# Properties

 Label 912.2.ch Level $912$ Weight $2$ Character orbit 912.ch Rep. character $\chi_{912}(47,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $240$ Newform subspaces $7$ Sturm bound $320$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.ch (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$228$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$7$$ Sturm bound: $$320$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(912, [\chi])$$.

Total New Old
Modular forms 1032 240 792
Cusp forms 888 240 648
Eisenstein series 144 0 144

## Trace form

 $$240q + 18q^{9} + O(q^{10})$$ $$240q + 18q^{9} + 12q^{13} - 18q^{33} + 120q^{49} + 24q^{61} + 228q^{73} - 18q^{81} + 72q^{85} + 108q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(912, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
912.2.ch.a $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\zeta_{18}-\zeta_{18}^{4})q^{3}+(3\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{7}+\cdots$$
912.2.ch.b $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-2\zeta_{18}+\zeta_{18}^{4})q^{3}+(-3\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{7}+\cdots$$
912.2.ch.c $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-2\zeta_{18}+\zeta_{18}^{4})q^{3}+(\zeta_{18}+3\zeta_{18}^{2}+\cdots)q^{7}+\cdots$$
912.2.ch.d $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\zeta_{18}-\zeta_{18}^{4})q^{3}+(-\zeta_{18}-3\zeta_{18}^{2}+\cdots)q^{7}+\cdots$$
912.2.ch.e $$72$$ $$7.282$$ None $$0$$ $$0$$ $$0$$ $$0$$
912.2.ch.f $$72$$ $$7.282$$ None $$0$$ $$0$$ $$0$$ $$0$$
912.2.ch.g $$72$$ $$7.282$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(912, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(912, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 3}$$