# Properties

 Label 304.2.be Level $304$ Weight $2$ Character orbit 304.be Rep. character $\chi_{304}(15,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $60$ Newform subspaces $4$ Sturm bound $80$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$304 = 2^{4} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 304.be (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$76$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$4$$ Sturm bound: $$80$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(304, [\chi])$$.

Total New Old
Modular forms 276 60 216
Cusp forms 204 60 144
Eisenstein series 72 0 72

## Trace form

 $$60 q + 18 q^{9} + O(q^{10})$$ $$60 q + 18 q^{9} - 12 q^{13} - 12 q^{21} + 18 q^{33} - 54 q^{41} + 30 q^{49} + 36 q^{53} + 12 q^{61} - 108 q^{65} - 96 q^{73} - 72 q^{77} - 126 q^{81} - 72 q^{85} - 36 q^{89} - 24 q^{93} - 18 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(304, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
304.2.be.a $12$ $2.427$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots$$
304.2.be.b $12$ $2.427$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots$$
304.2.be.c $18$ $2.427$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-9$$ $$q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots$$
304.2.be.d $18$ $2.427$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$9$$ $$q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(304, [\chi])$$ into lower level spaces

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