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Results (4 matches)

 

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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1739.1.c.a	$1739$	$1$	1739.c	1739.c	$2$	$1$	$1$	$0.868$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-47}) \), \(\Q(\sqrt{-1739}) \)	\(\Q(\sqrt{37}) \)	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$1$		\(q-2q^{3}+q^{4}+2q^{7}+3q^{9}-2q^{12}+\cdots\)
1739.1.c.b	$1739$	$1$	1739.c	1739.c	$2$	$2$	$2$	$0.868$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1739}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
1739.1.c.c	$1739$	$1$	1739.c	1739.c	$2$	$2$	$2$	$0.868$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1739}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
1739.1.c.e	$1739$	$1$	1739.c	1739.c	$2$	$4$	$4$	$0.868$	\(\Q(\zeta_{20})^+\)	$D_{10}$	\(\Q(\sqrt{-1739}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$1$		\(q-\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{2}q^{9}+\cdots\)