# Properties

 Label 2500.1.n Level $2500$ Weight $1$ Character orbit 2500.n Rep. character $\chi_{2500}(99,\cdot)$ Character field $\Q(\zeta_{50})$ Dimension $40$ Newform subspaces $1$ Sturm bound $375$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2500 = 2^{2} \cdot 5^{4}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2500.n (of order $$50$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$500$$ Character field: $$\Q(\zeta_{50})$$ Newform subspaces: $$1$$ Sturm bound: $$375$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2500, [\chi])$$.

Total New Old
Modular forms 240 160 80
Cusp forms 40 40 0
Eisenstein series 200 120 80

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 40 0 0 0

## Trace form

 $$40 q + O(q^{10})$$ $$40 q + 10 q^{34} + 10 q^{49} + 10 q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2500, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2500.1.n.a $40$ $1.248$ $$\Q(\zeta_{100})$$ $D_{25}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{100}q^{2}+\zeta_{100}^{2}q^{4}-\zeta_{100}^{3}q^{8}+\zeta_{100}^{14}q^{9}+\cdots$$