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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
731.1.c.a \(1\) \(0.365\) \(\Q\) \(\Q(\sqrt{-731}) \) None \(0\) \(-1\) \(-1\) \(2\) \(q-q^{3}+q^{4}-q^{5}+2q^{7}-q^{12}-q^{13}+\cdots\)
731.1.c.b \(1\) \(0.365\) \(\Q\) \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-731}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-q^{9}+2q^{13}+q^{16}-q^{17}+\cdots\)
731.1.c.c \(1\) \(0.365\) \(\Q\) \(\Q(\sqrt{-731}) \) None \(0\) \(1\) \(1\) \(-2\) \(q+q^{3}+q^{4}+q^{5}-2q^{7}+q^{12}-q^{13}+\cdots\)
731.1.c.d \(2\) \(0.365\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-731}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}+q^{4}+\beta q^{5}+2q^{9}-\beta q^{12}+\cdots\)
731.1.g.a \(2\) \(0.365\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-43}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-iq^{9}+(-1-i)q^{11}+q^{13}+\cdots\)
731.1.l.a \(4\) \(0.365\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-43}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{2})q^{11}+\cdots\)
731.2.a.a \(1\) \(5.837\) \(\Q\) None None \(1\) \(1\) \(-1\) \(0\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
731.2.a.b \(2\) \(5.837\) \(\Q(\sqrt{17}) \) None None \(-2\) \(1\) \(-1\) \(0\) \(+\) \(q-q^{2}+(1-\beta )q^{3}-q^{4}+(-1+\beta )q^{5}+\cdots\)
731.2.a.c \(6\) \(5.837\) 6.6.2460365.1 None None \(-1\) \(-3\) \(3\) \(-7\) \(+\) \(q+(-\beta _{3}-\beta _{4})q^{2}+(-1+\beta _{4})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
731.2.a.d \(8\) \(5.837\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(-3\) \(-7\) \(-5\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{3}+\beta _{4})q^{3}+(\beta _{2}-\beta _{3})q^{4}+\cdots\)
731.2.a.e \(19\) \(5.837\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(2\) \(5\) \(11\) \(7\) \(-\) \(q+\beta _{1}q^{2}+\beta _{16}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
731.2.a.f \(21\) \(5.837\) None None \(2\) \(-1\) \(-3\) \(5\) \(-\)
731.2.d.a \(2\) \(5.837\) \(\Q(\sqrt{-2}) \) None None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+3q^{9}+\beta q^{10}+\cdots\)
731.2.d.b \(8\) \(5.837\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{7})q^{7}+\cdots\)
731.2.d.c \(20\) \(5.837\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+\beta _{13}q^{3}+(2+\beta _{1})q^{4}+\beta _{10}q^{5}+\cdots\)
731.2.d.d \(34\) \(5.837\) None None \(-6\) \(0\) \(0\) \(0\)
731.2.e.a \(58\) \(5.837\) None None \(-6\) \(3\) \(-1\) \(7\)
731.2.e.b \(58\) \(5.837\) None None \(2\) \(-5\) \(-3\) \(-13\)
731.2.f.a \(2\) \(5.837\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(-4\) \(q-iq^{2}+q^{4}+(-1-i)q^{5}+(-2+2i)q^{7}+\cdots\)
731.2.f.b \(2\) \(5.837\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(0\) \(0\) \(q+iq^{2}+(2+2i)q^{3}+q^{4}+(-2+2i)q^{6}+\cdots\)
731.2.f.c \(56\) \(5.837\) None None \(0\) \(-4\) \(-2\) \(4\)
731.2.f.d \(68\) \(5.837\) None None \(0\) \(0\) \(-4\) \(0\)
731.2.j.a \(128\) \(5.837\) None None \(-4\) \(0\) \(0\) \(0\)
731.2.k.a \(180\) \(5.837\) None None \(-4\) \(-6\) \(-6\) \(66\)
731.2.k.b \(180\) \(5.837\) None None \(0\) \(2\) \(2\) \(-54\)
731.2.m.a \(4\) \(5.837\) \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-8\) \(-4\) \(q+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
731.2.m.b \(116\) \(5.837\) None None \(0\) \(0\) \(0\) \(0\)
731.2.m.c \(128\) \(5.837\) None None \(4\) \(4\) \(8\) \(4\)
731.2.n.a \(256\) \(5.837\) None None \(0\) \(-6\) \(2\) \(0\)
731.2.p.a \(384\) \(5.837\) None None \(-12\) \(0\) \(0\) \(0\)
731.2.s.a \(16\) \(5.837\) 16.0.\(\cdots\).1 \(\Q(\sqrt{-43}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{4}q^{4}-3\beta _{5}q^{9}+(-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{11}+\cdots\)
731.2.s.b \(496\) \(5.837\) None None \(0\) \(0\) \(0\) \(0\)
731.2.u.a \(348\) \(5.837\) None None \(-2\) \(5\) \(3\) \(-71\)
731.2.u.b \(348\) \(5.837\) None None \(6\) \(-3\) \(1\) \(49\)
731.2.v.a \(512\) \(5.837\) None None \(-16\) \(-4\) \(-12\) \(-4\)
731.2.y.a \(768\) \(5.837\) None None \(0\) \(-14\) \(-6\) \(-28\)
731.2.z.a \(768\) \(5.837\) None None \(-24\) \(0\) \(0\) \(0\)
731.2.bd.a \(1024\) \(5.837\) None None \(0\) \(-24\) \(-24\) \(-24\)
731.2.be.a \(1536\) \(5.837\) None None \(-20\) \(-20\) \(-28\) \(-48\)
731.2.bh.a \(1536\) \(5.837\) None None \(0\) \(-22\) \(-30\) \(-14\)
731.2.bj.a \(3072\) \(5.837\) None None \(-56\) \(-56\) \(-56\) \(0\)
731.2.bl.a \(3072\) \(5.837\) None None \(-40\) \(-52\) \(-44\) \(-24\)
731.2.bm.a \(6144\) \(5.837\) None None \(-112\) \(-88\) \(-88\) \(-144\)
731.4.a.a \(35\) \(43.130\) None None \(-4\) \(2\) \(6\) \(-26\) \(-\)
731.4.a.b \(37\) \(43.130\) None None \(-4\) \(-16\) \(-64\) \(-74\) \(-\)
731.4.a.c \(47\) \(43.130\) None None \(4\) \(2\) \(-14\) \(58\) \(+\)
731.4.a.d \(49\) \(43.130\) None None \(4\) \(20\) \(56\) \(66\) \(+\)
731.6.a.a \(63\) \(117.241\) None None \(-8\) \(-55\) \(-271\) \(-433\) \(+\)
731.6.a.b \(65\) \(117.241\) None None \(-8\) \(-1\) \(79\) \(-275\) \(+\)
731.6.a.c \(75\) \(117.241\) None None \(8\) \(53\) \(329\) \(547\) \(-\)
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