# Properties

 Label 224.1.v Level $224$ Weight $1$ Character orbit 224.v Rep. character $\chi_{224}(13,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $4$ Newform subspaces $1$ Sturm bound $32$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$224 = 2^{5} \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 224.v (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$224$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(224, [\chi])$$.

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

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4 q + O(q^{10})$$ $$4 q - 4 q^{16} - 4 q^{18} + 4 q^{22} - 4 q^{23} - 4 q^{43} + 4 q^{44} - 4 q^{53} + 4 q^{56} + 4 q^{63} + 4 q^{67} + 4 q^{74} - 4 q^{77} - 4 q^{92} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(224, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
224.1.v.a $4$ $0.112$ $$\Q(\zeta_{8})$$ $D_{8}$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$$