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Properties

Label 3960.2.cy
Level $3960$
Weight $2$
Character orbit 3960.cy
Rep. character $\chi_{3960}(529,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $360$
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.cy (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 360 1400
Cusp forms 1696 360 1336
Eisenstein series 64 0 64

Trace form

\( 360 q + 4 q^{9} + O(q^{10}) \) \( 360 q + 4 q^{9} - 12 q^{11} - 10 q^{15} + 8 q^{21} + 12 q^{29} - 24 q^{35} - 16 q^{39} + 4 q^{41} - 6 q^{45} + 168 q^{49} + 24 q^{51} + 72 q^{59} + 12 q^{61} - 24 q^{65} - 8 q^{69} - 6 q^{75} + 108 q^{81} - 24 q^{85} + 72 q^{89} + 72 q^{95} + O(q^{100}) \)

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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

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1980, [\chi])\)\(^{\oplus 2}\)