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Results (1-50 of 69 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
639.1.d.a	$639$	$1$	639.d	71.b	$2$	$3$	$3$	$0.319$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-71}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$1$		\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+(1+\beta _{2})q^{8}+\cdots\)
639.1.g.a	$639$	$1$	639.g	639.g	$6$	$2$	$1$	$0.319$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-71}) \)	None		$4$	$0$	\(1\)	\(-1\)	\(-2\)	\(0\)		$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{5}-q^{6}+q^{8}+\cdots\)
639.1.g.b	$639$	$1$	639.g	639.g	$6$	$12$	$6$	$0.319$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-71}) \)	None		$4$	$0$	\(-1\)	\(1\)	\(2\)	\(0\)		$1$		\(q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}-\zeta_{42}^{19}q^{3}+\cdots\)
639.2.a.a	$639$	$2$	639.a	1.a	$1$	$1$	$1$	$5.102$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+2q^{7}+3q^{8}+2q^{10}+\cdots\)
639.2.a.b	$639$	$2$	639.a	1.a	$1$	$2$	$2$	$5.102$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
639.2.a.c	$639$	$2$	639.a	1.a	$1$	$2$	$2$	$5.102$	\(\Q(\sqrt{13}) \)	$_{}$	None	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}-q^{7}-3q^{8}+\cdots\)
639.2.a.d	$639$	$2$	639.a	1.a	$1$	$2$	$2$	$5.102$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}-\beta q^{5}-3q^{7}+\cdots\)
639.2.a.e	$639$	$2$	639.a	1.a	$1$	$2$	$2$	$5.102$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(-2+\cdots)q^{7}+\cdots\)
639.2.a.f	$639$	$2$	639.a	1.a	$1$	$2$	$2$	$5.102$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	$1$	$0$	\(3\)	\(0\)	\(5\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+(3-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
639.2.a.g	$639$	$2$	639.a	1.a	$1$	$3$	$3$	$5.102$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
639.2.a.h	$639$	$2$	639.a	1.a	$1$	$3$	$3$	$5.102$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	\(1\)	\(0\)	\(-5\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2+\beta _{1}+\beta _{2})q^{5}+\cdots\)
639.2.a.i	$639$	$2$	639.a	1.a	$1$	$4$	$4$	$5.102$	4.4.2225.1	$_{}$	None	None	✓	$1$	$0$	\(-3\)	\(0\)	\(3\)	\(6\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
639.2.a.j	$639$	$2$	639.a	1.a	$1$	$4$	$4$	$5.102$	4.4.8112.1	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-8\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2-\beta _{1})q^{5}+\cdots\)
639.2.a.k	$639$	$2$	639.a	1.a	$1$	$4$	$4$	$5.102$	4.4.8112.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(8\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots\)
639.2.b.a	$639$	$2$	639.b	213.b	$2$	$24$	$24$	$5.102$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
639.2.e.a	$639$	$2$	639.e	9.c	$3$	$4$	$2$	$5.102$	\(\Q(\sqrt{-3}, \sqrt{5})\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(0\)	\(-4\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-1-2\beta _{3})q^{3}+\cdots\)
639.2.e.b	$639$	$2$	639.e	9.c	$3$	$56$	$28$	$5.102$		$_{}$	None	None		$2$	$0$	\(-1\)	\(-1\)	\(-2\)	\(11\)			$\mathrm{SU}(2)[C_{3}]$
639.2.e.c	$639$	$2$	639.e	9.c	$3$	$80$	$40$	$5.102$		$_{}$	None	None		$2$	$0$	\(2\)	\(-1\)	\(2\)	\(-17\)			$\mathrm{SU}(2)[C_{3}]$
639.2.f.a	$639$	$2$	639.f	71.c	$5$	$4$	$1$	$5.102$	\(\Q(\zeta_{10})\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(0\)	\(8\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}^{3})q^{2}+(1-\zeta_{10})q^{4}+(3\zeta_{10}+\cdots)q^{5}+\cdots\)
639.2.f.b	$639$	$2$	639.f	71.c	$5$	$20$	$5$	$5.102$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(-3\)		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{13}+\beta _{15}+\cdots)q^{4}+\cdots\)
639.2.f.c	$639$	$2$	639.f	71.c	$5$	$20$	$5$	$5.102$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(6\)	\(0\)	\(1\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{14}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)
639.2.f.d	$639$	$2$	639.f	71.c	$5$	$24$	$6$	$5.102$		$_{}$	None	None		$2$	$0$	\(-3\)	\(0\)	\(2\)	\(-4\)			$\mathrm{SU}(2)[C_{5}]$
639.2.f.e	$639$	$2$	639.f	71.c	$5$	$48$	$12$	$5.102$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)			$\mathrm{SU}(2)[C_{5}]$
639.2.i.a	$639$	$2$	639.i	639.i	$6$	$28$	$14$	$5.102$		$_{}$	\(\Q(\sqrt{-71}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{U}(1)[D_{6}]$
639.2.i.b	$639$	$2$	639.i	639.i	$6$	$112$	$56$	$5.102$		$_{}$	None	None		$4$	$0$	\(-6\)	\(-2\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
639.2.j.a	$639$	$2$	639.j	71.d	$7$	$6$	$1$	$5.102$	\(\Q(\zeta_{14})\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(0\)	\(6\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4})q^{2}+(1-\zeta_{14}^{2}+\cdots)q^{4}+\cdots\)
639.2.j.b	$639$	$2$	639.j	71.d	$7$	$6$	$1$	$5.102$	\(\Q(\zeta_{14})\)	$_{}$	None	None		$2$	$0$	\(3\)	\(0\)	\(-6\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4})q^{2}+(1+\cdots)q^{4}+\cdots\)
639.2.j.c	$639$	$2$	639.j	71.d	$7$	$30$	$5$	$5.102$		$_{}$	None	None		$2$	$0$	\(3\)	\(0\)	\(10\)	\(-3\)			$\mathrm{SU}(2)[C_{7}]$
639.2.j.d	$639$	$2$	639.j	71.d	$7$	$36$	$6$	$5.102$		$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{7}]$
639.2.j.e	$639$	$2$	639.j	71.d	$7$	$36$	$6$	$5.102$		$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)			$\mathrm{SU}(2)[C_{7}]$
639.2.j.f	$639$	$2$	639.j	71.d	$7$	$60$	$10$	$5.102$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(20\)			$\mathrm{SU}(2)[C_{7}]$
639.2.m.a	$639$	$2$	639.m	213.i	$10$	$96$	$24$	$5.102$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{10}]$
639.2.p.a	$639$	$2$	639.p	213.l	$14$	$144$	$24$	$5.102$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{14}]$
639.2.q.a	$639$	$2$	639.q	639.q	$15$	$560$	$70$	$5.102$		$_{}$	None	None		$4$	$0$	\(-3\)	\(-8\)	\(-1\)	\(-3\)			$\mathrm{SU}(2)[C_{15}]$
639.2.r.a	$639$	$2$	639.r	639.r	$21$	$840$	$70$	$5.102$		$_{}$	None	None		$4$	$0$	\(-5\)	\(-5\)	\(-10\)	\(-5\)			$\mathrm{SU}(2)[C_{21}]$
639.2.s.a	$639$	$2$	639.s	639.s	$30$	$560$	$70$	$5.102$		$_{}$	None	None		$4$	$0$	\(-9\)	\(-8\)	\(-15\)	\(-5\)			$\mathrm{SU}(2)[C_{30}]$
639.2.v.a	$639$	$2$	639.v	71.g	$35$	$120$	$5$	$5.102$		$_{}$	None	None		$2$	$0$	\(22\)	\(0\)	\(20\)	\(-27\)			$\mathrm{SU}(2)[C_{35}]$
639.2.v.b	$639$	$2$	639.v	71.g	$35$	$144$	$6$	$5.102$		$_{}$	None	None		$2$	$0$	\(3\)	\(0\)	\(-2\)	\(4\)			$\mathrm{SU}(2)[C_{35}]$
639.2.v.c	$639$	$2$	639.v	71.g	$35$	$144$	$6$	$5.102$		$_{}$	None	None		$2$	$0$	\(3\)	\(0\)	\(2\)	\(0\)			$\mathrm{SU}(2)[C_{35}]$
639.2.v.d	$639$	$2$	639.v	71.g	$35$	$288$	$12$	$5.102$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{35}]$
639.2.w.a	$639$	$2$	639.w	639.w	$42$	$840$	$70$	$5.102$		$_{}$	None	None		$4$	$0$	\(-15\)	\(-5\)	\(-42\)	\(-7\)			$\mathrm{SU}(2)[C_{42}]$
639.2.z.a	$639$	$2$	639.z	213.n	$70$	$576$	$24$	$5.102$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{70}]$
639.2.bc.a	$639$	$2$	639.bc	639.ac	$105$	$3360$	$70$	$5.102$		$_{}$	None	None		$4$	$0$	\(-25\)	\(-55\)	\(-20\)	\(-25\)			$\mathrm{SU}(2)[C_{105}]$
639.2.bf.a	$639$	$2$	639.bf	639.af	$210$	$3360$	$70$	$5.102$		$_{}$	None	None		$4$	$0$	\(-75\)	\(-55\)	\(-48\)	\(-23\)			$\mathrm{SU}(2)[C_{210}]$
639.3.c.a	$639$	$3$	639.c	3.b	$2$	$48$	$48$	$17.411$		$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
639.3.d.a	$639$	$3$	639.d	71.b	$2$	$4$	$4$	$17.411$	4.0.2836736.1	$_{}$	None	None		$2$	$0$	\(4\)	\(0\)	\(8\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{2}+(-1+2\beta _{1})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
639.3.d.b	$639$	$3$	639.d	71.b	$2$	$7$	$7$	$17.411$	7.7.\(\cdots\).1	$_{}$	\(\Q(\sqrt{-71}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$3^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}+(4+\beta _{3})q^{4}+(\beta _{3}+\beta _{4})q^{5}+\cdots\)
639.3.d.c	$639$	$3$	639.d	71.b	$2$	$24$	$24$	$17.411$		$_{}$	None	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
639.3.d.d	$639$	$3$	639.d	71.b	$2$	$24$	$24$	$17.411$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
639.4.a.a	$639$	$4$	639.a	1.a	$1$	$1$	$1$	$37.702$	\(\Q\)	$_{}$	None	None	✓	$1$	$2$	\(-5\)	\(0\)	\(-13\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}+17q^{4}-13q^{5}-7q^{7}-45q^{8}+\cdots\)