## 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

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

## 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 the 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

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