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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
77.1.j.a \(4\) \(0.038\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
77.2.a.a \(1\) \(0.615\) \(\Q\) None None \(0\) \(-3\) \(-1\) \(-1\) \(+\) \(q-3q^{3}-2q^{4}-q^{5}-q^{7}+6q^{9}-q^{11}+\cdots\)
77.2.a.b \(1\) \(0.615\) \(\Q\) None None \(0\) \(1\) \(3\) \(1\) \(-\) \(q+q^{3}-2q^{4}+3q^{5}+q^{7}-2q^{9}-q^{11}+\cdots\)
77.2.a.c \(1\) \(0.615\) \(\Q\) None None \(1\) \(2\) \(-2\) \(-1\) \(-\) \(q+q^{2}+2q^{3}-q^{4}-2q^{5}+2q^{6}-q^{7}+\cdots\)
77.2.a.d \(2\) \(0.615\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-4\) \(2\) \(-\) \(q-\beta q^{2}+(1+\beta )q^{3}+3q^{4}-2q^{5}+(-5+\cdots)q^{6}+\cdots\)
77.2.b.a \(2\) \(0.615\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-5q^{4}-\beta q^{7}+3\beta q^{8}+3q^{9}+\cdots\)
77.2.b.b \(4\) \(0.615\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{3}q^{5}+(2\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)
77.2.e.a \(6\) \(0.615\) \(\Q(\zeta_{18})\) None None \(0\) \(-3\) \(-6\) \(0\) \(q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
77.2.e.b \(6\) \(0.615\) 6.0.1783323.2 None None \(0\) \(1\) \(2\) \(2\) \(q+(-\beta _{3}+\beta _{5})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
77.2.f.a \(8\) \(0.615\) 8.0.159390625.1 None None \(-1\) \(-4\) \(3\) \(2\) \(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
77.2.f.b \(16\) \(0.615\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(-2\) \(-5\) \(-4\) \(q+(-\beta _{5}-\beta _{6})q^{2}+(\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots\)
77.2.i.a \(12\) \(0.615\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-6\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{7})q^{2}+(-1+\beta _{2}-\beta _{8}-\beta _{9}+\cdots)q^{3}+\cdots\)
77.2.l.a \(8\) \(0.615\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(1-\beta _{1}+\beta _{3}+\beta _{4}+\beta _{5}-\beta _{6})q^{2}+\cdots\)
77.2.l.b \(16\) \(0.615\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-10\) \(0\) \(0\) \(-10\) \(q+(-1-\beta _{9}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
77.2.m.a \(8\) \(0.615\) \(\Q(\zeta_{15})\) None None \(-2\) \(1\) \(-5\) \(-5\) \(q+(-1+\zeta_{15}^{4}-\zeta_{15}^{5}+\zeta_{15}^{7})q^{2}+\cdots\)
77.2.m.b \(40\) \(0.615\) None None \(-3\) \(-4\) \(4\) \(-2\)
77.2.n.a \(48\) \(0.615\) None None \(-5\) \(-9\) \(-15\) \(-5\)
77.3.c.a \(2\) \(2.098\) \(\Q(\sqrt{-7}) \) None None \(0\) \(4\) \(12\) \(0\) \(q-\beta q^{2}+2q^{3}-3q^{4}+6q^{5}-2\beta q^{6}+\cdots\)
77.3.c.b \(10\) \(2.098\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(2\) \(-18\) \(0\) \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-2+\beta _{7})q^{4}+(-2+\cdots)q^{5}+\cdots\)
77.3.d.a \(12\) \(2.098\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(10\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{3}+\beta _{5})q^{4}+\cdots\)
77.3.g.a \(28\) \(2.098\) None None \(0\) \(-6\) \(0\) \(-2\)
77.3.h.a \(4\) \(2.098\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(0\) \(-10\) \(12\) \(0\) \(q+\beta _{1}q^{2}-5\beta _{2}q^{3}+3\beta _{2}q^{4}+(6-6\beta _{2}+\cdots)q^{5}+\cdots\)
77.3.h.b \(24\) \(2.098\) None None \(0\) \(8\) \(-16\) \(0\)
77.3.j.a \(8\) \(2.098\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) None \(6\) \(0\) \(0\) \(14\) \(q+(-\beta _{2}-\beta _{4}-2\beta _{5}+\beta _{7})q^{2}+(-1+\cdots)q^{4}+\cdots\)
77.3.j.b \(48\) \(2.098\) None None \(-10\) \(0\) \(0\) \(0\)
77.3.k.a \(48\) \(2.098\) None None \(0\) \(-6\) \(6\) \(0\)
77.3.o.a \(112\) \(2.098\) None None \(-5\) \(-3\) \(-1\) \(-25\)
77.3.p.a \(112\) \(2.098\) None None \(-5\) \(-9\) \(-15\) \(-23\)
77.4.a.a \(1\) \(4.543\) \(\Q\) None None \(3\) \(4\) \(12\) \(7\) \(+\) \(q+3q^{2}+4q^{3}+q^{4}+12q^{5}+12q^{6}+\cdots\)
77.4.a.b \(2\) \(4.543\) \(\Q(\sqrt{2}) \) None None \(-2\) \(-4\) \(-4\) \(14\) \(-\) \(q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots\)
77.4.a.c \(4\) \(4.543\) 4.4.509800.1 None None \(-4\) \(-12\) \(-18\) \(-28\) \(-\) \(q+(-1+\beta _{2})q^{2}+(-3+\beta _{3})q^{3}+(6+\cdots)q^{4}+\cdots\)
77.4.a.d \(4\) \(4.543\) 4.4.522072.1 None None \(-2\) \(14\) \(10\) \(-28\) \(+\) \(q+\beta _{2}q^{2}+(4+\beta _{1})q^{3}+(6-\beta _{2}-2\beta _{3})q^{4}+\cdots\)
77.4.a.e \(5\) \(4.543\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(1\) \(2\) \(-24\) \(35\) \(+\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(9+\beta _{1}+\beta _{2})q^{4}+\cdots\)
77.4.b.a \(2\) \(4.543\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+q^{4}-7\beta q^{7}-9\beta q^{8}+3^{3}q^{9}+\cdots\)
77.4.b.b \(20\) \(4.543\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{10}q^{2}+\beta _{11}q^{3}+(-5+\beta _{3})q^{4}+\cdots\)
77.4.e.a \(2\) \(4.543\) \(\Q(\sqrt{-3}) \) None None \(-3\) \(-3\) \(-2\) \(-35\) \(q-3\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
77.4.e.b \(18\) \(4.543\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(3\) \(15\) \(32\) \(-3\) \(q+\beta _{1}q^{2}+(2+\beta _{1}-\beta _{3}-2\beta _{5}+\beta _{7}+\cdots)q^{3}+\cdots\)
77.4.e.c \(20\) \(4.543\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(-10\) \(-30\) \(q-\beta _{4}q^{2}+\beta _{6}q^{3}+(-5+\beta _{3}+5\beta _{5}+\cdots)q^{4}+\cdots\)
77.4.f.a \(32\) \(4.543\) None None \(-2\) \(18\) \(16\) \(-56\)
77.4.f.b \(40\) \(4.543\) None None \(8\) \(-18\) \(-24\) \(70\)
77.4.i.a \(44\) \(4.543\) None None \(0\) \(-6\) \(-30\) \(0\)
77.4.l.a \(8\) \(4.543\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{4}+3\beta _{5}+2\beta _{7})q^{2}+(13+\cdots)q^{4}+\cdots\)
77.4.l.b \(80\) \(4.543\) None None \(-10\) \(0\) \(0\) \(-15\)
77.4.m.a \(176\) \(4.543\) None None \(-1\) \(-3\) \(-11\) \(12\)
77.4.n.a \(176\) \(4.543\) None None \(-5\) \(-9\) \(15\) \(0\)
77.5.c.a \(24\) \(7.959\) None None \(0\) \(-6\) \(6\) \(0\)
77.5.d.a \(28\) \(7.959\) None None \(0\) \(0\) \(0\) \(-50\)
77.5.g.a \(52\) \(7.959\) None None \(0\) \(-18\) \(0\) \(-54\)
77.5.h.a \(60\) \(7.959\) None None \(0\) \(-2\) \(16\) \(0\)
77.5.j.a \(8\) \(7.959\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-98\) \(q+(-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6})q^{2}+(-2^{4}+\cdots)q^{4}+\cdots\)
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