Properties

Label 3920.1.cx
Level $3920$
Weight $1$
Character orbit 3920.cx
Rep. character $\chi_{3920}(607,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $16$
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.cx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{12})\)
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 256 16 240
Cusp forms 64 16 48
Eisenstein series 192 0 192

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16q + O(q^{10}) \) \( 16q + 8q^{53} + 8q^{81} + O(q^{100}) \)

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.cx.a \(16\) \(1.956\) \(\Q(\zeta_{48})\) \(D_{8}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{5}q^{5}-\zeta_{48}^{20}q^{9}+(-\zeta_{48}^{15}+\cdots)q^{13}+\cdots\)

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

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