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Properties

Label 966.4.i
Level $966$
Weight $4$
Character orbit 966.i
Rep. character $\chi_{966}(277,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $176$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1168 176 992
Cusp forms 1136 176 960
Eisenstein series 32 0 32

Trace form

\( 176 q + 12 q^{3} - 352 q^{4} - 48 q^{6} - 40 q^{7} - 792 q^{9} + O(q^{10}) \) \( 176 q + 12 q^{3} - 352 q^{4} - 48 q^{6} - 40 q^{7} - 792 q^{9} + 24 q^{10} + 48 q^{12} - 24 q^{13} + 80 q^{14} - 168 q^{15} - 1408 q^{16} - 8 q^{17} - 188 q^{19} + 72 q^{21} - 560 q^{22} + 96 q^{24} - 2284 q^{25} - 216 q^{27} + 80 q^{28} - 112 q^{29} - 136 q^{31} + 12 q^{33} - 1552 q^{35} + 6336 q^{36} + 196 q^{37} + 496 q^{38} + 1092 q^{39} + 96 q^{40} + 1024 q^{41} - 408 q^{42} - 1064 q^{43} - 832 q^{47} - 384 q^{48} - 872 q^{49} - 2944 q^{50} + 48 q^{52} + 344 q^{53} + 216 q^{54} + 1416 q^{55} + 320 q^{56} + 504 q^{57} + 536 q^{58} + 816 q^{59} + 336 q^{60} + 368 q^{61} + 4288 q^{62} + 180 q^{63} + 11264 q^{64} + 3424 q^{65} + 1268 q^{67} - 32 q^{68} - 1104 q^{69} - 264 q^{70} - 6656 q^{71} + 116 q^{73} - 1024 q^{74} + 2100 q^{75} + 1504 q^{76} - 576 q^{77} + 672 q^{78} - 2896 q^{79} - 7128 q^{81} + 576 q^{82} + 5312 q^{83} - 1296 q^{84} + 1616 q^{85} - 768 q^{86} + 948 q^{87} + 1120 q^{88} + 2800 q^{89} - 432 q^{90} - 1420 q^{91} - 3612 q^{93} + 4896 q^{94} - 3824 q^{95} + 384 q^{96} + 3832 q^{97} + 1504 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)