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Properties

Label 3920.2.fj
Level $3920$
Weight $2$
Character orbit 3920.fj
Rep. character $\chi_{3920}(157,\cdot)$
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.fj (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

\( 16032 q - 26 q^{2} - 44 q^{3} - 22 q^{5} - 56 q^{6} - 8 q^{8} - 1320 q^{9} + O(q^{10}) \) \( 16032 q - 26 q^{2} - 44 q^{3} - 22 q^{5} - 56 q^{6} - 8 q^{8} - 1320 q^{9} - 22 q^{10} - 52 q^{11} - 22 q^{12} - 56 q^{13} - 40 q^{15} - 52 q^{16} - 44 q^{17} - 26 q^{18} - 28 q^{20} - 48 q^{21} - 28 q^{22} + 36 q^{24} - 44 q^{26} - 56 q^{27} - 6 q^{28} + 16 q^{30} - 144 q^{31} - 26 q^{32} - 44 q^{33} - 56 q^{34} - 2 q^{35} - 72 q^{36} - 52 q^{37} - 12 q^{38} - 24 q^{39} + 8 q^{40} - 18 q^{42} - 4 q^{45} - 52 q^{46} - 44 q^{47} - 48 q^{50} - 52 q^{51} + 8 q^{52} + 60 q^{54} - 48 q^{56} - 60 q^{57} - 14 q^{58} + 48 q^{59} - 20 q^{60} - 44 q^{61} - 56 q^{62} - 76 q^{63} - 52 q^{65} + 28 q^{66} + 30 q^{68} - 52 q^{70} + 242 q^{72} - 44 q^{74} - 22 q^{75} - 56 q^{76} - 140 q^{78} - 150 q^{80} + 1168 q^{81} - 90 q^{82} - 56 q^{83} + 60 q^{84} - 60 q^{86} + 36 q^{87} + 244 q^{88} + 476 q^{90} - 64 q^{91} - 72 q^{92} - 112 q^{93} - 72 q^{94} - 28 q^{95} - 296 q^{96} - 452 q^{98} + 24 q^{99} + O(q^{100}) \)

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.