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Properties

Label 3960.2.ce
Level $3960$
Weight $2$
Character orbit 3960.ce
Rep. character $\chi_{3960}(419,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1440$
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.ce (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
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 1440 304
Cusp forms 1712 1440 272
Eisenstein series 32 0 32

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q + 42 q^{20} - 28 q^{24} + 34 q^{30} - 12 q^{34} - 40 q^{36} - 24 q^{46} - 720 q^{49} + 78 q^{50} + 52 q^{54} + 2 q^{60} - 24 q^{64} + 84 q^{74} - 112 q^{75} + 12 q^{76} - 16 q^{81} - 188 q^{84} - 12 q^{86} - 36 q^{90} - 72 q^{96} + O(q^{100}) \)

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.

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

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