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Properties

Label 1287.2.cs
Level $1287$
Weight $2$
Character orbit 1287.cs
Rep. character $\chi_{1287}(295,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1312$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1287.cs (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1287 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1287, [\chi])\).

Total New Old
Modular forms 1376 1376 0
Cusp forms 1312 1312 0
Eisenstein series 64 64 0

Trace form

\( 1312 q + 3 q^{2} - 3 q^{3} + 163 q^{4} - 6 q^{5} - 11 q^{6} - 6 q^{7} - 16 q^{8} - 9 q^{9} + O(q^{10}) \) \( 1312 q + 3 q^{2} - 3 q^{3} + 163 q^{4} - 6 q^{5} - 11 q^{6} - 6 q^{7} - 16 q^{8} - 9 q^{9} - 20 q^{10} + 8 q^{11} - 22 q^{12} - 3 q^{13} + 2 q^{14} + 15 q^{15} + 151 q^{16} - 22 q^{17} - 6 q^{19} - 14 q^{20} + 10 q^{21} - 4 q^{22} - 16 q^{23} + 15 q^{24} + 142 q^{25} - 4 q^{26} - 24 q^{27} + 6 q^{28} - 4 q^{29} + 39 q^{30} - 6 q^{31} - 16 q^{32} - 89 q^{33} - 20 q^{34} - 33 q^{35} - 21 q^{36} - 6 q^{37} + 18 q^{38} + 67 q^{39} + 34 q^{40} - 6 q^{41} + 71 q^{42} - 16 q^{43} - 84 q^{44} - 42 q^{45} - 18 q^{46} - 30 q^{47} + 33 q^{48} - 286 q^{49} - 52 q^{50} - 56 q^{51} - 27 q^{52} - 88 q^{53} - 260 q^{54} - 13 q^{55} - 196 q^{56} - 18 q^{57} - 13 q^{58} + 3 q^{59} + 88 q^{60} - 6 q^{61} - 42 q^{62} + 81 q^{63} - 292 q^{64} - 24 q^{65} - 57 q^{66} - 16 q^{67} + 4 q^{68} - 3 q^{69} - 29 q^{70} + 2 q^{71} + 9 q^{72} - 24 q^{73} + 26 q^{74} - 53 q^{75} - 64 q^{76} + 2 q^{77} - 20 q^{78} - 18 q^{79} - 100 q^{80} + 31 q^{81} + 2 q^{82} + 43 q^{83} + 4 q^{84} - 19 q^{85} - 130 q^{86} - 88 q^{87} + 26 q^{88} - 6 q^{89} + 108 q^{90} - 16 q^{91} - 24 q^{92} - 94 q^{93} + 26 q^{94} - 103 q^{95} - 33 q^{96} - 6 q^{97} + 26 q^{98} + 62 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1287, [\chi])\) into newform subspaces

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