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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
368.1.f.a	$368$	$1$	368.f	23.b	$2$	$1$	$1$	$0.184$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-23}) \)	None	✓		✓	✓	23.1.b.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$1$		\(q+q^{3}-q^{13}-q^{23}+q^{25}-q^{27}+\cdots\)
368.1.k.a	$368$	$1$	368.k	368.k	$4$	$2$	$1$	$0.184$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-23}) \)	None		✓			368.1.k.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$1$		\(q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots\)
368.1.k.b	$368$	$1$	368.k	368.k	$4$	$4$	$2$	$0.184$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-23}) \)	None		✓	✓		368.1.k.b	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$		\(q+\zeta_{12}^{5}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
368.2.a.a	$368$	$2$	368.a	1.a	$1$	$1$	$1$	$2.938$	\(\Q\)	$_{}$	None	None	✓				184.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{7}+6q^{9}-5q^{13}-6q^{17}+\cdots\)
368.2.a.b	$368$	$2$	368.a	1.a	$1$	$1$	$1$	$2.938$	\(\Q\)	$_{}$	None	None	✓		✓	✓	92.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}-2q^{9}-q^{13}-6q^{17}+\cdots\)
368.2.a.c	$368$	$2$	368.a	1.a	$1$	$1$	$1$	$2.938$	\(\Q\)	$_{}$	None	None	✓				184.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-3q^{9}-6q^{11}-2q^{13}+6q^{17}+\cdots\)
368.2.a.d	$368$	$2$	368.a	1.a	$1$	$1$	$1$	$2.938$	\(\Q\)	$_{}$	None	None	✓				46.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+4q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots\)
368.2.a.e	$368$	$2$	368.a	1.a	$1$	$1$	$1$	$2.938$	\(\Q\)	$_{}$	None	None	✓				184.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-2q^{7}-2q^{9}+4q^{11}+\cdots\)
368.2.a.f	$368$	$2$	368.a	1.a	$1$	$1$	$1$	$2.938$	\(\Q\)	$_{}$	None	None	✓				184.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+4q^{7}-2q^{9}+2q^{11}+\cdots\)
368.2.a.g	$368$	$2$	368.a	1.a	$1$	$1$	$1$	$2.938$	\(\Q\)	$_{}$	None	None	✓				92.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{5}+4q^{7}+6q^{9}-2q^{11}+\cdots\)
368.2.a.h	$368$	$2$	368.a	1.a	$1$	$2$	$2$	$2.938$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓		✓		23.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
368.2.a.i	$368$	$2$	368.a	1.a	$1$	$2$	$2$	$2.938$	\(\Q(\sqrt{17}) \)	$_{}$	None	None	✓		✓		184.2.a.e	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
368.2.c.a	$368$	$2$	368.c	92.b	$2$	$4$	$4$	$2.938$	\(\Q(\sqrt{2}, \sqrt{-5})\)	$_{}$	None	None		✓			368.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-2q^{9}+3\beta _{1}q^{11}+\cdots\)
368.2.c.b	$368$	$2$	368.c	92.b	$2$	$8$	$8$	$2.938$	8.0.303595776.1	$_{}$	None	None		✓	✓		368.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{6}q^{7}+\beta _{7}q^{9}+\cdots\)
368.2.i.a	$368$	$2$	368.i	368.i	$4$	$12$	$6$	$2.938$	12.0.\(\cdots\).1	$_{}$	\(\Q(\sqrt{-23}) \)	None		✓			368.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{1}q^{2}+(-\beta _{7}+\beta _{9}+\beta _{10})q^{3}+\beta _{2}q^{4}+\cdots\)
368.2.i.b	$368$	$2$	368.i	368.i	$4$	$80$	$40$	$2.938$		$_{}$	None	None		✓	✓		368.2.i.b	$4$	$0$	\(-4\)	\(-4\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
368.2.j.a	$368$	$2$	368.j	16.e	$4$	$2$	$1$	$2.938$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			368.2.j.a	$2$	$0$	\(2\)	\(2\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{2}+(1-i)q^{3}-2iq^{4}-2iq^{6}+\cdots\)
368.2.j.b	$368$	$2$	368.j	16.e	$4$	$4$	$2$	$2.938$	\(\Q(\zeta_{12})\)	$_{}$	None	None		✓			368.2.j.b	$2$	$1$	\(-2\)	\(-6\)	\(-4\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
368.2.j.c	$368$	$2$	368.j	16.e	$4$	$12$	$6$	$2.938$	12.0.\(\cdots\).1	$_{}$	None	None		✓			368.2.j.c	$2$	$0$	\(2\)	\(2\)	\(-4\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+\beta _{10}q^{3}+(\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
368.2.j.d	$368$	$2$	368.j	16.e	$4$	$24$	$12$	$2.938$		$_{}$	None	None		✓			368.2.j.d	$2$	$0$	\(-4\)	\(-4\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
368.2.j.e	$368$	$2$	368.j	16.e	$4$	$46$	$23$	$2.938$		$_{}$	None	None		✓	✓		368.2.j.e	$2$	$0$	\(2\)	\(6\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
368.2.m.a	$368$	$2$	368.m	23.c	$11$	$10$	$1$	$2.938$	\(\Q(\zeta_{22})\)	$_{}$	None	None					46.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(7\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{3}+\cdots\)
368.2.m.b	$368$	$2$	368.m	23.c	$11$	$10$	$1$	$2.938$	\(\Q(\zeta_{22})\)	$_{}$	None	None					46.2.c.a	$2$	$0$	\(0\)	\(4\)	\(-6\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{6})q^{3}+\cdots\)
368.2.m.c	$368$	$2$	368.m	23.c	$11$	$10$	$1$	$2.938$	\(\Q(\zeta_{22})\)	$_{}$	None	None					23.2.c.a	$2$	$0$	\(0\)	\(7\)	\(-3\)	\(5\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1+\zeta_{22}^{4}-\zeta_{22}^{5}-\zeta_{22}^{9})q^{3}+(-1+\cdots)q^{5}+\cdots\)
368.2.m.d	$368$	$2$	368.m	23.c	$11$	$20$	$2$	$2.938$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None					92.2.e.a	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-1+\beta _{6}-\beta _{8}+\beta _{9}+\beta _{10}+\beta _{11}+\cdots)q^{3}+\cdots\)
368.2.m.e	$368$	$2$	368.m	23.c	$11$	$30$	$3$	$2.938$		$_{}$	None	None					184.2.i.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(13\)			$\mathrm{SU}(2)[C_{11}]$
368.2.m.f	$368$	$2$	368.m	23.c	$11$	$30$	$3$	$2.938$		$_{}$	None	None					184.2.i.a	$2$	$0$	\(0\)	\(2\)	\(2\)	\(-13\)			$\mathrm{SU}(2)[C_{11}]$
368.2.s.a	$368$	$2$	368.s	92.h	$22$	$40$	$4$	$2.938$		$_{}$	None	None		✓			368.2.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
368.2.s.b	$368$	$2$	368.s	92.h	$22$	$80$	$8$	$2.938$		$_{}$	None	None		✓	✓		368.2.s.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
368.2.w.a	$368$	$2$	368.w	368.w	$44$	$920$	$46$	$2.938$		$_{}$	None	None		✓	✓	✓	368.2.w.a	$4$	$0$	\(-18\)	\(-18\)	\(-18\)	\(0\)			$\mathrm{SU}(2)[C_{44}]$
368.2.x.a	$368$	$2$	368.x	368.x	$44$	$920$	$46$	$2.938$		$_{}$	None	None		✓	✓	✓	368.2.x.a	$4$	$0$	\(-18\)	\(-18\)	\(-22\)	\(-44\)			$\mathrm{SU}(2)[C_{44}]$
368.3.d.a	$368$	$3$	368.d	4.b	$2$	$2$	$2$	$10.027$	\(\Q(\sqrt{-23}) \)	$_{}$	None	None		✓			368.3.d.a	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-6q^{5}-14q^{9}+2\beta q^{11}-13q^{13}+\cdots\)
368.3.d.b	$368$	$3$	368.d	4.b	$2$	$4$	$4$	$10.027$	\(\Q(\sqrt{-7}, \sqrt{-23})\)	$_{}$	None	None		✓			368.3.d.b	$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{3}+4q^{5}+(2\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
368.3.d.c	$368$	$3$	368.d	4.b	$2$	$16$	$16$	$10.027$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		✓	✓		368.3.d.c	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}-\beta _{9}q^{7}+(-5+\cdots)q^{9}+\cdots\)
368.3.f.a	$368$	$3$	368.f	23.b	$2$	$3$	$3$	$10.027$	3.3.621.1	$_{}$	\(\Q(\sqrt{-23}) \)	None	✓				23.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+(9+2\beta _{1}+\beta _{2})q^{9}+(\beta _{1}-2\beta _{2})q^{13}+\cdots\)
368.3.f.b	$368$	$3$	368.f	23.b	$2$	$4$	$4$	$10.027$	4.0.53792.1	$_{}$	None	None					92.3.d.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
368.3.f.c	$368$	$3$	368.f	23.b	$2$	$4$	$4$	$10.027$	4.0.613376.1	$_{}$	None	None					46.3.b.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{2})q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+(-6+\cdots)q^{9}+\cdots\)
368.3.f.d	$368$	$3$	368.f	23.b	$2$	$12$	$12$	$10.027$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None			✓		184.3.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{14}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{9}q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
368.3.k.a	$368$	$3$	368.k	368.k	$4$	$12$	$6$	$10.027$	12.0.\(\cdots\).1	$_{}$	\(\Q(\sqrt{-23}) \)	None		✓			368.3.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{U}(1)[D_{4}]$	\(q-\beta _{1}q^{2}+(\beta _{4}-\beta _{9}-2\beta _{10}+\beta _{11})q^{3}+\cdots\)
368.3.k.b	$368$	$3$	368.k	368.k	$4$	$176$	$88$	$10.027$		$_{}$	None	None		✓	✓		368.3.k.b	$4$	$0$	\(-4\)	\(-4\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
368.3.l.a	$368$	$3$	368.l	16.f	$4$	$176$	$88$	$10.027$		$_{}$	None	None		✓	✓	✓	368.3.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
368.3.p.a	$368$	$3$	368.p	23.d	$22$	$30$	$3$	$10.027$		$_{}$	None	None					23.3.d.a	$2$	$0$	\(0\)	\(11\)	\(-11\)	\(11\)			$\mathrm{SU}(2)[C_{22}]$
368.3.p.b	$368$	$3$	368.p	23.d	$22$	$40$	$4$	$10.027$		$_{}$	None	None					46.3.d.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
368.3.p.c	$368$	$3$	368.p	23.d	$22$	$40$	$4$	$10.027$		$_{}$	None	None					92.3.f.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
368.3.p.d	$368$	$3$	368.p	23.d	$22$	$120$	$12$	$10.027$		$_{}$	None	None			✓		184.3.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
368.3.r.a	$368$	$3$	368.r	92.g	$22$	$80$	$8$	$10.027$		$_{}$	None	None		✓			368.3.r.a	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
368.3.r.b	$368$	$3$	368.r	92.g	$22$	$160$	$16$	$10.027$		$_{}$	None	None		✓	✓		368.3.r.b	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
368.3.u.a	$368$	$3$	368.u	368.u	$44$	$1880$	$94$	$10.027$		$_{}$	None	None		✓	✓	✓	368.3.u.a	$4$	$0$	\(-18\)	\(-18\)	\(-18\)	\(-36\)			$\mathrm{SU}(2)[C_{44}]$
368.3.v.a	$368$	$3$	368.v	368.v	$44$	$1880$	$94$	$10.027$		$_{}$	None	None		✓	✓	✓	368.3.v.a	$4$	$0$	\(-18\)	\(-18\)	\(-22\)	\(0\)			$\mathrm{SU}(2)[C_{44}]$
368.4.a.a	$368$	$4$	368.a	1.a	$1$	$1$	$1$	$21.713$	\(\Q\)	$_{}$	None	None	✓				184.4.a.b	$1$	$1$	\(0\)	\(-8\)	\(-4\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{3}-4q^{5}+4q^{7}+37q^{9}-26q^{11}+\cdots\)

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