## Defining parameters

 Level: $$N$$ = $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$13$$ Sturm bound: $$4096$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(192))$$.

Total New Old
Modular forms 1168 454 714
Cusp forms 881 410 471
Eisenstein series 287 44 243

## Trace form

 $$410 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} + O(q^{10})$$ $$410 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} - 16 q^{10} + 8 q^{11} - 8 q^{12} - 16 q^{16} + 16 q^{17} - 8 q^{18} + 4 q^{19} - 12 q^{21} - 32 q^{22} - 48 q^{24} - 42 q^{25} - 80 q^{26} - 18 q^{27} - 96 q^{28} - 32 q^{29} - 88 q^{30} - 56 q^{31} - 80 q^{32} - 44 q^{33} - 96 q^{34} - 24 q^{35} - 88 q^{36} - 48 q^{37} - 80 q^{38} - 28 q^{39} - 96 q^{40} - 32 q^{41} - 48 q^{42} - 20 q^{43} - 16 q^{44} - 52 q^{45} - 16 q^{46} - 8 q^{48} - 42 q^{49} + 48 q^{50} - 72 q^{51} + 80 q^{52} + 8 q^{54} - 168 q^{55} + 112 q^{56} - 36 q^{57} + 128 q^{58} - 160 q^{59} + 88 q^{60} - 16 q^{61} + 96 q^{62} - 40 q^{63} + 176 q^{64} - 16 q^{65} + 72 q^{66} - 188 q^{67} + 96 q^{68} + 28 q^{69} + 176 q^{70} - 128 q^{71} - 8 q^{72} - 20 q^{73} + 112 q^{74} - 54 q^{75} + 112 q^{76} + 48 q^{77} + 64 q^{78} - 56 q^{79} + 48 q^{80} + 50 q^{81} - 16 q^{82} + 40 q^{83} + 104 q^{84} + 32 q^{85} + 52 q^{87} - 16 q^{88} + 32 q^{89} + 136 q^{90} + 48 q^{91} + 48 q^{93} - 16 q^{94} + 48 q^{95} + 128 q^{96} + 36 q^{97} + 52 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$

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
192.2.a $$\chi_{192}(1, \cdot)$$ 192.2.a.a 1 1
192.2.a.b 1
192.2.a.c 1
192.2.a.d 1
192.2.c $$\chi_{192}(191, \cdot)$$ 192.2.c.a 2 1
192.2.c.b 4
192.2.d $$\chi_{192}(97, \cdot)$$ 192.2.d.a 4 1
192.2.f $$\chi_{192}(95, \cdot)$$ 192.2.f.a 4 1
192.2.f.b 4
192.2.j $$\chi_{192}(49, \cdot)$$ 192.2.j.a 8 2
192.2.k $$\chi_{192}(47, \cdot)$$ 192.2.k.a 12 2
192.2.n $$\chi_{192}(25, \cdot)$$ None 0 4
192.2.o $$\chi_{192}(23, \cdot)$$ None 0 4
192.2.r $$\chi_{192}(13, \cdot)$$ 192.2.r.a 128 8
192.2.s $$\chi_{192}(11, \cdot)$$ 192.2.s.a 240 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(192))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(192)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 2}$$