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Results (1-50 of 183 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.2.a.a	$54$	$2$	54.a	1.a	$1$	$1$	$1$	$0.431$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots\)
54.2.a.b	$54$	$2$	54.a	1.a	$1$	$1$	$1$	$0.431$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)
54.2.c.a	$54$	$2$	54.c	9.c	$3$	$2$	$1$	$0.431$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
54.2.e.a	$54$	$2$	54.e	27.e	$9$	$6$	$1$	$0.431$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+\cdots\)
54.2.e.b	$54$	$2$	54.e	27.e	$9$	$12$	$2$	$0.431$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{11}q^{3}+\beta _{3}q^{4}+\cdots\)
54.3.b.a	$54$	$3$	54.b	3.b	$2$	$2$	$2$	$1.471$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}+6\beta q^{5}+5q^{7}-2\beta q^{8}+\cdots\)
54.3.d.a	$54$	$3$	54.d	9.d	$6$	$4$	$2$	$1.471$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(18\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(6-3\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
54.3.f.a	$54$	$3$	54.f	27.f	$18$	$36$	$6$	$1.471$		None		$2$	$0$	\(0\)	\(0\)	\(18\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
54.4.a.a	$54$	$4$	54.a	1.a	$1$	$1$	$1$	$3.186$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-12\)	\(-7\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}-12q^{5}-7q^{7}-8q^{8}+\cdots\)
54.4.a.b	$54$	$4$	54.a	1.a	$1$	$1$	$1$	$3.186$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-3\)	\(29\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}-3q^{5}+29q^{7}-8q^{8}+\cdots\)
54.4.a.c	$54$	$4$	54.a	1.a	$1$	$1$	$1$	$3.186$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(3\)	\(29\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+4q^{4}+3q^{5}+29q^{7}+8q^{8}+\cdots\)
54.4.a.d	$54$	$4$	54.a	1.a	$1$	$1$	$1$	$3.186$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(12\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+4q^{4}+12q^{5}-7q^{7}+8q^{8}+\cdots\)
54.4.c.a	$54$	$4$	54.c	9.c	$3$	$2$	$1$	$3.186$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-9\)	\(31\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-9\zeta_{6}q^{5}+\cdots\)
54.4.c.b	$54$	$4$	54.c	9.c	$3$	$4$	$2$	$3.186$	\(\Q(\sqrt{-3}, \sqrt{-35})\)	None		$2$	$0$	\(-4\)	\(0\)	\(-9\)	\(-19\)		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{1}q^{2}+(-4-4\beta _{1})q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots\)
54.4.e.a	$54$	$4$	54.e	27.e	$9$	$24$	$4$	$3.186$		None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(-33\)			$\mathrm{SU}(2)[C_{9}]$
54.4.e.b	$54$	$4$	54.e	27.e	$9$	$30$	$5$	$3.186$		None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(33\)			$\mathrm{SU}(2)[C_{9}]$
54.5.b.a	$54$	$5$	54.b	3.b	$2$	$2$	$2$	$5.582$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-146\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-8q^{4}-12\beta q^{5}-73q^{7}-8\beta q^{8}+\cdots\)
54.5.b.b	$54$	$5$	54.b	3.b	$2$	$4$	$4$	$5.582$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(68\)		$2^{3}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}-8q^{4}+(\zeta_{8}-3\zeta_{8}^{2})q^{5}+\cdots\)
54.5.d.a	$54$	$5$	54.d	9.d	$6$	$8$	$4$	$5.582$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(0\)	\(-18\)	\(-26\)		$2^{4}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+8\beta _{2}q^{4}+(-3-\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
54.5.f.a	$54$	$5$	54.f	27.f	$18$	$72$	$12$	$5.582$		None		$2$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
54.6.a.a	$54$	$6$	54.a	1.a	$1$	$1$	$1$	$8.661$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(0\)	\(-33\)	\(59\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-33q^{5}+59q^{7}-2^{6}q^{8}+\cdots\)
54.6.a.b	$54$	$6$	54.a	1.a	$1$	$1$	$1$	$8.661$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(0\)	\(-24\)	\(77\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-24q^{5}+77q^{7}-2^{6}q^{8}+\cdots\)
54.6.a.c	$54$	$6$	54.a	1.a	$1$	$1$	$1$	$8.661$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(0\)	\(84\)	\(-193\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+84q^{5}-193q^{7}+\cdots\)
54.6.a.d	$54$	$6$	54.a	1.a	$1$	$1$	$1$	$8.661$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(0\)	\(-84\)	\(-193\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}-84q^{5}-193q^{7}+\cdots\)
54.6.a.e	$54$	$6$	54.a	1.a	$1$	$1$	$1$	$8.661$	\(\Q\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(24\)	\(77\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+24q^{5}+77q^{7}+2^{6}q^{8}+\cdots\)
54.6.a.f	$54$	$6$	54.a	1.a	$1$	$1$	$1$	$8.661$	\(\Q\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(33\)	\(59\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+33q^{5}+59q^{7}+2^{6}q^{8}+\cdots\)
54.6.c.a	$54$	$6$	54.c	9.c	$3$	$4$	$2$	$8.661$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(-8\)	\(0\)	\(54\)	\(74\)		$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\beta _{1})q^{2}-2^{4}\beta _{1}q^{4}+(3^{3}\beta _{1}+\cdots)q^{5}+\cdots\)
54.6.c.b	$54$	$6$	54.c	9.c	$3$	$6$	$3$	$8.661$	6.0.\(\cdots\).3	None		$2$	$0$	\(12\)	\(0\)	\(54\)	\(-132\)		$2^{2}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\beta _{1}q^{2}+(-2^{4}+2^{4}\beta _{1})q^{4}+(18+\cdots)q^{5}+\cdots\)
54.6.e.a	$54$	$6$	54.e	27.e	$9$	$42$	$7$	$8.661$		None		$2$	$0$	\(0\)	\(0\)	\(87\)	\(-15\)			$\mathrm{SU}(2)[C_{9}]$
54.6.e.b	$54$	$6$	54.e	27.e	$9$	$48$	$8$	$8.661$		None		$2$	$0$	\(0\)	\(0\)	\(87\)	\(15\)			$\mathrm{SU}(2)[C_{9}]$
54.7.b.a	$54$	$7$	54.b	3.b	$2$	$2$	$2$	$12.423$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-410\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2^{5}q^{4}+6\beta q^{5}-205q^{7}+\cdots\)
54.7.b.b	$54$	$7$	54.b	3.b	$2$	$2$	$2$	$12.423$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(778\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{2}-2^{5}q^{4}-15\beta q^{5}+389q^{7}+\cdots\)
54.7.b.c	$54$	$7$	54.b	3.b	$2$	$4$	$4$	$12.423$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(836\)		$2^{5}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}-2^{5}q^{4}+(5\zeta_{8}+15\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
54.7.d.a	$54$	$7$	54.d	9.d	$6$	$12$	$6$	$12.423$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-432\)	\(240\)		$2^{10}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}-2^{5}\beta _{2}q^{4}+(-48-24\beta _{2}+\cdots)q^{5}+\cdots\)
54.7.f.a	$54$	$7$	54.f	27.f	$18$	$108$	$18$	$12.423$		None		$2$	$0$	\(0\)	\(0\)	\(-432\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
54.8.a.a	$54$	$8$	54.a	1.a	$1$	$1$	$1$	$16.869$	\(\Q\)	None	✓	$1$	$1$	\(-8\)	\(0\)	\(-120\)	\(377\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+2^{6}q^{4}-120q^{5}+377q^{7}+\cdots\)
54.8.a.b	$54$	$8$	54.a	1.a	$1$	$1$	$1$	$16.869$	\(\Q\)	None	✓	$1$	$1$	\(-8\)	\(0\)	\(105\)	\(-937\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+2^{6}q^{4}+105q^{5}-937q^{7}+\cdots\)
54.8.a.c	$54$	$8$	54.a	1.a	$1$	$1$	$1$	$16.869$	\(\Q\)	None	✓	$1$	$0$	\(-8\)	\(0\)	\(312\)	\(323\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+2^{6}q^{4}+312q^{5}+323q^{7}+\cdots\)
54.8.a.d	$54$	$8$	54.a	1.a	$1$	$1$	$1$	$16.869$	\(\Q\)	None	✓	$1$	$1$	\(8\)	\(0\)	\(-312\)	\(323\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+2^{6}q^{4}-312q^{5}+323q^{7}+\cdots\)
54.8.a.e	$54$	$8$	54.a	1.a	$1$	$1$	$1$	$16.869$	\(\Q\)	None	✓	$1$	$1$	\(8\)	\(0\)	\(-105\)	\(-937\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+2^{6}q^{4}-105q^{5}-937q^{7}+\cdots\)
54.8.a.f	$54$	$8$	54.a	1.a	$1$	$1$	$1$	$16.869$	\(\Q\)	None	✓	$1$	$0$	\(8\)	\(0\)	\(120\)	\(377\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+2^{6}q^{4}+120q^{5}+377q^{7}+\cdots\)
54.8.a.g	$54$	$8$	54.a	1.a	$1$	$2$	$2$	$16.869$	\(\Q(\sqrt{329}) \)	None	✓	$1$	$0$	\(-16\)	\(0\)	\(48\)	\(880\)	$+$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q-8q^{2}+2^{6}q^{4}+(24+\beta )q^{5}+(440+\cdots)q^{7}+\cdots\)
54.8.a.h	$54$	$8$	54.a	1.a	$1$	$2$	$2$	$16.869$	\(\Q(\sqrt{329}) \)	None	✓	$1$	$0$	\(16\)	\(0\)	\(-48\)	\(880\)	$+$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+8q^{2}+2^{6}q^{4}+(-24-\beta )q^{5}+(440+\cdots)q^{7}+\cdots\)
54.8.c.a	$54$	$8$	54.c	9.c	$3$	$6$	$3$	$16.869$	6.0.\(\cdots\).1	None		$2$	$0$	\(24\)	\(0\)	\(-54\)	\(210\)		$2^{2}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{3}]$	\(q+8\beta _{1}q^{2}+(-2^{6}+2^{6}\beta _{1})q^{4}+(-18+\cdots)q^{5}+\cdots\)
54.8.c.b	$54$	$8$	54.c	9.c	$3$	$8$	$4$	$16.869$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(-32\)	\(0\)	\(-54\)	\(-44\)		$2^{4}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{3}]$	\(q-8\beta _{1}q^{2}+(-2^{6}+2^{6}\beta _{1})q^{4}+(-14+\cdots)q^{5}+\cdots\)
54.8.e.a	$54$	$8$	54.e	27.e	$9$	$60$	$10$	$16.869$		None		$2$	$0$	\(0\)	\(0\)	\(213\)	\(1677\)			$\mathrm{SU}(2)[C_{9}]$
54.8.e.b	$54$	$8$	54.e	27.e	$9$	$66$	$11$	$16.869$		None		$2$	$0$	\(0\)	\(0\)	\(213\)	\(-1677\)			$\mathrm{SU}(2)[C_{9}]$
54.9.b.a	$54$	$9$	54.b	3.b	$2$	$2$	$2$	$21.998$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4130\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2^{7}q^{4}+60\beta q^{5}-2065q^{7}+\cdots\)
54.9.b.b	$54$	$9$	54.b	3.b	$2$	$4$	$4$	$21.998$	\(\Q(\sqrt{-2}, \sqrt{79})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(164\)		$2^{9}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2^{7}q^{4}+(-21\beta _{1}+\beta _{2})q^{5}+\cdots\)
54.9.b.c	$54$	$9$	54.b	3.b	$2$	$4$	$4$	$21.998$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(308\)		$2^{5}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{8}^{2}q^{2}-2^{7}q^{4}+(-11\zeta_{8}+51\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)