# Properties

 Label 160.6.f Level 160 Weight 6 Character orbit f Rep. character $$\chi_{160}(49,\cdot)$$ Character field $$\Q$$ Dimension 28 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.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q$$ 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 128 32 96
Cusp forms 112 28 84
Eisenstein series 16 4 12

## Trace form

 $$28q + 1940q^{9} + O(q^{10})$$ $$28q + 1940q^{9} + 488q^{15} + 1556q^{25} - 4368q^{31} - 23360q^{39} - 2480q^{41} - 38420q^{49} + 48776q^{55} + 37200q^{65} + 69232q^{71} + 35984q^{79} + 122596q^{81} - 178744q^{89} - 89416q^{95} + O(q^{100})$$

## 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.f.a $$28$$ $$25.661$$ None $$0$$ $$0$$ $$0$$ $$0$$

## 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