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Properties

Label 3920.2.be
Level $3920$
Weight $2$
Character orbit 3920.be
Rep. character $\chi_{3920}(979,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $944$
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.be (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
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 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

Trace form

\( 944 q + 8 q^{4} + O(q^{10}) \) \( 944 q + 8 q^{4} + 8 q^{11} + 8 q^{16} - 16 q^{29} - 28 q^{30} + 32 q^{36} + 16 q^{39} + 24 q^{44} + 40 q^{46} + 12 q^{50} - 40 q^{51} - 20 q^{60} + 104 q^{64} + 8 q^{65} - 96 q^{71} - 128 q^{74} - 800 q^{81} + 12 q^{85} + 104 q^{86} - 64 q^{99} + O(q^{100}) \)

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

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