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Properties

Label 1287.2.bw
Level $1287$
Weight $2$
Character orbit 1287.bw
Rep. character $\chi_{1287}(116,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $224$
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.bw (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
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 704 224 480
Cusp forms 640 224 416
Eisenstein series 64 0 64

Trace form

\( 224 q + 56 q^{4} + O(q^{10}) \) \( 224 q + 56 q^{4} - 80 q^{16} + 88 q^{22} - 32 q^{25} - 72 q^{49} + 80 q^{52} - 16 q^{55} - 40 q^{61} + 8 q^{64} + 80 q^{79} - 176 q^{82} + 104 q^{88} - 56 q^{91} + 80 q^{94} + O(q^{100}) \)

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

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