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Properties

Label 1287.2.de
Level $1287$
Weight $2$
Character orbit 1287.de
Rep. character $\chi_{1287}(25,\cdot)$
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.de (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

\( 1312 q - 12 q^{3} - 166 q^{4} + 12 q^{9} + O(q^{10}) \) \( 1312 q - 12 q^{3} - 166 q^{4} + 12 q^{9} - 48 q^{10} - 36 q^{12} - 3 q^{13} + 10 q^{14} + 138 q^{16} + 8 q^{17} - 16 q^{23} - 154 q^{25} - 60 q^{26} + 12 q^{27} + 20 q^{29} + 8 q^{30} + 12 q^{35} - 120 q^{36} - 60 q^{38} - 85 q^{39} - 34 q^{40} - 46 q^{42} - 16 q^{43} - 50 q^{48} - 146 q^{49} - 44 q^{51} - 23 q^{52} - 56 q^{53} - 12 q^{55} - 164 q^{56} - 6 q^{61} + 56 q^{62} + 192 q^{64} + 20 q^{65} + 42 q^{66} + 112 q^{68} - 126 q^{69} + 42 q^{74} - 28 q^{75} + 36 q^{77} + 8 q^{78} + 18 q^{79} - 20 q^{81} - 8 q^{82} - 24 q^{87} - 92 q^{88} - 24 q^{90} - 20 q^{91} + 44 q^{92} - 14 q^{94} - 58 q^{95} + O(q^{100}) \)

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.