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Results (1-50 of 193 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
56.1.h.a	$56$	$1$	56.h	56.h	$2$	$1$	$1$	$0.028$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$1$		\(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots\)
56.2.a.a	$56$	$2$	56.a	1.a	$1$	$1$	$1$	$0.447$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{9}-4q^{11}+2q^{13}+\cdots\)
56.2.a.b	$56$	$2$	56.a	1.a	$1$	$1$	$1$	$0.447$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}+q^{7}+q^{9}-8q^{15}+\cdots\)
56.2.b.a	$56$	$2$	56.b	8.b	$2$	$2$	$2$	$0.447$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+\beta q^{3}-2q^{4}-\beta q^{5}-2q^{6}+\cdots\)
56.2.b.b	$56$	$2$	56.b	8.b	$2$	$4$	$4$	$0.447$	4.0.2312.1	$_{}$	None	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
56.2.e.a	$56$	$2$	56.e	56.e	$2$	$2$	$2$	$0.447$	\(\Q(\sqrt{-7}) \)	$_{}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+(-2+\beta )q^{4}+(1-2\beta )q^{7}+\cdots\)
56.2.e.b	$56$	$2$	56.e	56.e	$2$	$4$	$4$	$0.447$	\(\Q(i, \sqrt{6})\)	$_{}$	None	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+\cdots\)
56.2.i.a	$56$	$2$	56.i	7.c	$3$	$2$	$1$	$0.447$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-3\)	\(1\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
56.2.i.b	$56$	$2$	56.i	7.c	$3$	$2$	$1$	$0.447$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
56.2.m.a	$56$	$2$	56.m	56.m	$6$	$12$	$6$	$0.447$	12.0.\(\cdots\).2	$_{}$	None	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{8})q^{2}+(-1-\beta _{10})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
56.2.p.a	$56$	$2$	56.p	56.p	$6$	$12$	$6$	$0.447$	12.0.\(\cdots\).1	$_{}$	None	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{5})q^{2}+\beta _{6}q^{3}-\beta _{3}q^{4}+\cdots\)
56.3.c.a	$56$	$3$	56.c	7.b	$2$	$4$	$4$	$1.526$	4.0.2048.2	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
56.3.g.a	$56$	$3$	56.g	8.d	$2$	$4$	$4$	$1.526$	\(\Q(\sqrt{2}, \sqrt{-7})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(2-\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
56.3.g.b	$56$	$3$	56.g	8.d	$2$	$8$	$8$	$1.526$	8.0.\(\cdots\).3	$_{}$	None	None		$2$	$0$	\(1\)	\(-8\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-1+\beta _{3}-\beta _{4})q^{3}+(1+\beta _{6}+\cdots)q^{4}+\cdots\)
56.3.h.a	$56$	$3$	56.h	56.h	$2$	$2$	$2$	$1.526$	\(\Q(\sqrt{7}) \)	$_{}$	\(\Q(\sqrt{-14}) \)	None	✓	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(14\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+\beta q^{3}+4q^{4}-\beta q^{5}-2\beta q^{6}+\cdots\)
56.3.h.b	$56$	$3$	56.h	56.h	$2$	$2$	$2$	$1.526$	\(\Q(\sqrt{-7}) \)	$_{}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(3\)	\(0\)	\(0\)	\(14\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+\beta )q^{2}+(-1+3\beta )q^{4}+7q^{7}+\cdots\)
56.3.h.c	$56$	$3$	56.h	56.h	$2$	$2$	$2$	$1.526$	\(\Q(\sqrt{2}) \)	$_{}$	\(\Q(\sqrt{-14}) \)	None	✓	$4$	$0$	\(4\)	\(0\)	\(0\)	\(-14\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+\beta q^{3}+4q^{4}-3\beta q^{5}+2\beta q^{6}+\cdots\)
56.3.h.d	$56$	$3$	56.h	56.h	$2$	$8$	$8$	$1.526$	8.0.\(\cdots\).51	$_{}$	None	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(-16\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{6}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
56.3.j.a	$56$	$3$	56.j	56.j	$6$	$28$	$14$	$1.526$		$_{}$	None	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{6}]$
56.3.k.a	$56$	$3$	56.k	56.k	$6$	$2$	$1$	$1.526$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(-4\)	\(-1\)	\(-9\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-2q^{2}-\zeta_{6}q^{3}+4q^{4}+(-3-3\zeta_{6})q^{5}+\cdots\)
56.3.k.b	$56$	$3$	56.k	56.k	$6$	$2$	$1$	$1.526$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(2\)	\(-1\)	\(9\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{6}q^{2}-\zeta_{6}q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
56.3.k.c	$56$	$3$	56.k	56.k	$6$	$12$	$6$	$1.526$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{7}q^{2}+(1+\beta _{1}+\beta _{4}+\beta _{8})q^{3}+(-1+\cdots)q^{4}+\cdots\)
56.3.k.d	$56$	$3$	56.k	56.k	$6$	$12$	$6$	$1.526$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		$4$	$0$	\(2\)	\(-6\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(\beta _{8}-\beta _{9}-\beta _{10})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
56.3.o.a	$56$	$3$	56.o	7.d	$6$	$8$	$4$	$1.526$	8.0.\(\cdots\).2	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{3}+\beta _{4}q^{5}+(1-3\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
56.4.a.a	$56$	$4$	56.a	1.a	$1$	$1$	$1$	$3.304$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-16\)	\(-7\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2^{4}q^{5}-7q^{7}-23q^{9}+24q^{11}+\cdots\)
56.4.a.b	$56$	$4$	56.a	1.a	$1$	$1$	$1$	$3.304$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(6\)	\(8\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+6q^{3}+8q^{5}-7q^{7}+9q^{9}+56q^{11}+\cdots\)
56.4.a.c	$56$	$4$	56.a	1.a	$1$	$2$	$2$	$3.304$	\(\Q(\sqrt{57}) \)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-2\)	\(22\)	\(14\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(11+\beta )q^{5}+7q^{7}+\cdots\)
56.4.b.a	$56$	$4$	56.b	8.b	$2$	$8$	$8$	$3.304$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-56\)		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
56.4.b.b	$56$	$4$	56.b	8.b	$2$	$10$	$10$	$3.304$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(3\)	\(0\)	\(0\)	\(70\)		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)
56.4.e.a	$56$	$4$	56.e	56.e	$2$	$2$	$2$	$3.304$	\(\Q(\sqrt{-7}) \)	$_{}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(-5\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2-\beta )q^{2}+(2+5\beta )q^{4}+(-7+14\beta )q^{7}+\cdots\)
56.4.e.b	$56$	$4$	56.e	56.e	$2$	$4$	$4$	$3.304$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	$_{}$	None	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(-6-2\beta _{2}+\cdots)q^{4}+\cdots\)
56.4.e.c	$56$	$4$	56.e	56.e	$2$	$16$	$16$	$3.304$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2})q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}+\beta _{12}q^{5}+\cdots\)
56.4.i.a	$56$	$4$	56.i	7.c	$3$	$6$	$3$	$3.304$	6.0.11163123.4	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(-13\)	\(-20\)		$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{3}+(-5+5\beta _{1}-\beta _{3}-\beta _{4}-2\beta _{5})q^{5}+\cdots\)
56.4.i.b	$56$	$4$	56.i	7.c	$3$	$6$	$3$	$3.304$	6.0.11163123.4	$_{}$	None	None		$2$	$0$	\(0\)	\(7\)	\(3\)	\(-4\)		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
56.4.m.a	$56$	$4$	56.m	56.m	$6$	$44$	$22$	$3.304$		$_{}$	None	None		$4$	$0$	\(-2\)	\(-6\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
56.4.p.a	$56$	$4$	56.p	56.p	$6$	$44$	$22$	$3.304$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{6}]$
56.5.c.a	$56$	$5$	56.c	7.b	$2$	$8$	$8$	$5.789$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(56\)		$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(7-\beta _{5})q^{7}+(-31+\cdots)q^{9}+\cdots\)
56.5.g.a	$56$	$5$	56.g	8.d	$2$	$2$	$2$	$5.789$	\(\Q(\sqrt{-7}) \)	$_{}$	None	None		$2$	$0$	\(6\)	\(-12\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3+\beta )q^{2}-6q^{3}+(2+6\beta )q^{4}+4\beta q^{5}+\cdots\)
56.5.g.b	$56$	$5$	56.g	8.d	$2$	$22$	$22$	$5.789$		$_{}$	None	None		$2$	$0$	\(-9\)	\(12\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
56.5.h.a	$56$	$5$	56.h	56.h	$2$	$1$	$1$	$5.789$	\(\Q\)	$_{}$	\(\Q(\sqrt{-14}) \)	None	✓	$2$	$0$	\(4\)	\(-10\)	\(22\)	\(49\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{2}-10q^{3}+2^{4}q^{4}+22q^{5}-40q^{6}+\cdots\)
56.5.h.b	$56$	$5$	56.h	56.h	$2$	$1$	$1$	$5.789$	\(\Q\)	$_{}$	\(\Q(\sqrt{-14}) \)	None	✓	$2$	$0$	\(4\)	\(10\)	\(-22\)	\(49\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{2}+10q^{3}+2^{4}q^{4}-22q^{5}+40q^{6}+\cdots\)
56.5.h.c	$56$	$5$	56.h	56.h	$2$	$2$	$2$	$5.789$	\(\Q(\sqrt{14}) \)	$_{}$	\(\Q(\sqrt{-14}) \)	None	✓	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(-98\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{2}+\beta q^{3}+2^{4}q^{4}+3\beta q^{5}-4\beta q^{6}+\cdots\)
56.5.h.d	$56$	$5$	56.h	56.h	$2$	$2$	$2$	$5.789$	\(\Q(\sqrt{-7}) \)	$_{}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-98\)		$3$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}+(-2^{4}+\beta )q^{4}-7^{2}q^{7}+(2^{4}+\cdots)q^{8}+\cdots\)
56.5.h.e	$56$	$5$	56.h	56.h	$2$	$24$	$24$	$5.789$		$_{}$	None	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(96\)			$\mathrm{SU}(2)[C_{2}]$
56.5.j.a	$56$	$5$	56.j	56.j	$6$	$60$	$30$	$5.789$		$_{}$	None	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{6}]$
56.5.k.a	$56$	$5$	56.k	56.k	$6$	$60$	$30$	$5.789$		$_{}$	None	None		$4$	$0$	\(-4\)	\(-2\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
56.5.o.a	$56$	$5$	56.o	7.d	$6$	$16$	$8$	$5.789$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-56\)		$2^{38}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}-\beta _{6})q^{3}+\beta _{4}q^{5}+(-5-3\beta _{1}+\cdots)q^{7}+\cdots\)
56.6.a.a	$56$	$6$	56.a	1.a	$1$	$1$	$1$	$8.981$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-6\)	\(4\)	\(49\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{3}+4q^{5}+7^{2}q^{7}-207q^{9}-240q^{11}+\cdots\)
56.6.a.b	$56$	$6$	56.a	1.a	$1$	$1$	$1$	$8.981$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(30\)	\(32\)	\(49\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+30q^{3}+2^{5}q^{5}+7^{2}q^{7}+657q^{9}+\cdots\)
56.6.a.c	$56$	$6$	56.a	1.a	$1$	$2$	$2$	$8.981$	\(\Q(\sqrt{177}) \)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-26\)	\(-62\)	\(98\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-13-\beta )q^{3}+(-31-5\beta )q^{5}+7^{2}q^{7}+\cdots\)