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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
483.2.a.a	$483$	$2$	483.a	1.a	$1$	$1$	$1$	$3.857$	$\Q$	None	✓	✓			483.2.a.a	$1$	$0$	$2$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots$
483.2.a.b	$483$	$2$	483.a	1.a	$1$	$1$	$1$	$3.857$	$\Q$	None	✓	✓			483.2.a.b	$1$	$0$	$2$	$1$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots$
483.2.a.c	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	$\Q(\sqrt{5})$	None	✓	✓	✓	✓	483.2.a.c	$1$	$1$	$-3$	$2$	$-5$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots$
483.2.a.d	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	$\Q(\sqrt{5})$	None	✓	✓	✓	✓	483.2.a.d	$1$	$1$	$-1$	$-2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-\beta )q^{5}+\cdots$
483.2.a.e	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	$\Q(\sqrt{5})$	None	✓	✓	✓		483.2.a.e	$1$	$0$	$-1$	$2$	$5$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(3-\beta )q^{5}+\cdots$
483.2.a.f	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	$\Q(\sqrt{13})$	None	✓	✓	✓	✓	483.2.a.f	$1$	$1$	$-1$	$2$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots$
483.2.a.g	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	$\Q(\sqrt{5})$	None	✓	✓	✓	✓	483.2.a.g	$1$	$1$	$1$	$-2$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
483.2.a.h	$483$	$2$	483.a	1.a	$1$	$3$	$3$	$3.857$	3.3.837.1	None	✓	✓	✓		483.2.a.h	$1$	$0$	$0$	$3$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
483.2.a.i	$483$	$2$	483.a	1.a	$1$	$4$	$4$	$3.857$	4.4.24197.1	None	✓	✓	✓	✓	483.2.a.i	$1$	$0$	$0$	$-4$	$5$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots$
483.2.a.j	$483$	$2$	483.a	1.a	$1$	$4$	$4$	$3.857$	4.4.15317.1	None	✓	✓	✓	✓	483.2.a.j	$1$	$0$	$2$	$-4$	$5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$
483.2.d.a	$483$	$2$	483.d	21.c	$2$	$4$	$4$	$3.857$	$\Q(i, \sqrt{5})$	None		✓			483.2.d.a	$2$	$0$	$0$	$-2$	$-6$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
483.2.d.b	$483$	$2$	483.d	21.c	$2$	$4$	$4$	$3.857$	$\Q(i, \sqrt{5})$	None		✓			483.2.d.a	$2$	$0$	$0$	$2$	$6$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
483.2.d.c	$483$	$2$	483.d	21.c	$2$	$8$	$8$	$3.857$	$\Q(\zeta_{16})$	None		✓			483.2.d.c	$4$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{16}^{4}q^{2}+(\zeta_{16}+\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots$
483.2.d.d	$483$	$2$	483.d	21.c	$2$	$44$	$44$	$3.857$		None		✓	✓		483.2.d.d	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
483.2.e.a	$483$	$2$	483.e	69.c	$2$	$48$	$48$	$3.857$		None		✓	✓	✓	483.2.e.a	$4$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
483.2.h.a	$483$	$2$	483.h	161.c	$2$	$8$	$8$	$3.857$	8.0.342102016.5	None		✓			483.2.h.a	$4$	$0$	$-8$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{1}q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots$
483.2.h.b	$483$	$2$	483.h	161.c	$2$	$12$	$12$	$3.857$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			483.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}-\beta _{5}q^{3}+(1-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
483.2.h.c	$483$	$2$	483.h	161.c	$2$	$12$	$12$	$3.857$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			483.2.h.c	$4$	$0$	$4$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{9}q^{3}+(3+\beta _{7})q^{4}-\beta _{5}q^{5}+\cdots$
483.2.i.a	$483$	$2$	483.i	7.c	$3$	$2$	$1$	$3.857$	$\Q(\sqrt{-3})$	None		✓			483.2.i.a	$2$	$0$	$0$	$-1$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots$
483.2.i.b	$483$	$2$	483.i	7.c	$3$	$2$	$1$	$3.857$	$\Q(\sqrt{-3})$	None		✓			483.2.i.b	$2$	$0$	$0$	$-1$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots$
483.2.i.c	$483$	$2$	483.i	7.c	$3$	$2$	$1$	$3.857$	$\Q(\sqrt{-3})$	None		✓			483.2.i.c	$2$	$0$	$1$	$-1$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
483.2.i.d	$483$	$2$	483.i	7.c	$3$	$2$	$1$	$3.857$	$\Q(\sqrt{-3})$	None		✓			483.2.i.d	$2$	$0$	$1$	$-1$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
483.2.i.e	$483$	$2$	483.i	7.c	$3$	$4$	$2$	$3.857$	$\Q(\sqrt{-3}, \sqrt{17})$	None		✓			483.2.i.e	$2$	$0$	$1$	$-2$	$1$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
483.2.i.f	$483$	$2$	483.i	7.c	$3$	$12$	$6$	$3.857$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			483.2.i.f	$2$	$0$	$1$	$6$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{5})q^{2}+\beta _{7}q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots$
483.2.i.g	$483$	$2$	483.i	7.c	$3$	$16$	$8$	$3.857$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			483.2.i.g	$2$	$0$	$-1$	$-8$	$-5$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots$
483.2.i.h	$483$	$2$	483.i	7.c	$3$	$20$	$10$	$3.857$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		483.2.i.h	$2$	$0$	$-3$	$10$	$5$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{4})q^{2}-\beta _{9}q^{3}+(-\beta _{1}-\beta _{8}+\cdots)q^{4}+\cdots$
483.2.j.a	$483$	$2$	483.j	161.g	$6$	$64$	$32$	$3.857$		None		✓	✓	✓	483.2.j.a	$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
483.2.m.a	$483$	$2$	483.m	483.m	$6$	$120$	$60$	$3.857$		None		✓	✓	✓	483.2.m.a	$8$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
483.2.n.a	$483$	$2$	483.n	21.g	$6$	$116$	$58$	$3.857$		None		✓	✓	✓	483.2.n.a	$4$	$0$	$0$	$0$	$0$	$-10$			$\mathrm{SU}(2)[C_{6}]$
483.2.q.a	$483$	$2$	483.q	23.c	$11$	$10$	$1$	$3.857$	$\Q(\zeta_{22})$	None		✓			483.2.q.a	$2$	$0$	$4$	$-1$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
483.2.q.b	$483$	$2$	483.q	23.c	$11$	$10$	$1$	$3.857$	$\Q(\zeta_{22})$	None		✓			483.2.q.b	$2$	$0$	$5$	$-1$	$-5$	$-1$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots$
483.2.q.c	$483$	$2$	483.q	23.c	$11$	$20$	$2$	$3.857$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			483.2.q.c	$2$	$0$	$-4$	$-2$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{12}q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots$
483.2.q.d	$483$	$2$	483.q	23.c	$11$	$60$	$6$	$3.857$		None		✓			483.2.q.d	$2$	$0$	$-1$	$6$	$-13$	$-6$			$\mathrm{SU}(2)[C_{11}]$
483.2.q.e	$483$	$2$	483.q	23.c	$11$	$60$	$6$	$3.857$		None		✓			483.2.q.e	$2$	$0$	$-1$	$6$	$5$	$6$			$\mathrm{SU}(2)[C_{11}]$
483.2.q.f	$483$	$2$	483.q	23.c	$11$	$80$	$8$	$3.857$		None		✓	✓		483.2.q.f	$2$	$0$	$1$	$-8$	$13$	$8$			$\mathrm{SU}(2)[C_{11}]$
483.2.r.a	$483$	$2$	483.r	161.k	$22$	$320$	$32$	$3.857$		None		✓	✓	✓	483.2.r.a	$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
483.2.u.a	$483$	$2$	483.u	69.g	$22$	$480$	$48$	$3.857$		None		✓	✓	✓	483.2.u.a	$4$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
483.2.v.a	$483$	$2$	483.v	483.v	$22$	$600$	$60$	$3.857$		None		✓	✓	✓	483.2.v.a	$8$	$0$	$0$	$0$	$0$	$-18$			$\mathrm{SU}(2)[C_{22}]$
483.2.y.a	$483$	$2$	483.y	161.m	$33$	$320$	$16$	$3.857$		None		✓			483.2.y.a	$4$	$0$	$2$	$-16$	$-2$	$2$			$\mathrm{SU}(2)[C_{33}]$
483.2.y.b	$483$	$2$	483.y	161.m	$33$	$320$	$16$	$3.857$		None		✓			483.2.y.b	$4$	$0$	$2$	$16$	$-2$	$2$			$\mathrm{SU}(2)[C_{33}]$
483.2.bb.a	$483$	$2$	483.bb	483.ab	$66$	$1200$	$60$	$3.857$		None		✓	✓	✓	483.2.bb.a	$8$	$0$	$0$	$-27$	$0$	$-36$			$\mathrm{SU}(2)[C_{66}]$
483.2.bc.a	$483$	$2$	483.bc	483.ac	$66$	$1200$	$60$	$3.857$		None		✓	✓	✓	483.2.bc.a	$8$	$0$	$0$	$-9$	$0$	$-44$			$\mathrm{SU}(2)[C_{66}]$
483.2.bf.a	$483$	$2$	483.bf	161.o	$66$	$640$	$32$	$3.857$		None		✓	✓	✓	483.2.bf.a	$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{66}]$
483.3.b.a	$483$	$3$	483.b	3.b	$2$	$88$	$88$	$13.161$		None		✓	✓	✓	483.3.b.a	$2$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
483.3.f.a	$483$	$3$	483.f	23.b	$2$	$48$	$48$	$13.161$		None		✓	✓	✓	483.3.f.a	$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
483.3.g.a	$483$	$3$	483.g	7.b	$2$	$60$	$60$	$13.161$		None		✓	✓	✓	483.3.g.a	$2$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$
483.4.a.a	$483$	$4$	483.a	1.a	$1$	$3$	$3$	$28.498$	3.3.3877.1	None	✓	✓			483.4.a.a	$1$	$1$	$-4$	$9$	$2$	$-21$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+3q^{3}+(1+4\beta _{1}+\beta _{2})q^{4}+\cdots$
483.4.a.b	$483$	$4$	483.a	1.a	$1$	$4$	$4$	$28.498$	4.4.8184789.1	None	✓	✓	✓		483.4.a.b	$1$	$1$	$2$	$12$	$-23$	$-28$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+3q^{3}+(3+\beta _{1})q^{4}+(-6+\cdots)q^{5}+\cdots$
483.4.a.c	$483$	$4$	483.a	1.a	$1$	$7$	$7$	$28.498$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	483.4.a.c	$1$	$1$	$-6$	$21$	$-41$	$49$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+3q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
483.4.a.d	$483$	$4$	483.a	1.a	$1$	$7$	$7$	$28.498$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	483.4.a.d	$1$	$1$	$-2$	$-21$	$-11$	$-49$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{4}+\beta _{5})q^{4}+\cdots$

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