# Properties

 Label 160.6.ba Level 160 Weight 6 Character orbit ba Rep. character $$\chi_{160}(3,\cdot)$$ 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.ba (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

 $$472q - 4q^{2} - 4q^{3} - 4q^{5} - 8q^{6} - 8q^{7} + 488q^{8} + O(q^{10})$$ $$472q - 4q^{2} - 4q^{3} - 4q^{5} - 8q^{6} - 8q^{7} + 488q^{8} - 1072q^{10} - 8q^{11} + 1580q^{12} - 4q^{13} - 256q^{14} - 8q^{15} - 8q^{16} - 132q^{18} + 4720q^{19} + 1648q^{20} - 8q^{21} + 5580q^{22} - 8q^{23} + 16160q^{24} - 4q^{25} - 8q^{26} + 968q^{27} - 4100q^{28} + 1384q^{30} - 25584q^{32} - 8q^{33} - 27640q^{34} - 7728q^{35} - 8q^{36} - 4q^{37} + 71676q^{38} - 31184q^{40} - 8q^{41} - 59548q^{42} + 1308q^{43} - 9680q^{44} - 4q^{45} - 8q^{46} - 8q^{47} - 22808q^{48} + 1018024q^{49} + 124q^{50} + 20872q^{51} + 128128q^{52} - 4q^{53} + 154280q^{54} - 110052q^{55} - 129368q^{56} + 97564q^{58} + 4092q^{60} - 96168q^{61} + 103408q^{62} - 134456q^{63} + 234960q^{64} - 8q^{65} + 109992q^{66} + 89252q^{67} - 155832q^{68} - 1944q^{69} - 266996q^{70} - 143848q^{71} - 48872q^{72} - 976q^{75} - 12488q^{76} - 67232q^{77} + 141712q^{78} + 116240q^{80} - 68052q^{82} + 126436q^{83} - 134456q^{84} - 4q^{85} - 91048q^{86} - 790264q^{88} - 528524q^{90} - 8q^{91} + 110252q^{92} + 968q^{93} - 238240q^{94} + 304152q^{96} - 8q^{97} - 160344q^{98} + O(q^{100})$$

## 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