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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1143.1.d.a \(1\) \(0.570\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-127}) \) \(\Q(\sqrt{381}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+2q^{13}+q^{16}-2q^{19}+q^{25}+\cdots\)
1143.1.d.b \(2\) \(0.570\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-127}) \) None \(1\) \(0\) \(0\) \(0\) \(q+(1-\beta )q^{2}+(1-\beta )q^{4}+q^{8}+\beta q^{11}+\cdots\)
1143.1.d.c \(4\) \(0.570\) \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-127}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{8}+\cdots\)
1143.1.i.a \(4\) \(0.570\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{11}+(-1+\cdots)q^{13}+\cdots\)
1143.1.l.a \(4\) \(0.570\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{6}+\cdots\)
1143.1.t.a \(2\) \(0.570\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+\zeta_{6}q^{13}+q^{16}+q^{19}+q^{25}+\cdots\)
1143.1.y.a \(6\) \(0.570\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(7\) \(q+\zeta_{14}q^{4}+(1+\zeta_{14}^{5})q^{7}+(-\zeta_{14}+\cdots)q^{13}+\cdots\)
1143.1.bo.a \(12\) \(0.570\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-7\) \(q+\zeta_{42}^{9}q^{4}+(-\zeta_{42}^{7}-\zeta_{42}^{10})q^{7}+\cdots\)
1143.2.a.a \(1\) \(9.127\) \(\Q\) None None \(-2\) \(0\) \(-3\) \(-4\) \(-\) \(q-2q^{2}+2q^{4}-3q^{5}-4q^{7}+6q^{10}+\cdots\)
1143.2.a.b \(1\) \(9.127\) \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) \(+\) \(q-2q^{4}-q^{5}+4q^{11}+q^{13}+4q^{16}+\cdots\)
1143.2.a.c \(1\) \(9.127\) \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) \(+\) \(q-2q^{4}+q^{5}-2q^{7}+4q^{11}-3q^{13}+\cdots\)
1143.2.a.d \(1\) \(9.127\) \(\Q\) None None \(0\) \(0\) \(1\) \(0\) \(+\) \(q-2q^{4}+q^{5}-4q^{11}+q^{13}+4q^{16}+\cdots\)
1143.2.a.e \(3\) \(9.127\) \(\Q(\zeta_{18})^+\) None None \(3\) \(0\) \(6\) \(-3\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
1143.2.a.f \(4\) \(9.127\) \(\Q(\sqrt{3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(-6\) \(+\) \(q+(\beta _{1}+\beta _{3})q^{2}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1143.2.a.g \(5\) \(9.127\) 5.5.246832.1 None None \(-2\) \(0\) \(-1\) \(0\) \(+\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
1143.2.a.h \(5\) \(9.127\) 5.5.81509.1 None None \(1\) \(0\) \(5\) \(0\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1}+\beta _{2}+\beta _{4})q^{5}+\cdots\)
1143.2.a.i \(7\) \(9.127\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-2\) \(0\) \(-8\) \(-3\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
1143.2.a.j \(9\) \(9.127\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(2\) \(0\) \(4\) \(10\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(1-\beta _{8})q^{7}+\cdots\)
1143.2.a.k \(16\) \(9.127\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(10\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+(1+\cdots)q^{7}+\cdots\)
1143.2.c.a \(4\) \(9.127\) \(\Q(\sqrt{-2}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+\beta _{3}q^{5}+\beta _{2}q^{7}-2\beta _{1}q^{11}+\cdots\)
1143.2.c.b \(20\) \(9.127\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) \(\Q(\sqrt{-127}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3}+\cdots)q^{8}+\cdots\)
1143.2.c.c \(20\) \(9.127\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{2}+(-1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)
1143.2.j.a \(88\) \(9.127\) None None \(0\) \(0\) \(0\) \(12\)
1143.3.b.a \(84\) \(31.144\) None None \(0\) \(0\) \(0\) \(0\)
1143.4.a.a \(1\) \(67.439\) \(\Q\) None None \(1\) \(0\) \(15\) \(-25\) \(-\) \(q+q^{2}-7q^{4}+15q^{5}-5^{2}q^{7}-15q^{8}+\cdots\)
1143.4.a.b \(4\) \(67.439\) \(\Q(\sqrt{13}, \sqrt{73})\) None None \(0\) \(0\) \(0\) \(-42\) \(-\) \(q-8q^{4}+\beta _{2}q^{5}+(-11-\beta _{3})q^{7}-\beta _{1}q^{11}+\cdots\)
1143.4.a.c \(11\) \(67.439\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(5\) \(0\) \(10\) \(-51\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
1143.4.a.d \(13\) \(67.439\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(8\) \(0\) \(46\) \(-26\) \(+\) \(q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{8}+\beta _{9})q^{4}+\cdots\)
1143.4.a.e \(16\) \(67.439\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(0\) \(-10\) \(-9\) \(-\) \(q-\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(-1+\beta _{11}+\cdots)q^{5}+\cdots\)
1143.4.a.f \(16\) \(67.439\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(3\) \(0\) \(20\) \(-9\) \(+\) \(q+\beta _{1}q^{2}+(4+\beta _{2})q^{4}+(1+\beta _{13})q^{5}+\cdots\)
1143.4.a.g \(17\) \(67.439\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(-9\) \(0\) \(-69\) \(55\) \(-\) \(q+(-1+\beta _{1})q^{2}+(5+\beta _{2})q^{4}+(-4+\cdots)q^{5}+\cdots\)
1143.4.a.h \(21\) \(67.439\) None None \(-1\) \(0\) \(-20\) \(61\) \(+\)
1143.4.a.i \(22\) \(67.439\) None None \(0\) \(0\) \(0\) \(-10\) \(-\)
1143.4.a.j \(36\) \(67.439\) None None \(0\) \(0\) \(0\) \(60\) \(+\)
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