# Properties

 Label 2500.1.j Level $2500$ Weight $1$ Character orbit 2500.j Rep. character $\chi_{2500}(251,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $24$ Newform subspaces $4$ Sturm bound $375$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2500 = 2^{2} \cdot 5^{4}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2500.j (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$100$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$4$$ Sturm bound: $$375$$ Trace bound: $$6$$

## Dimensions

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

Total New Old
Modular forms 164 72 92
Cusp forms 44 24 20
Eisenstein series 120 48 72

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 24 0 0 0

## Trace form

 $$24 q + 2 q^{4} + 2 q^{6} + O(q^{10})$$ $$24 q + 2 q^{4} + 2 q^{6} - 2 q^{14} - 6 q^{16} + 4 q^{21} + 8 q^{24} - 4 q^{26} + 4 q^{29} - 4 q^{34} - 4 q^{36} + 8 q^{41} + 2 q^{46} - 4 q^{54} + 2 q^{56} + 8 q^{61} + 2 q^{64} - 4 q^{69} - 4 q^{74} - 2 q^{81} - 4 q^{84} + 2 q^{86} - 6 q^{89} - 2 q^{94} + 2 q^{96} + O(q^{100})$$

## 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.j.a $4$ $1.248$ $$\Q(\zeta_{10})$$ $D_{5}$ $$\Q(\sqrt{-1})$$ None $$-1$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{8}+\zeta_{10}^{2}q^{9}+\cdots$$
2500.1.j.b $4$ $1.248$ $$\Q(\zeta_{10})$$ $D_{5}$ $$\Q(\sqrt{-1})$$ None $$1$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}-\zeta_{10}^{4}q^{8}+\zeta_{10}^{2}q^{9}+\cdots$$
2500.1.j.c $8$ $1.248$ $$\Q(\zeta_{20})$$ $D_{5}$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}q^{2}+(\zeta_{20}-\zeta_{20}^{3})q^{3}+\zeta_{20}^{2}q^{4}+\cdots$$
2500.1.j.d $8$ $1.248$ $$\Q(\zeta_{20})$$ $D_{5}$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}q^{2}+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{3}+\zeta_{20}^{2}q^{4}+\cdots$$

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

$$S_{1}^{\mathrm{old}}(2500, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(500, [\chi])$$$$^{\oplus 2}$$