# Properties

 Label 160.2.o Level $160$ Weight $2$ Character orbit 160.o Rep. character $\chi_{160}(47,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $8$ 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.o (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q(i)$$ 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 64 16 48
Cusp forms 32 8 24
Eisenstein series 32 8 24

## Trace form

 $$8q + 4q^{3} + O(q^{10})$$ $$8q + 4q^{3} + 8q^{11} - 8q^{17} - 8q^{27} - 16q^{33} - 20q^{35} - 8q^{41} - 28q^{43} - 8q^{51} + 8q^{57} + 28q^{67} + 16q^{73} + 60q^{75} + 32q^{81} + 44q^{83} + 40q^{91} + 16q^{97} + O(q^{100})$$

## 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.o.a $$8$$ $$1.278$$ $$\Q(\zeta_{20})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\zeta_{20}^{3}q^{3}+\zeta_{20}^{5}q^{5}-\zeta_{20}^{6}q^{7}+\cdots$$

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

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