# Properties

 Label 624.2.bv Level $624$ Weight $2$ Character orbit 624.bv Rep. character $\chi_{624}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $28$ Newform subspaces $7$ Sturm bound $224$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$624 = 2^{4} \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 624.bv (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$7$$ Sturm bound: $$224$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(624, [\chi])$$.

Total New Old
Modular forms 248 28 220
Cusp forms 200 28 172
Eisenstein series 48 0 48

## Trace form

 $$28 q + 2 q^{3} - 6 q^{7} - 14 q^{9} + O(q^{10})$$ $$28 q + 2 q^{3} - 6 q^{7} - 14 q^{9} - 2 q^{13} - 2 q^{17} - 32 q^{25} - 4 q^{27} + 2 q^{29} + 6 q^{37} + 4 q^{39} + 6 q^{41} - 18 q^{43} - 6 q^{45} + 26 q^{49} + 24 q^{51} - 12 q^{53} + 4 q^{55} + 84 q^{59} + 6 q^{61} + 6 q^{63} + 22 q^{65} - 30 q^{67} - 22 q^{75} + 16 q^{77} + 44 q^{79} - 14 q^{81} - 6 q^{85} - 24 q^{87} - 50 q^{91} + 4 q^{95} - 36 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(624, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
624.2.bv.a $2$ $4.983$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-6$$ $$q+(-1+\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(-4+\cdots)q^{7}+\cdots$$
624.2.bv.b $2$ $4.983$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$3$$ $$q+(-1+\zeta_{6})q^{3}+(-2+4\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots$$
624.2.bv.c $4$ $4.983$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$-6$$ $$q-\zeta_{12}^{2}q^{3}+(-1+2\zeta_{12}^{2})q^{5}+(-1+\cdots)q^{7}+\cdots$$
624.2.bv.d $4$ $4.983$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$6$$ $$q+(-1+\zeta_{12}^{2})q^{3}+(1-2\zeta_{12}^{2})q^{5}+\cdots$$
624.2.bv.e $4$ $4.983$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$-6$$ $$q+\zeta_{12}^{2}q^{3}+(1-2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots$$
624.2.bv.f $4$ $4.983$ $$\Q(\sqrt{-3}, \sqrt{-43})$$ None $$0$$ $$2$$ $$0$$ $$3$$ $$q+(1-\beta _{2})q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$$
624.2.bv.g $8$ $4.983$ 8.0.649638144.4 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{3}+(\beta _{2}-\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(624, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(624, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(156, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(208, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(312, [\chi])$$$$^{\oplus 2}$$