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Properties

Label 1140.2.bc
Level $1140$
Weight $2$
Character orbit 1140.bc
Rep. character $\chi_{1140}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
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.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
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 496 160 336
Cusp forms 464 160 304
Eisenstein series 32 0 32

Trace form

\( 160 q - 2 q^{4} + 2 q^{6} - 80 q^{9} + O(q^{10}) \) \( 160 q - 2 q^{4} + 2 q^{6} - 80 q^{9} + 6 q^{10} - 24 q^{13} - 2 q^{16} - 24 q^{21} - 4 q^{24} - 80 q^{25} - 40 q^{26} - 40 q^{28} + 60 q^{32} + 66 q^{34} - 2 q^{36} - 60 q^{38} - 24 q^{41} + 20 q^{44} + 48 q^{48} - 128 q^{49} - 12 q^{52} + 48 q^{53} + 2 q^{54} - 24 q^{57} + 88 q^{58} - 6 q^{60} - 8 q^{61} + 72 q^{62} + 64 q^{64} + 8 q^{66} - 104 q^{68} - 36 q^{70} + 24 q^{73} - 80 q^{74} + 60 q^{76} + 32 q^{77} - 60 q^{78} - 16 q^{80} - 80 q^{81} + 44 q^{82} + 16 q^{85} - 84 q^{86} + 72 q^{89} - 6 q^{90} + 24 q^{92} + 8 q^{93} + 36 q^{96} + 48 q^{97} + 24 q^{98} + O(q^{100}) \)

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

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