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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.1.p.a	$72$	$1$	72.p	72.p	$6$	$2$	$1$	$0.036$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		✓	✓	✓	72.1.p.a	$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)		$1$		\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
72.2.a.a	$72$	$2$	72.a	1.a	$1$	$1$	$1$	$0.575$	\(\Q\)	$_{}$	None	None	✓		✓	✓	24.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
72.2.d.a	$72$	$2$	72.d	8.b	$2$	$2$	$2$	$0.575$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-6}) \)	None		✓			72.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-2q^{4}+2\beta q^{5}+2q^{7}-2\beta q^{8}+\cdots\)
72.2.d.b	$72$	$2$	72.d	8.b	$2$	$2$	$2$	$0.575$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None					24.2.d.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+1)q^{2}+2 i q^{4}-2 i q^{5}-2 q^{7}+\cdots\)
72.2.f.a	$72$	$2$	72.f	24.f	$2$	$4$	$4$	$0.575$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		✓	✓	✓	72.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
72.2.i.a	$72$	$2$	72.i	9.c	$3$	$2$	$1$	$0.575$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			72.2.i.a	$2$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots\)
72.2.i.b	$72$	$2$	72.i	9.c	$3$	$4$	$2$	$0.575$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	$_{}$	None	None		✓	✓		72.2.i.b	$2$	$0$	\(0\)	\(1\)	\(1\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
72.2.l.a	$72$	$2$	72.l	72.l	$6$	$4$	$2$	$0.575$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	\(\Q(\sqrt{-2}) \)	None		✓			72.2.l.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
72.2.l.b	$72$	$2$	72.l	72.l	$6$	$16$	$8$	$0.575$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		✓	✓		72.2.l.b	$4$	$0$	\(-3\)	\(-6\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
72.2.n.a	$72$	$2$	72.n	72.n	$6$	$4$	$2$	$0.575$	\(\Q(\zeta_{12})\)	$_{}$	None	None		✓			72.2.n.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
72.2.n.b	$72$	$2$	72.n	72.n	$6$	$16$	$8$	$0.575$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		✓	✓		72.2.n.b	$4$	$0$	\(1\)	\(0\)	\(0\)	\(6\)		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots\)
72.3.b.a	$72$	$3$	72.b	8.d	$2$	$1$	$1$	$1.962$	\(\Q\)	$_{}$	\(\Q(\sqrt{-2}) \)	None	✓				8.3.d.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+4q^{4}+8q^{8}-14q^{11}+2^{4}q^{16}+\cdots\)
72.3.b.b	$72$	$3$	72.b	8.d	$2$	$4$	$4$	$1.962$	4.0.4752.1	$_{}$	None	None					24.3.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-2+\beta _{1}-\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
72.3.b.c	$72$	$3$	72.b	8.d	$2$	$4$	$4$	$1.962$	\(\Q(\sqrt{-6}, \sqrt{10})\)	$_{}$	None	None		✓			72.3.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots\)
72.3.e.a	$72$	$3$	72.e	3.b	$2$	$2$	$2$	$1.962$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		✓	✓	✓	72.3.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(24\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{5}+12q^{7}-4\beta q^{11}-8q^{13}+\cdots\)
72.3.h.a	$72$	$3$	72.h	24.h	$2$	$8$	$8$	$1.962$	8.0.\(\cdots\).2	$_{}$	None	None		✓	✓	✓	72.3.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(1+\beta _{5})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
72.3.j.a	$72$	$3$	72.j	72.j	$6$	$44$	$22$	$1.962$		$_{}$	None	None		✓	✓	✓	72.3.j.a	$4$	$0$	\(-3\)	\(0\)	\(0\)	\(-2\)			$\mathrm{SU}(2)[C_{6}]$
72.3.m.a	$72$	$3$	72.m	9.d	$6$	$4$	$2$	$1.962$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		✓			72.3.m.a	$2$	$0$	\(0\)	\(-12\)	\(6\)	\(-6\)		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-3q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
72.3.m.b	$72$	$3$	72.m	9.d	$6$	$8$	$4$	$1.962$	8.0.\(\cdots\).9	$_{}$	None	None		✓	✓		72.3.m.b	$2$	$0$	\(0\)	\(10\)	\(-6\)	\(6\)		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
72.3.p.a	$72$	$3$	72.p	72.p	$6$	$4$	$2$	$1.962$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	\(\Q(\sqrt{-2}) \)	None		✓			72.3.p.a	$4$	$0$	\(4\)	\(2\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+2\beta _{2}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots\)
72.3.p.b	$72$	$3$	72.p	72.p	$6$	$40$	$20$	$1.962$		$_{}$	None	None		✓	✓		72.3.p.b	$4$	$0$	\(-5\)	\(-6\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
72.4.a.a	$72$	$4$	72.a	1.a	$1$	$1$	$1$	$4.248$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	72.4.a.a	$1$	$1$	\(0\)	\(0\)	\(-16\)	\(-12\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{5}-12q^{7}-2^{6}q^{11}+58q^{13}+\cdots\)
72.4.a.b	$72$	$4$	72.a	1.a	$1$	$1$	$1$	$4.248$	\(\Q\)	$_{}$	None	None	✓		✓	✓	24.4.a.a	$1$	$1$	\(0\)	\(0\)	\(-14\)	\(-24\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-14q^{5}-24q^{7}+28q^{11}-74q^{13}+\cdots\)
72.4.a.c	$72$	$4$	72.a	1.a	$1$	$1$	$1$	$4.248$	\(\Q\)	$_{}$	None	None	✓		✓	✓	8.4.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+24q^{7}+44q^{11}+22q^{13}+\cdots\)
72.4.a.d	$72$	$4$	72.a	1.a	$1$	$1$	$1$	$4.248$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	72.4.a.a	$1$	$0$	\(0\)	\(0\)	\(16\)	\(-12\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{5}-12q^{7}+2^{6}q^{11}+58q^{13}+\cdots\)
72.4.d.a	$72$	$4$	72.d	8.b	$2$	$2$	$2$	$4.248$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-6}) \)	None		✓			72.4.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-68\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-8q^{4}-7\beta q^{5}-34q^{7}-8\beta q^{8}+\cdots\)
72.4.d.b	$72$	$4$	72.d	8.b	$2$	$2$	$2$	$4.248$	\(\Q(\sqrt{-7}) \)	$_{}$	None	None					8.4.b.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-16\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta )q^{2}+(-6+2\beta )q^{4}+4\beta q^{5}+\cdots\)
72.4.d.c	$72$	$4$	72.d	8.b	$2$	$4$	$4$	$4.248$	\(\Q(\sqrt{-10}, \sqrt{22})\)	$_{}$	None	None		✓			72.4.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(40\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(3+\beta _{3})q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
72.4.d.d	$72$	$4$	72.d	8.b	$2$	$6$	$6$	$4.248$	6.0.8248384.1	$_{}$	None	None			✓		24.4.d.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(28\)		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(3+\beta _{5})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
72.4.f.a	$72$	$4$	72.f	24.f	$2$	$12$	$12$	$4.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		✓	✓	✓	72.4.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{15}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-1+\beta _{6})q^{4}-\beta _{5}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
72.4.i.a	$72$	$4$	72.i	9.c	$3$	$8$	$4$	$4.248$	8.0.5206055409.1	$_{}$	None	None		✓			72.4.i.a	$2$	$0$	\(0\)	\(-3\)	\(-5\)	\(3\)		$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{3}+(2\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
72.4.i.b	$72$	$4$	72.i	9.c	$3$	$10$	$5$	$4.248$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None		✓	✓		72.4.i.b	$2$	$0$	\(0\)	\(4\)	\(-5\)	\(-3\)		$2^{8}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{8})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
72.4.l.a	$72$	$4$	72.l	72.l	$6$	$4$	$2$	$4.248$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	\(\Q(\sqrt{-2}) \)	None		✓			72.4.l.a	$4$	$0$	\(0\)	\(-10\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+2\beta _{1}q^{2}+(-5+\beta _{1}+5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots\)
72.4.l.b	$72$	$4$	72.l	72.l	$6$	$64$	$32$	$4.248$		$_{}$	None	None		✓	✓		72.4.l.b	$4$	$0$	\(-3\)	\(6\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
72.4.n.a	$72$	$4$	72.n	72.n	$6$	$68$	$34$	$4.248$		$_{}$	None	None		✓	✓	✓	72.4.n.a	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)			$\mathrm{SU}(2)[C_{6}]$
72.5.b.a	$72$	$5$	72.b	8.d	$2$	$1$	$1$	$7.443$	\(\Q\)	$_{}$	\(\Q(\sqrt{-2}) \)	None	✓				8.5.d.a	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{2}+2^{4}q^{4}-2^{6}q^{8}+46q^{11}+\cdots\)
72.5.b.b	$72$	$5$	72.b	8.d	$2$	$2$	$2$	$7.443$	\(\Q(\sqrt{-15}) \)	$_{}$	None	None					8.5.d.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta )q^{2}+(-14+2\beta )q^{4}-8\beta q^{5}+\cdots\)
72.5.b.c	$72$	$5$	72.b	8.d	$2$	$8$	$8$	$7.443$	8.0.\(\cdots\).5	$_{}$	None	None		✓			72.5.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{12}\cdot 3^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(3-\beta _{4})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
72.5.b.d	$72$	$5$	72.b	8.d	$2$	$8$	$8$	$7.443$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	$_{}$	None	None					24.5.b.a	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)		$2^{12}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{2}+(1+\beta _{1}+\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots\)
72.5.e.a	$72$	$5$	72.e	3.b	$2$	$2$	$2$	$7.443$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		✓			72.5.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-120\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+11\beta q^{5}-60q^{7}+44\beta q^{11}-176q^{13}+\cdots\)
72.5.e.b	$72$	$5$	72.e	3.b	$2$	$2$	$2$	$7.443$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		✓			72.5.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(72\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{5}+6^{2}q^{7}+116\beta q^{11}+304q^{13}+\cdots\)
72.5.h.a	$72$	$5$	72.h	24.h	$2$	$16$	$16$	$7.443$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		✓	✓	✓	72.5.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{28}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{4}+\beta _{5}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
72.5.j.a	$72$	$5$	72.j	72.j	$6$	$92$	$46$	$7.443$		$_{}$	None	None		✓	✓	✓	72.5.j.a	$4$	$0$	\(-3\)	\(0\)	\(0\)	\(-2\)			$\mathrm{SU}(2)[C_{6}]$
72.5.m.a	$72$	$5$	72.m	9.d	$6$	$24$	$12$	$7.443$		$_{}$	None	None		✓	✓	✓	72.5.m.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
72.5.p.a	$72$	$5$	72.p	72.p	$6$	$4$	$2$	$7.443$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	\(\Q(\sqrt{-2}) \)	None		✓			72.5.p.a	$4$	$0$	\(-8\)	\(14\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{U}(1)[D_{6}]$	\(q-4\beta _{2}q^{2}+(\beta _{1}+7\beta _{2}-\beta _{3})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
72.5.p.b	$72$	$5$	72.p	72.p	$6$	$88$	$44$	$7.443$		$_{}$	None	None		✓	✓		72.5.p.b	$4$	$0$	\(7\)	\(-18\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
72.6.a.a	$72$	$6$	72.a	1.a	$1$	$1$	$1$	$11.548$	\(\Q\)	$_{}$	None	None	✓				24.6.a.b	$1$	$0$	\(0\)	\(0\)	\(-94\)	\(144\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-94q^{5}+12^{2}q^{7}+380q^{11}+814q^{13}+\cdots\)
72.6.a.b	$72$	$6$	72.a	1.a	$1$	$1$	$1$	$11.548$	\(\Q\)	$_{}$	None	None	✓				24.6.a.c	$1$	$1$	\(0\)	\(0\)	\(-38\)	\(120\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-38q^{5}+120q^{7}-524q^{11}-962q^{13}+\cdots\)
72.6.a.c	$72$	$6$	72.a	1.a	$1$	$1$	$1$	$11.548$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	72.6.a.c	$1$	$1$	\(0\)	\(0\)	\(-16\)	\(12\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{5}+12q^{7}-448q^{11}-206q^{13}+\cdots\)
72.6.a.d	$72$	$6$	72.a	1.a	$1$	$1$	$1$	$11.548$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	72.6.a.c	$1$	$0$	\(0\)	\(0\)	\(16\)	\(12\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{5}+12q^{7}+448q^{11}-206q^{13}+\cdots\)

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