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Properties

Label 720.4.cp
Level $720$
Weight $4$
Character orbit 720.cp
Rep. character $\chi_{720}(43,\cdot)$
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.cp (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

\( 1712 q - 2 q^{2} - 2 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + O(q^{10}) \) \( 1712 q - 2 q^{2} - 2 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 24 q^{10} - 4 q^{11} - 58 q^{12} - 4 q^{13} - 108 q^{15} - 4 q^{16} - 16 q^{17} - 464 q^{18} - 2 q^{20} - 8 q^{21} - 34 q^{22} - 4 q^{23} + 216 q^{24} - 560 q^{26} - 264 q^{28} + 684 q^{30} + 458 q^{32} - 8 q^{33} - 396 q^{34} + 492 q^{35} + 248 q^{36} - 16 q^{37} - 1222 q^{38} + 248 q^{40} + 670 q^{42} - 4 q^{43} + 2368 q^{44} + 246 q^{45} + 56 q^{46} + 142 q^{48} - 2 q^{50} - 8 q^{51} + 254 q^{52} + 1040 q^{54} - 16 q^{55} - 4 q^{56} + 216 q^{57} - 34 q^{58} - 1548 q^{60} - 4 q^{61} + 3140 q^{62} - 1368 q^{64} - 4 q^{65} - 3304 q^{66} - 4 q^{67} - 550 q^{68} - 108 q^{69} - 18 q^{70} - 32 q^{71} - 802 q^{72} - 424 q^{74} - 3362 q^{75} - 1120 q^{76} - 4642 q^{78} + 5268 q^{80} - 16 q^{81} - 40 q^{82} - 2772 q^{84} - 252 q^{85} - 4 q^{86} + 1280 q^{87} - 3114 q^{88} - 9386 q^{90} - 16 q^{91} - 3412 q^{92} - 116 q^{93} + 6464 q^{96} - 4 q^{97} - 3996 q^{98} - 2656 q^{99} + O(q^{100}) \)

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.