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Properties

Label 2340.2.hp
Level $2340$
Weight $2$
Character orbit 2340.hp
Rep. character $\chi_{2340}(227,\cdot)$
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.hp (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

\( 1984 q - 6 q^{2} - 12 q^{5} - 8 q^{6} + O(q^{10}) \) \( 1984 q - 6 q^{2} - 12 q^{5} - 8 q^{6} - 16 q^{10} - 18 q^{12} - 4 q^{13} + 4 q^{16} - 12 q^{18} - 6 q^{20} - 16 q^{21} + 2 q^{22} + 8 q^{24} - 48 q^{26} - 12 q^{28} + 2 q^{30} - 6 q^{32} + 20 q^{33} - 16 q^{34} - 12 q^{36} - 24 q^{37} - 12 q^{38} - 4 q^{40} - 24 q^{41} + 4 q^{42} + 12 q^{45} - 16 q^{46} - 92 q^{48} + 1792 q^{49} - 6 q^{50} + 14 q^{52} + 40 q^{54} - 24 q^{56} + 24 q^{57} - 6 q^{58} - 8 q^{60} - 16 q^{61} + 12 q^{62} - 12 q^{65} - 16 q^{66} + 12 q^{70} + 42 q^{72} - 32 q^{73} - 36 q^{76} + 58 q^{78} + 144 q^{80} - 8 q^{81} - 4 q^{82} - 80 q^{84} + 16 q^{85} - 120 q^{86} + 34 q^{88} + 24 q^{90} - 12 q^{92} + 24 q^{93} - 112 q^{96} - 8 q^{97} - 66 q^{98} + O(q^{100}) \)

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.