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Properties

Label 720.4.ce
Level $720$
Weight $4$
Character orbit 720.ce
Rep. character $\chi_{720}(229,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1712$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.ce (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(720, [\chi])\).

Total New Old
Modular forms 1744 1744 0
Cusp forms 1712 1712 0
Eisenstein series 32 32 0

Trace form

\( 1712 q - 4 q^{4} - 2 q^{5} - 8 q^{6} + O(q^{10}) \) \( 1712 q - 4 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{10} - 4 q^{11} + 60 q^{14} - 8 q^{15} - 4 q^{16} - 16 q^{19} + 152 q^{20} + 100 q^{21} - 376 q^{24} + 528 q^{26} - 4 q^{29} - 334 q^{30} - 8 q^{31} + 28 q^{34} + 492 q^{35} + 176 q^{36} - 2 q^{40} - 16 q^{44} - 254 q^{45} + 120 q^{46} - 39600 q^{49} - 1036 q^{50} + 208 q^{51} + 2960 q^{54} - 1376 q^{56} - 4 q^{59} + 1038 q^{60} - 4 q^{61} - 16 q^{64} - 4 q^{65} + 1584 q^{66} + 100 q^{69} - 688 q^{70} - 4 q^{74} - 3254 q^{75} + 1112 q^{76} - 8 q^{79} + 112 q^{80} - 16 q^{81} + 9296 q^{84} + 248 q^{85} - 5564 q^{86} + 5896 q^{90} + 2728 q^{91} - 68 q^{94} - 4 q^{95} - 304 q^{96} - 268 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

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