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Properties

Label 966.4.t
Level $966$
Weight $4$
Character orbit 966.t
Rep. character $\chi_{966}(41,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1920$
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.t (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
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 1920 3920
Cusp forms 5680 1920 3760
Eisenstein series 160 0 160

Trace form

\( 1920 q + 768 q^{4} + 56 q^{9} + O(q^{10}) \) \( 1920 q + 768 q^{4} + 56 q^{9} - 88 q^{15} - 3072 q^{16} + 152 q^{18} - 936 q^{21} + 144 q^{22} - 4872 q^{25} - 1784 q^{30} - 224 q^{36} + 1308 q^{37} + 1328 q^{39} + 776 q^{42} + 1284 q^{43} - 1344 q^{46} + 1908 q^{49} - 880 q^{51} - 2152 q^{57} - 3072 q^{58} + 352 q^{60} + 32 q^{63} + 12288 q^{64} - 2280 q^{67} - 6864 q^{70} + 3968 q^{72} - 1424 q^{78} - 6048 q^{79} + 1580 q^{81} + 2248 q^{84} + 11088 q^{85} - 576 q^{88} - 192 q^{91} + 544 q^{93} - 6580 q^{99} + O(q^{100}) \)

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

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