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Results (1-50 of 176 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
57.1.h.a	$57$	$1$	57.h	57.h	$6$	$2$	$1$	$0.028$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	57.1.h.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots\)
57.2.a.a	$57$	$2$	57.a	1.a	$1$	$1$	$1$	$0.455$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	57.2.a.a	$1$	$1$	\(-2\)	\(-1\)	\(-3\)	\(-5\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
57.2.a.b	$57$	$2$	57.a	1.a	$1$	$1$	$1$	$0.455$	\(\Q\)	$_{}$	None	None	✓	✓			57.2.a.b	$1$	$0$	\(-2\)	\(1\)	\(1\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
57.2.a.c	$57$	$2$	57.a	1.a	$1$	$1$	$1$	$0.455$	\(\Q\)	$_{}$	None	None	✓	✓			57.2.a.c	$1$	$0$	\(1\)	\(1\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
57.2.d.a	$57$	$2$	57.d	57.d	$2$	$4$	$4$	$0.455$	\(\Q(\sqrt{2}, \sqrt{-5})\)	$_{}$	None	None		✓	✓	✓	57.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+\beta _{3}q^{5}+(-1-\beta _{3})q^{6}+\cdots\)
57.2.e.a	$57$	$2$	57.e	19.c	$3$	$2$	$1$	$0.455$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			57.2.e.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
57.2.e.b	$57$	$2$	57.e	19.c	$3$	$6$	$3$	$0.455$	6.0.954288.1	$_{}$	None	None		✓	✓		57.2.e.b	$2$	$0$	\(1\)	\(-3\)	\(-2\)	\(-2\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
57.2.f.a	$57$	$2$	57.f	57.f	$6$	$8$	$4$	$0.455$	\(\Q(\zeta_{24})\)	$_{}$	None	None		✓	✓	✓	57.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
57.2.i.a	$57$	$2$	57.i	19.e	$9$	$6$	$1$	$0.455$	\(\Q(\zeta_{18})\)	$_{}$	None	None		✓			57.2.i.a	$2$	$0$	\(3\)	\(0\)	\(-6\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}-\zeta_{18}^{4}q^{3}+\cdots\)
57.2.i.b	$57$	$2$	57.i	19.e	$9$	$12$	$2$	$0.455$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		✓	✓		57.2.i.b	$2$	$0$	\(-3\)	\(0\)	\(6\)	\(-9\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{6}q^{3}+\cdots\)
57.2.j.a	$57$	$2$	57.j	57.j	$18$	$6$	$1$	$0.455$	\(\Q(\zeta_{18})\)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			57.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{18}]$	\(q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+2\zeta_{18}q^{4}+\cdots\)
57.2.j.b	$57$	$2$	57.j	57.j	$18$	$24$	$4$	$0.455$		$_{}$	None	None		✓	✓		57.2.j.b	$4$	$0$	\(0\)	\(-9\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
57.3.b.a	$57$	$3$	57.b	3.b	$2$	$12$	$12$	$1.553$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		✓	✓	✓	57.3.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(8\)		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
57.3.c.a	$57$	$3$	57.c	19.b	$2$	$2$	$2$	$1.553$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			57.3.c.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(-20\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+q^{4}+4q^{5}-3q^{6}+\cdots\)
57.3.c.b	$57$	$3$	57.c	19.b	$2$	$4$	$4$	$1.553$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	$_{}$	None	None		✓	✓		57.3.c.b	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(34\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{3})q^{2}-\beta _{1}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
57.3.g.a	$57$	$3$	57.g	19.d	$6$	$6$	$3$	$1.553$	6.0.6967728.1	$_{}$	None	None		✓			57.3.g.a	$2$	$0$	\(-3\)	\(9\)	\(-2\)	\(26\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(2-\beta _{1})q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
57.3.g.b	$57$	$3$	57.g	19.d	$6$	$6$	$3$	$1.553$	6.0.92607408.1	$_{}$	None	None		✓			57.3.g.b	$2$	$0$	\(3\)	\(-9\)	\(4\)	\(-22\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}+(-2-\beta _{3})q^{3}+(1+\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
57.3.h.a	$57$	$3$	57.h	57.h	$6$	$8$	$4$	$1.553$	8.0.\(\cdots\).5	$_{}$	None	None		✓			57.3.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(48\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{6})q^{4}+\cdots\)
57.3.h.b	$57$	$3$	57.h	57.h	$6$	$16$	$8$	$1.553$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		✓	✓		57.3.h.b	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-68\)		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}-\beta _{6}q^{3}+(-2\beta _{1}-3\beta _{8}-2\beta _{9}+\cdots)q^{4}+\cdots\)
57.3.k.a	$57$	$3$	57.k	19.f	$18$	$18$	$3$	$1.553$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	$_{}$	None	None		✓			57.3.k.a	$2$	$0$	\(9\)	\(0\)	\(0\)	\(-9\)		$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(1+\beta _{8}+\beta _{9}-\beta _{13}+\beta _{14})q^{2}+(-2\beta _{3}+\cdots)q^{3}+\cdots\)
57.3.k.b	$57$	$3$	57.k	19.f	$18$	$24$	$4$	$1.553$		$_{}$	None	None		✓	✓		57.3.k.b	$2$	$0$	\(-9\)	\(0\)	\(0\)	\(-9\)			$\mathrm{SU}(2)[C_{18}]$
57.3.l.a	$57$	$3$	57.l	57.l	$18$	$6$	$1$	$1.553$	\(\Q(\zeta_{18})\)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			57.3.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{18}]$	\(q-3\zeta_{18}^{4}q^{3}+4\zeta_{18}^{2}q^{4}+(3\zeta_{18}+5\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
57.3.l.b	$57$	$3$	57.l	57.l	$18$	$60$	$10$	$1.553$		$_{}$	None	None		✓	✓		57.3.l.b	$4$	$0$	\(0\)	\(-12\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
57.4.a.a	$57$	$4$	57.a	1.a	$1$	$1$	$1$	$3.363$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	57.4.a.a	$1$	$1$	\(-1\)	\(3\)	\(-12\)	\(-20\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-7q^{4}-12q^{5}-3q^{6}+\cdots\)
57.4.a.b	$57$	$4$	57.a	1.a	$1$	$2$	$2$	$3.363$	\(\Q(\sqrt{33}) \)	$_{}$	None	None	✓	✓	✓	✓	57.4.a.b	$1$	$0$	\(1\)	\(-6\)	\(22\)	\(36\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-3q^{3}+\beta q^{4}+(10+2\beta )q^{5}+\cdots\)
57.4.a.c	$57$	$4$	57.a	1.a	$1$	$3$	$3$	$3.363$	3.3.2700.1	$_{}$	None	None	✓	✓	✓	✓	57.4.a.c	$1$	$1$	\(-3\)	\(-9\)	\(-12\)	\(-18\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}-3q^{3}+(3+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
57.4.a.d	$57$	$4$	57.a	1.a	$1$	$4$	$4$	$3.363$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	57.4.a.d	$1$	$0$	\(3\)	\(12\)	\(-6\)	\(38\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
57.4.d.a	$57$	$4$	57.d	57.d	$2$	$2$	$2$	$3.363$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			57.4.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-40\)		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{3}-8q^{4}-20q^{7}-3^{3}q^{9}+8\zeta_{6}q^{12}+\cdots\)
57.4.d.b	$57$	$4$	57.d	57.d	$2$	$4$	$4$	$3.363$	\(\Q(\sqrt{-10}, \sqrt{17})\)	$_{}$	None	None		✓			57.4.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-80\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+9q^{4}-\beta _{3}q^{5}+\cdots\)
57.4.d.c	$57$	$4$	57.d	57.d	$2$	$12$	$12$	$3.363$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		✓	✓		57.4.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(124\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(\beta _{1}-\beta _{7})q^{3}+(2+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
57.4.e.a	$57$	$4$	57.e	19.c	$3$	$10$	$5$	$3.363$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None		✓			57.4.e.a	$2$	$0$	\(-1\)	\(15\)	\(-4\)	\(30\)		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}-3\beta _{5}q^{3}+(-4-4\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)
57.4.e.b	$57$	$4$	57.e	19.c	$3$	$10$	$5$	$3.363$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None		✓			57.4.e.b	$2$	$0$	\(1\)	\(-15\)	\(12\)	\(-54\)		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-3-3\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
57.4.f.a	$57$	$4$	57.f	57.f	$6$	$2$	$1$	$3.363$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			57.4.f.a	$4$	$0$	\(0\)	\(-9\)	\(0\)	\(74\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-3-3\zeta_{6})q^{3}+8\zeta_{6}q^{4}+37q^{7}+\cdots\)
57.4.f.b	$57$	$4$	57.f	57.f	$6$	$2$	$1$	$3.363$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			57.4.f.b	$4$	$0$	\(0\)	\(9\)	\(0\)	\(-34\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(3+3\zeta_{6})q^{3}+8\zeta_{6}q^{4}-17q^{7}+3^{3}\zeta_{6}q^{9}+\cdots\)
57.4.f.c	$57$	$4$	57.f	57.f	$6$	$32$	$16$	$3.363$		$_{}$	None	None		✓	✓		57.4.f.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-56\)			$\mathrm{SU}(2)[C_{6}]$
57.4.i.a	$57$	$4$	57.i	19.e	$9$	$24$	$4$	$3.363$		$_{}$	None	None		✓			57.4.i.a	$2$	$0$	\(-3\)	\(0\)	\(-12\)	\(36\)			$\mathrm{SU}(2)[C_{9}]$
57.4.i.b	$57$	$4$	57.i	19.e	$9$	$36$	$6$	$3.363$		$_{}$	None	None		✓	✓		57.4.i.b	$2$	$0$	\(3\)	\(0\)	\(12\)	\(-48\)			$\mathrm{SU}(2)[C_{9}]$
57.4.j.a	$57$	$4$	57.j	57.j	$18$	$108$	$18$	$3.363$		$_{}$	None	None		✓	✓	✓	57.4.j.a	$4$	$0$	\(0\)	\(-9\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
57.5.b.a	$57$	$5$	57.b	3.b	$2$	$24$	$24$	$5.892$		$_{}$	None	None		✓	✓	✓	57.5.b.a	$2$	$0$	\(0\)	\(-10\)	\(0\)	\(-80\)			$\mathrm{SU}(2)[C_{2}]$
57.5.c.a	$57$	$5$	57.c	19.b	$2$	$14$	$14$	$5.892$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	$_{}$	None	None		✓	✓	✓	57.5.c.a	$2$	$0$	\(0\)	\(0\)	\(18\)	\(-54\)		$2^{11}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-11+\beta _{2})q^{4}+\cdots\)
57.5.g.a	$57$	$5$	57.g	19.d	$6$	$14$	$7$	$5.892$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	$_{}$	None	None		✓			57.5.g.a	$2$	$0$	\(-3\)	\(-63\)	\(-30\)	\(138\)		$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(-3-3\beta _{4})q^{3}+(8\beta _{4}+\beta _{10}+\cdots)q^{4}+\cdots\)
57.5.g.b	$57$	$5$	57.g	19.d	$6$	$14$	$7$	$5.892$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	$_{}$	None	None		✓			57.5.g.b	$2$	$0$	\(3\)	\(63\)	\(12\)	\(-174\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(3+3\beta _{7})q^{3}+(-\beta _{3}+8\beta _{7}+\cdots)q^{4}+\cdots\)
57.5.h.a	$57$	$5$	57.h	57.h	$6$	$48$	$24$	$5.892$		$_{}$	None	None		✓	✓	✓	57.5.h.a	$4$	$0$	\(0\)	\(-5\)	\(0\)	\(68\)			$\mathrm{SU}(2)[C_{6}]$
57.5.k.a	$57$	$5$	57.k	19.f	$18$	$36$	$6$	$5.892$		$_{}$	None	None		✓			57.5.k.a	$2$	$0$	\(-9\)	\(0\)	\(0\)	\(45\)			$\mathrm{SU}(2)[C_{18}]$
57.5.k.b	$57$	$5$	57.k	19.f	$18$	$42$	$7$	$5.892$		$_{}$	None	None		✓	✓		57.5.k.b	$2$	$0$	\(9\)	\(0\)	\(0\)	\(45\)			$\mathrm{SU}(2)[C_{18}]$
57.5.l.a	$57$	$5$	57.l	57.l	$18$	$6$	$1$	$5.892$	\(\Q(\zeta_{18})\)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			57.5.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{18}]$	\(q+9\zeta_{18}^{4}q^{3}+2^{4}\zeta_{18}^{2}q^{4}+(39\zeta_{18}+\cdots)q^{7}+\cdots\)
57.5.l.b	$57$	$5$	57.l	57.l	$18$	$144$	$24$	$5.892$		$_{}$	None	None		✓	✓		57.5.l.b	$4$	$0$	\(0\)	\(6\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
57.6.a.a	$57$	$6$	57.a	1.a	$1$	$1$	$1$	$9.142$	\(\Q\)	$_{}$	None	None	✓	✓			57.6.a.a	$1$	$0$	\(-2\)	\(9\)	\(-98\)	\(240\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+9q^{3}-28q^{4}-98q^{5}-18q^{6}+\cdots\)
57.6.a.b	$57$	$6$	57.a	1.a	$1$	$1$	$1$	$9.142$	\(\Q\)	$_{}$	None	None	✓	✓			57.6.a.b	$1$	$0$	\(11\)	\(9\)	\(6\)	\(-176\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+11q^{2}+9q^{3}+89q^{4}+6q^{5}+99q^{6}+\cdots\)
57.6.a.c	$57$	$6$	57.a	1.a	$1$	$2$	$2$	$9.142$	\(\Q(\sqrt{17}) \)	$_{}$	None	None	✓	✓	✓	✓	57.6.a.c	$1$	$1$	\(-3\)	\(18\)	\(-87\)	\(-251\)	$+$	$3$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+9q^{3}+(7+3\beta )q^{4}+\cdots\)