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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.3.b.a \(1\) \(0.191\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(-7\) \(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)
7.4.a.a \(1\) \(0.413\) \(\Q\) None \(-1\) \(-2\) \(16\) \(-7\) \(+\) \(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)
7.4.c.a \(2\) \(0.413\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-7\) \(-7\) \(28\) \(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)
7.5.b.a \(1\) \(0.724\) \(\Q\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(49\) \(q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots\)
7.5.d.a \(4\) \(0.724\) \(\Q(\sqrt{-3}, \sqrt{22})\) None \(-4\) \(6\) \(-30\) \(0\) \(q+(-2+\beta _{1}-2\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
7.6.a.a \(1\) \(1.123\) \(\Q\) None \(-10\) \(-14\) \(-56\) \(-49\) \(+\) \(q-10q^{2}-14q^{3}+68q^{4}-56q^{5}+\cdots\)
7.6.a.b \(2\) \(1.123\) \(\Q(\sqrt{57}) \) None \(9\) \(-6\) \(-18\) \(98\) \(-\) \(q+(5-\beta )q^{2}+(-6+6\beta )q^{3}+(7-9\beta )q^{4}+\cdots\)
7.6.c.a \(4\) \(1.123\) \(\Q(\sqrt{-3}, \sqrt{37})\) None \(-2\) \(8\) \(38\) \(-168\) \(q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
7.7.b.a \(1\) \(1.610\) \(\Q\) \(\Q(\sqrt{-7}) \) \(9\) \(0\) \(0\) \(-343\) \(q+9q^{2}+17q^{4}-7^{3}q^{7}-423q^{8}+\cdots\)
7.7.b.b \(2\) \(1.610\) \(\Q(\sqrt{-510}) \) None \(-16\) \(0\) \(0\) \(266\) \(q-8q^{2}+\beta q^{3}-\beta q^{5}-8\beta q^{6}+(133+\cdots)q^{7}+\cdots\)
7.7.d.a \(2\) \(1.610\) \(\Q(\sqrt{-3}) \) None \(12\) \(-21\) \(315\) \(-686\) \(q+12\zeta_{6}q^{2}+(-7-7\zeta_{6})q^{3}+(-80+\cdots)q^{4}+\cdots\)
7.7.d.b \(4\) \(1.610\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-8\) \(18\) \(-150\) \(280\) \(q+(-4-4\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(6+3\beta _{1}+\cdots)q^{3}+\cdots\)
7.8.a.a \(1\) \(2.187\) \(\Q\) None \(-6\) \(-42\) \(-84\) \(343\) \(-\) \(q-6q^{2}-42q^{3}-92q^{4}-84q^{5}+252q^{6}+\cdots\)
7.8.a.b \(2\) \(2.187\) \(\Q(\sqrt{865}) \) None \(-3\) \(94\) \(330\) \(-686\) \(+\) \(q+(-1-\beta )q^{2}+(46+2\beta )q^{3}+(89+3\beta )q^{4}+\cdots\)
7.8.c.a \(8\) \(2.187\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(6\) \(-28\) \(-252\) \(672\) \(q+(-1+2\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(-6+\cdots)q^{3}+\cdots\)
7.9.b.a \(1\) \(2.852\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-31\) \(0\) \(0\) \(2401\) \(q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots\)
7.9.b.b \(4\) \(2.852\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(32\) \(0\) \(0\) \(1428\) \(q+(8+\beta _{3})q^{2}-\beta _{1}q^{3}+(-8+2^{4}\beta _{3})q^{4}+\cdots\)
7.9.d.a \(8\) \(2.852\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-4\) \(-84\) \(-840\) \(-140\) \(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-7+7\beta _{2}+\cdots)q^{3}+\cdots\)
7.10.a.a \(2\) \(3.605\) \(\Q(\sqrt{193}) \) None \(-6\) \(-86\) \(-2238\) \(-4802\) \(+\) \(q+(-3-\beta )q^{2}+(-43+11\beta )q^{3}+(-310+\cdots)q^{4}+\cdots\)
7.10.a.b \(3\) \(3.605\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(21\) \(84\) \(1554\) \(7203\) \(-\) \(q+(7-\beta _{2})q^{2}+(28-\beta _{1}-\beta _{2})q^{3}+(519+\cdots)q^{4}+\cdots\)
7.10.c.a \(10\) \(3.605\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-18\) \(161\) \(1533\) \(-1036\) \(q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots\)
7.11.b.a \(1\) \(4.448\) \(\Q\) \(\Q(\sqrt{-7}) \) \(57\) \(0\) \(0\) \(-16807\) \(q+57q^{2}+2225q^{4}-7^{5}q^{7}+68457q^{8}+\cdots\)
7.11.b.b \(4\) \(4.448\) 4.0.373770240.2 None \(-48\) \(0\) \(0\) \(4900\) \(q+(-12+\beta _{2})q^{2}-\beta _{1}q^{3}+(-12^{2}+\cdots)q^{4}+\cdots\)
7.11.d.a \(12\) \(4.448\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(-246\) \(3330\) \(-12572\) \(q+(-2-\beta _{1}-2\beta _{2})q^{2}+(-3^{3}+2\beta _{1}+\cdots)q^{3}+\cdots\)
7.12.a.a \(2\) \(5.378\) \(\Q(\sqrt{3369}) \) None \(-54\) \(120\) \(-13500\) \(33614\) \(-\) \(q+(-3^{3}-\beta )q^{2}+(60+6\beta )q^{3}+(2050+\cdots)q^{4}+\cdots\)
7.12.a.b \(3\) \(5.378\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(77\) \(-140\) \(5026\) \(-50421\) \(+\) \(q+(26+\beta _{2})q^{2}+(-47-11\beta _{1}+10\beta _{2})q^{3}+\cdots\)
7.12.c.a \(12\) \(5.378\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(22\) \(-244\) \(-8782\) \(-504\) \(q+(4-\beta _{1}-4\beta _{2})q^{2}+(\beta _{1}-40\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
7.13.b.a \(1\) \(6.398\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-47\) \(0\) \(0\) \(117649\) \(q-47q^{2}-1887q^{4}+7^{6}q^{7}+281201q^{8}+\cdots\)
7.13.b.b \(6\) \(6.398\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(-314650\) \(q+\beta _{2}q^{2}+\beta _{3}q^{3}+(2714+2\beta _{1}-26\beta _{2}+\cdots)q^{4}+\cdots\)
7.13.d.a \(14\) \(6.398\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(44\) \(-3\) \(-9075\) \(334278\) \(q+(6+\beta _{1}+6\beta _{2})q^{2}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
7.14.a.a \(3\) \(7.506\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(26\) \(-1796\) \(-24086\) \(-352947\) \(+\) \(q+(9-\beta _{1})q^{2}+(-601+7\beta _{1}-\beta _{2})q^{3}+\cdots\)
7.14.a.b \(4\) \(7.506\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-27\) \(336\) \(24192\) \(470596\) \(-\) \(q+(-7+\beta _{1})q^{2}+(84+\beta _{1}+\beta _{2})q^{3}+\cdots\)
7.14.c.a \(16\) \(7.506\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(728\) \(46928\) \(257992\) \(q-\beta _{1}q^{2}+(91\beta _{2}-\beta _{4})q^{3}+(-6\beta _{1}+\cdots)q^{4}+\cdots\)
7.15.b.a \(1\) \(8.703\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-87\) \(0\) \(0\) \(-823543\) \(q-87q^{2}-8815q^{4}-7^{7}q^{7}+2192313q^{8}+\cdots\)
7.15.b.b \(8\) \(8.703\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(176\) \(0\) \(0\) \(1475656\) \(q+(22+\beta _{2})q^{2}-\beta _{3}q^{3}+(10352+\beta _{1}+\cdots)q^{4}+\cdots\)
7.15.d.a \(16\) \(8.703\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-92\) \(2184\) \(-1680\) \(-1237432\) \(q+(-1+\beta _{1}+11\beta _{2}+\beta _{3})q^{2}+(92+\cdots)q^{3}+\cdots\)
7.16.a.a \(3\) \(9.989\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-438\) \(-1860\) \(-111414\) \(2470629\) \(-\) \(q+(-146-\beta _{1})q^{2}+(-620-23\beta _{1}+\cdots)q^{3}+\cdots\)
7.16.a.b \(4\) \(9.989\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(93\) \(8554\) \(7770\) \(-3294172\) \(+\) \(q+(23+\beta _{1})q^{2}+(2138+3\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
7.16.c.a \(18\) \(9.989\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-90\) \(-4375\) \(-234087\) \(-5213740\) \(q+(\beta _{1}+10\beta _{2}-\beta _{3})q^{2}+(-486-486\beta _{2}+\cdots)q^{3}+\cdots\)
7.17.b.a \(1\) \(11.363\) \(\Q\) \(\Q(\sqrt{-7}) \) \(449\) \(0\) \(0\) \(5764801\) \(q+449q^{2}+136065q^{4}+7^{8}q^{7}+31667521q^{8}+\cdots\)
7.17.b.b \(8\) \(11.363\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-544\) \(0\) \(0\) \(-3034472\) \(q+(-68-\beta _{2})q^{2}+\beta _{1}q^{3}+(2348+139\beta _{2}+\cdots)q^{4}+\cdots\)
7.17.d.a \(20\) \(11.363\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(92\) \(6558\) \(241890\) \(-1847944\) \(q+(9-\beta _{1}+9\beta _{2}-\beta _{3})q^{2}+(438+\beta _{1}+\cdots)q^{3}+\cdots\)
7.18.a.a \(4\) \(12.826\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(186\) \(-2786\) \(274722\) \(-23059204\) \(+\) \(q+(46-\beta _{1})q^{2}+(-698-3\beta _{1}-\beta _{3})q^{3}+\cdots\)
7.18.a.b \(5\) \(12.826\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(597\) \(-1770\) \(1612824\) \(28824005\) \(-\) \(q+(119+\beta _{1})q^{2}+(-349-13\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
7.18.c.a \(20\) \(12.826\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(270\) \(6560\) \(1089798\) \(14395360\) \(q+(\beta _{1}+3^{3}\beta _{2})q^{2}+(656-656\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
7.19.b.a \(1\) \(14.377\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-999\) \(0\) \(0\) \(-40353607\) \(q-999q^{2}+735857q^{4}-7^{9}q^{7}-473239287q^{8}+\cdots\)
7.19.b.b \(10\) \(14.377\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(912\) \(0\) \(0\) \(-6200670\) \(q+(91+\beta _{2})q^{2}+\beta _{1}q^{3}+(65935+211\beta _{2}+\cdots)q^{4}+\cdots\)
7.19.d.a \(22\) \(14.377\) None \(84\) \(-3\) \(-2135115\) \(63763714\)
7.20.a.a \(4\) \(16.017\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-342\) \(-29526\) \(-2486610\) \(161414428\) \(-\) \(q+(-86+\beta _{1})q^{2}+(-7378-8\beta _{1}+\cdots)q^{3}+\cdots\)
7.20.a.b \(5\) \(16.017\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-115\) \(-32414\) \(9485596\) \(-201768035\) \(+\) \(q+(-23-\beta _{1})q^{2}+(-6483+4\beta _{1}+\cdots)q^{3}+\cdots\)
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