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Properties

Label 966.4.h
Level $966$
Weight $4$
Character orbit 966.h
Rep. character $\chi_{966}(827,\cdot)$
Character field $\Q$
Dimension $144$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 584 144 440
Cusp forms 568 144 424
Eisenstein series 16 0 16

Trace form

\( 144 q - 16 q^{3} - 576 q^{4} - 128 q^{9} + O(q^{10}) \) \( 144 q - 16 q^{3} - 576 q^{4} - 128 q^{9} + 64 q^{12} - 192 q^{13} + 2304 q^{16} - 16 q^{18} + 4440 q^{25} - 328 q^{27} - 144 q^{31} + 512 q^{36} + 968 q^{39} - 480 q^{46} - 256 q^{48} - 7056 q^{49} + 768 q^{52} + 1200 q^{54} + 2688 q^{55} - 912 q^{58} - 9216 q^{64} + 240 q^{69} - 1008 q^{70} + 64 q^{72} + 3216 q^{73} - 1680 q^{75} - 1584 q^{78} - 1288 q^{81} - 288 q^{82} - 1392 q^{85} - 3320 q^{87} + 4184 q^{93} + 2592 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)