Properties

Label 960.4.y
Level $960$
Weight $4$
Character orbit 960.y
Rep. character $\chi_{960}(847,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 144 1040
Cusp forms 1120 144 976
Eisenstein series 64 0 64

Trace form

\( 144 q + 1296 q^{9} + O(q^{10}) \) \( 144 q + 1296 q^{9} + 24 q^{19} - 456 q^{35} + 816 q^{47} + 744 q^{51} - 1376 q^{59} + 912 q^{61} - 528 q^{69} - 448 q^{71} - 592 q^{73} - 1104 q^{75} + 11664 q^{81} - 5360 q^{83} + 1696 q^{91} - 2480 q^{95} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)