Space of modular forms of level 3920, weight 1, and Character 3920.v

• 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: $0$

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

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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3920.1.v.a	$3920$	$1$	3920.v	140.j	$4$	$8$	$4$	$1.956$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	3920.1.v.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}^{5}q^{5}-\zeta_{16}^{4}q^{9}+(\zeta_{16}^{5}+\zeta_{16}^{7}+\cdots)q^{13}+\cdots\)

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

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