# Properties

 Label 63.2.e Level $63$ Weight $2$ Character orbit 63.e Rep. character $\chi_{63}(37,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $4$ Newform subspaces $2$ Sturm bound $16$ Trace bound $2$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 24 8 16
Cusp forms 8 4 4
Eisenstein series 16 4 12

## Trace form

 $$4q + 2q^{2} - 2q^{5} - 6q^{7} + O(q^{10})$$ $$4q + 2q^{2} - 2q^{5} - 6q^{7} + 4q^{10} - 2q^{11} - 12q^{13} - 2q^{14} + 6q^{19} + 8q^{20} - 8q^{22} + 6q^{25} + 2q^{26} + 16q^{28} - 8q^{29} - 2q^{31} - 8q^{32} + 2q^{35} - 2q^{37} + 2q^{38} + 20q^{41} + 20q^{43} - 4q^{44} - 6q^{47} - 2q^{49} + 4q^{50} - 16q^{52} + 12q^{53} + 8q^{55} - 8q^{58} - 12q^{59} - 24q^{61} - 36q^{62} - 32q^{64} - 2q^{65} - 6q^{67} - 16q^{70} + 12q^{71} + 10q^{73} + 6q^{74} + 32q^{76} + 8q^{77} + 14q^{79} + 8q^{80} + 20q^{82} - 12q^{83} + 10q^{86} + 16q^{89} + 2q^{91} + 12q^{94} - 2q^{95} + 16q^{97} - 4q^{98} + O(q^{100})$$

## 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.e.a $$2$$ $$0.503$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-1$$ $$q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots$$
63.2.e.b $$2$$ $$0.503$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-2$$ $$-5$$ $$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots$$

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

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