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Properties

Label 1288.2.bj
Level $1288$
Weight $2$
Character orbit 1288.bj
Rep. character $\chi_{1288}(43,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1440$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1288.bj (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1288, [\chi])\).

Total New Old
Modular forms 1960 1440 520
Cusp forms 1880 1440 440
Eisenstein series 80 0 80

Trace form

\( 1440 q + 2 q^{2} - 10 q^{4} + 14 q^{6} - 4 q^{8} - 144 q^{9} + O(q^{10}) \) \( 1440 q + 2 q^{2} - 10 q^{4} + 14 q^{6} - 4 q^{8} - 144 q^{9} + 6 q^{12} - 18 q^{16} + 4 q^{18} + 8 q^{24} - 144 q^{25} - 26 q^{26} + 24 q^{27} + 22 q^{32} - 44 q^{34} + 7 q^{36} + 176 q^{40} + 77 q^{44} - 146 q^{46} + 202 q^{48} - 144 q^{49} + 9 q^{50} - 14 q^{52} - 178 q^{54} - 33 q^{58} - 24 q^{59} + 44 q^{60} + 50 q^{62} - 40 q^{64} - 32 q^{72} - 11 q^{74} - 110 q^{76} - 82 q^{78} - 144 q^{81} - 50 q^{82} - 154 q^{84} - 220 q^{86} - 11 q^{88} - 418 q^{90} + 50 q^{92} - 90 q^{94} - 236 q^{96} - 9 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1288, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)