## Defining parameters

 Level: $$N$$ = $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$360$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(76))$$.

Total New Old
Modular forms 46 17 29
Cusp forms 1 1 0
Eisenstein series 45 16 29

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

 $$q - q^{5} - q^{7} + q^{9} + O(q^{10})$$ $$q - q^{5} - q^{7} + q^{9} - q^{11} - q^{17} + q^{19} + 2 q^{23} + q^{35} - q^{43} - q^{45} - q^{47} + q^{55} - q^{61} - q^{63} - q^{73} + q^{77} + q^{81} + 2 q^{83} + q^{85} - q^{95} - q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(76))$$

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
76.1.b $$\chi_{76}(39, \cdot)$$ None 0 1
76.1.c $$\chi_{76}(37, \cdot)$$ 76.1.c.a 1 1
76.1.g $$\chi_{76}(7, \cdot)$$ None 0 2
76.1.h $$\chi_{76}(65, \cdot)$$ None 0 2
76.1.j $$\chi_{76}(13, \cdot)$$ None 0 6
76.1.l $$\chi_{76}(23, \cdot)$$ None 0 6