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Properties

Label 1656.2
Level 1656
Weight 2
Dimension 33352
Nonzero newspaces 24
Sturm bound 304128
Trace bound 6

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Defining parameters

Level: \( N \) = \( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(304128\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1656))\).

Total New Old
Modular forms 78144 34108 44036
Cusp forms 73921 33352 40569
Eisenstein series 4223 756 3467

Trace form

\( 33352 q - 62 q^{2} - 82 q^{3} - 62 q^{4} - 8 q^{5} - 72 q^{6} - 62 q^{7} - 38 q^{8} - 158 q^{9} + O(q^{10}) \) \( 33352 q - 62 q^{2} - 82 q^{3} - 62 q^{4} - 8 q^{5} - 72 q^{6} - 62 q^{7} - 38 q^{8} - 158 q^{9} - 150 q^{10} - 32 q^{11} - 60 q^{12} + 4 q^{13} - 38 q^{14} - 40 q^{15} - 46 q^{16} - 92 q^{17} - 88 q^{18} - 154 q^{19} - 86 q^{20} + 24 q^{21} - 94 q^{22} - 48 q^{23} - 224 q^{24} - 116 q^{25} - 122 q^{26} - 88 q^{27} - 214 q^{28} - 12 q^{29} - 180 q^{30} - 34 q^{31} - 142 q^{32} - 162 q^{33} - 38 q^{34} - 160 q^{35} - 188 q^{36} - 56 q^{37} - 142 q^{38} - 160 q^{39} - 86 q^{40} - 144 q^{41} - 188 q^{42} - 160 q^{43} - 150 q^{44} - 4 q^{45} - 214 q^{46} - 260 q^{47} - 128 q^{48} - 94 q^{49} - 122 q^{50} - 106 q^{51} - 14 q^{52} + 6 q^{53} - 64 q^{54} - 210 q^{55} - 2 q^{56} - 118 q^{57} - 46 q^{58} - 90 q^{59} + 44 q^{60} + 16 q^{61} + 62 q^{62} - 152 q^{63} - 158 q^{64} - 64 q^{65} + 120 q^{66} - 16 q^{67} + 102 q^{68} - 22 q^{69} - 40 q^{70} - 82 q^{71} + 116 q^{72} - 348 q^{73} + 176 q^{74} - 186 q^{75} + 112 q^{76} - 24 q^{77} + 60 q^{78} + 8 q^{79} + 324 q^{80} - 198 q^{81} - 106 q^{82} - 64 q^{83} + 40 q^{84} + 50 q^{85} + 254 q^{86} - 124 q^{87} + 82 q^{88} - 110 q^{89} - 60 q^{90} - 92 q^{91} + 78 q^{92} + 20 q^{93} + 84 q^{94} - 62 q^{95} - 184 q^{96} - 168 q^{97} - 82 q^{98} - 148 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1656))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1656.2.a \(\chi_{1656}(1, \cdot)\) 1656.2.a.a 1 1
1656.2.a.b 1
1656.2.a.c 1
1656.2.a.d 1
1656.2.a.e 1
1656.2.a.f 1
1656.2.a.g 1
1656.2.a.h 1
1656.2.a.i 1
1656.2.a.j 2
1656.2.a.k 2
1656.2.a.l 2
1656.2.a.m 2
1656.2.a.n 3
1656.2.a.o 4
1656.2.a.p 4
1656.2.b \(\chi_{1656}(413, \cdot)\) 1656.2.b.a 8 1
1656.2.b.b 8
1656.2.b.c 80
1656.2.e \(\chi_{1656}(1151, \cdot)\) None 0 1
1656.2.f \(\chi_{1656}(829, \cdot)\) n/a 110 1
1656.2.i \(\chi_{1656}(919, \cdot)\) None 0 1
1656.2.j \(\chi_{1656}(323, \cdot)\) 1656.2.j.a 44 1
1656.2.j.b 44
1656.2.m \(\chi_{1656}(1241, \cdot)\) 1656.2.m.a 24 1
1656.2.n \(\chi_{1656}(91, \cdot)\) n/a 118 1
1656.2.q \(\chi_{1656}(553, \cdot)\) n/a 132 2
1656.2.t \(\chi_{1656}(643, \cdot)\) n/a 568 2
1656.2.u \(\chi_{1656}(137, \cdot)\) n/a 144 2
1656.2.x \(\chi_{1656}(875, \cdot)\) n/a 528 2
1656.2.y \(\chi_{1656}(367, \cdot)\) None 0 2
1656.2.bb \(\chi_{1656}(277, \cdot)\) n/a 528 2
1656.2.bc \(\chi_{1656}(47, \cdot)\) None 0 2
1656.2.bf \(\chi_{1656}(965, \cdot)\) n/a 568 2
1656.2.bg \(\chi_{1656}(73, \cdot)\) n/a 300 10
1656.2.bj \(\chi_{1656}(19, \cdot)\) n/a 1180 10
1656.2.bk \(\chi_{1656}(17, \cdot)\) n/a 240 10
1656.2.bn \(\chi_{1656}(35, \cdot)\) n/a 960 10
1656.2.bo \(\chi_{1656}(199, \cdot)\) None 0 10
1656.2.br \(\chi_{1656}(325, \cdot)\) n/a 1180 10
1656.2.bs \(\chi_{1656}(71, \cdot)\) None 0 10
1656.2.bv \(\chi_{1656}(53, \cdot)\) n/a 960 10
1656.2.bw \(\chi_{1656}(25, \cdot)\) n/a 1440 20
1656.2.bx \(\chi_{1656}(5, \cdot)\) n/a 5680 20
1656.2.ca \(\chi_{1656}(95, \cdot)\) None 0 20
1656.2.cb \(\chi_{1656}(13, \cdot)\) n/a 5680 20
1656.2.ce \(\chi_{1656}(7, \cdot)\) None 0 20
1656.2.cf \(\chi_{1656}(59, \cdot)\) n/a 5680 20
1656.2.ci \(\chi_{1656}(65, \cdot)\) n/a 1440 20
1656.2.cj \(\chi_{1656}(43, \cdot)\) n/a 5680 20

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1656))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1656)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 2}\)