# Properties

 Label 912.2.ci Level $912$ Weight $2$ Character orbit 912.ci Rep. character $\chi_{912}(79,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $120$ Newform subspaces $8$ 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.ci (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$76$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$8$$ 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 120 912
Cusp forms 888 120 768
Eisenstein series 144 0 144

## Trace form

 $$120 q + O(q^{10})$$ $$120 q + 12 q^{13} + 12 q^{21} + 72 q^{41} + 60 q^{49} - 72 q^{53} - 48 q^{61} + 216 q^{65} - 12 q^{73} + 144 q^{77} + 72 q^{85} + 72 q^{89} + 24 q^{93} - 72 q^{97} + O(q^{100})$$

## 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.ci.a $6$ $7.282$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$-6$$ $$-9$$ $$q+\zeta_{18}^{2}q^{3}+(-1-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{5}+\cdots$$
912.2.ci.b $6$ $7.282$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$-6$$ $$9$$ $$q-\zeta_{18}^{2}q^{3}+(-1-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{5}+\cdots$$
912.2.ci.c $12$ $7.282$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$6$$ $$-18$$ $$q-\beta _{8}q^{3}+(1+\beta _{1}+\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots$$
912.2.ci.d $12$ $7.282$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$6$$ $$18$$ $$q+\beta _{8}q^{3}+(1+\beta _{1}+\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots$$
912.2.ci.e $18$ $7.282$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{3}+(-\beta _{1}-\beta _{5}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots$$
912.2.ci.f $18$ $7.282$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}+(-\beta _{1}-\beta _{5}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots$$
912.2.ci.g $24$ $7.282$ None $$0$$ $$0$$ $$0$$ $$-9$$
912.2.ci.h $24$ $7.282$ None $$0$$ $$0$$ $$0$$ $$9$$

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

$$S_{2}^{\mathrm{old}}(912, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 2}$$