Properties

Label 1140.2.ca
Level $1140$
Weight $2$
Character orbit 1140.ca
Rep. character $\chi_{1140}(79,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $720$
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.ca (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1488 720 768
Cusp forms 1392 720 672
Eisenstein series 96 0 96

Trace form

\( 720q + 6q^{4} + 6q^{6} + O(q^{10}) \) \( 720q + 6q^{4} + 6q^{6} + 18q^{10} - 36q^{14} - 6q^{16} + 60q^{20} - 6q^{34} - 6q^{36} + 114q^{40} - 24q^{41} - 360q^{49} + 54q^{50} - 6q^{54} - 6q^{64} + 144q^{69} + 36q^{70} - 96q^{74} + 36q^{76} - 18q^{80} - 108q^{84} + 24q^{85} - 120q^{86} + 48q^{89} + 18q^{90} + O(q^{100}) \)

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

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