# Properties

 Label 117.2.b Level $117$ Weight $2$ Character orbit 117.b Rep. character $\chi_{117}(64,\cdot)$ Character field $\Q$ Dimension $6$ 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.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ 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 18 8 10
Cusp forms 10 6 4
Eisenstein series 8 2 6

## Trace form

 $$6 q - 10 q^{4} + O(q^{10})$$ $$6 q - 10 q^{4} - 4 q^{10} - 2 q^{13} - 12 q^{14} + 26 q^{16} + 12 q^{17} - 16 q^{22} - 10 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{38} + 52 q^{40} - 24 q^{43} + 18 q^{49} - 50 q^{52} - 12 q^{53} + 32 q^{55} - 12 q^{56} - 4 q^{61} - 12 q^{62} - 74 q^{64} - 12 q^{68} + 24 q^{74} + 24 q^{77} - 16 q^{79} + 92 q^{82} + 64 q^{88} + 24 q^{91} + 8 q^{94} + O(q^{100})$$

## 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.b.a $2$ $0.934$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{2}-q^{4}-2\zeta_{6}q^{7}-\zeta_{6}q^{8}+2\zeta_{6}q^{11}+\cdots$$
117.2.b.b $4$ $0.934$ 4.0.8112.1 $$\Q(\sqrt{-39})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}-\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(117, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(117, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 2}$$