# Properties

 Label 115.2 Level 115 Weight 2 Dimension 417 Nonzero newspaces 6 Newform subspaces 11 Sturm bound 2112 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$115 = 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$11$$ Sturm bound: $$2112$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(115))$$.

Total New Old
Modular forms 616 545 71
Cusp forms 441 417 24
Eisenstein series 175 128 47

## Trace form

 $$417 q - 25 q^{2} - 26 q^{3} - 29 q^{4} - 34 q^{5} - 78 q^{6} - 30 q^{7} - 37 q^{8} - 35 q^{9} + O(q^{10})$$ $$417 q - 25 q^{2} - 26 q^{3} - 29 q^{4} - 34 q^{5} - 78 q^{6} - 30 q^{7} - 37 q^{8} - 35 q^{9} - 36 q^{10} - 78 q^{11} - 50 q^{12} - 36 q^{13} - 46 q^{14} - 26 q^{15} - 53 q^{16} - 18 q^{17} + 27 q^{18} - 20 q^{19} + 4 q^{20} - 32 q^{21} + 8 q^{22} - q^{23} + 28 q^{24} - 12 q^{25} - 64 q^{26} + 4 q^{27} + 10 q^{28} - 30 q^{29} - q^{30} - 76 q^{31} - 41 q^{32} - 48 q^{33} - 32 q^{34} - 19 q^{35} - 47 q^{36} + 28 q^{37} + 28 q^{38} + 10 q^{39} + 40 q^{40} - 64 q^{41} + 102 q^{42} + 22 q^{43} + 92 q^{44} + 31 q^{45} + 41 q^{46} - 4 q^{47} + 74 q^{48} + 53 q^{49} - 14 q^{50} - 50 q^{51} + 100 q^{52} - 32 q^{53} + 78 q^{54} + 21 q^{55} + 56 q^{56} + 52 q^{57} + 86 q^{58} + 50 q^{59} + 71 q^{60} - 40 q^{61} + 14 q^{62} - 16 q^{63} + 27 q^{64} + 30 q^{65} + 32 q^{66} - 46 q^{67} + 138 q^{68} - 4 q^{69} - 2 q^{70} - 28 q^{71} + 113 q^{72} - 52 q^{73} + 62 q^{74} + 84 q^{75} + 80 q^{76} + 80 q^{77} + 162 q^{78} + 74 q^{79} + 145 q^{80} + 165 q^{81} + 72 q^{82} + 48 q^{83} + 194 q^{84} + 81 q^{85} + 66 q^{86} + 122 q^{87} - 114 q^{88} + 20 q^{89} + 159 q^{90} + 20 q^{91} + 15 q^{92} + 92 q^{93} + 76 q^{94} + 2 q^{95} + 100 q^{96} - 54 q^{97} - 105 q^{98} - 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$

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
115.2.a $$\chi_{115}(1, \cdot)$$ 115.2.a.a 1 1
115.2.a.b 2
115.2.a.c 4
115.2.b $$\chi_{115}(24, \cdot)$$ 115.2.b.a 2 1
115.2.b.b 8
115.2.e $$\chi_{115}(22, \cdot)$$ 115.2.e.a 20 2
115.2.g $$\chi_{115}(6, \cdot)$$ 115.2.g.a 10 10
115.2.g.b 20
115.2.g.c 50
115.2.j $$\chi_{115}(4, \cdot)$$ 115.2.j.a 100 10
115.2.l $$\chi_{115}(7, \cdot)$$ 115.2.l.a 200 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(115))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(115)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 2}$$