# Properties

 Label 95.2 Level 95 Weight 2 Dimension 275 Nonzero newspaces 9 Newform subspaces 18 Sturm bound 1440 Trace bound 4

## 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

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

## 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 available 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(95)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 1}$$