# Properties

 Label 31.1 Level 31 Weight 1 Dimension 1 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 80 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$31$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$80$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(31))$$.

Total New Old
Modular forms 16 16 0
Cusp forms 1 1 0
Eisenstein series 15 15 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q - q^{2} - q^{5} - q^{7} + q^{8} + q^{9} + O(q^{10})$$ $$q - q^{2} - q^{5} - q^{7} + q^{8} + q^{9} + q^{10} + q^{14} - q^{16} - q^{18} - q^{19} + q^{31} + q^{35} + q^{38} - q^{40} - q^{41} - q^{45} + 2 q^{47} - q^{56} - q^{59} - q^{62} - q^{63} + q^{64} + 2 q^{67} - q^{70} - q^{71} + q^{72} + q^{80} + q^{81} + q^{82} + q^{90} - 2 q^{94} + q^{95} - q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(31))$$

We only show spaces with odd 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
31.1.b $$\chi_{31}(30, \cdot)$$ 31.1.b.a 1 1
31.1.e $$\chi_{31}(6, \cdot)$$ None 0 2
31.1.f $$\chi_{31}(15, \cdot)$$ None 0 4
31.1.h $$\chi_{31}(3, \cdot)$$ None 0 8