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Note: Search results may be incomplete due to uncomputed quantities: atkin_lehner_string (110727 objects)

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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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1386.4.a.o	$1386$	$4$	1386.a	1.a	$1$	$2$	$2$	$81.777$	\(\Q(\sqrt{193}) \)	None	✓	$1$	$0$	\(-4\)	\(0\)	\(-19\)	\(14\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}+(-9-\beta )q^{5}+7q^{7}+\cdots\)
1386.4.a.bf	$1386$	$4$	1386.a	1.a	$1$	$3$	$3$	$81.777$	3.3.195128.1	None	✓	$1$	$0$	\(-6\)	\(0\)	\(11\)	\(21\)		$+$	$+$	$-$	$-$	$+$	$3^{2}$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}+(4+\beta _{2})q^{5}+7q^{7}+\cdots\)

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