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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
640.1.e.a \(1\) \(0.319\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}+q^{9}+2q^{13}+q^{25}-2q^{37}+\cdots\)
640.1.e.b \(1\) \(0.319\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{5}+q^{9}-2q^{13}+q^{25}+2q^{37}+\cdots\)
640.1.e.c \(4\) \(0.319\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
640.1.m.a \(2\) \(0.319\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}-iq^{9}+(-1-i)q^{13}+(1+i+\cdots)q^{17}+\cdots\)
640.1.m.b \(2\) \(0.319\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}-iq^{9}+(1+i)q^{13}+(1+i+\cdots)q^{17}+\cdots\)
640.2.a.a \(1\) \(5.110\) \(\Q\) None None \(0\) \(-2\) \(-1\) \(0\) \(-\) \(q-2q^{3}-q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
640.2.a.b \(1\) \(5.110\) \(\Q\) None None \(0\) \(-2\) \(1\) \(0\) \(+\) \(q-2q^{3}+q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
640.2.a.c \(1\) \(5.110\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(q-q^{5}-2q^{7}-3q^{9}+6q^{11}-2q^{13}+\cdots\)
640.2.a.d \(1\) \(5.110\) \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) \(+\) \(q-q^{5}+2q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots\)
640.2.a.e \(1\) \(5.110\) \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) \(+\) \(q+q^{5}-2q^{7}-3q^{9}-6q^{11}+2q^{13}+\cdots\)
640.2.a.f \(1\) \(5.110\) \(\Q\) None None \(0\) \(0\) \(1\) \(2\) \(-\) \(q+q^{5}+2q^{7}-3q^{9}+6q^{11}+2q^{13}+\cdots\)
640.2.a.g \(1\) \(5.110\) \(\Q\) None None \(0\) \(2\) \(-1\) \(0\) \(-\) \(q+2q^{3}-q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
640.2.a.h \(1\) \(5.110\) \(\Q\) None None \(0\) \(2\) \(1\) \(0\) \(-\) \(q+2q^{3}+q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
640.2.a.i \(2\) \(5.110\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(q+(-1-\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+\cdots\)
640.2.a.j \(2\) \(5.110\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(2\) \(2\) \(-\) \(q+(-1-\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
640.2.a.k \(2\) \(5.110\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-2\) \(2\) \(-\) \(q+(1+\beta )q^{3}-q^{5}+(1-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
640.2.a.l \(2\) \(5.110\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(2\) \(-2\) \(-\) \(q+(1+\beta )q^{3}+q^{5}+(-1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
640.2.c.a \(6\) \(5.110\) 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{5})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
640.2.c.b \(6\) \(5.110\) 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
640.2.c.c \(6\) \(5.110\) 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
640.2.c.d \(6\) \(5.110\) 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
640.2.d.a \(4\) \(5.110\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}-7q^{9}-6\beta _{1}q^{13}+\cdots\)
640.2.d.b \(4\) \(5.110\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}+3\zeta_{8}^{3}q^{7}+q^{9}+\cdots\)
640.2.d.c \(4\) \(5.110\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+q^{9}+\cdots\)
640.2.d.d \(4\) \(5.110\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}-3\zeta_{8}^{3}q^{7}+q^{9}+\cdots\)
640.2.f.a \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+i)q^{5}-3q^{9}-6q^{13}-4iq^{17}+\cdots\)
640.2.f.b \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}-3q^{9}+6q^{13}+4iq^{17}+\cdots\)
640.2.f.c \(4\) \(5.110\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(-8\) \(0\) \(q-\beta _{3}q^{3}+(-2-\beta _{1})q^{5}+\beta _{2}q^{7}+3q^{9}+\cdots\)
640.2.f.d \(4\) \(5.110\) \(\Q(\sqrt{-2}, \sqrt{5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}-\beta _{1}q^{7}-3q^{9}-\beta _{2}q^{11}+\cdots\)
640.2.f.e \(4\) \(5.110\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-q^{9}+\beta _{2}q^{15}+\cdots\)
640.2.f.f \(4\) \(5.110\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{2}q^{5}-3\beta _{1}q^{7}+7q^{9}+\cdots\)
640.2.f.g \(4\) \(5.110\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{3}q^{3}+(2+\beta _{1})q^{5}+\beta _{2}q^{7}+3q^{9}+\cdots\)
640.2.j.a \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(-6\) \(q-2iq^{3}+(-1-2i)q^{5}+(-3-3i)q^{7}+\cdots\)
640.2.j.b \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(6\) \(q+2iq^{3}+(-1-2i)q^{5}+(3+3i)q^{7}+\cdots\)
640.2.j.c \(18\) \(5.110\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(4\) \(-2\) \(q-\beta _{12}q^{3}-\beta _{6}q^{5}-\beta _{11}q^{7}+(-1+\cdots)q^{9}+\cdots\)
640.2.j.d \(18\) \(5.110\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(4\) \(2\) \(q-\beta _{12}q^{3}+\beta _{4}q^{5}-\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots\)
640.2.l.a \(16\) \(5.110\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}-\beta _{7})q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{4}-\beta _{7}+\cdots)q^{7}+\cdots\)
640.2.l.b \(16\) \(5.110\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{5}+\beta _{7})q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
640.2.n.a \(12\) \(5.110\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{2}q^{3}+\beta _{9}q^{5}+(-1-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
640.2.n.b \(12\) \(5.110\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{3}q^{3}-\beta _{8}q^{5}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
640.2.n.c \(12\) \(5.110\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{3}q^{3}+\beta _{8}q^{5}+(1+\beta _{2}-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots\)
640.2.n.d \(12\) \(5.110\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{2}q^{3}-\beta _{9}q^{5}+(1+\beta _{3}+\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots\)
640.2.o.a \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(-4\) \(-4\) \(q+(-2+2i)q^{3}+(-2+i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
640.2.o.b \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(4\) \(4\) \(q+(-2+2i)q^{3}+(2-i)q^{5}+(2-2i)q^{7}+\cdots\)
640.2.o.c \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}+3iq^{9}+(-5-5i)q^{13}+\cdots\)
640.2.o.d \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2-i)q^{5}+3iq^{9}+(1+i)q^{13}+\cdots\)
640.2.o.e \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}+3iq^{9}+(-1-i)q^{13}+\cdots\)
640.2.o.f \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2-i)q^{5}+3iq^{9}+(5+5i)q^{13}+\cdots\)
640.2.o.g \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(-4\) \(4\) \(q+(2-2i)q^{3}+(-2+i)q^{5}+(2-2i)q^{7}+\cdots\)
640.2.o.h \(2\) \(5.110\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(4\) \(-4\) \(q+(2-2i)q^{3}+(2-i)q^{5}+(-2+2i)q^{7}+\cdots\)
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