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Properties

Label 1288.2.be
Level $1288$
Weight $2$
Character orbit 1288.be
Rep. character $\chi_{1288}(93,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $352$
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.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 392 352 40
Cusp forms 376 352 24
Eisenstein series 16 0 16

Trace form

\( 352 q - 12 q^{8} + 176 q^{9} + O(q^{10}) \) \( 352 q - 12 q^{8} + 176 q^{9} + 6 q^{10} - 10 q^{12} + 32 q^{14} - 8 q^{16} + 10 q^{18} - 40 q^{20} - 24 q^{22} - 32 q^{24} + 176 q^{25} + 16 q^{26} - 6 q^{28} - 20 q^{30} - 24 q^{31} + 30 q^{32} - 32 q^{34} + 40 q^{36} - 6 q^{38} - 42 q^{42} + 30 q^{44} - 64 q^{47} + 44 q^{48} + 16 q^{49} - 52 q^{50} + 12 q^{52} - 26 q^{54} - 64 q^{55} + 40 q^{56} - 32 q^{57} + 38 q^{58} - 16 q^{60} - 16 q^{62} - 80 q^{63} - 84 q^{64} + 80 q^{66} - 4 q^{68} + 122 q^{70} - 64 q^{71} - 32 q^{72} + 16 q^{73} - 6 q^{74} - 128 q^{76} - 52 q^{78} - 76 q^{80} - 176 q^{81} + 60 q^{82} - 60 q^{84} - 62 q^{86} + 48 q^{87} + 46 q^{88} - 164 q^{90} - 12 q^{94} + 24 q^{95} - 100 q^{96} - 96 q^{97} - 34 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)