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Properties

Label 2940.2.bf
Level $2940$
Weight $2$
Character orbit 2940.bf
Rep. character $\chi_{2940}(851,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $640$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1408 640 768
Cusp forms 1280 640 640
Eisenstein series 128 0 128

Trace form

\( 640 q + O(q^{10}) \) \( 640 q - 10 q^{12} - 16 q^{13} - 32 q^{16} - 10 q^{18} + 88 q^{22} - 20 q^{24} + 320 q^{25} + 48 q^{34} + 40 q^{36} - 8 q^{37} + 4 q^{45} + 32 q^{46} + 36 q^{48} + 12 q^{52} + 68 q^{54} + 32 q^{58} + 14 q^{60} + 16 q^{61} - 48 q^{64} + 48 q^{66} + 48 q^{69} + 34 q^{72} + 24 q^{73} - 48 q^{76} - 152 q^{78} + 20 q^{81} - 24 q^{82} + 8 q^{88} + 36 q^{90} + 16 q^{93} - 48 q^{94} - 84 q^{96} + 96 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)