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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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Results (4 matches)

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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
2679.1.h.a	$2679$	$1$	2679.h	2679.h	$2$	$6$	$6$	$1.337$	\(\Q(\zeta_{26})^+\)	$D_{13}$	\(\Q(\sqrt{-2679}) \)	None	✓	$2$	$0$	\(-1\)	\(6\)	\(-1\)	\(-1\)	$1$		\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
2679.1.h.b	$2679$	$1$	2679.h	2679.h	$2$	$6$	$6$	$1.337$	\(\Q(\zeta_{26})^+\)	$D_{13}$	\(\Q(\sqrt{-2679}) \)	None	✓	$2$	$0$	\(-1\)	\(6\)	\(1\)	\(-1\)	$1$		\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
2679.1.h.c	$2679$	$1$	2679.h	2679.h	$2$	$6$	$6$	$1.337$	\(\Q(\zeta_{26})^+\)	$D_{13}$	\(\Q(\sqrt{-2679}) \)	None	✓	$2$	$0$	\(1\)	\(-6\)	\(-1\)	\(-1\)	$1$		\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
2679.1.h.d	$2679$	$1$	2679.h	2679.h	$2$	$6$	$6$	$1.337$	\(\Q(\zeta_{26})^+\)	$D_{13}$	\(\Q(\sqrt{-2679}) \)	None	✓	$2$	$0$	\(1\)	\(-6\)	\(1\)	\(-1\)	$1$		\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)

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