## Defining parameters

 Level: $$N$$ = $$95 = 5 \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$2$$ Sturm bound: $$720$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(95))$$.

Total New Old
Modular forms 75 53 22
Cusp forms 3 3 0
Eisenstein series 72 50 22

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

 $$3q + q^{4} - q^{5} - 4q^{6} + q^{9} + O(q^{10})$$ $$3q + q^{4} - q^{5} - 4q^{6} + q^{9} - 2q^{11} - q^{16} - q^{19} - 3q^{20} + 3q^{25} + 4q^{26} + 4q^{30} + 3q^{36} - 4q^{39} + 2q^{44} - 3q^{45} + 3q^{49} - 2q^{55} - 2q^{61} - 3q^{64} - 4q^{74} - 3q^{76} + 3q^{80} - q^{81} + 3q^{95} + 4q^{96} + 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(95))$$

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
95.1.c $$\chi_{95}(56, \cdot)$$ None 0 1
95.1.d $$\chi_{95}(94, \cdot)$$ 95.1.d.a 1 1
95.1.d.b 2
95.1.f $$\chi_{95}(58, \cdot)$$ None 0 2
95.1.h $$\chi_{95}(69, \cdot)$$ None 0 2
95.1.j $$\chi_{95}(31, \cdot)$$ None 0 2
95.1.m $$\chi_{95}(7, \cdot)$$ None 0 4
95.1.n $$\chi_{95}(21, \cdot)$$ None 0 6
95.1.o $$\chi_{95}(14, \cdot)$$ None 0 6
95.1.q $$\chi_{95}(17, \cdot)$$ None 0 12