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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
65.2.a.a \(1\) \(0.519\) \(\Q\) None \(-1\) \(-2\) \(-1\) \(-4\) \(+\) \(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)
65.2.a.b \(2\) \(0.519\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(4\) \(-\) \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
65.2.a.c \(2\) \(0.519\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(4\) \(-\) \(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}-q^{5}+(-3+\cdots)q^{6}+\cdots\)
65.2.b.a \(6\) \(0.519\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
65.2.c.a \(6\) \(0.519\) 6.0.5089536.1 None \(0\) \(-4\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(-1-\beta _{1})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)
65.2.d.a \(2\) \(0.519\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-2\) \(0\) \(q-q^{2}+iq^{3}-q^{4}+(-1+i)q^{5}-iq^{6}+\cdots\)
65.2.d.b \(2\) \(0.519\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(2\) \(0\) \(q+q^{2}+iq^{3}-q^{4}+(1-i)q^{5}+iq^{6}+\cdots\)
65.2.e.a \(4\) \(0.519\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(0\) \(4\) \(-4\) \(q-\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
65.2.e.b \(4\) \(0.519\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(1\) \(-2\) \(-4\) \(2\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
65.2.f.a \(2\) \(0.519\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(-4\) \(q+iq^{2}+(1-i)q^{3}+q^{4}+(-2-i)q^{5}+\cdots\)
65.2.f.b \(8\) \(0.519\) 8.0.619810816.2 None \(0\) \(-6\) \(-2\) \(0\) \(q-\beta _{6}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
65.2.k.a \(2\) \(0.519\) \(\Q(\sqrt{-1}) \) None \(2\) \(2\) \(-2\) \(0\) \(q+q^{2}+(1+i)q^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
65.2.k.b \(8\) \(0.519\) 8.0.619810816.2 None \(-4\) \(-6\) \(2\) \(0\) \(q+\beta _{5}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
65.2.l.a \(8\) \(0.519\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{3}+\beta _{5})q^{3}+(\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
65.2.m.a \(8\) \(0.519\) 8.0.22581504.2 None \(0\) \(2\) \(0\) \(-6\) \(q+(-1+\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{2}+(\beta _{2}+\cdots)q^{3}+\cdots\)
65.2.n.a \(12\) \(0.519\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{4}-\beta _{11})q^{3}+(-\beta _{2}-\beta _{6}+\cdots)q^{4}+\cdots\)
65.2.o.a \(20\) \(0.519\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-4\) \(-2\) \(-6\) \(-6\) \(q+(-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}+\beta _{4}+\beta _{8}-\beta _{12}+\cdots)q^{3}+\cdots\)
65.2.t.a \(20\) \(0.519\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-6\) \(-2\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
65.3.g.a \(24\) \(1.771\) None \(0\) \(0\) \(-4\) \(0\)
65.3.h.a \(24\) \(1.771\) None \(0\) \(-4\) \(0\) \(0\)
65.3.i.a \(24\) \(1.771\) None \(0\) \(-4\) \(4\) \(-4\)
65.3.j.a \(16\) \(1.771\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(20\) \(q-\beta _{2}q^{2}+\beta _{6}q^{3}+(\beta _{1}-\beta _{2}+\beta _{8}+\beta _{12}+\cdots)q^{4}+\cdots\)
65.3.p.a \(40\) \(1.771\) None \(0\) \(0\) \(0\) \(-40\)
65.3.q.a \(48\) \(1.771\) None \(-6\) \(-2\) \(-16\) \(-2\)
65.3.r.a \(48\) \(1.771\) None \(-6\) \(-2\) \(0\) \(-6\)
65.3.s.a \(48\) \(1.771\) None \(0\) \(0\) \(-2\) \(0\)
65.4.a.a \(1\) \(3.835\) \(\Q\) None \(5\) \(2\) \(-5\) \(-12\) \(+\) \(q+5q^{2}+2q^{3}+17q^{4}-5q^{5}+10q^{6}+\cdots\)
65.4.a.b \(2\) \(3.835\) \(\Q(\sqrt{6}) \) None \(-2\) \(-4\) \(10\) \(-20\) \(-\) \(q+(-1+\beta )q^{2}+(-2-\beta )q^{3}+(-1+\cdots)q^{4}+\cdots\)
65.4.a.c \(2\) \(3.835\) \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(-10\) \(58\) \(+\) \(q+\beta q^{2}+(-2+4\beta )q^{3}+(-4+\beta )q^{4}+\cdots\)
65.4.a.d \(2\) \(3.835\) \(\Q(\sqrt{3}) \) None \(4\) \(-10\) \(-10\) \(-36\) \(-\) \(q+(2+\beta )q^{2}+(-5-3\beta )q^{3}+(-1+4\beta )q^{4}+\cdots\)
65.4.a.e \(5\) \(3.835\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(8\) \(25\) \(38\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{3})q^{3}+(7-\beta _{2}+\cdots)q^{4}+\cdots\)
65.4.b.a \(2\) \(3.835\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+3iq^{2}-4iq^{3}-q^{4}+(2-11i)q^{5}+\cdots\)
65.4.b.b \(16\) \(3.835\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-20\) \(0\) \(q+\beta _{2}q^{2}+\beta _{4}q^{3}+(-4+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
65.4.c.a \(14\) \(3.835\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-4+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
65.4.d.a \(2\) \(3.835\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(10\) \(48\) \(q-q^{2}+iq^{3}-7q^{4}+(5-5i)q^{5}-iq^{6}+\cdots\)
65.4.d.b \(2\) \(3.835\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-10\) \(-48\) \(q+q^{2}+iq^{3}-7q^{4}+(-5+5i)q^{5}+\cdots\)
65.4.d.c \(16\) \(3.835\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}-\beta _{6}q^{3}+(6+\beta _{2})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
65.4.e.a \(14\) \(3.835\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(4\) \(-70\) \(-7\) \(q-\beta _{1}q^{2}+(-\beta _{6}+\beta _{11})q^{3}+(-4-\beta _{5}+\cdots)q^{4}+\cdots\)
65.4.e.b \(14\) \(3.835\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(8\) \(70\) \(75\) \(q+(-\beta _{1}+\beta _{2})q^{2}+(1+\beta _{4}-\beta _{6}-\beta _{11}+\cdots)q^{3}+\cdots\)
65.4.f.a \(2\) \(3.835\) \(\Q(\sqrt{-1}) \) None \(0\) \(-10\) \(20\) \(-52\) \(q+iq^{2}+(-5+5i)q^{3}+7q^{4}+(10+\cdots)q^{5}+\cdots\)
65.4.f.b \(36\) \(3.835\) None \(0\) \(6\) \(-30\) \(48\)
65.4.k.a \(2\) \(3.835\) \(\Q(\sqrt{-1}) \) None \(2\) \(-10\) \(10\) \(0\) \(q+q^{2}+(-5-5i)q^{3}-7q^{4}+(5+10i)q^{5}+\cdots\)
65.4.k.b \(36\) \(3.835\) None \(-2\) \(6\) \(-26\) \(0\)
65.4.l.a \(40\) \(3.835\) None \(0\) \(0\) \(0\) \(0\)
65.4.m.a \(28\) \(3.835\) None \(0\) \(-12\) \(0\) \(-36\)
65.4.n.a \(36\) \(3.835\) None \(0\) \(0\) \(10\) \(0\)
65.4.o.a \(76\) \(3.835\) None \(-6\) \(-2\) \(10\) \(-6\)
65.4.t.a \(76\) \(3.835\) None \(-6\) \(-2\) \(4\) \(-2\)
65.5.g.a \(52\) \(6.719\) None \(0\) \(0\) \(58\) \(0\)
65.5.h.a \(52\) \(6.719\) None \(0\) \(-4\) \(0\) \(0\)
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