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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	223	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1338.2.a.b	$1338$	$2$	1338.a	1.a	$1$	$2$	$2$	$10.684$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-2\)	\(-2\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+2\beta q^{5}+q^{6}-q^{8}+\cdots\)
1338.2.a.c	$1338$	$2$	1338.a	1.a	$1$	$3$	$3$	$10.684$	3.3.473.1	None	✓	$1$	$0$	\(-3\)	\(-3\)	\(-1\)	\(9\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}+(3+\cdots)q^{7}+\cdots\)

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