Properties

Label 320.6.be
Level 320
Weight 6
Character orbit be
Rep. character \(\chi_{320}(21,\cdot)\)
Character field \(\Q(\zeta_{16})\)
Dimension 1280
Sturm bound 288

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.be (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(288\)

Dimensions

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

Total New Old
Modular forms 1936 1280 656
Cusp forms 1904 1280 624
Eisenstein series 32 0 32

Trace form

\( 1280q + O(q^{10}) \) \( 1280q - 27184q^{22} + 44080q^{24} - 8720q^{28} - 74320q^{32} - 25520q^{34} + 139280q^{38} - 92720q^{42} - 131024q^{44} - 41760q^{51} - 146976q^{52} - 233280q^{54} - 43120q^{56} - 51984q^{58} - 57920q^{59} + 351264q^{62} - 635040q^{63} + 374880q^{64} + 254880q^{66} - 244640q^{67} + 14304q^{68} + 287680q^{71} - 828144q^{72} - 107920q^{74} - 268480q^{76} - 665328q^{78} - 355360q^{79} - 193600q^{80} + 985040q^{84} + 1443728q^{86} + 446560q^{88} - 284400q^{90} - 136880q^{94} - 2428688q^{96} - 1914608q^{98} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database