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Properties

Label 720.4.cm
Level $720$
Weight $4$
Character orbit 720.cm
Rep. character $\chi_{720}(77,\cdot)$
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.cm (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

\( 1712 q - 6 q^{2} - 8 q^{3} - 6 q^{5} - 8 q^{6} + O(q^{10}) \) \( 1712 q - 6 q^{2} - 8 q^{3} - 6 q^{5} - 8 q^{6} - 40 q^{10} - 12 q^{11} + 50 q^{12} - 4 q^{13} - 8 q^{15} - 4 q^{16} + 456 q^{18} - 6 q^{20} - 8 q^{21} - 34 q^{22} + 216 q^{24} - 8 q^{27} + 248 q^{28} - 692 q^{30} - 8 q^{31} + 1374 q^{32} - 8 q^{33} - 396 q^{34} + 248 q^{36} - 16 q^{37} + 42 q^{38} + 216 q^{39} - 252 q^{40} - 226 q^{42} - 254 q^{45} - 88 q^{46} - 12 q^{47} + 250 q^{48} - 6 q^{50} - 8 q^{51} + 254 q^{52} - 1104 q^{54} - 12 q^{56} - 216 q^{57} + 30 q^{58} - 3448 q^{60} - 4 q^{61} + 1364 q^{63} + 1368 q^{64} - 12 q^{65} + 3288 q^{66} - 390 q^{68} - 108 q^{69} - 18 q^{70} + 4674 q^{72} - 96 q^{74} + 3354 q^{75} + 1112 q^{76} + 5682 q^{78} - 16 q^{81} + 24 q^{82} - 12 q^{83} - 3204 q^{84} + 248 q^{85} - 12 q^{86} - 108 q^{87} + 1062 q^{88} - 10714 q^{90} - 16 q^{91} + 9456 q^{92} + 100 q^{93} - 12 q^{95} - 6480 q^{96} - 4 q^{97} + 2656 q^{99} + O(q^{100}) \)

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.