# Properties

 Label 1216.2.t Level $1216$ Weight $2$ Character orbit 1216.t Rep. character $\chi_{1216}(353,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $5$ Sturm bound $320$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1216 = 2^{6} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1216.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$152$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$320$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1216, [\chi])$$.

Total New Old
Modular forms 344 80 264
Cusp forms 296 80 216
Eisenstein series 48 0 48

## Trace form

 $$80q + 40q^{9} + O(q^{10})$$ $$80q + 40q^{9} + 40q^{25} - 48q^{33} - 24q^{41} + 112q^{49} + 8q^{57} + 16q^{73} - 16q^{81} + 32q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1216, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1216.2.t.a $$8$$ $$9.710$$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{24}-\zeta_{24}^{3})q^{3}+(4\zeta_{24}^{2}-\zeta_{24}^{7})q^{9}+\cdots$$
1216.2.t.b $$8$$ $$9.710$$ 8.0.3317760000.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(3\beta _{1}-3\beta _{3})q^{3}+\beta _{5}q^{5}-\beta _{7}q^{7}+\cdots$$
1216.2.t.c $$16$$ $$9.710$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{8}q^{3}-\beta _{7}q^{5}-\beta _{11}q^{7}+2\beta _{1}q^{9}+\cdots$$
1216.2.t.d $$24$$ $$9.710$$ None $$0$$ $$0$$ $$-6$$ $$0$$
1216.2.t.e $$24$$ $$9.710$$ None $$0$$ $$0$$ $$6$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1216, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1216, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(608, [\chi])$$$$^{\oplus 2}$$