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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
117.1.j.a \(2\) \(0.058\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots\)
117.2.a.a \(1\) \(0.934\) \(\Q\) None None \(-1\) \(0\) \(-2\) \(-4\) \(+\) \(q-q^{2}-q^{4}-2q^{5}-4q^{7}+3q^{8}+2q^{10}+\cdots\)
117.2.a.b \(2\) \(0.934\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+\beta q^{2}+q^{4}+2q^{7}-\beta q^{8}-2\beta q^{11}+\cdots\)
117.2.a.c \(2\) \(0.934\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(0\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{5}-2\beta q^{7}+\cdots\)
117.2.b.a \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{2}-q^{4}-2\zeta_{6}q^{7}-\zeta_{6}q^{8}+2\zeta_{6}q^{11}+\cdots\)
117.2.b.b \(4\) \(0.934\) 4.0.8112.1 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}-\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)
117.2.e.a \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(-3\) \(-4\) \(-2\) \(q+(-2+2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
117.2.e.b \(10\) \(0.934\) 10.0.\(\cdots\).1 None None \(-2\) \(1\) \(-1\) \(2\) \(q-\beta _{9}q^{2}+(\beta _{1}-\beta _{5}+\beta _{9})q^{3}+(\beta _{1}-\beta _{6}+\cdots)q^{4}+\cdots\)
117.2.e.c \(12\) \(0.934\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(2\) \(-2\) \(3\) \(0\) \(q+(\beta _{3}-\beta _{7}-\beta _{8}+\beta _{10}-\beta _{11})q^{2}+\cdots\)
117.2.f.a \(24\) \(0.934\) None None \(1\) \(-1\) \(-2\) \(-6\)
117.2.g.a \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+2\zeta_{6}q^{4}+\zeta_{6}q^{7}+(4-3\zeta_{6})q^{13}+\cdots\)
117.2.g.b \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(2\) \(-2\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots\)
117.2.g.c \(4\) \(0.934\) \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(1\) \(0\) \(6\) \(3\) \(q+\beta _{1}q^{2}+(-2+\beta _{1}+2\beta _{2}+\beta _{3})q^{4}+\cdots\)
117.2.h.a \(24\) \(0.934\) None None \(-2\) \(-1\) \(-2\) \(3\)
117.2.i.a \(12\) \(0.934\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{9}q^{2}+(\beta _{3}-2\beta _{4})q^{4}-\beta _{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
117.2.l.a \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(3\) \(q+(1-2\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+\cdots\)
117.2.l.b \(22\) \(0.934\) None None \(0\) \(-1\) \(-3\) \(-6\)
117.2.q.a \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-3\) \(q-2\zeta_{6}q^{4}+(2-4\zeta_{6})q^{5}+(-2+\zeta_{6})q^{7}+\cdots\)
117.2.q.b \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(9\) \(q-2\zeta_{6}q^{4}+(6-3\zeta_{6})q^{7}+(-4+3\zeta_{6})q^{13}+\cdots\)
117.2.q.c \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) None None \(3\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+(-1+2\zeta_{6})q^{5}+\cdots\)
117.2.q.d \(4\) \(0.934\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-12\) \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}-\beta _{3}q^{5}+(-4+2\beta _{2}+\cdots)q^{7}+\cdots\)
117.2.r.a \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) None None \(-3\) \(-3\) \(-3\) \(0\) \(q+(-2+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
117.2.r.b \(22\) \(0.934\) None None \(0\) \(2\) \(3\) \(0\)
117.2.t.a \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-6\) \(-6\) \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-2+\cdots)q^{5}+\cdots\)
117.2.t.b \(2\) \(0.934\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(6\) \(6\) \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots\)
117.2.t.c \(20\) \(0.934\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(2\) \(0\) \(0\) \(q-\beta _{17}q^{2}+\beta _{10}q^{3}+(1-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots\)
117.2.x.a \(48\) \(0.934\) None None \(-6\) \(-2\) \(-6\) \(-4\)
117.2.z.a \(4\) \(0.934\) \(\Q(\zeta_{12})\) None None \(-6\) \(-6\) \(-6\) \(-4\) \(q+(-1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{2}+\cdots\)
117.2.z.b \(44\) \(0.934\) None None \(0\) \(-2\) \(0\) \(0\)
117.2.ba.a \(8\) \(0.934\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+(\zeta_{24}^{4}-\zeta_{24}^{5})q^{2}-2\zeta_{24}q^{4}+(\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
117.2.ba.b \(8\) \(0.934\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{24}^{7}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}+2\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
117.2.bc.a \(48\) \(0.934\) None None \(-6\) \(-2\) \(-6\) \(2\)
117.3.c.a \(8\) \(3.188\) 8.0.\(\cdots\).15 None None \(0\) \(0\) \(0\) \(-16\) \(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
117.3.d.a \(8\) \(3.188\) 8.0.\(\cdots\).5 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}-\beta _{4}q^{7}+\cdots\)
117.3.j.a \(4\) \(3.188\) \(\Q(i, \sqrt{10})\) None None \(4\) \(0\) \(-8\) \(-12\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+3\beta _{2}+2\beta _{3})q^{4}+\cdots\)
117.3.j.b \(8\) \(3.188\) 8.0.\(\cdots\).10 None None \(-4\) \(0\) \(20\) \(8\) \(q+\beta _{4}q^{2}+(-1-\beta _{1}-\beta _{4}-\beta _{7})q^{4}+\cdots\)
117.3.j.c \(8\) \(3.188\) 8.0.897122304.10 None None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{2}q^{2}+(\beta _{3}+\beta _{7})q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots\)
117.3.k.a \(52\) \(3.188\) None None \(0\) \(-1\) \(-6\) \(-1\)
117.3.m.a \(52\) \(3.188\) None None \(-3\) \(-1\) \(0\) \(0\)
117.3.n.a \(52\) \(3.188\) None None \(0\) \(-4\) \(0\) \(0\)
117.3.o.a \(20\) \(3.188\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(42\) \(q+\beta _{1}q^{2}+(-2\beta _{5}+\beta _{10})q^{4}+(\beta _{12}+\cdots)q^{5}+\cdots\)
117.3.p.a \(20\) \(3.188\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(-6\) \(q-\beta _{5}q^{2}+(2\beta _{3}-\beta _{4})q^{4}+(\beta _{8}-\beta _{15}+\cdots)q^{5}+\cdots\)
117.3.s.a \(48\) \(3.188\) None None \(0\) \(2\) \(-18\) \(0\)
117.3.u.a \(52\) \(3.188\) None None \(-3\) \(-1\) \(-6\) \(2\)
117.3.v.a \(52\) \(3.188\) None None \(-6\) \(-1\) \(0\) \(-3\)
117.3.w.a \(104\) \(3.188\) None None \(-2\) \(-2\) \(-2\) \(0\)
117.3.y.a \(104\) \(3.188\) None None \(-2\) \(-8\) \(-2\) \(0\)
117.3.bb.a \(104\) \(3.188\) None None \(-2\) \(-2\) \(-2\) \(-6\)
117.3.bd.a \(4\) \(3.188\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-22\) \(q-4\zeta_{12}q^{4}+(-8-8\zeta_{12}+5\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
117.3.bd.b \(4\) \(3.188\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(14\) \(16\) \(q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1-2\zeta_{12}+\cdots)q^{4}+\cdots\)
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