Properties

Label 3920.1.br
Level $3920$
Weight $1$
Character orbit 3920.br
Rep. character $\chi_{3920}(129,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $672$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3920.br (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(672\)
Trace bound: \(3\)

Dimensions

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

Total New Old
Modular forms 112 12 100
Cusp forms 16 4 12
Eisenstein series 96 8 88

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q + O(q^{10}) \) \( 4q - 2q^{11} + 4q^{15} - 2q^{25} - 4q^{29} + 2q^{39} + 2q^{51} + 2q^{65} - 8q^{71} - 2q^{79} + 2q^{81} - 4q^{85} + O(q^{100}) \)

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.br.a \(2\) \(1.956\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{11}-q^{13}+\cdots\)
3920.1.br.b \(2\) \(1.956\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(1\) \(0\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{11}+q^{13}+\cdots\)

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

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