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Properties

Label 3920.2.bd
Level $3920$
Weight $2$
Character orbit 3920.bd
Rep. character $\chi_{3920}(981,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $656$
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.bd (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 656 720
Cusp forms 1312 656 656
Eisenstein series 64 0 64

Trace form

\( 656 q + 4 q^{4} - 12 q^{6} + O(q^{10}) \) \( 656 q + 4 q^{4} - 12 q^{6} + 4 q^{10} + 8 q^{11} - 12 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{19} - 8 q^{20} + 20 q^{22} - 32 q^{24} - 16 q^{26} + 24 q^{27} + 16 q^{29} + 40 q^{32} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 8 q^{43} - 40 q^{44} + 36 q^{46} + 40 q^{47} + 40 q^{48} + 4 q^{50} + 48 q^{51} + 8 q^{52} - 16 q^{53} + 84 q^{58} - 40 q^{59} + 28 q^{60} + 16 q^{61} + 80 q^{62} - 56 q^{64} + 32 q^{66} - 40 q^{67} - 8 q^{68} + 16 q^{69} + 112 q^{72} + 32 q^{74} - 64 q^{78} + 16 q^{79} + 16 q^{80} - 656 q^{81} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 60 q^{86} + 40 q^{88} - 36 q^{90} - 164 q^{92} - 48 q^{93} + 12 q^{94} + 32 q^{95} - 56 q^{96} + 72 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)