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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
15.7.d.a	$15$	$7$	15.d	15.d	$2$	$1$	$1$	$3.451$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-11\)	\(-27\)	\(125\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-11q^{2}-3^{3}q^{3}+57q^{4}+5^{3}q^{5}+\cdots\)
15.7.d.b	$15$	$7$	15.d	15.d	$2$	$1$	$1$	$3.451$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(11\)	\(27\)	\(-125\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+11q^{2}+3^{3}q^{3}+57q^{4}-5^{3}q^{5}+\cdots\)

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