# Properties

 Label 320.6.s Level 320 Weight 6 Character orbit s Rep. character $$\chi_{320}(207,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 116 Sturm bound 288

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 320.s (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$80$$ Character field: $$\Q(i)$$ Sturm bound: $$288$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(320, [\chi])$$.

Total New Old
Modular forms 496 124 372
Cusp forms 464 116 348
Eisenstein series 32 8 24

## Trace form

 $$116q + 4q^{3} - 2q^{5} + 4q^{7} + 8748q^{9} + O(q^{10})$$ $$116q + 4q^{3} - 2q^{5} + 4q^{7} + 8748q^{9} + 4q^{11} + 972q^{15} - 4q^{17} - 2360q^{19} - 4q^{21} + 4q^{23} + 976q^{27} - 4q^{33} - 3860q^{35} - 6738q^{45} + 65256q^{47} - 10436q^{51} - 4q^{53} + 4q^{55} - 972q^{57} - 14480q^{59} + 48076q^{61} + 972q^{63} - 4q^{65} + 21348q^{69} + 143848q^{71} + 10072q^{73} - 160004q^{75} - 67232q^{77} + 551116q^{81} - 126436q^{83} + 6248q^{85} + 282188q^{87} + 164724q^{91} + 204760q^{95} - 4q^{97} - 168788q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(320, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{6}^{\mathrm{old}}(320, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(320, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 3}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database