# Properties

 Label 912.2.d Level $912$ Weight $2$ Character orbit 912.d Rep. character $\chi_{912}(191,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $2$ Sturm bound $320$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$320$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 172 36 136
Cusp forms 148 36 112
Eisenstein series 24 0 24

## Trace form

 $$36q + O(q^{10})$$ $$36q - 24q^{21} - 60q^{25} + 48q^{37} - 12q^{49} - 48q^{61} + 24q^{73} + 24q^{81} - 48q^{85} + 72q^{93} - 24q^{97} + O(q^{100})$$

## 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.d.a $$12$$ $$7.282$$ 12.0.$$\cdots$$.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{3}+(-\beta _{2}+\beta _{3}+\beta _{10})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
912.2.d.b $$24$$ $$7.282$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(912, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 3}$$