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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
69.8.a.a	$69$	$8$	69.a	1.a	$1$	$5$	$5$	$21.555$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-135\)	\(-266\)	\(-496\)		$+$	$-$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3^{3}q^{3}+(54+2\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
69.8.a.b	$69$	$8$	69.a	1.a	$1$	$6$	$6$	$21.555$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-8\)	\(162\)	\(-372\)	\(-1104\)		$-$	$+$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+3^{3}q^{3}+(29+3\beta _{1}+\cdots)q^{4}+\cdots\)

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