Properties

Label 1287.2.j
Level $1287$
Weight $2$
Character orbit 1287.j
Rep. character $\chi_{1287}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $280$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
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 344 280 64
Cusp forms 328 280 48
Eisenstein series 16 0 16

Trace form

\( 280 q - 140 q^{4} - 12 q^{6} + 8 q^{7} + 12 q^{8} + O(q^{10}) \) \( 280 q - 140 q^{4} - 12 q^{6} + 8 q^{7} + 12 q^{8} - 12 q^{12} - 2 q^{13} - 16 q^{14} - 16 q^{15} - 140 q^{16} - 4 q^{18} + 2 q^{19} + 64 q^{23} + 12 q^{24} - 140 q^{25} - 12 q^{26} - 16 q^{28} - 4 q^{30} + 8 q^{31} - 12 q^{32} + 12 q^{35} - 22 q^{36} + 2 q^{37} - 14 q^{38} - 4 q^{39} + 16 q^{41} - 16 q^{42} - 16 q^{43} + 42 q^{45} - 22 q^{47} + 46 q^{48} + 288 q^{49} - 88 q^{50} - 18 q^{51} + 34 q^{52} + 48 q^{53} + 86 q^{54} + 136 q^{56} - 20 q^{57} + 36 q^{58} + 40 q^{59} - 100 q^{60} - 28 q^{61} - 6 q^{62} - 2 q^{63} + 316 q^{64} - 24 q^{65} - 10 q^{66} - 28 q^{67} - 104 q^{68} - 2 q^{69} + 16 q^{72} - 28 q^{73} + 80 q^{74} + 12 q^{75} - 16 q^{76} - 16 q^{77} - 90 q^{78} + 2 q^{79} - 38 q^{80} + 16 q^{81} + 6 q^{82} + 28 q^{83} - 96 q^{84} + 24 q^{85} - 44 q^{86} + 4 q^{87} - 12 q^{89} + 10 q^{90} - 22 q^{91} - 6 q^{92} - 92 q^{93} - 72 q^{94} + 8 q^{95} + 156 q^{96} + 92 q^{97} + 76 q^{98} + O(q^{100}) \)

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

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