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Properties

Label 1288.2.ch
Level $1288$
Weight $2$
Character orbit 1288.ch
Rep. character $\chi_{1288}(5,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $3760$
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.ch (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1288 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 3920 3920 0
Cusp forms 3760 3760 0
Eisenstein series 160 160 0

Trace form

\( 3760 q - 11 q^{2} - 11 q^{4} - 44 q^{7} - 32 q^{8} + 162 q^{9} + O(q^{10}) \) \( 3760 q - 11 q^{2} - 11 q^{4} - 44 q^{7} - 32 q^{8} + 162 q^{9} - 33 q^{10} - 27 q^{12} - 22 q^{14} - 88 q^{15} - 19 q^{16} - 66 q^{17} - 21 q^{18} - 24 q^{23} - 78 q^{24} - 190 q^{25} - 45 q^{26} - 22 q^{28} - 11 q^{30} - 54 q^{31} - q^{32} - 66 q^{33} - 194 q^{36} - 33 q^{38} - 6 q^{39} - 33 q^{40} + 88 q^{42} + 66 q^{44} - 21 q^{46} - 120 q^{47} - 36 q^{49} + 138 q^{50} - 57 q^{52} - 51 q^{54} - 77 q^{56} - 88 q^{57} - 76 q^{58} - 11 q^{60} - 44 q^{63} - 8 q^{64} - 22 q^{65} - 132 q^{66} - 34 q^{70} - 88 q^{71} + 79 q^{72} - 54 q^{73} - 22 q^{74} + 116 q^{78} - 22 q^{79} - 330 q^{80} + 134 q^{81} + 123 q^{82} - 22 q^{84} - 11 q^{86} - 90 q^{87} - 176 q^{88} - 66 q^{89} + 138 q^{92} - 270 q^{94} + 22 q^{95} + 135 q^{96} - 8 q^{98} + O(q^{100}) \)

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.