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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1839.1.d.a	$1839$	$1$	1839.d	1839.d	$2$	$1$	$1$	$0.918$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1839}) \)	\(\Q(\sqrt{613}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(2\)	$1$		\(q+q^{3}-q^{4}+2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\)
1839.1.d.b	$1839$	$1$	1839.d	1839.d	$2$	$2$	$2$	$0.918$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1839}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(4\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}+2q^{5}+\cdots\)
1839.1.d.c	$1839$	$1$	1839.d	1839.d	$2$	$2$	$2$	$0.918$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-1839}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)	$1$		\(q-\beta q^{2}-q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+2q^{7}+\cdots\)
1839.1.d.d	$1839$	$1$	1839.d	1839.d	$2$	$2$	$2$	$0.918$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1839}) \)	None	✓	$2$	$0$	\(1\)	\(2\)	\(-4\)	\(-1\)	$1$		\(q+(1-\beta )q^{2}+q^{3}+(1-\beta )q^{4}-2q^{5}+\cdots\)
1839.1.d.e	$1839$	$1$	1839.d	1839.d	$2$	$4$	$4$	$0.918$	\(\Q(\zeta_{20})^+\)	$D_{10}$	\(\Q(\sqrt{-1839}) \)	None	✓	$4$	$0$	\(0\)	\(4\)	\(0\)	\(-2\)	$1$		\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1839.1.d.f	$1839$	$1$	1839.d	1839.d	$2$	$8$	$8$	$0.918$	\(\Q(\zeta_{40})^+\)	$D_{20}$	\(\Q(\sqrt{-1839}) \)	None	✓	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-4\)	$1$		\(q+\beta _{7}q^{2}-q^{3}+(1-\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)