Properties

 Label 63.2.h Level $63$ Weight $2$ Character orbit 63.h Rep. character $\chi_{63}(25,\cdot)$ 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.h (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

 $$12 q - 2 q^{2} - q^{3} + 6 q^{4} + 5 q^{5} - 2 q^{6} - 12 q^{8} + 5 q^{9} + O(q^{10})$$ $$12 q - 2 q^{2} - q^{3} + 6 q^{4} + 5 q^{5} - 2 q^{6} - 12 q^{8} + 5 q^{9} - 6 q^{10} - q^{11} - 20 q^{12} - 3 q^{13} - 16 q^{14} - 16 q^{15} - 6 q^{16} + 9 q^{17} - 2 q^{18} + 4 q^{20} + 19 q^{21} - 6 q^{22} + 6 q^{24} + 3 q^{25} + 16 q^{26} - 7 q^{27} - 6 q^{28} + 8 q^{29} + 19 q^{30} + 6 q^{31} + 14 q^{32} + 29 q^{33} + 4 q^{35} + 40 q^{36} - 3 q^{37} + 19 q^{38} - 13 q^{39} - 6 q^{40} + 10 q^{41} + 2 q^{42} - 6 q^{43} - 5 q^{44} - 19 q^{45} - 54 q^{47} - 5 q^{48} - 6 q^{49} + 23 q^{50} - 18 q^{51} - 15 q^{52} - 12 q^{53} + q^{54} - 6 q^{55} + 6 q^{56} - q^{57} - 9 q^{58} - 60 q^{59} + 7 q^{60} - 12 q^{62} - 71 q^{63} - 36 q^{64} + 32 q^{65} + 34 q^{66} + 12 q^{67} + 30 q^{68} + 6 q^{69} + 39 q^{70} - 30 q^{71} - 18 q^{72} + 12 q^{73} - 39 q^{74} - 26 q^{75} + 6 q^{76} - 14 q^{77} - 35 q^{78} + 24 q^{79} + 19 q^{80} + 41 q^{81} + 18 q^{83} + 29 q^{84} - 3 q^{85} - 7 q^{86} + 5 q^{87} - 3 q^{88} + 41 q^{89} + 25 q^{90} + 21 q^{91} + 30 q^{92} - 6 q^{93} + 6 q^{94} + 26 q^{95} + 59 q^{96} - 3 q^{97} + 61 q^{98} + 50 q^{99} + O(q^{100})$$

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.h.a $2$ $0.503$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$1$$ $$4$$ $$q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots$$
63.2.h.b $10$ $0.503$ 10.0.$$\cdots$$.1 None $$-4$$ $$-1$$ $$4$$ $$-4$$ $$q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$$