↑

Properties

Label 3960.2.bj
Level $3960$
Weight $2$
Character orbit 3960.bj
Rep. character $\chi_{3960}(1693,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $712$
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.bj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
Character field: \(\Q(i)\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 1760 728 1032
Cusp forms 1696 712 984
Eisenstein series 64 16 48

Trace form

\( 712 q + O(q^{10}) \) \( 712 q + 12 q^{22} + 8 q^{23} - 8 q^{25} + 48 q^{26} - 16 q^{31} + 24 q^{38} + 8 q^{47} + 16 q^{55} + 8 q^{56} - 48 q^{58} - 24 q^{70} + 48 q^{71} + 64 q^{80} + 40 q^{82} + 48 q^{86} - 24 q^{88} - 88 q^{92} + 24 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 3}\)