# Properties

 Label 63.2.c Level $63$ Weight $2$ Character orbit 63.c Rep. character $\chi_{63}(62,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $16$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 63.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$16$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(63, [\chi])$$.

Total New Old
Modular forms 12 4 8
Cusp forms 4 4 0
Eisenstein series 8 0 8

## Trace form

 $$4q - 8q^{4} + O(q^{10})$$ $$4q - 8q^{4} + 12q^{16} + 20q^{22} - 20q^{25} - 28q^{28} + 44q^{46} + 28q^{49} - 52q^{58} - 24q^{64} - 16q^{67} + 32q^{79} + 28q^{88} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(63, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
63.2.c.a $$4$$ $$0.503$$ $$\Q(\sqrt{-2}, \sqrt{7})$$ $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots$$