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Properties

Label 3960.2.fr
Level $3960$
Weight $2$
Character orbit 3960.fr
Rep. character $\chi_{3960}(139,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $6848$
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.fr (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3960 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 6976 6976 0
Cusp forms 6848 6848 0
Eisenstein series 128 128 0

Trace form

\( 6848 q - 6 q^{4} - 20 q^{6} - 24 q^{9} + O(q^{10}) \) \( 6848 q - 6 q^{4} - 20 q^{6} - 24 q^{9} - 16 q^{11} + 10 q^{14} - 6 q^{16} - 80 q^{19} + 13 q^{20} - 20 q^{24} - 6 q^{25} + 24 q^{26} - 40 q^{30} - 8 q^{34} - 40 q^{35} - 52 q^{36} - 5 q^{40} - 20 q^{41} - 16 q^{44} - 820 q^{49} - 5 q^{50} - 40 q^{51} - 16 q^{56} - 12 q^{59} + 53 q^{60} - 24 q^{64} + 60 q^{66} + 42 q^{70} - 150 q^{74} - 112 q^{80} - 24 q^{81} + 90 q^{84} + 18 q^{86} - 128 q^{89} + 90 q^{90} + 64 q^{91} - 10 q^{94} + 80 q^{96} - 36 q^{99} + O(q^{100}) \)

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.