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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1751.1.d.a	$1751$	$1$	1751.d	1751.d	$2$	$1$	$1$	$0.874$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1751}) \)	None	✓	$2$	$0$	\(-1\)	\(-2\)	\(1\)	\(0\)	$1$		\(q-q^{2}-2q^{3}+q^{5}+2q^{6}+q^{8}+3q^{9}+\cdots\)
1751.1.d.b	$1751$	$1$	1751.d	1751.d	$2$	$1$	$1$	$0.874$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1751}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(-1\)	\(0\)	$1$		\(q-q^{2}+2q^{3}-q^{5}-2q^{6}+q^{8}+3q^{9}+\cdots\)
1751.1.d.c	$1751$	$1$	1751.d	1751.d	$2$	$1$	$1$	$0.874$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-103}) \), \(\Q(\sqrt{-1751}) \)	\(\Q(\sqrt{17}) \)	✓	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+2q^{2}+3q^{4}+4q^{8}-q^{9}-2q^{13}+\cdots\)
1751.1.d.d	$1751$	$1$	1751.d	1751.d	$2$	$2$	$2$	$0.874$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-1751}) \)	None	✓	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-2q^{2}-\beta q^{3}+3q^{4}+\beta q^{5}+2\beta q^{6}+\cdots\)
1751.1.d.e	$1751$	$1$	1751.d	1751.d	$2$	$2$	$2$	$0.874$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-1751}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}-\beta q^{5}+q^{8}-q^{9}+\beta q^{10}-\beta q^{11}+\cdots\)
1751.1.d.g	$1751$	$1$	1751.d	1751.d	$2$	$4$	$4$	$0.874$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-1751}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{3}-q^{4}-\beta _{3}q^{5}+(1+\beta _{2})q^{9}+\cdots\)
1751.1.d.h	$1751$	$1$	1751.d	1751.d	$2$	$4$	$4$	$0.874$	\(\Q(\zeta_{24})^+\)	$D_{12}$	\(\Q(\sqrt{-1751}) \)	None	✓	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+(-\beta _{1}-\beta _{3})q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
1751.1.d.i	$1751$	$1$	1751.d	1751.d	$2$	$8$	$8$	$0.874$	\(\Q(\zeta_{48})^+\)	$D_{24}$	\(\Q(\sqrt{-1751}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{4}q^{2}-\beta _{3}q^{3}+2q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots\)