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Properties

Label 3920.2.bc
Level $3920$
Weight $2$
Character orbit 3920.bc
Rep. character $\chi_{3920}(1371,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $640$
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.bc (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 640 736
Cusp forms 1312 640 672
Eisenstein series 64 0 64

Trace form

\( 640 q + 8 q^{4} + O(q^{10}) \) \( 640 q + 8 q^{4} - 16 q^{11} - 40 q^{16} + 56 q^{22} + 32 q^{23} - 32 q^{29} - 40 q^{32} - 32 q^{37} + 16 q^{43} + 112 q^{44} + 40 q^{46} + 8 q^{50} - 80 q^{51} - 32 q^{53} + 96 q^{58} + 56 q^{60} + 56 q^{64} - 80 q^{67} + 64 q^{71} + 72 q^{72} - 120 q^{74} + 48 q^{78} - 640 q^{81} + 88 q^{86} - 40 q^{88} + 96 q^{92} + 80 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)