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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
225.4.a.k	$225$	$4$	225.a	1.a	$1$	$2$	$2$	$13.275$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-15}) \)	✓				45.4.b.a	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2$	$N(\mathrm{U}(1))$	\(q-\beta q^{2}-3q^{4}+11\beta q^{8}-31q^{16}+\cdots\)
225.4.a.l	$225$	$4$	225.a	1.a	$1$	$2$	$2$	$13.275$	\(\Q(\sqrt{10}) \)	None	✓	✓			225.4.a.l	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-30\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+2q^{4}-15q^{7}-6\beta q^{8}-20\beta q^{11}+\cdots\)

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