↑

Properties

Label 3960.2.cx
Level $3960$
Weight $2$
Character orbit 3960.cx
Rep. character $\chi_{3960}(1211,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $960$
Sturm bound $1728$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3960.cx (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
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 1744 960 784
Cusp forms 1712 960 752
Eisenstein series 32 0 32

Trace form

\( 960 q - 12 q^{6} + O(q^{10}) \) \( 960 q - 12 q^{6} + 4 q^{12} - 60 q^{14} + 8 q^{18} + 40 q^{24} - 480 q^{25} - 48 q^{27} - 12 q^{34} + 52 q^{36} + 60 q^{38} - 12 q^{40} + 60 q^{42} + 24 q^{46} + 4 q^{48} + 480 q^{49} + 80 q^{51} - 36 q^{52} + 20 q^{54} + 36 q^{58} + 144 q^{59} + 48 q^{64} - 20 q^{66} - 60 q^{68} - 112 q^{72} - 168 q^{74} - 12 q^{76} - 24 q^{78} + 16 q^{81} + 72 q^{82} + 240 q^{83} + 40 q^{84} - 108 q^{86} + 36 q^{90} + 60 q^{92} + 36 q^{94} + 152 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)