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Properties

Label 1143.3.bz
Level $1143$
Weight $3$
Character orbit 1143.bz
Rep. character $\chi_{1143}(152,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1008$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1143.bz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 381 \)
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 1008 2112
Cusp forms 3024 1008 2016
Eisenstein series 96 0 96

Trace form

\( 1008 q + 320 q^{4} + 32 q^{7} + O(q^{10}) \) \( 1008 q + 320 q^{4} + 32 q^{7} - 48 q^{10} - 20 q^{13} - 716 q^{16} + 64 q^{19} + 160 q^{22} + 920 q^{25} - 180 q^{28} + 80 q^{31} - 720 q^{34} + 136 q^{37} + 208 q^{40} + 316 q^{43} + 36 q^{46} + 420 q^{49} + 384 q^{52} - 216 q^{55} + 1332 q^{58} - 396 q^{61} + 1568 q^{64} + 76 q^{67} - 80 q^{70} + 612 q^{73} - 1088 q^{76} + 364 q^{79} + 1064 q^{82} - 188 q^{85} - 376 q^{88} - 568 q^{91} + 272 q^{94} - 2508 q^{97} + O(q^{100}) \)

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

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