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Properties

Label 1176.3
Level 1176
Weight 3
Dimension 30276
Nonzero newspaces 24
Sturm bound 225792
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(225792\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1176))\).

Total New Old
Modular forms 76704 30664 46040
Cusp forms 73824 30276 43548
Eisenstein series 2880 388 2492

Trace form

\( 30276 q + 2 q^{2} - 28 q^{3} - 72 q^{4} - 44 q^{6} - 72 q^{7} - 4 q^{8} - 16 q^{9} + O(q^{10}) \) \( 30276 q + 2 q^{2} - 28 q^{3} - 72 q^{4} - 44 q^{6} - 72 q^{7} - 4 q^{8} - 16 q^{9} - 72 q^{10} + 16 q^{11} - 14 q^{12} + 20 q^{13} - 90 q^{15} - 28 q^{16} - 104 q^{17} + 32 q^{18} - 360 q^{19} - 432 q^{20} - 84 q^{21} - 660 q^{22} - 288 q^{23} - 298 q^{24} - 336 q^{25} - 216 q^{26} - 88 q^{27} + 24 q^{28} + 86 q^{30} + 340 q^{31} + 512 q^{32} - 16 q^{33} + 880 q^{34} + 288 q^{35} + 270 q^{36} + 228 q^{37} + 832 q^{38} + 66 q^{39} + 788 q^{40} + 40 q^{41} + 180 q^{42} - 488 q^{43} + 1120 q^{44} - 104 q^{45} + 1172 q^{46} - 1152 q^{47} + 738 q^{48} - 360 q^{49} + 722 q^{50} - 374 q^{51} + 428 q^{52} - 144 q^{53} - 16 q^{54} + 4 q^{55} - 84 q^{56} + 336 q^{57} - 464 q^{58} + 1120 q^{59} - 714 q^{60} + 836 q^{61} - 1308 q^{62} + 480 q^{63} - 1380 q^{64} + 1104 q^{65} - 702 q^{66} + 1608 q^{67} - 1448 q^{68} + 944 q^{69} - 792 q^{70} + 672 q^{71} + 530 q^{72} - 64 q^{73} - 120 q^{74} + 1024 q^{75} - 132 q^{76} - 288 q^{77} + 626 q^{78} - 620 q^{79} - 96 q^{80} - 840 q^{81} - 408 q^{82} - 2192 q^{83} - 144 q^{84} - 1376 q^{85} + 88 q^{86} - 1278 q^{87} - 108 q^{88} - 1160 q^{89} - 1582 q^{90} - 348 q^{91} + 552 q^{92} - 1700 q^{93} + 2220 q^{94} + 1824 q^{95} - 454 q^{96} - 3184 q^{97} + 1092 q^{98} - 560 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1176))\)

We only show spaces with odd 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
1176.3.d \(\chi_{1176}(785, \cdot)\) 1176.3.d.a 2 1
1176.3.d.b 2
1176.3.d.c 2
1176.3.d.d 8
1176.3.d.e 12
1176.3.d.f 16
1176.3.d.g 16
1176.3.d.h 24
1176.3.e \(\chi_{1176}(587, \cdot)\) n/a 312 1
1176.3.f \(\chi_{1176}(97, \cdot)\) 1176.3.f.a 8 1
1176.3.f.b 8
1176.3.f.c 8
1176.3.f.d 16
1176.3.g \(\chi_{1176}(883, \cdot)\) n/a 164 1
1176.3.l \(\chi_{1176}(685, \cdot)\) n/a 160 1
1176.3.m \(\chi_{1176}(295, \cdot)\) None 0 1
1176.3.n \(\chi_{1176}(197, \cdot)\) n/a 318 1
1176.3.o \(\chi_{1176}(1175, \cdot)\) None 0 1
1176.3.r \(\chi_{1176}(215, \cdot)\) None 0 2
1176.3.s \(\chi_{1176}(557, \cdot)\) n/a 624 2
1176.3.w \(\chi_{1176}(79, \cdot)\) None 0 2
1176.3.x \(\chi_{1176}(325, \cdot)\) n/a 320 2
1176.3.y \(\chi_{1176}(67, \cdot)\) n/a 320 2
1176.3.z \(\chi_{1176}(313, \cdot)\) 1176.3.z.a 8 2
1176.3.z.b 8
1176.3.z.c 8
1176.3.z.d 8
1176.3.z.e 8
1176.3.z.f 8
1176.3.z.g 16
1176.3.z.h 16
1176.3.be \(\chi_{1176}(227, \cdot)\) n/a 624 2
1176.3.bf \(\chi_{1176}(569, \cdot)\) n/a 160 2
1176.3.bi \(\chi_{1176}(167, \cdot)\) None 0 6
1176.3.bj \(\chi_{1176}(29, \cdot)\) n/a 2664 6
1176.3.bk \(\chi_{1176}(127, \cdot)\) None 0 6
1176.3.bl \(\chi_{1176}(13, \cdot)\) n/a 1344 6
1176.3.bq \(\chi_{1176}(43, \cdot)\) n/a 1344 6
1176.3.br \(\chi_{1176}(265, \cdot)\) n/a 336 6
1176.3.bs \(\chi_{1176}(83, \cdot)\) n/a 2664 6
1176.3.bt \(\chi_{1176}(113, \cdot)\) n/a 672 6
1176.3.bx \(\chi_{1176}(65, \cdot)\) n/a 1344 12
1176.3.by \(\chi_{1176}(59, \cdot)\) n/a 5328 12
1176.3.cd \(\chi_{1176}(73, \cdot)\) n/a 672 12
1176.3.ce \(\chi_{1176}(163, \cdot)\) n/a 2688 12
1176.3.cf \(\chi_{1176}(61, \cdot)\) n/a 2688 12
1176.3.cg \(\chi_{1176}(151, \cdot)\) None 0 12
1176.3.ck \(\chi_{1176}(53, \cdot)\) n/a 5328 12
1176.3.cl \(\chi_{1176}(47, \cdot)\) None 0 12

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1176))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1176)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)