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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
14.2.a.a \(1\) \(0.112\) \(\Q\) None \(-1\) \(-2\) \(0\) \(1\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots\)
14.3.d.a \(4\) \(0.381\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(-6\) \(8\) \(q+\beta _{1}q^{2}+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
14.4.a.a \(1\) \(0.826\) \(\Q\) None \(-2\) \(8\) \(-14\) \(-7\) \(+\) \(q-2q^{2}+8q^{3}+4q^{4}-14q^{5}-2^{4}q^{6}+\cdots\)
14.4.a.b \(1\) \(0.826\) \(\Q\) None \(2\) \(-2\) \(-12\) \(7\) \(+\) \(q+2q^{2}-2q^{3}+4q^{4}-12q^{5}-4q^{6}+\cdots\)
14.4.c.a \(2\) \(0.826\) \(\Q(\sqrt{-3}) \) None \(-2\) \(5\) \(9\) \(-28\) \(q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
14.4.c.b \(2\) \(0.826\) \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(-7\) \(-20\) \(q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots\)
14.5.b.a \(4\) \(1.447\) 4.0.1308672.3 None \(0\) \(0\) \(0\) \(-76\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
14.5.d.a \(4\) \(1.447\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-18\) \(54\) \(-28\) \(q+\beta _{1}q^{2}+(-6+2\beta _{1}-3\beta _{2}-2\beta _{3})q^{3}+\cdots\)
14.6.a.a \(1\) \(2.245\) \(\Q\) None \(-4\) \(10\) \(84\) \(49\) \(-\) \(q-4q^{2}+10q^{3}+2^{4}q^{4}+84q^{5}-40q^{6}+\cdots\)
14.6.a.b \(1\) \(2.245\) \(\Q\) None \(4\) \(8\) \(10\) \(-49\) \(-\) \(q+4q^{2}+8q^{3}+2^{4}q^{4}+10q^{5}+2^{5}q^{6}+\cdots\)
14.6.c.a \(4\) \(2.245\) \(\Q(\sqrt{-3}, \sqrt{79})\) None \(-8\) \(-14\) \(-70\) \(0\) \(q+4\beta _{2}q^{2}+(-7-\beta _{1}-7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
14.6.c.b \(4\) \(2.245\) \(\Q(\sqrt{-3}, \sqrt{130})\) None \(8\) \(14\) \(42\) \(232\) \(q-4\beta _{2}q^{2}+(7-\beta _{1}+7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
14.7.b.a \(4\) \(3.221\) 4.0.211968.1 None \(0\) \(0\) \(0\) \(308\) \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+2^{5}q^{4}-5\beta _{2}q^{5}+\cdots\)
14.7.d.a \(8\) \(3.221\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-336\) \(652\) \(q+(\beta _{2}-\beta _{3})q^{2}+(-\beta _{2}+2\beta _{3}-\beta _{6}+\cdots)q^{3}+\cdots\)
14.8.a.a \(1\) \(4.373\) \(\Q\) None \(-8\) \(-82\) \(448\) \(-343\) \(+\) \(q-8q^{2}-82q^{3}+2^{6}q^{4}+448q^{5}+\cdots\)
14.8.a.b \(1\) \(4.373\) \(\Q\) None \(8\) \(-66\) \(-400\) \(-343\) \(-\) \(q+8q^{2}-66q^{3}+2^{6}q^{4}-20^{2}q^{5}+\cdots\)
14.8.a.c \(2\) \(4.373\) \(\Q(\sqrt{1969}) \) None \(16\) \(70\) \(126\) \(686\) \(+\) \(q+8q^{2}+(35-\beta )q^{3}+2^{6}q^{4}+(63+9\beta )q^{5}+\cdots\)
14.8.c.a \(4\) \(4.373\) \(\Q(\sqrt{-3}, \sqrt{2389})\) None \(-16\) \(56\) \(238\) \(168\) \(q+(-8+8\beta _{1})q^{2}+(28\beta _{1}-\beta _{2})q^{3}+\cdots\)
14.8.c.b \(4\) \(4.373\) \(\Q(\sqrt{-3}, \sqrt{949})\) None \(16\) \(-56\) \(14\) \(-1848\) \(q+8\beta _{1}q^{2}+(-28+28\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
14.9.b.a \(4\) \(5.703\) 4.0.3520512.3 None \(0\) \(0\) \(0\) \(-6076\) \(q+2\beta _{3}q^{2}+(2\beta _{1}-\beta _{2})q^{3}+2^{7}q^{4}+\cdots\)
14.9.d.a \(12\) \(5.703\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(162\) \(1674\) \(-1308\) \(q+(-\beta _{2}+\beta _{3})q^{2}+(18-9\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
14.10.a.a \(1\) \(7.211\) \(\Q\) None \(-16\) \(-6\) \(560\) \(-2401\) \(+\) \(q-2^{4}q^{2}-6q^{3}+2^{8}q^{4}+560q^{5}+\cdots\)
14.10.a.b \(1\) \(7.211\) \(\Q\) None \(16\) \(170\) \(544\) \(-2401\) \(-\) \(q+2^{4}q^{2}+170q^{3}+2^{8}q^{4}+544q^{5}+\cdots\)
14.10.a.c \(2\) \(7.211\) \(\Q(\sqrt{2305}) \) None \(-32\) \(-14\) \(-2730\) \(4802\) \(-\) \(q-2^{4}q^{2}+(-7-5\beta )q^{3}+2^{8}q^{4}+(-1365+\cdots)q^{5}+\cdots\)
14.10.c.a \(6\) \(7.211\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-48\) \(-233\) \(-733\) \(5012\) \(q+(-2^{4}-2^{4}\beta _{2})q^{2}+(78\beta _{2}-\beta _{3})q^{3}+\cdots\)
14.10.c.b \(6\) \(7.211\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(48\) \(71\) \(-1085\) \(-6796\) \(q+(2^{4}+2^{4}\beta _{1})q^{2}+(-24\beta _{1}-\beta _{3})q^{3}+\cdots\)
14.11.b.a \(8\) \(8.895\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(18376\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+2^{9}q^{4}+(-3\beta _{3}+\cdots)q^{5}+\cdots\)
14.11.d.a \(12\) \(8.895\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(486\) \(-6666\) \(30576\) \(q-\beta _{2}q^{2}+(54+3^{3}\beta _{1}-2\beta _{2}-2\beta _{3}+\cdots)q^{3}+\cdots\)
14.12.a.a \(1\) \(10.757\) \(\Q\) None \(-32\) \(-396\) \(7350\) \(16807\) \(-\) \(q-2^{5}q^{2}-396q^{3}+2^{10}q^{4}+7350q^{5}+\cdots\)
14.12.a.b \(1\) \(10.757\) \(\Q\) None \(32\) \(-90\) \(-7480\) \(-16807\) \(-\) \(q+2^{5}q^{2}-90q^{3}+2^{10}q^{4}-7480q^{5}+\cdots\)
14.12.a.c \(2\) \(10.757\) \(\Q(\sqrt{153169}) \) None \(-64\) \(350\) \(266\) \(-33614\) \(+\) \(q-2^{5}q^{2}+(175-\beta )q^{3}+2^{10}q^{4}+(133+\cdots)q^{5}+\cdots\)
14.12.a.d \(2\) \(10.757\) \(\Q(\sqrt{352969}) \) None \(64\) \(-350\) \(3738\) \(33614\) \(+\) \(q+2^{5}q^{2}+(-175-\beta )q^{3}+2^{10}q^{4}+\cdots\)
14.12.c.a \(8\) \(10.757\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-128\) \(266\) \(7504\) \(-42224\) \(q+(-2^{5}+2^{5}\beta _{2})q^{2}+(67\beta _{2}-\beta _{3})q^{3}+\cdots\)
14.12.c.b \(8\) \(10.757\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(128\) \(-266\) \(3808\) \(110328\) \(q+2^{5}\beta _{2}q^{2}+(-67+\beta _{1}+67\beta _{2})q^{3}+\cdots\)
14.13.b.a \(8\) \(12.796\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(195160\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+2^{11}q^{4}+(-11\beta _{3}+\cdots)q^{5}+\cdots\)
14.13.d.a \(16\) \(12.796\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(18144\) \(-469720\) \(q+(-\beta _{2}-\beta _{4})q^{2}+(5\beta _{2}+2\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
14.14.a.a \(1\) \(15.012\) \(\Q\) None \(-64\) \(1626\) \(-36400\) \(-117649\) \(+\) \(q-2^{6}q^{2}+1626q^{3}+2^{12}q^{4}-36400q^{5}+\cdots\)
14.14.a.b \(1\) \(15.012\) \(\Q\) None \(64\) \(-1026\) \(4320\) \(117649\) \(+\) \(q+2^{6}q^{2}-1026q^{3}+2^{12}q^{4}+4320q^{5}+\cdots\)
14.14.a.c \(2\) \(15.012\) \(\Q(\sqrt{100129}) \) None \(-128\) \(952\) \(32004\) \(235298\) \(-\) \(q-2^{6}q^{2}+(476-\beta )q^{3}+2^{12}q^{4}+(16002+\cdots)q^{5}+\cdots\)
14.14.a.d \(2\) \(15.012\) \(\Q(\sqrt{78985}) \) None \(128\) \(1106\) \(75530\) \(-235298\) \(-\) \(q+2^{6}q^{2}+(553-5\beta )q^{3}+2^{12}q^{4}+\cdots\)
14.14.c.a \(8\) \(15.012\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-256\) \(-182\) \(-64400\) \(-113736\) \(q+(-2^{6}-2^{6}\beta _{1})q^{2}+(45\beta _{1}+\beta _{4})q^{3}+\cdots\)
14.14.c.b \(8\) \(15.012\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(256\) \(182\) \(1792\) \(-268352\) \(q+(2^{6}+2^{6}\beta _{1})q^{2}+(-46\beta _{1}-\beta _{2})q^{3}+\cdots\)
14.15.b.a \(8\) \(17.406\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(-284984\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+2^{13}q^{4}+(-17\beta _{2}+\cdots)q^{5}+\cdots\)
14.15.d.a \(20\) \(17.406\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-4374\) \(3354\) \(1455616\) \(q-\beta _{2}q^{2}+(-146-146\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{3}+\cdots\)
14.16.a.a \(1\) \(19.977\) \(\Q\) None \(-128\) \(1350\) \(-81060\) \(823543\) \(-\) \(q-2^{7}q^{2}+1350q^{3}+2^{14}q^{4}-81060q^{5}+\cdots\)
14.16.a.b \(2\) \(19.977\) \(\Q(\sqrt{169009}) \) None \(-256\) \(-4690\) \(-78022\) \(-1647086\) \(+\) \(q-2^{7}q^{2}+(-2345-\beta )q^{3}+2^{14}q^{4}+\cdots\)
14.16.a.c \(2\) \(19.977\) \(\Q(\sqrt{54961}) \) None \(256\) \(-7602\) \(180250\) \(-1647086\) \(-\) \(q+2^{7}q^{2}+(-3801-\beta )q^{3}+2^{14}q^{4}+\cdots\)
14.16.a.d \(3\) \(19.977\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(384\) \(2812\) \(-47094\) \(2470629\) \(+\) \(q+2^{7}q^{2}+(937+\beta _{1})q^{3}+2^{14}q^{4}+\cdots\)
14.16.c.a \(10\) \(19.977\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-640\) \(1979\) \(300953\) \(4054316\) \(q+(-2^{7}-2^{7}\beta _{1})q^{2}+(-396\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
14.16.c.b \(10\) \(19.977\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(640\) \(2395\) \(10969\) \(2375276\) \(q+(2^{7}+2^{7}\beta _{1})q^{2}+(-479\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
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