## Defining parameters

 Level: $$N$$ = $$71$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$420$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(71))$$.

Total New Old
Modular forms 38 38 0
Cusp forms 3 3 0
Eisenstein series 35 35 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3 q - q^{2} - q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + O(q^{10})$$ $$3 q - q^{2} - q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 3 q^{12} - 2 q^{15} + q^{16} + 4 q^{18} - q^{19} + 4 q^{20} + 3 q^{24} + 2 q^{25} - 2 q^{27} - q^{29} + 3 q^{30} - 3 q^{32} - q^{36} - q^{37} + 5 q^{38} - 4 q^{40} - q^{43} - 3 q^{45} + 2 q^{48} + 3 q^{49} - 3 q^{50} - 4 q^{54} - 2 q^{57} - 2 q^{58} + q^{60} + 3 q^{71} + q^{72} - q^{73} + 5 q^{74} + 4 q^{75} - 3 q^{76} - q^{79} + 2 q^{80} + q^{81} - q^{83} - 2 q^{86} + 5 q^{87} - q^{89} + q^{90} - 2 q^{95} + q^{96} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(71))$$

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
71.1.b $$\chi_{71}(70, \cdot)$$ 71.1.b.a 3 1
71.1.e $$\chi_{71}(14, \cdot)$$ None 0 4
71.1.f $$\chi_{71}(23, \cdot)$$ None 0 6
71.1.h $$\chi_{71}(7, \cdot)$$ None 0 24