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Properties

Label 1287.2.bm
Level $1287$
Weight $2$
Character orbit 1287.bm
Rep. character $\chi_{1287}(727,\cdot)$
Character field $\Q(\zeta_{6})$
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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
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 344 280 64
Cusp forms 328 280 48
Eisenstein series 16 0 16

Trace form

\( 280 q + 140 q^{4} + O(q^{10}) \) \( 280 q + 140 q^{4} - 24 q^{12} + 2 q^{13} + 16 q^{14} - 140 q^{16} - 40 q^{23} + 140 q^{25} + 24 q^{26} + 12 q^{27} - 40 q^{30} - 24 q^{35} - 32 q^{36} - 34 q^{38} + 8 q^{39} - 46 q^{42} - 16 q^{43} - 6 q^{48} + 136 q^{49} + 64 q^{51} + 10 q^{52} - 48 q^{53} - 28 q^{56} + 28 q^{61} + 48 q^{62} - 352 q^{64} - 30 q^{65} - 10 q^{66} - 104 q^{68} - 84 q^{69} + 32 q^{74} - 16 q^{75} - 16 q^{77} - 80 q^{78} + 4 q^{79} - 96 q^{81} - 24 q^{82} + 92 q^{87} - 44 q^{90} - 12 q^{91} + 218 q^{92} - 36 q^{94} - 48 q^{95} + O(q^{100}) \)

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

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