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Properties

Label 960.4.bf
Level $960$
Weight $4$
Character orbit 960.bf
Rep. character $\chi_{960}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 960.bf (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1184 296 888
Cusp forms 1120 280 840
Eisenstein series 64 16 48

Trace form

\( 280 q + 4 q^{3} + O(q^{10}) \) \( 280 q + 4 q^{3} - 8 q^{13} + 4 q^{15} + 24 q^{19} - 4 q^{21} + 4 q^{27} + 16 q^{31} - 4 q^{33} - 8 q^{37} + 216 q^{39} + 248 q^{45} + 4 q^{51} - 108 q^{57} + 904 q^{61} + 1376 q^{63} + 108 q^{69} - 1596 q^{75} - 8 q^{81} + 496 q^{85} - 108 q^{87} + 8 q^{91} - 112 q^{93} - 8 q^{97} + 2656 q^{99} + O(q^{100}) \)

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

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