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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
85.4.a.a	$85$	$4$	85.a	1.a	$1$	$1$	$1$	$5.015$	\(\Q\)	None	✓	✓			85.4.a.a	$1$	$1$	\(3\)	\(-7\)	\(5\)	\(-22\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}-7q^{3}+q^{4}+5q^{5}-21q^{6}+\cdots\)
85.4.a.d	$85$	$4$	85.a	1.a	$1$	$2$	$2$	$5.015$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓		85.4.a.d	$1$	$1$	\(-4\)	\(-2\)	\(10\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{2}+(-1+\beta )q^{3}+(-1+\cdots)q^{4}+\cdots\)

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