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Properties

Label 966.4.j
Level $966$
Weight $4$
Character orbit 966.j
Rep. character $\chi_{966}(137,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $384$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(966, [\chi])\).

Total New Old
Modular forms 1168 384 784
Cusp forms 1136 384 752
Eisenstein series 32 0 32

Trace form

\( 384 q + 768 q^{4} - 16 q^{6} - 28 q^{9} + O(q^{10}) \) \( 384 q + 768 q^{4} - 16 q^{6} - 28 q^{9} - 3072 q^{16} + 96 q^{18} - 32 q^{24} - 4728 q^{25} - 48 q^{27} - 224 q^{36} - 908 q^{39} - 840 q^{46} - 3336 q^{49} - 1016 q^{54} - 192 q^{55} + 288 q^{58} - 24576 q^{64} + 1780 q^{69} + 384 q^{70} - 384 q^{72} - 1080 q^{73} + 272 q^{75} - 2848 q^{78} - 1812 q^{81} - 1536 q^{82} - 10512 q^{85} - 3660 q^{87} + 992 q^{93} - 7344 q^{94} + 128 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(966, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(966, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)