Properties

Label 3920.1.v
Level $3920$
Weight $1$
Character orbit 3920.v
Rep. character $\chi_{3920}(783,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $1$
Sturm bound $672$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3920.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(672\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3920, [\chi])\).

Total New Old
Modular forms 128 8 120
Cusp forms 32 8 24
Eisenstein series 96 0 96

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q + O(q^{10}) \) \( 8q - 8q^{53} - 8q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3920, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3920.1.v.a \(8\) \(1.956\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{5}-\zeta_{16}^{4}q^{9}+(\zeta_{16}^{5}+\zeta_{16}^{7}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3920, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)