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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
539.2.a.e	$539$	$2$	539.a	1.a	$1$	$2$	$2$	$4.304$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}-q^{4}-\beta q^{5}-\beta q^{6}+3q^{8}+\cdots\)
539.2.a.h	$539$	$2$	539.a	1.a	$1$	$3$	$3$	$4.304$	3.3.257.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)

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