↑

Properties

Label 960.3.bj
Level $960$
Weight $3$
Character orbit 960.bj
Rep. character $\chi_{960}(383,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $184$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 960.bj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(960, [\chi])\).

Total New Old
Modular forms 816 200 616
Cusp forms 720 184 536
Eisenstein series 96 16 80

Trace form

\( 184 q + O(q^{10}) \) \( 184 q + 8 q^{13} + 8 q^{21} - 8 q^{25} - 40 q^{33} + 8 q^{37} + 104 q^{45} - 40 q^{57} - 48 q^{61} - 8 q^{73} - 72 q^{81} + 8 q^{85} + 640 q^{93} - 72 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)