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Properties

Label 2940.2.by
Level $2940$
Weight $2$
Character orbit 2940.by
Rep. character $\chi_{2940}(71,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $2688$
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.by (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 588 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4080 2688 1392
Cusp forms 3984 2688 1296
Eisenstein series 96 0 96

Trace form

\( 2688 q + O(q^{10}) \) \( 2688 q + 50 q^{12} + 16 q^{13} - 20 q^{18} - 4 q^{21} - 24 q^{22} + 20 q^{24} + 448 q^{25} + 72 q^{28} + 24 q^{34} - 40 q^{36} + 40 q^{37} + 12 q^{42} + 8 q^{45} + 84 q^{48} - 24 q^{49} + 24 q^{52} + 4 q^{54} - 70 q^{60} + 40 q^{61} + 48 q^{64} - 30 q^{66} + 88 q^{69} + 12 q^{70} - 44 q^{72} + 48 q^{73} - 24 q^{76} - 100 q^{78} - 100 q^{81} - 48 q^{82} + 110 q^{84} - 48 q^{88} - 36 q^{90} + 32 q^{93} - 120 q^{94} + 52 q^{96} + 48 q^{97} + O(q^{100}) \)

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

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