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Properties

Label 3920.2.en
Level $3920$
Weight $2$
Character orbit 3920.en
Rep. character $\chi_{3920}(43,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $8016$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3920.en (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3920 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3920, [\chi])\).

Total New Old
Modular forms 8112 8112 0
Cusp forms 8016 8016 0
Eisenstein series 96 96 0

Trace form

\( 8016 q - 10 q^{2} - 10 q^{5} - 20 q^{6} - 24 q^{7} + 2 q^{8} + 1320 q^{9} + O(q^{10}) \) \( 8016 q - 10 q^{2} - 10 q^{5} - 20 q^{6} - 24 q^{7} + 2 q^{8} + 1320 q^{9} - 2 q^{10} - 20 q^{11} - 22 q^{12} - 20 q^{13} - 24 q^{15} - 20 q^{16} - 20 q^{17} - 28 q^{18} - 22 q^{20} - 24 q^{21} - 18 q^{22} - 20 q^{23} - 24 q^{24} - 20 q^{26} + 2 q^{28} - 4 q^{30} - 10 q^{32} - 20 q^{33} - 40 q^{34} - 14 q^{35} + 12 q^{36} - 20 q^{37} - 42 q^{38} - 70 q^{40} - 22 q^{42} - 20 q^{43} - 2 q^{45} - 20 q^{46} + 48 q^{47} - 68 q^{48} - 24 q^{50} - 20 q^{51} + 82 q^{52} + 44 q^{54} - 20 q^{55} - 24 q^{56} + 60 q^{57} - 50 q^{58} + 32 q^{59} + 14 q^{60} - 20 q^{61} + 46 q^{62} - 12 q^{63} - 20 q^{65} - 68 q^{66} - 96 q^{67} - 84 q^{68} - 24 q^{69} + 34 q^{70} + 120 q^{71} + 160 q^{72} - 40 q^{74} - 22 q^{75} - 20 q^{76} + 70 q^{78} - 100 q^{80} - 1312 q^{81} + 142 q^{82} + 48 q^{84} + 10 q^{85} - 4 q^{86} - 20 q^{87} - 88 q^{88} - 116 q^{90} - 40 q^{91} + 10 q^{92} + 40 q^{93} - 48 q^{94} - 200 q^{96} - 48 q^{97} + 100 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3920, [\chi])\) into newform subspaces

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