# Properties

 Label 160.1.p Level $160$ Weight $1$ Character orbit 160.p Rep. character $\chi_{160}(33,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $24$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 160.p (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(160, [\chi])$$.

Total New Old
Modular forms 18 2 16
Cusp forms 2 2 0
Eisenstein series 16 0 16

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q + O(q^{10})$$ $$2 q - 2 q^{13} - 2 q^{17} - 2 q^{25} + 2 q^{37} + 2 q^{45} + 2 q^{53} + 2 q^{65} + 2 q^{73} - 2 q^{81} - 2 q^{85} + 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(160, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.1.p.a $2$ $0.080$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots$$