i
c4             = -207.00030836603713055 + 0.88559740335304574348e-2i
c6             = -6344.9150768269308434 + 0.15139340296933384891e-1i
j              = 311.98234445530719505 + -0.31592650513722851271e-1i

HECKE EIGENFORM:
f(q) = q + -1*q^2 + -1*q^4 + -2*q^5 + -4*q^7 + 3*q^8 + 2*q^10 + -4*q^11 + 1*q^13 + 4*q^14 + -1*q^16 + -2*q^17 + 2*q^20 + 4*q^22 + -1*q^25 + -1*q^26 + 4*q^28 + 10*q^29 + 4*q^31 + -5*q^32 + 2*q^34 + 8*q^35 + -2*q^37 + -6*q^40 + -6*q^41 + -12*q^43 + 4*q^44 + 9*q^49 + 1*q^50 + -1*q^52 + -6*q^53 + 8*q^55 + -12*q^56 + -10*q^58 + -12*q^59 + -2*q^61 + -4*q^62 + 7*q^64 + -2*q^65 + -8*q^67 + 2*q^68 + -8*q^70 + 2*q^73 + 2*q^74 + 16*q^77 + 8*q^79 + 2*q^80 + 6*q^82 + -4*q^83 + 4*q^85 + 12*q^86 + -12*q^88 + 2*q^89 + -4*q^91 + 10*q^97 + -9*q^98 + 1*q^100 + 18*q^101 + 3*q^104 + 6*q^106 + -12*q^107 + -2*q^109 + -8*q^110 + 4*q^112 + 6*q^113 + -10*q^116 + 12*q^118 + 8*q^119 + 5*q^121 + 2*q^122 + -4*q^124 + 12*q^125 + -16*q^127 + 3*q^128 + 2*q^130 + -4*q^131 + 8*q^134 + -6*q^136 + -6*q^137 + 12*q^139 + -8*q^140 + -4*q^143 + -20*q^145 + -2*q^146 + 2*q^148 + 6*q^149 + 4*q^151 + -16*q^154 + -8*q^155 + -18*q^157 + -8*q^158 + 10*q^160 + 8*q^163 + 6*q^164 + 4*q^166 + 8*q^167 + 1*q^169 + -4*q^170 + 12*q^172 + -6*q^173 + 4*q^175 + 4*q^176 + -2*q^178 + -4*q^179 + -10*q^181 + 4*q^182 + 4*q^185 + 8*q^187 + -8*q^191 + 18*q^193 + -10*q^194 + -9*q^196 + -18*q^197 + 8*q^199 + -3*q^200 +  ...

-------------------------------------------------------
117B (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) + 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   = 2^2*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+         = 3.2953610491551391528 + -0.37766187554520900553e-5i
Omega-         = 3.2953721841422529768 + 0.10504226756946916452e-5i
L(1)           = 1.0984536830524344109

HECKE EIGENFORM:
a^2-3 = 0,
f(q) = q + a*q^2 + 1*q^4 + 2*q^7 + -a*q^8 + -2*a*q^11 + 1*q^13 + 2*a*q^14 + -5*q^16 + -4*a*q^17 + 2*q^19 + -6*q^22 + 4*a*q^23 + -5*q^25 + a*q^26 + 2*q^28 + 4*a*q^29 + 2*q^31 + -3*a*q^32 + -12*q^34 + 2*q^37 + 2*a*q^38 + 4*a*q^41 + 8*q^43 + -2*a*q^44 + 12*q^46 + -6*a*q^47 + -3*q^49 + -5*a*q^50 + 1*q^52 + -2*a*q^56 + 12*q^58 + 2*a*q^59 + -10*q^61 + 2*a*q^62 + 1*q^64 + 14*q^67 + -4*a*q^68 + 2*a*q^71 + -10*q^73 + 2*a*q^74 + 2*q^76 + -4*a*q^77 + -4*q^79 + 12*q^82 + 6*a*q^83 + 8*a*q^86 + 6*q^88 + 4*a*q^89 + 2*q^91 + 4*a*q^92 + -18*q^94 + -10*q^97 + -3*a*q^98 + -5*q^100 + -8*a*q^101 + -4*q^103 + -a*q^104 + 4*a*q^107 + -10*q^109 + -10*q^112 + -4*a*q^113 + 4*a*q^116 + 6*q^118 + -8*a*q^119 + 1*q^121 + -10*a*q^122 + 2*q^124 + -16*q^127 + 7*a*q^128 + -12*a*q^131 + 4*q^133 + 14*a*q^134 + 12*q^136 + -4*a*q^137 + -4*q^139 + 6*q^142 + -2*a*q^143 + -10*a*q^146 + 2*q^148 + 8*a*q^149 + 14*q^151 + -2*a*q^152 + -12*q^154 + 2*q^157 + -4*a*q^158 + 8*a*q^161 + 14*q^163 + 4*a*q^164 + 18*q^166 + 10*a*q^167 + 1*q^169 + 8*q^172 + 8*a*q^173 + -10*q^175 + 10*a*q^176 + 12*q^178 + -8*a*q^179 + -10*q^181 + 2*a*q^182 + -12*q^184 + 24*q^187 + -6*a*q^188 + 8*a*q^191 + 26*q^193 + -10*a*q^194 + -3*q^196 + -8*a*q^197 + -16*q^199 + 5*a*q^200 +  ...

-------------------------------------------------------
117C (new) , dim = 2

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 + Z/2 + Z/2) + D(Z/2 + Z/2) + E(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2)

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|   = 1
Sha Bound      = 2^4

ANALYTIC INVARIANTS:

Omega+         = 1.9509503957681826454 + 0.38764509114028321364e-5i
Omega-         = 3.5656967538186231267 + 0.16028017946855262686e-4i
L(1)           = 1.9509503957720338124

HECKE EIGENFORM:
a^2-2*a-1 = 0,
f(q) = q + a*q^2 + (2*a-1)*q^4 + (-2*a+2)*q^5 + (-2*a+2)*q^7 + (a+2)*q^8 + (-2*a-2)*q^10 + 2*q^11 + -1*q^13 + (-2*a-2)*q^14 + 3*q^16 + (4*a-6)*q^17 + (2*a-2)*q^19 + (-2*a-6)*q^20 + 2*a*q^22 + 4*q^23 + 3*q^25 + -a*q^26 + (-2*a-6)*q^28 + -2*q^29 + (-2*a-2)*q^31 + (a-4)*q^32 + (2*a+4)*q^34 + 8*q^35 + (4*a-6)*q^37 + (2*a+2)*q^38 + (-6*a+2)*q^40 + (-2*a-6)*q^41 + 4*a*q^43 + (4*a-2)*q^44 + 4*a*q^46 + (-4*a+10)*q^47 + 1*q^49 + 3*a*q^50 + (-2*a+1)*q^52 + 2*q^53 + (-4*a+4)*q^55 + (-6*a+2)*q^56 + -2*a*q^58 + (4*a-6)*q^59 + (-8*a+10)*q^61 + (-6*a-2)*q^62 + (-2*a-5)*q^64 + (2*a-2)*q^65 + (-2*a+6)*q^67 + 14*q^68 + 8*a*q^70 + -2*q^71 + (4*a+2)*q^73 + (2*a+4)*q^74 + (2*a+6)*q^76 + (-4*a+4)*q^77 + (8*a-8)*q^79 + (-6*a+6)*q^80 + (-10*a-2)*q^82 + (4*a-2)*q^83 + (4*a-20)*q^85 + (8*a+4)*q^86 + (2*a+4)*q^88 + (2*a-14)*q^89 + (2*a-2)*q^91 + (8*a-4)*q^92 + (2*a-4)*q^94 + -8*q^95 + (-4*a+2)*q^97 + a*q^98 + (6*a-3)*q^100 + (4*a-6)*q^101 + (4*a+4)*q^103 + (-a-2)*q^104 + 2*a*q^106 + (-8*a+8)*q^107 + (-8*a+2)*q^109 + (-4*a-4)*q^110 + (-6*a+6)*q^112 + (-8*a+2)*q^113 + (-8*a+8)*q^115 + (-4*a+2)*q^116 + (2*a+4)*q^118 + (4*a-20)*q^119 + -7*q^121 + (-6*a-8)*q^122 + (-10*a-2)*q^124 + (4*a-4)*q^125 + (-4*a+4)*q^127 + (-11*a+6)*q^128 + (2*a+2)*q^130 + 8*q^131 + -8*q^133 + (2*a-2)*q^134 + (10*a-8)*q^136 + (-2*a+10)*q^137 + (8*a-4)*q^139 + (16*a-8)*q^140 + -2*a*q^142 + -2*q^143 + (4*a-4)*q^145 + (10*a+4)*q^146 + 14*q^148 + (2*a+10)*q^149 + (-6*a-6)*q^151 + (6*a-2)*q^152 + (-4*a-4)*q^154 + 8*a*q^155 + -10*q^157 + (8*a+8)*q^158 + (6*a-10)*q^160 + (-8*a+8)*q^161 + (-2*a+18)*q^163 + (-18*a+2)*q^164 + (6*a+4)*q^166 + (-4*a+2)*q^167 + 1*q^169 + (-12*a+4)*q^170 + (12*a+8)*q^172 + (-4*a+10)*q^173 + (-6*a+6)*q^175 + 6*q^176 + (-10*a+2)*q^178 + (-8*a+20)*q^179 + 14*q^181 + (2*a+2)*q^182 + (4*a+8)*q^184 + (4*a-20)*q^185 + (8*a-12)*q^187 + (8*a-18)*q^188 + -8*a*q^190 + 8*a*q^191 + (-8*a+2)*q^193 + (-6*a-4)*q^194 + (2*a-1)*q^196 + (6*a+2)*q^197 + (-4*a+20)*q^199 + (3*a+6)*q^200 +  ...

-------------------------------------------------------
117D (old = 39A), dim = 1

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 + Z/2) + C(Z/2 + Z/2) + E(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
117E (old = 39B), dim = 2

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 + Z/2) + B(Z/2 + Z/2 + Z/2 + Z/2) + C(Z/2^2 + Z/2^2 + Z/2^2 + Z/2^2) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(118)
Weight 2

-------------------------------------------------------
J_0(118), dim = 14

-------------------------------------------------------
118A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2
Ker(ModPolar)  = Z/2^2 + Z/2^2
= C(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+         = 4.1584473079621691906 + 0.80478379158167984116e-5i
Omega-         = 0.28436440756510612958e-5 + 2.7090081168058360323i
L(1)           =
w1             = -2.0792250758031224208 + -1.3545080823218759246i
w2             = -2.0792222321590467698 + 1.3545000344839601078i
c4             = -23.000262106636323997 + 0.59565691284519215265e-3i
c6             = -629.0083185154030764 + 0.71135123750879355818e-3i
j              = 51.555471686279254794 + -0.37728885286422912518e-2i

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

-------------------------------------------------------
118B (new) , dim = 1

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

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+         = 1.0990040904994854982 + -0.89148386284355505376e-6i
Omega-         = 0.45609956023342503034e-5 + 1.4247474667338035725i
L(1)           = 1.0990040904998470726
w1             = 0.54950432574754391621 + 0.71237328762497036445i
w2             = 0.54949976475194158196 + -0.71237417910883320801i
c4             = -2662.9994549675515281 + -0.39093710845874981684e-1i
c6             = 185926.47501608836875 + 1.1052552557028657098i
j              = 610.4932955868828009 + 0.12693837381875606986e-1i

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

-------------------------------------------------------
118C (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/3 + Z/3) + E(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|   = 2/5
Sha Bound      = 2*5

ANALYTIC INVARIANTS:

Omega+         = 3.4884494980672399981 + -0.51790136002225183537e-5i
Omega-         = 0.58746012475599431709e-6 + -1.0651315698493106511i
L(1)           = 1.3953797992284337702
w1             = 1.7442244553035576211 + 0.5325631954178552143i
w2             = 0.58746012475599431709e-6 + -1.0651315698493106511i
c4             = 1201.0169030285914519 + -0.28565072180387170928e-2i
c6             = -42857.867993595587656 + 0.12673291382762218126i
j              = -28674.124416215197126 + 0.61603917040882387363i

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

-------------------------------------------------------
118D (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))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.684088712916561381 + 0.45692663535211523627e-5i
Omega-         = 0.23224419387005406651e-4 + -5.9125215923229658284i
L(1)           = 1.6840887129227600435
w1             = 0.84203274424858718782 + 2.9562630807946596748i
w2             = 1.684088712916561381 + 0.45692663535211523627e-5i
c4             = 193.00404725017858788 + -0.20845324925772684689e-2i
c6             = 2719.0827155595158206 + -0.44559479303865657519e-1i
j              = -60928.780627006896002 + -0.82625456390994697453i

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

-------------------------------------------------------
118E (old = 59A), dim = 5

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

-------------------------------------------------------
Gamma_0(119)
Weight 2

-------------------------------------------------------
J_0(119), dim = 11

-------------------------------------------------------
119A (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   = 71*131
#CompGroup(Fpbar) = ??
c_p            = ??
c_inf          = 1
ord((0)-(oo))  = 3^2
Torsion Bound  = 3^2
|L(1)/Omega|   = 1/3^2
Sha Bound      = 3^2

ANALYTIC INVARIANTS:

Omega+         = 10.050547823062310131 + -0.74515491086982701429e-4i
Omega-         = 21.487096590059618894 + 0.1692656977462828009e-4i
L(1)           = 1.1167275359265046401

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

-------------------------------------------------------
119B (new) , dim = 5

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

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 311*1459
#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+         = 8.0496657778310824472 + 0.16240421827744819612e-4i
Omega-         = 0.52391806179648643361e-4 + -11.470011263305532272i
L(1)           = 0.50310411111546657474

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

-------------------------------------------------------
119C (old = 17A), dim = 1

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

-------------------------------------------------------
Gamma_0(120)
Weight 2

-------------------------------------------------------
J_0(120), dim = 17

-------------------------------------------------------
120A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2^3 + Z/2^3
= B(Z/2) + C(Z/2) + D(Z/2 + Z/2^2) + E(Z/2) + F(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+         = 2.4898275266308903615 + 0.20397237696003998055e-5i
Omega-         = -2.7966553523879221864i
L(1)           = 1.2449137633158629278
w1             = 1.2449137633154451807 + 1.3983286960558458934i
w2             = 1.2449137633154451807 + -1.398326656332076293i
c4             = -175.99987953901053056 + 0.13320665536405764653e-3i
c6             = 1087.9617360049198293 + -0.9792051763216347283e-2i
j              = 1419.7506280198537541 + 0.39838560305288497506e-2i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + -1*q^5 + 4*q^7 + 1*q^9 + -6*q^13 + -1*q^15 + -2*q^17 + 4*q^19 + 4*q^21 + -8*q^23 + 1*q^25 + 1*q^27 + -6*q^29 + -4*q^35 + -6*q^37 + -6*q^39 + 10*q^41 + -4*q^43 + -1*q^45 + 8*q^47 + 9*q^49 + -2*q^51 + 10*q^53 + 4*q^57 + 6*q^61 + 4*q^63 + 6*q^65 + -4*q^67 + -8*q^69 + -14*q^73 + 1*q^75 + 16*q^79 + 1*q^81 + 12*q^83 + 2*q^85 + -6*q^87 + 2*q^89 + -24*q^91 + -4*q^95 + 2*q^97 + -14*q^101 + 4*q^103 + -4*q^105 + 4*q^107 + -10*q^109 + -6*q^111 + 6*q^113 + 8*q^115 + -6*q^117 + -8*q^119 + -11*q^121 + 10*q^123 + -1*q^125 + -4*q^127 + -4*q^129 + 16*q^131 + 16*q^133 + -1*q^135 + -18*q^137 + -12*q^139 + 8*q^141 + 6*q^145 + 9*q^147 + -6*q^149 + -2*q^153 + 10*q^157 + 10*q^159 + -32*q^161 + -4*q^163 + -8*q^167 + 23*q^169 + 4*q^171 + 18*q^173 + 4*q^175 + 8*q^179 + 14*q^181 + 6*q^183 + 6*q^185 + 4*q^189 + 8*q^191 + -6*q^193 + 6*q^195 + 10*q^197 +  ...

-------------------------------------------------------
120B (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) + E(Z/2) + F(Z/2 + Z/2) + G(Z/2)

ARITHMETIC INVARIANTS:
W_q            = ---
discriminant   = 1
#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+         = 2.5376854975590948559 + 0.38418192930408291489e-3i
Omega-         = -1.2064434155605293503i
L(1)           = 0.63442138165996904058
w1             = 2.5376854975590948559 + 0.38418192930408291489e-3i
w2             = -1.2064434155605293503i
c4             = 736.00602710742753063 + -0.6432053797139188918e-3i
c6             = -19936.033294391917393 + -0.36639769744663134708e-1i
j              = 550002.03356149757432 + 1098.9711062654422592i

HECKE EIGENFORM:
f(q) = q + 1*q^3 + 1*q^5 + 1*q^9 + -4*q^11 + 6*q^13 + 1*q^15 + -6*q^17 + -4*q^19 + 1*q^25 + 1*q^27 + -2*q^29 + -8*q^31 + -4*q^33 + -2*q^37 + 6*q^39 + -6*q^41 + 12*q^43 + 1*q^45 + 8*q^47 + -7*q^49 + -6*q^51 + 6*q^53 + -4*q^55 + -4*q^57 + 12*q^59 + 14*q^61 + 6*q^65 + 4*q^67 + 8*q^71 + -6*q^73 + 1*q^75 + -8*q^79 + 1*q^81 + -12*q^83 + -6*q^85 + -2*q^87 + 10*q^89 + -8*q^93 + -4*q^95 + 2*q^97 + -4*q^99 + 6*q^101 + -4*q^107 + -18*q^109 + -2*q^111 + -6*q^113 + 6*q^117 + 5*q^121 + -6*q^123 + 1*q^125 + -8*q^127 + 12*q^129 + 4*q^131 + 1*q^135 + 2*q^137 + 4*q^139 + 8*q^141 + -24*q^143 + -2*q^145 + -7*q^147 + -10*q^149 + 16*q^151 + -6*q^153 + -8*q^155 + 6*q^157 + 6*q^159 + 4*q^163 + -4*q^165 + 16*q^167 + 23*q^169 + -4*q^171 + 14*q^173 + 12*q^177 + -12*q^179 + -10*q^181 + 14*q^183 + -2*q^185 + 24*q^187 + -14*q^193 + 6*q^195 + -10*q^197 +  ...

-------------------------------------------------------
120C (old = 40A), 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 + Z/2) + D(Z/2) + E(Z/2) + F(Z/2 + Z/2 + Z/2 + Z/2) + G(Z/2 + Z/2^2)

-------------------------------------------------------
120D (old = 30A), 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) + E(Z/2) + F(Z/3 + Z/3 + Z/3 + Z/2*3) + G(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
120E (old = 24A), 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) + D(Z/2) + F(Z/2) + G(Z/2^2)

-------------------------------------------------------
120F (old = 20A), dim = 1

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) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + D(Z/3 + Z/3 + Z/3 + Z/2*3) + E(Z/2) + G(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
120G (old = 15A), 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) + C(Z/2 + Z/2^2) + D(Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2^2) + F(Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(121)
Weight 2

-------------------------------------------------------
J_0(121), dim = 6

-------------------------------------------------------
121A (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)

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+         = 4.8024227147626444805 + -0.57471738345175815255e-5i
Omega-         = 0.57987364959514092504e-6 + -1.447985358832626395i
L(1)           =
w1             = -2.4012110674444974427 + -0.72398980582939593873i
w2             = -0.57987364959514092504e-6 + 1.447985358832626395i
c4             = 351.99916679930500785 + -0.60609913542325806721e-3i
c6             = -6775.9764767846717651 + 0.14613602636908037291e-1i
j              = -32767.896609091711731 + 0.55750779562057385139i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^4 + -3*q^5 + -2*q^9 + 2*q^12 + 3*q^15 + 4*q^16 + 6*q^20 + -9*q^23 + 4*q^25 + 5*q^27 + -5*q^31 + 4*q^36 + 7*q^37 + 6*q^45 + -12*q^47 + -4*q^48 + -7*q^49 + 6*q^53 + -15*q^59 + -6*q^60 + -8*q^64 + 13*q^67 + 9*q^69 + -3*q^71 + -4*q^75 + -12*q^80 + 1*q^81 + -9*q^89 + 18*q^92 + 5*q^93 + 17*q^97 + -8*q^100 + -4*q^103 + -10*q^108 + -7*q^111 + 21*q^113 + 27*q^115 + 10*q^124 + 3*q^125 + -15*q^135 + -3*q^137 + 12*q^141 + -8*q^144 + 7*q^147 + -14*q^148 + 15*q^155 + -23*q^157 + -6*q^159 + -16*q^163 + -13*q^169 + 15*q^177 + 21*q^179 + -12*q^180 + -25*q^181 + -21*q^185 + 24*q^188 + -15*q^191 + 8*q^192 + 14*q^196 + -20*q^199 +  ...

-------------------------------------------------------
121B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/2 + Z/2) + E(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+         = 1.6661571274256182165 + 0.84508604049354704292e-6i
Omega-         = 0.97258239097715253079e-5 + 3.3822776462995761093i
L(1)           = 1.6661571274258325332
w1             = -0.83307370080085422249 + 1.6911384006067678079i
w2             = 1.6661571274256182165 + 0.84508604049354704292e-6i
c4             = 120.99998607730720032 + -0.19710310037511300197e-2i
c6             = 5202.994854517973844 + 0.31460566058939983031e-1i
j              = -121.00021116305120747 + 0.78929091272401334693e-2i

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

-------------------------------------------------------
121C (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= B(Z/2 + Z/2) + D(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+         = 1.0197928133464007687 + 0.78562213291625474039e-7i
Omega-         = 0.68879880481923513474e-5 + -5.5259987830618556021i
L(1)           = 1.0197928133464037948
w1             = -0.50989296267917628818 + -2.7629994308120344469i
w2             = -1.0197928133464007687 + -0.78562213291625474039e-7i
c4             = 1441.0115777396030896 + -0.44376887301357415062e-3i
c6             = 54703.659313576341332 + -0.25307569388058070785e-1i
j              = -24728432.390219505951 + -492.30393125372490029i

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

-------------------------------------------------------
121D (new) , 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) + E(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|   = 2
Sha Bound      = 2

ANALYTIC INVARIANTS:

Omega+         = 0.8796933819039654816 + 0.33821913473080288331e-5i
Omega-         = 0.1618128329404215565e-4 + -1.9134098027558595058i
L(1)           = 1.7593867638209346058
w1             = -0.43983860031033571972 + -0.95670659247360340692i
w2             = -0.8796933819039654816 + -0.33821913473080288331e-5i
c4             = 1936.0967657545802744 + -0.89769489658541216782e-2i
c6             = 202316.12843512913456 + -6.7794599440159308033i
j              = -372.41303191839931037 + -0.24040905545140361528e-1i

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^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 + -1*q^23 + -4*q^25 + -8*q^26 + 5*q^27 + 4*q^28 + -2*q^30 + 7*q^31 + -8*q^32 + 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^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 + 5*q^59 + -2*q^60 + -12*q^61 + 14*q^62 + -4*q^63 + -8*q^64 + -4*q^65 + -7*q^67 + 4*q^68 + 1*q^69 + 4*q^70 + -3*q^71 + -4*q^73 + 6*q^74 + 4*q^75 + 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 + -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 + -3*q^111 + -8*q^112 + 9*q^113 + -1*q^115 + 8*q^117 + 10*q^118 + 4*q^119 + -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 + -14*q^134 + 5*q^135 + -7*q^137 + 2*q^138 + -10*q^139 + 4*q^140 + -8*q^141 + -6*q^142 + 8*q^144 + -8*q^146 + 3*q^147 + 6*q^148 + 10*q^149 + 8*q^150 + -2*q^151 + -4*q^153 + 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 + 12*q^166 + 12*q^167 + 3*q^169 + 4*q^170 + 12*q^172 + 6*q^173 + -8*q^175 + -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 + 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 +  ...

-------------------------------------------------------
121E (old = 11A), 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/3 + Z/3) + D(Z/2^2 + Z/2^2)

-------------------------------------------------------
Gamma_0(122)
Weight 2

-------------------------------------------------------
J_0(122), dim = 14

-------------------------------------------------------
122A (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+         = 2.9661003744067863934 + 0.19984051471192239368e-6i
Omega-         = 0.29919327628996453537e-6 + -2.9438733621220324707i
L(1)           =
w1             = -1.4830503368000313417 + 1.4719365811407588794i
w2             = 1.4830500376067550517 + 1.4719367809812735913i
c4             = -119.00078159513097977 + 0.39948501035122175176e-4i
c6             = -37.020885188758632927 + 0.18744595512985363561e-3i
j              = 1726.5957810442424806 + 0.12795227146194885306e-4i

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

-------------------------------------------------------
122B (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^2*13
Ker(ModPolar)  = Z/2 + Z/2 + Z/2*13 + Z/2*13
= C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/13 + Z/13)

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+         = 2.4871226467032013928 + -0.80159990017706389497e-5i
Omega-         = 1.9010901042121665076 + 0.46186028880376879935e-6i
L(1)           = 0.82904088223870639319

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

-------------------------------------------------------
122C (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))  = 31
Torsion Bound  = 31
|L(1)/Omega|   = 2^3/31
Sha Bound      = 2^3*31

ANALYTIC INVARIANTS:

Omega+         = 12.201782602416024829 + -0.49184426763631602821e-4i
Omega-         = 0.11217687982980522439e-4 + -2.0505987743140876852i
L(1)           = 3.1488471232297171894

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

-------------------------------------------------------
122D (old = 61A), 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)

-------------------------------------------------------
122E (old = 61B), dim = 3

CONGRUENCES:
Modular Degree = 2^4*13
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2*13 + Z/2*13
= A(Z/2 + Z/2) + B(Z/13 + Z/13) + C(Z/2 + Z/2) + D(Z/2 + Z/2 + Z/2 + Z/2)

-------------------------------------------------------
Gamma_0(123)
Weight 2

-------------------------------------------------------
J_0(123), dim = 13

-------------------------------------------------------
123A (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          = 1
ord((0)-(oo))  = 1
Torsion Bound  = 1
|L(1)/Omega|   = 0
Sha Bound      = 0

ANALYTIC INVARIANTS:

Omega+         = 2.9874203587617149911 + 0.40782162539284263205e-5i
Omega-         = 0.14430710137721733444e-4 + -4.1831010328451313014i
L(1)           =
w1             = -1.4937173947359263564 + 2.0915484773144386865i
w2             = 1.4937029640257886347 + 2.0915525555306926149i
c4             = -32.000704145188714638 + 0.59335964569262008542e-3i
c6             = 424.00156900022790562 + -0.49081679958983810465e-2i
j              = 266.4197116319362481 + -0.73179426974400411737e-2i

HECKE EIGENFORM:
f(q) = q + -1*q^3 + -2*q^4 + -2*q^5 + -4*q^7 + 1*q^9 + 5*q^11 + 2*q^12 + -4*q^13 + 2*q^15 + 4*q^16 + -5*q^17 + -2*q^19 + 4*q^20 + 4*q^21 + 4*q^23 + -1*q^25 + -1*q^27 + 8*q^28 + 1*q^29 + -5*q^31 + -5*q^33 + 8*q^35 + -2*q^36 + -7*q^37 + 4*q^39 + -1*q^41 + 7*q^43 + -10*q^44 + -2*q^45 + 7*q^47 + -4*q^48 + 9*q^49 + 5*q^51 + 8*q^52 + -14*q^53 + -10*q^55 + 2*q^57 + -12*q^59 + -4*q^60 + -3*q^61 + -4*q^63 + -8*q^64 + 8*q^65 + -2*q^67 + 10*q^68 + -4*q^69 + -3*q^71 + 13*q^73 + 1*q^75 + 4*q^76 + -20*q^77 + -2*q^79 + -8*q^80 + 1*q^81 + -2*q^83 + -8*q^84 + 10*q^85 + -1*q^87 + 18*q^89 + 16*q^91 + -8*q^92 + 5*q^93 + 4*q^95 + -14*q^97 + 5*q^99 + 2*q^100 + 3*q^101 + 7*q^103 + -8*q^105 + 10*q^107 + 2*q^108 + -8*q^109 + 7*q^111 + -16*q^112 + -6*q^113 + -8*q^115 + -2*q^116 + -4*q^117 + 20*q^119 + 14*q^121 + 1*q^123 + 10*q^124 + 12*q^125 + 12*q^127 + -7*q^129 + 12*q^131 + 10*q^132 + 8*q^133 + 2*q^135 + -1*q^137 + -4*q^139 + -16*q^140 + -7*q^141 + -20*q^143 + 4*q^144 + -2*q^145 + -9*q^147 + 14*q^148 + -10*q^149 + -5*q^153 + 10*q^155 + -8*q^156 + -22*q^157 + 14*q^159 + -16*q^161 + -9*q^163 + 2*q^164 + 10*q^165 + 3*q^169 + -2*q^171 + -14*q^172 + -2*q^173 + 4*q^175 + 20*q^176 + 12*q^177 + -25*q^179 + 4*q^180 + -8*q^181 + 3*q^183 + 14*q^185 + -25*q^187 + -14*q^188 + 4*q^189 + 20*q^191 + 8*q^192 + -20*q^193 + -8*q^195 + -18*q^196 + 10*q^197 + 6*q^199 +  ...

-------------------------------------------------------
123B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2^2*5
Ker(ModPolar)  = 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/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+         = 3.9950705116943530616 + 0.196882146337994709e-4i
Omega-         = 0.32006914460415055775e-5 + -1.325205633165863465i
L(1)           =
w1             = -1.9975368561928995516 + 0.66259297247561483275i
w2             = -0.32006914460415055775e-5 + 1.325205633165863465i
c4             = 496.00332255819382199 + -0.45697440829697348774e-2i
c6             = -11800.128188169717832 + 0.18144823352300718736i
j              = -12247.548585150224499 + -0.30847635811623702178i

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

-------------------------------------------------------
123C (new) , dim = 2

CONGRUENCES:
Modular Degree = 2^3
Ker(ModPolar)  = Z/2 + Z/2 + Z/2^2 + Z/2^2
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(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))  = 7
Torsion Bound  = 7
|L(1)/Omega|   = 2/7
Sha Bound      = 2*7

ANALYTIC INVARIANTS:

Omega+         = 5.1836980317149951068 + 0.24413001790415262949e-4i
Omega-         = 7.4510705364973726042 + 0.4416707746001175181e-5i
L(1)           = 1.4810565805064235737

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

-------------------------------------------------------
123D (new) , dim = 3

CONGRUENCES:
Modular Degree = 2^4*23
Ker(ModPolar)  = Z/2 + Z/2 + Z/2 + Z/2 + Z/2^2*23 + Z/2^2*23
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + C(Z/2 + Z/2 + Z/2 + Z/2) + E(Z/2*23 + Z/2*23)

ARITHMETIC INVARIANTS:
W_q            = +-
discriminant   = 2^2*79
#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+         = 2.3326081243398745059 + 0.35417908820787676914e-4i
Omega-         = 0.23535743392113983844e-5 + -0.69423228086596265894i
L(1)           = 0.58315203115219103365

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

-------------------------------------------------------
123E (old = 41A), dim = 3

CONGRUENCES:
Modular Degree = 2*5*23
Ker(ModPolar)  = Z/2*5*23 + Z/2*5*23
= B(Z/5 + Z/5) + D(Z/2*23 + Z/2*23)

-------------------------------------------------------
Gamma_0(124)
Weight 2

-------------------------------------------------------
J_0(124), dim = 14

-------------------------------------------------------
124A (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= C(Z/3 + Z/3) + 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|   = 1
Sha Bound      = 1

ANALYTIC INVARIANTS:

Omega+         = 1.1755278952096751215 + -0.23523170779028175408e-5i
Omega-         = 0.55292538594709399202e-5 + 5.2038975281386681019i
L(1)           = 1.1755278952120287005
w1             = -0.5877667122317672962 + -2.6019475879107950995i
w2             = -1.1755278952096751215 + 0.23523170779028175408e-5i
c4             = 816.00463505305667188 + 0.65338715648735020224e-2i
c6             = 23328.19793033689747 + 0.27994863356121440215i
j              = -1095490.0929562181197 + -14.308919576980400933i

HECKE EIGENFORM:
f(q) = q + 1*q^5 + 3*q^7 + -3*q^9 + 6*q^11 + -4*q^13 + -5*q^19 + -4*q^23 + -4*q^25 + 2*q^29 + -1*q^31 + 3*q^35 + -2*q^37 + -9*q^41 + 2*q^43 + -3*q^45 + 4*q^47 + 2*q^49 + 12*q^53 + 6*q^55 + 9*q^59 + 12*q^61 + -9*q^63 + -4*q^65 + -12*q^67 + 5*q^71 + -14*q^73 + 18*q^77 + 10*q^79 + 9*q^81 + 2*q^83 + 6*q^89 + -12*q^91 + -5*q^95 + -7*q^97 + -18*q^99 + -7*q^101 + -7*q^103 + -1*q^107 + 7*q^109 + -19*q^113 + -4*q^115 + 12*q^117 + 25*q^121 + -9*q^125 + -14*q^127 + 12*q^131 + -15*q^133 + -4*q^137 + 6*q^139 + -24*q^143 + 2*q^145 + -2*q^149 + 14*q^151 + -1*q^155 + 23*q^157 + -12*q^161 + 11*q^163 + 8*q^167 + 3*q^169 + 15*q^171 + -14*q^173 + -12*q^175 + 16*q^179 + 8*q^181 + -2*q^185 + 15*q^191 + 25*q^193 + 24*q^197 + -18*q^199 +  ...

-------------------------------------------------------
124B (new) , dim = 1

CONGRUENCES:
Modular Degree = 2*3
Ker(ModPolar)  = Z/2*3 + Z/2*3
= D(Z/3 + Z/3) + E(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+         = 4.9333432323363636052 + 0.73683717964217703362e-5i
Omega-         = 0.6084173134982076261e-5 + -1.8977214067574607395i
L(1)           =
w1             = 2.4666685740816143116 + 0.94886438756462858066i
w2             = 0.6084173134982076261e-5 + -1.8977214067574607395i
c4             = 112.00167025586586113 + -0.15502492184935995742e-2i
c6             = -1504.0163407763649435 + 0.26344891014620902848e-1i
j              = -2832.6881415982685449 + 0.48529968506059310581e-1i

HECKE EIGENFORM:
f(q) = q + -2*q^3 + -3*q^5 + -1*q^7 + 1*q^9 + -6*q^11 + 2*q^13 + 6*q^15 + 6*q^17 + -1*q^19 + 2*q^21 + -6*q^23 + 4*q^25 + 4*q^27 + 1*q^31 + 12*q^33 + 3*q^35 + -10*q^37 + -4*q^39 + -9*q^41 + 8*q^43 + -3*q^45 + -6*q^49 + -12*q^51 + 18*q^55 + 2*q^57 + -3*q^59 + -10*q^61 + -1*q^63 + -6*q^65 + -4*q^67 + 12*q^69 + -15*q^71 + 14*q^73 + -8*q^75 + 6*q^77 + 8*q^79 + -11*q^81 + 6*q^83 + -18*q^85 + 12*q^89 + -2*q^91 + -2*q^93 + 3*q^95 + -7*q^97 + -6*q^99 + -3*q^101 + -7*q^103 + -6*q^105 + 3*q^107 + 11*q^109 + 20*q^111 + 9*q^113 + 18*q^115 + 2*q^117 + -6*q^119 + 25*q^121 + 18*q^123 + 3*q^125 + 2*q^127 + -16*q^129 + 12*q^131 + 1*q^133 + -12*q^135 + -18*q^137 + 14*q^139 + -12*q^143 + 12*q^147 + -18*q^149 + -16*q^151 + 6*q^153 + -3*q^155 + -13*q^157 + 6*q^161 + -1*q^163 + -36*q^165 + 12*q^167 + -9*q^169 + -1*q^171 + -6*q^173 + -4*q^175 + 6*q^177 + 6*q^179 + -10*q^181 + 20*q^183 + 30*q^185 + -36*q^187 + -4*q^189 + -9*q^191 + -19*q^193 + 12*q^195 + 12*q^197 + 2*q^199 +  ...

-------------------------------------------------------
124C (old = 62A), 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)

-------------------------------------------------------
124D (old = 62B), dim = 2

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

-------------------------------------------------------
124E (old = 31A), dim = 2

CONGRUENCES:
Modular Degree = 2^2*11^2
Ker(ModPolar)  = Z/2*11 + Z/2*11 + Z/2*11 + Z/2*11
= A(Z/2 + Z/2) + B(Z/2 + Z/2) + D(Z/11 + Z/11 + Z/11 + Z/11)

-------------------------------------------------------
Gamma_0(125)
Weight 2

-------------------------------------------------------
J_0(125), dim = 8

-------------------------------------------------------
125A (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+         = 13.026196422331810968 + -0.456436453881497698e-4i
Omega-         = 7.7574941324747747895 + 0.3246236275744988014e-4i
L(1)           =

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

-------------------------------------------------------
125B (new) , dim = 2

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

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+         = 2.6052365591026649972 + -0.16853631852414936181e-5i
Omega-         = 1.551512122753058723 + -0.11473302066672099532e-5i
L(1)           = 2.0841892472825681116

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

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125C (new) , dim = 4

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

ARITHMETIC INVARIANTS:
W_q            = -
discriminant   = 2^4*5^2*11
#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+         = 6.0886544659993140931 + -0.36991007918062583728e-4i
Omega-         = 33.687913183785302464 + 0.17416087769240148144e-3i
L(1)           = 1.2177308932223363335

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

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