# Properties

 Label 475.1.c Level $475$ Weight $1$ Character orbit 475.c Rep. character $\chi_{475}(151,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $50$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 475.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$50$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(475, [\chi])$$.

Total New Old
Modular forms 9 6 3
Cusp forms 3 3 0
Eisenstein series 6 3 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3 q - q^{4} - 4 q^{6} - q^{9} + O(q^{10})$$ $$3 q - q^{4} - 4 q^{6} - q^{9} - 2 q^{11} - q^{16} + q^{19} + 4 q^{26} + 3 q^{36} + 4 q^{39} - 2 q^{44} - 3 q^{49} - 2 q^{61} + 3 q^{64} + 4 q^{74} - 3 q^{76} - q^{81} + 4 q^{96} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(475, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
475.1.c.a $1$ $0.237$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-95})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{4}+q^{9}-2q^{11}+q^{16}-q^{19}+\cdots$$
475.1.c.b $2$ $0.237$ $$\Q(\sqrt{-2})$$ $D_{4}$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}-\beta q^{3}-q^{4}-2q^{6}-q^{9}+\beta q^{12}+\cdots$$