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Properties

Label 2340.2.gr
Level $2340$
Weight $2$
Character orbit 2340.gr
Rep. character $\chi_{2340}(763,\cdot)$
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.gr (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

\( 1984 q + 2 q^{2} - 8 q^{5} - 4 q^{6} - 16 q^{8} + O(q^{10}) \) \( 1984 q + 2 q^{2} - 8 q^{5} - 4 q^{6} - 16 q^{8} - 4 q^{10} - 14 q^{12} - 4 q^{13} + 4 q^{16} - 8 q^{17} - 4 q^{18} - 36 q^{20} - 32 q^{21} - 14 q^{22} - 8 q^{25} - 20 q^{28} + 18 q^{30} + 2 q^{32} - 28 q^{33} - 68 q^{36} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 48 q^{42} - 44 q^{45} - 8 q^{46} + 12 q^{48} - 4 q^{50} - 18 q^{52} - 32 q^{53} - 8 q^{56} + 24 q^{57} - 14 q^{58} - 16 q^{60} - 16 q^{61} - 8 q^{62} + 12 q^{65} - 56 q^{66} + 68 q^{68} - 44 q^{70} + 14 q^{72} - 32 q^{73} + 56 q^{76} + 48 q^{77} + 18 q^{78} + 6 q^{80} - 8 q^{81} - 12 q^{82} + 4 q^{85} - 44 q^{86} - 38 q^{88} - 44 q^{90} - 20 q^{92} + 8 q^{93} + 112 q^{96} - 8 q^{97} + 94 q^{98} + O(q^{100}) \)

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.