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Properties

Label 2940.2.l
Level $2940$
Weight $2$
Character orbit 2940.l
Rep. character $\chi_{2940}(1079,\cdot)$
Character field $\Q$
Dimension $472$
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.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 704 512 192
Cusp forms 640 472 168
Eisenstein series 64 40 24

Trace form

\( 472 q + 2 q^{4} - 2 q^{6} + 4 q^{9} + O(q^{10}) \) \( 472 q + 2 q^{4} - 2 q^{6} + 4 q^{9} + 2 q^{10} + 10 q^{16} + 18 q^{24} - 24 q^{30} + 12 q^{34} + 26 q^{36} - 2 q^{40} + 4 q^{45} + 76 q^{46} - 22 q^{54} - 42 q^{60} + 40 q^{61} + 2 q^{64} + 76 q^{66} + 20 q^{69} - 36 q^{76} - 32 q^{81} + 26 q^{90} + 60 q^{94} - 38 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)