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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
31.1.b.a \(1\) \(0.015\) \(\Q\) \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
31.2.a.a \(2\) \(0.248\) \(\Q(\sqrt{5}) \) None None \(1\) \(-2\) \(2\) \(-4\) \(-\) \(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
31.2.c.a \(4\) \(0.248\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-4\) \(2\) \(-2\) \(-2\) \(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
31.2.d.a \(4\) \(0.248\) \(\Q(\zeta_{10})\) None None \(-3\) \(1\) \(-6\) \(-3\) \(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
31.2.g.a \(16\) \(0.248\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-6\) \(-12\) \(-3\) \(2\) \(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
31.3.b.a \(2\) \(0.845\) \(\Q(\sqrt{-26}) \) None None \(-2\) \(0\) \(4\) \(16\) \(q-q^{2}+\beta q^{3}-3q^{4}+2q^{5}-\beta q^{6}+\cdots\)
31.3.b.b \(3\) \(0.845\) 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
31.3.e.a \(2\) \(0.845\) \(\Q(\sqrt{-3}) \) None None \(-6\) \(3\) \(9\) \(1\) \(q-3q^{2}+(1+\zeta_{6})q^{3}+5q^{4}+9\zeta_{6}q^{5}+\cdots\)
31.3.e.b \(6\) \(0.845\) 6.0.954288.1 None None \(2\) \(-3\) \(-7\) \(-9\) \(q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
31.3.f.a \(20\) \(0.845\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-3\) \(-5\) \(-14\) \(-1\) \(q-\beta _{10}q^{2}-\beta _{13}q^{3}+(3\beta _{11}+\beta _{19})q^{4}+\cdots\)
31.3.h.a \(32\) \(0.845\) None None \(-6\) \(-10\) \(-7\) \(-22\)
31.4.a.a \(2\) \(1.829\) \(\Q(\sqrt{17}) \) None None \(-5\) \(-2\) \(-25\) \(-19\) \(-\) \(q+(-2-\beta )q^{2}+(-2+2\beta )q^{3}+5\beta q^{4}+\cdots\)
31.4.a.b \(5\) \(1.829\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(3\) \(4\) \(15\) \(9\) \(+\) \(q+(1-\beta _{1})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
31.4.c.a \(14\) \(1.829\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-4\) \(-11\) \(-5\) \(31\) \(q+(-\beta _{1}+\beta _{4})q^{2}+(-2+2\beta _{3}-\beta _{8}+\cdots)q^{3}+\cdots\)
31.4.d.a \(28\) \(1.829\) None None \(-3\) \(-7\) \(0\) \(35\)
31.4.g.a \(56\) \(1.829\) None None \(-6\) \(1\) \(0\) \(-71\)
31.5.b.a \(3\) \(3.204\) 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{2}+(2^{4}-6\beta _{1}+\beta _{2})q^{4}+\cdots\)
31.5.b.b \(6\) \(3.204\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None None \(-2\) \(0\) \(-8\) \(-132\) \(q-\beta _{3}q^{2}+\beta _{1}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
31.5.e.a \(20\) \(3.204\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-4\) \(6\) \(-4\) \(-98\) \(q-\beta _{3}q^{2}+\beta _{8}q^{3}+(6+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots\)
31.5.f.a \(36\) \(3.204\) None None \(-3\) \(-5\) \(-2\) \(-73\)
31.5.h.a \(80\) \(3.204\) None None \(-6\) \(-16\) \(-1\) \(288\)
31.6.a.a \(5\) \(4.972\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-9\) \(-20\) \(-72\) \(-108\) \(+\) \(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{3})q^{3}+\cdots\)
31.6.a.b \(8\) \(4.972\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(7\) \(-2\) \(128\) \(88\) \(-\) \(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(19-3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
31.6.c.a \(24\) \(4.972\) None None \(-4\) \(10\) \(28\) \(-134\)
31.6.d.a \(52\) \(4.972\) None None \(-3\) \(17\) \(-66\) \(205\)
31.6.g.a \(96\) \(4.972\) None None \(-6\) \(-20\) \(-33\) \(-66\)
31.7.b.a \(1\) \(7.132\) \(\Q\) \(\Q(\sqrt{-31}) \) None \(-15\) \(0\) \(-246\) \(-430\) \(q-15q^{2}+161q^{4}-246q^{5}-430q^{7}+\cdots\)
31.7.b.b \(2\) \(7.132\) \(\Q(\sqrt{93}) \) \(\Q(\sqrt{-31}) \) None \(15\) \(0\) \(246\) \(430\) \(q+(8-\beta )q^{2}+(23-15\beta )q^{4}+(127-8\beta )q^{5}+\cdots\)
31.7.b.c \(12\) \(7.132\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-2\) \(0\) \(-146\) \(6\) \(q-\beta _{8}q^{2}-\beta _{1}q^{3}+(10+\beta _{6}-\beta _{8})q^{4}+\cdots\)
31.7.e.a \(30\) \(7.132\) None None \(-4\) \(-3\) \(-73\) \(723\)
31.7.f.a \(60\) \(7.132\) None None \(-3\) \(-5\) \(136\) \(1009\)
31.7.h.a \(120\) \(7.132\) None None \(-6\) \(-7\) \(68\) \(-1753\)
31.8.a.a \(7\) \(9.684\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-17\) \(-14\) \(-430\) \(-832\) \(-\) \(q+(-2-\beta _{1})q^{2}+(-2+\beta _{1}+\beta _{3})q^{3}+\cdots\)
31.8.a.b \(10\) \(9.684\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(15\) \(40\) \(570\) \(540\) \(+\) \(q+(2-\beta _{1})q^{2}+(4+\beta _{2})q^{3}+(61+\beta _{1}+\cdots)q^{4}+\cdots\)
31.8.c.a \(36\) \(9.684\) None None \(-4\) \(-2\) \(70\) \(-2158\)
31.8.d.a \(68\) \(9.684\) None None \(-3\) \(-31\) \(-150\) \(-3083\)
31.8.g.a \(144\) \(9.684\) None None \(-6\) \(-8\) \(-75\) \(5518\)
31.9.b.a \(3\) \(12.629\) 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-6\beta _{1}+\beta _{2})q^{2}+(2^{8}-\beta _{1}+3^{4}\beta _{2})q^{4}+\cdots\)
31.9.b.b \(18\) \(12.629\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(-2\) \(0\) \(292\) \(-5472\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(140+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
31.9.e.a \(40\) \(12.629\) None None \(-4\) \(-84\) \(146\) \(272\)
31.9.f.a \(84\) \(12.629\) None None \(-3\) \(-5\) \(-302\) \(5067\)
31.9.h.a \(160\) \(12.629\) None None \(-6\) \(74\) \(-151\) \(118\)
31.10.a.a \(10\) \(15.966\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-33\) \(-8\) \(-3297\) \(-495\) \(+\) \(q+(-3-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots\)
31.10.a.b \(13\) \(15.966\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(31\) \(154\) \(1703\) \(9109\) \(-\) \(q+(2+\beta _{1})q^{2}+(12+\beta _{3})q^{3}+(300+6\beta _{1}+\cdots)q^{4}+\cdots\)
31.10.c.a \(46\) \(15.966\) None None \(-4\) \(13\) \(-797\) \(6359\)
31.10.d.a \(92\) \(15.966\) None None \(-3\) \(-151\) \(1584\) \(15771\)
31.10.g.a \(184\) \(15.966\) None None \(-6\) \(-23\) \(792\) \(-30759\)
31.11.b.a \(3\) \(19.696\) 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-15\beta _{1}+14\beta _{2})q^{2}+(2^{10}-644\beta _{1}+\cdots)q^{4}+\cdots\)
31.11.b.b \(22\) \(19.696\) None None \(-2\) \(0\) \(3304\) \(19916\)
31.11.e.a \(52\) \(19.696\) None None \(-4\) \(-246\) \(1652\) \(-19306\)
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