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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	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
578.2.a.f	$578$	$2$	578.a	1.a	$1$	$3$	$3$	$4.615$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(-3\)	\(3\)	\(0\)	\(9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
578.2.a.i	$578$	$2$	578.a	1.a	$1$	$4$	$4$	$4.615$	\(\Q(\zeta_{16})^+\)	None	✓	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+2\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)

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