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Properties

Label 2940.2.cn
Level $2940$
Weight $2$
Character orbit 2940.cn
Rep. character $\chi_{2940}(83,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $7968$
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.cn (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2940 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1344\)

Dimensions

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

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

Trace form

\( 7968 q - 28 q^{6} + O(q^{10}) \) \( 7968 q - 28 q^{6} - 28 q^{10} - 14 q^{12} - 56 q^{13} - 40 q^{16} - 16 q^{18} - 40 q^{21} - 4 q^{22} - 40 q^{25} + 8 q^{28} - 4 q^{30} - 28 q^{33} - 52 q^{36} - 40 q^{37} - 28 q^{40} + 2 q^{42} - 28 q^{45} - 40 q^{46} - 28 q^{52} + 40 q^{57} + 28 q^{58} + 6 q^{60} - 112 q^{61} + 168 q^{66} - 116 q^{70} + 22 q^{72} - 56 q^{73} + 168 q^{76} - 130 q^{78} - 240 q^{81} + 112 q^{82} - 40 q^{85} + 44 q^{88} - 14 q^{90} - 80 q^{93} + 224 q^{96} + O(q^{100}) \)

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.