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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
77.1.j.a	$77$	$1$	77.j	77.j	$10$	$4$	$1$	$0.038$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-7}) \)	None		✓	✓	✓	77.1.j.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-1\)		$1$		\(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
77.2.a.a	$77$	$2$	77.a	1.a	$1$	$1$	$1$	$0.615$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	77.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{4}-q^{5}-q^{7}+6q^{9}-q^{11}+\cdots\)
77.2.a.b	$77$	$2$	77.a	1.a	$1$	$1$	$1$	$0.615$	\(\Q\)	$_{}$	None	None	✓	✓			77.2.a.b	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}+q^{7}-2q^{9}-q^{11}+\cdots\)
77.2.a.c	$77$	$2$	77.a	1.a	$1$	$1$	$1$	$0.615$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	77.2.a.c	$1$	$0$	\(1\)	\(2\)	\(-2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}-q^{4}-2q^{5}+2q^{6}-q^{7}+\cdots\)
77.2.a.d	$77$	$2$	77.a	1.a	$1$	$2$	$2$	$0.615$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	✓	✓		77.2.a.d	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{3}+3q^{4}-2q^{5}+(-5+\cdots)q^{6}+\cdots\)
77.2.b.a	$77$	$2$	77.b	77.b	$2$	$2$	$2$	$0.615$	\(\Q(\sqrt{-7}) \)	$_{}$	\(\Q(\sqrt{-7}) \)	None		✓			77.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}-5q^{4}-\beta q^{7}+3\beta q^{8}+3q^{9}+\cdots\)
77.2.b.b	$77$	$2$	77.b	77.b	$2$	$4$	$4$	$0.615$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	$_{}$	None	None		✓	✓		77.2.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{3}q^{5}+(2\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)
77.2.e.a	$77$	$2$	77.e	7.c	$3$	$6$	$3$	$0.615$	\(\Q(\zeta_{18})\)	$_{}$	None	None		✓			77.2.e.a	$2$	$0$	\(0\)	\(-3\)	\(-6\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
77.2.e.b	$77$	$2$	77.e	7.c	$3$	$6$	$3$	$0.615$	6.0.1783323.2	$_{}$	None	None		✓			77.2.e.b	$2$	$0$	\(0\)	\(1\)	\(2\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{5})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
77.2.f.a	$77$	$2$	77.f	11.c	$5$	$8$	$2$	$0.615$	8.0.159390625.1	$_{}$	None	None		✓			77.2.f.a	$2$	$0$	\(-1\)	\(-4\)	\(3\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
77.2.f.b	$77$	$2$	77.f	11.c	$5$	$16$	$4$	$0.615$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		✓	✓		77.2.f.b	$2$	$0$	\(-3\)	\(-2\)	\(-5\)	\(-4\)		$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{5}-\beta _{6})q^{2}+(\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots\)
77.2.i.a	$77$	$2$	77.i	77.i	$6$	$12$	$6$	$0.615$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		✓	✓	✓	77.2.i.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{7})q^{2}+(-1+\beta _{2}-\beta _{8}-\beta _{9}+\cdots)q^{3}+\cdots\)
77.2.l.a	$77$	$2$	77.l	77.l	$10$	$8$	$2$	$0.615$	8.0.37515625.1	$_{}$	\(\Q(\sqrt{-7}) \)	None		✓			77.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{10}]$	\(q+(1-\beta _{1}+\beta _{3}+\beta _{4}+\beta _{5}-\beta _{6})q^{2}+\cdots\)
77.2.l.b	$77$	$2$	77.l	77.l	$10$	$16$	$4$	$0.615$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		✓	✓		77.2.l.b	$4$	$0$	\(-10\)	\(0\)	\(0\)	\(-10\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1-\beta _{9}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
77.2.m.a	$77$	$2$	77.m	77.m	$15$	$8$	$1$	$0.615$	\(\Q(\zeta_{15})\)	$_{}$	None	None		✓			77.2.m.a	$4$	$0$	\(-2\)	\(1\)	\(-5\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1+\zeta_{15}^{4}-\zeta_{15}^{5}+\zeta_{15}^{7})q^{2}+\cdots\)
77.2.m.b	$77$	$2$	77.m	77.m	$15$	$40$	$5$	$0.615$		$_{}$	None	None		✓	✓		77.2.m.b	$4$	$0$	\(-3\)	\(-4\)	\(4\)	\(-2\)			$\mathrm{SU}(2)[C_{15}]$
77.2.n.a	$77$	$2$	77.n	77.n	$30$	$48$	$6$	$0.615$		$_{}$	None	None		✓	✓	✓	77.2.n.a	$4$	$0$	\(-5\)	\(-9\)	\(-15\)	\(-5\)			$\mathrm{SU}(2)[C_{30}]$
77.3.c.a	$77$	$3$	77.c	11.b	$2$	$2$	$2$	$2.098$	\(\Q(\sqrt{-7}) \)	$_{}$	None	None		✓			77.3.c.a	$2$	$0$	\(0\)	\(4\)	\(12\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+2q^{3}-3q^{4}+6q^{5}-2\beta q^{6}+\cdots\)
77.3.c.b	$77$	$3$	77.c	11.b	$2$	$10$	$10$	$2.098$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None		✓	✓		77.3.c.b	$2$	$0$	\(0\)	\(2\)	\(-18\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-2+\beta _{7})q^{4}+(-2+\cdots)q^{5}+\cdots\)
77.3.d.a	$77$	$3$	77.d	7.b	$2$	$12$	$12$	$2.098$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		✓	✓	✓	77.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{3}+\beta _{5})q^{4}+\cdots\)
77.3.g.a	$77$	$3$	77.g	7.d	$6$	$28$	$14$	$2.098$		$_{}$	None	None		✓	✓	✓	77.3.g.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(-2\)			$\mathrm{SU}(2)[C_{6}]$
77.3.h.a	$77$	$3$	77.h	77.h	$6$	$4$	$2$	$2.098$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	$_{}$	None	None		✓			77.3.h.a	$4$	$0$	\(0\)	\(-10\)	\(12\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}-5\beta _{2}q^{3}+3\beta _{2}q^{4}+(6-6\beta _{2}+\cdots)q^{5}+\cdots\)
77.3.h.b	$77$	$3$	77.h	77.h	$6$	$24$	$12$	$2.098$		$_{}$	None	None		✓	✓		77.3.h.b	$4$	$0$	\(0\)	\(8\)	\(-16\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
77.3.j.a	$77$	$3$	77.j	77.j	$10$	$8$	$2$	$2.098$	8.0.37515625.1	$_{}$	\(\Q(\sqrt{-7}) \)	None		✓			77.3.j.a	$4$	$0$	\(6\)	\(0\)	\(0\)	\(14\)		$1$	$\mathrm{U}(1)[D_{10}]$	\(q+(-\beta _{2}-\beta _{4}-2\beta _{5}+\beta _{7})q^{2}+(-1+\cdots)q^{4}+\cdots\)
77.3.j.b	$77$	$3$	77.j	77.j	$10$	$48$	$12$	$2.098$		$_{}$	None	None		✓	✓		77.3.j.b	$4$	$0$	\(-10\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{10}]$
77.3.k.a	$77$	$3$	77.k	11.d	$10$	$48$	$12$	$2.098$		$_{}$	None	None		✓	✓	✓	77.3.k.a	$2$	$0$	\(0\)	\(-6\)	\(6\)	\(0\)			$\mathrm{SU}(2)[C_{10}]$
77.3.o.a	$77$	$3$	77.o	77.o	$30$	$112$	$14$	$2.098$		$_{}$	None	None		✓	✓	✓	77.3.o.a	$4$	$0$	\(-5\)	\(-3\)	\(-1\)	\(-25\)			$\mathrm{SU}(2)[C_{30}]$
77.3.p.a	$77$	$3$	77.p	77.p	$30$	$112$	$14$	$2.098$		$_{}$	None	None		✓	✓	✓	77.3.p.a	$4$	$0$	\(-5\)	\(-9\)	\(-15\)	\(-23\)			$\mathrm{SU}(2)[C_{30}]$
77.4.a.a	$77$	$4$	77.a	1.a	$1$	$1$	$1$	$4.543$	\(\Q\)	$_{}$	None	None	✓	✓			77.4.a.a	$1$	$0$	\(3\)	\(4\)	\(12\)	\(7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+4q^{3}+q^{4}+12q^{5}+12q^{6}+\cdots\)
77.4.a.b	$77$	$4$	77.a	1.a	$1$	$2$	$2$	$4.543$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	✓	✓	✓	77.4.a.b	$1$	$1$	\(-2\)	\(-4\)	\(-4\)	\(14\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots\)
77.4.a.c	$77$	$4$	77.a	1.a	$1$	$4$	$4$	$4.543$	4.4.509800.1	$_{}$	None	None	✓	✓	✓	✓	77.4.a.c	$1$	$1$	\(-4\)	\(-12\)	\(-18\)	\(-28\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{2}+(-3+\beta _{3})q^{3}+(6+\cdots)q^{4}+\cdots\)
77.4.a.d	$77$	$4$	77.a	1.a	$1$	$4$	$4$	$4.543$	4.4.522072.1	$_{}$	None	None	✓	✓	✓	✓	77.4.a.d	$1$	$0$	\(-2\)	\(14\)	\(10\)	\(-28\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(4+\beta _{1})q^{3}+(6-\beta _{2}-2\beta _{3})q^{4}+\cdots\)
77.4.a.e	$77$	$4$	77.a	1.a	$1$	$5$	$5$	$4.543$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	$_{}$	None	None	✓	✓	✓		77.4.a.e	$1$	$0$	\(1\)	\(2\)	\(-24\)	\(35\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(9+\beta _{1}+\beta _{2})q^{4}+\cdots\)
77.4.b.a	$77$	$4$	77.b	77.b	$2$	$2$	$2$	$4.543$	\(\Q(\sqrt{-7}) \)	$_{}$	\(\Q(\sqrt{-7}) \)	None		✓			77.4.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}+q^{4}-7\beta q^{7}-9\beta q^{8}+3^{3}q^{9}+\cdots\)
77.4.b.b	$77$	$4$	77.b	77.b	$2$	$20$	$20$	$4.543$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		✓	✓		77.4.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{2}+\beta _{11}q^{3}+(-5+\beta _{3})q^{4}+\cdots\)
77.4.e.a	$77$	$4$	77.e	7.c	$3$	$2$	$1$	$4.543$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			77.4.e.a	$2$	$1$	\(-3\)	\(-3\)	\(-2\)	\(-35\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
77.4.e.b	$77$	$4$	77.e	7.c	$3$	$18$	$9$	$4.543$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		✓			77.4.e.b	$2$	$0$	\(3\)	\(15\)	\(32\)	\(-3\)		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(2+\beta _{1}-\beta _{3}-2\beta _{5}+\beta _{7}+\cdots)q^{3}+\cdots\)
77.4.e.c	$77$	$4$	77.e	7.c	$3$	$20$	$10$	$4.543$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		✓	✓		77.4.e.c	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(-30\)		$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+\beta _{6}q^{3}+(-5+\beta _{3}+5\beta _{5}+\cdots)q^{4}+\cdots\)
77.4.f.a	$77$	$4$	77.f	11.c	$5$	$32$	$8$	$4.543$		$_{}$	None	None		✓			77.4.f.a	$2$	$0$	\(-2\)	\(18\)	\(16\)	\(-56\)			$\mathrm{SU}(2)[C_{5}]$
77.4.f.b	$77$	$4$	77.f	11.c	$5$	$40$	$10$	$4.543$		$_{}$	None	None		✓	✓		77.4.f.b	$2$	$0$	\(8\)	\(-18\)	\(-24\)	\(70\)			$\mathrm{SU}(2)[C_{5}]$
77.4.i.a	$77$	$4$	77.i	77.i	$6$	$44$	$22$	$4.543$		$_{}$	None	None		✓	✓	✓	77.4.i.a	$4$	$0$	\(0\)	\(-6\)	\(-30\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
77.4.l.a	$77$	$4$	77.l	77.l	$10$	$8$	$2$	$4.543$	8.0.37515625.1	$_{}$	\(\Q(\sqrt{-7}) \)	None		✓			77.4.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{10}]$	\(q+(-\beta _{2}+\beta _{4}+3\beta _{5}+2\beta _{7})q^{2}+(13+\cdots)q^{4}+\cdots\)
77.4.l.b	$77$	$4$	77.l	77.l	$10$	$80$	$20$	$4.543$		$_{}$	None	None		✓	✓		77.4.l.b	$4$	$0$	\(-10\)	\(0\)	\(0\)	\(-15\)			$\mathrm{SU}(2)[C_{10}]$
77.4.m.a	$77$	$4$	77.m	77.m	$15$	$176$	$22$	$4.543$		$_{}$	None	None		✓	✓	✓	77.4.m.a	$4$	$0$	\(-1\)	\(-3\)	\(-11\)	\(12\)			$\mathrm{SU}(2)[C_{15}]$
77.4.n.a	$77$	$4$	77.n	77.n	$30$	$176$	$22$	$4.543$		$_{}$	None	None		✓	✓	✓	77.4.n.a	$4$	$0$	\(-5\)	\(-9\)	\(15\)	\(0\)			$\mathrm{SU}(2)[C_{30}]$
77.5.c.a	$77$	$5$	77.c	11.b	$2$	$24$	$24$	$7.959$		$_{}$	None	None		✓	✓	✓	77.5.c.a	$2$	$0$	\(0\)	\(-6\)	\(6\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
77.5.d.a	$77$	$5$	77.d	7.b	$2$	$28$	$28$	$7.959$		$_{}$	None	None		✓	✓	✓	77.5.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-50\)			$\mathrm{SU}(2)[C_{2}]$
77.5.g.a	$77$	$5$	77.g	7.d	$6$	$52$	$26$	$7.959$		$_{}$	None	None		✓	✓	✓	77.5.g.a	$2$	$0$	\(0\)	\(-18\)	\(0\)	\(-54\)			$\mathrm{SU}(2)[C_{6}]$
77.5.h.a	$77$	$5$	77.h	77.h	$6$	$60$	$30$	$7.959$		$_{}$	None	None		✓	✓	✓	77.5.h.a	$4$	$0$	\(0\)	\(-2\)	\(16\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
77.5.j.a	$77$	$5$	77.j	77.j	$10$	$8$	$2$	$7.959$	8.0.37515625.1	$_{}$	\(\Q(\sqrt{-7}) \)	None		✓			77.5.j.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-98\)		$3^{4}$	$\mathrm{U}(1)[D_{10}]$	\(q+(-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6})q^{2}+(-2^{4}+\cdots)q^{4}+\cdots\)

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