# Properties

 Label 625.2.b Level $625$ Weight $2$ Character orbit 625.b Rep. character $\chi_{625}(624,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $4$ Sturm bound $125$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$625 = 5^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 625.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$125$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(625, [\chi])$$.

Total New Old
Modular forms 78 48 30
Cusp forms 48 32 16
Eisenstein series 30 16 14

## Trace form

 $$32 q - 24 q^{4} + 4 q^{6} - 16 q^{9} + O(q^{10})$$ $$32 q - 24 q^{4} + 4 q^{6} - 16 q^{9} + 4 q^{11} - 8 q^{14} + 12 q^{16} + 10 q^{19} - 6 q^{21} - 20 q^{24} - 6 q^{26} - 10 q^{29} - 6 q^{31} - 18 q^{34} + 12 q^{36} - 2 q^{39} + 14 q^{41} + 22 q^{44} - 26 q^{46} + 26 q^{49} - 46 q^{51} + 50 q^{54} - 10 q^{56} + 30 q^{59} + 4 q^{61} + 46 q^{64} - 2 q^{66} - 32 q^{69} + 24 q^{71} + 12 q^{74} - 40 q^{76} + 40 q^{79} - 8 q^{81} + 52 q^{84} - 56 q^{86} - 30 q^{89} - 46 q^{91} - 48 q^{94} + 84 q^{96} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(625, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
625.2.b.a $4$ $4.991$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$$
625.2.b.b $4$ $4.991$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$$
625.2.b.c $8$ $4.991$ 8.0.58140625.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(\beta _{5}+\beta _{6})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$$
625.2.b.d $16$ $4.991$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{8}q^{2}-\beta _{10}q^{3}+(-1-\beta _{12})q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(625, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(625, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(125, [\chi])$$$$^{\oplus 2}$$