# Properties

 Label 2025.1.j Level $2025$ Weight $1$ Character orbit 2025.j Rep. character $\chi_{2025}(26,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $3$ Sturm bound $270$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2025 = 3^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2025.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$270$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2025, [\chi])$$.

Total New Old
Modular forms 80 14 66
Cusp forms 8 8 0
Eisenstein series 72 6 66

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

## Trace form

 $$8 q - 2 q^{4} + O(q^{10})$$ $$8 q - 2 q^{4} + 4 q^{31} + 2 q^{34} + 4 q^{46} + 2 q^{49} + 4 q^{61} + 2 q^{76} - 8 q^{91} - 4 q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2025, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2025.1.j.a $2$ $1.011$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots$$
2025.1.j.b $2$ $1.011$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots$$
2025.1.j.c $4$ $1.011$ $$\Q(\zeta_{12})$$ $D_{3}$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{3}q^{8}-\zeta_{12}^{4}q^{16}+\cdots$$