Properties

Label 2940.2.dj
Level $2940$
Weight $2$
Character orbit 2940.dj
Rep. character $\chi_{2940}(179,\cdot)$
Character field $\Q(\zeta_{42})$
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.dj (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2940 \)
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 8160 0
Cusp forms 7968 7968 0
Eisenstein series 192 192 0

Trace form

\( 7968 q - 52 q^{4} - 12 q^{6} - 52 q^{9} + O(q^{10}) \) \( 7968 q - 52 q^{4} - 12 q^{6} - 52 q^{9} - 34 q^{10} - 52 q^{16} - 64 q^{21} - 32 q^{24} - 56 q^{25} - 19 q^{30} - 136 q^{34} - 36 q^{36} - 66 q^{40} - 6 q^{45} - 16 q^{46} - 88 q^{49} - 16 q^{54} - 30 q^{60} - 104 q^{61} - 64 q^{64} + 54 q^{66} + 68 q^{70} - 312 q^{76} - 212 q^{81} - 36 q^{84} - 80 q^{85} + 183 q^{90} - 48 q^{94} - 90 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2940, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.