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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
160.1.p.a \(2\) \(0.080\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots\)
160.2.a.a \(1\) \(1.278\) \(\Q\) None None \(0\) \(-2\) \(-1\) \(-2\) \(+\) \(q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
160.2.a.b \(1\) \(1.278\) \(\Q\) None None \(0\) \(2\) \(-1\) \(2\) \(-\) \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
160.2.a.c \(2\) \(1.278\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(2\) \(0\) \(-\) \(q+\beta q^{3}+q^{5}-\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots\)
160.2.c.a \(2\) \(1.278\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+3q^{9}+2iq^{13}-4iq^{17}+\cdots\)
160.2.c.b \(4\) \(1.278\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots\)
160.2.d.a \(4\) \(1.278\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(4\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}q^{5}+(1+\zeta_{12}^{3})q^{7}+\cdots\)
160.2.f.a \(4\) \(1.278\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
160.2.n.a \(2\) \(1.278\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(-4\) \(-4\) \(q+(-2-2i)q^{3}+(-2+i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
160.2.n.b \(2\) \(1.278\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(-2\) \(q+(-1-i)q^{3}+(1-2i)q^{5}+(-1+i)q^{7}+\cdots\)
160.2.n.c \(2\) \(1.278\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(6\) \(q+(-1-i)q^{3}+(1+2i)q^{5}+(3-3i)q^{7}+\cdots\)
160.2.n.d \(2\) \(1.278\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(2\) \(-6\) \(q+(1+i)q^{3}+(1+2i)q^{5}+(-3+3i)q^{7}+\cdots\)
160.2.n.e \(2\) \(1.278\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(2\) \(2\) \(q+(1+i)q^{3}+(1-2i)q^{5}+(1-i)q^{7}+\cdots\)
160.2.n.f \(2\) \(1.278\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(-4\) \(4\) \(q+(2+2i)q^{3}+(-2+i)q^{5}+(2-2i)q^{7}+\cdots\)
160.2.o.a \(8\) \(1.278\) \(\Q(\zeta_{20})\) None None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{20}^{3}q^{3}+\zeta_{20}^{5}q^{5}-\zeta_{20}^{6}q^{7}+\cdots\)
160.2.u.a \(88\) \(1.278\) None None \(-4\) \(-4\) \(-4\) \(0\)
160.2.x.a \(64\) \(1.278\) None None \(0\) \(0\) \(0\) \(0\)
160.2.z.a \(88\) \(1.278\) None None \(0\) \(0\) \(-4\) \(0\)
160.2.ba.a \(88\) \(1.278\) None None \(-4\) \(-4\) \(-4\) \(-8\)
160.3.b.a \(4\) \(4.360\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+4\beta _{2})q^{7}+\cdots\)
160.3.b.b \(4\) \(4.360\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots\)
160.3.e.a \(1\) \(4.360\) \(\Q\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(-5\) \(6\) \(q-5q^{5}+6q^{7}+9q^{9}+18q^{11}+6q^{13}+\cdots\)
160.3.e.b \(1\) \(4.360\) \(\Q\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(5\) \(-6\) \(q+5q^{5}-6q^{7}+9q^{9}+18q^{11}-6q^{13}+\cdots\)
160.3.e.c \(8\) \(4.360\) 8.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
160.3.g.a \(8\) \(4.360\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{6}q^{7}+(3+\beta _{3}+\cdots)q^{9}+\cdots\)
160.3.h.a \(6\) \(4.360\) 6.0.1827904.1 None None \(0\) \(-4\) \(-2\) \(-12\) \(q+(-1-\beta _{1})q^{3}-\beta _{4}q^{5}+(-2-\beta _{3}+\cdots)q^{7}+\cdots\)
160.3.h.b \(6\) \(4.360\) 6.0.1827904.1 None None \(0\) \(4\) \(-2\) \(12\) \(q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{4})q^{5}+\cdots\)
160.3.m.a \(20\) \(4.360\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{8}q^{3}+\beta _{9}q^{5}-\beta _{4}q^{7}+(2\beta _{2}-\beta _{13}+\cdots)q^{9}+\cdots\)
160.3.p.a \(2\) \(4.360\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-8\) \(0\) \(q+(-4+3i)q^{5}+9iq^{9}+(-17+17i)q^{13}+\cdots\)
160.3.p.b \(2\) \(4.360\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(8\) \(0\) \(q+(4+3i)q^{5}+9iq^{9}+(7-7i)q^{13}+\cdots\)
160.3.p.c \(4\) \(4.360\) \(\Q(i, \sqrt{15})\) None None \(0\) \(0\) \(-20\) \(0\) \(q-\beta _{2}q^{3}-5q^{5}+\beta _{3}q^{7}+21\beta _{1}q^{9}+\cdots\)
160.3.p.d \(4\) \(4.360\) \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(12\) \(0\) \(q-\beta _{2}q^{3}+(3+4\beta _{1})q^{5}-3\beta _{3}q^{7}+5\beta _{1}q^{9}+\cdots\)
160.3.p.e \(6\) \(4.360\) 6.0.3534400.1 None None \(0\) \(0\) \(4\) \(-8\) \(q+\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(-2-2\beta _{3}+\cdots)q^{7}+\cdots\)
160.3.p.f \(6\) \(4.360\) 6.0.3534400.1 None None \(0\) \(0\) \(4\) \(8\) \(q-\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(2+2\beta _{3}+\cdots)q^{7}+\cdots\)
160.3.v.a \(184\) \(4.360\) None None \(-4\) \(-4\) \(-4\) \(0\)
160.3.w.a \(128\) \(4.360\) None None \(0\) \(0\) \(0\) \(0\)
160.3.y.a \(184\) \(4.360\) None None \(0\) \(0\) \(-4\) \(0\)
160.3.bb.a \(184\) \(4.360\) None None \(-4\) \(-4\) \(-4\) \(-8\)
160.4.a.a \(1\) \(9.440\) \(\Q\) None None \(0\) \(-2\) \(-5\) \(6\) \(+\) \(q-2q^{3}-5q^{5}+6q^{7}-23q^{9}+60q^{11}+\cdots\)
160.4.a.b \(1\) \(9.440\) \(\Q\) None None \(0\) \(2\) \(-5\) \(-6\) \(-\) \(q+2q^{3}-5q^{5}-6q^{7}-23q^{9}-60q^{11}+\cdots\)
160.4.a.c \(2\) \(9.440\) \(\Q(\sqrt{6}) \) None None \(0\) \(-8\) \(10\) \(-8\) \(-\) \(q+(-4+\beta )q^{3}+5q^{5}+(-4-5\beta )q^{7}+\cdots\)
160.4.a.d \(2\) \(9.440\) \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-10\) \(0\) \(-\) \(q-\beta q^{3}-5q^{5}+7\beta q^{7}-7q^{9}+2\beta q^{11}+\cdots\)
160.4.a.e \(2\) \(9.440\) \(\Q(\sqrt{13}) \) None None \(0\) \(0\) \(-10\) \(0\) \(+\) \(q-\beta q^{3}-5q^{5}-\beta q^{7}+5^{2}q^{9}-6\beta q^{11}+\cdots\)
160.4.a.f \(2\) \(9.440\) \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(10\) \(0\) \(+\) \(q+\beta q^{3}+5q^{5}+3\beta q^{7}+13q^{9}-2\beta q^{11}+\cdots\)
160.4.a.g \(2\) \(9.440\) \(\Q(\sqrt{6}) \) None None \(0\) \(8\) \(10\) \(8\) \(+\) \(q+(4+\beta )q^{3}+5q^{5}+(4-5\beta )q^{7}+(13+\cdots)q^{9}+\cdots\)
160.4.c.a \(2\) \(9.440\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-22\) \(0\) \(q+(-11+i)q^{5}+3^{3}q^{9}-46iq^{13}+\cdots\)
160.4.c.b \(4\) \(9.440\) \(\Q(i, \sqrt{29})\) None None \(0\) \(0\) \(-12\) \(0\) \(q+\beta _{2}q^{3}+(-3+\beta _{1})q^{5}+\beta _{2}q^{7}+11q^{9}+\cdots\)
160.4.c.c \(4\) \(9.440\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+2\beta _{3})q^{3}-5\beta _{2}q^{5}+(-6\beta _{1}+\cdots)q^{7}+\cdots\)
160.4.c.d \(8\) \(9.440\) 8.0.\(\cdots\).22 None None \(0\) \(0\) \(32\) \(0\) \(q+\beta _{1}q^{3}+(4-\beta _{4})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
160.4.d.a \(12\) \(9.440\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-28\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-2+\beta _{4})q^{7}+(-9+\cdots)q^{9}+\cdots\)
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