## Defining parameters

 Level: $$N$$ = $$190 = 2 \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$9$$ Newform subspaces: $$20$$ Sturm bound: $$4320$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(190))$$.

Total New Old
Modular forms 1224 331 893
Cusp forms 937 331 606
Eisenstein series 287 0 287

## Trace form

 $$331q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + O(q^{10})$$ $$331q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + q^{10} + 12q^{11} - 8q^{12} - 34q^{13} - 28q^{14} - 32q^{15} + q^{16} - 18q^{17} - 41q^{18} - 65q^{19} - 17q^{20} - 52q^{21} - 42q^{22} - 12q^{23} + 4q^{24} - 35q^{25} - 22q^{26} - 26q^{27} - 4q^{28} - 6q^{29} + 4q^{30} - 4q^{31} + q^{32} - 60q^{33} + 18q^{34} - 28q^{35} + 13q^{36} + 2q^{37} + 19q^{38} - 52q^{39} + q^{40} + 6q^{41} + 32q^{42} - 40q^{43} - 6q^{44} - 95q^{45} - 48q^{46} - 96q^{47} - 14q^{48} - 63q^{49} - 71q^{50} - 126q^{51} + 2q^{52} - 90q^{53} - 68q^{54} - 60q^{55} - 64q^{56} - 104q^{57} - 42q^{58} - 120q^{59} - 32q^{60} - 94q^{61} - 76q^{62} - 88q^{63} - 11q^{64} - 94q^{65} - 96q^{66} - 88q^{67} - 12q^{69} - 28q^{70} - 72q^{71} - 5q^{72} + 8q^{73} + 38q^{74} - 8q^{75} + 19q^{76} + 96q^{77} + 128q^{78} + 68q^{79} + q^{80} + 211q^{81} + 114q^{82} + 156q^{83} + 140q^{84} + 234q^{85} + 116q^{86} + 336q^{87} + 12q^{88} + 162q^{89} + 283q^{90} + 208q^{91} + 96q^{92} + 404q^{93} + 192q^{94} + 145q^{95} + 4q^{96} + 134q^{97} + 201q^{98} + 318q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$

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
190.2.a $$\chi_{190}(1, \cdot)$$ 190.2.a.a 1 1
190.2.a.b 1
190.2.a.c 1
190.2.a.d 2
190.2.b $$\chi_{190}(39, \cdot)$$ 190.2.b.a 4 1
190.2.b.b 6
190.2.e $$\chi_{190}(11, \cdot)$$ 190.2.e.a 2 2
190.2.e.b 2
190.2.e.c 4
190.2.f $$\chi_{190}(37, \cdot)$$ 190.2.f.a 4 2
190.2.f.b 16
190.2.i $$\chi_{190}(49, \cdot)$$ 190.2.i.a 20 2
190.2.k $$\chi_{190}(61, \cdot)$$ 190.2.k.a 6 6
190.2.k.b 12
190.2.k.c 12
190.2.k.d 18
190.2.m $$\chi_{190}(27, \cdot)$$ 190.2.m.a 8 4
190.2.m.b 32
190.2.p $$\chi_{190}(9, \cdot)$$ 190.2.p.a 60 6
190.2.r $$\chi_{190}(3, \cdot)$$ 190.2.r.a 120 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(190))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(190)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 2}$$