# Properties

 Label 400.1.b Level $400$ Weight $1$ Character orbit 400.b Rep. character $\chi_{400}(351,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $60$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$400 = 2^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 400.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(400, [\chi])$$.

Total New Old
Modular forms 19 1 18
Cusp forms 1 1 0
Eisenstein series 18 0 18

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q + q^{9} + O(q^{10})$$ $$q + q^{9} - 2 q^{29} - 2 q^{41} + q^{49} - 2 q^{61} + q^{81} - 2 q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(400, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
400.1.b.a $1$ $0.200$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{9}-2q^{29}-2q^{41}+q^{49}-2q^{61}+\cdots$$