# Properties

 Label 31.2 Level 31 Weight 2 Dimension 26 Nonzero newspaces 4 Newform subspaces 4 Sturm bound 160 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$4$$ Sturm bound: $$160$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(31))$$.

Total New Old
Modular forms 55 55 0
Cusp forms 26 26 0
Eisenstein series 29 29 0

## Trace form

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

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$

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
31.2.a $$\chi_{31}(1, \cdot)$$ 31.2.a.a 2 1
31.2.c $$\chi_{31}(5, \cdot)$$ 31.2.c.a 4 2
31.2.d $$\chi_{31}(2, \cdot)$$ 31.2.d.a 4 4
31.2.g $$\chi_{31}(7, \cdot)$$ 31.2.g.a 16 8