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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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Results (4 matches)

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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
608.4.a.b	$608$	$4$	608.a	1.a	$1$	$1$	$1$	$35.873$	\(\Q\)	None	✓	✓			608.4.a.a	$1$	$0$	\(0\)	\(1\)	\(-8\)	\(17\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-8q^{5}+17q^{7}-26q^{9}+70q^{11}+\cdots\)
608.4.a.d	$608$	$4$	608.a	1.a	$1$	$2$	$2$	$35.873$	\(\Q(\sqrt{93}) \)	None	✓	✓			608.4.a.c	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(-44\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2-2\beta )q^{5}+(-22-\beta )q^{7}+\cdots\)
608.4.a.f	$608$	$4$	608.a	1.a	$1$	$5$	$5$	$35.873$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			608.4.a.f	$1$	$0$	\(0\)	\(-3\)	\(27\)	\(20\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(5-\beta _{1})q^{5}+(5-\beta _{1}+\cdots)q^{7}+\cdots\)
608.4.a.k	$608$	$4$	608.a	1.a	$1$	$7$	$7$	$35.873$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		608.4.a.j	$1$	$0$	\(0\)	\(3\)	\(-17\)	\(42\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-2-\beta _{3})q^{5}+(6-\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)

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