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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
147.4.a.j	$147$	$4$	147.a	1.a	$1$	$2$	$2$	$8.673$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(-6\)	\(20\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-3q^{3}+(-5+2\beta )q^{4}+\cdots\)
147.4.a.l	$147$	$4$	147.a	1.a	$1$	$3$	$3$	$8.673$	3.3.57516.1	None	✓	$1$	$0$	\(1\)	\(-9\)	\(11\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(8+\beta _{1}+\beta _{2})q^{4}+\cdots\)

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