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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
405.2.a.b	$405$	$2$	405.a	1.a	$1$	$1$	$1$	$3.234$	\(\Q\)	None	✓				45.2.e.a	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}-3q^{7}+3q^{8}-q^{10}+\cdots\)
405.2.a.g	$405$	$2$	405.a	1.a	$1$	$2$	$2$	$3.234$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓		405.2.a.g	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{7}+\cdots\)

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