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Properties

Label 966.4.r
Level $966$
Weight $4$
Character orbit 966.r
Rep. character $\chi_{966}(113,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1440$
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.r (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 5840 1440 4400
Cusp forms 5680 1440 4240
Eisenstein series 160 0 160

Trace form

\( 1440 q + 16 q^{3} + 576 q^{4} + 128 q^{9} + O(q^{10}) \) \( 1440 q + 16 q^{3} + 576 q^{4} + 128 q^{9} - 64 q^{12} + 192 q^{13} + 1496 q^{15} - 2304 q^{16} - 72 q^{18} - 4440 q^{25} + 328 q^{27} + 1496 q^{30} + 144 q^{31} + 3872 q^{33} - 512 q^{36} + 1188 q^{37} - 968 q^{39} - 1716 q^{43} + 480 q^{46} + 256 q^{48} + 7056 q^{49} - 768 q^{52} - 1200 q^{54} - 8760 q^{55} - 8448 q^{57} + 912 q^{58} - 176 q^{60} + 9216 q^{64} + 10912 q^{66} + 5808 q^{67} + 14720 q^{69} + 1008 q^{70} - 64 q^{72} + 1008 q^{73} + 9644 q^{75} - 1320 q^{78} - 13364 q^{81} + 288 q^{82} - 16560 q^{85} + 3320 q^{87} - 4184 q^{93} - 2592 q^{94} + 50688 q^{97} + O(q^{100}) \)

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

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