## Defining parameters

 Level: $$N$$ = $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$6$$ Newform subspaces: $$9$$ Sturm bound: $$1536$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(96))$$.

Total New Old
Modular forms 576 226 350
Cusp forms 448 206 242
Eisenstein series 128 20 108

## Trace form

 $$206q - 4q^{3} - 8q^{4} - 8q^{5} - 4q^{6} - 4q^{7} + 2q^{9} + O(q^{10})$$ $$206q - 4q^{3} - 8q^{4} - 8q^{5} - 4q^{6} - 4q^{7} + 2q^{9} + 72q^{10} + 32q^{11} + 44q^{12} + 48q^{13} + 32q^{14} + 20q^{15} - 48q^{16} - 32q^{17} - 28q^{18} - 40q^{19} - 160q^{20} - 36q^{21} - 304q^{22} + 128q^{23} - 216q^{24} - 14q^{25} - 200q^{26} + 92q^{27} - 128q^{28} - 40q^{29} - 60q^{30} - 76q^{31} + 40q^{32} - 132q^{33} + 80q^{34} - 288q^{35} + 64q^{36} - 48q^{37} + 280q^{38} - 308q^{39} + 352q^{40} - 48q^{41} + 16q^{42} - 232q^{43} + 104q^{44} - 108q^{45} - 8q^{46} + 48q^{48} + 18q^{49} - 312q^{50} - 136q^{51} - 536q^{52} + 344q^{53} + 232q^{54} - 288q^{55} - 392q^{56} + 260q^{57} - 368q^{58} - 128q^{59} + 280q^{60} + 336q^{61} - 48q^{62} + 252q^{63} + 448q^{64} + 400q^{65} + 572q^{66} + 568q^{67} + 856q^{68} + 188q^{69} + 1312q^{70} + 512q^{71} + 416q^{72} - 92q^{73} + 1056q^{74} + 88q^{75} + 1016q^{76} - 512q^{77} + 636q^{78} + 132q^{79} + 328q^{80} - 266q^{81} - 248q^{82} - 160q^{83} + 232q^{84} - 800q^{85} - 448q^{86} - 848q^{87} - 800q^{88} - 512q^{89} - 304q^{90} - 296q^{91} - 784q^{92} - 296q^{93} - 64q^{94} - 16q^{96} + 284q^{97} + 272q^{98} + 348q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(96))$$

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
96.3.b $$\chi_{96}(79, \cdot)$$ 96.3.b.a 4 1
96.3.e $$\chi_{96}(65, \cdot)$$ 96.3.e.a 4 1
96.3.e.b 4
96.3.g $$\chi_{96}(31, \cdot)$$ 96.3.g.a 4 1
96.3.h $$\chi_{96}(17, \cdot)$$ 96.3.h.a 1 1
96.3.h.b 1
96.3.h.c 4
96.3.i $$\chi_{96}(41, \cdot)$$ None 0 2
96.3.l $$\chi_{96}(7, \cdot)$$ None 0 2
96.3.m $$\chi_{96}(19, \cdot)$$ 96.3.m.a 64 4
96.3.p $$\chi_{96}(5, \cdot)$$ 96.3.p.a 120 4

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(96))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(96)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$