Properties

Label 320.6.bf
Level 320
Weight 6
Character orbit bf
Rep. character \(\chi_{320}(29,\cdot)\)
Character field \(\Q(\zeta_{16})\)
Dimension 1904
Sturm bound 288

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.bf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
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 1936 0
Cusp forms 1904 1904 0
Eisenstein series 32 32 0

Trace form

\( 1904q - 16q^{4} - 8q^{5} - 16q^{6} - 16q^{9} + O(q^{10}) \) \( 1904q - 16q^{4} - 8q^{5} - 16q^{6} - 16q^{9} - 8q^{10} - 16q^{11} - 16q^{14} - 8q^{15} - 16q^{16} - 16q^{19} - 8q^{20} - 16q^{21} - 16q^{24} - 8q^{25} + 51904q^{26} - 16q^{29} + 64872q^{30} - 16q^{34} - 8q^{35} + 124624q^{36} - 16q^{39} - 62368q^{40} - 16q^{41} - 16q^{44} - 8q^{45} - 16q^{46} - 16q^{49} + 137056q^{50} + 41744q^{51} - 233296q^{54} + 220088q^{55} + 258704q^{56} - 57936q^{59} + 197848q^{60} - 16q^{61} + 374864q^{64} - 16q^{65} - 255408q^{66} - 16q^{69} - 286952q^{70} - 287696q^{71} - 647536q^{74} + 386488q^{75} + 268464q^{76} - 355376q^{79} + 493456q^{80} - 16q^{81} + 985024q^{84} - 8q^{85} - 16q^{86} - 16q^{89} - 8q^{90} - 16q^{91} - 1505696q^{94} - 16q^{96} - 3904q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database