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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.6.a.a \(1\) \(0.481\) \(\Q\) None \(-6\) \(9\) \(6\) \(-40\) \(-\) \(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\)
3.7.b.a \(1\) \(0.690\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-27\) \(0\) \(-286\) \(q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots\)
3.8.a.a \(1\) \(0.937\) \(\Q\) None \(6\) \(-27\) \(390\) \(-64\) \(+\) \(q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots\)
3.9.b.a \(2\) \(1.222\) \(\Q(\sqrt{-14}) \) None \(0\) \(90\) \(0\) \(-3500\) \(q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots\)
3.10.a.a \(1\) \(1.545\) \(\Q\) None \(-36\) \(-81\) \(-1314\) \(-4480\) \(+\) \(q-6^{2}q^{2}-3^{4}q^{3}+28^{2}q^{4}-1314q^{5}+\cdots\)
3.10.a.b \(1\) \(1.545\) \(\Q\) None \(18\) \(81\) \(-1530\) \(9128\) \(-\) \(q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots\)
3.11.b.a \(2\) \(1.906\) \(\Q(\sqrt{-5}) \) None \(0\) \(-54\) \(0\) \(34468\) \(q+\beta q^{2}+(-3^{3}+9\beta )q^{3}+304q^{4}+\cdots\)
3.12.a.a \(1\) \(2.305\) \(\Q\) None \(78\) \(-243\) \(-5370\) \(-27760\) \(+\) \(q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots\)
3.13.b.a \(1\) \(2.742\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(729\) \(0\) \(-153502\) \(q+3^{6}q^{3}+2^{12}q^{4}-153502q^{7}+3^{12}q^{9}+\cdots\)
3.13.b.b \(2\) \(2.742\) \(\Q(\sqrt{-26}) \) None \(0\) \(-1350\) \(0\) \(80500\) \(q+\beta q^{2}+(-675-3\beta )q^{3}-4328q^{4}+\cdots\)
3.14.a.a \(1\) \(3.217\) \(\Q\) None \(-12\) \(-729\) \(-30210\) \(235088\) \(+\) \(q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots\)
3.14.a.b \(2\) \(3.217\) \(\Q(\sqrt{1969}) \) None \(-54\) \(1458\) \(40716\) \(-21008\) \(-\) \(q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots\)
3.15.b.a \(4\) \(3.730\) 4.0.1929141760.2 None \(0\) \(2196\) \(0\) \(825608\) \(q+\beta _{1}q^{2}+(549+3\beta _{1}-\beta _{2})q^{3}+(-9824+\cdots)q^{4}+\cdots\)
3.16.a.a \(1\) \(4.281\) \(\Q\) None \(-234\) \(-2187\) \(280710\) \(-1373344\) \(+\) \(q-234q^{2}-3^{7}q^{3}+21988q^{4}+280710q^{5}+\cdots\)
3.16.a.b \(1\) \(4.281\) \(\Q\) None \(-72\) \(2187\) \(-221490\) \(-2149000\) \(-\) \(q-72q^{2}+3^{7}q^{3}-27584q^{4}-221490q^{5}+\cdots\)
3.17.b.a \(4\) \(4.870\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(-2052\) \(0\) \(-3141544\) \(q+\beta _{1}q^{2}+(-513+\beta _{1}+\beta _{2})q^{3}+(-3116+\cdots)q^{4}+\cdots\)
3.18.a.a \(1\) \(5.497\) \(\Q\) None \(204\) \(-6561\) \(-163554\) \(-20846560\) \(+\) \(q+204q^{2}-3^{8}q^{3}-89456q^{4}-163554q^{5}+\cdots\)
3.18.a.b \(2\) \(5.497\) \(\Q(\sqrt{14569}) \) None \(594\) \(13122\) \(382860\) \(24471568\) \(-\) \(q+(297-\beta )q^{2}+3^{8}q^{3}+(88258-594\beta )q^{4}+\cdots\)
3.19.b.a \(1\) \(6.162\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-19683\) \(0\) \(77549186\) \(q-3^{9}q^{3}+2^{18}q^{4}+77549186q^{7}+\cdots\)
3.19.b.b \(4\) \(6.162\) 4.0.601940665.1 None \(0\) \(15876\) \(0\) \(-95744152\) \(q-\beta _{1}q^{2}+(63^{2}+11\beta _{1}+\beta _{2})q^{3}+(-263384+\cdots)q^{4}+\cdots\)
3.20.a.a \(1\) \(6.865\) \(\Q\) None \(-1104\) \(19683\) \(3516270\) \(-195590584\) \(-\) \(q-1104q^{2}+3^{9}q^{3}+694528q^{4}+\cdots\)
3.20.a.b \(2\) \(6.865\) \(\Q(\sqrt{87481}) \) None \(702\) \(-39366\) \(6016140\) \(113892064\) \(+\) \(q+(351-\beta )q^{2}-3^{9}q^{3}+(386242-702\beta )q^{4}+\cdots\)
3.21.b.a \(6\) \(7.605\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(-4122\) \(0\) \(559607916\) \(q+\beta _{1}q^{2}+(-687+11\beta _{1}+\beta _{2})q^{3}+\cdots\)
3.22.a.a \(1\) \(8.384\) \(\Q\) None \(-2844\) \(-59049\) \(3109950\) \(363303920\) \(+\) \(q-2844q^{2}-3^{10}q^{3}+5991184q^{4}+\cdots\)
3.22.a.b \(1\) \(8.384\) \(\Q\) None \(1728\) \(-59049\) \(-41512770\) \(538429808\) \(+\) \(q+12^{3}q^{2}-3^{10}q^{3}+888832q^{4}+\cdots\)
3.22.a.c \(2\) \(8.384\) \(\Q(\sqrt{649}) \) None \(666\) \(118098\) \(996876\) \(679896112\) \(-\) \(q+(333-\beta )q^{2}+3^{10}q^{3}+(589618+\cdots)q^{4}+\cdots\)
3.23.b.a \(6\) \(9.201\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(86670\) \(0\) \(-3447063060\) \(q+\beta _{1}q^{2}+(14445-8\beta _{1}+\beta _{2})q^{3}+\cdots\)
3.24.a.a \(1\) \(10.056\) \(\Q\) None \(1128\) \(177147\) \(-48863730\) \(-1723688680\) \(-\) \(q+1128q^{2}+3^{11}q^{3}-7116224q^{4}+\cdots\)
3.24.a.b \(2\) \(10.056\) \(\Q(\sqrt{530401}) \) None \(-1242\) \(-354294\) \(-46808820\) \(-211963904\) \(+\) \(q+(-621-\beta )q^{2}-3^{11}q^{3}+(-3229358+\cdots)q^{4}+\cdots\)
3.25.b.a \(1\) \(10.949\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(531441\) \(0\) \(-4119710398\) \(q+3^{12}q^{3}+2^{24}q^{4}-4119710398q^{7}+\cdots\)
3.25.b.b \(6\) \(10.949\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(-616842\) \(0\) \(1988064876\) \(q+\beta _{1}q^{2}+(-102807+2^{4}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
3.26.a.a \(2\) \(11.880\) \(\Q(\sqrt{1287001}) \) None \(-324\) \(-1062882\) \(570861756\) \(-29687385728\) \(+\) \(q+(-162-\beta )q^{2}-3^{12}q^{3}+(12803848+\cdots)q^{4}+\cdots\)
3.26.a.b \(3\) \(11.880\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-3678\) \(1594323\) \(-163152750\) \(-9622572744\) \(-\) \(q+(-1226+\beta _{1})q^{2}+3^{12}q^{3}+(30249196+\cdots)q^{4}+\cdots\)
3.27.b.a \(8\) \(12.849\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-1261080\) \(0\) \(-83723264240\) \(q+\beta _{1}q^{2}+(-157635-5\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.28.a.a \(2\) \(13.856\) \(\Q(\sqrt{6469}) \) None \(3168\) \(3188646\) \(-4906065060\) \(-151657089584\) \(-\) \(q+(1584-\beta )q^{2}+3^{13}q^{3}+(2432512+\cdots)q^{4}+\cdots\)
3.28.a.b \(2\) \(13.856\) \(\Q(\sqrt{30001}) \) None \(21582\) \(-3188646\) \(-1771946100\) \(369665199904\) \(+\) \(q+(10791-\beta )q^{2}-3^{13}q^{3}+(101301922+\cdots)q^{4}+\cdots\)
3.29.b.a \(8\) \(14.901\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(6092280\) \(0\) \(401156726320\) \(q+\beta _{1}q^{2}+(761535-18\beta _{1}-\beta _{2})q^{3}+\cdots\)
3.30.a.a \(2\) \(15.983\) \(\Q(\sqrt{77089}) \) None \(-45036\) \(-9565938\) \(187613820\) \(26\!\cdots\!48\) \(+\) \(q+(-22518-\beta )q^{2}-3^{14}q^{3}+(106174408+\cdots)q^{4}+\cdots\)
3.30.a.b \(3\) \(15.983\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(11370\) \(14348907\) \(35492909586\) \(723913582632\) \(-\) \(q+(3790-\beta _{1})q^{2}+3^{14}q^{3}+(701653900+\cdots)q^{4}+\cdots\)
3.31.b.a \(1\) \(17.104\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-14348907\) \(0\) \(-7\!\cdots\!86\) \(q-3^{15}q^{3}+2^{30}q^{4}-7945347009886q^{7}+\cdots\)
3.31.b.b \(8\) \(17.104\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(5373000\) \(0\) \(11\!\cdots\!80\) \(q+\beta _{1}q^{2}+(671625-17\beta _{1}-\beta _{2})q^{3}+\cdots\)
3.32.a.a \(2\) \(18.263\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-39528\) \(28697814\) \(-7930517220\) \(-1\!\cdots\!76\) \(-\) \(q+(-19764-\beta )q^{2}+3^{15}q^{3}+(-100683488+\cdots)q^{4}+\cdots\)
3.32.a.b \(3\) \(18.263\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-7626\) \(-43046721\) \(50622172050\) \(-2\!\cdots\!08\) \(+\) \(q+(-2542+\beta _{1})q^{2}-3^{15}q^{3}+(1406276044+\cdots)q^{4}+\cdots\)
3.33.b.a \(10\) \(19.460\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-21387150\) \(0\) \(-5\!\cdots\!40\) \(q+\beta _{1}q^{2}+(-2138715+35\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.34.a.a \(3\) \(20.695\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(41202\) \(129140163\) \(51261823890\) \(76\!\cdots\!56\) \(-\) \(q+(13734-\beta _{1})q^{2}+3^{16}q^{3}+(-369155924+\cdots)q^{4}+\cdots\)
3.34.a.b \(3\) \(20.695\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(136620\) \(-129140163\) \(-260488036134\) \(10\!\cdots\!32\) \(+\) \(q+(45540-\beta _{1})q^{2}-3^{16}q^{3}+(4863185200+\cdots)q^{4}+\cdots\)
3.35.b.a \(10\) \(21.968\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(119369106\) \(0\) \(-1\!\cdots\!72\) \(q+\beta _{1}q^{2}+(11936911+41\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.36.a.a \(2\) \(23.279\) \(\Q(\sqrt{2196841}) \) None \(-60912\) \(258280326\) \(-1\!\cdots\!40\) \(-1\!\cdots\!44\) \(-\) \(q+(-30456-\beta )q^{2}+3^{17}q^{3}+(28571469952+\cdots)q^{4}+\cdots\)
3.36.a.b \(3\) \(23.279\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-87330\) \(-387420489\) \(27\!\cdots\!10\) \(48\!\cdots\!64\) \(+\) \(q+(-29110+\beta _{1})q^{2}-3^{17}q^{3}+(10829584300+\cdots)q^{4}+\cdots\)
3.37.b.a \(1\) \(24.627\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(387420489\) \(0\) \(27\!\cdots\!98\) \(q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots\)
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