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Properties

Label 1287.2.bz
Level $1287$
Weight $2$
Character orbit 1287.bz
Rep. character $\chi_{1287}(64,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $272$
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.bz (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 704 288 416
Cusp forms 640 272 368
Eisenstein series 64 16 48

Trace form

\( 272 q + 60 q^{4} + O(q^{10}) \) \( 272 q + 60 q^{4} - 32 q^{10} - 10 q^{13} + 38 q^{14} - 72 q^{16} + 8 q^{17} - 52 q^{22} - 4 q^{23} + 66 q^{25} - 12 q^{26} - 14 q^{29} + 68 q^{35} + 82 q^{38} - 114 q^{40} - 64 q^{43} + 90 q^{49} - 18 q^{52} + 40 q^{53} - 74 q^{55} + 40 q^{56} + 6 q^{61} + 68 q^{62} + 68 q^{64} + 60 q^{65} - 110 q^{68} + 56 q^{74} + 24 q^{77} + 30 q^{79} + 18 q^{82} + 14 q^{88} + 46 q^{91} + 62 q^{92} - 40 q^{94} - 86 q^{95} + O(q^{100}) \)

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

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