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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
80.1.h.a \(1\) \(0.040\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots\)
80.2.a.a \(1\) \(0.639\) \(\Q\) None None \(0\) \(0\) \(1\) \(4\) \(-\) \(q+q^{5}+4q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots\)
80.2.a.b \(1\) \(0.639\) \(\Q\) None None \(0\) \(2\) \(-1\) \(-2\) \(-\) \(q+2q^{3}-q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
80.2.c.a \(2\) \(0.639\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1+i)q^{5}-iq^{7}-q^{9}+\cdots\)
80.2.j.a \(2\) \(0.639\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(2\) \(-6\) \(q+(1-i)q^{2}+2iq^{3}-2iq^{4}+(1+2i)q^{5}+\cdots\)
80.2.j.b \(18\) \(0.639\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(-4\) \(0\) \(-4\) \(2\) \(q+\beta _{6}q^{2}-\beta _{16}q^{3}-\beta _{13}q^{4}+(-1+\cdots)q^{5}+\cdots\)
80.2.l.a \(16\) \(0.639\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}+(\beta _{3}-\beta _{6}+\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
80.2.n.a \(2\) \(0.639\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}-3iq^{9}+(-5+5i)q^{13}+\cdots\)
80.2.n.b \(4\) \(0.639\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{12}^{2}q^{3}+(-1-2\zeta_{12})q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
80.2.q.a \(2\) \(0.639\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(2\) \(2\) \(0\) \(q+(-1-i)q^{2}+(1+i)q^{3}+2iq^{4}+\cdots\)
80.2.q.b \(2\) \(0.639\) \(\Q(\sqrt{-1}) \) None None \(2\) \(-2\) \(4\) \(0\) \(q+(1+i)q^{2}+(-1-i)q^{3}+2iq^{4}+\cdots\)
80.2.q.c \(16\) \(0.639\) 16.0.\(\cdots\).1 None None \(0\) \(0\) \(-8\) \(0\) \(q-\beta _{12}q^{2}+(-\beta _{3}-\beta _{11}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
80.2.s.a \(2\) \(0.639\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(-4\) \(-4\) \(-6\) \(q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
80.2.s.b \(18\) \(0.639\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(2\) \(2\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{13}q^{4}+\beta _{17}q^{5}+\cdots\)
80.3.b.a \(4\) \(2.180\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+(-9+6\beta _{1}+\cdots)q^{9}+\cdots\)
80.3.h.a \(2\) \(2.180\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(10\) \(0\) \(q-\beta q^{3}+5q^{5}+3\beta q^{7}+11q^{9}-5\beta q^{15}+\cdots\)
80.3.h.b \(4\) \(2.180\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+3\beta _{1}q^{7}+\cdots\)
80.3.i.a \(44\) \(2.180\) None None \(-2\) \(0\) \(-2\) \(0\)
80.3.k.a \(44\) \(2.180\) None None \(0\) \(0\) \(-2\) \(0\)
80.3.p.a \(2\) \(2.180\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-6\) \(14\) \(q+(-1+i)q^{3}+(-3+4i)q^{5}+(7+7i)q^{7}+\cdots\)
80.3.p.b \(2\) \(2.180\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(10\) \(6\) \(q+(-1+i)q^{3}+5q^{5}+(3+3i)q^{7}+\cdots\)
80.3.p.c \(2\) \(2.180\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(0\) \(-4\) \(q+(2-2i)q^{3}-5iq^{5}+(-2-2i)q^{7}+\cdots\)
80.3.p.d \(4\) \(2.180\) \(\Q(i, \sqrt{41})\) None None \(0\) \(2\) \(-6\) \(-14\) \(q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
80.3.r.a \(32\) \(2.180\) None None \(0\) \(0\) \(0\) \(0\)
80.3.t.a \(44\) \(2.180\) None None \(-2\) \(-4\) \(-2\) \(0\)
80.4.a.a \(1\) \(4.720\) \(\Q\) None None \(0\) \(-10\) \(-5\) \(18\) \(+\) \(q-10q^{3}-5q^{5}+18q^{7}+73q^{9}+2^{4}q^{11}+\cdots\)
80.4.a.b \(1\) \(4.720\) \(\Q\) None None \(0\) \(-4\) \(5\) \(-16\) \(-\) \(q-4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-6^{2}q^{11}+\cdots\)
80.4.a.c \(1\) \(4.720\) \(\Q\) None None \(0\) \(-4\) \(5\) \(16\) \(+\) \(q-4q^{3}+5q^{5}+2^{4}q^{7}-11q^{9}+60q^{11}+\cdots\)
80.4.a.d \(1\) \(4.720\) \(\Q\) None None \(0\) \(-2\) \(-5\) \(-6\) \(-\) \(q-2q^{3}-5q^{5}-6q^{7}-23q^{9}-2^{5}q^{11}+\cdots\)
80.4.a.e \(1\) \(4.720\) \(\Q\) None None \(0\) \(6\) \(-5\) \(34\) \(+\) \(q+6q^{3}-5q^{5}+34q^{7}+9q^{9}-2^{4}q^{11}+\cdots\)
80.4.a.f \(1\) \(4.720\) \(\Q\) None None \(0\) \(8\) \(5\) \(4\) \(+\) \(q+8q^{3}+5q^{5}+4q^{7}+37q^{9}-12q^{11}+\cdots\)
80.4.c.a \(2\) \(4.720\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-10\) \(0\) \(q+iq^{3}+(-5-5i)q^{5}-13iq^{7}+23q^{9}+\cdots\)
80.4.c.b \(2\) \(4.720\) \(\Q(\sqrt{-19}) \) None None \(0\) \(0\) \(14\) \(0\) \(q-\beta q^{3}+(7-\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)
80.4.c.c \(4\) \(4.720\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
80.4.j.a \(68\) \(4.720\) None None \(-2\) \(0\) \(-2\) \(-4\)
80.4.l.a \(48\) \(4.720\) None None \(0\) \(0\) \(0\) \(0\)
80.4.n.a \(2\) \(4.720\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2-11i)q^{5}-3^{3}iq^{9}+(55-55i)q^{13}+\cdots\)
80.4.n.b \(4\) \(4.720\) \(\Q(i, \sqrt{35})\) None None \(0\) \(0\) \(-20\) \(0\) \(q-\beta _{2}q^{3}+(-5+10\beta _{1})q^{5}+\beta _{3}q^{7}+\cdots\)
80.4.n.c \(12\) \(4.720\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(16\) \(0\) \(q-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+(-2\beta _{2}+\cdots)q^{7}+\cdots\)
80.4.q.a \(68\) \(4.720\) None None \(0\) \(0\) \(-2\) \(0\)
80.4.s.a \(68\) \(4.720\) None None \(-2\) \(-4\) \(-2\) \(-4\)
80.5.b.a \(4\) \(8.270\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-9-6\beta _{2}+\cdots)q^{9}+\cdots\)
80.5.b.b \(4\) \(8.270\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-5\beta _{1}q^{5}+(2\beta _{2}+7\beta _{3})q^{7}+\cdots\)
80.5.h.a \(2\) \(8.270\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-50\) \(0\) \(q-\beta q^{3}-5^{2}q^{5}-3\beta q^{7}+239q^{9}+\cdots\)
80.5.h.b \(2\) \(8.270\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(14\) \(0\) \(q+(7+i)q^{5}-3^{4}q^{9}+10iq^{13}+20iq^{17}+\cdots\)
80.5.h.c \(8\) \(8.270\) 8.0.\(\cdots\).10 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+\beta _{4}q^{5}+(2\beta _{3}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
80.5.i.a \(92\) \(8.270\) None None \(-2\) \(0\) \(-2\) \(0\)
80.5.k.a \(92\) \(8.270\) None None \(0\) \(0\) \(-2\) \(0\)
80.5.p.a \(2\) \(8.270\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-20\) \(40\) \(84\) \(q+(-10+10i)q^{3}+(20+15i)q^{5}+\cdots\)
80.5.p.b \(2\) \(8.270\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-18\) \(-30\) \(-58\) \(q+(-9+9i)q^{3}+(-15+20i)q^{5}+\cdots\)
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