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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1224.1.m.a	$1224$	$1$	1224.m	51.c	$2$	$2$	$2$	$0.611$	$\Q(\sqrt{-2})$	$S_{4}$	None	None		✓			1224.1.m.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}-\beta q^{7}-q^{11}-q^{13}-q^{17}+\cdots$
1224.1.m.b	$1224$	$1$	1224.m	51.c	$2$	$2$	$2$	$0.611$	$\Q(\sqrt{-2})$	$S_{4}$	None	None		✓			1224.1.m.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}-\beta q^{7}+q^{11}-q^{13}+q^{17}+\cdots$
1224.1.n.a	$1224$	$1$	1224.n	136.e	$2$	$1$	$1$	$0.611$	$\Q$	$D_{2}$	$\Q(\sqrt{-2})$, $\Q(\sqrt{-34})$	$\Q(\sqrt{17})$	✓				136.1.e.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}+q^{17}-2q^{19}+\cdots$
1224.1.n.b	$1224$	$1$	1224.n	136.e	$2$	$2$	$2$	$0.611$	$\Q(\sqrt{2})$	$D_{4}$	$\Q(\sqrt{-34})$	None	✓	✓			1224.1.n.b	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-\beta q^{5}-\beta q^{7}-q^{8}+\beta q^{10}+\cdots$
1224.1.n.c	$1224$	$1$	1224.n	136.e	$2$	$2$	$2$	$0.611$	$\Q(\sqrt{2})$	$D_{4}$	$\Q(\sqrt{-34})$	None	✓	✓			1224.1.n.b	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\beta q^{5}+\beta q^{7}+q^{8}-\beta q^{10}+\cdots$
1224.1.s.a	$1224$	$1$	1224.s	136.j	$4$	$2$	$1$	$0.611$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-2})$	None			✓	✓	136.1.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+i q^{8}+(-i-1)q^{11}+\cdots$
1224.1.bb.a	$1224$	$1$	1224.bb	1224.ab	$6$	$2$	$1$	$0.611$	$\Q(\sqrt{-3})$	$D_{6}$	$\Q(\sqrt{-2})$	None		✓			1224.1.bb.a	$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
1224.1.bb.b	$1224$	$1$	1224.bb	1224.ab	$6$	$2$	$1$	$0.611$	$\Q(\sqrt{-3})$	$D_{6}$	$\Q(\sqrt{-2})$	None		✓			1224.1.bb.a	$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
1224.1.bu.a	$1224$	$1$	1224.bu	408.ae	$8$	$4$	$1$	$0.611$	$\Q(\zeta_{8})$	$D_{8}$	None	$\Q(\sqrt{2})$		✓			1224.1.bu.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{3})q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
1224.1.bu.b	$1224$	$1$	1224.bu	408.ae	$8$	$4$	$1$	$0.611$	$\Q(\zeta_{8})$	$D_{8}$	None	$\Q(\sqrt{2})$		✓			1224.1.bu.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{3})q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
1224.1.bv.a	$1224$	$1$	1224.bv	136.p	$8$	$4$	$1$	$0.611$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2})$	None			✓	✓	136.1.p.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+(1-\zeta_{8}+\cdots)q^{11}+\cdots$
1224.1.cb.a	$1224$	$1$	1224.cb	1224.bb	$12$	$4$	$1$	$0.611$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2})$	None		✓			1224.1.cb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots$
1224.1.cb.b	$1224$	$1$	1224.cb	1224.bb	$12$	$4$	$1$	$0.611$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2})$	None		✓			1224.1.cb.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{6}+\cdots$
1224.1.cp.a	$1224$	$1$	1224.cp	1224.bp	$24$	$8$	$1$	$0.611$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-2})$	None		✓			1224.1.cp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{2}q^{6}+\cdots$
1224.1.cp.b	$1224$	$1$	1224.cp	1224.bp	$24$	$8$	$1$	$0.611$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-2})$	None		✓			1224.1.cp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}q^{2}-\zeta_{24}^{10}q^{3}+\zeta_{24}^{2}q^{4}+\cdots$
1224.1.cx.a	$1224$	$1$	1224.cx	1224.bx	$48$	$16$	$1$	$0.611$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-2})$	None		✓			1224.1.cx.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{48}^{5}q^{2}+\zeta_{48}^{14}q^{3}+\zeta_{48}^{10}q^{4}+\cdots$
1224.1.cx.b	$1224$	$1$	1224.cx	1224.bx	$48$	$16$	$1$	$0.611$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-2})$	None		✓			1224.1.cx.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{48}^{5}q^{2}+\zeta_{48}^{17}q^{3}+\zeta_{48}^{10}q^{4}+\cdots$
1224.2.a.a	$1224$	$2$	1224.a	1.a	$1$	$1$	$1$	$9.774$	$\Q$	$_{}$	None	None	✓				408.2.a.a	$1$	$1$	$0$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{11}+3q^{13}+q^{17}+q^{19}+\cdots$
1224.2.a.b	$1224$	$2$	1224.a	1.a	$1$	$1$	$1$	$9.774$	$\Q$	$_{}$	None	None	✓				408.2.a.d	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-4q^{11}+6q^{13}-q^{17}+\cdots$
1224.2.a.c	$1224$	$2$	1224.a	1.a	$1$	$1$	$1$	$9.774$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1224.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+3q^{11}-q^{13}-q^{17}+\cdots$
1224.2.a.d	$1224$	$2$	1224.a	1.a	$1$	$1$	$1$	$9.774$	$\Q$	$_{}$	None	None	✓				136.2.a.b	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{11}-6q^{13}+q^{17}+4q^{19}-4q^{23}+\cdots$
1224.2.a.e	$1224$	$2$	1224.a	1.a	$1$	$1$	$1$	$9.774$	$\Q$	$_{}$	None	None	✓				408.2.a.c	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+2q^{13}+q^{17}+4q^{19}-2q^{23}+\cdots$
1224.2.a.f	$1224$	$2$	1224.a	1.a	$1$	$1$	$1$	$9.774$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1224.2.a.c	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{11}-q^{13}+q^{17}+\cdots$
1224.2.a.g	$1224$	$2$	1224.a	1.a	$1$	$1$	$1$	$9.774$	$\Q$	$_{}$	None	None	✓				136.2.a.a	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}+6q^{11}+2q^{13}-q^{17}+\cdots$
1224.2.a.h	$1224$	$2$	1224.a	1.a	$1$	$1$	$1$	$9.774$	$\Q$	$_{}$	None	None	✓				408.2.a.b	$1$	$1$	$0$	$0$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-4q^{7}-q^{11}-5q^{13}-q^{17}+\cdots$
1224.2.a.i	$1224$	$2$	1224.a	1.a	$1$	$2$	$2$	$9.774$	$\Q(\sqrt{5})$	$_{}$	None	None	✓		✓		136.2.a.c	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{5}+(1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots$
1224.2.a.j	$1224$	$2$	1224.a	1.a	$1$	$2$	$2$	$9.774$	$\Q(\sqrt{17})$	$_{}$	None	None	✓		✓		408.2.a.e	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2+2\beta )q^{7}+(4+\beta )q^{11}+\cdots$
1224.2.a.k	$1224$	$2$	1224.a	1.a	$1$	$2$	$2$	$9.774$	$\Q(\sqrt{57})$	$_{}$	None	None	✓		✓		408.2.a.f	$1$	$0$	$0$	$0$	$1$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+4q^{7}+(2-\beta )q^{11}+\beta q^{13}+\cdots$
1224.2.a.l	$1224$	$2$	1224.a	1.a	$1$	$3$	$3$	$9.774$	3.3.1304.1	$_{}$	None	None	✓	✓	✓	✓	1224.2.a.l	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
1224.2.a.m	$1224$	$2$	1224.a	1.a	$1$	$3$	$3$	$9.774$	3.3.1304.1	$_{}$	None	None	✓	✓	✓	✓	1224.2.a.l	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots$
1224.2.c.a	$1224$	$2$	1224.c	17.b	$2$	$2$	$2$	$9.774$	$\Q(\sqrt{-1})$	$_{}$	None	None		✓			1224.2.c.a	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{5}-4 i q^{7}+i q^{11}-5 q^{13}+\cdots$
1224.2.c.b	$1224$	$2$	1224.c	17.b	$2$	$2$	$2$	$9.774$	$\Q(\sqrt{-1})$	$_{}$	None	None		✓			1224.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{5}+4 i q^{7}+i q^{11}-5 q^{13}+\cdots$
1224.2.c.c	$1224$	$2$	1224.c	17.b	$2$	$2$	$2$	$9.774$	$\Q(\sqrt{-1})$	$_{}$	None	None					136.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{7}+\beta q^{11}-2 q^{13}+(-2\beta-1)q^{17}+\cdots$
1224.2.c.d	$1224$	$2$	1224.c	17.b	$2$	$2$	$2$	$9.774$	$\Q(\sqrt{-2})$	$_{}$	None	None		✓			1224.2.c.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-\beta q^{7}-2\beta q^{11}+2q^{13}+(-3+\cdots)q^{17}+\cdots$
1224.2.c.e	$1224$	$2$	1224.c	17.b	$2$	$2$	$2$	$9.774$	$\Q(\sqrt{-2})$	$_{}$	None	None					136.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-\beta q^{7}-2\beta q^{11}+2q^{13}+(3+\cdots)q^{17}+\cdots$
1224.2.c.f	$1224$	$2$	1224.c	17.b	$2$	$2$	$2$	$9.774$	$\Q(\sqrt{-2})$	$_{}$	None	None		✓			1224.2.c.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+\beta q^{7}-2\beta q^{11}+2q^{13}+(3+\cdots)q^{17}+\cdots$
1224.2.c.g	$1224$	$2$	1224.c	17.b	$2$	$4$	$4$	$9.774$	$\Q(i, \sqrt{33})$	$_{}$	None	None					408.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}-\beta _{1}q^{11}+\cdots$
1224.2.c.h	$1224$	$2$	1224.c	17.b	$2$	$6$	$6$	$9.774$	6.0.399424.1	$_{}$	None	None			✓		408.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+(\beta _{2}+\beta _{5})q^{7}-\beta _{5}q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
1224.2.f.a	$1224$	$2$	1224.f	8.b	$2$	$2$	$2$	$9.774$	$\Q(\sqrt{-1})$	$_{}$	None	None					408.2.f.a	$2$	$0$	$2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+1)q^{2}+2 i q^{4}+4 i q^{5}-4 q^{7}+\cdots$
1224.2.f.b	$1224$	$2$	1224.f	8.b	$2$	$4$	$4$	$9.774$	$\Q(i, \sqrt{5})$	$_{}$	None	None					408.2.f.b	$2$	$0$	$-4$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
1224.2.f.c	$1224$	$2$	1224.f	8.b	$2$	$8$	$8$	$9.774$	8.0.4469724736.1	$_{}$	None	None					136.2.c.b	$2$	$0$	$1$	$0$	$0$	$-12$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{7})q^{5}+\cdots$
1224.2.f.d	$1224$	$2$	1224.f	8.b	$2$	$8$	$8$	$9.774$	8.0.1649659456.5	$_{}$	None	None					136.2.c.a	$2$	$0$	$1$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{6})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
1224.2.f.e	$1224$	$2$	1224.f	8.b	$2$	$12$	$12$	$9.774$	12.0.$\cdots$.1	$_{}$	None	None					408.2.f.c	$2$	$0$	$2$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{8}q^{4}+(\beta _{1}-\beta _{3}-\beta _{5}-\beta _{8}+\cdots)q^{5}+\cdots$
1224.2.f.f	$1224$	$2$	1224.f	8.b	$2$	$14$	$14$	$9.774$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None					408.2.f.d	$2$	$0$	$-4$	$0$	$0$	$12$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{2}q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{8}+\cdots)q^{7}+\cdots$
1224.2.f.g	$1224$	$2$	1224.f	8.b	$2$	$16$	$16$	$9.774$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1224.2.f.g	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{4}q^{5}+\beta _{5}q^{7}+\cdots$
1224.2.f.h	$1224$	$2$	1224.f	8.b	$2$	$16$	$16$	$9.774$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1224.2.f.g	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}-\beta _{5}q^{4}+\beta _{4}q^{5}+\beta _{9}q^{7}+\cdots$
1224.2.h.a	$1224$	$2$	1224.h	408.h	$2$	$8$	$8$	$9.774$	8.0.$\cdots$.11	$_{}$	$\Q(\sqrt{-34})$	None		✓			1224.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-\beta _{4}q^{7}+2\beta _{1}q^{8}+\cdots$
1224.2.h.b	$1224$	$2$	1224.h	408.h	$2$	$8$	$8$	$9.774$	8.0.$\cdots$.11	$_{}$	$\Q(\sqrt{-34})$	None		✓			1224.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}+\beta _{4}q^{5}+\beta _{6}q^{7}-2\beta _{1}q^{8}+\cdots$
1224.2.h.c	$1224$	$2$	1224.h	408.h	$2$	$56$	$56$	$9.774$		$_{}$	None	None		✓	✓		1224.2.h.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1224.2.j.a	$1224$	$2$	1224.j	24.f	$2$	$64$	$64$	$9.774$		$_{}$	None	None		✓	✓	✓	1224.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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