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Properties

Label 1143.3.bo
Level $1143$
Weight $3$
Character orbit 1143.bo
Rep. character $\chi_{1143}(10,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1260$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1143.bo (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 127 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 3120 1284 1836
Cusp forms 3024 1260 1764
Eisenstein series 96 24 72

Trace form

\( 1260 q + 5 q^{2} - 433 q^{4} + 14 q^{5} - 2 q^{7} - 66 q^{8} + O(q^{10}) \) \( 1260 q + 5 q^{2} - 433 q^{4} + 14 q^{5} - 2 q^{7} - 66 q^{8} - 14 q^{10} + 42 q^{11} - 16 q^{13} + 28 q^{14} - 837 q^{16} + 18 q^{17} - 208 q^{19} + 39 q^{22} - 20 q^{23} + 910 q^{25} - 326 q^{26} + 477 q^{28} - 139 q^{29} - 11 q^{31} + 237 q^{32} + 194 q^{34} - 157 q^{35} - 27 q^{37} + 37 q^{38} + 42 q^{40} - 232 q^{41} - 169 q^{43} + 334 q^{44} + 305 q^{46} - 51 q^{47} - 643 q^{49} - 456 q^{50} + 166 q^{52} - 136 q^{53} + 337 q^{55} - 4 q^{56} + 240 q^{58} - 159 q^{59} - 214 q^{61} + 635 q^{62} - 1770 q^{64} + 369 q^{65} - 144 q^{67} - 156 q^{68} - 211 q^{70} + 339 q^{71} - 544 q^{73} + 903 q^{74} - 397 q^{76} + 371 q^{77} + 783 q^{79} - 742 q^{80} + 652 q^{82} - 248 q^{83} - 468 q^{85} - 805 q^{86} + 912 q^{88} - 378 q^{89} + 388 q^{91} + 1701 q^{92} + 228 q^{94} - 672 q^{95} + 616 q^{97} + 1095 q^{98} + O(q^{100}) \)

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

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