# Properties

 Label 160.6.o Level 160 Weight 6 Character orbit o Rep. character $$\chi_{160}(47,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 56 Newform subspaces 1 Sturm bound 144 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ 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: $$144$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(160, [\chi])$$.

Total New Old
Modular forms 256 64 192
Cusp forms 224 56 168
Eisenstein series 32 8 24

## Trace form

 $$56q + 4q^{3} + O(q^{10})$$ $$56q + 4q^{3} + 8q^{11} - 408q^{17} - 3120q^{25} - 968q^{27} - 976q^{33} + 4780q^{35} - 8q^{41} - 1308q^{43} - 20872q^{51} + 968q^{57} + 17680q^{65} - 89252q^{67} - 25184q^{73} + 127740q^{75} - 67792q^{81} + 126444q^{83} - 329432q^{91} + 212576q^{97} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(160, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
160.6.o.a $$56$$ $$25.661$$ None $$0$$ $$4$$ $$0$$ $$0$$

## Decomposition of $$S_{6}^{\mathrm{old}}(160, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(160, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 3}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database