## Defining parameters

 Level: $$N$$ = $$95 = 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$9$$ Newform subspaces: $$18$$ Sturm bound: $$1440$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(95))$$.

Total New Old
Modular forms 432 379 53
Cusp forms 289 275 14
Eisenstein series 143 104 39

## Trace form

 $$275q - 21q^{2} - 22q^{3} - 25q^{4} - 28q^{5} - 66q^{6} - 26q^{7} - 33q^{8} - 31q^{9} + O(q^{10})$$ $$275q - 21q^{2} - 22q^{3} - 25q^{4} - 28q^{5} - 66q^{6} - 26q^{7} - 33q^{8} - 31q^{9} - 30q^{10} - 66q^{11} - 22q^{12} - 8q^{13} - 6q^{14} - 13q^{15} - 13q^{16} - 18q^{17} + 15q^{18} + 5q^{19} - 25q^{20} - 44q^{21} - 24q^{23} - 6q^{24} - 10q^{25} - 60q^{26} - 16q^{27} + 4q^{28} - 12q^{29} + 24q^{30} - 50q^{31} + 9q^{32} + 42q^{33} + 18q^{34} + q^{35} + 71q^{36} - 2q^{37} + 51q^{38} + 16q^{39} + 39q^{40} - 60q^{41} + 66q^{42} + 16q^{43} + 42q^{44} + 41q^{45} + 36q^{46} + 24q^{47} + 110q^{48} + 3q^{49} + 69q^{50} - 18q^{51} + 16q^{52} + 24q^{54} - 3q^{55} + 60q^{56} - 4q^{57} - 54q^{58} + 12q^{59} + 98q^{60} + 16q^{61} + 84q^{62} + 46q^{63} + 131q^{64} + 58q^{65} + 90q^{66} + 100q^{67} + 108q^{68} + 84q^{69} + 93q^{70} + 39q^{72} + 76q^{73} + 48q^{74} + 2q^{75} - 7q^{76} + 30q^{77} - 42q^{78} + 34q^{79} - 112q^{80} - 85q^{81} + 54q^{82} - 84q^{83} - 242q^{84} - 81q^{85} - 132q^{86} - 138q^{87} - 234q^{88} - 54q^{89} - 219q^{90} - 142q^{91} - 240q^{92} - 230q^{93} - 252q^{94} - 91q^{95} - 504q^{96} - 98q^{97} - 135q^{98} - 192q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$

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
95.2.a $$\chi_{95}(1, \cdot)$$ 95.2.a.a 3 1
95.2.a.b 4
95.2.b $$\chi_{95}(39, \cdot)$$ 95.2.b.a 2 1
95.2.b.b 6
95.2.e $$\chi_{95}(11, \cdot)$$ 95.2.e.a 2 2
95.2.e.b 6
95.2.e.c 8
95.2.g $$\chi_{95}(18, \cdot)$$ 95.2.g.a 4 2
95.2.g.b 12
95.2.i $$\chi_{95}(49, \cdot)$$ 95.2.i.a 4 2
95.2.i.b 12
95.2.k $$\chi_{95}(6, \cdot)$$ 95.2.k.a 18 6
95.2.k.b 18
95.2.l $$\chi_{95}(8, \cdot)$$ 95.2.l.a 4 4
95.2.l.b 4
95.2.l.c 24
95.2.p $$\chi_{95}(4, \cdot)$$ 95.2.p.a 48 6
95.2.r $$\chi_{95}(2, \cdot)$$ 95.2.r.a 96 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(95))$$ into lower level spaces

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