# Properties

 Label 325.2.m Level $325$ Weight $2$ Character orbit 325.m Rep. character $\chi_{325}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $40$ Newform subspaces $4$ Sturm bound $70$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$325 = 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 325.m (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$70$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 80 48 32
Cusp forms 56 40 16
Eisenstein series 24 8 16

## Trace form

 $$40 q - 18 q^{4} - 6 q^{6} + 26 q^{9} + O(q^{10})$$ $$40 q - 18 q^{4} - 6 q^{6} + 26 q^{9} - 18 q^{11} + 8 q^{14} - 18 q^{16} - 12 q^{19} - 48 q^{24} - 8 q^{26} + 8 q^{29} + 36 q^{36} - 44 q^{39} + 30 q^{41} - 42 q^{46} - 8 q^{49} - 8 q^{51} - 42 q^{54} - 18 q^{56} + 96 q^{59} - 32 q^{61} + 88 q^{64} - 60 q^{66} - 32 q^{69} - 42 q^{71} + 62 q^{74} + 72 q^{76} + 8 q^{79} + 4 q^{81} + 240 q^{84} - 72 q^{89} + 82 q^{91} - 62 q^{94} + O(q^{100})$$

## 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.m.a $4$ $2.595$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots$$
325.2.m.b $8$ $2.595$ 8.0.22581504.2 None $$-2$$ $$6$$ $$0$$ $$10$$ $$q+(1-\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(2-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$$
325.2.m.c $8$ $2.595$ 8.0.22581504.2 None $$2$$ $$-6$$ $$0$$ $$-10$$ $$q+(-1+\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-2+\beta _{3}+\cdots)q^{3}+\cdots$$
325.2.m.d $20$ $2.595$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{12}q^{2}+(-\beta _{13}+\beta _{17}-\beta _{19})q^{3}+\cdots$$

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

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