Properties

Label 3920.2.fh
Level $3920$
Weight $2$
Character orbit 3920.fh
Rep. character $\chi_{3920}(123,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $16032$
Sturm bound $1344$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3920.fh (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

\( 16032q - 26q^{2} - 26q^{5} - 40q^{6} - 48q^{7} - 32q^{8} - 1320q^{9} + O(q^{10}) \) \( 16032q - 26q^{2} - 26q^{5} - 40q^{6} - 48q^{7} - 32q^{8} - 1320q^{9} - 34q^{10} - 52q^{11} - 14q^{12} - 40q^{13} + 24q^{15} - 52q^{16} - 52q^{17} - 26q^{18} - 44q^{20} - 48q^{21} - 12q^{22} - 52q^{23} - 12q^{24} - 52q^{26} + 10q^{28} + 16q^{30} - 26q^{32} - 52q^{33} + 40q^{34} - 22q^{35} - 72q^{36} - 52q^{37} - 12q^{38} - 56q^{40} + 22q^{42} - 40q^{43} - 52q^{45} - 52q^{46} + 24q^{47} - 4q^{48} - 48q^{50} - 52q^{51} - 40q^{52} - 68q^{54} - 40q^{55} - 48q^{56} - 60q^{57} - 46q^{58} + 16q^{59} - 44q^{60} - 52q^{61} + 32q^{62} + 12q^{63} - 52q^{65} - 76q^{66} - 48q^{67} - 18q^{68} + 24q^{69} + 68q^{70} - 240q^{71} - 238q^{72} - 44q^{74} - 14q^{75} - 40q^{76} - 28q^{78} - 50q^{80} + 1168q^{81} - 250q^{82} + 60q^{84} - 40q^{85} - 44q^{86} - 52q^{87} - 296q^{88} - 556q^{90} - 32q^{91} - 40q^{92} - 112q^{93} - 24q^{94} + 128q^{96} - 96q^{97} + 368q^{98} + 24q^{99} + O(q^{100}) \)

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

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