# Properties

 Label 96.4 Level 96 Weight 4 Dimension 314 Nonzero newspaces 6 Newform subspaces 12 Sturm bound 2048 Trace bound 5

## 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

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

## 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

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