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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	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
159.1.d.a	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-159}) \)	None	✓	✓			159.1.d.a	$2$	$0$	\(-1\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots\)
159.1.d.b	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-159}) \)	None	✓	✓			159.1.d.a	$2$	$0$	\(1\)	\(-2\)	\(1\)	\(-1\)	$1$		\(q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+\beta q^{5}+\cdots\)

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