# Properties

 Label 117.2.t Level $117$ Weight $2$ Character orbit 117.t Rep. character $\chi_{117}(25,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $3$ Sturm bound $28$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$117 = 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 117.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$117$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$28$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$5$$

## 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

 $$24 q - 4 q^{3} + 8 q^{4} + 4 q^{9} + O(q^{10})$$ $$24 q - 4 q^{3} + 8 q^{4} + 4 q^{9} - 16 q^{10} + 10 q^{12} - 2 q^{13} - 18 q^{14} - 4 q^{16} - 24 q^{17} - 10 q^{22} + 18 q^{23} + 2 q^{25} - 12 q^{26} - 22 q^{27} - 54 q^{30} + 36 q^{35} + 26 q^{36} + 12 q^{38} - 14 q^{39} - 8 q^{40} + 6 q^{42} + 6 q^{43} + 38 q^{48} - 60 q^{51} + 4 q^{52} + 72 q^{53} - 28 q^{55} + 36 q^{56} - 16 q^{61} - 72 q^{62} + 40 q^{64} + 78 q^{66} + 36 q^{68} + 90 q^{69} - 42 q^{74} - 8 q^{75} - 30 q^{77} + 66 q^{78} - 16 q^{79} + 28 q^{81} - 4 q^{82} - 54 q^{87} + 22 q^{88} + 24 q^{90} - 24 q^{91} - 96 q^{92} + 20 q^{94} + 48 q^{95} + O(q^{100})$$

## 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.t.a $2$ $0.934$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$-6$$ $$-6$$ $$q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-2+\cdots)q^{5}+\cdots$$
117.2.t.b $2$ $0.934$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$6$$ $$6$$ $$q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots$$
117.2.t.c $20$ $0.934$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\beta _{17}q^{2}+\beta _{10}q^{3}+(1-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots$$