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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
165.4.a.b	$165$	$4$	165.a	1.a	$1$	$1$	$1$	$9.735$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(3\)	\(-5\)	\(36\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}-7q^{4}-5q^{5}+3q^{6}+\cdots\)
165.4.a.e	$165$	$4$	165.a	1.a	$1$	$3$	$3$	$9.735$	3.3.47528.1	None	✓	$1$	$0$	\(-2\)	\(9\)	\(-15\)	\(10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(10+\beta _{2})q^{4}+\cdots\)

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