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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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.3.c.a	$10$	$3$	10.c	5.c	$4$	$2$	$1$	$0.272$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	10.3.c.a	$2$	$0$	\(-2\)	\(-4\)	\(0\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+(2 i-2)q^{3}+2 i q^{4}+\cdots\)
10.4.a.a	$10$	$4$	10.a	1.a	$1$	$1$	$1$	$0.590$	\(\Q\)	None	✓	✓	✓	✓	10.4.a.a	$1$	$0$	\(2\)	\(-8\)	\(5\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots\)
10.4.b.a	$10$	$4$	10.b	5.b	$2$	$2$	$2$	$0.590$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	10.4.b.a	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-\beta q^{3}-4 q^{4}+(-5\beta-5)q^{5}+\cdots\)
10.5.c.a	$10$	$5$	10.c	5.c	$4$	$2$	$1$	$1.034$	\(\Q(\sqrt{-1}) \)	None		✓			10.5.c.a	$2$	$0$	\(-4\)	\(18\)	\(-30\)	\(58\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2 i-2)q^{2}+(-9 i+9)q^{3}+\cdots\)
10.5.c.b	$10$	$5$	10.c	5.c	$4$	$2$	$1$	$1.034$	\(\Q(\sqrt{-1}) \)	None		✓			10.5.c.b	$2$	$0$	\(4\)	\(2\)	\(-30\)	\(-38\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2 i+2)q^{2}+(-i+1)q^{3}+8 i q^{4}+\cdots\)
10.6.a.a	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	\(\Q\)	None	✓	✓	✓	✓	10.6.a.a	$1$	$1$	\(-4\)	\(-26\)	\(-25\)	\(-22\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-26q^{3}+2^{4}q^{4}-5^{2}q^{5}+104q^{6}+\cdots\)
10.6.a.b	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	\(\Q\)	None	✓	✓	✓	✓	10.6.a.b	$1$	$0$	\(-4\)	\(24\)	\(25\)	\(-172\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+24q^{3}+2^{4}q^{4}+5^{2}q^{5}-96q^{6}+\cdots\)
10.6.a.c	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	\(\Q\)	None	✓	✓	✓	✓	10.6.a.c	$1$	$0$	\(4\)	\(6\)	\(-25\)	\(-118\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+6q^{3}+2^{4}q^{4}-5^{2}q^{5}+24q^{6}+\cdots\)
10.6.b.a	$10$	$6$	10.b	5.b	$2$	$2$	$2$	$1.604$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	10.6.b.a	$2$	$0$	\(0\)	\(0\)	\(110\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{2}+7\beta q^{3}-16 q^{4}+(5\beta+55)q^{5}+\cdots\)
10.7.c.a	$10$	$7$	10.c	5.c	$4$	$2$	$1$	$2.301$	\(\Q(\sqrt{-1}) \)	None		✓			10.7.c.a	$2$	$0$	\(-8\)	\(-46\)	\(-150\)	\(-494\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-4 i-4)q^{2}+(23 i-23)q^{3}+\cdots\)
10.7.c.b	$10$	$7$	10.c	5.c	$4$	$4$	$2$	$2.301$	\(\Q(i, \sqrt{129})\)	None		✓	✓		10.7.c.b	$2$	$0$	\(16\)	\(-18\)	\(330\)	\(-202\)		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(4+4\beta _{1})q^{2}+(-5+4\beta _{1}-\beta _{3})q^{3}+\cdots\)
10.8.a.a	$10$	$8$	10.a	1.a	$1$	$1$	$1$	$3.124$	\(\Q\)	None	✓	✓	✓	✓	10.8.a.a	$1$	$0$	\(8\)	\(28\)	\(125\)	\(104\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+28q^{3}+2^{6}q^{4}+5^{3}q^{5}+224q^{6}+\cdots\)
10.8.b.a	$10$	$8$	10.b	5.b	$2$	$4$	$4$	$3.124$	\(\Q(i, \sqrt{31})\)	None		✓	✓	✓	10.8.b.a	$2$	$0$	\(0\)	\(0\)	\(60\)	\(0\)		$2^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(3\beta _{1}-\beta _{3})q^{3}-2^{6}q^{4}+(15+\cdots)q^{5}+\cdots\)
10.9.c.a	$10$	$9$	10.c	5.c	$4$	$4$	$2$	$4.074$	\(\Q(i, \sqrt{249})\)	None		✓			10.9.c.a	$2$	$0$	\(-32\)	\(54\)	\(90\)	\(-1186\)		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-8+8\beta _{1})q^{2}+(13+13\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.9.c.b	$10$	$9$	10.c	5.c	$4$	$4$	$2$	$4.074$	\(\Q(i, \sqrt{601})\)	None		✓			10.9.c.b	$2$	$0$	\(32\)	\(86\)	\(-870\)	\(5726\)		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(8+8\beta _{1})q^{2}+(22-21\beta _{1}+\beta _{3})q^{3}+\cdots\)
10.10.a.a	$10$	$10$	10.a	1.a	$1$	$1$	$1$	$5.150$	\(\Q\)	None	✓	✓	✓	✓	10.10.a.a	$1$	$0$	\(-16\)	\(-204\)	\(625\)	\(5432\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}-204q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
10.10.a.b	$10$	$10$	10.a	1.a	$1$	$1$	$1$	$5.150$	\(\Q\)	None	✓	✓	✓	✓	10.10.a.b	$1$	$1$	\(-16\)	\(46\)	\(-625\)	\(-10318\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+46q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
10.10.a.c	$10$	$10$	10.a	1.a	$1$	$1$	$1$	$5.150$	\(\Q\)	None	✓	✓	✓	✓	10.10.a.c	$1$	$0$	\(16\)	\(174\)	\(-625\)	\(4658\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+174q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
10.10.b.a	$10$	$10$	10.b	5.b	$2$	$4$	$4$	$5.150$	\(\Q(i, \sqrt{319})\)	None		✓	✓	✓	10.10.b.a	$2$	$0$	\(0\)	\(0\)	\(-2580\)	\(0\)		$2^{10}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-5\beta _{1}-\beta _{3})q^{3}-2^{8}q^{4}+\cdots\)
10.11.c.a	$10$	$11$	10.c	5.c	$4$	$2$	$1$	$6.354$	\(\Q(\sqrt{-1}) \)	None		✓			10.11.c.a	$2$	$0$	\(32\)	\(-366\)	\(-3750\)	\(-16814\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(16 i+16)q^{2}+(183 i-183)q^{3}+\cdots\)
10.11.c.b	$10$	$11$	10.c	5.c	$4$	$2$	$1$	$6.354$	\(\Q(\sqrt{-1}) \)	None		✓			10.11.c.b	$2$	$0$	\(32\)	\(114\)	\(5850\)	\(13906\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(16 i+16)q^{2}+(-57 i+57)q^{3}+\cdots\)
10.11.c.c	$10$	$11$	10.c	5.c	$4$	$6$	$3$	$6.354$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓	✓		10.11.c.c	$2$	$0$	\(-96\)	\(128\)	\(5460\)	\(13512\)		$2^{8}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{4}-2^{4}\beta _{1})q^{2}+(21-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.12.a.a	$10$	$12$	10.a	1.a	$1$	$1$	$1$	$7.683$	\(\Q\)	None	✓	✓	✓	✓	10.12.a.a	$1$	$1$	\(-32\)	\(-12\)	\(3125\)	\(-14176\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{5}q^{2}-12q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)
10.12.a.b	$10$	$12$	10.a	1.a	$1$	$1$	$1$	$7.683$	\(\Q\)	None	✓	✓	✓	✓	10.12.a.b	$1$	$0$	\(-32\)	\(738\)	\(-3125\)	\(25574\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{5}q^{2}+738q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.c	$10$	$12$	10.a	1.a	$1$	$1$	$1$	$7.683$	\(\Q\)	None	✓	✓	✓	✓	10.12.a.c	$1$	$1$	\(32\)	\(-318\)	\(-3125\)	\(-70714\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{5}q^{2}-318q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.d	$10$	$12$	10.a	1.a	$1$	$2$	$2$	$7.683$	\(\Q(\sqrt{1969}) \)	None	✓	✓	✓	✓	10.12.a.d	$1$	$0$	\(64\)	\(604\)	\(6250\)	\(14092\)	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{5}q^{2}+(302-\beta )q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)
10.12.b.a	$10$	$12$	10.b	5.b	$2$	$6$	$6$	$7.683$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓	✓	✓	10.12.b.a	$2$	$0$	\(0\)	\(0\)	\(530\)	\(0\)		$2^{19}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{1}+3\beta _{2})q^{3}-2^{10}q^{4}+\cdots\)
10.13.c.a	$10$	$13$	10.c	5.c	$4$	$6$	$3$	$9.140$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓			10.13.c.a	$2$	$0$	\(-192\)	\(-936\)	\(-16260\)	\(-45336\)		$2^{5}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{5}-2^{5}\beta _{1})q^{2}+(-156+156\beta _{1}+\cdots)q^{3}+\cdots\)
10.13.c.b	$10$	$13$	10.c	5.c	$4$	$6$	$3$	$9.140$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓			10.13.c.b	$2$	$0$	\(192\)	\(296\)	\(14460\)	\(-322104\)		$2^{5}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{5}+2^{5}\beta _{1})q^{2}+(7^{2}-7^{2}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.14.a.a	$10$	$14$	10.a	1.a	$1$	$1$	$1$	$10.723$	\(\Q\)	None	✓	✓	✓	✓	10.14.a.a	$1$	$1$	\(-64\)	\(-26\)	\(-15625\)	\(538538\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}-26q^{3}+2^{12}q^{4}-5^{6}q^{5}+\cdots\)
10.14.a.b	$10$	$14$	10.a	1.a	$1$	$1$	$1$	$10.723$	\(\Q\)	None	✓	✓	✓	✓	10.14.a.b	$1$	$0$	\(-64\)	\(1224\)	\(15625\)	\(-65212\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+1224q^{3}+2^{12}q^{4}+5^{6}q^{5}+\cdots\)
10.14.a.c	$10$	$14$	10.a	1.a	$1$	$1$	$1$	$10.723$	\(\Q\)	None	✓	✓	✓	✓	10.14.a.c	$1$	$0$	\(64\)	\(-2394\)	\(-15625\)	\(438122\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}-2394q^{3}+2^{12}q^{4}-5^{6}q^{5}+\cdots\)
10.14.b.a	$10$	$14$	10.b	5.b	$2$	$6$	$6$	$10.723$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓	✓	✓	10.14.b.a	$2$	$0$	\(0\)	\(0\)	\(-2470\)	\(0\)		$2^{21}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}-2^{12}q^{4}+(-412+\cdots)q^{5}+\cdots\)
10.15.c.a	$10$	$15$	10.c	5.c	$4$	$6$	$3$	$12.433$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓			10.15.c.a	$2$	$0$	\(-384\)	\(2912\)	\(82500\)	\(943128\)		$2^{7}\cdot 3^{2}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{6}+2^{6}\beta _{1})q^{2}+(485+485\beta _{1}+\cdots)q^{3}+\cdots\)
10.15.c.b	$10$	$15$	10.c	5.c	$4$	$8$	$4$	$12.433$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		10.15.c.b	$2$	$0$	\(512\)	\(1404\)	\(-100860\)	\(1333276\)		$2^{14}\cdot 3^{4}\cdot 5^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{6}-2^{6}\beta _{1})q^{2}+(175+176\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
10.16.a.a	$10$	$16$	10.a	1.a	$1$	$1$	$1$	$14.269$	\(\Q\)	None	✓	✓	✓	✓	10.16.a.a	$1$	$1$	\(-128\)	\(-5568\)	\(78125\)	\(2564996\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}-5568q^{3}+2^{14}q^{4}+5^{7}q^{5}+\cdots\)
10.16.a.b	$10$	$16$	10.a	1.a	$1$	$1$	$1$	$14.269$	\(\Q\)	None	✓	✓	✓	✓	10.16.a.b	$1$	$0$	\(-128\)	\(-918\)	\(-78125\)	\(-953554\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}-918q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots\)
10.16.a.c	$10$	$16$	10.a	1.a	$1$	$1$	$1$	$14.269$	\(\Q\)	None	✓	✓	✓	✓	10.16.a.c	$1$	$1$	\(128\)	\(-1302\)	\(-78125\)	\(-90706\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}-1302q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots\)
10.16.a.d	$10$	$16$	10.a	1.a	$1$	$2$	$2$	$14.269$	\(\Q(\sqrt{239569}) \)	None	✓	✓	✓	✓	10.16.a.d	$1$	$0$	\(256\)	\(-1844\)	\(156250\)	\(-984932\)	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}+(-922-\beta )q^{3}+2^{14}q^{4}+\cdots\)
10.16.b.a	$10$	$16$	10.b	5.b	$2$	$8$	$8$	$14.269$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓	✓	10.16.b.a	$2$	$0$	\(0\)	\(0\)	\(251400\)	\(0\)		$2^{38}\cdot 3^{2}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{3}-2^{14}q^{4}+(31425+\cdots)q^{5}+\cdots\)
10.17.c.a	$10$	$17$	10.c	5.c	$4$	$8$	$4$	$16.232$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			10.17.c.a	$2$	$0$	\(-1024\)	\(-5382\)	\(184830\)	\(-1586702\)		$2^{13}\cdot 3^{8}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{7}+2^{7}\beta _{1})q^{2}+(-673-673\beta _{1}+\cdots)q^{3}+\cdots\)
10.17.c.b	$10$	$17$	10.c	5.c	$4$	$8$	$4$	$16.232$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			10.17.c.b	$2$	$0$	\(1024\)	\(-10438\)	\(-216450\)	\(3127282\)		$2^{13}\cdot 3^{2}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{7}+2^{7}\beta _{1})q^{2}+(-1305+1305\beta _{1}+\cdots)q^{3}+\cdots\)
10.18.a.a	$10$	$18$	10.a	1.a	$1$	$1$	$1$	$18.322$	\(\Q\)	None	✓	✓	✓	✓	10.18.a.a	$1$	$1$	\(256\)	\(-14976\)	\(390625\)	\(14808668\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{8}q^{2}-14976q^{3}+2^{16}q^{4}+5^{8}q^{5}+\cdots\)
10.18.a.b	$10$	$18$	10.a	1.a	$1$	$2$	$2$	$18.322$	\(\Q(\sqrt{36061}) \)	None	✓	✓	✓	✓	10.18.a.b	$1$	$1$	\(-512\)	\(-6308\)	\(-781250\)	\(6543844\)	$+$	$2^{5}\cdot 5$	$\mathrm{SU}(2)$	\(q-2^{8}q^{2}+(-3154-\beta )q^{3}+2^{16}q^{4}+\cdots\)
10.18.a.c	$10$	$18$	10.a	1.a	$1$	$2$	$2$	$18.322$	\(\Q(\sqrt{83281}) \)	None	✓	✓	✓	✓	10.18.a.c	$1$	$0$	\(-512\)	\(-1308\)	\(781250\)	\(603844\)	$-$	$2^{2}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q-2^{8}q^{2}+(-654-\beta )q^{3}+2^{16}q^{4}+\cdots\)
10.18.a.d	$10$	$18$	10.a	1.a	$1$	$2$	$2$	$18.322$	\(\Q(\sqrt{2941}) \)	None	✓	✓	✓	✓	10.18.a.d	$1$	$0$	\(512\)	\(17628\)	\(-781250\)	\(27684196\)	$-$	$2^{5}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{8}q^{2}+(8814-\beta )q^{3}+2^{16}q^{4}+\cdots\)
10.18.b.a	$10$	$18$	10.b	5.b	$2$	$8$	$8$	$18.322$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓	✓	10.18.b.a	$2$	$0$	\(0\)	\(0\)	\(-1225560\)	\(0\)		$2^{40}\cdot 3^{4}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2})q^{3}-2^{16}q^{4}+\cdots\)
10.19.c.a	$10$	$19$	10.c	5.c	$4$	$8$	$4$	$20.539$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			10.19.c.a	$2$	$0$	\(2048\)	\(37026\)	\(-3132450\)	\(-43579766\)		$2^{15}\cdot 3^{4}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{8}-2^{8}\beta _{1})q^{2}+(4628+4628\beta _{1}+\cdots)q^{3}+\cdots\)
10.19.c.b	$10$	$19$	10.c	5.c	$4$	$10$	$5$	$20.539$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		10.19.c.b	$2$	$0$	\(-2560\)	\(3230\)	\(-1436130\)	\(-71828530\)		$2^{22}\cdot 3^{8}\cdot 5^{17}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{8}-2^{8}\beta _{1})q^{2}+(323-323\beta _{1}+\cdots)q^{3}+\cdots\)
10.20.a.a	$10$	$20$	10.a	1.a	$1$	$1$	$1$	$22.882$	\(\Q\)	None	✓	✓	✓	✓	10.20.a.a	$1$	$0$	\(-512\)	\(-26622\)	\(-1953125\)	\(-39884026\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{9}q^{2}-26622q^{3}+2^{18}q^{4}-5^{9}q^{5}+\cdots\)

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