# Properties

 Label 160.2.f Level $160$ Weight $2$ Character orbit 160.f Rep. character $\chi_{160}(49,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 160.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(160, [\chi])$$.

Total New Old
Modular forms 32 8 24
Cusp forms 16 4 12
Eisenstein series 16 4 12

## Trace form

 $$4 q - 4 q^{9} + O(q^{10})$$ $$4 q - 4 q^{9} + 8 q^{15} - 4 q^{25} - 16 q^{31} + 4 q^{49} - 24 q^{55} + 48 q^{71} + 16 q^{79} - 20 q^{81} + 24 q^{89} + 24 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(160, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.2.f.a $4$ $1.278$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(160, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(160, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 3}$$