Properties

 Label 624.2.c Level $624$ Weight $2$ Character orbit 624.c Rep. character $\chi_{624}(337,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $7$ Sturm bound $224$ Trace bound $17$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$624 = 2^{4} \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 624.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$224$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$11$$

Dimensions

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

Total New Old
Modular forms 124 14 110
Cusp forms 100 14 86
Eisenstein series 24 0 24

Trace form

 $$14 q - 2 q^{3} + 14 q^{9} + O(q^{10})$$ $$14 q - 2 q^{3} + 14 q^{9} + 2 q^{13} - 4 q^{17} - 10 q^{25} - 2 q^{27} + 4 q^{29} + 2 q^{39} + 24 q^{43} + 10 q^{49} + 12 q^{51} - 12 q^{53} + 32 q^{55} - 12 q^{61} - 16 q^{65} + 22 q^{75} + 8 q^{77} + 16 q^{79} + 14 q^{81} - 12 q^{87} - 40 q^{91} - 64 q^{95} + O(q^{100})$$

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.c.a $2$ $4.983$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{5}+iq^{7}+q^{9}+(-3-i)q^{13}+\cdots$$
624.2.c.b $2$ $4.983$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots$$
624.2.c.c $2$ $4.983$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+2iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots$$
624.2.c.d $2$ $4.983$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{5}-2iq^{7}+q^{9}+3iq^{11}+\cdots$$
624.2.c.e $2$ $4.983$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots$$
624.2.c.f $2$ $4.983$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots$$
624.2.c.g $2$ $4.983$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{7}+q^{9}+iq^{11}+(3-i)q^{13}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(624, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(156, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(208, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(312, [\chi])$$$$^{\oplus 2}$$