# Properties

 Label 912.2.bo Level $912$ Weight $2$ Character orbit 912.bo Rep. character $\chi_{912}(289,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $120$ Newform subspaces $12$ Sturm bound $320$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.bo (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$12$$ Sturm bound: $$320$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## 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

 $$120q + O(q^{10})$$ $$120q - 6q^{19} - 6q^{27} + 36q^{31} + 24q^{41} - 6q^{43} + 36q^{47} - 60q^{49} + 12q^{51} + 24q^{53} - 36q^{55} + 24q^{61} + 12q^{63} - 24q^{65} + 66q^{67} + 24q^{69} + 72q^{71} - 12q^{73} + 84q^{75} + 84q^{79} + 72q^{85} + 36q^{87} - 24q^{89} + 12q^{91} + 60q^{95} + 24q^{97} + O(q^{100})$$

## 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.bo.a $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$-9$$ $$-9$$ $$q+\zeta_{18}q^{3}+(-1+\zeta_{18}^{2}-\zeta_{18}^{3}-2\zeta_{18}^{5})q^{5}+\cdots$$
912.2.bo.b $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$-6$$ $$-3$$ $$q-\zeta_{18}q^{3}+(-1+\zeta_{18}^{2}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{5}+\cdots$$
912.2.bo.c $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$-3$$ $$-3$$ $$q+\zeta_{18}q^{3}+(-1+\zeta_{18}^{2}+\zeta_{18}^{3}-2\zeta_{18}^{4}+\cdots)q^{5}+\cdots$$
912.2.bo.d $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$3$$ $$3$$ $$q-\zeta_{18}q^{3}+(1-\zeta_{18}^{2}-\zeta_{18}^{3}-2\zeta_{18}^{4}+\cdots)q^{5}+\cdots$$
912.2.bo.e $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$6$$ $$-3$$ $$q+\zeta_{18}q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+\cdots$$
912.2.bo.f $$6$$ $$7.282$$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$9$$ $$-3$$ $$q-\zeta_{18}q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+2\zeta_{18}^{5})q^{5}+\cdots$$
912.2.bo.g $$12$$ $$7.282$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-6$$ $$9$$ $$q+\beta _{7}q^{3}+(-1+\beta _{2}-\beta _{5}+\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots$$
912.2.bo.h $$12$$ $$7.282$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+(-\beta _{2}+\beta _{11})q^{3}-\beta _{1}q^{5}+(\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$
912.2.bo.i $$12$$ $$7.282$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$3$$ $$6$$ $$q+\beta _{3}q^{3}+(\beta _{3}-\beta _{5}+\beta _{10})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots$$
912.2.bo.j $$12$$ $$7.282$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$6$$ $$9$$ $$q-\beta _{3}q^{3}+(1-2\beta _{3}-\beta _{4}+\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots$$
912.2.bo.k $$18$$ $$7.282$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+\beta _{7}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$$
912.2.bo.l $$18$$ $$7.282$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$0$$ $$3$$ $$-6$$ $$q-\beta _{9}q^{3}+(1+\beta _{5}-\beta _{6}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(912, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(456, [\chi])$$$$^{\oplus 2}$$