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Properties

Label 1287.2.dh
Level $1287$
Weight $2$
Character orbit 1287.dh
Rep. character $\chi_{1287}(140,\cdot)$
Character field $\Q(\zeta_{30})$
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.dh (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1287 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 1312 q - 15 q^{2} - 3 q^{3} - 157 q^{4} - 15 q^{6} - 9 q^{9} + O(q^{10}) \) \( 1312 q - 15 q^{2} - 3 q^{3} - 157 q^{4} - 15 q^{6} - 9 q^{9} - 12 q^{11} - 30 q^{12} - 5 q^{13} - 18 q^{14} - 27 q^{15} + 159 q^{16} - 30 q^{19} - 18 q^{20} + 12 q^{22} - 15 q^{24} + 142 q^{25} + 96 q^{26} - 24 q^{27} - 30 q^{28} - 60 q^{29} - 95 q^{30} + 15 q^{33} + 12 q^{34} - 75 q^{35} + 59 q^{36} - 18 q^{37} - 54 q^{38} - 65 q^{39} - 30 q^{40} - 30 q^{41} + 59 q^{42} - 12 q^{44} - 54 q^{45} - 30 q^{46} + 25 q^{48} - 286 q^{49} - 180 q^{50} - 60 q^{51} - 5 q^{52} - 13 q^{55} - 9 q^{58} - 9 q^{59} - 42 q^{60} - 10 q^{61} - 15 q^{63} + 276 q^{64} - 25 q^{66} + 21 q^{69} - 51 q^{70} - 24 q^{71} - 15 q^{72} - 13 q^{75} + 36 q^{77} + 28 q^{78} - 10 q^{79} - 18 q^{80} - 49 q^{81} - 14 q^{82} + 45 q^{83} + 210 q^{84} - 15 q^{85} + 24 q^{86} + 46 q^{88} - 30 q^{89} - 220 q^{90} + 20 q^{91} - 10 q^{94} - 15 q^{95} - 45 q^{96} - 66 q^{99} + O(q^{100}) \)

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.