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Properties

Label 2340.2.fk
Level $2340$
Weight $2$
Character orbit 2340.fk
Rep. character $\chi_{2340}(799,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1984$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.fk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2340 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2340, [\chi])\).

Total New Old
Modular forms 2048 2048 0
Cusp forms 1984 1984 0
Eisenstein series 64 64 0

Trace form

\( 1984 q - 12 q^{4} - 4 q^{5} - 8 q^{9} + O(q^{10}) \) \( 1984 q - 12 q^{4} - 4 q^{5} - 8 q^{9} - 12 q^{10} - 8 q^{14} + 4 q^{16} - 18 q^{20} + 8 q^{21} + 20 q^{24} - 32 q^{26} + 8 q^{29} - 6 q^{30} - 12 q^{34} - 12 q^{36} - 4 q^{40} - 8 q^{41} - 64 q^{44} + 12 q^{45} - 8 q^{46} - 46 q^{50} - 136 q^{54} + 46 q^{60} - 16 q^{61} - 4 q^{65} - 28 q^{66} - 24 q^{69} - 14 q^{70} - 8 q^{74} + 28 q^{76} + 58 q^{80} - 8 q^{81} + 108 q^{84} + 36 q^{85} + 64 q^{86} - 32 q^{89} - 114 q^{90} + 88 q^{94} - 72 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2340, [\chi])\) into newform subspaces

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