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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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
22.2.c.a	$22$	$2$	22.c	11.c	$5$	$4$	$1$	$0.176$	$\Q(\zeta_{10})$	None		✓	✓	✓	22.2.c.a	$2$	$0$	$-1$	$-4$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
22.3.b.a	$22$	$3$	22.b	11.b	$2$	$2$	$2$	$0.599$	$\Q(\sqrt{-2})$	None		✓	✓	✓	22.3.b.a	$2$	$0$	$0$	$2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots$
22.3.d.a	$22$	$3$	22.d	11.d	$10$	$8$	$2$	$0.599$	8.0.64000000.1	None		✓	✓	✓	22.3.d.a	$2$	$0$	$0$	$-2$	$2$	$-30$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(1-\beta _{1}-2\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots$
22.4.a.a	$22$	$4$	22.a	1.a	$1$	$1$	$1$	$1.298$	$\Q$	None	✓	✓	✓	✓	22.4.a.a	$1$	$1$	$-2$	$-7$	$-19$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-7q^{3}+4q^{4}-19q^{5}+14q^{6}+\cdots$
22.4.a.b	$22$	$4$	22.a	1.a	$1$	$1$	$1$	$1.298$	$\Q$	None	✓	✓	✓	✓	22.4.a.b	$1$	$0$	$-2$	$4$	$14$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{3}+4q^{4}+14q^{5}-8q^{6}+\cdots$
22.4.a.c	$22$	$4$	22.a	1.a	$1$	$1$	$1$	$1.298$	$\Q$	None	✓	✓	✓	✓	22.4.a.c	$1$	$0$	$2$	$1$	$-3$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+4q^{4}-3q^{5}+2q^{6}+\cdots$
22.4.c.a	$22$	$4$	22.c	11.c	$5$	$4$	$1$	$1.298$	$\Q(\zeta_{10})$	None		✓			22.4.c.a	$2$	$0$	$-2$	$-1$	$3$	$25$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\zeta_{10}q^{2}+(-3+3\zeta_{10}+8\zeta_{10}^{3})q^{3}+\cdots$
22.4.c.b	$22$	$4$	22.c	11.c	$5$	$8$	$2$	$1.298$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓		22.4.c.b	$2$	$0$	$4$	$3$	$5$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$
22.5.b.a	$22$	$5$	22.b	11.b	$2$	$4$	$4$	$2.274$	$\Q(\sqrt{-2}, \sqrt{553})$	None		✓	✓	✓	22.5.b.a	$2$	$0$	$0$	$2$	$-30$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}-8q^{4}+(-8-\beta _{1}+\cdots)q^{5}+\cdots$
22.5.d.a	$22$	$5$	22.d	11.d	$10$	$16$	$4$	$2.274$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	22.5.d.a	$2$	$0$	$0$	$-2$	$30$	$150$		$2^{8}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{4}q^{2}+(1+\beta _{2}+3\beta _{3}-\beta _{10}-\beta _{13}+\cdots)q^{3}+\cdots$
22.6.a.a	$22$	$6$	22.a	1.a	$1$	$1$	$1$	$3.528$	$\Q$	None	✓	✓	✓	✓	22.6.a.a	$1$	$0$	$-4$	$-21$	$81$	$98$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-21q^{3}+2^{4}q^{4}+3^{4}q^{5}+84q^{6}+\cdots$
22.6.a.b	$22$	$6$	22.a	1.a	$1$	$1$	$1$	$3.528$	$\Q$	None	✓	✓	✓	✓	22.6.a.b	$1$	$1$	$-4$	$1$	$-51$	$-166$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+q^{3}+2^{4}q^{4}-51q^{5}-4q^{6}+\cdots$
22.6.a.c	$22$	$6$	22.a	1.a	$1$	$1$	$1$	$3.528$	$\Q$	None	✓	✓	✓	✓	22.6.a.c	$1$	$1$	$4$	$-29$	$-31$	$-230$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-29q^{3}+2^{4}q^{4}-31q^{5}-116q^{6}+\cdots$
22.6.a.d	$22$	$6$	22.a	1.a	$1$	$2$	$2$	$3.528$	$\Q(\sqrt{793})$	None	✓	✓	✓	✓	22.6.a.d	$1$	$0$	$8$	$29$	$-13$	$-14$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+(15-\beta )q^{3}+2^{4}q^{4}+(-9+\cdots)q^{5}+\cdots$
22.6.c.a	$22$	$6$	22.c	11.c	$5$	$8$	$2$	$3.528$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			22.6.c.a	$2$	$0$	$8$	$20$	$-30$	$48$		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q-4\beta _{3}q^{2}+(3+3\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots$
22.6.c.b	$22$	$6$	22.c	11.c	$5$	$12$	$3$	$3.528$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		22.6.c.b	$2$	$0$	$-12$	$0$	$44$	$-326$		$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-4+4\beta _{1}+4\beta _{2}-4\beta _{3})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots$
22.7.b.a	$22$	$7$	22.b	11.b	$2$	$6$	$6$	$5.061$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		✓	✓	✓	22.7.b.a	$2$	$0$	$0$	$-52$	$368$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-9+\beta _{1})q^{3}-2^{5}q^{4}+(61+\cdots)q^{5}+\cdots$
22.7.d.a	$22$	$7$	22.d	11.d	$10$	$24$	$6$	$5.061$		None		✓	✓	✓	22.7.d.a	$2$	$0$	$0$	$52$	$-368$	$720$			$\mathrm{SU}(2)[C_{10}]$
22.8.a.a	$22$	$8$	22.a	1.a	$1$	$1$	$1$	$6.872$	$\Q$	None	✓	✓	✓	✓	22.8.a.a	$1$	$1$	$-8$	$-19$	$317$	$-1030$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}-19q^{3}+2^{6}q^{4}+317q^{5}+\cdots$
22.8.a.b	$22$	$8$	22.a	1.a	$1$	$1$	$1$	$6.872$	$\Q$	None	✓	✓	✓	✓	22.8.a.b	$1$	$0$	$-8$	$91$	$185$	$-722$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}+91q^{3}+2^{6}q^{4}+185q^{5}+\cdots$
22.8.a.c	$22$	$8$	22.a	1.a	$1$	$1$	$1$	$6.872$	$\Q$	None	✓	✓	✓	✓	22.8.a.c	$1$	$1$	$8$	$-21$	$-551$	$62$	$-$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}-21q^{3}+2^{6}q^{4}-551q^{5}+\cdots$
22.8.a.d	$22$	$8$	22.a	1.a	$1$	$2$	$2$	$6.872$	$\Q(\sqrt{14881})$	None	✓	✓	✓	✓	22.8.a.d	$1$	$0$	$16$	$-23$	$331$	$1794$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}+(-11-\beta )q^{3}+2^{6}q^{4}+(165+\cdots)q^{5}+\cdots$
22.8.c.a	$22$	$8$	22.c	11.c	$5$	$12$	$3$	$6.872$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			22.8.c.a	$2$	$0$	$-24$	$44$	$220$	$534$		$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-8+8\beta _{1}+8\beta _{2}+8\beta _{3})q^{2}+(5\beta _{1}+\cdots)q^{3}+\cdots$
22.8.c.b	$22$	$8$	22.c	11.c	$5$	$16$	$4$	$6.872$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		22.8.c.b	$2$	$0$	$32$	$-96$	$-82$	$-700$		$2^{8}\cdot 5\cdot 11^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q-8\beta _{2}q^{2}+(-10-10\beta _{2}+3\beta _{3}+3\beta _{5}+\cdots)q^{3}+\cdots$
22.9.b.a	$22$	$9$	22.b	11.b	$2$	$8$	$8$	$8.962$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓	✓	22.9.b.a	$2$	$0$	$0$	$182$	$-1410$	$0$		$2^{16}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(23+\beta _{1})q^{3}-2^{7}q^{4}+(-176+\cdots)q^{5}+\cdots$
22.9.d.a	$22$	$9$	22.d	11.d	$10$	$32$	$8$	$8.962$		None		✓	✓	✓	22.9.d.a	$2$	$0$	$0$	$-182$	$1410$	$-10950$			$\mathrm{SU}(2)[C_{10}]$
22.10.a.a	$22$	$10$	22.a	1.a	$1$	$1$	$1$	$11.331$	$\Q$	None	✓	✓	✓	✓	22.10.a.a	$1$	$1$	$16$	$-41$	$-1039$	$-3482$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}-41q^{3}+2^{8}q^{4}-1039q^{5}+\cdots$
22.10.a.b	$22$	$10$	22.a	1.a	$1$	$1$	$1$	$11.331$	$\Q$	None	✓	✓			22.10.a.b	$1$	$0$	$16$	$137$	$-595$	$11354$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+137q^{3}+2^{8}q^{4}-595q^{5}+\cdots$
22.10.a.c	$22$	$10$	22.a	1.a	$1$	$1$	$1$	$11.331$	$\Q$	None	✓	✓			22.10.a.c	$1$	$0$	$16$	$201$	$2349$	$-8806$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+201q^{3}+2^{8}q^{4}+2349q^{5}+\cdots$
22.10.a.d	$22$	$10$	22.a	1.a	$1$	$2$	$2$	$11.331$	$\Q(\sqrt{889})$	None	✓	✓	✓	✓	22.10.a.d	$1$	$0$	$-32$	$-21$	$-521$	$-7490$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(-6-9\beta )q^{3}+2^{8}q^{4}+(-212+\cdots)q^{5}+\cdots$
22.10.a.e	$22$	$10$	22.a	1.a	$1$	$2$	$2$	$11.331$	$\Q(\sqrt{463})$	None	✓	✓	✓	✓	22.10.a.e	$1$	$1$	$-32$	$34$	$-1478$	$8196$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(17+\beta )q^{3}+2^{8}q^{4}+(-739+\cdots)q^{5}+\cdots$
22.10.c.a	$22$	$10$	22.c	11.c	$5$	$16$	$4$	$11.331$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			22.10.c.a	$2$	$0$	$64$	$-13$	$1999$	$3779$		$2^{12}\cdot 3^{4}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+(2^{4}+2^{4}\beta _{1}+2^{4}\beta _{2}-2^{4}\beta _{3})q^{2}+\cdots$
22.10.c.b	$22$	$10$	22.c	11.c	$5$	$20$	$5$	$11.331$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		22.10.c.b	$2$	$0$	$-80$	$15$	$-2455$	$17413$		$2^{16}\cdot 3^{4}\cdot 5\cdot 11^{7}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2^{4}+2^{4}\beta _{3}-2^{4}\beta _{4}-2^{4}\beta _{5})q^{2}+\cdots$
22.11.b.a	$22$	$11$	22.b	11.b	$2$	$10$	$10$	$13.978$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓	✓	22.11.b.a	$2$	$0$	$0$	$-106$	$1138$	$0$		$2^{24}\cdot 3^{2}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-11-\beta _{2})q^{3}-2^{9}q^{4}+\cdots$
22.11.d.a	$22$	$11$	22.d	11.d	$10$	$40$	$10$	$13.978$		None		✓	✓	✓	22.11.d.a	$2$	$0$	$0$	$106$	$-1138$	$19470$			$\mathrm{SU}(2)[C_{10}]$
22.12.a.a	$22$	$12$	22.a	1.a	$1$	$2$	$2$	$16.904$	$\Q(\sqrt{331})$	None	✓	✓	✓	✓	22.12.a.a	$1$	$1$	$64$	$-426$	$2290$	$-86324$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+2^{5}q^{2}+(-213+3\beta )q^{3}+2^{10}q^{4}+\cdots$
22.12.a.b	$22$	$12$	22.a	1.a	$1$	$3$	$3$	$16.904$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	22.12.a.b	$1$	$1$	$-96$	$-70$	$-5624$	$-30576$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-2^{5}q^{2}+(-23+\beta _{2})q^{3}+2^{10}q^{4}+\cdots$
22.12.a.c	$22$	$12$	22.a	1.a	$1$	$3$	$3$	$16.904$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	22.12.a.c	$1$	$0$	$-96$	$106$	$17344$	$13204$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q-2^{5}q^{2}+(35+\beta _{1})q^{3}+2^{10}q^{4}+(5771+\cdots)q^{5}+\cdots$
22.12.a.d	$22$	$12$	22.a	1.a	$1$	$3$	$3$	$16.904$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	22.12.a.d	$1$	$0$	$96$	$370$	$-1928$	$58472$	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	$q+2^{5}q^{2}+(123-\beta _{1})q^{3}+2^{10}q^{4}+\cdots$
22.12.c.a	$22$	$12$	22.c	11.c	$5$	$20$	$5$	$16.904$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			22.12.c.a	$2$	$0$	$-160$	$56$	$-362$	$-167178$		$2^{24}\cdot 3^{4}\cdot 5\cdot 11^{8}$	$\mathrm{SU}(2)[C_{5}]$	$q+2^{5}\beta _{2}q^{2}+(7+\beta _{1}+7\beta _{2}+9\beta _{4}+\cdots)q^{3}+\cdots$
22.12.c.b	$22$	$12$	22.c	11.c	$5$	$24$	$6$	$16.904$		None		✓	✓		22.12.c.b	$2$	$0$	$192$	$-36$	$-11720$	$20572$			$\mathrm{SU}(2)[C_{5}]$
22.13.b.a	$22$	$13$	22.b	11.b	$2$	$12$	$12$	$20.108$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	22.13.b.a	$2$	$0$	$0$	$-1240$	$-1440$	$0$		$2^{38}\cdot 3^{2}\cdot 11^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-103-\beta _{1})q^{3}-2^{11}q^{4}+\cdots$
22.13.d.a	$22$	$13$	22.d	11.d	$10$	$48$	$12$	$20.108$		None		✓	✓	✓	22.13.d.a	$2$	$0$	$0$	$1240$	$1440$	$439200$			$\mathrm{SU}(2)[C_{10}]$
22.14.a.a	$22$	$14$	22.a	1.a	$1$	$2$	$2$	$23.591$	$\Q(\sqrt{100039})$	None	✓	✓	✓	✓	22.14.a.a	$1$	$1$	$-128$	$-662$	$-48566$	$404508$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}+(-331+\beta )q^{3}+2^{12}q^{4}+\cdots$
22.14.a.b	$22$	$14$	22.a	1.a	$1$	$2$	$2$	$23.591$	$\Q(\sqrt{55441})$	None	✓	✓	✓	✓	22.14.a.b	$1$	$0$	$-128$	$1626$	$7666$	$637048$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}+(813-3\beta )q^{3}+2^{12}q^{4}+\cdots$
22.14.a.c	$22$	$14$	22.a	1.a	$1$	$2$	$2$	$23.591$	$\Q(\sqrt{45769})$	None	✓	✓	✓	✓	22.14.a.c	$1$	$1$	$128$	$-926$	$2914$	$-170560$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+2^{6}q^{2}+(-463-\beta )q^{3}+2^{12}q^{4}+\cdots$
22.14.a.d	$22$	$14$	22.a	1.a	$1$	$3$	$3$	$23.591$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	22.14.a.d	$1$	$0$	$192$	$-298$	$40432$	$40452$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+2^{6}q^{2}+(-10^{2}-\beta _{1}-\beta _{2})q^{3}+2^{12}q^{4}+\cdots$
22.14.c.a	$22$	$14$	22.c	11.c	$5$	$24$	$6$	$23.591$		None		✓			22.14.c.a	$2$	$0$	$384$	$2708$	$32920$	$-509572$			$\mathrm{SU}(2)[C_{5}]$
22.14.c.b	$22$	$14$	22.c	11.c	$5$	$28$	$7$	$23.591$		None		✓	✓		22.14.c.b	$2$	$0$	$-448$	$-1248$	$71554$	$361734$			$\mathrm{SU}(2)[C_{5}]$
22.15.b.a	$22$	$15$	22.b	11.b	$2$	$14$	$14$	$27.352$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓	✓	✓	22.15.b.a	$2$	$0$	$0$	$4394$	$69758$	$0$		$2^{56}\cdot 3^{6}\cdot 11^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(314+\beta _{1})q^{3}-2^{13}q^{4}+\cdots$

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