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Properties

Label 720.6.ce
Level $720$
Weight $6$
Character orbit 720.ce
Rep. character $\chi_{720}(229,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2864$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 720.ce (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(720, [\chi])\).

Total New Old
Modular forms 2896 2896 0
Cusp forms 2864 2864 0
Eisenstein series 32 32 0

Trace form

\( 2864 q - 4 q^{4} - 2 q^{5} - 8 q^{6} + O(q^{10}) \) \( 2864 q - 4 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{10} - 4 q^{11} + 252 q^{14} - 8 q^{15} - 4 q^{16} - 16 q^{19} + 824 q^{20} + 964 q^{21} + 8072 q^{24} - 1776 q^{26} - 4 q^{29} + 626 q^{30} - 8 q^{31} + 124 q^{34} + 12492 q^{35} + 27056 q^{36} - 2 q^{40} - 16 q^{44} - 6254 q^{45} - 53640 q^{46} - 3322992 q^{49} + 32132 q^{50} + 1936 q^{51} - 154288 q^{54} - 67232 q^{56} - 4 q^{59} - 163890 q^{60} - 4 q^{61} - 16 q^{64} - 4 q^{65} + 13584 q^{66} + 964 q^{69} - 33616 q^{70} - 4 q^{74} + 128218 q^{75} - 50344 q^{76} - 8 q^{79} - 777488 q^{80} - 16 q^{81} + 103568 q^{84} + 6248 q^{85} + 1156 q^{86} - 294872 q^{90} + 134440 q^{91} - 260 q^{94} - 4 q^{95} - 27568 q^{96} - 405964 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

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