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Properties

Label 3960.2.cj
Level $3960$
Weight $2$
Character orbit 3960.cj
Rep. character $\chi_{3960}(661,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $960$
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.cj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 1744 960 784
Cusp forms 1712 960 752
Eisenstein series 32 0 32

Trace form

\( 960 q + 12 q^{6} - 24 q^{8} + O(q^{10}) \) \( 960 q + 12 q^{6} - 24 q^{8} - 44 q^{12} + 20 q^{14} + 8 q^{18} - 48 q^{23} - 40 q^{24} + 480 q^{25} + 48 q^{26} + 40 q^{32} - 12 q^{34} + 52 q^{36} + 20 q^{38} + 48 q^{39} - 12 q^{40} - 20 q^{42} - 24 q^{46} + 80 q^{47} + 44 q^{48} - 480 q^{49} + 36 q^{52} - 20 q^{54} + 40 q^{56} - 36 q^{58} + 24 q^{62} + 160 q^{63} + 96 q^{64} + 20 q^{66} + 20 q^{68} - 112 q^{72} - 56 q^{74} + 12 q^{76} - 64 q^{78} - 16 q^{81} + 72 q^{82} - 112 q^{84} + 36 q^{86} + 96 q^{87} + 32 q^{89} + 36 q^{90} - 92 q^{92} + 36 q^{94} - 16 q^{96} + 136 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)