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Properties

Label 1287.2.i
Level $1287$
Weight $2$
Character orbit 1287.i
Rep. character $\chi_{1287}(430,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $240$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 344 240 104
Cusp forms 328 240 88
Eisenstein series 16 0 16

Trace form

\( 240 q + 2 q^{3} - 120 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{9} + O(q^{10}) \) \( 240 q + 2 q^{3} - 120 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{9} + 8 q^{11} + 28 q^{12} - 28 q^{14} + 16 q^{15} - 120 q^{16} + 24 q^{17} - 36 q^{18} - 12 q^{20} + 8 q^{21} + 4 q^{23} + 12 q^{24} - 126 q^{25} - 24 q^{26} + 8 q^{27} - 24 q^{29} + 52 q^{30} - 6 q^{31} - 4 q^{33} + 24 q^{34} - 24 q^{35} - 44 q^{36} + 12 q^{37} + 46 q^{38} + 24 q^{40} - 8 q^{41} - 98 q^{42} - 40 q^{44} - 14 q^{45} + 32 q^{47} + 38 q^{48} - 144 q^{49} + 80 q^{50} + 68 q^{51} + 72 q^{53} + 28 q^{54} + 12 q^{55} - 44 q^{56} - 56 q^{57} + 46 q^{59} - 120 q^{60} - 24 q^{61} + 24 q^{62} - 16 q^{63} + 192 q^{64} + 10 q^{66} - 6 q^{67} - 68 q^{68} + 38 q^{69} - 24 q^{70} - 132 q^{71} + 16 q^{72} - 28 q^{74} - 98 q^{75} + 24 q^{76} + 10 q^{78} + 40 q^{80} + 50 q^{81} - 56 q^{83} - 20 q^{84} + 16 q^{86} + 4 q^{87} - 24 q^{89} + 44 q^{90} + 6 q^{92} - 150 q^{93} - 24 q^{94} - 88 q^{95} + 220 q^{96} - 6 q^{97} + 232 q^{98} + 10 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1287, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)