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Properties

Label 720.6.cm
Level $720$
Weight $6$
Character orbit 720.cm
Rep. character $\chi_{720}(77,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2864$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 720.cm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(720, [\chi])\).

Total New Old
Modular forms 2896 2896 0
Cusp forms 2864 2864 0
Eisenstein series 32 32 0

Trace form

\( 2864 q - 6 q^{2} - 8 q^{3} - 6 q^{5} - 8 q^{6} + O(q^{10}) \) \( 2864 q - 6 q^{2} - 8 q^{3} - 6 q^{5} - 8 q^{6} - 136 q^{10} - 12 q^{11} + 482 q^{12} - 4 q^{13} - 8 q^{15} - 4 q^{16} - 7656 q^{18} - 6 q^{20} - 8 q^{21} - 130 q^{22} + 1944 q^{24} - 8 q^{27} + 4088 q^{28} + 15244 q^{30} - 8 q^{31} - 14466 q^{32} - 8 q^{33} + 12660 q^{34} + 4088 q^{36} - 16 q^{37} + 186 q^{38} + 1944 q^{39} - 6252 q^{40} - 96466 q^{42} - 6254 q^{45} + 53864 q^{46} - 12 q^{47} - 48998 q^{48} - 6 q^{50} - 8 q^{51} + 4094 q^{52} + 32592 q^{54} - 12 q^{56} - 1944 q^{57} + 126 q^{58} - 13816 q^{60} - 4 q^{61} + 67220 q^{63} - 107880 q^{64} - 12 q^{65} - 17448 q^{66} - 6150 q^{68} - 972 q^{69} - 66 q^{70} + 165858 q^{72} - 384 q^{74} - 127254 q^{75} - 50344 q^{76} - 600510 q^{78} - 16 q^{81} + 120 q^{82} - 12 q^{83} + 243036 q^{84} + 6248 q^{85} - 12 q^{86} - 972 q^{87} - 245082 q^{88} - 416266 q^{90} - 16 q^{91} - 690960 q^{92} + 964 q^{93} - 12 q^{95} - 331728 q^{96} - 4 q^{97} - 169760 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

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