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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
648.1.b.a \(1\) \(0.323\) \(\Q\) \(\Q(\sqrt{-2}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}+q^{17}+\cdots\)
648.1.b.b \(1\) \(0.323\) \(\Q\) \(\Q(\sqrt{-2}) \) None \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}-q^{11}+q^{16}-q^{17}+\cdots\)
648.1.j.a \(2\) \(0.323\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(-1\) \(0\) \(1\) \(1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
648.1.j.b \(2\) \(0.323\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(1\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
648.1.r.a \(6\) \(0.323\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots\)
648.1.bf.a \(18\) \(0.323\) \(\Q(\zeta_{54})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{54}^{7}q^{2}-\zeta_{54}^{19}q^{3}+\zeta_{54}^{14}q^{4}+\cdots\)
648.2.a.a \(1\) \(5.174\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-3\) \(+\) \(q-q^{5}-3q^{7}+5q^{11}-5q^{13}-2q^{17}+\cdots\)
648.2.a.b \(1\) \(5.174\) \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) \(+\) \(q-q^{5}-4q^{11}-5q^{13}-5q^{17}+8q^{19}+\cdots\)
648.2.a.c \(1\) \(5.174\) \(\Q\) None None \(0\) \(0\) \(1\) \(-3\) \(+\) \(q+q^{5}-3q^{7}-5q^{11}-5q^{13}+2q^{17}+\cdots\)
648.2.a.d \(1\) \(5.174\) \(\Q\) None None \(0\) \(0\) \(1\) \(0\) \(-\) \(q+q^{5}+4q^{11}-5q^{13}+5q^{17}+8q^{19}+\cdots\)
648.2.a.e \(2\) \(5.174\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-4\) \(0\) \(+\) \(q+(-2+\beta )q^{5}-2\beta q^{7}-2q^{11}+(1+\cdots)q^{13}+\cdots\)
648.2.a.f \(2\) \(5.174\) \(\Q(\sqrt{33}) \) None None \(0\) \(0\) \(-1\) \(3\) \(-\) \(q-\beta q^{5}+(2-\beta )q^{7}+q^{11}+(2+\beta )q^{13}+\cdots\)
648.2.a.g \(2\) \(5.174\) \(\Q(\sqrt{33}) \) None None \(0\) \(0\) \(1\) \(3\) \(-\) \(q+\beta q^{5}+(2-\beta )q^{7}-q^{11}+(2+\beta )q^{13}+\cdots\)
648.2.a.h \(2\) \(5.174\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(4\) \(0\) \(-\) \(q+(2+\beta )q^{5}+2\beta q^{7}+2q^{11}+(1-2\beta )q^{13}+\cdots\)
648.2.d.a \(2\) \(5.174\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(8\) \(q+(-1+i)q^{2}-2iq^{4}-2iq^{5}+4q^{7}+\cdots\)
648.2.d.b \(2\) \(5.174\) \(\Q(\sqrt{-7}) \) None None \(-1\) \(0\) \(0\) \(-4\) \(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
648.2.d.c \(2\) \(5.174\) \(\Q(\sqrt{-7}) \) None None \(1\) \(0\) \(0\) \(-4\) \(q+\beta q^{2}+(-2+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
648.2.d.d \(2\) \(5.174\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(8\) \(q+(1+i)q^{2}+2iq^{4}-2iq^{5}+4q^{7}+\cdots\)
648.2.d.e \(4\) \(5.174\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(4\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
648.2.d.f \(4\) \(5.174\) \(\Q(\sqrt{3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-16\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}-4q^{7}+\cdots\)
648.2.d.g \(4\) \(5.174\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)
648.2.d.h \(4\) \(5.174\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(\beta _{2}+\beta _{3})q^{5}+\cdots\)
648.2.d.i \(4\) \(5.174\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(4\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
648.2.d.j \(8\) \(5.174\) 8.0.\(\cdots\).1 None None \(-1\) \(0\) \(0\) \(-6\) \(q+\beta _{4}q^{2}-\beta _{5}q^{4}+(\beta _{1}+\beta _{4}-\beta _{7})q^{5}+\cdots\)
648.2.d.k \(8\) \(5.174\) 8.0.\(\cdots\).1 None None \(1\) \(0\) \(0\) \(-6\) \(q-\beta _{4}q^{2}-\beta _{5}q^{4}+(-\beta _{1}-\beta _{4}+\beta _{7})q^{5}+\cdots\)
648.2.f.a \(4\) \(5.174\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
648.2.f.b \(16\) \(5.174\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(1-\beta _{9})q^{4}-\beta _{4}q^{5}+(-\beta _{7}+\cdots)q^{7}+\cdots\)
648.2.f.c \(24\) \(5.174\) None None \(0\) \(0\) \(0\) \(0\)
648.2.i.a \(2\) \(5.174\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(3\) \(q-4\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
648.2.i.b \(2\) \(5.174\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
648.2.i.c \(2\) \(5.174\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-3\) \(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
648.2.i.d \(2\) \(5.174\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
648.2.i.e \(2\) \(5.174\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-3\) \(q+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
648.2.i.f \(2\) \(5.174\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
648.2.i.g \(2\) \(5.174\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
648.2.i.h \(2\) \(5.174\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(4\) \(3\) \(q+4\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
648.2.i.i \(4\) \(5.174\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+(-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
648.2.i.j \(4\) \(5.174\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(0\) \(q+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\)
648.2.l.a \(4\) \(5.174\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-12\) \(q+\beta _{3}q^{2}-2q^{4}+(-\beta _{1}+2\beta _{3})q^{5}+\cdots\)
648.2.l.b \(4\) \(5.174\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{3}q^{8}+2\beta _{1}q^{11}+\cdots\)
648.2.l.c \(4\) \(5.174\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(12\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-\beta _{1}+2\beta _{3})q^{5}+\cdots\)
648.2.l.d \(8\) \(5.174\) 8.0.170772624.1 None None \(-3\) \(0\) \(0\) \(0\) \(q+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{2}+(-\beta _{2}-\beta _{7})q^{4}+\cdots\)
648.2.l.e \(8\) \(5.174\) 8.0.170772624.1 None None \(3\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{3}+\beta _{7})q^{5}+(2+\cdots)q^{7}+\cdots\)
648.2.l.f \(16\) \(5.174\) 16.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{6}+\beta _{12})q^{2}+(1-\beta _{3}-\beta _{8})q^{4}+\cdots\)
648.2.l.g \(48\) \(5.174\) None None \(0\) \(0\) \(0\) \(0\)
648.2.n.a \(4\) \(5.174\) \(\Q(\zeta_{12})\) None None \(-4\) \(0\) \(-6\) \(-2\) \(q+(-1+\zeta_{12}^{3})q^{2}-2\zeta_{12}^{3}q^{4}+(-1+\cdots)q^{5}+\cdots\)
648.2.n.b \(4\) \(5.174\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(-6\) \(-2\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
648.2.n.c \(4\) \(5.174\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(4\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
648.2.n.d \(4\) \(5.174\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(-1\) \(0\) \(0\) \(4\) \(q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\)
648.2.n.e \(4\) \(5.174\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(-6\) \(-4\) \(q+\beta _{3}q^{2}-2q^{4}+(-2-\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
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