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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3567.1.f.a	$3567$	$1$	3567.f	3567.f	$2$	$2$	$2$	$1.780$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3567}) \)	None	✓	$2$	$0$	\(-1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+(-1+\beta )q^{2}-q^{3}+(1-\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
3567.1.f.b	$3567$	$1$	3567.f	3567.f	$2$	$2$	$2$	$1.780$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3567}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+q^{3}+\beta q^{4}-\beta q^{6}-q^{8}+q^{9}+\cdots\)
3567.1.f.d	$3567$	$1$	3567.f	3567.f	$2$	$2$	$2$	$1.780$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3567}) \)	None	✓	$2$	$0$	\(1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+\beta q^{2}-q^{3}+\beta q^{4}-\beta q^{6}+q^{8}+q^{9}+\cdots\)
3567.1.f.e	$3567$	$1$	3567.f	3567.f	$2$	$2$	$2$	$1.780$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3567}) \)	None	✓	$2$	$0$	\(1\)	\(2\)	\(0\)	\(0\)	$1$		\(q+(1-\beta )q^{2}+q^{3}+(1-\beta )q^{4}+(1-\beta )q^{6}+\cdots\)