## Defining parameters

 Level: $$N$$ = $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$6$$ Newform subspaces: $$12$$ Sturm bound: $$2048$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(96))$$.

Total New Old
Modular forms 832 334 498
Cusp forms 704 314 390
Eisenstein series 128 20 108

## Trace form

 $$314q - 2q^{3} - 8q^{4} - 4q^{5} - 4q^{6} - 36q^{7} - 26q^{9} + O(q^{10})$$ $$314q - 2q^{3} - 8q^{4} - 4q^{5} - 4q^{6} - 36q^{7} - 26q^{9} - 248q^{10} + 44q^{12} + 228q^{13} + 416q^{14} + 52q^{15} + 592q^{16} + 208q^{17} + 68q^{18} + 20q^{19} - 160q^{20} + 12q^{21} - 400q^{22} - 984q^{23} + 40q^{24} - 350q^{25} - 40q^{26} + 394q^{27} - 768q^{28} + 284q^{29} - 1132q^{30} + 2124q^{31} - 1240q^{32} + 32q^{33} - 1072q^{34} + 912q^{35} + 576q^{36} - 668q^{37} + 440q^{38} - 916q^{39} + 1632q^{40} - 1064q^{41} + 896q^{42} - 2052q^{43} + 1000q^{44} - 584q^{45} - 8q^{46} + 408q^{47} - 2448q^{48} + 702q^{49} + 2856q^{50} + 624q^{51} + 3304q^{52} - 1716q^{53} - 8q^{54} - 456q^{55} - 392q^{56} - 776q^{57} - 2384q^{58} - 2752q^{59} + 344q^{60} + 2772q^{61} - 2928q^{62} - 756q^{63} - 9920q^{64} - 2024q^{65} - 6004q^{66} - 2452q^{67} - 5032q^{68} + 2364q^{69} - 2816q^{70} + 1256q^{71} + 1376q^{72} + 4796q^{73} + 6944q^{74} + 4662q^{75} + 10232q^{76} + 64q^{77} + 6844q^{78} + 5692q^{79} + 11336q^{80} + 4050q^{81} + 5832q^{82} + 2408q^{84} - 1624q^{85} + 2368q^{86} - 2336q^{87} + 608q^{88} + 2816q^{90} - 3176q^{91} - 7696q^{92} - 5016q^{93} - 16640q^{94} - 5104q^{95} - 4880q^{96} - 7724q^{97} - 10288q^{98} - 9428q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(96))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
96.4.a $$\chi_{96}(1, \cdot)$$ 96.4.a.a 1 1
96.4.a.b 1
96.4.a.c 1
96.4.a.d 1
96.4.a.e 1
96.4.a.f 1
96.4.c $$\chi_{96}(95, \cdot)$$ 96.4.c.a 12 1
96.4.d $$\chi_{96}(49, \cdot)$$ 96.4.d.a 6 1
96.4.f $$\chi_{96}(47, \cdot)$$ 96.4.f.a 2 1
96.4.f.b 8
96.4.j $$\chi_{96}(25, \cdot)$$ None 0 2
96.4.k $$\chi_{96}(23, \cdot)$$ None 0 2
96.4.n $$\chi_{96}(13, \cdot)$$ 96.4.n.a 96 4
96.4.o $$\chi_{96}(11, \cdot)$$ 96.4.o.a 184 4

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(96))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(96)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$