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Properties

Label 1152.3
Level 1152
Weight 3
Dimension 32616
Nonzero newspaces 20
Sturm bound 221184
Trace bound 33

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Defining parameters

Level: \( N \) = \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(221184\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1152))\).

Total New Old
Modular forms 75008 33048 41960
Cusp forms 72448 32616 39832
Eisenstein series 2560 432 2128

Trace form

\( 32616 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 64 q^{6} - 36 q^{7} - 48 q^{8} - 80 q^{9} + O(q^{10}) \) \( 32616 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 64 q^{6} - 36 q^{7} - 48 q^{8} - 80 q^{9} - 144 q^{10} - 36 q^{11} - 64 q^{12} - 48 q^{13} - 48 q^{14} - 48 q^{15} - 48 q^{16} - 72 q^{17} - 64 q^{18} - 108 q^{19} - 48 q^{20} - 64 q^{21} - 48 q^{22} + 28 q^{23} - 64 q^{24} + 36 q^{25} - 48 q^{26} - 48 q^{27} - 144 q^{28} - 16 q^{29} - 64 q^{30} - 40 q^{31} - 48 q^{32} - 128 q^{33} - 48 q^{34} - 132 q^{35} - 64 q^{36} - 240 q^{37} - 48 q^{38} - 48 q^{39} - 48 q^{40} - 220 q^{41} - 64 q^{42} - 132 q^{43} - 48 q^{44} - 64 q^{45} - 144 q^{46} - 48 q^{47} - 64 q^{48} - 268 q^{49} - 672 q^{50} - 48 q^{51} - 1104 q^{52} - 368 q^{53} - 64 q^{54} - 364 q^{55} - 832 q^{56} - 80 q^{57} - 768 q^{58} - 164 q^{59} - 64 q^{60} - 176 q^{61} - 144 q^{62} - 48 q^{63} + 48 q^{64} + 80 q^{65} - 64 q^{66} + 124 q^{67} + 432 q^{68} - 136 q^{69} + 1296 q^{70} + 220 q^{71} - 64 q^{72} + 460 q^{73} + 1184 q^{74} - 248 q^{75} + 1616 q^{76} - 188 q^{77} - 64 q^{78} - 544 q^{79} + 768 q^{80} - 992 q^{81} - 144 q^{82} - 1476 q^{83} - 64 q^{84} - 808 q^{85} - 48 q^{86} - 944 q^{87} - 48 q^{88} - 1212 q^{89} - 64 q^{90} - 684 q^{91} - 48 q^{92} - 256 q^{93} - 48 q^{94} - 24 q^{95} - 64 q^{96} + 288 q^{97} - 48 q^{98} + 464 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1152))\)

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
1152.3.b \(\chi_{1152}(703, \cdot)\) 1152.3.b.a 2 1
1152.3.b.b 2
1152.3.b.c 2
1152.3.b.d 2
1152.3.b.e 4
1152.3.b.f 4
1152.3.b.g 4
1152.3.b.h 4
1152.3.b.i 8
1152.3.b.j 8
1152.3.e \(\chi_{1152}(1025, \cdot)\) 1152.3.e.a 4 1
1152.3.e.b 4
1152.3.e.c 4
1152.3.e.d 4
1152.3.e.e 4
1152.3.e.f 4
1152.3.e.g 4
1152.3.e.h 4
1152.3.g \(\chi_{1152}(127, \cdot)\) 1152.3.g.a 4 1
1152.3.g.b 4
1152.3.g.c 8
1152.3.g.d 8
1152.3.g.e 8
1152.3.g.f 8
1152.3.h \(\chi_{1152}(449, \cdot)\) 1152.3.h.a 4 1
1152.3.h.b 4
1152.3.h.c 4
1152.3.h.d 4
1152.3.h.e 8
1152.3.h.f 8
1152.3.j \(\chi_{1152}(161, \cdot)\) 1152.3.j.a 32 2
1152.3.j.b 32
1152.3.m \(\chi_{1152}(415, \cdot)\) 1152.3.m.a 6 2
1152.3.m.b 6
1152.3.m.c 16
1152.3.m.d 16
1152.3.m.e 16
1152.3.m.f 16
1152.3.n \(\chi_{1152}(65, \cdot)\) n/a 192 2
1152.3.o \(\chi_{1152}(511, \cdot)\) n/a 192 2
1152.3.q \(\chi_{1152}(257, \cdot)\) n/a 192 2
1152.3.t \(\chi_{1152}(319, \cdot)\) n/a 192 2
1152.3.u \(\chi_{1152}(271, \cdot)\) n/a 156 4
1152.3.x \(\chi_{1152}(17, \cdot)\) n/a 128 4
1152.3.z \(\chi_{1152}(31, \cdot)\) n/a 368 4
1152.3.ba \(\chi_{1152}(353, \cdot)\) n/a 368 4
1152.3.bc \(\chi_{1152}(89, \cdot)\) None 0 8
1152.3.bf \(\chi_{1152}(55, \cdot)\) None 0 8
1152.3.bh \(\chi_{1152}(79, \cdot)\) n/a 752 8
1152.3.bi \(\chi_{1152}(113, \cdot)\) n/a 752 8
1152.3.bk \(\chi_{1152}(19, \cdot)\) n/a 2544 16
1152.3.bn \(\chi_{1152}(53, \cdot)\) n/a 2048 16
1152.3.bo \(\chi_{1152}(7, \cdot)\) None 0 16
1152.3.br \(\chi_{1152}(41, \cdot)\) None 0 16
1152.3.bt \(\chi_{1152}(5, \cdot)\) n/a 12224 32
1152.3.bu \(\chi_{1152}(43, \cdot)\) n/a 12224 32

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1152))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1152)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)