## Defining parameters

 Level: $$N$$ = $$135 = 3^{3} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$2$$ Sturm bound: $$1296$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(135))$$.

Total New Old
Modular forms 122 50 72
Cusp forms 2 2 0
Eisenstein series 120 48 72

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

 $$2 q + O(q^{10})$$ $$2 q - 2 q^{10} - 2 q^{16} - 2 q^{19} + 2 q^{25} - 2 q^{31} + 2 q^{34} + 2 q^{40} + 2 q^{46} + 2 q^{49} - 2 q^{61} + 2 q^{64} - 2 q^{79} - 2 q^{85} - 4 q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(135))$$

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
135.1.c $$\chi_{135}(26, \cdot)$$ None 0 1
135.1.d $$\chi_{135}(134, \cdot)$$ 135.1.d.a 1 1
135.1.d.b 1
135.1.g $$\chi_{135}(28, \cdot)$$ None 0 2
135.1.h $$\chi_{135}(44, \cdot)$$ None 0 2
135.1.i $$\chi_{135}(71, \cdot)$$ None 0 2
135.1.l $$\chi_{135}(37, \cdot)$$ None 0 4
135.1.n $$\chi_{135}(14, \cdot)$$ None 0 6
135.1.o $$\chi_{135}(11, \cdot)$$ None 0 6
135.1.r $$\chi_{135}(7, \cdot)$$ None 0 12