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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	5	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1690.2.a.t	$1690$	$2$	1690.a	1.a	$1$	$4$	$4$	$13.495$	4.4.4752.1	None	✓	$1$	$0$	\(-4\)	\(2\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+q^{4}-q^{5}+\cdots\)
1690.2.a.u	$1690$	$2$	1690.a	1.a	$1$	$4$	$4$	$13.495$	4.4.4752.1	None	✓	$1$	$0$	\(4\)	\(2\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+q^{4}+q^{5}+\cdots\)

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