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Properties

Label 1287.2.dg
Level $1287$
Weight $2$
Character orbit 1287.dg
Rep. character $\chi_{1287}(49,\cdot)$
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.dg (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

\( 1312 q - 9 q^{2} - 3 q^{3} - 157 q^{4} - 9 q^{6} + 3 q^{9} + O(q^{10}) \) \( 1312 q - 9 q^{2} - 3 q^{3} - 157 q^{4} - 9 q^{6} + 3 q^{9} - 12 q^{10} - 12 q^{11} - 30 q^{12} - 3 q^{13} - 14 q^{14} + 9 q^{15} + 159 q^{16} - 22 q^{17} + 36 q^{18} - 18 q^{19} - 30 q^{21} + 12 q^{22} - 16 q^{23} - 75 q^{24} - 154 q^{25} + 12 q^{26} - 24 q^{27} - 30 q^{28} + 26 q^{29} + 23 q^{30} - 48 q^{32} - 3 q^{33} + 12 q^{34} + 51 q^{35} - 81 q^{36} - 18 q^{37} + 6 q^{38} - 7 q^{39} - 22 q^{40} - 25 q^{42} - 16 q^{43} - 54 q^{45} - 18 q^{46} + 25 q^{48} + 274 q^{49} - 8 q^{51} - 11 q^{52} - 8 q^{53} + 12 q^{54} - 3 q^{55} + 100 q^{56} - 18 q^{57} - 9 q^{58} - 9 q^{59} + 18 q^{60} - 6 q^{61} - 34 q^{62} - 9 q^{63} + 276 q^{64} + 32 q^{65} - 105 q^{66} - 80 q^{68} - 99 q^{69} + 75 q^{70} + 102 q^{71} - 57 q^{72} - 102 q^{74} + 23 q^{75} - 42 q^{77} + 32 q^{78} - 18 q^{79} + 144 q^{80} - 17 q^{81} - 14 q^{82} - 27 q^{83} + 126 q^{84} - 3 q^{85} - 60 q^{86} - 48 q^{87} - 50 q^{88} - 18 q^{89} - 24 q^{90} - 8 q^{91} - 16 q^{92} + 108 q^{93} + 58 q^{94} - 19 q^{95} - 27 q^{96} - 42 q^{98} + 18 q^{99} + O(q^{100}) \)

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.