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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.2.a.a \(1\) \(0.152\) \(\Q\) None \(0\) \(-2\) \(3\) \(-1\) \(-\) \(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
19.2.e.a \(6\) \(0.152\) \(\Q(\zeta_{18})\) None \(-6\) \(-3\) \(-6\) \(0\) \(q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
19.3.b.a \(1\) \(0.518\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-9\) \(-5\) \(q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots\)
19.3.b.b \(2\) \(0.518\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(8\) \(-10\) \(q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots\)
19.3.d.a \(6\) \(0.518\) 6.0.6967728.1 None \(-3\) \(-9\) \(-2\) \(0\) \(q+(-1-\beta _{5})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{5})q^{3}+\cdots\)
19.3.f.a \(12\) \(0.518\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(-6\) \(6\) \(q+\beta _{10}q^{2}+(\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots\)
19.4.a.a \(1\) \(1.121\) \(\Q\) None \(-3\) \(-5\) \(-12\) \(11\) \(-\) \(q-3q^{2}-5q^{3}+q^{4}-12q^{5}+15q^{6}+\cdots\)
19.4.a.b \(3\) \(1.121\) 3.3.3144.1 None \(3\) \(1\) \(14\) \(-35\) \(+\) \(q+(1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
19.4.c.a \(4\) \(1.121\) \(\Q(\sqrt{-3}, \sqrt{55})\) None \(-2\) \(0\) \(14\) \(-28\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(7+7\beta _{2})q^{4}+\cdots\)
19.4.c.b \(4\) \(1.121\) \(\Q(\sqrt{-3}, \sqrt{73})\) None \(-1\) \(-2\) \(-19\) \(40\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-11+\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots\)
19.4.e.a \(24\) \(1.121\) None \(-6\) \(-3\) \(-6\) \(3\)
19.5.b.a \(1\) \(1.964\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(31\) \(-73\) \(q+2^{4}q^{4}+31q^{5}-73q^{7}+3^{4}q^{9}+\cdots\)
19.5.b.b \(4\) \(1.964\) 4.0.12107488.1 None \(0\) \(0\) \(-42\) \(136\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-3+3\beta _{2})q^{4}+\cdots\)
19.5.d.a \(10\) \(1.964\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-3\) \(9\) \(8\) \(-24\) \(q-\beta _{1}q^{2}+(\beta _{3}+\beta _{5})q^{3}+(6\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
19.5.f.a \(36\) \(1.964\) None \(-6\) \(-18\) \(-6\) \(-48\)
19.6.a.a \(1\) \(3.047\) \(\Q\) None \(-6\) \(4\) \(54\) \(248\) \(-\) \(q-6q^{2}+4q^{3}+4q^{4}+54q^{5}-24q^{6}+\cdots\)
19.6.a.b \(1\) \(3.047\) \(\Q\) None \(-2\) \(-1\) \(-24\) \(-167\) \(+\) \(q-2q^{2}-q^{3}-28q^{4}-24q^{5}+2q^{6}+\cdots\)
19.6.a.c \(2\) \(3.047\) \(\Q(\sqrt{177}) \) None \(-7\) \(-7\) \(-133\) \(72\) \(+\) \(q+(-3-\beta )q^{2}+(-5+3\beta )q^{3}+(21+\cdots)q^{4}+\cdots\)
19.6.a.d \(4\) \(3.047\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(9\) \(6\) \(90\) \(-190\) \(-\) \(q+(3-\beta _{1}+\beta _{2})q^{2}+(3+3\beta _{2})q^{3}+(23+\cdots)q^{4}+\cdots\)
19.6.c.a \(16\) \(3.047\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(3\) \(28\) \(10\) \(208\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(3+3\beta _{2}+\beta _{5})q^{3}+\cdots\)
19.6.e.a \(42\) \(3.047\) None \(-6\) \(-39\) \(-6\) \(-180\)
19.7.b.a \(1\) \(4.371\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-54\) \(610\) \(q+2^{6}q^{4}-54q^{5}+610q^{7}+3^{6}q^{9}+\cdots\)
19.7.b.b \(8\) \(4.371\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(108\) \(-140\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-57+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
19.7.d.a \(18\) \(4.371\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-3\) \(27\) \(-57\) \(-260\) \(q+(\beta _{1}-\beta _{3})q^{2}+(2+\beta _{2}-\beta _{7})q^{3}+(21+\cdots)q^{4}+\cdots\)
19.7.f.a \(54\) \(4.371\) None \(-6\) \(-36\) \(-6\) \(-219\)
19.8.a.a \(4\) \(5.935\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-9\) \(-14\) \(-222\) \(-1246\) \(-\) \(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{2})q^{3}+\cdots\)
19.8.a.b \(6\) \(5.935\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(15\) \(40\) \(219\) \(2105\) \(+\) \(q+(2+\beta _{1})q^{2}+(6+\beta _{1}+\beta _{4})q^{3}+(57+\cdots)q^{4}+\cdots\)
19.8.c.a \(20\) \(5.935\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-9\) \(-68\) \(0\) \(-1456\) \(q+(\beta _{1}+\beta _{2})q^{2}+(7\beta _{2}+\beta _{7})q^{3}+(-48+\cdots)q^{4}+\cdots\)
19.8.e.a \(66\) \(5.935\) None \(-6\) \(33\) \(-6\) \(588\)
19.9.b.a \(1\) \(7.740\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-289\) \(527\) \(q+2^{8}q^{4}-17^{2}q^{5}+527q^{7}+3^{8}q^{9}+\cdots\)
19.9.b.b \(12\) \(7.740\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(8\) \(3686\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-131+\beta _{2})q^{4}+\cdots\)
19.9.d.a \(26\) \(7.740\) None \(-3\) \(-171\) \(278\) \(-7504\)
19.9.f.a \(72\) \(7.740\) None \(-6\) \(162\) \(-6\) \(3282\)
19.10.a.a \(6\) \(9.786\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-33\) \(-155\) \(-3612\) \(4085\) \(+\) \(q+(-6+\beta _{1})q^{2}+(-26+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
19.10.a.b \(8\) \(9.786\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(15\) \(7\) \(3894\) \(-7133\) \(-\) \(q+(2-\beta _{1})q^{2}+(1+\beta _{1}-\beta _{3})q^{3}+(331+\cdots)q^{4}+\cdots\)
19.10.c.a \(28\) \(9.786\) None \(15\) \(-74\) \(-285\) \(-2676\)
19.10.e.a \(84\) \(9.786\) None \(-6\) \(213\) \(-6\) \(5715\)
19.11.b.a \(1\) \(12.072\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(3951\) \(-32525\) \(q+2^{10}q^{4}+3951q^{5}-32525q^{7}+\cdots\)
19.11.b.b \(14\) \(12.072\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(-2842\) \(-3840\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-599+\beta _{2})q^{4}+\cdots\)
19.11.d.a \(30\) \(12.072\) None \(-3\) \(63\) \(-1112\) \(42200\)
19.11.f.a \(96\) \(12.072\) None \(-6\) \(-72\) \(-6\) \(-5844\)
19.12.a.a \(7\) \(14.599\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-9\) \(10\) \(-14307\) \(-2209\) \(-\) \(q+(-1-\beta _{1})q^{2}+(1+3\beta _{1}-\beta _{4})q^{3}+\cdots\)
19.12.a.b \(9\) \(14.599\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(87\) \(496\) \(2114\) \(-19080\) \(+\) \(q+(10-\beta _{1})q^{2}+(56-3\beta _{1}+\beta _{3})q^{3}+\cdots\)
19.12.c.a \(36\) \(14.599\) None \(-33\) \(-224\) \(2530\) \(112320\)
19.12.e.a \(102\) \(14.599\) None \(-6\) \(-795\) \(-6\) \(-57552\)
19.13.b.a \(1\) \(17.366\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-28334\) \(136802\) \(q+2^{12}q^{4}-28334q^{5}+136802q^{7}+\cdots\)
19.13.b.b \(18\) \(17.366\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(25308\) \(-207284\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-2224+\beta _{2})q^{4}+\cdots\)
19.13.d.a \(38\) \(17.366\) None \(-3\) \(1377\) \(3023\) \(202236\)
19.13.f.a \(114\) \(17.366\) None \(-6\) \(-1386\) \(-6\) \(-131763\)
19.14.a.a \(9\) \(20.374\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-129\) \(-1328\) \(-61942\) \(-435960\) \(+\) \(q+(-14-\beta _{1})q^{2}+(-148+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
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