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Properties

Label 3640.2.hn
Level $3640$
Weight $2$
Character orbit 3640.hn
Rep. character $\chi_{3640}(1739,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1328$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.hn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3640 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3640, [\chi])\).

Total New Old
Modular forms 1360 1360 0
Cusp forms 1328 1328 0
Eisenstein series 32 32 0

Trace form

\( 1328 q + 2 q^{4} + 1288 q^{9} + O(q^{10}) \) \( 1328 q + 2 q^{4} + 1288 q^{9} + 4 q^{14} - 2 q^{16} - 24 q^{19} - 12 q^{20} - 48 q^{24} - 4 q^{25} - 6 q^{26} - 24 q^{30} + 24 q^{34} - 12 q^{35} - 14 q^{36} - 6 q^{40} + 60 q^{44} + 54 q^{46} - 4 q^{49} - 39 q^{50} - 32 q^{51} - 18 q^{54} + 38 q^{56} + 36 q^{59} - 57 q^{60} - 64 q^{64} - 12 q^{65} + 6 q^{66} - 30 q^{70} - 14 q^{74} - 6 q^{75} - 120 q^{80} + 1168 q^{81} + 6 q^{84} - 42 q^{86} - 12 q^{89} + 4 q^{91} - 60 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3640, [\chi])\) into newform subspaces

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