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

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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