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The results below are complete, since the LMFDB contains all newforms with $Nk^2$ at most 4000

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
39.4.a.c	$39$	$4$	39.a	1.a	$1$	$3$	$3$	$2.301$	3.3.3144.1	None	✓	✓	✓	✓	39.4.a.c	$1$	$0$	\(2\)	\(9\)	\(4\)	\(30\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(3+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)

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