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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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
16.22.a.a	$16$	$22$	16.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓				2.22.a.a	$1$	$0$	\(0\)	\(-71604\)	\(-28693770\)	\(853202392\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-71604q^{3}-28693770q^{5}+853202392q^{7}+\cdots\)
16.22.a.b	$16$	$22$	16.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓				2.22.a.b	$1$	$0$	\(0\)	\(-59316\)	\(4975350\)	\(-1427425832\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-59316q^{3}+4975350q^{5}-1427425832q^{7}+\cdots\)
16.22.a.c	$16$	$22$	16.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓				1.22.a.a	$1$	$0$	\(0\)	\(128844\)	\(21640950\)	\(768078808\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+128844q^{3}+21640950q^{5}+768078808q^{7}+\cdots\)
16.22.a.d	$16$	$22$	16.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{2161}) \)	None	✓		✓		4.22.a.a	$1$	$0$	\(0\)	\(-65640\)	\(13689324\)	\(260508080\)		$-$	$-$	$2^{8}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	\(q+(-32820-\beta )q^{3}+(6844662+204\beta )q^{5}+\cdots\)

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