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Results (8 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2991.1.d.a	$2991$	$1$	2991.d	2991.d	$2$	$1$	$1$	$1.493$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2991}) \)	None	✓	$2$	$0$	\(-2\)	\(1\)	\(1\)	\(0\)	$1$		\(q-2q^{2}+q^{3}+3q^{4}+q^{5}-2q^{6}-4q^{8}+\cdots\)
2991.1.d.b	$2991$	$1$	2991.d	2991.d	$2$	$1$	$1$	$1.493$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2991}) \)	\(\Q(\sqrt{997}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}-q^{4}+q^{9}-q^{12}+2q^{13}+q^{16}+\cdots\)
2991.1.d.c	$2991$	$1$	2991.d	2991.d	$2$	$1$	$1$	$1.493$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2991}) \)	None	✓	$2$	$0$	\(2\)	\(1\)	\(-1\)	\(0\)	$1$		\(q+2q^{2}+q^{3}+3q^{4}-q^{5}+2q^{6}+4q^{8}+\cdots\)
2991.1.d.d	$2991$	$1$	2991.d	2991.d	$2$	$2$	$2$	$1.493$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-2991}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{3}-q^{4}-\beta q^{5}+q^{9}-\beta q^{11}-q^{12}+\cdots\)
2991.1.d.e	$2991$	$1$	2991.d	2991.d	$2$	$2$	$2$	$1.493$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-2991}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+\beta q^{2}+q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+q^{9}+\cdots\)
2991.1.d.f	$2991$	$1$	2991.d	2991.d	$2$	$4$	$4$	$1.493$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-2991}) \)	None	✓	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q+\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
2991.1.d.g	$2991$	$1$	2991.d	2991.d	$2$	$4$	$4$	$1.493$	\(\Q(\zeta_{24})^+\)	$D_{12}$	\(\Q(\sqrt{-2991}) \)	None	✓	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q+(-\beta _{1}-\beta _{3})q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
2991.1.d.h	$2991$	$1$	2991.d	2991.d	$2$	$8$	$8$	$1.493$	\(\Q(\zeta_{48})^+\)	$D_{24}$	\(\Q(\sqrt{-2991}) \)	None	✓	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$1$		\(q+\beta _{3}q^{2}-q^{3}+(1+\beta _{2}+\beta _{6})q^{4}-\beta _{1}q^{5}+\cdots\)