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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.2.a.a \(1\) \(0.303\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
38.2.a.b \(1\) \(0.303\) \(\Q\) None \(1\) \(-1\) \(-4\) \(3\) \(-\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots\)
38.2.c.a \(2\) \(0.303\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-8\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
38.2.c.b \(4\) \(0.303\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(-2\) \(4\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
38.2.e.a \(6\) \(0.303\) \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(0\) \(-6\) \(q-\zeta_{18}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{2}q^{4}+\cdots\)
38.3.b.a \(2\) \(1.035\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-2\) \(10\) \(q+\beta q^{2}+2\beta q^{3}-2q^{4}-q^{5}-4q^{6}+\cdots\)
38.3.d.a \(4\) \(1.035\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(6\) \(2\) \(8\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
38.3.f.a \(24\) \(1.035\) None \(0\) \(-6\) \(0\) \(-18\)
38.4.a.a \(1\) \(2.242\) \(\Q\) None \(-2\) \(-2\) \(-9\) \(-31\) \(-\) \(q-2q^{2}-2q^{3}+4q^{4}-9q^{5}+4q^{6}+\cdots\)
38.4.a.b \(2\) \(2.242\) \(\Q(\sqrt{177}) \) None \(-4\) \(1\) \(10\) \(57\) \(+\) \(q-2q^{2}+(1-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)
38.4.a.c \(2\) \(2.242\) \(\Q(\sqrt{73}) \) None \(4\) \(9\) \(-9\) \(-18\) \(+\) \(q+2q^{2}+(5-\beta )q^{3}+4q^{4}+(-6+3\beta )q^{5}+\cdots\)
38.4.c.a \(2\) \(2.242\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-5\) \(-3\) \(-64\) \(q+(-2+2\zeta_{6})q^{2}+(-5+5\zeta_{6})q^{3}+\cdots\)
38.4.c.b \(2\) \(2.242\) \(\Q(\sqrt{-3}) \) None \(-2\) \(5\) \(12\) \(16\) \(q+(-2+2\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
38.4.c.c \(6\) \(2.242\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(-5\) \(-1\) \(52\) \(q+(2-2\beta _{4})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{4}+\cdots)q^{3}+\cdots\)
38.4.e.a \(12\) \(2.242\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-9\) \(0\) \(21\) \(q-2\beta _{3}q^{2}+(-1+2\beta _{2}-\beta _{4}+2\beta _{6}+\cdots)q^{3}+\cdots\)
38.4.e.b \(18\) \(2.242\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(6\) \(0\) \(-33\) \(q-2\beta _{8}q^{2}+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{9})q^{3}+\cdots\)
38.5.b.a \(8\) \(3.928\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(18\) \(-162\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-8q^{4}+(2-\beta _{6}+\cdots)q^{5}+\cdots\)
38.5.d.a \(16\) \(3.928\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-12\) \(-18\) \(72\) \(q+(-\beta _{5}+\beta _{9})q^{2}+(-1+\beta _{3})q^{3}+8\beta _{7}q^{4}+\cdots\)
38.5.f.a \(36\) \(3.928\) None \(0\) \(12\) \(0\) \(90\)
38.6.a.a \(1\) \(6.095\) \(\Q\) None \(-4\) \(-6\) \(31\) \(-27\) \(+\) \(q-4q^{2}-6q^{3}+2^{4}q^{4}+31q^{5}+24q^{6}+\cdots\)
38.6.a.b \(1\) \(6.095\) \(\Q\) None \(4\) \(-14\) \(-45\) \(-121\) \(+\) \(q+4q^{2}-14q^{3}+2^{4}q^{4}-45q^{5}-56q^{6}+\cdots\)
38.6.a.c \(2\) \(6.095\) \(\Q(\sqrt{1441}) \) None \(-8\) \(3\) \(-45\) \(114\) \(-\) \(q-4q^{2}+(2-\beta )q^{3}+2^{4}q^{4}+(-21+\cdots)q^{5}+\cdots\)
38.6.a.d \(3\) \(6.095\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12\) \(13\) \(81\) \(228\) \(-\) \(q+4q^{2}+(4+\beta _{1})q^{3}+2^{4}q^{4}+(3^{3}-\beta _{1}+\cdots)q^{5}+\cdots\)
38.6.c.a \(6\) \(6.095\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(12\) \(-15\) \(14\) \(-624\) \(q+(4-4\beta _{3})q^{2}+(-5+\beta _{1}+\beta _{2}+5\beta _{3}+\cdots)q^{3}+\cdots\)
38.6.c.b \(8\) \(6.095\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(-14\) \(-36\) \(76\) \(q+(-4+4\beta _{2})q^{2}+(-3+3\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
38.6.e.a \(24\) \(6.095\) None \(0\) \(18\) \(0\) \(438\)
38.6.e.b \(30\) \(6.095\) None \(0\) \(15\) \(0\) \(-84\)
38.7.b.a \(10\) \(8.742\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-112\) \(-224\) \(q-\beta _{6}q^{2}+(\beta _{5}+\beta _{6})q^{3}-2^{5}q^{4}+(-11+\cdots)q^{5}+\cdots\)
38.7.d.a \(20\) \(8.742\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-30\) \(112\) \(-208\) \(q-\beta _{8}q^{2}+(-2+\beta _{2}+\beta _{6})q^{3}+(2^{5}+\cdots)q^{4}+\cdots\)
38.7.f.a \(60\) \(8.742\) None \(0\) \(30\) \(0\) \(432\)
38.8.a.a \(1\) \(11.871\) \(\Q\) None \(-8\) \(77\) \(440\) \(951\) \(+\) \(q-8q^{2}+77q^{3}+2^{6}q^{4}+440q^{5}+\cdots\)
38.8.a.b \(2\) \(11.871\) \(\Q(\sqrt{2737}) \) None \(-16\) \(-61\) \(175\) \(-2592\) \(+\) \(q-8q^{2}+(-30-\beta )q^{3}+2^{6}q^{4}+(95+\cdots)q^{5}+\cdots\)
38.8.a.c \(2\) \(11.871\) \(\Q(\sqrt{17953}) \) None \(-16\) \(-11\) \(-69\) \(-348\) \(-\) \(q-8q^{2}+(-5-\beta )q^{3}+2^{6}q^{4}+(-6^{2}+\cdots)q^{5}+\cdots\)
38.8.a.d \(2\) \(11.871\) \(\Q(\sqrt{633}) \) None \(16\) \(-69\) \(155\) \(-2238\) \(-\) \(q+8q^{2}+(-33-3\beta )q^{3}+2^{6}q^{4}+(62+\cdots)q^{5}+\cdots\)
38.8.a.e \(4\) \(11.871\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32\) \(12\) \(-279\) \(2485\) \(+\) \(q+8q^{2}+(3-\beta _{1})q^{3}+2^{6}q^{4}+(-70+\cdots)q^{5}+\cdots\)
38.8.c.a \(12\) \(11.871\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-48\) \(12\) \(124\) \(-1036\) \(q+8\beta _{2}q^{2}+(\beta _{1}-2\beta _{2})q^{3}+(-2^{6}-2^{6}\beta _{2}+\cdots)q^{4}+\cdots\)
38.8.c.b \(14\) \(11.871\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(56\) \(55\) \(-126\) \(1928\) \(q+8\beta _{3}q^{2}+(\beta _{1}+\beta _{2}+8\beta _{3})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots\)
38.8.e.a \(30\) \(11.871\) None \(0\) \(45\) \(0\) \(1806\)
38.8.e.b \(36\) \(11.871\) None \(0\) \(-84\) \(0\) \(-2988\)
38.9.b.a \(12\) \(15.480\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(558\) \(-5422\) \(q+\beta _{7}q^{2}+(\beta _{6}-\beta _{7})q^{3}-2^{7}q^{4}+(47+\cdots)q^{5}+\cdots\)
38.9.d.a \(24\) \(15.480\) None \(0\) \(168\) \(-558\) \(11992\)
38.9.f.a \(84\) \(15.480\) None \(0\) \(-168\) \(0\) \(-6570\)
38.10.a.a \(1\) \(19.571\) \(\Q\) None \(16\) \(-119\) \(-684\) \(9149\) \(+\) \(q+2^{4}q^{2}-119q^{3}+2^{8}q^{4}-684q^{5}+\cdots\)
38.10.a.b \(1\) \(19.571\) \(\Q\) None \(16\) \(102\) \(-1581\) \(-4865\) \(+\) \(q+2^{4}q^{2}+102q^{3}+2^{8}q^{4}-1581q^{5}+\cdots\)
38.10.a.c \(3\) \(19.571\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-48\) \(3\) \(486\) \(-13317\) \(+\) \(q-2^{4}q^{2}+(1+\beta _{1})q^{3}+2^{8}q^{4}+(162+\cdots)q^{5}+\cdots\)
38.10.a.d \(4\) \(19.571\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-64\) \(84\) \(-1395\) \(12307\) \(-\) \(q-2^{4}q^{2}+(21+\beta _{1})q^{3}+2^{8}q^{4}+(-350+\cdots)q^{5}+\cdots\)
38.10.a.e \(4\) \(19.571\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(64\) \(226\) \(866\) \(2670\) \(-\) \(q+2^{4}q^{2}+(57+\beta _{2})q^{3}+2^{8}q^{4}+(218+\cdots)q^{5}+\cdots\)
38.10.c.a \(14\) \(19.571\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(112\) \(165\) \(909\) \(3692\) \(q+(2^{4}-2^{4}\beta _{2})q^{2}+(24-\beta _{1}-24\beta _{2}+\cdots)q^{3}+\cdots\)
38.10.c.b \(16\) \(19.571\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-128\) \(70\) \(-341\) \(3704\) \(q+(-2^{4}+2^{4}\beta _{2})q^{2}+(9-\beta _{1}-9\beta _{2}+\cdots)q^{3}+\cdots\)
38.10.e.a \(42\) \(19.571\) None \(0\) \(-252\) \(0\) \(14373\)
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