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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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
238.2.a.a	$238$	$2$	238.a	1.a	$1$	$1$	$1$	$1.900$	\(\Q\)	None	✓	✓	✓	✓	238.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
238.2.a.b	$238$	$2$	238.a	1.a	$1$	$1$	$1$	$1.900$	\(\Q\)	None	✓	✓	✓	✓	238.2.a.b	$1$	$0$	\(-1\)	\(2\)	\(4\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+4q^{5}-2q^{6}+q^{7}+\cdots\)
238.2.a.c	$238$	$2$	238.a	1.a	$1$	$1$	$1$	$1.900$	\(\Q\)	None	✓	✓	✓	✓	238.2.a.c	$1$	$1$	\(1\)	\(-2\)	\(-4\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-4q^{5}-2q^{6}+q^{7}+\cdots\)
238.2.a.d	$238$	$2$	238.a	1.a	$1$	$1$	$1$	$1.900$	\(\Q\)	None	✓	✓	✓	✓	238.2.a.d	$1$	$0$	\(1\)	\(0\)	\(2\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
238.2.a.e	$238$	$2$	238.a	1.a	$1$	$1$	$1$	$1.900$	\(\Q\)	None	✓	✓	✓	✓	238.2.a.e	$1$	$0$	\(1\)	\(2\)	\(0\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots\)
238.2.a.f	$238$	$2$	238.a	1.a	$1$	$2$	$2$	$1.900$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	238.2.a.f	$1$	$0$	\(-2\)	\(2\)	\(2\)	\(-2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+(1-\beta )q^{5}+\cdots\)
238.2.b.a	$238$	$2$	238.b	17.b	$2$	$2$	$2$	$1.900$	\(\Q(\sqrt{-1}) \)	None		✓			238.2.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+i q^{7}-q^{8}+3 q^{9}+\cdots\)
238.2.b.b	$238$	$2$	238.b	17.b	$2$	$6$	$6$	$1.900$	6.0.350464.1	None		✓	✓		238.2.b.b	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(\beta _{1}+\beta _{4})q^{3}+q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
238.2.e.a	$238$	$2$	238.e	7.c	$3$	$2$	$1$	$1.900$	\(\Q(\sqrt{-3}) \)	None		✓			238.2.e.a	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
238.2.e.b	$238$	$2$	238.e	7.c	$3$	$2$	$1$	$1.900$	\(\Q(\sqrt{-3}) \)	None		✓			238.2.e.b	$2$	$0$	\(1\)	\(-3\)	\(2\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
238.2.e.c	$238$	$2$	238.e	7.c	$3$	$2$	$1$	$1.900$	\(\Q(\sqrt{-3}) \)	None		✓			238.2.e.c	$2$	$0$	\(1\)	\(1\)	\(2\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
238.2.e.d	$238$	$2$	238.e	7.c	$3$	$2$	$1$	$1.900$	\(\Q(\sqrt{-3}) \)	None		✓			238.2.e.d	$2$	$0$	\(1\)	\(2\)	\(-3\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
238.2.e.e	$238$	$2$	238.e	7.c	$3$	$6$	$3$	$1.900$	6.0.4406832.1	None		✓			238.2.e.e	$2$	$0$	\(3\)	\(0\)	\(1\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
238.2.e.f	$238$	$2$	238.e	7.c	$3$	$10$	$5$	$1.900$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		238.2.e.f	$2$	$0$	\(-5\)	\(0\)	\(1\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{4})q^{2}-\beta _{1}q^{3}+\beta _{4}q^{4}+\beta _{9}q^{5}+\cdots\)
238.2.g.a	$238$	$2$	238.g	17.c	$4$	$8$	$4$	$1.900$	\(\Q(\zeta_{16})\)	None		✓			238.2.g.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta_{3} q^{2}+\beta_{7} q^{3}-q^{4}+(-\beta_{7}-\beta_{6}-\beta_{5}+\cdots+1)q^{5}+\cdots\)
238.2.g.b	$238$	$2$	238.g	17.c	$4$	$8$	$4$	$1.900$	8.0.110166016.2	None		✓			238.2.g.b	$2$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{2}+(1-\beta _{3}+\beta _{6})q^{3}-q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
238.2.j.a	$238$	$2$	238.j	119.j	$6$	$4$	$2$	$1.900$	\(\Q(\zeta_{12})\)	None		✓			238.2.j.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{2}q^{2}-3\zeta_{12}q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
238.2.j.b	$238$	$2$	238.j	119.j	$6$	$8$	$4$	$1.900$	8.0.3317760000.8	None		✓			238.2.j.b	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{3})q^{2}+(\beta _{4}+\beta _{5})q^{3}-\beta _{3}q^{4}+\cdots\)
238.2.j.c	$238$	$2$	238.j	119.j	$6$	$12$	$6$	$1.900$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		238.2.j.c	$4$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{7}q^{2}+(-\beta _{1}+\beta _{6}+\beta _{10})q^{3}+(-1+\cdots)q^{4}+\cdots\)
238.2.k.a	$238$	$2$	238.k	17.d	$8$	$16$	$4$	$1.900$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			238.2.k.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	\(q+\beta _{12}q^{2}+(-\beta _{7}+\beta _{12}-\beta _{15})q^{3}+\cdots\)
238.2.k.b	$238$	$2$	238.k	17.d	$8$	$24$	$6$	$1.900$		None		✓	✓		238.2.k.b	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)			$\mathrm{SU}(2)[C_{8}]$
238.2.n.a	$238$	$2$	238.n	119.n	$12$	$4$	$1$	$1.900$	\(\Q(\zeta_{12})\)	None		✓			238.2.n.a	$2$	$0$	\(0\)	\(-4\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{12}q^{2}+(-1+\zeta_{12})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
238.2.n.b	$238$	$2$	238.n	119.n	$12$	$4$	$1$	$1.900$	\(\Q(\zeta_{12})\)	None		✓			238.2.n.a	$2$	$0$	\(0\)	\(2\)	\(2\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
238.2.n.c	$238$	$2$	238.n	119.n	$12$	$16$	$4$	$1.900$	16.0.\(\cdots\).1	None		✓			238.2.n.c	$4$	$0$	\(0\)	\(2\)	\(-2\)	\(12\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{7}q^{2}+(-\beta _{14}-\beta _{15})q^{3}+(1+\beta _{11}+\cdots)q^{4}+\cdots\)
238.2.n.d	$238$	$2$	238.n	119.n	$12$	$24$	$6$	$1.900$		None		✓	✓		238.2.n.d	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
238.2.p.a	$238$	$2$	238.p	119.p	$16$	$48$	$6$	$1.900$		None		✓			238.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
238.2.p.b	$238$	$2$	238.p	119.p	$16$	$48$	$6$	$1.900$		None		✓			238.2.p.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
238.2.q.a	$238$	$2$	238.q	119.q	$24$	$16$	$2$	$1.900$	16.0.\(\cdots\).2	None		✓			238.2.q.a	$4$	$0$	\(0\)	\(4\)	\(8\)	\(12\)		$2^{2}$	$\mathrm{SU}(2)[C_{24}]$	\(q+\beta _{12}q^{2}+(-\beta _{6}-\beta _{13})q^{3}-\beta _{10}q^{4}+\cdots\)
238.2.q.b	$238$	$2$	238.q	119.q	$24$	$32$	$4$	$1.900$		None		✓			238.2.q.b	$4$	$0$	\(0\)	\(-4\)	\(-12\)	\(-12\)			$\mathrm{SU}(2)[C_{24}]$
238.2.q.c	$238$	$2$	238.q	119.q	$24$	$48$	$6$	$1.900$		None		✓	✓		238.2.q.c	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)			$\mathrm{SU}(2)[C_{24}]$
238.2.s.a	$238$	$2$	238.s	119.s	$48$	$96$	$6$	$1.900$		None		✓			238.2.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{48}]$
238.2.s.b	$238$	$2$	238.s	119.s	$48$	$96$	$6$	$1.900$		None		✓			238.2.s.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{48}]$
238.3.c.a	$238$	$3$	238.c	7.b	$2$	$24$	$24$	$6.485$		None		✓	✓	✓	238.3.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)			$\mathrm{SU}(2)[C_{2}]$
238.3.d.a	$238$	$3$	238.d	119.d	$2$	$24$	$24$	$6.485$		None		✓	✓	✓	238.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
238.3.f.a	$238$	$3$	238.f	119.f	$4$	$48$	$24$	$6.485$		None		✓	✓	✓	238.3.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)			$\mathrm{SU}(2)[C_{4}]$
238.3.h.a	$238$	$3$	238.h	119.h	$6$	$48$	$24$	$6.485$		None		✓	✓	✓	238.3.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
238.3.i.a	$238$	$3$	238.i	7.d	$6$	$40$	$20$	$6.485$		None		✓	✓	✓	238.3.i.a	$2$	$0$	\(0\)	\(12\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{6}]$
238.3.l.a	$238$	$3$	238.l	119.l	$8$	$48$	$12$	$6.485$		None		✓			238.3.l.a	$4$	$0$	\(-48\)	\(0\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{8}]$
238.3.l.b	$238$	$3$	238.l	119.l	$8$	$48$	$12$	$6.485$		None		✓			238.3.l.b	$4$	$0$	\(48\)	\(0\)	\(0\)	\(4\)			$\mathrm{SU}(2)[C_{8}]$
238.3.m.a	$238$	$3$	238.m	119.m	$12$	$96$	$24$	$6.485$		None		✓	✓	✓	238.3.m.a	$4$	$0$	\(0\)	\(0\)	\(-12\)	\(-12\)			$\mathrm{SU}(2)[C_{12}]$
238.3.o.a	$238$	$3$	238.o	17.e	$16$	$64$	$8$	$6.485$		None		✓			238.3.o.a	$2$	$0$	\(0\)	\(16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
238.3.o.b	$238$	$3$	238.o	17.e	$16$	$80$	$10$	$6.485$		None		✓	✓		238.3.o.b	$2$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
238.3.r.a	$238$	$3$	238.r	119.r	$24$	$96$	$12$	$6.485$		None		✓			238.3.r.a	$4$	$0$	\(-48\)	\(0\)	\(12\)	\(-4\)			$\mathrm{SU}(2)[C_{24}]$
238.3.r.b	$238$	$3$	238.r	119.r	$24$	$96$	$12$	$6.485$		None		✓			238.3.r.b	$4$	$0$	\(48\)	\(0\)	\(12\)	\(4\)			$\mathrm{SU}(2)[C_{24}]$
238.3.t.a	$238$	$3$	238.t	119.t	$48$	$192$	$12$	$6.485$		None		✓			238.3.t.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)			$\mathrm{SU}(2)[C_{48}]$
238.3.t.b	$238$	$3$	238.t	119.t	$48$	$192$	$12$	$6.485$		None		✓			238.3.t.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)			$\mathrm{SU}(2)[C_{48}]$
238.4.a.a	$238$	$4$	238.a	1.a	$1$	$2$	$2$	$14.042$	\(\Q(\sqrt{93}) \)	None	✓	✓	✓	✓	238.4.a.a	$1$	$1$	\(-4\)	\(-5\)	\(9\)	\(-14\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-2-\beta )q^{3}+4q^{4}+(5-\beta )q^{5}+\cdots\)
238.4.a.b	$238$	$4$	238.a	1.a	$1$	$2$	$2$	$14.042$	\(\Q(\sqrt{69}) \)	None	✓	✓	✓	✓	238.4.a.b	$1$	$1$	\(4\)	\(-11\)	\(-7\)	\(14\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-5-\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
238.4.a.c	$238$	$4$	238.a	1.a	$1$	$3$	$3$	$14.042$	3.3.69061.1	None	✓	✓	✓	✓	238.4.a.c	$1$	$1$	\(-6\)	\(-5\)	\(-21\)	\(21\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-7+\cdots)q^{5}+\cdots\)
238.4.a.d	$238$	$4$	238.a	1.a	$1$	$3$	$3$	$14.042$	3.3.48173.1	None	✓	✓	✓	✓	238.4.a.d	$1$	$0$	\(-6\)	\(1\)	\(-5\)	\(-21\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-2+2\beta _{1}+\cdots)q^{5}+\cdots\)

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