# Properties

 Label 63.2.f Level $63$ Weight $2$ Character orbit 63.f Rep. character $\chi_{63}(22,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $12$ 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.f (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ 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 20 12 8
Cusp forms 12 12 0
Eisenstein series 8 0 8

## Trace form

 $$12 q - 2 q^{2} - 4 q^{3} - 6 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{9} + O(q^{10})$$ $$12 q - 2 q^{2} - 4 q^{3} - 6 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{9} - 4 q^{11} + 16 q^{12} - 4 q^{14} + 2 q^{15} - 6 q^{16} - 12 q^{17} + 22 q^{18} - 12 q^{19} + 22 q^{20} - 2 q^{21} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 8 q^{26} + 20 q^{27} - 10 q^{29} - 8 q^{30} + 6 q^{31} + 8 q^{32} + 8 q^{33} - 6 q^{34} + 16 q^{35} - 38 q^{36} - 12 q^{37} - 14 q^{38} - 16 q^{39} - 12 q^{40} + 22 q^{41} + 20 q^{42} + 6 q^{43} + 76 q^{44} + 14 q^{45} + 24 q^{46} + 6 q^{47} - 14 q^{48} - 6 q^{49} - 4 q^{50} + 18 q^{51} + 18 q^{52} - 24 q^{53} - 44 q^{54} - 12 q^{55} - 12 q^{56} + 2 q^{57} + 18 q^{58} + 12 q^{59} - 20 q^{60} - 96 q^{62} - 8 q^{63} - 10 q^{65} + 34 q^{66} + 12 q^{67} - 12 q^{68} - 48 q^{69} + 36 q^{71} - 60 q^{72} - 36 q^{73} + 24 q^{74} + 22 q^{75} + 6 q^{76} - 8 q^{77} + 64 q^{78} + 6 q^{79} - 8 q^{80} + 32 q^{81} + 30 q^{83} + 2 q^{84} - 18 q^{85} - 40 q^{86} + 8 q^{87} - 6 q^{88} + 20 q^{89} + 100 q^{90} - 12 q^{91} - 18 q^{92} + 6 q^{93} - 6 q^{94} - 4 q^{95} + 32 q^{96} + 4 q^{98} - 28 q^{99} + O(q^{100})$$

## 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.f.a $6$ $0.503$ $$\Q(\zeta_{18})$$ None $$-3$$ $$0$$ $$-3$$ $$-3$$ $$q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{3}+\cdots)q^{3}+\cdots$$
63.2.f.b $6$ $0.503$ 6.0.309123.1 None $$1$$ $$-4$$ $$5$$ $$3$$ $$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$$