# Properties

 Label 117.2.r Level $117$ Weight $2$ Character orbit 117.r Rep. character $\chi_{117}(43,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $2$ Sturm bound $28$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$117 = 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 117.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$117$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$28$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(117, [\chi])$$.

Total New Old
Modular forms 32 32 0
Cusp forms 24 24 0
Eisenstein series 8 8 0

## Trace form

 $$24 q - 3 q^{2} - q^{3} + 11 q^{4} - 3 q^{6} + q^{9} + O(q^{10})$$ $$24 q - 3 q^{2} - q^{3} + 11 q^{4} - 3 q^{6} + q^{9} - 4 q^{10} - 3 q^{11} - 11 q^{12} - 2 q^{13} - 6 q^{14} - 12 q^{15} - 7 q^{16} + 6 q^{17} - 30 q^{18} - 9 q^{19} + 15 q^{21} - 7 q^{22} - 18 q^{23} + 48 q^{24} + 2 q^{25} + 14 q^{27} - 18 q^{29} - 39 q^{30} + 12 q^{31} - 9 q^{32} - 12 q^{33} - 6 q^{34} - 24 q^{35} - q^{36} - 3 q^{37} + 24 q^{38} + 25 q^{39} + 16 q^{40} + 18 q^{42} + 6 q^{43} + 27 q^{45} - 6 q^{46} - 3 q^{47} - 4 q^{48} - 6 q^{49} + 21 q^{51} - 14 q^{52} - 12 q^{53} - 42 q^{54} - 7 q^{55} + 12 q^{56} + 45 q^{57} - 3 q^{58} - 27 q^{59} - 9 q^{60} - 16 q^{61} + 15 q^{62} - 12 q^{63} - 26 q^{64} + 15 q^{65} + 30 q^{66} + 132 q^{68} + 6 q^{69} + 15 q^{70} - 6 q^{71} - 15 q^{72} + 30 q^{74} + 22 q^{75} + 48 q^{77} - 63 q^{78} + 5 q^{79} + 90 q^{80} + q^{81} + 5 q^{82} - 51 q^{83} - 12 q^{84} - 42 q^{85} - 42 q^{86} + 9 q^{87} - 5 q^{88} - 3 q^{89} + 21 q^{90} + 6 q^{91} - 6 q^{92} + 21 q^{93} - 70 q^{94} + 27 q^{96} + 105 q^{98} - 18 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(117, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
117.2.r.a $2$ $0.934$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$-3$$ $$-3$$ $$0$$ $$q+(-2+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots$$
117.2.r.b $22$ $0.934$ None $$0$$ $$2$$ $$3$$ $$0$$