# Properties

 Label 63.2.g Level $63$ Weight $2$ Character orbit 63.g Rep. character $\chi_{63}(4,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $12$ Newform subspaces $2$ Sturm bound $16$ Trace bound $1$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

## Trace form

 $$12q + q^{2} - q^{3} - 3q^{4} - 10q^{5} - 2q^{6} - 12q^{8} - q^{9} + O(q^{10})$$ $$12q + q^{2} - q^{3} - 3q^{4} - 10q^{5} - 2q^{6} - 12q^{8} - q^{9} - 6q^{10} + 2q^{11} + 19q^{12} - 3q^{13} + 11q^{14} - 16q^{15} + 3q^{16} + 9q^{17} + q^{18} + 4q^{20} - 8q^{21} - 6q^{22} + 12q^{24} - 6q^{25} + 16q^{26} - 7q^{27} - 6q^{28} + 8q^{29} - 26q^{30} - 3q^{31} - 7q^{32} - 16q^{33} + 4q^{35} + 40q^{36} - 3q^{37} - 38q^{38} + 20q^{39} + 12q^{40} + 10q^{41} + 41q^{42} - 6q^{43} - 5q^{44} - 4q^{45} + 27q^{47} - 5q^{48} + 12q^{49} + 23q^{50} + 24q^{51} + 30q^{52} - 12q^{53} - 62q^{54} - 6q^{55} - 48q^{56} - q^{57} + 18q^{58} + 30q^{59} - 38q^{60} - 12q^{62} - 20q^{63} - 36q^{64} - 16q^{65} - 41q^{66} - 6q^{67} - 60q^{68} + 6q^{69} - 24q^{70} - 30q^{71} + 39q^{72} + 12q^{73} + 78q^{74} + 43q^{75} + 6q^{76} - 26q^{77} - 35q^{78} - 12q^{79} + 19q^{80} - q^{81} + 18q^{83} + 5q^{84} - 3q^{85} + 14q^{86} + 29q^{87} + 6q^{88} + 41q^{89} + 25q^{90} + 21q^{91} + 30q^{92} - 12q^{93} - 3q^{94} - 13q^{95} + 14q^{96} - 3q^{97} + 61q^{98} + 50q^{99} + O(q^{100})$$

## 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.g.a $$2$$ $$0.503$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$-2$$ $$1$$ $$q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
63.2.g.b $$10$$ $$0.503$$ 10.0.$$\cdots$$.1 None $$2$$ $$2$$ $$-8$$ $$-1$$ $$q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$$