# Properties

 Label 63.2.p Level $63$ Weight $2$ Character orbit 63.p Rep. character $\chi_{63}(17,\cdot)$ Character field $\Q(\zeta_{6})$ 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.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ 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 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

## Trace form

 $$4q - 2q^{7} + O(q^{10})$$ $$4q - 2q^{7} - 12q^{10} + 8q^{16} + 6q^{19} - 8q^{22} - 2q^{25} + 6q^{31} + 2q^{37} + 24q^{40} - 4q^{43} + 16q^{46} - 26q^{49} - 8q^{58} - 12q^{61} - 32q^{64} - 22q^{67} + 24q^{70} + 6q^{73} - 10q^{79} - 36q^{82} + 48q^{85} + 8q^{88} + 54q^{91} + 60q^{94} + O(q^{100})$$

## 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.p.a $$4$$ $$0.503$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+2\beta _{3})q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(63, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(63, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$