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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	5	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
315.4.a.e	$315$	$4$	315.a	1.a	$1$	$1$	$1$	$18.586$	\(\Q\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(5\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+q^{4}+5q^{5}+7q^{7}-21q^{8}+\cdots\)
315.4.a.o	$315$	$4$	315.a	1.a	$1$	$3$	$3$	$18.586$	3.3.22952.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(15\)	\(21\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(5-2\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)

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