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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	3	59	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
354.4.a.b	$354$	$4$	354.a	1.a	$1$	$2$	$2$	$20.887$	\(\Q(\sqrt{51}) \)	None	✓	$1$	$0$	\(-4\)	\(6\)	\(26\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}+(13+\beta )q^{5}+\cdots\)
354.4.a.f	$354$	$4$	354.a	1.a	$1$	$3$	$3$	$20.887$	3.3.18989.1	None	✓	$1$	$0$	\(-6\)	\(9\)	\(-28\)	\(26\)		$+$	$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}+(-9+\beta _{1}+\beta _{2})q^{5}+\cdots\)

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