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Properties

Label 1287.2.cm
Level $1287$
Weight $2$
Character orbit 1287.cm
Rep. character $\chi_{1287}(254,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
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.cm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 688 560 128
Cusp forms 656 560 96
Eisenstein series 32 0 32

Trace form

\( 560 q - 12 q^{6} - 8 q^{7} + 36 q^{8} + O(q^{10}) \) \( 560 q - 12 q^{6} - 8 q^{7} + 36 q^{8} + 16 q^{15} + 280 q^{16} - 20 q^{18} - 8 q^{19} - 24 q^{24} + 24 q^{27} - 16 q^{28} - 48 q^{30} - 16 q^{31} - 72 q^{32} + 72 q^{35} - 4 q^{37} - 48 q^{41} - 112 q^{42} - 52 q^{45} - 72 q^{47} - 16 q^{48} - 48 q^{50} - 4 q^{52} + 80 q^{54} - 4 q^{57} + 36 q^{58} - 72 q^{59} - 4 q^{60} + 36 q^{62} - 48 q^{63} - 20 q^{66} + 28 q^{67} + 84 q^{69} - 200 q^{72} + 28 q^{73} + 60 q^{75} + 16 q^{76} - 152 q^{78} + 16 q^{81} + 164 q^{84} - 96 q^{85} - 216 q^{86} - 24 q^{87} - 228 q^{90} + 16 q^{91} - 204 q^{92} + 36 q^{93} - 108 q^{96} - 100 q^{97} + O(q^{100}) \)

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

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