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Properties

Label 1143.3.cd
Level $1143$
Weight $3$
Character orbit 1143.cd
Rep. character $\chi_{1143}(46,\cdot)$
Character field $\Q(\zeta_{126})$
Dimension $3816$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1143.cd (of order \(126\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 127 \)
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 9360 3888 5472
Cusp forms 9072 3816 5256
Eisenstein series 288 72 216

Trace form

\( 3816 q + 30 q^{2} - 1302 q^{4} + 33 q^{5} - 24 q^{7} + 57 q^{8} + O(q^{10}) \) \( 3816 q + 30 q^{2} - 1302 q^{4} + 33 q^{5} - 24 q^{7} + 57 q^{8} + 3 q^{10} + 9 q^{11} - 12 q^{13} - 30 q^{14} - 2406 q^{16} + 21 q^{17} - 18 q^{19} - 126 q^{20} + 183 q^{22} + 54 q^{23} - 1515 q^{25} + 282 q^{26} - 414 q^{28} + 168 q^{29} - 246 q^{31} - 300 q^{32} - 900 q^{34} + 315 q^{35} - 75 q^{37} + 18 q^{38} + 288 q^{40} + 414 q^{41} + 24 q^{43} - 192 q^{44} - 351 q^{46} + 48 q^{47} - 180 q^{49} - 123 q^{50} + 924 q^{52} - 177 q^{53} + 651 q^{55} + 162 q^{56} - 387 q^{58} + 348 q^{59} + 345 q^{61} - 873 q^{62} - 3453 q^{64} - 525 q^{65} + 216 q^{67} + 342 q^{68} - 546 q^{70} - 624 q^{71} - 39 q^{73} - 1182 q^{74} + 621 q^{76} - 255 q^{77} - 507 q^{79} - 612 q^{80} - 1347 q^{82} + 72 q^{83} - 204 q^{85} - 255 q^{86} + 1485 q^{88} + 1074 q^{89} + 876 q^{91} - 87 q^{92} + 243 q^{94} - 42 q^{95} + 1257 q^{97} - 1125 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{3}^{\mathrm{old}}(1143, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1143, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(127, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(381, [\chi])\)\(^{\oplus 2}\)