# Properties

 Label 325.2.c Level $325$ Weight $2$ Character orbit 325.c Rep. character $\chi_{325}(51,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $7$ Sturm bound $70$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$325 = 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 325.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$70$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$2$$, $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(325, [\chi])$$.

Total New Old
Modular forms 42 24 18
Cusp forms 30 18 12
Eisenstein series 12 6 6

## Trace form

 $$18 q + 4 q^{3} - 10 q^{4} + 6 q^{9} + O(q^{10})$$ $$18 q + 4 q^{3} - 10 q^{4} + 6 q^{9} + 8 q^{13} + 12 q^{14} - 14 q^{16} - 8 q^{17} + 24 q^{22} - 16 q^{23} - 6 q^{26} + 28 q^{27} - 12 q^{29} - 10 q^{36} + 20 q^{38} + 4 q^{39} - 44 q^{42} - 24 q^{43} - 36 q^{48} - 30 q^{49} - 24 q^{51} - 20 q^{52} - 12 q^{53} + 12 q^{56} + 44 q^{61} - 8 q^{62} + 6 q^{64} + 16 q^{66} + 88 q^{68} - 12 q^{69} + 12 q^{74} - 36 q^{77} + 52 q^{78} + 44 q^{79} - 54 q^{81} + 28 q^{82} + 4 q^{87} - 60 q^{88} - 24 q^{91} + 20 q^{92} + 52 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(325, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
325.2.c.a $2$ $2.595$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+iq^{2}-2q^{3}+q^{4}-2iq^{6}-5iq^{7}+\cdots$$
325.2.c.b $2$ $2.595$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+iq^{2}-2q^{3}+q^{4}-2iq^{6}+3iq^{8}+\cdots$$
325.2.c.c $2$ $2.595$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}-2q^{4}-iq^{6}+iq^{7}+\cdots$$
325.2.c.d $2$ $2.595$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-2q^{4}+iq^{6}+iq^{7}+\cdots$$
325.2.c.e $2$ $2.595$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+iq^{2}+2q^{3}+q^{4}+2iq^{6}+3iq^{8}+\cdots$$
325.2.c.f $2$ $2.595$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+iq^{2}+2q^{3}+q^{4}+2iq^{6}-5iq^{7}+\cdots$$
325.2.c.g $6$ $2.595$ 6.0.5089536.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(1+\beta _{1})q^{3}+(-2+\beta _{3})q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(325, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(325, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 2}$$