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Properties

Label 3960.2.w
Level $3960$
Weight $2$
Character orbit 3960.w
Rep. character $\chi_{3960}(1981,\cdot)$
Character field $\Q$
Dimension $200$
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.w (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 880 200 680
Cusp forms 848 200 648
Eisenstein series 32 0 32

Trace form

\( 200 q - 4 q^{4} - 12 q^{8} + O(q^{10}) \) \( 200 q - 4 q^{4} - 12 q^{8} + 4 q^{10} - 24 q^{14} + 8 q^{16} - 4 q^{20} - 24 q^{23} - 200 q^{25} + 12 q^{26} - 20 q^{28} - 16 q^{31} + 40 q^{32} + 16 q^{34} - 40 q^{38} + 8 q^{40} - 4 q^{44} - 32 q^{46} + 40 q^{47} + 168 q^{49} + 36 q^{52} + 8 q^{55} + 16 q^{56} - 64 q^{58} + 16 q^{62} - 4 q^{64} - 36 q^{68} - 4 q^{70} - 16 q^{71} + 32 q^{73} + 96 q^{74} + 16 q^{79} + 16 q^{80} + 8 q^{82} - 28 q^{86} + 16 q^{89} - 64 q^{92} + 56 q^{94} - 32 q^{97} + 24 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)