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Properties

Label 1287.2.r
Level $1287$
Weight $2$
Character orbit 1287.r
Rep. character $\chi_{1287}(329,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $328$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1287 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 344 344 0
Cusp forms 328 328 0
Eisenstein series 16 16 0

Trace form

\( 328 q - 2 q^{3} - 324 q^{4} - 6 q^{9} + O(q^{10}) \) \( 328 q - 2 q^{3} - 324 q^{4} - 6 q^{9} - 6 q^{11} - 10 q^{12} - 12 q^{14} + 6 q^{15} + 308 q^{16} - 6 q^{20} + 14 q^{22} - 6 q^{23} - 152 q^{25} + 36 q^{26} + 4 q^{27} + 9 q^{33} + 12 q^{34} - 20 q^{36} - 12 q^{37} - 66 q^{38} + 8 q^{42} - 12 q^{44} + 24 q^{45} + 4 q^{48} - 138 q^{49} + 3 q^{55} + 60 q^{56} - 12 q^{59} - 42 q^{60} - 296 q^{64} - 60 q^{66} - 6 q^{67} - 30 q^{69} + 54 q^{70} + 96 q^{71} + 48 q^{75} - 66 q^{77} - 92 q^{78} - 18 q^{80} + 2 q^{81} + 4 q^{82} + 24 q^{86} - 38 q^{88} - 30 q^{89} - 10 q^{91} - 30 q^{92} - 24 q^{93} - 6 q^{97} - 66 q^{99} + O(q^{100}) \)

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.