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Properties

Label 3960.2.hh
Level $3960$
Weight $2$
Character orbit 3960.hh
Rep. character $\chi_{3960}(427,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $13696$
Sturm bound $1728$

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Defining parameters

Level: \( N \) \(=\) \( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3960.hh (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3960 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3960, [\chi])\).

Total New Old
Modular forms 13952 13952 0
Cusp forms 13696 13696 0
Eisenstein series 256 256 0

Trace form

\( 13696 q - 6 q^{2} - 24 q^{3} - 24 q^{6} - 24 q^{8} + O(q^{10}) \) \( 13696 q - 6 q^{2} - 24 q^{3} - 24 q^{6} - 24 q^{8} - 64 q^{10} - 32 q^{11} - 20 q^{12} - 12 q^{16} - 48 q^{17} - 4 q^{18} - 38 q^{20} - 16 q^{22} - 12 q^{25} + 16 q^{26} - 24 q^{27} - 56 q^{28} + 8 q^{30} - 16 q^{32} - 44 q^{33} - 48 q^{35} + 56 q^{36} - 14 q^{38} - 6 q^{40} - 24 q^{41} + 12 q^{42} - 32 q^{43} - 48 q^{46} - 24 q^{48} - 6 q^{50} - 48 q^{51} - 38 q^{52} - 88 q^{56} - 72 q^{57} - 22 q^{58} + 32 q^{60} - 188 q^{62} - 32 q^{65} + 4 q^{66} - 32 q^{67} - 22 q^{68} - 46 q^{70} + 14 q^{72} - 48 q^{73} - 24 q^{75} - 64 q^{76} + 8 q^{78} - 224 q^{80} - 48 q^{81} - 40 q^{82} - 12 q^{83} - 12 q^{86} - 88 q^{88} + 188 q^{90} - 96 q^{91} - 34 q^{92} + 28 q^{96} - 12 q^{97} - 104 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3960, [\chi])\) into newform subspaces

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