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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
209.2.a.a	$209$	$2$	209.a	1.a	$1$	$1$	$1$	$1.669$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-3q^{5}-4q^{7}-2q^{9}+\cdots\)
209.2.a.b	$209$	$2$	209.a	1.a	$1$	$2$	$2$	$1.669$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1-\beta )q^{3}-q^{5}+(-2-\beta )q^{6}+\cdots\)

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