# Properties

 Label 160.2.n Level $160$ Weight $2$ Character orbit 160.n Rep. character $\chi_{160}(63,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $12$ Newform subspaces $6$ Sturm bound $48$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 160.n (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$48$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 64 12 52
Cusp forms 32 12 20
Eisenstein series 32 0 32

## Trace form

 $$12 q + O(q^{10})$$ $$12 q + 4 q^{13} - 12 q^{17} + 16 q^{21} - 12 q^{25} - 16 q^{33} - 20 q^{37} - 16 q^{41} - 20 q^{45} - 52 q^{53} + 32 q^{57} + 44 q^{65} + 28 q^{73} + 48 q^{77} + 36 q^{81} + 68 q^{85} + 80 q^{93} - 36 q^{97} + O(q^{100})$$

## 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.n.a $2$ $1.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$-4$$ $$-4$$ $$q+(-2-2i)q^{3}+(-2+i)q^{5}+(-2+\cdots)q^{7}+\cdots$$
160.2.n.b $2$ $1.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$2$$ $$-2$$ $$q+(-1-i)q^{3}+(1-2i)q^{5}+(-1+i)q^{7}+\cdots$$
160.2.n.c $2$ $1.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$2$$ $$6$$ $$q+(-1-i)q^{3}+(1+2i)q^{5}+(3-3i)q^{7}+\cdots$$
160.2.n.d $2$ $1.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$2$$ $$-6$$ $$q+(1+i)q^{3}+(1+2i)q^{5}+(-3+3i)q^{7}+\cdots$$
160.2.n.e $2$ $1.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$2$$ $$2$$ $$q+(1+i)q^{3}+(1-2i)q^{5}+(1-i)q^{7}+\cdots$$
160.2.n.f $2$ $1.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$-4$$ $$4$$ $$q+(2+2i)q^{3}+(-2+i)q^{5}+(2-2i)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(160, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 2}$$