# Properties

 Label 25.3.c Level $25$ Weight $3$ Character orbit 25.c Rep. character $\chi_{25}(7,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $1$ Sturm bound $7$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 25.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$7$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(25, [\chi])$$.

Total New Old
Modular forms 16 8 8
Cusp forms 4 4 0
Eisenstein series 12 4 8

## Trace form

 $$4 q - 12 q^{6} + O(q^{10})$$ $$4 q - 12 q^{6} - 12 q^{11} + 44 q^{16} + 48 q^{21} - 72 q^{26} - 152 q^{31} + 24 q^{36} + 228 q^{41} + 168 q^{46} - 132 q^{51} - 240 q^{56} - 112 q^{61} + 36 q^{66} + 168 q^{71} + 20 q^{76} - 36 q^{81} + 48 q^{86} + 288 q^{91} + 108 q^{96} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(25, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.3.c.a $4$ $0.681$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots$$