↑

Properties

Label 960.4.o
Level $960$
Weight $4$
Character orbit 960.o
Rep. character $\chi_{960}(959,\cdot)$
Character field $\Q$
Dimension $140$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 960.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(960, [\chi])\).

Total New Old
Modular forms 600 148 452
Cusp forms 552 140 412
Eisenstein series 48 8 40

Trace form

\( 140 q - 4 q^{9} + O(q^{10}) \) \( 140 q - 4 q^{9} + 112 q^{21} - 4 q^{25} - 1232 q^{45} + 5676 q^{49} + 920 q^{61} + 1384 q^{69} + 1228 q^{81} + 504 q^{85} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

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