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Properties

Label 3960.2.ge
Level $3960$
Weight $2$
Character orbit 3960.ge
Rep. character $\chi_{3960}(229,\cdot)$
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.ge (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

\( 6848 q - 6 q^{4} - 20 q^{6} - 24 q^{9} + O(q^{10}) \) \( 6848 q - 6 q^{4} - 20 q^{6} - 24 q^{9} - 40 q^{10} + 10 q^{14} - 24 q^{15} - 6 q^{16} + 13 q^{20} + 28 q^{24} - 6 q^{25} - 72 q^{26} - 10 q^{30} - 12 q^{31} - 24 q^{34} - 52 q^{36} - 48 q^{39} + 7 q^{40} - 12 q^{41} + 16 q^{44} - 48 q^{46} - 820 q^{49} + 5 q^{50} - 32 q^{54} - 12 q^{55} - 72 q^{56} + 25 q^{60} - 24 q^{64} - 56 q^{65} - 36 q^{66} + 42 q^{70} - 48 q^{71} + 86 q^{74} - 32 q^{76} - 12 q^{79} + 128 q^{80} - 24 q^{81} - 26 q^{84} + 18 q^{86} - 128 q^{89} - 170 q^{90} + 58 q^{94} - 26 q^{95} - 128 q^{96} + O(q^{100}) \)

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.