## Defining parameters

 Level: $$N$$ = $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$8$$ Newform subspaces: $$19$$ Sturm bound: $$6144$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(192))$$.

Total New Old
Modular forms 2192 886 1306
Cusp forms 1904 842 1062
Eisenstein series 288 44 244

## Trace form

 $$842q - 6q^{3} - 16q^{4} - 8q^{6} - 16q^{7} - 10q^{9} + O(q^{10})$$ $$842q - 6q^{3} - 16q^{4} - 8q^{6} - 16q^{7} - 10q^{9} - 16q^{10} - 32q^{11} - 8q^{12} - 48q^{13} - 4q^{15} - 16q^{16} + 32q^{17} - 8q^{18} + 52q^{19} + 76q^{21} + 128q^{22} + 128q^{23} + 272q^{24} + 222q^{25} + 400q^{26} + 42q^{27} + 224q^{28} + 64q^{29} + 72q^{30} + 8q^{31} - 80q^{32} - 52q^{33} - 256q^{34} - 96q^{35} - 408q^{36} - 208q^{37} - 560q^{38} - 8q^{39} - 736q^{40} - 320q^{41} - 448q^{42} - 108q^{43} - 208q^{44} - 60q^{45} - 16q^{46} - 8q^{48} + 70q^{49} - 624q^{50} + 376q^{51} - 1072q^{52} - 152q^{54} + 1264q^{55} - 784q^{56} - 92q^{57} - 736q^{58} + 640q^{59} - 296q^{60} - 16q^{61} - 96q^{62} - 208q^{63} + 176q^{64} - 288q^{65} + 248q^{66} - 1100q^{67} + 480q^{68} - 284q^{69} + 1328q^{70} - 1536q^{71} - 8q^{72} - 532q^{73} + 1232q^{74} - 1146q^{75} + 1648q^{76} - 96q^{77} + 304q^{78} - 1288q^{79} + 816q^{80} - 398q^{81} - 16q^{82} + 160q^{83} - 1240q^{84} + 272q^{85} - 8q^{87} - 16q^{88} + 320q^{89} - 728q^{90} + 176q^{91} + 160q^{93} - 16q^{94} + 128q^{96} - 172q^{97} + 188q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(192))$$

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
192.3.b $$\chi_{192}(31, \cdot)$$ 192.3.b.a 4 1
192.3.b.b 4
192.3.e $$\chi_{192}(65, \cdot)$$ 192.3.e.a 1 1
192.3.e.b 1
192.3.e.c 2
192.3.e.d 2
192.3.e.e 4
192.3.e.f 4
192.3.g $$\chi_{192}(127, \cdot)$$ 192.3.g.a 2 1
192.3.g.b 2
192.3.g.c 4
192.3.h $$\chi_{192}(161, \cdot)$$ 192.3.h.a 4 1
192.3.h.b 4
192.3.h.c 8
192.3.i $$\chi_{192}(17, \cdot)$$ 192.3.i.a 8 2
192.3.i.b 20
192.3.l $$\chi_{192}(79, \cdot)$$ 192.3.l.a 16 2
192.3.m $$\chi_{192}(7, \cdot)$$ None 0 4
192.3.p $$\chi_{192}(41, \cdot)$$ None 0 4
192.3.q $$\chi_{192}(5, \cdot)$$ 192.3.q.a 496 8
192.3.t $$\chi_{192}(19, \cdot)$$ 192.3.t.a 256 8

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(192))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(192)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 2}$$