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Properties

Label 3960.2.ev
Level $3960$
Weight $2$
Character orbit 3960.ev
Rep. character $\chi_{3960}(1013,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2880$
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.ev (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 3488 2880 608
Cusp forms 3424 2880 544
Eisenstein series 64 0 64

Trace form

\( 2880 q + O(q^{10}) \) \( 2880 q + 56 q^{18} - 40 q^{30} + 120 q^{32} + 80 q^{42} - 48 q^{46} + 80 q^{48} - 80 q^{60} + 40 q^{72} - 24 q^{76} - 28 q^{78} - 32 q^{81} - 216 q^{86} + 112 q^{87} + 144 q^{96} + O(q^{100}) \)

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

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