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Results (45 matches)

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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
471.1.d.a \(1\) \(0.235\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-471}) \) \(\Q(\sqrt{157}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}-q^{4}+q^{9}-q^{12}+2q^{13}+q^{16}+\cdots\)
471.1.d.b \(2\) \(0.235\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-471}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\beta q^{2}+q^{3}+q^{4}+\beta q^{5}-\beta q^{6}+q^{9}+\cdots\)
471.1.d.c \(4\) \(0.235\) \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-471}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
471.1.n.a \(12\) \(0.235\) \(\Q(\zeta_{26})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{26}^{2}q^{3}+\zeta_{26}^{11}q^{4}+(\zeta_{26}^{5}+\zeta_{26}^{12}+\cdots)q^{7}+\cdots\)
471.1.o.a \(12\) \(0.235\) \(\Q(\zeta_{26})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{26}^{3}q^{3}+\zeta_{26}^{10}q^{4}+(-\zeta_{26}-\zeta_{26}^{5}+\cdots)q^{7}+\cdots\)
471.2.a.a \(1\) \(3.761\) \(\Q\) None None \(-1\) \(-1\) \(-2\) \(3\) \(+\) \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{7}+\cdots\)
471.2.a.b \(2\) \(3.761\) \(\Q(\sqrt{5}) \) None None \(-1\) \(2\) \(-2\) \(-6\) \(+\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
471.2.a.c \(3\) \(3.761\) 3.3.229.1 None None \(0\) \(-3\) \(-2\) \(-3\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
471.2.a.d \(9\) \(3.761\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(2\) \(-9\) \(8\) \(-2\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots\)
471.2.a.e \(12\) \(3.761\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-1\) \(12\) \(4\) \(8\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
471.2.b.a \(12\) \(3.761\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(-12\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
471.2.b.b \(14\) \(3.761\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(14\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
471.2.e.a \(4\) \(3.761\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(2\) \(0\) \(-8\) \(q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-2\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)
471.2.e.b \(22\) \(3.761\) None None \(2\) \(11\) \(-4\) \(4\)
471.2.e.c \(28\) \(3.761\) None None \(2\) \(-14\) \(-2\) \(4\)
471.2.f.a \(100\) \(3.761\) None None \(0\) \(0\) \(0\) \(-12\)
471.2.h.a \(24\) \(3.761\) None None \(0\) \(12\) \(0\) \(0\)
471.2.h.b \(26\) \(3.761\) None None \(0\) \(-13\) \(-6\) \(0\)
471.2.l.a \(4\) \(3.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(6\) \(0\) \(-8\) \(q+(2-\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{4}+(-3+\cdots)q^{7}+\cdots\)
471.2.l.b \(200\) \(3.761\) None None \(0\) \(-6\) \(0\) \(0\)
471.2.m.a \(156\) \(3.761\) None None \(-1\) \(13\) \(-4\) \(2\)
471.2.m.b \(180\) \(3.761\) None None \(-1\) \(-15\) \(-8\) \(-10\)
471.2.p.a \(144\) \(3.761\) None None \(0\) \(12\) \(0\) \(0\)
471.2.p.b \(168\) \(3.761\) None None \(0\) \(-14\) \(0\) \(0\)
471.2.q.a \(312\) \(3.761\) None None \(-2\) \(-13\) \(4\) \(4\)
471.2.q.b \(336\) \(3.761\) None None \(-2\) \(14\) \(2\) \(-4\)
471.2.s.a \(1200\) \(3.761\) None None \(0\) \(-26\) \(0\) \(-40\)
471.2.v.a \(288\) \(3.761\) None None \(0\) \(-12\) \(0\) \(0\)
471.2.v.b \(312\) \(3.761\) None None \(0\) \(13\) \(6\) \(0\)
471.2.w.a \(48\) \(3.761\) \(\Q(\sqrt{-3}) \) None \(0\) \(-6\) \(0\) \(8\)
471.2.w.b \(2400\) \(3.761\) None None \(0\) \(-46\) \(0\) \(-104\)
471.4.a.a \(14\) \(27.790\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-2\) \(42\) \(-32\) \(-60\) \(-\) \(q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
471.4.a.b \(17\) \(27.790\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(-2\) \(-51\) \(-28\) \(10\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
471.4.a.c \(22\) \(27.790\) None None \(4\) \(-66\) \(32\) \(-4\) \(+\)
471.4.a.d \(25\) \(27.790\) None None \(4\) \(75\) \(28\) \(94\) \(+\)
471.4.b.a \(40\) \(27.790\) None None \(0\) \(-120\) \(0\) \(0\)
471.4.b.b \(40\) \(27.790\) None None \(0\) \(120\) \(0\) \(0\)
471.6.a.a \(27\) \(75.541\) None None \(-2\) \(243\) \(-164\) \(-618\) \(+\)
471.6.a.b \(30\) \(75.541\) None None \(-8\) \(-270\) \(-136\) \(68\) \(+\)
471.6.a.c \(35\) \(75.541\) None None \(4\) \(-315\) \(164\) \(-30\) \(-\)
471.6.a.d \(38\) \(75.541\) None None \(10\) \(342\) \(136\) \(460\) \(-\)
471.8.a.a \(40\) \(147.133\) None None \(-16\) \(1080\) \(-428\) \(-3424\) \(-\)
471.8.a.b \(43\) \(147.133\) None None \(-22\) \(-1161\) \(-1072\) \(6\) \(-\)
471.8.a.c \(48\) \(147.133\) None None \(2\) \(-1296\) \(428\) \(-680\) \(+\)
471.8.a.d \(51\) \(147.133\) None None \(8\) \(1377\) \(1072\) \(4122\) \(+\)
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