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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
161.1.l.a \(10\) \(0.080\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q+(-\zeta_{22}+\zeta_{22}^{8})q^{2}+(\zeta_{22}^{2}-\zeta_{22}^{5}+\cdots)q^{4}+\cdots\)
161.2.a.a \(1\) \(1.286\) \(\Q\) None None \(-1\) \(0\) \(2\) \(1\) \(-\) \(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-3q^{9}+\cdots\)
161.2.a.b \(2\) \(1.286\) \(\Q(\sqrt{5}) \) None None \(-1\) \(-2\) \(-2\) \(-2\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\)
161.2.a.c \(3\) \(1.286\) 3.3.148.1 None None \(-1\) \(2\) \(2\) \(-3\) \(-\) \(q+(-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
161.2.a.d \(5\) \(1.286\) 5.5.2147108.1 None None \(2\) \(0\) \(-4\) \(5\) \(-\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
161.2.c.a \(2\) \(1.286\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-q^{4}-\beta q^{7}+3q^{8}+3q^{9}-2\beta q^{11}+\cdots\)
161.2.c.b \(12\) \(1.286\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{6}q^{3}+(1-\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
161.2.e.a \(14\) \(1.286\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(-5\) \(-4\) \(-2\) \(q-\beta _{2}q^{2}+(-1-\beta _{6}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)
161.2.e.b \(14\) \(1.286\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(3\) \(4\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{5}-\beta _{12})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
161.2.g.a \(28\) \(1.286\) None None \(-4\) \(-6\) \(0\) \(0\)
161.2.i.a \(50\) \(1.286\) None None \(2\) \(0\) \(-11\) \(5\)
161.2.i.b \(70\) \(1.286\) None None \(-4\) \(-4\) \(7\) \(-7\)
161.2.k.a \(20\) \(1.286\) 20.0.\(\cdots\).2 \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(\beta _{4}+\beta _{6}-\beta _{14})q^{2}+(-\beta _{2}+\beta _{13}+\cdots)q^{4}+\cdots\)
161.2.k.b \(120\) \(1.286\) None None \(-22\) \(0\) \(0\) \(-11\)
161.2.m.a \(280\) \(1.286\) None None \(-11\) \(-9\) \(-11\) \(-20\)
161.2.o.a \(280\) \(1.286\) None None \(-7\) \(-27\) \(-33\) \(-22\)
161.3.b.a \(28\) \(4.387\) None None \(0\) \(0\) \(0\) \(18\)
161.3.d.a \(24\) \(4.387\) None None \(-2\) \(-4\) \(0\) \(0\)
161.3.f.a \(60\) \(4.387\) None None \(-4\) \(-2\) \(0\) \(0\)
161.3.h.a \(60\) \(4.387\) None None \(0\) \(-6\) \(0\) \(-10\)
161.3.j.a \(240\) \(4.387\) None None \(2\) \(4\) \(0\) \(0\)
161.3.l.a \(20\) \(4.387\) 20.0.\(\cdots\).2 \(\Q(\sqrt{-7}) \) None \(6\) \(0\) \(0\) \(14\) \(q+(\beta _{4}-\beta _{5}+2\beta _{6}-\beta _{14})q^{2}+(-3\beta _{2}+\cdots)q^{4}+\cdots\)
161.3.l.b \(280\) \(4.387\) None None \(-22\) \(0\) \(0\) \(-29\)
161.3.n.a \(600\) \(4.387\) None None \(-11\) \(-27\) \(-33\) \(-12\)
161.3.p.a \(600\) \(4.387\) None None \(-7\) \(-9\) \(-11\) \(-22\)
161.4.a.a \(5\) \(9.499\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-4\) \(-11\) \(-4\) \(35\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-2-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
161.4.a.b \(8\) \(9.499\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-3\) \(-24\) \(-56\) \(-\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
161.4.a.c \(9\) \(9.499\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(9\) \(-4\) \(-63\) \(+\) \(q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(5+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
161.4.a.d \(12\) \(9.499\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(4\) \(1\) \(16\) \(84\) \(+\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(6+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
161.4.c.a \(2\) \(9.499\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(10\) \(0\) \(0\) \(0\) \(q+5q^{2}+17q^{4}+7\beta q^{7}+45q^{8}+3^{3}q^{9}+\cdots\)
161.4.c.b \(8\) \(9.499\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{2}q^{3}-7q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
161.4.c.c \(36\) \(9.499\) None None \(-8\) \(0\) \(0\) \(0\)
161.4.e.a \(44\) \(9.499\) None None \(0\) \(-6\) \(-20\) \(-12\)
161.4.e.b \(44\) \(9.499\) None None \(0\) \(18\) \(20\) \(-44\)
161.4.g.a \(92\) \(9.499\) None None \(0\) \(-6\) \(0\) \(0\)
161.4.i.a \(170\) \(9.499\) None None \(0\) \(10\) \(10\) \(-119\)
161.4.i.b \(190\) \(9.499\) None None \(2\) \(-2\) \(-26\) \(133\)
161.4.k.a \(20\) \(9.499\) 20.0.\(\cdots\).2 \(\Q(\sqrt{-7}) \) None \(-10\) \(0\) \(0\) \(0\) \(q+(-3-\beta _{2}-3\beta _{3}-3\beta _{5}+3\beta _{6}-3\beta _{8}+\cdots)q^{2}+\cdots\)
161.4.k.b \(440\) \(9.499\) None None \(-6\) \(0\) \(0\) \(-11\)
161.4.m.a \(920\) \(9.499\) None None \(-7\) \(-9\) \(3\) \(-22\)
161.4.o.a \(920\) \(9.499\) None None \(-11\) \(-27\) \(-33\) \(-22\)
161.5.b.a \(60\) \(16.643\) None None \(0\) \(0\) \(0\) \(-130\)
161.5.d.a \(48\) \(16.643\) None None \(6\) \(20\) \(0\) \(0\)
161.6.a.a \(10\) \(25.822\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-8\) \(-2\) \(-92\) \(490\) \(+\) \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(7-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
161.6.a.b \(13\) \(25.822\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(0\) \(-12\) \(8\) \(-637\) \(+\) \(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(12+\beta _{1}+\cdots)q^{4}+\cdots\)
161.6.a.c \(14\) \(25.822\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(24\) \(108\) \(-686\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2})q^{3}+(19+\beta _{1}+\cdots)q^{4}+\cdots\)
161.6.a.d \(17\) \(25.822\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(8\) \(34\) \(8\) \(833\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{1}-\beta _{3})q^{3}+(20+\beta _{1}+\cdots)q^{4}+\cdots\)
161.6.c.a \(2\) \(25.822\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(-22\) \(0\) \(0\) \(0\) \(q-11q^{2}+89q^{4}+7^{2}\beta q^{7}-627q^{8}+\cdots\)
161.6.c.b \(76\) \(25.822\) None None \(16\) \(0\) \(0\) \(0\)
161.7.b.a \(88\) \(37.039\) None None \(0\) \(0\) \(0\) \(8\)
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