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Properties

Label 3960.2.by
Level $3960$
Weight $2$
Character orbit 3960.by
Rep. character $\chi_{3960}(329,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $432$
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.by (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
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 1760 432 1328
Cusp forms 1696 432 1264
Eisenstein series 64 0 64

Trace form

\( 432 q + O(q^{10}) \) \( 432 q + 6 q^{15} + 2 q^{45} - 216 q^{49} - 12 q^{55} - 72 q^{59} - 28 q^{69} - 14 q^{75} + 32 q^{81} + 64 q^{99} + O(q^{100}) \)

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

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