# Properties

 Label 160.2.c Level $160$ Weight $2$ Character orbit 160.c Rep. character $\chi_{160}(129,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $48$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 160.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 32 6 26
Cusp forms 16 6 10
Eisenstein series 16 0 16

## Trace form

 $$6 q + 2 q^{5} - 6 q^{9} + O(q^{10})$$ $$6 q + 2 q^{5} - 6 q^{9} - 8 q^{21} + 14 q^{25} + 4 q^{29} - 20 q^{41} - 34 q^{45} - 14 q^{49} + 20 q^{61} - 16 q^{65} + 56 q^{69} + 62 q^{81} + 32 q^{85} - 4 q^{89} + O(q^{100})$$

## 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.c.a $2$ $1.278$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+i)q^{5}+3q^{9}+2iq^{13}-4iq^{17}+\cdots$$
160.2.c.b $4$ $1.278$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(160, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 2}$$