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Properties

Label 3920.2.bn
Level $3920$
Weight $2$
Character orbit 3920.bn
Rep. character $\chi_{3920}(1077,\cdot)$
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.bn (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

\( 944 q + 4 q^{2} - 20 q^{8} + 912 q^{9} + O(q^{10}) \) \( 944 q + 4 q^{2} - 20 q^{8} + 912 q^{9} + 8 q^{11} - 16 q^{15} + 8 q^{16} - 16 q^{22} - 12 q^{30} - 36 q^{32} + 16 q^{36} + 48 q^{39} - 16 q^{43} + 48 q^{44} + 8 q^{46} - 8 q^{50} + 8 q^{51} + 8 q^{53} + 24 q^{57} + 92 q^{58} - 80 q^{60} + 8 q^{65} + 56 q^{67} - 8 q^{72} + 88 q^{74} - 8 q^{78} + 832 q^{81} + 12 q^{85} - 8 q^{86} + 40 q^{88} + 44 q^{92} + 56 q^{95} + 24 q^{99} + O(q^{100}) \)

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

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