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Properties

Label 1288.2.b
Level $1288$
Weight $2$
Character orbit 1288.b
Rep. character $\chi_{1288}(645,\cdot)$
Character field $\Q$
Dimension $132$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 196 132 64
Cusp forms 188 132 56
Eisenstein series 8 0 8

Trace form

\( 132 q - 6 q^{6} + 6 q^{8} - 132 q^{9} + O(q^{10}) \) \( 132 q - 6 q^{6} + 6 q^{8} - 132 q^{9} + 16 q^{10} - 22 q^{12} + 16 q^{16} + 8 q^{17} + 34 q^{18} - 28 q^{20} - 16 q^{22} + 12 q^{23} - 4 q^{24} - 140 q^{25} - 26 q^{26} - 32 q^{30} - 16 q^{33} - 20 q^{34} + 6 q^{36} - 36 q^{38} + 8 q^{39} + 44 q^{40} + 8 q^{41} + 20 q^{42} + 24 q^{44} + 34 q^{48} + 132 q^{49} + 48 q^{50} + 22 q^{52} + 50 q^{54} - 64 q^{55} + 16 q^{57} + 34 q^{58} - 12 q^{60} + 74 q^{62} + 6 q^{64} - 32 q^{65} - 76 q^{66} - 28 q^{68} - 24 q^{70} + 56 q^{71} - 58 q^{72} + 40 q^{73} + 8 q^{74} + 40 q^{76} + 10 q^{78} - 64 q^{80} + 116 q^{81} - 42 q^{82} - 20 q^{86} - 88 q^{87} - 100 q^{88} + 40 q^{89} - 96 q^{90} + 54 q^{94} - 64 q^{95} - 66 q^{96} + 8 q^{97} + O(q^{100}) \)

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

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