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Properties

Label 3960.2.he
Level $3960$
Weight $2$
Character orbit 3960.he
Rep. character $\chi_{3960}(13,\cdot)$
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.he (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

\( 13696 q - 10 q^{2} - 40 q^{6} - 20 q^{7} - 40 q^{8} + O(q^{10}) \) \( 13696 q - 10 q^{2} - 40 q^{6} - 20 q^{7} - 40 q^{8} - 44 q^{12} - 24 q^{15} - 12 q^{16} - 80 q^{17} - 20 q^{18} - 38 q^{20} - 16 q^{22} - 32 q^{23} - 12 q^{25} - 112 q^{26} - 40 q^{28} - 20 q^{30} - 24 q^{31} - 20 q^{33} + 56 q^{36} - 14 q^{38} - 10 q^{40} - 40 q^{41} + 12 q^{42} - 80 q^{46} - 12 q^{47} - 10 q^{50} - 10 q^{52} - 24 q^{55} + 24 q^{56} - 40 q^{57} + 10 q^{58} + 64 q^{60} + 260 q^{62} - 40 q^{63} - 52 q^{66} - 10 q^{68} - 46 q^{70} - 96 q^{71} - 170 q^{72} - 80 q^{73} - 88 q^{78} + 256 q^{80} - 48 q^{81} - 8 q^{82} - 12 q^{86} - 88 q^{88} - 200 q^{90} - 130 q^{92} - 20 q^{95} - 180 q^{96} - 12 q^{97} + O(q^{100}) \)

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.