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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
531.1.c.a \(1\) \(0.265\) \(\Q\) \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(1\) \(-1\) \(q+q^{4}+q^{5}-q^{7}+q^{16}-2q^{17}-q^{19}+\cdots\)
531.1.g.a \(6\) \(0.265\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots\)
531.2.a.a \(2\) \(4.240\) \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(-2\) \(1\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(1-\beta )q^{7}+\cdots\)
531.2.a.b \(2\) \(4.240\) \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(0\) \(-7\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
531.2.a.c \(2\) \(4.240\) \(\Q(\sqrt{5}) \) None None \(3\) \(0\) \(6\) \(-7\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}+3q^{5}+(-4+\beta )q^{7}+\cdots\)
531.2.a.d \(3\) \(4.240\) 3.3.229.1 None None \(0\) \(0\) \(2\) \(9\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
531.2.a.e \(5\) \(4.240\) 5.5.246832.1 None None \(-3\) \(0\) \(-8\) \(2\) \(+\) \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
531.2.a.f \(5\) \(4.240\) 5.5.138136.1 None None \(0\) \(0\) \(-2\) \(2\) \(-\) \(q+(-\beta _{1}+\beta _{3})q^{2}+(2+\beta _{2}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
531.2.a.g \(5\) \(4.240\) 5.5.246832.1 None None \(3\) \(0\) \(8\) \(2\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
531.2.d.a \(20\) \(4.240\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{12}q^{2}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}-\beta _{4}q^{7}+\cdots\)
531.2.e.a \(4\) \(4.240\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-6\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{6}+\cdots\)
531.2.e.b \(42\) \(4.240\) None None \(0\) \(6\) \(-2\) \(11\)
531.2.e.c \(70\) \(4.240\) None None \(0\) \(0\) \(-2\) \(-11\)
531.2.f.a \(12\) \(4.240\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{3}+2\beta _{5}q^{4}+(\beta _{2}+\beta _{10})q^{5}+\cdots\)
531.2.f.b \(104\) \(4.240\) None None \(0\) \(-4\) \(0\) \(-2\)
531.2.i.a \(112\) \(4.240\) None None \(26\) \(0\) \(25\) \(-23\)
531.2.i.b \(140\) \(4.240\) None None \(-1\) \(0\) \(-2\) \(-2\)
531.2.i.c \(140\) \(4.240\) None None \(1\) \(0\) \(2\) \(-2\)
531.2.i.d \(280\) \(4.240\) None None \(0\) \(0\) \(0\) \(-4\)
531.2.j.a \(560\) \(4.240\) None None \(0\) \(0\) \(0\) \(8\)
531.2.m.a \(3248\) \(4.240\) None None \(-29\) \(-58\) \(-25\) \(-27\)
531.2.p.a \(3248\) \(4.240\) None None \(-87\) \(-54\) \(-87\) \(-27\)
531.3.b.a \(40\) \(14.469\) None None \(0\) \(0\) \(0\) \(16\)
531.3.c.a \(3\) \(14.469\) 3.3.1593.1 \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4q^{4}+(\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
531.3.c.b \(6\) \(14.469\) 6.0.7196038400.1 None None \(0\) \(0\) \(8\) \(6\) \(q+\beta _{1}q^{2}+(-5-\beta _{3}+\beta _{4})q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
531.3.c.c \(20\) \(14.469\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{6}q^{5}-\beta _{12}q^{7}+\cdots\)
531.3.c.d \(20\) \(14.469\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{11}q^{2}+(-2+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)
531.4.a.a \(2\) \(31.330\) \(\Q(\sqrt{17}) \) None None \(-1\) \(0\) \(31\) \(-8\) \(-\) \(q-\beta q^{2}+(-4+\beta )q^{4}+(17-3\beta )q^{5}+\cdots\)
531.4.a.b \(2\) \(31.330\) \(\Q(\sqrt{5}) \) None None \(4\) \(0\) \(-6\) \(-22\) \(-\) \(q+(2+\beta )q^{2}+(1+4\beta )q^{4}+(-3-2\beta )q^{5}+\cdots\)
531.4.a.c \(7\) \(31.330\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(0\) \(2\) \(-59\) \(-\) \(q+\beta _{1}q^{2}+(4+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
531.4.a.d \(7\) \(31.330\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(8\) \(0\) \(28\) \(-59\) \(+\) \(q+(1+\beta _{1})q^{2}+(3+2\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
531.4.a.e \(8\) \(31.330\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-6\) \(0\) \(-42\) \(53\) \(-\) \(q+(-1+\beta _{1})q^{2}+(5-\beta _{1}+\beta _{2})q^{4}+\cdots\)
531.4.a.f \(8\) \(31.330\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-2\) \(0\) \(12\) \(53\) \(+\) \(q-\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(2-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
531.4.a.g \(10\) \(31.330\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-3\) \(0\) \(-15\) \(40\) \(+\) \(q-\beta _{1}q^{2}+(6+\beta _{2})q^{4}+(-2-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
531.4.a.h \(14\) \(31.330\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-6\) \(0\) \(-40\) \(-26\) \(-\) \(q-\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
531.4.a.i \(14\) \(31.330\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(6\) \(0\) \(40\) \(-26\) \(+\) \(q+\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2}+\cdots)q^{5}+\cdots\)
531.4.d.a \(60\) \(31.330\) None None \(0\) \(0\) \(0\) \(24\)
531.5.b.a \(76\) \(54.889\) None None \(0\) \(0\) \(0\) \(-48\)
531.5.c.a \(3\) \(54.889\) 3.3.1593.1 \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2^{4}q^{4}+(2\beta _{1}+9\beta _{2})q^{5}+(7\beta _{1}+15\beta _{2})q^{7}+\cdots\)
531.5.c.b \(16\) \(54.889\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-4\) \(-82\) \(q+\beta _{1}q^{2}+(-12+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
531.5.c.c \(40\) \(54.889\) None None \(0\) \(0\) \(0\) \(80\)
531.5.c.d \(40\) \(54.889\) None None \(0\) \(0\) \(0\) \(80\)
531.6.a.a \(9\) \(85.164\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(9\) \(0\) \(72\) \(-208\) \(+\) \(q+(1-\beta _{1})q^{2}+(7-2\beta _{1}+\beta _{2})q^{4}+(8+\cdots)q^{5}+\cdots\)
531.6.a.b \(11\) \(85.164\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(6\) \(0\) \(192\) \(-371\) \(-\) \(q+(1-\beta _{1})q^{2}+(14-\beta _{1}+\beta _{2})q^{4}+(17+\cdots)q^{5}+\cdots\)
531.6.a.c \(12\) \(85.164\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-22\) \(0\) \(-158\) \(413\) \(+\) \(q+(-2+\beta _{1})q^{2}+(17-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
531.6.a.d \(12\) \(85.164\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(4\) \(0\) \(-36\) \(-411\) \(+\) \(q+\beta _{1}q^{2}+(17+\beta _{2})q^{4}+(-3-\beta _{1}+\cdots)q^{5}+\cdots\)
531.6.a.e \(13\) \(85.164\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(0\) \(0\) \(14\) \(373\) \(-\) \(q-\beta _{1}q^{2}+(19+\beta _{2})q^{4}+(1-\beta _{7})q^{5}+\cdots\)
531.6.a.f \(15\) \(85.164\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(-3\) \(0\) \(-128\) \(282\) \(-\) \(q-\beta _{1}q^{2}+(20+\beta _{2})q^{4}+(-8-\beta _{1}+\cdots)q^{5}+\cdots\)
531.6.a.g \(25\) \(85.164\) None None \(-12\) \(0\) \(-200\) \(-38\) \(+\)
531.6.a.h \(25\) \(85.164\) None None \(12\) \(0\) \(200\) \(-38\) \(-\)
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