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Properties

Label 3960.2.hi
Level $3960$
Weight $2$
Character orbit 3960.hi
Rep. character $\chi_{3960}(113,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3456$
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.hi (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 14080 3456 10624
Cusp forms 13568 3456 10112
Eisenstein series 512 0 512

Trace form

\( 3456 q + O(q^{10}) \) \( 3456 q - 12 q^{15} + 24 q^{27} - 12 q^{33} + 32 q^{45} + 36 q^{47} - 168 q^{51} - 48 q^{57} + 12 q^{75} - 192 q^{77} + 64 q^{81} + 120 q^{83} - 12 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1980, [\chi])\)\(^{\oplus 2}\)