Properties

Label 3920.2.ci
Level $3920$
Weight $2$
Character orbit 3920.ci
Rep. character $\chi_{3920}(117,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1888$
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.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2752 1952 800
Cusp forms 2624 1888 736
Eisenstein series 128 64 64

Trace form

\( 1888q + 2q^{2} + 6q^{5} - 4q^{8} - 912q^{9} + O(q^{10}) \) \( 1888q + 2q^{2} + 6q^{5} - 4q^{8} - 912q^{9} + 6q^{10} + 4q^{11} + 6q^{12} - 32q^{15} + 4q^{16} + 12q^{17} + 24q^{18} - 8q^{22} - 36q^{24} + 12q^{26} - 30q^{30} + 24q^{31} + 42q^{32} + 12q^{33} - 64q^{36} + 24q^{38} + 24q^{39} + 96q^{40} - 32q^{43} - 48q^{44} - 12q^{45} + 4q^{46} + 12q^{47} - 16q^{50} + 4q^{51} + 84q^{52} + 4q^{53} + 24q^{54} - 24q^{57} - 26q^{58} - 48q^{59} + 80q^{60} + 12q^{61} + 4q^{65} + 84q^{66} + 28q^{67} - 60q^{68} - 28q^{72} - 4q^{74} + 6q^{75} - 304q^{78} + 120q^{80} - 808q^{81} + 78q^{82} - 36q^{85} - 4q^{86} - 36q^{87} - 52q^{88} - 68q^{92} + 72q^{94} + 28q^{95} + 12q^{96} - 24q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(3920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)