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Properties

Label 1143.2.by
Level $1143$
Weight $2$
Character orbit 1143.by
Rep. character $\chi_{1143}(80,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $528$
Sturm bound $256$

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Defining parameters

Level: \( N \) \(=\) \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1143.by (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 381 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1143, [\chi])\).

Total New Old
Modular forms 1584 528 1056
Cusp forms 1488 528 960
Eisenstein series 96 0 96

Trace form

\( 528 q + 96 q^{4} - 40 q^{7} + O(q^{10}) \) \( 528 q + 96 q^{4} - 40 q^{7} - 16 q^{13} - 124 q^{16} - 24 q^{19} + 8 q^{22} - 112 q^{25} - 276 q^{28} - 8 q^{31} - 88 q^{34} - 28 q^{37} + 76 q^{43} + 100 q^{46} - 148 q^{49} - 60 q^{52} + 48 q^{55} + 92 q^{58} + 52 q^{61} + 224 q^{64} - 40 q^{67} + 40 q^{70} + 8 q^{73} + 152 q^{76} + 56 q^{79} + 136 q^{82} - 28 q^{85} - 240 q^{88} + 24 q^{91} + 232 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1143, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1143, [\chi])\) into lower level spaces

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