# Properties

 Label 912.2.cc Level $912$ Weight $2$ Character orbit 912.cc Rep. character $\chi_{912}(257,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $228$ Newform subspaces $8$ Sturm bound $320$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.cc (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$8$$ Sturm bound: $$320$$ Trace bound: $$13$$ 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 252 780
Cusp forms 888 228 660
Eisenstein series 144 24 120

## Trace form

 $$228q + 6q^{3} + 6q^{7} - 12q^{9} + O(q^{10})$$ $$228q + 6q^{3} + 6q^{7} - 12q^{9} - 12q^{13} + 6q^{15} + 6q^{19} + 3q^{21} - 12q^{25} + 9q^{27} + 18q^{31} - 9q^{33} + 12q^{39} + 54q^{43} - 3q^{45} - 84q^{49} + 6q^{51} + 6q^{55} - 6q^{57} - 12q^{61} - 69q^{63} + 90q^{67} - 9q^{69} - 72q^{73} + 96q^{79} + 60q^{85} + 3q^{87} + 54q^{91} - 15q^{93} + 24q^{97} + 33q^{99} + O(q^{100})$$

## 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.cc.a $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{18}^{2}-2\zeta_{18}^{5})q^{3}+(3\zeta_{18}-2\zeta_{18}^{2}+\cdots)q^{7}+\cdots$$
912.2.cc.b $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+(\zeta_{18}+2\zeta_{18}^{2}+\cdots)q^{7}+\cdots$$
912.2.cc.c $$18$$ $$7.282$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$-3$$ $$0$$ $$0$$ $$q+\beta _{12}q^{3}+(-\beta _{2}-\beta _{14}+\beta _{15})q^{5}+\cdots$$
912.2.cc.d $$18$$ $$7.282$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{14}q^{3}+(-\beta _{9}+\beta _{17})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$$
912.2.cc.e $$24$$ $$7.282$$ None $$0$$ $$9$$ $$0$$ $$6$$
912.2.cc.f $$36$$ $$7.282$$ None $$0$$ $$-3$$ $$0$$ $$0$$
912.2.cc.g $$60$$ $$7.282$$ None $$0$$ $$0$$ $$0$$ $$0$$
912.2.cc.h $$60$$ $$7.282$$ None $$0$$ $$3$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(912, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(456, [\chi])$$$$^{\oplus 2}$$