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Properties

Label 1287.2.cq
Level $1287$
Weight $2$
Character orbit 1287.cq
Rep. character $\chi_{1287}(16,\cdot)$
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.cq (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

\( 1312 q - 6 q^{2} - 3 q^{3} - 326 q^{4} - 6 q^{5} + 13 q^{6} + 3 q^{7} - 16 q^{8} - 9 q^{9} + O(q^{10}) \) \( 1312 q - 6 q^{2} - 3 q^{3} - 326 q^{4} - 6 q^{5} + 13 q^{6} + 3 q^{7} - 16 q^{8} - 9 q^{9} - 20 q^{10} - 16 q^{11} - 22 q^{12} - 3 q^{13} + 2 q^{14} - 21 q^{15} - 302 q^{16} - 22 q^{17} - 6 q^{19} + 7 q^{20} + 10 q^{21} + 8 q^{22} + 8 q^{23} - 3 q^{24} + 142 q^{25} - 4 q^{26} - 24 q^{27} + 6 q^{28} + 8 q^{29} + 39 q^{30} - 6 q^{31} + 32 q^{32} + 34 q^{33} - 20 q^{34} - 33 q^{35} + 15 q^{36} - 6 q^{37} + 18 q^{38} + 10 q^{39} + 34 q^{40} + 3 q^{41} - 31 q^{42} + 8 q^{43} - 84 q^{44} - 42 q^{45} - 18 q^{46} - 30 q^{47} + 27 q^{48} + 143 q^{49} + 26 q^{50} - 56 q^{51} + 33 q^{52} - 88 q^{53} + 136 q^{54} - 13 q^{55} + 98 q^{56} - 18 q^{57} + 26 q^{58} - 6 q^{59} + 88 q^{60} + 3 q^{61} - 42 q^{62} - 45 q^{63} - 292 q^{64} - 12 q^{65} - 57 q^{66} + 8 q^{67} - 2 q^{68} + 15 q^{69} - 29 q^{70} + 2 q^{71} + 27 q^{72} - 24 q^{73} - 13 q^{74} - 53 q^{75} + 32 q^{76} + 2 q^{77} - 32 q^{78} - 18 q^{79} - 100 q^{80} - 101 q^{81} + 2 q^{82} + 43 q^{83} - 125 q^{84} + 38 q^{85} - 130 q^{86} + 26 q^{87} - 52 q^{88} - 6 q^{89} + 108 q^{90} - 16 q^{91} - 24 q^{92} + 38 q^{93} - 13 q^{94} + 206 q^{95} - 33 q^{96} + 3 q^{97} + 26 q^{98} + 62 q^{99} + O(q^{100}) \)

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.