## Defining parameters

 Level: $$N$$ = $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ = $$9$$ Nonzero newspaces: $$6$$ Newform subspaces: $$10$$ Sturm bound: $$4608$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(\Gamma_1(96))$$.

Total New Old
Modular forms 2112 874 1238
Cusp forms 1984 854 1130
Eisenstein series 128 20 108

## Trace form

 $$854 q - 4 q^{3} - 8 q^{4} - 672 q^{5} - 4 q^{6} - 4 q^{7} - 3814 q^{9} + O(q^{10})$$ $$854 q - 4 q^{3} - 8 q^{4} - 672 q^{5} - 4 q^{6} - 4 q^{7} - 3814 q^{9} - 70008 q^{10} + 39552 q^{11} + 45356 q^{12} - 159912 q^{13} - 291168 q^{14} + 13124 q^{15} + 556752 q^{16} + 309120 q^{17} + 52484 q^{18} - 167560 q^{19} - 1380000 q^{20} - 585348 q^{21} - 12112 q^{22} - 1691136 q^{23} + 310824 q^{24} - 72974 q^{25} - 3364200 q^{26} + 51068 q^{27} + 3615232 q^{28} - 137760 q^{29} + 3966132 q^{30} + 245492 q^{31} - 4840920 q^{32} + 1189140 q^{33} - 8278576 q^{34} + 7247232 q^{35} + 4835584 q^{36} + 6053592 q^{37} + 16322040 q^{38} - 11488196 q^{39} - 1151648 q^{40} - 2419392 q^{41} - 18128864 q^{42} + 194168 q^{43} + 22652136 q^{44} + 18441948 q^{45} - 8 q^{46} - 21819984 q^{48} + 7586394 q^{49} + 5145192 q^{50} + 13835768 q^{51} + 45948136 q^{52} + 38848224 q^{53} + 32802136 q^{54} - 67927680 q^{55} - 56874888 q^{56} - 4551652 q^{57} + 50876272 q^{58} + 44938752 q^{59} - 3478760 q^{60} - 79155240 q^{61} + 43931664 q^{62} + 52142076 q^{63} - 54270272 q^{64} - 39256512 q^{65} - 226680340 q^{66} - 193653512 q^{67} + 1507800 q^{68} + 14777084 q^{69} + 334477888 q^{70} + 159664128 q^{71} + 53585696 q^{72} + 125707444 q^{73} - 56030304 q^{74} + 11356024 q^{75} - 403579912 q^{76} - 40574976 q^{77} - 173869572 q^{78} - 196042236 q^{79} + 360917832 q^{80} + 226330078 q^{81} + 393464392 q^{82} + 209328000 q^{83} + 688968232 q^{84} + 228840112 q^{85} + 18570048 q^{86} - 92085824 q^{87} - 486276128 q^{88} - 261359616 q^{89} - 931912864 q^{90} - 395802248 q^{91} + 152934384 q^{92} - 118704776 q^{93} - 109034752 q^{94} + 367154672 q^{96} + 373369004 q^{97} - 239975856 q^{98} - 543516804 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(\Gamma_1(96))$$

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
96.9.b $$\chi_{96}(79, \cdot)$$ 96.9.b.a 16 1
96.9.e $$\chi_{96}(65, \cdot)$$ 96.9.e.a 16 1
96.9.e.b 16
96.9.g $$\chi_{96}(31, \cdot)$$ 96.9.g.a 8 1
96.9.g.b 8
96.9.h $$\chi_{96}(17, \cdot)$$ 96.9.h.a 1 1
96.9.h.b 1
96.9.h.c 28
96.9.i $$\chi_{96}(41, \cdot)$$ None 0 2
96.9.l $$\chi_{96}(7, \cdot)$$ None 0 2
96.9.m $$\chi_{96}(19, \cdot)$$ 96.9.m.a 256 4
96.9.p $$\chi_{96}(5, \cdot)$$ 96.9.p.a 504 4

## Decomposition of $$S_{9}^{\mathrm{old}}(\Gamma_1(96))$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(\Gamma_1(96)) \cong$$ $$S_{9}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 8}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 5}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$