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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	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
1535.1.d.a	$1535$	$1$	1535.d	1535.d	$2$	$9$	$9$	$0.766$	\(\Q(\zeta_{38})^+\)	$D_{19}$	\(\Q(\sqrt{-1535}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(9\)	\(0\)	$1$		\(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
1535.1.d.b	$1535$	$1$	1535.d	1535.d	$2$	$9$	$9$	$0.766$	\(\Q(\zeta_{38})^+\)	$D_{19}$	\(\Q(\sqrt{-1535}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(-9\)	\(0\)	$1$		\(q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)

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