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Results (6 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1239.1.h.a	$1239$	$1$	1239.h	1239.h	$2$	$1$	$1$	$0.618$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1239}) \)	\(\Q(\sqrt{21}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)	$1$		\(q-q^{3}-q^{4}+2q^{5}+q^{7}+q^{9}+q^{12}+\cdots\)
1239.1.h.b	$1239$	$1$	1239.h	1239.h	$2$	$1$	$1$	$0.618$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1239}) \)	\(\Q(\sqrt{21}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)	$1$		\(q+q^{3}-q^{4}-2q^{5}+q^{7}+q^{9}-q^{12}+\cdots\)
1239.1.h.c	$1239$	$1$	1239.h	1239.h	$2$	$2$	$2$	$0.618$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-1239}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$1$		\(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{9}+\cdots\)
1239.1.h.f	$1239$	$1$	1239.h	1239.h	$2$	$2$	$2$	$0.618$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-1239}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(2\)	$1$		\(q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{7}+q^{9}+\cdots\)
1239.1.h.g	$1239$	$1$	1239.h	1239.h	$2$	$4$	$4$	$0.618$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-1239}) \)	None	✓	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-4\)	$1$		\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
1239.1.h.h	$1239$	$1$	1239.h	1239.h	$2$	$4$	$4$	$0.618$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-1239}) \)	None	✓	$4$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$1$		\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)