# Properties

 Label 2500.1.b Level $2500$ Weight $1$ Character orbit 2500.b Rep. character $\chi_{2500}(1251,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $375$ Trace bound $2$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 42 20 22
Cusp forms 12 4 8
Eisenstein series 30 16 14

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4 q + 4 q^{4} + 4 q^{9} + O(q^{10})$$ $$4 q + 4 q^{4} + 4 q^{9} + 4 q^{16} - 2 q^{26} - 2 q^{29} - 2 q^{34} + 4 q^{36} - 2 q^{41} + 4 q^{49} - 2 q^{61} + 4 q^{64} - 2 q^{74} + 4 q^{81} - 2 q^{89} + O(q^{100})$$

## 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.b.a $2$ $1.248$ $$\Q(\sqrt{5})$$ $D_{5}$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-q^{8}+q^{9}+(1-\beta )q^{13}+\cdots$$
2500.1.b.b $2$ $1.248$ $$\Q(\sqrt{5})$$ $D_{5}$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}+q^{8}+q^{9}+(-1+\beta )q^{13}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(2500, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2500, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(500, [\chi])$$$$^{\oplus 2}$$