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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
639.1.d.a \(3\) \(0.319\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-71}) \) None \(1\) \(0\) \(1\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+(1+\beta _{2})q^{8}+\cdots\)
639.1.g.a \(2\) \(0.319\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-71}) \) None \(1\) \(-1\) \(-2\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{5}-q^{6}+q^{8}+\cdots\)
639.1.g.b \(12\) \(0.319\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-71}) \) None \(-1\) \(1\) \(2\) \(0\) \(q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}-\zeta_{42}^{19}q^{3}+\cdots\)
639.2.a.a \(1\) \(5.102\) \(\Q\) None None \(-1\) \(0\) \(-2\) \(2\) \(+\) \(q-q^{2}-q^{4}-2q^{5}+2q^{7}+3q^{8}+2q^{10}+\cdots\)
639.2.a.b \(2\) \(5.102\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(-4\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
639.2.a.c \(2\) \(5.102\) \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(1\) \(-2\) \(+\) \(q-\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}-q^{7}-3q^{8}+\cdots\)
639.2.a.d \(2\) \(5.102\) \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(-1\) \(-6\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}-\beta q^{5}-3q^{7}+\cdots\)
639.2.a.e \(2\) \(5.102\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(-4\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(-2+\cdots)q^{7}+\cdots\)
639.2.a.f \(2\) \(5.102\) \(\Q(\sqrt{5}) \) None None \(3\) \(0\) \(5\) \(-4\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}+(3-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
639.2.a.g \(3\) \(5.102\) 3.3.257.1 None None \(0\) \(0\) \(3\) \(2\) \(-\) \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
639.2.a.h \(3\) \(5.102\) 3.3.257.1 None None \(1\) \(0\) \(-5\) \(2\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2+\beta _{1}+\beta _{2})q^{5}+\cdots\)
639.2.a.i \(4\) \(5.102\) 4.4.2225.1 None None \(-3\) \(0\) \(3\) \(6\) \(-\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
639.2.a.j \(4\) \(5.102\) 4.4.8112.1 None None \(0\) \(0\) \(-8\) \(2\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2-\beta _{1})q^{5}+\cdots\)
639.2.a.k \(4\) \(5.102\) 4.4.8112.1 None None \(0\) \(0\) \(8\) \(2\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots\)
639.2.b.a \(24\) \(5.102\) None None \(0\) \(0\) \(0\) \(0\)
639.2.e.a \(4\) \(5.102\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-3\) \(0\) \(-4\) \(4\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-1-2\beta _{3})q^{3}+\cdots\)
639.2.e.b \(56\) \(5.102\) None None \(-1\) \(-1\) \(-2\) \(11\)
639.2.e.c \(80\) \(5.102\) None None \(2\) \(-1\) \(2\) \(-17\)
639.2.f.a \(4\) \(5.102\) \(\Q(\zeta_{10})\) None None \(-3\) \(0\) \(8\) \(3\) \(q+(-1+\zeta_{10}^{3})q^{2}+(1-\zeta_{10})q^{4}+(3\zeta_{10}+\cdots)q^{5}+\cdots\)
639.2.f.b \(20\) \(5.102\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(-10\) \(-3\) \(q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{13}+\beta _{15}+\cdots)q^{4}+\cdots\)
639.2.f.c \(20\) \(5.102\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(6\) \(0\) \(1\) \(-1\) \(q+\beta _{14}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)
639.2.f.d \(24\) \(5.102\) None None \(-3\) \(0\) \(2\) \(-4\)
639.2.f.e \(48\) \(5.102\) None None \(0\) \(0\) \(0\) \(4\)
639.2.i.a \(28\) \(5.102\) \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\)
639.2.i.b \(112\) \(5.102\) None None \(-6\) \(-2\) \(0\) \(0\)
639.2.j.a \(6\) \(5.102\) \(\Q(\zeta_{14})\) None None \(-3\) \(0\) \(6\) \(-8\) \(q+(\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4})q^{2}+(1-\zeta_{14}^{2}+\cdots)q^{4}+\cdots\)
639.2.j.b \(6\) \(5.102\) \(\Q(\zeta_{14})\) None None \(3\) \(0\) \(-6\) \(-8\) \(q+(-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4})q^{2}+(1+\cdots)q^{4}+\cdots\)
639.2.j.c \(30\) \(5.102\) None None \(3\) \(0\) \(10\) \(-3\)
639.2.j.d \(36\) \(5.102\) None None \(2\) \(0\) \(-2\) \(0\)
639.2.j.e \(36\) \(5.102\) None None \(2\) \(0\) \(2\) \(-4\)
639.2.j.f \(60\) \(5.102\) None None \(0\) \(0\) \(0\) \(20\)
639.2.m.a \(96\) \(5.102\) None None \(0\) \(0\) \(0\) \(0\)
639.2.p.a \(144\) \(5.102\) None None \(0\) \(0\) \(0\) \(0\)
639.2.q.a \(560\) \(5.102\) None None \(-3\) \(-8\) \(-1\) \(-3\)
639.2.r.a \(840\) \(5.102\) None None \(-5\) \(-5\) \(-10\) \(-5\)
639.2.s.a \(560\) \(5.102\) None None \(-9\) \(-8\) \(-15\) \(-5\)
639.2.v.a \(120\) \(5.102\) None None \(22\) \(0\) \(20\) \(-27\)
639.2.v.b \(144\) \(5.102\) None None \(3\) \(0\) \(-2\) \(4\)
639.2.v.c \(144\) \(5.102\) None None \(3\) \(0\) \(2\) \(0\)
639.2.v.d \(288\) \(5.102\) None None \(0\) \(0\) \(0\) \(-4\)
639.2.w.a \(840\) \(5.102\) None None \(-15\) \(-5\) \(-42\) \(-7\)
639.2.z.a \(576\) \(5.102\) None None \(0\) \(0\) \(0\) \(0\)
639.2.bc.a \(3360\) \(5.102\) None None \(-25\) \(-55\) \(-20\) \(-25\)
639.2.bf.a \(3360\) \(5.102\) None None \(-75\) \(-55\) \(-48\) \(-23\)
639.3.c.a \(48\) \(17.411\) None None \(0\) \(0\) \(0\) \(0\)
639.3.d.a \(4\) \(17.411\) 4.0.2836736.1 None None \(4\) \(0\) \(8\) \(0\) \(q+(1+\beta _{1})q^{2}+(-1+2\beta _{1})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
639.3.d.b \(7\) \(17.411\) 7.7.\(\cdots\).1 \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(4+\beta _{3})q^{4}+(\beta _{3}+\beta _{4})q^{5}+\cdots\)
639.3.d.c \(24\) \(17.411\) None None \(-4\) \(0\) \(0\) \(0\)
639.3.d.d \(24\) \(17.411\) None None \(0\) \(0\) \(0\) \(0\)
639.4.a.a \(1\) \(37.702\) \(\Q\) None None \(-5\) \(0\) \(-13\) \(-7\) \(+\) \(q-5q^{2}+17q^{4}-13q^{5}-7q^{7}-45q^{8}+\cdots\)
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