# Properties

 Label 160.6.z Level 160 Weight 6 Character orbit z Rep. character $$\chi_{160}(29,\cdot)$$ Character field $$\Q(\zeta_{8})$$ Dimension 472 Sturm bound 144

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 160.z (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$160$$ Character field: $$\Q(\zeta_{8})$$ Sturm bound: $$144$$

## Dimensions

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

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

## Trace form

 $$472q - 8q^{4} - 4q^{5} - 8q^{6} - 8q^{9} + O(q^{10})$$ $$472q - 8q^{4} - 4q^{5} - 8q^{6} - 8q^{9} - 4q^{10} - 8q^{11} - 2488q^{14} - 8q^{16} - 8q^{19} - 4q^{20} - 8q^{21} - 10448q^{24} - 4q^{25} - 25968q^{26} - 8q^{29} - 32572q^{30} - 46144q^{31} - 264q^{34} - 4780q^{35} - 62328q^{36} - 8q^{39} + 91304q^{40} - 8q^{41} - 8q^{44} - 976q^{45} - 8q^{46} + 4516q^{50} - 22832q^{51} - 116648q^{54} - 110052q^{55} + 129352q^{56} + 28952q^{59} + 54272q^{60} + 96152q^{61} + 463936q^{64} - 8q^{65} - 144632q^{66} + 44632q^{69} - 343240q^{70} + 143832q^{71} - 275280q^{74} - 193252q^{75} + 255992q^{76} + 493168q^{80} - 282616q^{84} - 12504q^{85} - 91048q^{86} - 8q^{89} - 564640q^{90} - 8q^{91} + 529192q^{94} - 8q^{95} + 700872q^{96} - 337584q^{99} + O(q^{100})$$

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

The newforms in this space have not yet been added to the LMFDB.

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database