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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
10.3.c.a \(2\) \(0.272\) \(\Q(\sqrt{-1}) \) None \(-2\) \(-4\) \(0\) \(4\) \(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)
10.4.a.a \(1\) \(0.590\) \(\Q\) None \(2\) \(-8\) \(5\) \(-4\) \(+\) \(q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots\)
10.4.b.a \(2\) \(0.590\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-10\) \(0\) \(q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots\)
10.5.c.a \(2\) \(1.034\) \(\Q(\sqrt{-1}) \) None \(-4\) \(18\) \(-30\) \(58\) \(q+(-2-2i)q^{2}+(9-9i)q^{3}+8iq^{4}+\cdots\)
10.5.c.b \(2\) \(1.034\) \(\Q(\sqrt{-1}) \) None \(4\) \(2\) \(-30\) \(-38\) \(q+(2+2i)q^{2}+(1-i)q^{3}+8iq^{4}+(-15+\cdots)q^{5}+\cdots\)
10.6.a.a \(1\) \(1.604\) \(\Q\) None \(-4\) \(-26\) \(-25\) \(-22\) \(+\) \(q-4q^{2}-26q^{3}+2^{4}q^{4}-5^{2}q^{5}+104q^{6}+\cdots\)
10.6.a.b \(1\) \(1.604\) \(\Q\) None \(-4\) \(24\) \(25\) \(-172\) \(-\) \(q-4q^{2}+24q^{3}+2^{4}q^{4}+5^{2}q^{5}-96q^{6}+\cdots\)
10.6.a.c \(1\) \(1.604\) \(\Q\) None \(4\) \(6\) \(-25\) \(-118\) \(-\) \(q+4q^{2}+6q^{3}+2^{4}q^{4}-5^{2}q^{5}+24q^{6}+\cdots\)
10.6.b.a \(2\) \(1.604\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(110\) \(0\) \(q+2iq^{2}+7iq^{3}-2^{4}q^{4}+(55+5i)q^{5}+\cdots\)
10.7.c.a \(2\) \(2.301\) \(\Q(\sqrt{-1}) \) None \(-8\) \(-46\) \(-150\) \(-494\) \(q+(-4-4i)q^{2}+(-23+23i)q^{3}+\cdots\)
10.7.c.b \(4\) \(2.301\) \(\Q(i, \sqrt{129})\) None \(16\) \(-18\) \(330\) \(-202\) \(q+(4+4\beta _{1})q^{2}+(-5+4\beta _{1}-\beta _{3})q^{3}+\cdots\)
10.8.a.a \(1\) \(3.124\) \(\Q\) None \(8\) \(28\) \(125\) \(104\) \(+\) \(q+8q^{2}+28q^{3}+2^{6}q^{4}+5^{3}q^{5}+224q^{6}+\cdots\)
10.8.b.a \(4\) \(3.124\) \(\Q(i, \sqrt{31})\) None \(0\) \(0\) \(60\) \(0\) \(q-\beta _{1}q^{2}+(3\beta _{1}-\beta _{3})q^{3}-2^{6}q^{4}+(15+\cdots)q^{5}+\cdots\)
10.9.c.a \(4\) \(4.074\) \(\Q(i, \sqrt{249})\) None \(-32\) \(54\) \(90\) \(-1186\) \(q+(-8+8\beta _{1})q^{2}+(13+13\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.9.c.b \(4\) \(4.074\) \(\Q(i, \sqrt{601})\) None \(32\) \(86\) \(-870\) \(5726\) \(q+(8+8\beta _{1})q^{2}+(22-21\beta _{1}+\beta _{3})q^{3}+\cdots\)
10.10.a.a \(1\) \(5.150\) \(\Q\) None \(-16\) \(-204\) \(625\) \(5432\) \(-\) \(q-2^{4}q^{2}-204q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
10.10.a.b \(1\) \(5.150\) \(\Q\) None \(-16\) \(46\) \(-625\) \(-10318\) \(+\) \(q-2^{4}q^{2}+46q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
10.10.a.c \(1\) \(5.150\) \(\Q\) None \(16\) \(174\) \(-625\) \(4658\) \(-\) \(q+2^{4}q^{2}+174q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
10.10.b.a \(4\) \(5.150\) \(\Q(i, \sqrt{319})\) None \(0\) \(0\) \(-2580\) \(0\) \(q-\beta _{1}q^{2}+(-5\beta _{1}-\beta _{3})q^{3}-2^{8}q^{4}+\cdots\)
10.11.c.a \(2\) \(6.354\) \(\Q(\sqrt{-1}) \) None \(32\) \(-366\) \(-3750\) \(-16814\) \(q+(2^{4}+2^{4}i)q^{2}+(-183+183i)q^{3}+\cdots\)
10.11.c.b \(2\) \(6.354\) \(\Q(\sqrt{-1}) \) None \(32\) \(114\) \(5850\) \(13906\) \(q+(2^{4}+2^{4}i)q^{2}+(57-57i)q^{3}+2^{9}iq^{4}+\cdots\)
10.11.c.c \(6\) \(6.354\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-96\) \(128\) \(5460\) \(13512\) \(q+(-2^{4}-2^{4}\beta _{1})q^{2}+(21-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.12.a.a \(1\) \(7.683\) \(\Q\) None \(-32\) \(-12\) \(3125\) \(-14176\) \(-\) \(q-2^{5}q^{2}-12q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)
10.12.a.b \(1\) \(7.683\) \(\Q\) None \(-32\) \(738\) \(-3125\) \(25574\) \(+\) \(q-2^{5}q^{2}+738q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.c \(1\) \(7.683\) \(\Q\) None \(32\) \(-318\) \(-3125\) \(-70714\) \(-\) \(q+2^{5}q^{2}-318q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.d \(2\) \(7.683\) \(\Q(\sqrt{1969}) \) None \(64\) \(604\) \(6250\) \(14092\) \(+\) \(q+2^{5}q^{2}+(302-\beta )q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)
10.12.b.a \(6\) \(7.683\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(530\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}+3\beta _{2})q^{3}-2^{10}q^{4}+\cdots\)
10.13.c.a \(6\) \(9.140\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(-192\) \(-936\) \(-16260\) \(-45336\) \(q+(-2^{5}-2^{5}\beta _{1})q^{2}+(-156+156\beta _{1}+\cdots)q^{3}+\cdots\)
10.13.c.b \(6\) \(9.140\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(192\) \(296\) \(14460\) \(-322104\) \(q+(2^{5}+2^{5}\beta _{1})q^{2}+(7^{2}-7^{2}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.14.a.a \(1\) \(10.723\) \(\Q\) None \(-64\) \(-26\) \(-15625\) \(538538\) \(+\) \(q-2^{6}q^{2}-26q^{3}+2^{12}q^{4}-5^{6}q^{5}+\cdots\)
10.14.a.b \(1\) \(10.723\) \(\Q\) None \(-64\) \(1224\) \(15625\) \(-65212\) \(-\) \(q-2^{6}q^{2}+1224q^{3}+2^{12}q^{4}+5^{6}q^{5}+\cdots\)
10.14.a.c \(1\) \(10.723\) \(\Q\) None \(64\) \(-2394\) \(-15625\) \(438122\) \(-\) \(q+2^{6}q^{2}-2394q^{3}+2^{12}q^{4}-5^{6}q^{5}+\cdots\)
10.14.b.a \(6\) \(10.723\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(-2470\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}-2^{12}q^{4}+(-412+\cdots)q^{5}+\cdots\)
10.15.c.a \(6\) \(12.433\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-384\) \(2912\) \(82500\) \(943128\) \(q+(-2^{6}+2^{6}\beta _{1})q^{2}+(485+485\beta _{1}+\cdots)q^{3}+\cdots\)
10.15.c.b \(8\) \(12.433\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(512\) \(1404\) \(-100860\) \(1333276\) \(q+(2^{6}-2^{6}\beta _{1})q^{2}+(175+176\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
10.16.a.a \(1\) \(14.269\) \(\Q\) None \(-128\) \(-5568\) \(78125\) \(2564996\) \(-\) \(q-2^{7}q^{2}-5568q^{3}+2^{14}q^{4}+5^{7}q^{5}+\cdots\)
10.16.a.b \(1\) \(14.269\) \(\Q\) None \(-128\) \(-918\) \(-78125\) \(-953554\) \(+\) \(q-2^{7}q^{2}-918q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots\)
10.16.a.c \(1\) \(14.269\) \(\Q\) None \(128\) \(-1302\) \(-78125\) \(-90706\) \(-\) \(q+2^{7}q^{2}-1302q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots\)
10.16.a.d \(2\) \(14.269\) \(\Q(\sqrt{239569}) \) None \(256\) \(-1844\) \(156250\) \(-984932\) \(+\) \(q+2^{7}q^{2}+(-922-\beta )q^{3}+2^{14}q^{4}+\cdots\)
10.16.b.a \(8\) \(14.269\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(251400\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}-2^{14}q^{4}+(31425+\cdots)q^{5}+\cdots\)
10.17.c.a \(8\) \(16.232\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1024\) \(-5382\) \(184830\) \(-1586702\) \(q+(-2^{7}+2^{7}\beta _{1})q^{2}+(-673-673\beta _{1}+\cdots)q^{3}+\cdots\)
10.17.c.b \(8\) \(16.232\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(1024\) \(-10438\) \(-216450\) \(3127282\) \(q+(2^{7}+2^{7}\beta _{1})q^{2}+(-1305+1305\beta _{1}+\cdots)q^{3}+\cdots\)
10.18.a.a \(1\) \(18.322\) \(\Q\) None \(256\) \(-14976\) \(390625\) \(14808668\) \(+\) \(q+2^{8}q^{2}-14976q^{3}+2^{16}q^{4}+5^{8}q^{5}+\cdots\)
10.18.a.b \(2\) \(18.322\) \(\Q(\sqrt{36061}) \) None \(-512\) \(-6308\) \(-781250\) \(6543844\) \(+\) \(q-2^{8}q^{2}+(-3154-\beta )q^{3}+2^{16}q^{4}+\cdots\)
10.18.a.c \(2\) \(18.322\) \(\Q(\sqrt{83281}) \) None \(-512\) \(-1308\) \(781250\) \(603844\) \(-\) \(q-2^{8}q^{2}+(-654-\beta )q^{3}+2^{16}q^{4}+\cdots\)
10.18.a.d \(2\) \(18.322\) \(\Q(\sqrt{2941}) \) None \(512\) \(17628\) \(-781250\) \(27684196\) \(-\) \(q+2^{8}q^{2}+(8814-\beta )q^{3}+2^{16}q^{4}+\cdots\)
10.18.b.a \(8\) \(18.322\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-1225560\) \(0\) \(q-\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2})q^{3}-2^{16}q^{4}+\cdots\)
10.19.c.a \(8\) \(20.539\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(2048\) \(37026\) \(-3132450\) \(-43579766\) \(q+(2^{8}-2^{8}\beta _{1})q^{2}+(4628+4628\beta _{1}+\cdots)q^{3}+\cdots\)
10.19.c.b \(10\) \(20.539\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-2560\) \(3230\) \(-1436130\) \(-71828530\) \(q+(-2^{8}-2^{8}\beta _{1})q^{2}+(323-323\beta _{1}+\cdots)q^{3}+\cdots\)
10.20.a.a \(1\) \(22.882\) \(\Q\) None \(-512\) \(-26622\) \(-1953125\) \(-39884026\) \(+\) \(q-2^{9}q^{2}-26622q^{3}+2^{18}q^{4}-5^{9}q^{5}+\cdots\)
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