# Properties

 Label 912.2.bb Level $912$ Weight $2$ Character orbit 912.bb Rep. character $\chi_{912}(31,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $40$ Newform subspaces $8$ Sturm bound $320$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.bb (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$76$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$8$$ Sturm bound: $$320$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$, $$23$$, $$31$$

## Dimensions

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

Total New Old
Modular forms 344 40 304
Cusp forms 296 40 256
Eisenstein series 48 0 48

## Trace form

 $$40 q - 20 q^{9} + O(q^{10})$$ $$40 q - 20 q^{9} - 12 q^{13} - 12 q^{21} - 20 q^{25} - 72 q^{41} - 80 q^{49} + 72 q^{53} - 4 q^{57} + 28 q^{61} + 4 q^{73} + 96 q^{77} - 20 q^{81} - 48 q^{85} + 144 q^{89} - 44 q^{93} + 72 q^{97} + O(q^{100})$$

## 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.bb.a $2$ $7.282$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+(1-2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
912.2.bb.b $2$ $7.282$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
912.2.bb.c $4$ $7.282$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$4$$ $$0$$ $$q+(-1+\beta _{2})q^{3}+(2-2\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$$
912.2.bb.d $4$ $7.282$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$4$$ $$0$$ $$q+(1-\beta _{2})q^{3}+(2-2\beta _{2})q^{5}+(1-2\beta _{2}+\cdots)q^{7}+\cdots$$
912.2.bb.e $6$ $7.282$ 6.0.954288.1 None $$0$$ $$-3$$ $$-2$$ $$0$$ $$q+\beta _{3}q^{3}+(\beta _{3}+\beta _{4})q^{5}+(1+\beta _{1}+2\beta _{3}+\cdots)q^{7}+\cdots$$
912.2.bb.f $6$ $7.282$ 6.0.954288.1 None $$0$$ $$3$$ $$-2$$ $$0$$ $$q-\beta _{3}q^{3}+(\beta _{3}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$$
912.2.bb.g $8$ $7.282$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$-4$$ $$-2$$ $$0$$ $$q+(-1-\beta _{6})q^{3}+(-\beta _{3}-\beta _{6}+\beta _{7})q^{5}+\cdots$$
912.2.bb.h $8$ $7.282$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$4$$ $$-2$$ $$0$$ $$q+(1+\beta _{6})q^{3}+(-\beta _{3}-\beta _{6}+\beta _{7})q^{5}+\cdots$$

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

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