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Properties

Label 2940.2.bt
Level $2940$
Weight $2$
Character orbit 2940.bt
Rep. character $\chi_{2940}(67,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $960$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2940.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2940, [\chi])\).

Total New Old
Modular forms 2816 960 1856
Cusp forms 2560 960 1600
Eisenstein series 256 0 256

Trace form

\( 960 q - 24 q^{8} + O(q^{10}) \) \( 960 q - 24 q^{8} - 16 q^{16} + 32 q^{26} - 8 q^{33} + 12 q^{38} - 20 q^{40} + 32 q^{41} - 96 q^{46} + 32 q^{48} - 72 q^{50} + 76 q^{52} + 64 q^{58} + 20 q^{60} + 144 q^{62} + 24 q^{66} + 44 q^{68} + 12 q^{72} - 16 q^{73} + 96 q^{76} + 96 q^{78} + 36 q^{80} + 480 q^{81} - 4 q^{82} + 96 q^{85} + 112 q^{86} + 4 q^{88} + 24 q^{90} + 72 q^{92} - 32 q^{93} - 80 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2940, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2940, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)