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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1716.1.m.a \(1\) \(0.856\) \(\Q\) \(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-429}) \) \(\Q(\sqrt{3}) \) \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
1716.1.m.b \(1\) \(0.856\) \(\Q\) \(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-429}) \) \(\Q(\sqrt{3}) \) \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
1716.1.m.c \(1\) \(0.856\) \(\Q\) \(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-429}) \) \(\Q(\sqrt{3}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
1716.1.m.d \(1\) \(0.856\) \(\Q\) \(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-429}) \) \(\Q(\sqrt{3}) \) \(1\) \(1\) \(0\) \(0\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
1716.1.m.e \(4\) \(0.856\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-143}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{10}^{2}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots\)
1716.1.m.f \(4\) \(0.856\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-143}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-\zeta_{10}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{2}q^{6}+\cdots\)
1716.1.m.g \(4\) \(0.856\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
1716.1.m.h \(4\) \(0.856\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{3}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
1716.1.m.i \(4\) \(0.856\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-143}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{10}^{2}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots\)
1716.1.m.j \(4\) \(0.856\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-143}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\zeta_{10}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{2}q^{6}+\cdots\)
1716.1.bt.a \(16\) \(0.856\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{40}^{15}q^{2}+\zeta_{40}^{14}q^{3}-\zeta_{40}^{10}q^{4}+\cdots\)
1716.1.bt.b \(16\) \(0.856\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{11}q^{2}+\zeta_{40}^{14}q^{3}-\zeta_{40}^{2}q^{4}+\cdots\)
1716.2.a.a \(1\) \(13.702\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(q-q^{3}-2q^{7}+q^{9}-q^{11}+q^{13}-2q^{17}+\cdots\)
1716.2.a.b \(1\) \(13.702\) \(\Q\) None None \(0\) \(1\) \(-2\) \(-2\) \(+\) \(q+q^{3}-2q^{5}-2q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
1716.2.a.c \(1\) \(13.702\) \(\Q\) None None \(0\) \(1\) \(0\) \(2\) \(-\) \(q+q^{3}+2q^{7}+q^{9}-q^{11}+q^{13}+6q^{17}+\cdots\)
1716.2.a.d \(2\) \(13.702\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(q-q^{3}+(-1+\beta )q^{5}+q^{9}+q^{11}-q^{13}+\cdots\)
1716.2.a.e \(2\) \(13.702\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-4\) \(0\) \(+\) \(q+q^{3}+(-2+\beta )q^{5}-2\beta q^{7}+q^{9}+\cdots\)
1716.2.a.f \(3\) \(13.702\) 3.3.1620.1 None None \(0\) \(-3\) \(0\) \(0\) \(-\) \(q-q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}-q^{11}+\cdots\)
1716.2.a.g \(3\) \(13.702\) 3.3.564.1 None None \(0\) \(3\) \(2\) \(4\) \(-\) \(q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots\)
1716.2.a.h \(3\) \(13.702\) 3.3.404.1 None None \(0\) \(3\) \(4\) \(-4\) \(-\) \(q+q^{3}+(1+2\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
1716.2.a.i \(4\) \(13.702\) 4.4.90996.1 None None \(0\) \(-4\) \(2\) \(2\) \(-\) \(q-q^{3}-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{9}+q^{11}+\cdots\)
1716.2.d.a \(48\) \(13.702\) None None \(0\) \(2\) \(0\) \(0\)
1716.2.e.a \(10\) \(13.702\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(-10\) \(0\) \(0\) \(q-q^{3}-\beta _{8}q^{5}+(-\beta _{8}-\beta _{9})q^{7}+q^{9}+\cdots\)
1716.2.e.b \(10\) \(13.702\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(10\) \(0\) \(0\) \(q+q^{3}-\beta _{6}q^{5}+\beta _{9}q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)
1716.2.p.a \(56\) \(13.702\) None None \(0\) \(0\) \(0\) \(0\)
1716.2.q.a \(2\) \(13.702\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(-2\) \(q+(-1+\zeta_{6})q^{3}+q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1716.2.q.b \(12\) \(13.702\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(-6\) \(0\) \(2\) \(q+\beta _{5}q^{3}-\beta _{3}q^{5}-\beta _{4}q^{7}+(-1-\beta _{5}+\cdots)q^{9}+\cdots\)
1716.2.q.c \(12\) \(13.702\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(6\) \(-6\) \(1\) \(q-\beta _{5}q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+(-1-\beta _{5}+\cdots)q^{9}+\cdots\)
1716.2.q.d \(12\) \(13.702\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(6\) \(2\) \(1\) \(q+(1+\beta _{4})q^{3}-\beta _{9}q^{5}+(\beta _{3}-\beta _{10})q^{7}+\cdots\)
1716.2.q.e \(14\) \(13.702\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(-7\) \(-6\) \(0\) \(q+(-1+\beta _{1})q^{3}-\beta _{9}q^{5}+(-\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots\)
1716.2.v.a \(4\) \(13.702\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(4\) \(-4\) \(q+q^{3}+(1+\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1716.2.v.b \(4\) \(13.702\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(4\) \(4\) \(q+q^{3}+(1+\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1716.2.v.c \(20\) \(13.702\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(20\) \(-12\) \(0\) \(q+q^{3}+(-1+\beta _{6}-\beta _{9})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)
1716.2.v.d \(28\) \(13.702\) None None \(0\) \(-28\) \(4\) \(0\)
1716.2.x.a \(96\) \(13.702\) None None \(0\) \(0\) \(0\) \(-8\)
1716.2.z.a \(4\) \(13.702\) \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(0\) \(2\) \(q-\zeta_{10}^{2}q^{3}+(1-3\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
1716.2.z.b \(4\) \(13.702\) \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(2\) \(-2\) \(q-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
1716.2.z.c \(4\) \(13.702\) \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(4\) \(-6\) \(q-\zeta_{10}^{2}q^{3}+(1+\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
1716.2.z.d \(16\) \(13.702\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(4\) \(-2\) \(1\) \(q+\beta _{10}q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{6}+\beta _{10}+\cdots)q^{5}+\cdots\)
1716.2.z.e \(20\) \(13.702\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(-5\) \(2\) \(-9\) \(q-\beta _{3}q^{3}+\beta _{1}q^{5}+(-1+\beta _{3}-\beta _{6}+\cdots)q^{7}+\cdots\)
1716.2.z.f \(20\) \(13.702\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(5\) \(4\) \(-1\) \(q-\beta _{8}q^{3}+(1-\beta _{4}+\beta _{8}+\beta _{16})q^{5}+\cdots\)
1716.2.z.g \(28\) \(13.702\) None None \(0\) \(-7\) \(-2\) \(-5\)
1716.2.be.a \(20\) \(13.702\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(-10\) \(0\) \(6\) \(q+(-1-\beta _{11})q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
1716.2.be.b \(24\) \(13.702\) None None \(0\) \(12\) \(0\) \(-12\)
1716.3.f.a \(80\) \(46.758\) None None \(0\) \(-2\) \(0\) \(0\)
1716.3.g.a \(56\) \(46.758\) None None \(0\) \(0\) \(0\) \(0\)
1716.3.j.a \(92\) \(46.758\) None None \(0\) \(0\) \(0\) \(0\)
1716.3.k.a \(48\) \(46.758\) None None \(0\) \(0\) \(-8\) \(0\)
1716.3.s.a \(96\) \(46.758\) None None \(0\) \(0\) \(-24\) \(16\)
1716.4.a.a \(1\) \(101.247\) \(\Q\) None None \(0\) \(-3\) \(-9\) \(-25\) \(+\) \(q-3q^{3}-9q^{5}-5^{2}q^{7}+9q^{9}-11q^{11}+\cdots\)
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