## Defining parameters

 Level: $$N$$ = $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newforms: $$1$$ Sturm bound: $$384$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(80))$$.

Total New Old
Modular forms 57 15 42
Cusp forms 1 1 0
Eisenstein series 56 14 42

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

 $$q - q^{5} - q^{9} + O(q^{10})$$ $$q - q^{5} - q^{9} + q^{25} + 2q^{29} - 2q^{41} + q^{45} - q^{49} - 2q^{61} + q^{81} + 2q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$

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
80.1.b $$\chi_{80}(31, \cdot)$$ None 0 1
80.1.e $$\chi_{80}(39, \cdot)$$ None 0 1
80.1.g $$\chi_{80}(71, \cdot)$$ None 0 1
80.1.h $$\chi_{80}(79, \cdot)$$ 80.1.h.a 1 1
80.1.i $$\chi_{80}(13, \cdot)$$ None 0 2
80.1.k $$\chi_{80}(19, \cdot)$$ None 0 2
80.1.m $$\chi_{80}(57, \cdot)$$ None 0 2
80.1.p $$\chi_{80}(17, \cdot)$$ None 0 2
80.1.r $$\chi_{80}(11, \cdot)$$ None 0 2
80.1.t $$\chi_{80}(53, \cdot)$$ None 0 2