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Results (25 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
439.1.b.a	$439$	$1$	439.b	439.b	$2$	$1$	$1$	$0.219$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-439}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(-1\)	$1$		\(q-q^{2}+2q^{5}-q^{7}+q^{8}+q^{9}-2q^{10}+\cdots\)
439.1.b.b	$439$	$1$	439.b	439.b	$2$	$2$	$2$	$0.219$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-439}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
439.1.b.c	$439$	$1$	439.b	439.b	$2$	$4$	$4$	$0.219$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-439}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(1\)	$1$		\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2195.1.c.a	$2195$	$1$	2195.c	2195.c	$2$	$1$	$1$	$1.095$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-439}) \), \(\Q(\sqrt{-2195}) \)	\(\Q(\sqrt{5}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{4}+q^{5}-q^{9}+2q^{11}+q^{16}-2q^{19}+\cdots\)
2195.1.c.b	$2195$	$1$	2195.c	2195.c	$2$	$2$	$2$	$1.095$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)
2195.1.c.d	$2195$	$1$	2195.c	2195.c	$2$	$4$	$4$	$1.095$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
2195.1.c.g	$2195$	$1$	2195.c	2195.c	$2$	$8$	$8$	$1.095$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(\zeta_{30}^{4}+\zeta_{30}^{11})q^{2}+(-1-\zeta_{30}^{7}+\cdots)q^{4}+\cdots\)
3073.1.m.a	$3073$	$1$	3073.m	3073.m	$6$	$2$	$1$	$1.534$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(-2\)	\(0\)	\(1\)	\(2\)	$1$		\(q+\zeta_{6}^{2}q^{2}-3\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{7}+\cdots\)
3073.1.m.b	$3073$	$1$	3073.m	3073.m	$6$	$2$	$1$	$1.534$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+q^{8}+\cdots\)
3073.1.m.c	$3073$	$1$	3073.m	3073.m	$6$	$2$	$1$	$1.534$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+q^{8}+\cdots\)
3073.1.m.d	$3073$	$1$	3073.m	3073.m	$6$	$8$	$4$	$1.534$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)	$1$		\(q+(\zeta_{30}^{6}+\zeta_{30}^{14})q^{2}+(-\zeta_{30}^{5}+\zeta_{30}^{12}+\cdots)q^{4}+\cdots\)
3073.1.m.e	$3073$	$1$	3073.m	3073.m	$6$	$8$	$4$	$1.534$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)	$1$		\(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{8}+\zeta_{30}^{10}+\cdots)q^{4}+\cdots\)
3073.1.m.f	$3073$	$1$	3073.m	3073.m	$6$	$8$	$4$	$1.534$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(2\)	\(0\)	\(-1\)	\(-2\)	$1$		\(q+(-\zeta_{30}^{11}+\zeta_{30}^{14})q^{2}+(-\zeta_{30}^{7}+\cdots)q^{4}+\cdots\)
3512.1.g.a	$3512$	$1$	3512.g	3512.g	$2$	$1$	$1$	$1.753$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-439}) \), \(\Q(\sqrt{-878}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{2}+q^{4}-2q^{7}-q^{8}-q^{9}+2q^{14}+\cdots\)
3512.1.g.b	$3512$	$1$	3512.g	3512.g	$2$	$2$	$2$	$1.753$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{7}-q^{8}-q^{9}+\cdots\)
3512.1.g.f	$3512$	$1$	3512.g	3512.g	$2$	$4$	$4$	$1.753$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)
3512.1.g.g	$3512$	$1$	3512.g	3512.g	$2$	$8$	$8$	$1.753$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-439}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{30}^{11}q^{2}-\zeta_{30}^{7}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{9}+\cdots)q^{5}+\cdots\)
3951.1.d.a	$3951$	$1$	3951.d	439.b	$2$	$1$	$1$	$1.972$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-439}) \)	\(\Q(\sqrt{1317}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{4}-2q^{7}-2q^{13}+q^{16}+2q^{19}+\cdots\)
3951.1.d.b	$3951$	$1$	3951.d	439.b	$2$	$1$	$1$	$1.972$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-439}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(-1\)	$1$		\(q+q^{2}-2q^{5}-q^{7}-q^{8}-2q^{10}+q^{11}+\cdots\)
3951.1.d.c	$3951$	$1$	3951.d	439.b	$2$	$2$	$2$	$1.972$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-439}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\beta q^{2}+2q^{4}+q^{7}-\beta q^{8}+\beta q^{11}+\cdots\)
3951.1.d.d	$3951$	$1$	3951.d	439.b	$2$	$2$	$2$	$1.972$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-439}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$1$		\(q+(1-\beta )q^{2}+(1-\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
3951.1.d.e	$3951$	$1$	3951.d	439.b	$2$	$4$	$4$	$1.972$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-439}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(1\)	$1$		\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
3951.1.d.f	$3951$	$1$	3951.d	439.b	$2$	$4$	$4$	$1.972$	\(\Q(\zeta_{20})^+\)	$D_{10}$	\(\Q(\sqrt{-439}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots\)
3951.1.d.g	$3951$	$1$	3951.d	439.b	$2$	$8$	$8$	$1.972$	\(\Q(\zeta_{60})^+\)	$D_{30}$	\(\Q(\sqrt{-439}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{7})q^{5}+\cdots\)
439.3.b.a	$439$	$3$	439.b	439.b	$2$	$15$	$15$	$11.962$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	$_{}$	\(\Q(\sqrt{-439}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}+(4+\beta _{4})q^{4}+(\beta _{3}-\beta _{12})q^{5}+\cdots\)