## Defining parameters

 Level: $$N$$ = $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$6$$ Newform subspaces: $$10$$ Sturm bound: $$2560$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(96))$$.

Total New Old
Modular forms 1088 442 646
Cusp forms 960 422 538
Eisenstein series 128 20 108

## Trace form

 $$422 q - 4 q^{3} - 8 q^{4} + 48 q^{5} - 4 q^{6} - 4 q^{7} - 118 q^{9} + O(q^{10})$$ $$422 q - 4 q^{3} - 8 q^{4} + 48 q^{5} - 4 q^{6} - 4 q^{7} - 118 q^{9} + 392 q^{10} - 192 q^{11} - 724 q^{12} - 472 q^{13} - 864 q^{14} + 164 q^{15} + 1232 q^{16} + 960 q^{17} + 644 q^{18} + 696 q^{19} + 2400 q^{20} - 324 q^{21} - 3792 q^{22} + 2304 q^{23} - 2520 q^{24} - 1934 q^{25} + 5400 q^{26} - 3652 q^{27} + 5632 q^{28} - 1680 q^{29} + 2292 q^{30} - 140 q^{31} - 2520 q^{32} + 900 q^{33} - 7216 q^{34} + 15552 q^{35} - 15872 q^{36} + 2792 q^{37} - 7560 q^{38} + 3868 q^{39} + 352 q^{40} - 3936 q^{41} + 19936 q^{42} - 21192 q^{43} + 8424 q^{44} + 2028 q^{45} - 8 q^{46} - 4944 q^{48} + 6954 q^{49} - 21528 q^{50} - 4360 q^{51} - 8984 q^{52} + 6384 q^{53} - 16232 q^{54} + 20160 q^{55} + 24696 q^{56} - 1012 q^{57} + 32752 q^{58} + 13056 q^{59} + 34840 q^{60} - 26008 q^{61} + 5904 q^{62} - 5124 q^{63} + 22720 q^{64} + 7968 q^{65} - 2260 q^{66} - 31112 q^{67} - 35880 q^{68} + 12668 q^{69} - 99392 q^{70} - 39936 q^{71} - 39904 q^{72} - 25516 q^{73} - 70752 q^{74} - 3656 q^{75} - 13320 q^{76} - 24576 q^{77} + 40188 q^{78} + 61700 q^{79} + 65352 q^{80} + 27886 q^{81} + 37192 q^{82} + 24000 q^{83} + 25384 q^{84} + 28752 q^{85} + 55104 q^{86} + 58336 q^{87} + 75232 q^{88} + 15360 q^{89} - 16864 q^{90} - 1352 q^{91} + 40944 q^{92} + 15544 q^{93} + 51200 q^{94} - 19984 q^{96} - 43956 q^{97} - 94896 q^{98} - 51780 q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(96))$$

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
96.5.b $$\chi_{96}(79, \cdot)$$ 96.5.b.a 8 1
96.5.e $$\chi_{96}(65, \cdot)$$ 96.5.e.a 8 1
96.5.e.b 8
96.5.g $$\chi_{96}(31, \cdot)$$ 96.5.g.a 4 1
96.5.g.b 4
96.5.h $$\chi_{96}(17, \cdot)$$ 96.5.h.a 1 1
96.5.h.b 1
96.5.h.c 12
96.5.i $$\chi_{96}(41, \cdot)$$ None 0 2
96.5.l $$\chi_{96}(7, \cdot)$$ None 0 2
96.5.m $$\chi_{96}(19, \cdot)$$ 96.5.m.a 128 4
96.5.p $$\chi_{96}(5, \cdot)$$ 96.5.p.a 248 4

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(96))$$ into lower level spaces

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