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Properties

Label 2940.2.de
Level $2940$
Weight $2$
Character orbit 2940.de
Rep. character $\chi_{2940}(11,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $5376$
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.de (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 588 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 8160 5376 2784
Cusp forms 7968 5376 2592
Eisenstein series 192 0 192

Trace form

\( 5376 q + O(q^{10}) \) \( 5376 q - 80 q^{12} - 16 q^{13} - 10 q^{18} + 4 q^{21} + 24 q^{22} - 20 q^{24} - 448 q^{25} - 72 q^{28} + 48 q^{34} + 40 q^{36} - 64 q^{37} + 54 q^{42} + 4 q^{45} + 36 q^{48} + 24 q^{49} + 12 q^{52} + 68 q^{54} + 112 q^{60} - 40 q^{61} - 48 q^{64} + 90 q^{66} - 64 q^{69} - 12 q^{70} - 22 q^{72} + 24 q^{73} - 48 q^{76} + 100 q^{78} + 160 q^{81} - 24 q^{82} + 232 q^{84} - 24 q^{88} + 36 q^{90} + 16 q^{93} + 120 q^{94} + 518 q^{96} + 96 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)