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Properties

Label 1143.3.cf
Level $1143$
Weight $3$
Character orbit 1143.cf
Rep. character $\chi_{1143}(41,\cdot)$
Character field $\Q(\zeta_{126})$
Dimension $9144$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1143.cf (of order \(126\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1143 \)
Character field: \(\Q(\zeta_{126})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1143, [\chi])\).

Total New Old
Modular forms 9288 9288 0
Cusp forms 9144 9144 0
Eisenstein series 144 144 0

Trace form

\( 9144 q - 45 q^{2} - 36 q^{3} - 1527 q^{4} - 54 q^{5} - 6 q^{6} - 18 q^{7} - 36 q^{9} + O(q^{10}) \) \( 9144 q - 45 q^{2} - 36 q^{3} - 1527 q^{4} - 54 q^{5} - 6 q^{6} - 18 q^{7} - 36 q^{9} - 66 q^{10} - 54 q^{11} - 6 q^{12} + 12 q^{13} - 162 q^{14} + 9 q^{15} + 2937 q^{16} - 81 q^{17} - 72 q^{18} - 36 q^{19} - 141 q^{21} + 6 q^{22} - 135 q^{23} - 114 q^{24} - 3714 q^{25} + 216 q^{26} - 39 q^{27} - 144 q^{28} - 378 q^{29} + 216 q^{30} + 30 q^{31} - 333 q^{32} - 39 q^{33} - 30 q^{34} + 225 q^{35} - 570 q^{36} - 6 q^{37} - 18 q^{38} + 420 q^{39} + 315 q^{40} - 54 q^{41} - 168 q^{42} - 18 q^{43} + 297 q^{44} - 765 q^{45} - 48 q^{46} - 63 q^{47} - 495 q^{48} + 126 q^{49} - 63 q^{50} - 39 q^{51} - 6 q^{52} + 1053 q^{54} - 75 q^{55} - 459 q^{56} + 126 q^{57} - 264 q^{58} - 54 q^{59} + 381 q^{60} - 15 q^{61} + 2349 q^{62} + 87 q^{63} + 11316 q^{64} + 594 q^{65} - 675 q^{66} - 123 q^{67} - 846 q^{68} + 108 q^{69} + 87 q^{70} - 114 q^{72} - 78 q^{73} + 414 q^{74} + 3468 q^{75} - 207 q^{76} - 1575 q^{77} + 2196 q^{78} - 276 q^{79} + 1053 q^{80} - 612 q^{81} + 249 q^{82} - 54 q^{83} + 3132 q^{84} + 132 q^{85} - 486 q^{86} + 339 q^{87} - 534 q^{88} - 648 q^{89} + 327 q^{90} - 687 q^{91} - 666 q^{92} + 669 q^{93} - 750 q^{94} + 1305 q^{95} - 27 q^{96} - 18 q^{97} - 804 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1143, [\chi])\) into newform subspaces

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