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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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
15.9.d.a	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-17\)	\(-81\)	\(-625\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots\)
15.9.d.b	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(17\)	\(81\)	\(625\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots\)

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