# Properties

 Label 304.2.n Level $304$ Weight $2$ Character orbit 304.n Rep. character $\chi_{304}(31,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ Newform subspaces $5$ Sturm bound $80$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$304 = 2^{4} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 304.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$76$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$80$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 92 20 72
Cusp forms 68 20 48
Eisenstein series 24 0 24

## Trace form

 $$20 q - 16 q^{9} + O(q^{10})$$ $$20 q - 16 q^{9} + 12 q^{13} - 12 q^{17} + 12 q^{21} - 10 q^{25} - 18 q^{33} + 54 q^{41} - 4 q^{49} - 36 q^{53} + 28 q^{57} - 16 q^{61} - 22 q^{73} - 48 q^{77} - 70 q^{81} + 36 q^{85} - 72 q^{89} + 44 q^{93} + 18 q^{97} + O(q^{100})$$

## 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.n.a $2$ $2.427$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-3$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots$$
304.2.n.b $2$ $2.427$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-3$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$$
304.2.n.c $4$ $2.427$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots$$
304.2.n.d $6$ $2.427$ 6.0.31726512.1 None $$0$$ $$-1$$ $$2$$ $$0$$ $$q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$$
304.2.n.e $6$ $2.427$ 6.0.31726512.1 None $$0$$ $$1$$ $$2$$ $$0$$ $$q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(304, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 2}$$