Properties

Label 960.4.cn
Level $960$
Weight $4$
Character orbit 960.cn
Rep. character $\chi_{960}(11,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $3072$
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.cn (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 4640 3072 1568
Cusp forms 4576 3072 1504
Eisenstein series 64 0 64

Trace form

\( 3072 q + O(q^{10}) \) \( 3072 q + 2000 q^{24} + 6320 q^{42} - 6624 q^{52} + 9504 q^{58} + 6048 q^{64} - 13056 q^{67} - 10416 q^{76} - 10128 q^{78} + 5664 q^{79} - 4144 q^{84} + 6240 q^{88} + 9360 q^{90} + 1488 q^{94} + 25840 q^{96} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)