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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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
92.2.a.a	$92$	$2$	92.a	1.a	$1$	$1$	$1$	$0.735$	\(\Q\)	None	✓	✓	✓	✓	92.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{5}-4q^{7}+6q^{9}+2q^{11}+\cdots\)
92.2.a.b	$92$	$2$	92.a	1.a	$1$	$1$	$1$	$0.735$	\(\Q\)	None	✓	✓	✓	✓	92.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}-2q^{9}-q^{13}-6q^{17}+\cdots\)
92.2.b.a	$92$	$2$	92.b	92.b	$2$	$4$	$4$	$0.735$	\(\Q(i, \sqrt{14})\)	None		✓			92.2.b.a	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{3}+2\beta _{1}q^{4}+\cdots\)
92.2.b.b	$92$	$2$	92.b	92.b	$2$	$6$	$6$	$0.735$	6.0.8869743.1	\(\Q(\sqrt{-23}) \)		✓	✓		92.2.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
92.2.e.a	$92$	$2$	92.e	23.c	$11$	$20$	$2$	$0.735$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	92.2.e.a	$2$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1-\beta _{6}+\beta _{8}-\beta _{9}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)
92.2.h.a	$92$	$2$	92.h	92.h	$22$	$100$	$10$	$0.735$		None		✓	✓	✓	92.2.h.a	$4$	$0$	\(-7\)	\(0\)	\(-22\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.3.c.a	$92$	$3$	92.c	4.b	$2$	$22$	$22$	$2.507$		None		✓	✓	✓	92.3.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
92.3.d.a	$92$	$3$	92.d	23.b	$2$	$4$	$4$	$2.507$	4.0.53792.1	None		✓	✓	✓	92.3.d.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
92.3.f.a	$92$	$3$	92.f	23.d	$22$	$40$	$4$	$2.507$		None		✓	✓	✓	92.3.f.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.3.g.a	$92$	$3$	92.g	92.g	$22$	$220$	$22$	$2.507$		None		✓	✓	✓	92.3.g.a	$4$	$0$	\(-11\)	\(0\)	\(-18\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.4.a.a	$92$	$4$	92.a	1.a	$1$	$3$	$3$	$5.428$	3.3.1229.1	None	✓	✓	✓	✓	92.4.a.a	$1$	$1$	\(0\)	\(-4\)	\(-10\)	\(-46\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-4-\beta _{1}+3\beta _{2})q^{5}+\cdots\)
92.4.a.b	$92$	$4$	92.a	1.a	$1$	$3$	$3$	$5.428$	3.3.28669.1	None	✓	✓	✓	✓	92.4.a.b	$1$	$0$	\(0\)	\(8\)	\(0\)	\(42\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(3+\beta _{2})q^{3}+\beta _{1}q^{5}+(14-\beta _{1})q^{7}+\cdots\)
92.4.b.a	$92$	$4$	92.b	92.b	$2$	$2$	$2$	$5.428$	\(\Q(\sqrt{-23}) \)	\(\Q(\sqrt{-23}) \)		✓			92.4.b.a	$4$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-\beta )q^{2}+(-2+4\beta )q^{3}+(-5+\cdots)q^{4}+\cdots\)
92.4.b.b	$92$	$4$	92.b	92.b	$2$	$4$	$4$	$5.428$	\(\Q(\sqrt{-3}, \sqrt{-23})\)	\(\Q(\sqrt{-23}) \)		✓			92.4.b.b	$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+\beta _{1}+\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
92.4.b.c	$92$	$4$	92.b	92.b	$2$	$28$	$28$	$5.428$		None		✓	✓		92.4.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
92.4.e.a	$92$	$4$	92.e	23.c	$11$	$60$	$6$	$5.428$		None		✓	✓	✓	92.4.e.a	$2$	$0$	\(0\)	\(-4\)	\(10\)	\(4\)			$\mathrm{SU}(2)[C_{11}]$
92.4.h.a	$92$	$4$	92.h	92.h	$22$	$340$	$34$	$5.428$		None		✓	✓	✓	92.4.h.a	$4$	$0$	\(-11\)	\(0\)	\(-22\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.5.c.a	$92$	$5$	92.c	4.b	$2$	$44$	$44$	$9.510$		None		✓	✓	✓	92.5.c.a	$2$	$0$	\(0\)	\(0\)	\(24\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
92.5.d.a	$92$	$5$	92.d	23.b	$2$	$8$	$8$	$9.510$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓	✓	92.5.d.a	$2$	$0$	\(0\)	\(-10\)	\(0\)	\(0\)		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2})q^{3}+\beta _{3}q^{5}-\beta _{6}q^{7}+(40+\cdots)q^{9}+\cdots\)
92.5.f.a	$92$	$5$	92.f	23.d	$22$	$80$	$8$	$9.510$		None		✓	✓	✓	92.5.f.a	$2$	$0$	\(0\)	\(10\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.5.g.a	$92$	$5$	92.g	92.g	$22$	$460$	$46$	$9.510$		None		✓	✓	✓	92.5.g.a	$4$	$0$	\(-3\)	\(0\)	\(-18\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.6.a.a	$92$	$6$	92.a	1.a	$1$	$4$	$4$	$14.755$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	92.6.a.a	$1$	$1$	\(0\)	\(-7\)	\(-36\)	\(46\)	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(-9-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
92.6.a.b	$92$	$6$	92.a	1.a	$1$	$4$	$4$	$14.755$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	92.6.a.b	$1$	$0$	\(0\)	\(29\)	\(14\)	\(248\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(7+\beta _{1})q^{3}+(3+2\beta _{1}-\beta _{2})q^{5}+(62+\cdots)q^{7}+\cdots\)
92.6.b.a	$92$	$6$	92.b	92.b	$2$	$6$	$6$	$14.755$	6.0.8869743.1	\(\Q(\sqrt{-23}) \)		✓			92.6.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-3\beta _{1}-2\beta _{3}+\beta _{4}+\beta _{5})q^{2}+(-5\beta _{1}+\cdots)q^{3}+\cdots\)
92.6.b.b	$92$	$6$	92.b	92.b	$2$	$52$	$52$	$14.755$		None		✓	✓		92.6.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
92.6.e.a	$92$	$6$	92.e	23.c	$11$	$100$	$10$	$14.755$		None		✓	✓	✓	92.6.e.a	$2$	$0$	\(0\)	\(2\)	\(-86\)	\(-118\)			$\mathrm{SU}(2)[C_{11}]$
92.6.h.a	$92$	$6$	92.h	92.h	$22$	$580$	$58$	$14.755$		None		✓	✓	✓	92.6.h.a	$4$	$0$	\(-11\)	\(0\)	\(-22\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.7.c.a	$92$	$7$	92.c	4.b	$2$	$66$	$66$	$21.165$		None		✓	✓	✓	92.7.c.a	$2$	$0$	\(0\)	\(0\)	\(-44\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
92.7.d.a	$92$	$7$	92.d	23.b	$2$	$12$	$12$	$21.165$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓	✓	92.7.d.a	$2$	$0$	\(0\)	\(32\)	\(0\)	\(0\)		$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3+\beta _{2})q^{3}-\beta _{1}q^{5}+\beta _{7}q^{7}+(320+\cdots)q^{9}+\cdots\)
92.7.f.a	$92$	$7$	92.f	23.d	$22$	$120$	$12$	$21.165$		None		✓	✓	✓	92.7.f.a	$2$	$0$	\(0\)	\(-32\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.7.g.a	$92$	$7$	92.g	92.g	$22$	$700$	$70$	$21.165$		None		✓	✓	✓	92.7.g.a	$4$	$0$	\(-19\)	\(0\)	\(-18\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.8.a.a	$92$	$8$	92.a	1.a	$1$	$7$	$7$	$28.739$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	92.8.a.a	$1$	$1$	\(0\)	\(-67\)	\(-180\)	\(-1640\)	$-$	$2^{10}$	$\mathrm{SU}(2)$	\(q+(-10+\beta _{1})q^{3}+(-26-\beta _{5})q^{5}+\cdots\)
92.8.a.b	$92$	$8$	92.a	1.a	$1$	$7$	$7$	$28.739$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	92.8.a.b	$1$	$0$	\(0\)	\(41\)	\(70\)	\(1246\)	$+$	$2^{10}$	$\mathrm{SU}(2)$	\(q+(6-\beta _{1})q^{3}+(10-\beta _{1}-\beta _{2})q^{5}+(179+\cdots)q^{7}+\cdots\)
92.8.b.a	$92$	$8$	92.b	92.b	$2$	$6$	$6$	$28.739$	6.0.8869743.1	\(\Q(\sqrt{-23}) \)		✓			92.8.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(3\beta _{1}-4\beta _{3}+\beta _{5})q^{2}+(-11\beta _{1}+18\beta _{3}+\cdots)q^{3}+\cdots\)
92.8.b.b	$92$	$8$	92.b	92.b	$2$	$76$	$76$	$28.739$		None		✓	✓		92.8.b.b	$4$	$0$	\(-16\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
92.8.e.a	$92$	$8$	92.e	23.c	$11$	$140$	$14$	$28.739$		None		✓	✓	✓	92.8.e.a	$2$	$0$	\(0\)	\(26\)	\(110\)	\(394\)			$\mathrm{SU}(2)[C_{11}]$
92.8.h.a	$92$	$8$	92.h	92.h	$22$	$820$	$82$	$28.739$		None		✓	✓	✓	92.8.h.a	$4$	$0$	\(5\)	\(0\)	\(-22\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.9.c.a	$92$	$9$	92.c	4.b	$2$	$88$	$88$	$37.479$		None		✓	✓	✓	92.9.c.a	$2$	$0$	\(0\)	\(0\)	\(-336\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
92.9.d.a	$92$	$9$	92.d	23.b	$2$	$16$	$16$	$37.479$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	92.9.d.a	$2$	$0$	\(0\)	\(-70\)	\(0\)	\(0\)		$2^{34}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-4+\beta _{2})q^{3}+\beta _{1}q^{5}-\beta _{9}q^{7}+(1370+\cdots)q^{9}+\cdots\)
92.9.f.a	$92$	$9$	92.f	23.d	$22$	$160$	$16$	$37.479$		None		✓	✓	✓	92.9.f.a	$2$	$0$	\(0\)	\(70\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.9.g.a	$92$	$9$	92.g	92.g	$22$	$940$	$94$	$37.479$		None		✓	✓	✓	92.9.g.a	$4$	$0$	\(-3\)	\(0\)	\(-18\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.10.a.a	$92$	$10$	92.a	1.a	$1$	$8$	$8$	$47.383$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓	✓	92.10.a.a	$1$	$1$	\(0\)	\(-316\)	\(154\)	\(-9198\)	$+$	$2^{16}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(-40+\beta _{1})q^{3}+(18+2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
92.10.a.b	$92$	$10$	92.a	1.a	$1$	$8$	$8$	$47.383$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓	✓	92.10.a.b	$1$	$0$	\(0\)	\(8\)	\(1404\)	\(18042\)	$-$	$2^{15}\cdot 3$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(176-\beta _{3})q^{5}+(2255+\cdots)q^{7}+\cdots\)
92.10.b.a	$92$	$10$	92.b	92.b	$2$	$2$	$2$	$47.383$	\(\Q(\sqrt{-23}) \)	\(\Q(\sqrt{-23}) \)		✓			92.10.b.a	$4$	$0$	\(45\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(23-\beta )q^{2}+(22-44\beta )q^{3}+(523+\cdots)q^{4}+\cdots\)
92.10.b.b	$92$	$10$	92.b	92.b	$2$	$4$	$4$	$47.383$	\(\Q(\sqrt{-3}, \sqrt{-23})\)	\(\Q(\sqrt{-23}) \)		✓			92.10.b.b	$4$	$0$	\(-45\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-11+5\beta _{1}-6\beta _{2})q^{2}+(11+65\beta _{1}+\cdots)q^{3}+\cdots\)
92.10.b.c	$92$	$10$	92.b	92.b	$2$	$100$	$100$	$47.383$		None		✓	✓		92.10.b.c	$4$	$0$	\(32\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
92.10.e.a	$92$	$10$	92.e	23.c	$11$	$180$	$18$	$47.383$		None		✓	✓	✓	92.10.e.a	$2$	$0$	\(0\)	\(-148\)	\(-226\)	\(3812\)			$\mathrm{SU}(2)[C_{11}]$
92.10.h.a	$92$	$10$	92.h	92.h	$22$	$1060$	$106$	$47.383$		None		✓	✓	✓	92.10.h.a	$4$	$0$	\(-43\)	\(0\)	\(-22\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
92.11.c.a	$92$	$11$	92.c	4.b	$2$	$110$	$110$	$58.453$		None		✓	✓	✓	92.11.c.a	$2$	$0$	\(0\)	\(0\)	\(3116\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
92.11.d.a	$92$	$11$	92.d	23.b	$2$	$20$	$20$	$58.453$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓	✓	92.11.d.a	$2$	$0$	\(0\)	\(62\)	\(0\)	\(0\)		$2^{59}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3+\beta _{2})q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+(13723+\cdots)q^{9}+\cdots\)

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