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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
38.8.a.c	$38$	$8$	38.a	1.a	$1$	$2$	$2$	$11.871$	\(\Q(\sqrt{17953}) \)	None	✓	$1$	$1$	\(-16\)	\(-11\)	\(-69\)	\(-348\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+(-5-\beta )q^{3}+2^{6}q^{4}+(-6^{2}+\cdots)q^{5}+\cdots\)
38.8.a.d	$38$	$8$	38.a	1.a	$1$	$2$	$2$	$11.871$	\(\Q(\sqrt{633}) \)	None	✓	$1$	$1$	\(16\)	\(-69\)	\(155\)	\(-2238\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+(-33-3\beta )q^{3}+2^{6}q^{4}+(62+\cdots)q^{5}+\cdots\)

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