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Note: Search results may be incomplete due to uncomputed quantities: CM/RM discriminant (18154 objects)

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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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Results (4 matches)

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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
1547.1.e.a	$1547$	$1$	1547.e	1547.e	$2$	$1$	$1$	$0.772$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1547}) \)	None	✓	✓			1547.1.e.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-q^{3}+q^{4}-q^{7}+q^{11}-q^{12}-q^{13}+\cdots\)
1547.1.e.b	$1547$	$1$	1547.e	1547.e	$2$	$1$	$1$	$0.772$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1547}) \)	None	✓	✓			1547.1.e.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-q^{3}+q^{4}+q^{7}-q^{11}-q^{12}+q^{13}+\cdots\)
1547.1.e.c	$1547$	$1$	1547.e	1547.e	$2$	$1$	$1$	$0.772$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1547}) \)	None	✓	✓			1547.1.e.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+q^{3}+q^{4}-q^{7}+q^{11}+q^{12}+q^{13}+\cdots\)
1547.1.e.d	$1547$	$1$	1547.e	1547.e	$2$	$1$	$1$	$0.772$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1547}) \)	None	✓	✓			1547.1.e.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}-q^{13}+\cdots\)

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