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Properties

Label 3920.2.t
Level $3920$
Weight $2$
Character orbit 3920.t
Rep. character $\chi_{3920}(1667,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $964$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1376 1004 372
Cusp forms 1312 964 348
Eisenstein series 64 40 24

Trace form

\( 964 q + 2 q^{2} - 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} - 924 q^{9} + O(q^{10}) \) \( 964 q + 2 q^{2} - 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} - 924 q^{9} + 6 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} - 12 q^{15} + 4 q^{17} - 10 q^{18} + 8 q^{19} - 4 q^{20} - 16 q^{22} + 4 q^{23} - 12 q^{24} - 12 q^{26} + 36 q^{30} + 32 q^{32} + 4 q^{33} - 8 q^{34} + 12 q^{36} + 4 q^{37} + 28 q^{38} - 32 q^{40} - 52 q^{43} - 8 q^{44} + 6 q^{45} + 20 q^{46} + 24 q^{47} + 20 q^{48} + 14 q^{50} + 12 q^{51} + 56 q^{52} - 36 q^{54} + 4 q^{55} - 12 q^{57} - 8 q^{58} + 16 q^{59} - 52 q^{60} + 20 q^{61} + 36 q^{62} - 16 q^{64} + 4 q^{65} - 36 q^{66} - 20 q^{67} - 16 q^{68} + 4 q^{69} - 72 q^{71} + 8 q^{72} + 8 q^{73} - 52 q^{74} + 40 q^{75} + 4 q^{76} - 44 q^{78} - 100 q^{80} + 812 q^{81} - 20 q^{82} - 4 q^{86} + 60 q^{87} + 32 q^{88} - 18 q^{90} + 68 q^{92} + 64 q^{93} - 20 q^{94} - 40 q^{95} + 24 q^{96} + 4 q^{97} - 44 q^{99} + O(q^{100}) \)

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.

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)