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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
712.1.c.a \(1\) \(0.355\) \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-178}) \) \(\Q(\sqrt{89}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{9}-2q^{11}+q^{16}+\cdots\)
712.1.c.b \(2\) \(0.355\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-178}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\beta q^{7}-q^{8}+q^{9}+\beta q^{13}+\cdots\)
712.1.l.a \(2\) \(0.355\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(-2\) \(2\) \(0\) \(0\) \(q-q^{2}+(1-i)q^{3}+q^{4}+(-1+i)q^{6}+\cdots\)
712.1.s.a \(10\) \(0.355\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q-\zeta_{22}^{5}q^{2}+(\zeta_{22}^{4}-\zeta_{22}^{9})q^{3}+\zeta_{22}^{10}q^{4}+\cdots\)
712.1.w.a \(10\) \(0.355\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-2}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\zeta_{22}^{9}q^{2}+(\zeta_{22}^{3}-\zeta_{22}^{5})q^{3}-\zeta_{22}^{7}q^{4}+\cdots\)
712.1.y.a \(20\) \(0.355\) \(\Q(\zeta_{44})\) \(\Q(\sqrt{-2}) \) None \(2\) \(-2\) \(0\) \(0\) \(q-\zeta_{44}^{20}q^{2}+(-\zeta_{44}^{3}+\zeta_{44}^{16})q^{3}+\cdots\)
712.2.a.a \(1\) \(5.685\) \(\Q\) None None \(0\) \(-2\) \(2\) \(-4\) \(-\) \(q-2q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{13}+\cdots\)
712.2.a.b \(3\) \(5.685\) 3.3.148.1 None None \(0\) \(-1\) \(-3\) \(-2\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
712.2.a.c \(5\) \(5.685\) 5.5.758752.1 None None \(0\) \(3\) \(1\) \(2\) \(-\) \(q+(1-\beta _{1})q^{3}+(-\beta _{1}+\beta _{3}+\beta _{4})q^{5}+\cdots\)
712.2.a.d \(6\) \(5.685\) 6.6.20603984.1 None None \(0\) \(-5\) \(-3\) \(-2\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{5})q^{5}+\cdots\)
712.2.a.e \(7\) \(5.685\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(3\) \(3\) \(6\) \(-\) \(q+\beta _{1}q^{3}+\beta _{5}q^{5}+(1+\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
712.2.b.a \(2\) \(5.685\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta q^{2}+\beta q^{3}-2q^{4}+2\beta q^{5}-2q^{6}+\cdots\)
712.2.b.b \(2\) \(5.685\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-\beta q^{3}-2q^{4}-2\beta q^{5}+2q^{6}+\cdots\)
712.2.b.c \(4\) \(5.685\) 4.0.2312.1 None None \(-1\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
712.2.b.d \(36\) \(5.685\) None None \(0\) \(0\) \(0\) \(-16\)
712.2.b.e \(44\) \(5.685\) None None \(-1\) \(0\) \(0\) \(20\)
712.2.e.a \(2\) \(5.685\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(6\) \(0\) \(q+iq^{3}+3q^{5}+4iq^{7}+2q^{9}+4q^{11}+\cdots\)
712.2.e.b \(10\) \(5.685\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{8})q^{7}+\cdots\)
712.2.e.c \(10\) \(5.685\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{8}q^{7}+(-1-\beta _{5}+\cdots)q^{9}+\cdots\)
712.2.f.a \(88\) \(5.685\) None None \(-2\) \(0\) \(0\) \(0\)
712.2.j.a \(2\) \(5.685\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(2\) \(q+(-1-i)q^{3}+(1+i)q^{7}-iq^{9}+4q^{11}+\cdots\)
712.2.j.b \(22\) \(5.685\) None None \(0\) \(-4\) \(0\) \(4\)
712.2.j.c \(22\) \(5.685\) None None \(0\) \(4\) \(0\) \(-6\)
712.2.k.a \(4\) \(5.685\) \(\Q(\zeta_{12})\) None None \(-2\) \(-2\) \(-12\) \(4\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
712.2.k.b \(4\) \(5.685\) \(\Q(\zeta_{12})\) None None \(-2\) \(2\) \(12\) \(4\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}+(\zeta_{12}+\cdots)q^{4}+\cdots\)
712.2.k.c \(168\) \(5.685\) None None \(0\) \(0\) \(0\) \(-12\)
712.2.m.a \(4\) \(5.685\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-8\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+(-2-2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
712.2.m.b \(4\) \(5.685\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
712.2.m.c \(344\) \(5.685\) None None \(-8\) \(0\) \(0\) \(0\)
712.2.q.a \(110\) \(5.685\) None None \(0\) \(0\) \(-2\) \(0\)
712.2.q.b \(110\) \(5.685\) None None \(0\) \(2\) \(2\) \(0\)
712.2.t.a \(880\) \(5.685\) None None \(-9\) \(0\) \(0\) \(-22\)
712.2.u.a \(100\) \(5.685\) None None \(0\) \(0\) \(0\) \(0\)
712.2.u.b \(120\) \(5.685\) None None \(0\) \(0\) \(-4\) \(0\)
712.2.x.a \(880\) \(5.685\) None None \(-9\) \(0\) \(0\) \(-18\)
712.2.z.a \(1760\) \(5.685\) None None \(-18\) \(0\) \(0\) \(-40\)
712.2.ba.a \(220\) \(5.685\) None None \(0\) \(4\) \(0\) \(-4\)
712.2.ba.b \(240\) \(5.685\) None None \(0\) \(-2\) \(0\) \(4\)
712.2.bf.a \(40\) \(5.685\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\)
712.2.bf.b \(40\) \(5.685\) \(\Q(\sqrt{-2}) \) None \(0\) \(8\) \(0\) \(0\)
712.2.bf.c \(3440\) \(5.685\) None None \(-36\) \(-88\) \(0\) \(0\)
712.4.a.a \(14\) \(42.009\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(-3\) \(-17\) \(-28\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+(-2-\beta _{6}+\cdots)q^{7}+\cdots\)
712.4.a.b \(16\) \(42.009\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(15\) \(7\) \(4\) \(+\) \(q+(1-\beta _{1})q^{3}-\beta _{4}q^{5}+\beta _{6}q^{7}+(10+\cdots)q^{9}+\cdots\)
712.4.a.c \(17\) \(42.009\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(0\) \(-9\) \(-13\) \(-24\) \(-\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots\)
712.4.a.d \(19\) \(42.009\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(0\) \(3\) \(23\) \(0\) \(+\) \(q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}-\beta _{3}q^{7}+(12+\cdots)q^{9}+\cdots\)
712.4.e.a \(34\) \(42.009\) None None \(0\) \(0\) \(-16\) \(0\)
712.4.e.b \(34\) \(42.009\) None None \(0\) \(0\) \(-8\) \(0\)
712.6.a.a \(25\) \(114.193\) None None \(0\) \(-9\) \(-131\) \(-48\) \(+\)
712.6.a.b \(27\) \(114.193\) None None \(0\) \(27\) \(81\) \(72\) \(-\)
712.6.a.c \(28\) \(114.193\) None None \(0\) \(-45\) \(-19\) \(-124\) \(+\)
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