# Properties

 Label 55.1 Level 55 Weight 1 Dimension 1 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 240 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$55 = 5 \cdot 11$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$240$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(55))$$.

Total New Old
Modular forms 41 27 14
Cusp forms 1 1 0
Eisenstein series 40 26 14

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

 $$q - q^{4} - q^{5} + q^{9} + O(q^{10})$$ $$q - q^{4} - q^{5} + q^{9} - q^{11} + q^{16} + q^{20} + q^{25} - 2 q^{31} - q^{36} + q^{44} - q^{45} - q^{49} + q^{55} + 2 q^{59} - q^{64} + 2 q^{71} - q^{80} + q^{81} - 2 q^{89} - q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(55))$$

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
55.1.c $$\chi_{55}(21, \cdot)$$ None 0 1
55.1.d $$\chi_{55}(54, \cdot)$$ 55.1.d.a 1 1
55.1.f $$\chi_{55}(12, \cdot)$$ None 0 2
55.1.h $$\chi_{55}(19, \cdot)$$ None 0 4
55.1.i $$\chi_{55}(6, \cdot)$$ None 0 4
55.1.k $$\chi_{55}(3, \cdot)$$ None 0 8