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Properties

Label 2940.2.c
Level $2940$
Weight $2$
Character orbit 2940.c
Rep. character $\chi_{2940}(391,\cdot)$
Character field $\Q$
Dimension $160$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
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 704 160 544
Cusp forms 640 160 480
Eisenstein series 64 0 64

Trace form

\( 160 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 160 q^{9} + O(q^{10}) \) \( 160 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 160 q^{9} - 8 q^{16} - 8 q^{18} + 24 q^{22} - 160 q^{25} - 64 q^{29} + 32 q^{32} + 8 q^{36} - 80 q^{37} + 16 q^{44} + 40 q^{46} + 8 q^{50} + 96 q^{53} - 48 q^{57} + 72 q^{58} + 8 q^{64} + 16 q^{65} - 8 q^{72} + 16 q^{74} - 24 q^{78} + 160 q^{81} + 40 q^{86} - 64 q^{88} + 40 q^{92} + 16 q^{93} + O(q^{100}) \)

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

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