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Properties

Label 3920.2.ft
Level $3920$
Weight $2$
Character orbit 3920.ft
Rep. character $\chi_{3920}(59,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $16032$
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.ft (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3920 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 16224 16224 0
Cusp forms 16032 16032 0
Eisenstein series 192 192 0

Trace form

\( 16032 q - 52 q^{4} - 22 q^{5} - 56 q^{6} + O(q^{10}) \) \( 16032 q - 52 q^{4} - 22 q^{5} - 56 q^{6} - 40 q^{10} - 52 q^{11} - 24 q^{14} - 52 q^{16} - 72 q^{19} - 28 q^{20} - 60 q^{21} - 44 q^{24} - 44 q^{26} - 40 q^{29} - 8 q^{30} + 168 q^{34} - 46 q^{35} - 8 q^{36} - 104 q^{39} - 74 q^{40} + 12 q^{44} - 4 q^{45} - 36 q^{46} - 96 q^{49} - 68 q^{50} - 76 q^{51} + 112 q^{54} - 56 q^{55} - 104 q^{56} + 4 q^{59} - 34 q^{60} - 44 q^{61} - 112 q^{64} - 52 q^{65} - 116 q^{66} - 56 q^{69} + 40 q^{70} - 240 q^{71} - 96 q^{74} - 22 q^{75} - 476 q^{76} - 144 q^{80} - 1376 q^{81} - 28 q^{84} - 40 q^{85} - 44 q^{86} - 28 q^{90} - 8 q^{91} - 44 q^{94} + 88 q^{96} - 48 q^{99} + O(q^{100}) \)

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.