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Properties

Label 1287.2.ec
Level $1287$
Weight $2$
Character orbit 1287.ec
Rep. character $\chi_{1287}(19,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1088$
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.ec (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 2816 1152 1664
Cusp forms 2560 1088 1472
Eisenstein series 256 64 192

Trace form

\( 1088 q + 20 q^{2} - 18 q^{4} + 12 q^{5} - 20 q^{7} + 20 q^{8} + O(q^{10}) \) \( 1088 q + 20 q^{2} - 18 q^{4} + 12 q^{5} - 20 q^{7} + 20 q^{8} + 32 q^{11} - 10 q^{13} + 24 q^{14} - 106 q^{16} + 30 q^{17} - 20 q^{19} - 30 q^{20} - 6 q^{22} + 96 q^{23} - 24 q^{26} - 20 q^{28} - 10 q^{29} + 8 q^{31} + 36 q^{34} - 40 q^{35} + 40 q^{40} - 40 q^{41} + 76 q^{44} - 120 q^{46} + 62 q^{47} - 18 q^{49} - 30 q^{50} + 30 q^{52} + 60 q^{53} - 6 q^{55} + 72 q^{56} - 128 q^{58} + 104 q^{59} + 30 q^{61} + 30 q^{62} - 92 q^{67} + 70 q^{68} + 206 q^{70} - 132 q^{71} + 10 q^{73} + 10 q^{74} + 40 q^{79} - 136 q^{80} - 150 q^{82} + 150 q^{83} - 60 q^{85} - 104 q^{86} - 126 q^{88} - 24 q^{89} + 120 q^{91} + 80 q^{92} + 30 q^{94} + 330 q^{95} - 22 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 2}\)