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Properties

Label 1140.2.bh
Level $1140$
Weight $2$
Character orbit 1140.bh
Rep. character $\chi_{1140}(259,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1140.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1140, [\chi])\).

Total New Old
Modular forms 496 240 256
Cusp forms 464 240 224
Eisenstein series 32 0 32

Trace form

\( 240 q - 2 q^{4} - 2 q^{6} + 120 q^{9} + O(q^{10}) \) \( 240 q - 2 q^{4} - 2 q^{6} + 120 q^{9} - 18 q^{10} + 36 q^{14} + 2 q^{16} - 52 q^{20} - 4 q^{24} + 40 q^{26} + 6 q^{34} + 2 q^{36} + 12 q^{40} + 24 q^{41} + 56 q^{44} + 224 q^{49} + 2 q^{54} + 32 q^{61} + 40 q^{64} - 24 q^{66} - 36 q^{70} - 16 q^{74} - 8 q^{76} - 6 q^{80} - 120 q^{81} + 16 q^{85} + 120 q^{86} + 24 q^{89} - 18 q^{90} + 44 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1140, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)