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Properties

Label 720.4.cq
Level $720$
Weight $4$
Character orbit 720.cq
Rep. character $\chi_{720}(173,\cdot)$
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.cq (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

\( 1712 q - 6 q^{2} - 6 q^{5} - 8 q^{6} + O(q^{10}) \) \( 1712 q - 6 q^{2} - 6 q^{5} - 8 q^{6} + 24 q^{10} - 12 q^{11} - 58 q^{12} - 8 q^{15} - 4 q^{16} - 496 q^{18} - 6 q^{20} - 8 q^{21} + 30 q^{22} - 216 q^{24} + 248 q^{28} - 476 q^{30} - 8 q^{31} - 1386 q^{32} - 8 q^{33} + 396 q^{34} + 248 q^{36} - 54 q^{38} - 216 q^{39} + 248 q^{40} - 646 q^{42} - 4 q^{43} - 254 q^{45} - 88 q^{46} - 12 q^{47} + 2186 q^{48} - 6 q^{50} - 8 q^{51} - 258 q^{52} + 1104 q^{54} - 12 q^{56} + 216 q^{57} - 34 q^{58} - 1696 q^{60} - 4 q^{61} + 1364 q^{63} - 1368 q^{64} - 12 q^{65} + 3288 q^{66} - 4 q^{67} - 390 q^{68} + 108 q^{69} + 14 q^{70} + 794 q^{72} + 96 q^{74} + 3246 q^{75} + 1112 q^{76} - 12 q^{77} + 130 q^{78} - 16 q^{81} + 24 q^{82} + 3204 q^{84} - 252 q^{85} - 12 q^{86} + 108 q^{87} + 3110 q^{88} + 3014 q^{90} - 16 q^{91} + 9456 q^{92} - 12 q^{95} - 6480 q^{96} - 4 q^{97} - 2656 q^{99} + O(q^{100}) \)

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.