Properties

Label 1140.2.bd
Level $1140$
Weight $2$
Character orbit 1140.bd
Rep. character $\chi_{1140}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
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 496 320 176
Cusp forms 464 320 144
Eisenstein series 32 0 32

Trace form

\( 320q - 2q^{4} - 4q^{9} + O(q^{10}) \) \( 320q - 2q^{4} - 4q^{9} - 2q^{10} - 8q^{13} + 2q^{16} - 8q^{24} + 160q^{25} + 16q^{30} + 44q^{33} + 10q^{34} + 28q^{36} - 16q^{37} - 28q^{40} - 2q^{42} - 8q^{46} + 18q^{48} - 368q^{49} + 16q^{52} + 30q^{54} - 24q^{57} + 32q^{58} + 40q^{61} - 32q^{64} - 12q^{66} - 12q^{70} - 16q^{72} - 36q^{76} - 76q^{78} + 20q^{81} + 40q^{82} - 24q^{84} + 16q^{85} - 104q^{88} + 18q^{90} - 36q^{94} + 156q^{96} + 24q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)