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Results (3 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1636.1.c.a	$1636$	$1$	1636.c	1636.c	$2$	$1$	$1$	$0.816$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-409}) \)	\(\Q(\sqrt{409}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+q^{2}+q^{4}-2q^{5}+q^{8}+q^{9}-2q^{10}+\cdots\)
1636.1.c.b	$1636$	$1$	1636.c	1636.c	$2$	$2$	$2$	$0.816$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-409}) \)	None	✓	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+q^{9}+\beta q^{11}+\cdots\)
1636.1.c.c	$1636$	$1$	1636.c	1636.c	$2$	$4$	$4$	$0.816$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-409}) \)	None	✓	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{8}+\cdots\)