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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
1007.1.d.e	$1007$	$1$	1007.d	1007.d	$2$	$4$	$4$	$0.503$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-1007}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1007.1.d.f	$1007$	$1$	1007.d	1007.d	$2$	$4$	$4$	$0.503$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-1007}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(-2\)	$1$		\(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)

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