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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
29.2.a.a \(2\) \(0.232\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) \(-\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
29.2.b.a \(2\) \(0.232\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-6\) \(4\) \(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)
29.2.d.a \(6\) \(0.232\) \(\Q(\zeta_{14})\) None \(-2\) \(-5\) \(1\) \(1\) \(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
29.2.e.a \(12\) \(0.232\) 12.0.\(\cdots\).1 None \(-7\) \(-7\) \(-1\) \(-11\) \(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)
29.3.c.a \(8\) \(0.790\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(2\) \(-2\) \(0\) \(-4\) \(q-\beta _{6}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
29.3.f.a \(48\) \(0.790\) None \(-16\) \(-12\) \(-14\) \(-10\)
29.4.a.a \(2\) \(1.711\) \(\Q(\sqrt{2}) \) None \(-2\) \(-10\) \(-10\) \(-16\) \(-\) \(q+(-1+\beta )q^{2}+(-5-3\beta )q^{3}+(-5+\cdots)q^{4}+\cdots\)
29.4.a.b \(5\) \(1.711\) 5.5.13458092.1 None \(0\) \(8\) \(10\) \(40\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots\)
29.4.b.a \(6\) \(1.711\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(22\) \(-28\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-5+\beta _{4}+\beta _{5})q^{4}+\cdots\)
29.4.d.a \(42\) \(1.711\) None \(-5\) \(-5\) \(-7\) \(-31\)
29.4.e.a \(36\) \(1.711\) None \(-7\) \(-7\) \(-29\) \(21\)
29.5.c.a \(18\) \(2.998\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-8\) \(-2\) \(0\) \(-4\) \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}-\beta _{2}+6\beta _{4}+\cdots)q^{4}+\cdots\)
29.5.f.a \(108\) \(2.998\) None \(-6\) \(-12\) \(-14\) \(-10\)
29.6.a.a \(4\) \(4.651\) 4.4.3257317.1 None \(0\) \(-28\) \(-68\) \(-208\) \(+\) \(q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.a.b \(7\) \(4.651\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(26\) \(32\) \(184\) \(-\) \(q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.b.a \(12\) \(4.651\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(46\) \(20\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-14+\beta _{2})q^{4}+\cdots\)
29.6.d.a \(66\) \(4.651\) None \(-11\) \(-5\) \(29\) \(17\)
29.6.e.a \(72\) \(4.651\) None \(-7\) \(-7\) \(-53\) \(-27\)
29.7.c.a \(28\) \(6.672\) None \(0\) \(-2\) \(0\) \(-4\)
29.7.f.a \(168\) \(6.672\) None \(-14\) \(-12\) \(-14\) \(-10\)
29.8.a.a \(7\) \(9.059\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-8\) \(-82\) \(-320\) \(-1704\) \(-\) \(q+(-1-\beta _{1})q^{2}+(-12+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
29.8.a.b \(10\) \(9.059\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(80\) \(180\) \(1040\) \(+\) \(q-\beta _{1}q^{2}+(8+\beta _{2})q^{3}+(92+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
29.8.b.a \(16\) \(9.059\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-198\) \(660\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{6})q^{3}+(-45+\beta _{2}+\cdots)q^{4}+\cdots\)
29.8.d.a \(102\) \(9.059\) None \(1\) \(-5\) \(133\) \(657\)
29.8.e.a \(96\) \(9.059\) None \(-7\) \(-7\) \(191\) \(-667\)
29.9.c.a \(38\) \(11.814\) None \(-8\) \(-2\) \(0\) \(-4\)
29.9.f.a \(228\) \(11.814\) None \(-6\) \(-12\) \(-14\) \(-10\)
29.10.a.a \(9\) \(14.936\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-244\) \(-738\) \(-7128\) \(+\) \(q-\beta _{1}q^{2}+(-3^{3}-\beta _{4})q^{3}+(133+2\beta _{1}+\cdots)q^{4}+\cdots\)
29.10.a.b \(12\) \(14.936\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(16\) \(242\) \(1762\) \(12080\) \(-\) \(q+(1+\beta _{1})q^{2}+(20+\beta _{1}-\beta _{3})q^{3}+(291+\cdots)q^{4}+\cdots\)
29.10.b.a \(22\) \(14.936\) None \(0\) \(0\) \(-1374\) \(-4956\)
29.10.d.a \(126\) \(14.936\) None \(-23\) \(-5\) \(-1031\) \(-4959\)
29.10.e.a \(132\) \(14.936\) None \(-7\) \(-7\) \(1367\) \(4949\)
29.11.c.a \(48\) \(18.425\) None \(8\) \(-2\) \(0\) \(-4\)
29.11.f.a \(288\) \(18.425\) None \(-22\) \(-12\) \(-14\) \(-10\)
29.12.a.a \(11\) \(22.282\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-32\) \(-982\) \(-2740\) \(-49432\) \(-\) \(q+(-3+\beta _{1})q^{2}+(-89-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
29.12.a.b \(14\) \(22.282\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(476\) \(9760\) \(85024\) \(+\) \(q+\beta _{1}q^{2}+(34-\beta _{3})q^{3}+(1312+3\beta _{1}+\cdots)q^{4}+\cdots\)
29.12.b.a \(26\) \(22.282\) None \(0\) \(0\) \(3742\) \(-2108\)
29.12.d.a \(162\) \(22.282\) None \(73\) \(-5\) \(-16687\) \(-2111\)
29.12.e.a \(156\) \(22.282\) None \(-7\) \(-7\) \(-3749\) \(2101\)
29.13.c.a \(58\) \(26.506\) None \(88\) \(-2\) \(0\) \(-4\)
29.14.a.a \(14\) \(31.097\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2188\) \(-67808\) \(-669728\) \(+\) \(q+\beta _{1}q^{2}+(-156-\beta _{1}+\beta _{3})q^{3}+(2912+\cdots)q^{4}+\cdots\)
29.14.a.b \(17\) \(31.097\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(64\) \(2186\) \(-5308\) \(271464\) \(-\) \(q+(4-\beta _{1})q^{2}+(129-\beta _{1}+\beta _{3})q^{3}+\cdots\)
29.14.b.a \(32\) \(31.097\) None \(0\) \(0\) \(-90794\) \(398260\)
29.15.c.a \(68\) \(36.055\) None \(-312\) \(-2\) \(0\) \(-4\)
29.16.a.a \(16\) \(41.381\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-128\) \(-3214\) \(-82010\) \(-3706320\) \(-\) \(q+(-8-\beta _{1})q^{2}+(-201+\beta _{2})q^{3}+\cdots\)
29.16.a.b \(19\) \(41.381\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(9908\) \(230490\) \(2882024\) \(+\) \(q+\beta _{1}q^{2}+(521+2\beta _{1}+\beta _{2})q^{3}+(20389+\cdots)q^{4}+\cdots\)
29.16.b.a \(36\) \(41.381\) None \(0\) \(0\) \(470082\) \(-4820620\)
29.17.c.a \(78\) \(47.074\) None \(184\) \(-2\) \(0\) \(-4\)
29.18.a.a \(18\) \(53.134\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-15400\) \(-564228\) \(-43925040\) \(+\) \(q+\beta _{1}q^{2}+(-856-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
29.18.a.b \(21\) \(53.134\) None \(256\) \(23966\) \(998272\) \(2193368\) \(-\)
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