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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
261.1.f.a	$261$	$1$	261.f	29.c	$4$	$4$	$2$	$0.130$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		✓	✓	✓	261.1.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$1$		\(q-\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
261.2.a.a	$261$	$2$	261.a	1.a	$1$	$2$	$2$	$2.084$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	✓	✓	✓	261.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}-2q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.2.a.b	$261$	$2$	261.a	1.a	$1$	$2$	$2$	$2.084$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓		✓	✓	87.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\)
261.2.a.c	$261$	$2$	261.a	1.a	$1$	$2$	$2$	$2.084$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	✓	✓	✓	261.2.a.a	$1$	$0$	\(1\)	\(0\)	\(4\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.2.a.d	$261$	$2$	261.a	1.a	$1$	$2$	$2$	$2.084$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓				29.2.a.a	$1$	$0$	\(2\)	\(0\)	\(2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}-2\beta q^{7}+\cdots\)
261.2.a.e	$261$	$2$	261.a	1.a	$1$	$3$	$3$	$2.084$	3.3.229.1	$_{}$	None	None	✓		✓		87.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+2\beta _{1}q^{5}+\cdots\)
261.2.c.a	$261$	$2$	261.c	29.b	$2$	$2$	$2$	$2.084$	\(\Q(\sqrt{-5}) \)	$_{}$	None	None					29.2.b.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-3q^{4}+3q^{5}+2q^{7}-\beta q^{8}+\cdots\)
261.2.c.b	$261$	$2$	261.c	29.b	$2$	$4$	$4$	$2.084$	\(\Q(i, \sqrt{5})\)	$_{}$	None	None					87.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+2\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.2.c.c	$261$	$2$	261.c	29.b	$2$	$6$	$6$	$2.084$	6.0.\(\cdots\).1	$_{}$	\(\Q(\sqrt{-87}) \)	None		✓	✓		261.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
261.2.e.a	$261$	$2$	261.e	9.c	$3$	$22$	$11$	$2.084$		$_{}$	None	None		✓			261.2.e.a	$2$	$0$	\(-1\)	\(-2\)	\(1\)	\(7\)			$\mathrm{SU}(2)[C_{3}]$
261.2.e.b	$261$	$2$	261.e	9.c	$3$	$34$	$17$	$2.084$		$_{}$	None	None		✓	✓		261.2.e.b	$2$	$0$	\(-1\)	\(-2\)	\(1\)	\(-9\)			$\mathrm{SU}(2)[C_{3}]$
261.2.g.a	$261$	$2$	261.g	87.f	$4$	$4$	$2$	$2.084$	\(\Q(\zeta_{8})\)	$_{}$	None	None		✓			261.2.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
261.2.g.b	$261$	$2$	261.g	87.f	$4$	$8$	$4$	$2.084$	\(\Q(i, \sqrt{2}, \sqrt{5})\)	$_{}$	None	None		✓			261.2.g.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$3^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+(2\beta _{2}+\beta _{6})q^{4}+(\beta _{4}-\beta _{7})q^{5}+\cdots\)
261.2.g.c	$261$	$2$	261.g	87.f	$4$	$8$	$4$	$2.084$	\(\Q(i, \sqrt{2}, \sqrt{13})\)	$_{}$	None	None		✓			261.2.g.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(2\beta _{3}+\beta _{5})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
261.2.i.a	$261$	$2$	261.i	261.i	$6$	$56$	$28$	$2.084$		$_{}$	None	None		✓	✓	✓	261.2.i.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)			$\mathrm{SU}(2)[C_{6}]$
261.2.k.a	$261$	$2$	261.k	29.d	$7$	$6$	$1$	$2.084$	\(\Q(\zeta_{14})\)	$_{}$	None	None					29.2.d.a	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1-\zeta_{14}-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+\cdots\)
261.2.k.b	$261$	$2$	261.k	29.d	$7$	$18$	$3$	$2.084$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None					87.2.g.b	$2$	$0$	\(2\)	\(0\)	\(7\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+\beta _{3}q^{2}+(-\beta _{10}-\beta _{16})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
261.2.k.c	$261$	$2$	261.k	29.d	$7$	$18$	$3$	$2.084$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None					87.2.g.a	$2$	$0$	\(4\)	\(0\)	\(1\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\beta _{3}-\beta _{9})q^{2}+(2\beta _{1}+\beta _{5}-\beta _{6}+2\beta _{12}+\cdots)q^{4}+\cdots\)
261.2.k.d	$261$	$2$	261.k	29.d	$7$	$24$	$4$	$2.084$		$_{}$	None	None		✓	✓		261.2.k.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{7}]$
261.2.l.a	$261$	$2$	261.l	261.l	$12$	$112$	$28$	$2.084$		$_{}$	None	None		✓	✓	✓	261.2.l.a	$4$	$0$	\(-6\)	\(-4\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{12}]$
261.2.o.a	$261$	$2$	261.o	29.e	$14$	$12$	$2$	$2.084$	12.0.\(\cdots\).1	$_{}$	None	None					29.2.e.a	$2$	$0$	\(7\)	\(0\)	\(1\)	\(-11\)		$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(1-\beta _{3}-\beta _{7}-\beta _{9}-\beta _{10})q^{2}+(\beta _{1}+\cdots)q^{4}+\cdots\)
261.2.o.b	$261$	$2$	261.o	29.e	$14$	$24$	$4$	$2.084$		$_{}$	None	None					87.2.i.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(8\)			$\mathrm{SU}(2)[C_{14}]$
261.2.o.c	$261$	$2$	261.o	29.e	$14$	$36$	$6$	$2.084$		$_{}$	None	None		✓	✓		261.2.o.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{14}]$
261.2.q.a	$261$	$2$	261.q	261.q	$21$	$336$	$28$	$2.084$		$_{}$	None	None		✓	✓	✓	261.2.q.a	$4$	$0$	\(-5\)	\(-10\)	\(-9\)	\(-5\)			$\mathrm{SU}(2)[C_{21}]$
261.2.r.a	$261$	$2$	261.r	87.k	$28$	$120$	$10$	$2.084$		$_{}$	None	None		✓	✓	✓	261.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{28}]$
261.2.u.a	$261$	$2$	261.u	261.u	$42$	$336$	$28$	$2.084$		$_{}$	None	None		✓	✓	✓	261.2.u.a	$4$	$0$	\(-7\)	\(-14\)	\(-9\)	\(-5\)			$\mathrm{SU}(2)[C_{42}]$
261.2.x.a	$261$	$2$	261.x	261.x	$84$	$672$	$28$	$2.084$		$_{}$	None	None		✓	✓	✓	261.2.x.a	$4$	$0$	\(-36\)	\(-24\)	\(-42\)	\(-10\)			$\mathrm{SU}(2)[C_{84}]$
261.3.b.a	$261$	$3$	261.b	3.b	$2$	$20$	$20$	$7.112$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		✓	✓	✓	261.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$2^{9}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)
261.3.d.a	$261$	$3$	261.d	87.d	$2$	$20$	$20$	$7.112$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		✓	✓	✓	261.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$2^{9}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{2}+(2+\beta _{1})q^{4}-\beta _{13}q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.3.f.a	$261$	$3$	261.f	29.c	$4$	$8$	$4$	$7.112$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	$_{}$	None	None					29.3.c.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{4}+\cdots\)
261.3.f.b	$261$	$3$	261.f	29.c	$4$	$8$	$4$	$7.112$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	$_{}$	None	None					87.3.e.a	$2$	$0$	\(8\)	\(0\)	\(0\)	\(12\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{2}-\beta _{3})q^{2}+(\beta _{2}-2\beta _{3}-2\beta _{4}+\cdots)q^{4}+\cdots\)
261.3.f.c	$261$	$3$	261.f	29.c	$4$	$12$	$6$	$7.112$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None					87.3.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{1}-\beta _{9})q^{2}+(-\beta _{2}-\beta _{6}+3\beta _{7}+\cdots)q^{4}+\cdots\)
261.3.f.d	$261$	$3$	261.f	29.c	$4$	$20$	$10$	$7.112$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		✓	✓		261.3.f.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(-2\beta _{10}+\beta _{13})q^{4}-\beta _{16}q^{5}+\cdots\)
261.3.h.a	$261$	$3$	261.h	261.h	$6$	$116$	$58$	$7.112$		$_{}$	None	None		✓	✓	✓	261.3.h.a	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(-2\)			$\mathrm{SU}(2)[C_{6}]$
261.3.j.a	$261$	$3$	261.j	9.d	$6$	$112$	$56$	$7.112$		$_{}$	None	None		✓	✓	✓	261.3.j.a	$2$	$0$	\(0\)	\(2\)	\(-18\)	\(2\)			$\mathrm{SU}(2)[C_{6}]$
261.3.m.a	$261$	$3$	261.m	261.m	$12$	$232$	$58$	$7.112$		$_{}$	None	None		✓	✓	✓	261.3.m.a	$4$	$0$	\(-2\)	\(-4\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{12}]$
261.3.n.a	$261$	$3$	261.n	87.h	$14$	$120$	$20$	$7.112$		$_{}$	None	None		✓	✓	✓	261.3.n.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)			$\mathrm{SU}(2)[C_{14}]$
261.3.p.a	$261$	$3$	261.p	87.j	$14$	$120$	$20$	$7.112$		$_{}$	None	None		✓	✓	✓	261.3.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)			$\mathrm{SU}(2)[C_{14}]$
261.3.s.a	$261$	$3$	261.s	29.f	$28$	$48$	$4$	$7.112$		$_{}$	None	None					29.3.f.a	$2$	$0$	\(16\)	\(0\)	\(14\)	\(-10\)			$\mathrm{SU}(2)[C_{28}]$
261.3.s.b	$261$	$3$	261.s	29.f	$28$	$120$	$10$	$7.112$		$_{}$	None	None					87.3.l.a	$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{28}]$
261.3.s.c	$261$	$3$	261.s	29.f	$28$	$120$	$10$	$7.112$		$_{}$	None	None		✓			261.3.s.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{28}]$
261.3.t.a	$261$	$3$	261.t	261.t	$42$	$696$	$58$	$7.112$		$_{}$	None	None		✓	✓	✓	261.3.t.a	$4$	$0$	\(-15\)	\(-10\)	\(-15\)	\(-5\)			$\mathrm{SU}(2)[C_{42}]$
261.3.v.a	$261$	$3$	261.v	261.v	$42$	$696$	$58$	$7.112$		$_{}$	None	None		✓	✓	✓	261.3.v.a	$4$	$0$	\(-21\)	\(-14\)	\(-15\)	\(-5\)			$\mathrm{SU}(2)[C_{42}]$
261.3.w.a	$261$	$3$	261.w	261.w	$84$	$1392$	$58$	$7.112$		$_{}$	None	None		✓	✓	✓	261.3.w.a	$4$	$0$	\(-12\)	\(-24\)	\(-14\)	\(-10\)			$\mathrm{SU}(2)[C_{84}]$
261.4.a.a	$261$	$4$	261.a	1.a	$1$	$2$	$2$	$15.399$	\(\Q(\sqrt{41}) \)	$_{}$	None	None	✓				87.4.a.b	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-24\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{4}+(2-3\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
261.4.a.b	$261$	$4$	261.a	1.a	$1$	$2$	$2$	$15.399$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓				29.4.a.a	$1$	$1$	\(2\)	\(0\)	\(10\)	\(-16\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(-5+2\beta )q^{4}+(5+4\beta )q^{5}+\cdots\)
261.4.a.c	$261$	$4$	261.a	1.a	$1$	$2$	$2$	$15.399$	\(\Q(\sqrt{17}) \)	$_{}$	None	None	✓				87.4.a.a	$1$	$0$	\(5\)	\(0\)	\(11\)	\(-24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(3-\beta )q^{2}+(5-5\beta )q^{4}+(7-3\beta )q^{5}+\cdots\)
261.4.a.d	$261$	$4$	261.a	1.a	$1$	$5$	$5$	$15.399$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	$_{}$	None	None	✓		✓		87.4.a.d	$1$	$1$	\(-3\)	\(0\)	\(-29\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(6+\beta _{2}+\beta _{3})q^{4}+\cdots\)
261.4.a.e	$261$	$4$	261.a	1.a	$1$	$5$	$5$	$15.399$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	$_{}$	None	None	✓				87.4.a.c	$1$	$0$	\(-3\)	\(0\)	\(1\)	\(4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(6-2\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
261.4.a.f	$261$	$4$	261.a	1.a	$1$	$5$	$5$	$15.399$	5.5.13458092.1	$_{}$	None	None	✓				29.4.a.b	$1$	$0$	\(0\)	\(0\)	\(-10\)	\(40\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(6+2\beta _{1}+2\beta _{3}+\beta _{4})q^{4}+\cdots\)

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