Properties

Label 320.6.j
Level 320
Weight 6
Character orbit j
Rep. character \(\chi_{320}(47,\cdot)\)
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.j (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

\( 116q - 2q^{5} + 4q^{7} - 8748q^{9} + O(q^{10}) \) \( 116q - 2q^{5} + 4q^{7} - 8748q^{9} + 4q^{11} - 4q^{13} - 972q^{15} - 4q^{17} + 2360q^{19} - 4q^{21} + 4q^{23} - 4q^{33} + 8640q^{35} - 4q^{37} + 1316q^{43} - 5766q^{45} - 65256q^{47} - 10436q^{51} + 4q^{55} + 972q^{57} + 14480q^{59} + 48076q^{61} - 972q^{63} - 4q^{65} + 89260q^{67} - 21348q^{69} + 143848q^{71} - 10072q^{73} + 32272q^{75} + 551116q^{81} - 6252q^{85} + 282188q^{87} + 164724q^{91} + 968q^{93} - 204760q^{95} - 4q^{97} + 168788q^{99} + O(q^{100}) \)

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