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Results (1-50 of 143 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
111.1.d.a	$111$	$1$	111.d	111.d	$2$	$1$	$1$	$0.055$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \)	\(\Q(\sqrt{37}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$1$		\(q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\)
111.1.d.b	$111$	$1$	111.d	111.d	$2$	$2$	$2$	$0.055$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-111}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$		\(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots\)
111.1.h.a	$111$	$1$	111.h	111.h	$6$	$2$	$1$	$0.055$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$1$		\(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
111.1.i.a	$111$	$1$	111.i	111.i	$6$	$2$	$1$	$0.055$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$1$		\(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
111.2.a.a	$111$	$2$	111.a	1.a	$1$	$3$	$3$	$0.886$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	\(3\)	\(-3\)	\(4\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
111.2.a.b	$111$	$2$	111.a	1.a	$1$	$4$	$4$	$0.886$	4.4.6224.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
111.2.c.a	$111$	$2$	111.c	37.b	$2$	$2$	$2$	$0.886$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots\)
111.2.c.b	$111$	$2$	111.c	37.b	$2$	$4$	$4$	$0.886$	4.0.27648.1	$_{}$	None	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
111.2.e.a	$111$	$2$	111.e	37.c	$3$	$6$	$3$	$0.886$	6.0.1415907.1	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(2\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(1+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
111.2.e.b	$111$	$2$	111.e	37.c	$3$	$10$	$5$	$0.886$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-5\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}+(-1+\beta _{6})q^{3}+(-2+2\beta _{6}+\cdots)q^{4}+\cdots\)
111.2.g.a	$111$	$2$	111.g	111.g	$4$	$20$	$10$	$0.886$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{13}q^{3}+(-\beta _{6}+\beta _{8})q^{4}+\cdots\)
111.2.j.a	$111$	$2$	111.j	37.e	$6$	$2$	$1$	$0.886$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$1$	\(-3\)	\(-1\)	\(-6\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{4}+(-4+\cdots)q^{5}+\cdots\)
111.2.j.b	$111$	$2$	111.j	37.e	$6$	$4$	$2$	$0.886$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(2\)	\(3\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
111.2.j.c	$111$	$2$	111.j	37.e	$6$	$6$	$3$	$0.886$	6.0.16553403.1	$_{}$	None	None		$2$	$0$	\(0\)	\(-3\)	\(9\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(-1+\beta _{2})q^{3}+(2-2\beta _{2}+\cdots)q^{4}+\cdots\)
111.2.k.a	$111$	$2$	111.k	37.f	$9$	$18$	$3$	$0.886$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{7}q^{2}+(\beta _{9}+\beta _{13})q^{3}+(\beta _{13}+\beta _{16}+\cdots)q^{4}+\cdots\)
111.2.k.b	$111$	$2$	111.k	37.f	$9$	$24$	$4$	$0.886$		$_{}$	None	None		$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(-9\)			$\mathrm{SU}(2)[C_{9}]$
111.2.m.a	$111$	$2$	111.m	111.m	$12$	$40$	$10$	$0.886$		$_{}$	None	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{12}]$
111.2.o.a	$111$	$2$	111.o	37.h	$18$	$12$	$2$	$0.886$	12.0.\(\cdots\).1	$_{}$	None	None		$2$	$0$	\(3\)	\(0\)	\(-3\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\beta _{3}q^{2}+\beta _{9}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
111.2.o.b	$111$	$2$	111.o	37.h	$18$	$18$	$3$	$0.886$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(3\)	\(0\)	\(-3\)	\(9\)		$1$	$\mathrm{SU}(2)[C_{18}]$	\(q-\beta _{16}q^{2}+(-\beta _{10}+\beta _{17})q^{3}+(-\beta _{9}+\cdots)q^{4}+\cdots\)
111.2.q.a	$111$	$2$	111.q	111.q	$36$	$12$	$1$	$0.886$	\(\Q(\zeta_{36})\)	$_{}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{36}]$	\(q+(\zeta_{36}^{4}-2\zeta_{36}^{10})q^{3}+2\zeta_{36}q^{4}+\cdots\)
111.2.q.b	$111$	$2$	111.q	111.q	$36$	$120$	$10$	$0.886$		$_{}$	None	None		$4$	$0$	\(0\)	\(-12\)	\(0\)	\(-24\)			$\mathrm{SU}(2)[C_{36}]$
111.3.b.a	$111$	$3$	111.b	3.b	$2$	$24$	$24$	$3.025$		$_{}$	None	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(8\)			$\mathrm{SU}(2)[C_{2}]$
111.3.d.a	$111$	$3$	111.d	111.d	$2$	$4$	$4$	$3.025$	4.4.65712.1	$_{}$	\(\Q(\sqrt{-111}) \)	None	✓	$4$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}-3q^{3}+(4-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
111.3.d.b	$111$	$3$	111.d	111.d	$2$	$4$	$4$	$3.025$	4.4.85248.1	$_{}$	\(\Q(\sqrt{-111}) \)	None	✓	$4$	$0$	\(0\)	\(12\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+3q^{3}+(4+3\beta _{2})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
111.3.d.c	$111$	$3$	111.d	111.d	$2$	$16$	$16$	$3.025$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}+\beta _{5}q^{3}+(1+\beta _{6})q^{4}-\beta _{2}q^{5}+\cdots\)
111.3.f.a	$111$	$3$	111.f	37.d	$4$	$24$	$12$	$3.025$		$_{}$	None	None		$2$	$0$	\(8\)	\(0\)	\(20\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
111.3.h.a	$111$	$3$	111.h	111.h	$6$	$48$	$24$	$3.025$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)			$\mathrm{SU}(2)[C_{6}]$
111.3.i.a	$111$	$3$	111.i	111.i	$6$	$48$	$24$	$3.025$		$_{}$	None	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)			$\mathrm{SU}(2)[C_{6}]$
111.3.l.a	$111$	$3$	111.l	37.g	$12$	$24$	$6$	$3.025$		$_{}$	None	None		$2$	$0$	\(-4\)	\(-36\)	\(8\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
111.3.l.b	$111$	$3$	111.l	37.g	$12$	$24$	$6$	$3.025$		$_{}$	None	None		$2$	$0$	\(-4\)	\(36\)	\(8\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
111.3.n.a	$111$	$3$	111.n	111.n	$18$	$6$	$1$	$3.025$	\(\Q(\zeta_{18})\)	$_{}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(39\)		$1$	$\mathrm{U}(1)[D_{18}]$	\(q-3\zeta_{18}^{4}q^{3}+4\zeta_{18}q^{4}+(5-3\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
111.3.n.b	$111$	$3$	111.n	111.n	$18$	$132$	$22$	$3.025$		$_{}$	None	None		$4$	$0$	\(0\)	\(-9\)	\(0\)	\(-54\)			$\mathrm{SU}(2)[C_{18}]$
111.3.p.a	$111$	$3$	111.p	111.p	$18$	$6$	$1$	$3.025$	\(\Q(\zeta_{18})\)	$_{}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-39\)		$1$	$\mathrm{U}(1)[D_{18}]$	\(q+(3\zeta_{18}^{2}-3\zeta_{18}^{5})q^{3}+4\zeta_{18}^{2}q^{4}+\cdots\)
111.3.p.b	$111$	$3$	111.p	111.p	$18$	$132$	$22$	$3.025$		$_{}$	None	None		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(30\)			$\mathrm{SU}(2)[C_{18}]$
111.3.r.a	$111$	$3$	111.r	37.i	$36$	$72$	$6$	$3.025$		$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)			$\mathrm{SU}(2)[C_{36}]$
111.3.r.b	$111$	$3$	111.r	37.i	$36$	$84$	$7$	$3.025$		$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)			$\mathrm{SU}(2)[C_{36}]$
111.4.a.a	$111$	$4$	111.a	1.a	$1$	$1$	$1$	$6.549$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(-4\)	\(3\)	\(2\)	\(-28\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+3q^{3}+8q^{4}+2q^{5}-12q^{6}+\cdots\)
111.4.a.b	$111$	$4$	111.a	1.a	$1$	$1$	$1$	$6.549$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(-1\)	\(-3\)	\(-4\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}-7q^{4}-4q^{5}+3q^{6}+\cdots\)
111.4.a.c	$111$	$4$	111.a	1.a	$1$	$1$	$1$	$6.549$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(1\)	\(3\)	\(-8\)	\(-13\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}-7q^{4}-8q^{5}+3q^{6}+\cdots\)
111.4.a.d	$111$	$4$	111.a	1.a	$1$	$3$	$3$	$6.549$	3.3.2700.1	$_{}$	None	None	✓	$1$	$1$	\(-3\)	\(-9\)	\(-6\)	\(15\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}-3q^{3}+(3-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
111.4.a.e	$111$	$4$	111.a	1.a	$1$	$5$	$5$	$6.549$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(4\)	\(-15\)	\(18\)	\(-12\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-3q^{3}+(7+\beta _{2}+\beta _{4})q^{4}+\cdots\)
111.4.a.f	$111$	$4$	111.a	1.a	$1$	$7$	$7$	$6.549$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(3\)	\(21\)	\(14\)	\(43\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{1}+\beta _{2})q^{4}+\cdots\)
111.4.c.a	$111$	$4$	111.c	37.b	$2$	$10$	$10$	$6.549$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-30\)	\(0\)	\(26\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-3q^{3}+(-3+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
111.4.c.b	$111$	$4$	111.c	37.b	$2$	$10$	$10$	$6.549$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(30\)	\(0\)	\(-30\)		$2^{5}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+3q^{3}+(-4+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
111.4.e.a	$111$	$4$	111.e	37.c	$3$	$18$	$9$	$6.549$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(-27\)	\(4\)	\(43\)		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{4}q^{3}+(-\beta _{1}+3\beta _{4}+\cdots)q^{4}+\cdots\)
111.4.e.b	$111$	$4$	111.e	37.c	$3$	$18$	$9$	$6.549$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(27\)	\(4\)	\(1\)		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(3+3\beta _{5})q^{3}+(-2+\cdots)q^{4}+\cdots\)
111.4.g.a	$111$	$4$	111.g	111.g	$4$	$4$	$2$	$6.549$	\(\Q(\zeta_{12})\)	$_{}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q-\zeta_{12}^{2}q^{3}+8\zeta_{12}q^{4}-6\zeta_{12}^{3}q^{7}+\cdots\)
111.4.g.b	$111$	$4$	111.g	111.g	$4$	$68$	$34$	$6.549$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)			$\mathrm{SU}(2)[C_{4}]$
111.4.j.a	$111$	$4$	111.j	37.e	$6$	$20$	$10$	$6.549$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(3\)	\(-30\)	\(-21\)	\(-15\)		$3^{5}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-3+3\beta _{7})q^{3}+(5-\beta _{1}+\cdots)q^{4}+\cdots\)
111.4.j.b	$111$	$4$	111.j	37.e	$6$	$20$	$10$	$6.549$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(3\)	\(30\)	\(-21\)	\(-29\)		$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+3\beta _{6}q^{3}+(-\beta _{2}+5\beta _{6}+\beta _{13}+\cdots)q^{4}+\cdots\)