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Properties

Label 1156.2
Level 1156
Weight 2
Dimension 23740
Nonzero newspaces 10
Sturm bound 166464
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1156 = 2^{2} \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(166464\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1156))\).

Total New Old
Modular forms 42616 24476 18140
Cusp forms 40617 23740 16877
Eisenstein series 1999 736 1263

Trace form

\( 23740 q - 120 q^{2} - 120 q^{4} - 240 q^{5} - 120 q^{6} - 120 q^{8} - 240 q^{9} + O(q^{10}) \) \( 23740 q - 120 q^{2} - 120 q^{4} - 240 q^{5} - 120 q^{6} - 120 q^{8} - 240 q^{9} - 120 q^{10} + 16 q^{11} - 120 q^{12} - 224 q^{13} - 120 q^{14} + 48 q^{15} - 136 q^{16} - 248 q^{17} - 232 q^{18} + 16 q^{19} - 120 q^{20} - 192 q^{21} - 120 q^{22} + 16 q^{23} - 152 q^{24} - 264 q^{25} - 184 q^{26} - 48 q^{27} - 216 q^{28} - 280 q^{29} - 248 q^{30} - 64 q^{31} - 200 q^{32} - 336 q^{33} - 192 q^{34} - 64 q^{35} - 248 q^{36} - 304 q^{37} - 200 q^{38} - 32 q^{39} - 248 q^{40} - 232 q^{41} - 216 q^{42} - 16 q^{43} - 184 q^{44} - 216 q^{45} - 152 q^{46} + 80 q^{47} - 72 q^{48} - 176 q^{49} - 136 q^{50} + 32 q^{51} - 232 q^{52} - 200 q^{53} - 88 q^{54} + 32 q^{55} - 40 q^{56} - 336 q^{57} - 8 q^{58} + 32 q^{59} + 88 q^{60} - 304 q^{61} - 8 q^{62} - 48 q^{63} - 24 q^{64} - 424 q^{65} + 56 q^{66} - 32 q^{67} - 40 q^{68} - 624 q^{69} + 24 q^{70} + 88 q^{72} - 376 q^{73} - 24 q^{74} - 32 q^{75} - 8 q^{76} - 272 q^{77} + 88 q^{78} + 32 q^{79} - 88 q^{80} - 320 q^{81} - 40 q^{82} - 136 q^{84} - 252 q^{85} - 392 q^{86} - 248 q^{88} - 288 q^{89} - 280 q^{90} - 32 q^{91} - 344 q^{92} - 304 q^{93} - 312 q^{94} - 96 q^{95} - 424 q^{96} - 240 q^{97} - 392 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)

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
1156.2.a \(\chi_{1156}(1, \cdot)\) 1156.2.a.a 2 1
1156.2.a.b 2
1156.2.a.c 2
1156.2.a.d 2
1156.2.a.e 3
1156.2.a.f 3
1156.2.a.g 4
1156.2.a.h 4
1156.2.b \(\chi_{1156}(577, \cdot)\) 1156.2.b.a 4 1
1156.2.b.b 4
1156.2.b.c 4
1156.2.b.d 4
1156.2.b.e 6
1156.2.e \(\chi_{1156}(829, \cdot)\) 1156.2.e.a 2 2
1156.2.e.b 2
1156.2.e.c 4
1156.2.e.d 8
1156.2.e.e 8
1156.2.e.f 8
1156.2.e.g 12
1156.2.h \(\chi_{1156}(733, \cdot)\) 1156.2.h.a 4 4
1156.2.h.b 4
1156.2.h.c 4
1156.2.h.d 8
1156.2.h.e 16
1156.2.h.f 16
1156.2.h.g 16
1156.2.h.h 24
1156.2.i \(\chi_{1156}(75, \cdot)\) n/a 968 8
1156.2.k \(\chi_{1156}(69, \cdot)\) n/a 416 16
1156.2.n \(\chi_{1156}(33, \cdot)\) n/a 416 16
1156.2.p \(\chi_{1156}(13, \cdot)\) n/a 832 32
1156.2.q \(\chi_{1156}(9, \cdot)\) n/a 1600 64
1156.2.t \(\chi_{1156}(3, \cdot)\) n/a 19328 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1156))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1156)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 2}\)