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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 (3 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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
112.6.a.a	$112$	$6$	112.a	1.a	$1$	$1$	$1$	$17.963$	\(\Q\)	None	✓				56.6.a.b	$1$	$1$	\(0\)	\(-30\)	\(32\)	\(-49\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-30q^{3}+2^{5}q^{5}-7^{2}q^{7}+657q^{9}+\cdots\)
112.6.a.f	$112$	$6$	112.a	1.a	$1$	$1$	$1$	$17.963$	\(\Q\)	None	✓				56.6.a.a	$1$	$1$	\(0\)	\(6\)	\(4\)	\(-49\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+6q^{3}+4q^{5}-7^{2}q^{7}-207q^{9}+240q^{11}+\cdots\)
112.6.a.k	$112$	$6$	112.a	1.a	$1$	$2$	$2$	$17.963$	\(\Q(\sqrt{177}) \)	None	✓		✓		56.6.a.c	$1$	$1$	\(0\)	\(26\)	\(-62\)	\(-98\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(13-\beta )q^{3}+(-31+5\beta )q^{5}-7^{2}q^{7}+\cdots\)

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