Properties

Label 320.6.q
Level 320
Weight 6
Character orbit q
Rep. character \(\chi_{320}(49,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 116
Sturm bound 288

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.q (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

\( 116q - 2q^{5} + O(q^{10}) \) \( 116q - 2q^{5} + 4q^{11} + 4q^{15} - 2356q^{19} - 976q^{21} - 4q^{29} - 23056q^{31} + 3864q^{35} + 6734q^{45} + 220884q^{49} + 9472q^{51} - 14476q^{59} - 48084q^{61} - 27692q^{65} - 23296q^{69} + 33244q^{75} - 427312q^{79} - 551132q^{81} + 6248q^{85} + 231952q^{91} - 38420q^{95} - 406924q^{99} + O(q^{100}) \)

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