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Properties

Label 3960.2.gh
Level $3960$
Weight $2$
Character orbit 3960.gh
Rep. character $\chi_{3960}(301,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $4608$
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.gh (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 792 \)
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 4608 2368
Cusp forms 6848 4608 2240
Eisenstein series 128 0 128

Trace form

\( 4608 q + O(q^{10}) \) \( 4608 q + 16 q^{24} - 576 q^{25} + 32 q^{26} + 32 q^{30} - 16 q^{33} + 64 q^{36} + 20 q^{38} + 16 q^{41} + 86 q^{42} + 76 q^{44} - 112 q^{48} + 576 q^{49} + 52 q^{54} - 132 q^{56} - 16 q^{57} - 42 q^{60} - 176 q^{62} + 74 q^{66} + 78 q^{68} - 96 q^{72} + 84 q^{74} - 24 q^{78} - 48 q^{80} + 16 q^{81} - 60 q^{84} + 104 q^{86} + 20 q^{92} + 64 q^{95} + 162 q^{96} - 88 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)