# Properties

 Label 624.2.cn Level $624$ Weight $2$ Character orbit 624.cn Rep. character $\chi_{624}(305,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $104$ Newform subspaces $6$ 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.cn (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$39$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$6$$ 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 496 120 376
Cusp forms 400 104 296
Eisenstein series 96 16 80

## Trace form

 $$104q + 2q^{3} + 4q^{7} - 2q^{9} + O(q^{10})$$ $$104q + 2q^{3} + 4q^{7} - 2q^{9} - 8q^{13} + 10q^{15} + 4q^{19} + 2q^{21} + 8q^{27} + 36q^{31} - 10q^{33} + 8q^{37} - 26q^{39} + 96q^{43} - 14q^{45} + 12q^{49} + 44q^{55} - 14q^{57} - 20q^{61} - 10q^{63} + 40q^{67} - 6q^{69} - 16q^{73} - 12q^{75} + 16q^{79} - 2q^{81} - 4q^{85} + 2q^{87} - 44q^{91} - 54q^{93} - 66q^{99} + O(q^{100})$$

## 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.cn.a $$4$$ $$4.983$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-2$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}+\cdots)q^{7}+\cdots$$
624.2.cn.b $$4$$ $$4.983$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$10$$ $$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots$$
624.2.cn.c $$8$$ $$4.983$$ 8.0.56070144.2 None $$0$$ $$2$$ $$0$$ $$4$$ $$q+(\beta _{1}+\beta _{2}+\beta _{4}-2\beta _{5}-\beta _{6})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
624.2.cn.d $$16$$ $$4.983$$ 16.0.$$\cdots$$.9 None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+(-\beta _{10}-\beta _{12})q^{3}+(\beta _{1}-\beta _{3}-\beta _{9}+\cdots)q^{5}+\cdots$$
624.2.cn.e $$16$$ $$4.983$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(\beta _{9}+\beta _{13}+\beta _{15})q^{3}+(-\beta _{3}-\beta _{9}+\cdots)q^{5}+\cdots$$
624.2.cn.f $$56$$ $$4.983$$ None $$0$$ $$0$$ $$0$$ $$-4$$

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

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