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Properties

Label 720.4.da
Level $720$
Weight $4$
Character orbit 720.da
Rep. character $\chi_{720}(59,\cdot)$
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.da (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

\( 1712 q - 4 q^{4} - 6 q^{5} - 8 q^{6} + O(q^{10}) \) \( 1712 q - 4 q^{4} - 6 q^{5} - 8 q^{6} - 8 q^{10} - 12 q^{11} - 12 q^{14} - 4 q^{16} - 16 q^{19} - 468 q^{20} - 116 q^{21} - 376 q^{24} - 12 q^{29} + 826 q^{30} - 36 q^{34} - 704 q^{36} - 16 q^{39} - 2 q^{40} + 246 q^{45} - 24 q^{46} + 39584 q^{49} + 3192 q^{50} - 224 q^{51} - 2976 q^{54} - 16 q^{55} - 4128 q^{56} - 12 q^{59} + 782 q^{60} - 4 q^{61} - 16 q^{64} - 12 q^{65} + 8240 q^{66} + 100 q^{69} + 684 q^{70} - 12 q^{74} + 3354 q^{75} - 1120 q^{76} - 16 q^{81} - 11384 q^{84} - 252 q^{85} - 16692 q^{86} - 72 q^{90} - 2760 q^{91} - 68 q^{94} + 288 q^{96} + 5564 q^{99} + O(q^{100}) \)

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.