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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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
75.6.a.d	$75$	$6$	75.a	1.a	$1$	$1$	$1$	$12.029$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(9\)	\(0\)	\(-225\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+9q^{3}-2^{4}q^{4}+6^{2}q^{6}-15^{2}q^{7}+\cdots\)
75.6.a.f	$75$	$6$	75.a	1.a	$1$	$2$	$2$	$12.029$	\(\Q(\sqrt{89}) \)	None	✓	$1$	$1$	\(-9\)	\(18\)	\(0\)	\(-108\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-4-\beta )q^{2}+9q^{3}+(6+9\beta )q^{4}+\cdots\)

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