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Properties

Label 320.6.bf
Level $320$
Weight $6$
Character orbit 320.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

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

Display 100 coefficients 10 coefficients

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

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