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Level	Weight	Analytic conductor	\(Nk^2\)	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1638.2.a.f	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
1638.2.a.w	$1638$	$2$	1638.a	1.a	$1$	$2$	$2$	$13.079$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)

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