# Properties

 Label 190.2 Level 190 Weight 2 Dimension 331 Nonzero newspaces 9 Newform subspaces 20 Sturm bound 4320 Trace bound 4

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## 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

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

## 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 available 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

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