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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		13	31	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
403.2.a.a	$403$	$2$	403.a	1.a	$1$	$2$	$2$	$3.218$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(3\)	\(-4\)	\(0\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-2q^{3}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
403.2.a.e	$403$	$2$	403.a	1.a	$1$	$8$	$8$	$3.218$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(7\)	\(11\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

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