## Defining parameters

 Level: $$N$$ = $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$288$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(63))$$.

Total New Old
Modular forms 49 24 25
Cusp forms 1 1 0
Eisenstein series 48 23 25

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

 $$q - q^{4} - q^{7} + O(q^{10})$$ $$q - q^{4} - q^{7} + q^{16} + q^{25} + q^{28} - 2q^{37} - 2q^{43} + q^{49} - q^{64} + 2q^{67} + 2q^{79} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(63))$$

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
63.1.b $$\chi_{63}(8, \cdot)$$ None 0 1
63.1.d $$\chi_{63}(55, \cdot)$$ 63.1.d.a 1 1
63.1.j $$\chi_{63}(11, \cdot)$$ None 0 2
63.1.k $$\chi_{63}(31, \cdot)$$ None 0 2
63.1.l $$\chi_{63}(13, \cdot)$$ None 0 2
63.1.m $$\chi_{63}(10, \cdot)$$ None 0 2
63.1.n $$\chi_{63}(2, \cdot)$$ None 0 2
63.1.q $$\chi_{63}(44, \cdot)$$ None 0 2
63.1.r $$\chi_{63}(29, \cdot)$$ None 0 2
63.1.t $$\chi_{63}(40, \cdot)$$ None 0 2