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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
18.2.c.a \(2\) \(0.144\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(0\) \(-2\) \(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
18.3.b.a \(2\) \(0.490\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots\)
18.3.d.a \(4\) \(0.490\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-18\) \(2\) \(q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
18.4.a.a \(1\) \(1.062\) \(\Q\) None \(2\) \(0\) \(-6\) \(-16\) \(+\) \(q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)
18.4.c.a \(2\) \(1.062\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(9\) \(31\) \(q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
18.4.c.b \(4\) \(1.062\) \(\Q(\sqrt{-3}, \sqrt{-35})\) None \(4\) \(3\) \(9\) \(-19\) \(q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots\)
18.5.d.a \(8\) \(1.861\) 8.0.\(\cdots\).4 None \(0\) \(6\) \(18\) \(-26\) \(q-\beta _{3}q^{2}+(2+\beta _{1}-3\beta _{2}-\beta _{5})q^{3}+\cdots\)
18.6.a.a \(1\) \(2.887\) \(\Q\) None \(-4\) \(0\) \(-96\) \(-148\) \(+\) \(q-4q^{2}+2^{4}q^{4}-96q^{5}-148q^{7}+\cdots\)
18.6.a.b \(1\) \(2.887\) \(\Q\) None \(-4\) \(0\) \(66\) \(176\) \(-\) \(q-4q^{2}+2^{4}q^{4}+66q^{5}+176q^{7}+\cdots\)
18.6.a.c \(1\) \(2.887\) \(\Q\) None \(4\) \(0\) \(96\) \(-148\) \(-\) \(q+4q^{2}+2^{4}q^{4}+96q^{5}-148q^{7}+\cdots\)
18.6.c.a \(4\) \(2.887\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(8\) \(0\) \(-54\) \(74\) \(q+4\beta _{1}q^{2}+(-3+6\beta _{1}+\beta _{3})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
18.6.c.b \(6\) \(2.887\) 6.0.\(\cdots\).3 None \(-12\) \(9\) \(-54\) \(-132\) \(q-4\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
18.7.b.a \(2\) \(4.141\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-968\) \(q+4\beta q^{2}-2^{5}q^{4}+123\beta q^{5}-22^{2}q^{7}+\cdots\)
18.7.d.a \(12\) \(4.141\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-42\) \(432\) \(240\) \(q-\beta _{3}q^{2}+(-6+4\beta _{1}+\beta _{2}-\beta _{3}+\beta _{7}+\cdots)q^{3}+\cdots\)
18.8.a.a \(1\) \(5.623\) \(\Q\) None \(-8\) \(0\) \(114\) \(-1576\) \(-\) \(q-8q^{2}+2^{6}q^{4}+114q^{5}-1576q^{7}+\cdots\)
18.8.a.b \(1\) \(5.623\) \(\Q\) None \(8\) \(0\) \(210\) \(1016\) \(+\) \(q+8q^{2}+2^{6}q^{4}+210q^{5}+1016q^{7}+\cdots\)
18.8.c.a \(6\) \(5.623\) 6.0.\(\cdots\).1 None \(-24\) \(-27\) \(54\) \(210\) \(q-8\beta _{1}q^{2}+(-14+19\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
18.8.c.b \(8\) \(5.623\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(32\) \(-12\) \(54\) \(-44\) \(q+(8-8\beta _{1})q^{2}+(-7+11\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
18.9.b.a \(2\) \(7.333\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-7064\) \(q+8\beta q^{2}-2^{7}q^{4}+165\beta q^{5}-3532q^{7}+\cdots\)
18.9.b.b \(2\) \(7.333\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(3304\) \(q+8\beta q^{2}-2^{7}q^{4}-645\beta q^{5}+1652q^{7}+\cdots\)
18.9.d.a \(16\) \(7.333\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(126\) \(-882\) \(-1846\) \(q+\beta _{4}q^{2}+(7+2\beta _{1}+\beta _{3}+\beta _{4})q^{3}+\cdots\)
18.10.a.a \(1\) \(9.271\) \(\Q\) None \(-16\) \(0\) \(-870\) \(-952\) \(-\) \(q-2^{4}q^{2}+2^{8}q^{4}-870q^{5}-952q^{7}+\cdots\)
18.10.a.b \(1\) \(9.271\) \(\Q\) None \(-16\) \(0\) \(-384\) \(5852\) \(+\) \(q-2^{4}q^{2}+2^{8}q^{4}-384q^{5}+5852q^{7}+\cdots\)
18.10.a.c \(1\) \(9.271\) \(\Q\) None \(16\) \(0\) \(-2694\) \(-3544\) \(+\) \(q+2^{4}q^{2}+2^{8}q^{4}-2694q^{5}-3544q^{7}+\cdots\)
18.10.a.d \(1\) \(9.271\) \(\Q\) None \(16\) \(0\) \(384\) \(5852\) \(-\) \(q+2^{4}q^{2}+2^{8}q^{4}+384q^{5}+5852q^{7}+\cdots\)
18.10.c.a \(8\) \(9.271\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(64\) \(-81\) \(171\) \(7135\) \(q+(2^{4}-2^{4}\beta _{1})q^{2}+(-21+22\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
18.10.c.b \(10\) \(9.271\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-80\) \(156\) \(171\) \(-6451\) \(q-2^{4}\beta _{1}q^{2}+(29-3^{3}\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
18.11.b.a \(2\) \(11.436\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(41272\) \(q+2^{4}\beta q^{2}-2^{9}q^{4}-1443\beta q^{5}+20636q^{7}+\cdots\)
18.11.d.a \(20\) \(11.436\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-84\) \(-9918\) \(12238\) \(q+\beta _{2}q^{2}+(-2-4\beta _{1}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
18.12.a.a \(1\) \(13.830\) \(\Q\) None \(-32\) \(0\) \(-3630\) \(32936\) \(-\) \(q-2^{5}q^{2}+2^{10}q^{4}-3630q^{5}+32936q^{7}+\cdots\)
18.12.a.b \(1\) \(13.830\) \(\Q\) None \(-32\) \(0\) \(5280\) \(-49036\) \(+\) \(q-2^{5}q^{2}+2^{10}q^{4}+5280q^{5}-49036q^{7}+\cdots\)
18.12.a.c \(1\) \(13.830\) \(\Q\) None \(32\) \(0\) \(-5766\) \(72464\) \(+\) \(q+2^{5}q^{2}+2^{10}q^{4}-5766q^{5}+72464q^{7}+\cdots\)
18.12.a.d \(1\) \(13.830\) \(\Q\) None \(32\) \(0\) \(-5280\) \(-49036\) \(-\) \(q+2^{5}q^{2}+2^{10}q^{4}-5280q^{5}-49036q^{7}+\cdots\)
18.12.a.e \(1\) \(13.830\) \(\Q\) None \(32\) \(0\) \(11730\) \(-50008\) \(+\) \(q+2^{5}q^{2}+2^{10}q^{4}+11730q^{5}-50008q^{7}+\cdots\)
18.12.c.a \(10\) \(13.830\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-160\) \(-243\) \(4104\) \(44528\) \(q+2^{5}\beta _{1}q^{2}+(-55-62\beta _{1}+\beta _{5})q^{3}+\cdots\)
18.12.c.b \(12\) \(13.830\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(192\) \(0\) \(4104\) \(-61554\) \(q-2^{5}\beta _{1}q^{2}+(-39-77\beta _{1}-\beta _{3})q^{3}+\cdots\)
18.13.b.a \(2\) \(16.452\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-98744\) \(q+2^{5}\beta q^{2}-2^{11}q^{4}+795\beta q^{5}-49372q^{7}+\cdots\)
18.13.b.b \(2\) \(16.452\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(67144\) \(q+2^{5}\beta q^{2}-2^{11}q^{4}+14565\beta q^{5}+\cdots\)
18.13.d.a \(24\) \(16.452\) None \(0\) \(-780\) \(31968\) \(-68640\)
18.14.a.a \(1\) \(19.302\) \(\Q\) None \(-64\) \(0\) \(-54654\) \(176336\) \(-\) \(q-2^{6}q^{2}+2^{12}q^{4}-54654q^{5}+176336q^{7}+\cdots\)
18.14.a.b \(1\) \(19.302\) \(\Q\) None \(-64\) \(0\) \(-15936\) \(98252\) \(+\) \(q-2^{6}q^{2}+2^{12}q^{4}-15936q^{5}+98252q^{7}+\cdots\)
18.14.a.c \(1\) \(19.302\) \(\Q\) None \(-64\) \(0\) \(57450\) \(64232\) \(-\) \(q-2^{6}q^{2}+2^{12}q^{4}+57450q^{5}+64232q^{7}+\cdots\)
18.14.a.d \(1\) \(19.302\) \(\Q\) None \(64\) \(0\) \(-3990\) \(-433432\) \(+\) \(q+2^{6}q^{2}+2^{12}q^{4}-3990q^{5}-433432q^{7}+\cdots\)
18.14.a.e \(1\) \(19.302\) \(\Q\) None \(64\) \(0\) \(15936\) \(98252\) \(-\) \(q+2^{6}q^{2}+2^{12}q^{4}+15936q^{5}+98252q^{7}+\cdots\)
18.14.c.a \(12\) \(19.302\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(384\) \(1836\) \(-36504\) \(153942\) \(q+2^{6}\beta _{1}q^{2}+(191-76\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
18.14.c.b \(14\) \(19.302\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-448\) \(-507\) \(-36504\) \(33880\) \(q-2^{6}\beta _{1}q^{2}+(7-87\beta _{1}-\beta _{4})q^{3}+(-2^{12}+\cdots)q^{4}+\cdots\)
18.15.b.a \(2\) \(22.379\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-522152\) \(q-2^{6}\beta q^{2}-2^{13}q^{4}+9075\beta q^{5}-261076q^{7}+\cdots\)
18.15.b.b \(4\) \(22.379\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(0\) \(2659664\) \(q+2^{6}\beta _{1}q^{2}-2^{13}q^{4}+(-3081\beta _{1}+\cdots)q^{5}+\cdots\)
18.15.d.a \(28\) \(22.379\) None \(0\) \(3276\) \(215982\) \(292658\)
18.16.a.a \(1\) \(25.685\) \(\Q\) None \(-128\) \(0\) \(-77646\) \(762104\) \(-\) \(q-2^{7}q^{2}+2^{14}q^{4}-77646q^{5}+762104q^{7}+\cdots\)
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