## Defining parameters

 Level: $$N$$ = $$79$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$520$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(79))$$.

Total New Old
Modular forms 41 41 0
Cusp forms 2 2 0
Eisenstein series 39 39 0

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

 $$2q - q^{2} + q^{4} - q^{5} - 2q^{8} + 2q^{9} + O(q^{10})$$ $$2q - q^{2} + q^{4} - q^{5} - 2q^{8} + 2q^{9} - 2q^{10} - q^{11} - q^{13} - q^{18} - q^{19} + 2q^{20} + 3q^{22} - q^{23} + q^{25} + 3q^{26} - q^{31} + 2q^{32} + q^{36} - 2q^{38} + q^{40} - 3q^{44} - q^{45} - 2q^{46} + 2q^{49} + 2q^{50} - 3q^{52} - 2q^{55} + 3q^{62} - q^{64} - 2q^{65} - q^{67} - 2q^{72} - q^{73} + 2q^{76} + 2q^{79} + 2q^{81} + 4q^{83} + q^{88} - q^{89} - 2q^{90} + 2q^{92} + 3q^{95} - q^{97} - q^{98} - q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(79))$$

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
79.1.b $$\chi_{79}(78, \cdot)$$ 79.1.b.a 2 1
79.1.d $$\chi_{79}(24, \cdot)$$ None 0 2
79.1.f $$\chi_{79}(12, \cdot)$$ None 0 12
79.1.h $$\chi_{79}(3, \cdot)$$ None 0 24