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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
9.3.d.a \(2\) \(0.245\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(6\) \(-2\) \(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
9.4.a.a \(1\) \(0.531\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(20\) \(+\) \(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
9.4.c.a \(4\) \(0.531\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-3\) \(-3\) \(-15\) \(-7\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
9.5.b.a \(2\) \(0.930\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-56\) \(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)
9.5.d.a \(6\) \(0.930\) 6.0.39400128.1 None \(-3\) \(-3\) \(-12\) \(12\) \(q+\beta _{2}q^{2}+(-3-3\beta _{1}+\beta _{3}+\beta _{5})q^{3}+\cdots\)
9.6.a.a \(1\) \(1.443\) \(\Q\) None \(6\) \(0\) \(-6\) \(-40\) \(-\) \(q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots\)
9.6.c.a \(8\) \(1.443\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(3\) \(-12\) \(78\) \(28\) \(q+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)
9.7.b.a \(2\) \(2.070\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(1048\) \(q+\beta q^{2}-98q^{4}+5\beta q^{5}+524q^{7}+\cdots\)
9.7.d.a \(10\) \(2.070\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(24\) \(-219\) \(-121\) \(q-\beta _{2}q^{2}+(2+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
9.8.a.a \(1\) \(2.811\) \(\Q\) None \(-6\) \(0\) \(-390\) \(-64\) \(-\) \(q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots\)
9.8.a.b \(2\) \(2.811\) \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(0\) \(520\) \(+\) \(q+\beta q^{2}+232q^{4}-2^{4}\beta q^{5}+260q^{7}+\cdots\)
9.8.c.a \(12\) \(2.811\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-9\) \(24\) \(-180\) \(-84\) \(q+(-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
9.9.b.a \(2\) \(3.666\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(3304\) \(q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots\)
9.9.d.a \(14\) \(3.666\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-93\) \(438\) \(922\) \(q-\beta _{2}q^{2}+(-5-3\beta _{1}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
9.10.a.a \(1\) \(4.635\) \(\Q\) None \(-18\) \(0\) \(1530\) \(9128\) \(-\) \(q-18q^{2}-188q^{4}+1530q^{5}+9128q^{7}+\cdots\)
9.10.a.b \(1\) \(4.635\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-12580\) \(+\) \(q-2^{9}q^{4}-12580q^{7}+118370q^{13}+\cdots\)
9.10.a.c \(1\) \(4.635\) \(\Q\) None \(36\) \(0\) \(1314\) \(-4480\) \(-\) \(q+6^{2}q^{2}+28^{2}q^{4}+1314q^{5}-4480q^{7}+\cdots\)
9.10.c.a \(16\) \(4.635\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(15\) \(-3\) \(453\) \(-343\) \(q+(2-2\beta _{1}+\beta _{2})q^{2}+(9-18\beta _{1}+\beta _{5}+\cdots)q^{3}+\cdots\)
9.11.b.a \(4\) \(5.718\) \(\Q(\sqrt{-2}, \sqrt{385})\) None \(0\) \(0\) \(0\) \(-44464\) \(q-\beta _{1}q^{2}+(-1073-\beta _{3})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots\)
9.11.d.a \(18\) \(5.718\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-3\) \(51\) \(4956\) \(-6120\) \(q-\beta _{3}q^{2}+(3-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
9.12.a.a \(1\) \(6.915\) \(\Q\) None \(-78\) \(0\) \(5370\) \(-27760\) \(-\) \(q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots\)
9.12.a.b \(1\) \(6.915\) \(\Q\) None \(24\) \(0\) \(-4830\) \(-16744\) \(-\) \(q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots\)
9.12.a.c \(2\) \(6.915\) \(\Q(\sqrt{70}) \) None \(0\) \(0\) \(0\) \(116200\) \(+\) \(q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots\)
9.12.c.a \(20\) \(6.915\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-33\) \(-12\) \(-7230\) \(8512\) \(q+(-3\beta _{1}+\beta _{2})q^{2}+(24-51\beta _{1}+\beta _{4}+\cdots)q^{3}+\cdots\)
9.13.b.a \(2\) \(8.226\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-223736\) \(q+8\beta q^{2}-6272q^{4}-2291\beta q^{5}-111868q^{7}+\cdots\)
9.13.b.b \(2\) \(8.226\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(232456\) \(q+\beta q^{2}+2638q^{4}-175\beta q^{5}+116228q^{7}+\cdots\)
9.13.d.a \(22\) \(8.226\) None \(-3\) \(618\) \(-15987\) \(34319\)
9.14.a.a \(1\) \(9.651\) \(\Q\) None \(12\) \(0\) \(30210\) \(235088\) \(-\) \(q+12q^{2}-8048q^{4}+30210q^{5}+235088q^{7}+\cdots\)
9.14.a.b \(2\) \(9.651\) \(\Q(\sqrt{55}) \) None \(0\) \(0\) \(0\) \(-266600\) \(+\) \(q+\beta q^{2}-272q^{4}-520\beta q^{5}-133300q^{7}+\cdots\)
9.14.a.c \(2\) \(9.651\) \(\Q(\sqrt{1969}) \) None \(54\) \(0\) \(-40716\) \(-21008\) \(-\) \(q+(3^{3}-\beta )q^{2}+(10258-54\beta )q^{4}+(-20358+\cdots)q^{5}+\cdots\)
9.14.c.a \(24\) \(9.651\) None \(63\) \(-732\) \(52128\) \(-93912\)
9.15.b.a \(4\) \(11.190\) \(\Q(\sqrt{-2}, \sqrt{3745})\) None \(0\) \(0\) \(0\) \(-1065904\) \(q-\beta _{1}q^{2}+(-833-\beta _{3})q^{4}+(-296\beta _{1}+\cdots)q^{5}+\cdots\)
9.15.d.a \(26\) \(11.190\) None \(-3\) \(-2199\) \(-107994\) \(-146330\)
9.16.a.a \(1\) \(12.842\) \(\Q\) None \(-216\) \(0\) \(-52110\) \(2822456\) \(-\) \(q-6^{3}q^{2}+13888q^{4}-52110q^{5}+\cdots\)
9.16.a.b \(1\) \(12.842\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1244900\) \(+\) \(q-2^{15}q^{4}+1244900q^{7}+397771850q^{13}+\cdots\)
9.16.a.c \(1\) \(12.842\) \(\Q\) None \(72\) \(0\) \(221490\) \(-2149000\) \(-\) \(q+72q^{2}-27584q^{4}+221490q^{5}+\cdots\)
9.16.a.d \(1\) \(12.842\) \(\Q\) None \(234\) \(0\) \(-280710\) \(-1373344\) \(-\) \(q+234q^{2}+21988q^{4}-280710q^{5}+\cdots\)
9.16.a.e \(2\) \(12.842\) \(\Q(\sqrt{370}) \) None \(0\) \(0\) \(0\) \(-5182520\) \(+\) \(q+\beta q^{2}+87112q^{4}+464\beta q^{5}-2591260q^{7}+\cdots\)
9.16.c.a \(28\) \(12.842\) None \(-129\) \(3345\) \(-152655\) \(803705\)
9.17.b.a \(6\) \(14.609\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(5400696\) \(q-\beta _{1}q^{2}+(-61382-\beta _{3})q^{4}+(-189\beta _{1}+\cdots)q^{5}+\cdots\)
9.17.d.a \(30\) \(14.609\) None \(-3\) \(2049\) \(507588\) \(220596\)
9.18.a.a \(1\) \(16.490\) \(\Q\) None \(-204\) \(0\) \(163554\) \(-20846560\) \(-\) \(q-204q^{2}-89456q^{4}+163554q^{5}+\cdots\)
9.18.a.b \(1\) \(16.490\) \(\Q\) None \(528\) \(0\) \(1025850\) \(3225992\) \(-\) \(q+528q^{2}+147712q^{4}+1025850q^{5}+\cdots\)
9.18.a.c \(2\) \(16.490\) \(\Q(\sqrt{14569}) \) None \(-594\) \(0\) \(-382860\) \(24471568\) \(-\) \(q+(-297-\beta )q^{2}+(88258+594\beta )q^{4}+\cdots\)
9.18.a.d \(2\) \(16.490\) \(\Q(\sqrt{910}) \) None \(0\) \(0\) \(0\) \(-392840\) \(+\) \(q+\beta q^{2}-2^{5}q^{4}-280\beta q^{5}-196420q^{7}+\cdots\)
9.18.c.a \(32\) \(16.490\) None \(255\) \(-2280\) \(255678\) \(-5846540\)
9.19.b.a \(6\) \(18.485\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(19180488\) \(q+\beta _{1}q^{2}+(-42038-\beta _{2})q^{4}+(1082\beta _{1}+\cdots)q^{5}+\cdots\)
9.19.d.a \(34\) \(18.485\) None \(-3\) \(3804\) \(2192181\) \(4302359\)
9.20.a.a \(1\) \(20.594\) \(\Q\) None \(-456\) \(0\) \(2377410\) \(-16917544\) \(-\) \(q-456q^{2}-316352q^{4}+2377410q^{5}+\cdots\)
9.20.a.b \(1\) \(20.594\) \(\Q\) None \(1104\) \(0\) \(-3516270\) \(-195590584\) \(-\) \(q+1104q^{2}+694528q^{4}-3516270q^{5}+\cdots\)
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