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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
63.1.d.a \(1\) \(0.031\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(-1\) \(q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots\)
63.2.a.a \(1\) \(0.503\) \(\Q\) None None \(1\) \(0\) \(2\) \(-1\) \(-\) \(q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots\)
63.2.a.b \(2\) \(0.503\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(2\) \(-\) \(q+\beta q^{2}+q^{4}-2\beta q^{5}+q^{7}-\beta q^{8}+\cdots\)
63.2.c.a \(4\) \(0.503\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
63.2.e.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots\)
63.2.e.b \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-2\) \(-5\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)
63.2.f.a \(6\) \(0.503\) \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(-3\) \(-3\) \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
63.2.f.b \(6\) \(0.503\) 6.0.309123.1 None None \(1\) \(-4\) \(5\) \(3\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
63.2.g.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(-2\) \(1\) \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
63.2.g.b \(10\) \(0.503\) 10.0.\(\cdots\).1 None None \(2\) \(2\) \(-8\) \(-1\) \(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
63.2.h.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(1\) \(4\) \(q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots\)
63.2.h.b \(10\) \(0.503\) 10.0.\(\cdots\).1 None None \(-4\) \(-1\) \(4\) \(-4\) \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
63.2.i.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(4\) \(q+(1-2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\cdots\)
63.2.i.b \(10\) \(0.503\) 10.0.\(\cdots\).1 None None \(0\) \(-3\) \(0\) \(-6\) \(q+(-\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots\)
63.2.o.a \(12\) \(0.503\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-6\) \(0\) \(0\) \(-2\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{4}+\beta _{7})q^{4}+\cdots\)
63.2.p.a \(4\) \(0.503\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-\beta _{1}+2\beta _{3})q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots\)
63.2.s.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None None \(-3\) \(-3\) \(-6\) \(-5\) \(q+(-1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
63.2.s.b \(10\) \(0.503\) 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(3\) \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
63.3.b.a \(4\) \(1.717\) \(\Q(\sqrt{-2}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+2\beta _{1}q^{5}+\beta _{2}q^{7}+\cdots\)
63.3.d.a \(1\) \(1.717\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(3\) \(0\) \(0\) \(-7\) \(q+3q^{2}+5q^{4}-7q^{7}+3q^{8}+6q^{11}+\cdots\)
63.3.d.b \(2\) \(1.717\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}-3q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
63.3.d.c \(2\) \(1.717\) \(\Q(\sqrt{7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(14\) \(q+\beta q^{2}+3q^{4}+7q^{7}-\beta q^{8}-8\beta q^{11}+\cdots\)
63.3.j.a \(6\) \(1.717\) 6.0.63369648.1 None None \(0\) \(18\) \(-15\) \(-2\) \(q+(-1-\beta _{4}-\beta _{5})q^{2}+3q^{3}+(-4+\cdots)q^{4}+\cdots\)
63.3.j.b \(22\) \(1.717\) None None \(0\) \(-19\) \(12\) \(0\)
63.3.k.a \(28\) \(1.717\) None None \(1\) \(-3\) \(0\) \(0\)
63.3.l.a \(28\) \(1.717\) None None \(-2\) \(0\) \(0\) \(0\)
63.3.m.a \(2\) \(1.717\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(6\) \(-7\) \(q-2\zeta_{6}q^{2}+(4-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots\)
63.3.m.b \(2\) \(1.717\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(13\) \(q+(4-4\zeta_{6})q^{4}+(8-3\zeta_{6})q^{7}+(-7+\cdots)q^{13}+\cdots\)
63.3.m.c \(2\) \(1.717\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(9\) \(-7\) \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{4}+(6-3\zeta_{6})q^{5}+\cdots\)
63.3.m.d \(2\) \(1.717\) \(\Q(\sqrt{-3}) \) None None \(3\) \(0\) \(-9\) \(13\) \(q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}+(-6+3\zeta_{6})q^{5}+\cdots\)
63.3.m.e \(4\) \(1.717\) \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(-26\) \(q-\beta _{2}q^{2}+(-9+9\beta _{1})q^{4}+(\beta _{2}+2\beta _{3})q^{5}+\cdots\)
63.3.n.a \(6\) \(1.717\) 6.0.63369648.1 None None \(3\) \(-9\) \(0\) \(-5\) \(q+(1+\beta _{5})q^{2}+3\beta _{2}q^{3}+(\beta _{1}-4\beta _{2}+\cdots)q^{4}+\cdots\)
63.3.n.b \(22\) \(1.717\) None None \(-6\) \(8\) \(0\) \(3\)
63.3.q.a \(12\) \(1.717\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-3\beta _{8}+\beta _{9})q^{4}-\beta _{6}q^{5}+\cdots\)
63.3.r.a \(24\) \(1.717\) None None \(0\) \(2\) \(-18\) \(0\)
63.3.t.a \(28\) \(1.717\) None None \(-2\) \(-3\) \(-3\) \(0\)
63.4.a.a \(1\) \(3.717\) \(\Q\) None None \(-4\) \(0\) \(4\) \(-7\) \(-\) \(q-4q^{2}+8q^{4}+4q^{5}-7q^{7}-2^{4}q^{10}+\cdots\)
63.4.a.b \(1\) \(3.717\) \(\Q\) None None \(1\) \(0\) \(-16\) \(-7\) \(-\) \(q+q^{2}-7q^{4}-2^{4}q^{5}-7q^{7}-15q^{8}+\cdots\)
63.4.a.c \(1\) \(3.717\) \(\Q\) None None \(3\) \(0\) \(18\) \(7\) \(+\) \(q+3q^{2}+q^{4}+18q^{5}+7q^{7}-21q^{8}+\cdots\)
63.4.a.d \(2\) \(3.717\) \(\Q(\sqrt{19}) \) None None \(0\) \(0\) \(0\) \(-14\) \(+\) \(q+\beta q^{2}+11q^{4}+2\beta q^{5}-7q^{7}+3\beta q^{8}+\cdots\)
63.4.a.e \(2\) \(3.717\) \(\Q(\sqrt{57}) \) None None \(3\) \(0\) \(-6\) \(14\) \(+\) \(q+(1+\beta )q^{2}+(7+3\beta )q^{4}+(-2-2\beta )q^{5}+\cdots\)
63.4.c.a \(4\) \(3.717\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-8-5\beta _{3})q^{4}-7\beta _{3}q^{7}+\cdots\)
63.4.c.b \(4\) \(3.717\) \(\Q(\sqrt{-2}, \sqrt{111})\) None None \(0\) \(0\) \(0\) \(-44\) \(q+2\beta _{1}q^{2}+\beta _{3}q^{5}+(-11-\beta _{2})q^{7}+\cdots\)
63.4.e.a \(2\) \(3.717\) \(\Q(\sqrt{-3}) \) None None \(-3\) \(0\) \(-3\) \(-7\) \(q+(-3+3\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
63.4.e.b \(2\) \(3.717\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(7\) \(28\) \(q+(2-2\zeta_{6})q^{2}+4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots\)
63.4.e.c \(6\) \(3.717\) 6.0.9924270768.1 None None \(1\) \(0\) \(11\) \(-13\) \(q+\beta _{1}q^{2}+(-8+\beta _{1}+\beta _{2}+8\beta _{4}+\beta _{5})q^{4}+\cdots\)
63.4.e.d \(8\) \(3.717\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(-12\) \(q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{2}-\beta _{6})q^{4}+\cdots\)
63.4.f.a \(2\) \(3.717\) \(\Q(\sqrt{-3}) \) None None \(1\) \(-9\) \(14\) \(7\) \(q+\zeta_{6}q^{2}+(-6+3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
63.4.f.b \(16\) \(3.717\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(2\) \(-30\) \(56\) \(q-\beta _{1}q^{2}+(-\beta _{3}-\beta _{7})q^{3}+(5\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
63.4.f.c \(18\) \(3.717\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(6\) \(9\) \(24\) \(-63\) \(q+(1-\beta _{2}-\beta _{3}-\beta _{5})q^{2}+(1+\beta _{8})q^{3}+\cdots\)
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