# Properties

 Label 57.1 Level 57 Weight 1 Dimension 2 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 240 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$57 = 3 \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$240$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(57))$$.

Total New Old
Modular forms 38 18 20
Cusp forms 2 2 0
Eisenstein series 36 16 20

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q - q^{3} - q^{4} - 2 q^{7} - q^{9} + O(q^{10})$$ $$2 q - q^{3} - q^{4} - 2 q^{7} - q^{9} + 2 q^{12} + q^{13} - q^{16} + 2 q^{19} + q^{21} - q^{25} + 2 q^{27} + q^{28} - 2 q^{31} - q^{36} - 2 q^{37} - 2 q^{39} + q^{43} - q^{48} + q^{52} - q^{57} + q^{61} + q^{63} + 2 q^{64} + q^{67} + q^{73} + 2 q^{75} - q^{76} + q^{79} - q^{81} - 2 q^{84} - q^{91} + q^{93} - 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(57))$$

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
57.1.b $$\chi_{57}(20, \cdot)$$ None 0 1
57.1.c $$\chi_{57}(37, \cdot)$$ None 0 1
57.1.g $$\chi_{57}(31, \cdot)$$ None 0 2
57.1.h $$\chi_{57}(11, \cdot)$$ 57.1.h.a 2 2
57.1.k $$\chi_{57}(10, \cdot)$$ None 0 6
57.1.l $$\chi_{57}(5, \cdot)$$ None 0 6