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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
666.2.a.a \(1\) \(5.318\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-q^{13}+\cdots\)
666.2.a.b \(1\) \(5.318\) \(\Q\) None \(-1\) \(0\) \(0\) \(3\) \(-\) \(q-q^{2}+q^{4}+3q^{7}-q^{8}-q^{11}+q^{13}+\cdots\)
666.2.a.c \(1\) \(5.318\) \(\Q\) None \(-1\) \(0\) \(2\) \(-3\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-3q^{7}-q^{8}-2q^{10}+\cdots\)
666.2.a.d \(1\) \(5.318\) \(\Q\) None \(1\) \(0\) \(-4\) \(-1\) \(+\) \(q+q^{2}+q^{4}-4q^{5}-q^{7}+q^{8}-4q^{10}+\cdots\)
666.2.a.e \(1\) \(5.318\) \(\Q\) None \(1\) \(0\) \(-2\) \(-3\) \(+\) \(q+q^{2}+q^{4}-2q^{5}-3q^{7}+q^{8}-2q^{10}+\cdots\)
666.2.a.f \(1\) \(5.318\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+4q^{11}+\cdots\)
666.2.a.g \(1\) \(5.318\) \(\Q\) None \(1\) \(0\) \(4\) \(3\) \(-\) \(q+q^{2}+q^{4}+4q^{5}+3q^{7}+q^{8}+4q^{10}+\cdots\)
666.2.a.h \(2\) \(5.318\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-4\) \(1\) \(+\) \(q-q^{2}+q^{4}-2q^{5}+(1-\beta )q^{7}-q^{8}+\cdots\)
666.2.a.i \(2\) \(5.318\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(-2\) \(-\) \(q-q^{2}+q^{4}+(1-3\beta )q^{5}-2\beta q^{7}-q^{8}+\cdots\)
666.2.a.j \(2\) \(5.318\) \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(1\) \(2\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}+(2-2\beta )q^{7}+q^{8}+\cdots\)
666.2.a.k \(2\) \(5.318\) \(\Q(\sqrt{17}) \) None \(2\) \(0\) \(4\) \(1\) \(-\) \(q+q^{2}+q^{4}+2q^{5}+(1-\beta )q^{7}+q^{8}+\cdots\)
666.2.c.a \(2\) \(5.318\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(6\) \(q+iq^{2}-q^{4}+2iq^{5}+3q^{7}-iq^{8}+\cdots\)
666.2.c.b \(4\) \(5.318\) \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{5}-2q^{7}+\cdots\)
666.2.c.c \(4\) \(5.318\) \(\Q(i, \sqrt{65})\) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{2}q^{2}-q^{4}+2\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
666.2.c.d \(4\) \(5.318\) \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{2}-q^{4}+q^{7}+\beta _{1}q^{8}-\beta _{3}q^{11}+\cdots\)
666.2.e.a \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
666.2.e.b \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(4\) \(0\) \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
666.2.e.c \(12\) \(5.318\) 12.0.\(\cdots\).1 None \(-6\) \(2\) \(5\) \(5\) \(q-\beta _{9}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{11})q^{3}+\cdots\)
666.2.e.d \(14\) \(5.318\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(7\) \(-1\) \(-3\) \(3\) \(q+(1+\beta _{10})q^{2}+\beta _{2}q^{3}+\beta _{10}q^{4}-\beta _{12}q^{5}+\cdots\)
666.2.e.e \(20\) \(5.318\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-10\) \(2\) \(-1\) \(-1\) \(q-\beta _{11}q^{2}+\beta _{7}q^{3}+(-1+\beta _{11})q^{4}+\cdots\)
666.2.e.f \(22\) \(5.318\) None \(11\) \(-4\) \(1\) \(-5\)
666.2.f.a \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-4\) \(-3\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots\)
666.2.f.b \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+q^{8}+\cdots\)
666.2.f.c \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)
666.2.f.d \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
666.2.f.e \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(3\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{7}-q^{8}+\cdots\)
666.2.f.f \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(-3\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}-3\zeta_{6}q^{7}+\cdots\)
666.2.f.g \(4\) \(5.318\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(0\) \(1\) \(-3\) \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
666.2.f.h \(4\) \(5.318\) \(\Q(\sqrt{-3}, \sqrt{11})\) None \(-2\) \(0\) \(2\) \(2\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
666.2.f.i \(4\) \(5.318\) \(\Q(\sqrt{-3}, \sqrt{11})\) None \(2\) \(0\) \(-2\) \(2\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
666.2.f.j \(6\) \(5.318\) 6.0.4406832.1 None \(3\) \(0\) \(1\) \(0\) \(q+(1+\beta _{3})q^{2}+\beta _{3}q^{4}-\beta _{5}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
666.2.g.a \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-2\) \(6\) \(q+\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
666.2.g.b \(36\) \(5.318\) None \(18\) \(-2\) \(4\) \(-8\)
666.2.g.c \(38\) \(5.318\) None \(-19\) \(1\) \(2\) \(-2\)
666.2.h.a \(2\) \(5.318\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(4\) \(-3\) \(q-q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+2q^{5}+\cdots\)
666.2.h.b \(36\) \(5.318\) None \(-36\) \(-2\) \(-8\) \(4\)
666.2.h.c \(38\) \(5.318\) None \(38\) \(-2\) \(-4\) \(1\)
666.2.j.a \(4\) \(5.318\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(4\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2+2\zeta_{8}^{2})q^{5}+\cdots\)
666.2.j.b \(4\) \(5.318\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-16\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-4q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
666.2.j.c \(4\) \(5.318\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(4\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2+2\zeta_{8}^{2})q^{5}+\cdots\)
666.2.j.d \(8\) \(5.318\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{1}q^{2}+\beta _{3}q^{4}+(1-\beta _{2}+\beta _{7})q^{7}+\cdots\)
666.2.k.a \(76\) \(5.318\) None \(0\) \(4\) \(0\) \(-2\)
666.2.q.a \(4\) \(5.318\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-1+2\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
666.2.q.b \(72\) \(5.318\) None \(0\) \(4\) \(0\) \(4\)
666.2.s.a \(4\) \(5.318\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-6\) \(4\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
666.2.s.b \(4\) \(5.318\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{8}+\cdots\)
666.2.s.c \(4\) \(5.318\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{5}+\cdots\)
666.2.s.d \(4\) \(5.318\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(6\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
666.2.s.e \(4\) \(5.318\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(6\) \(-8\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}^{2})q^{5}+\cdots\)
666.2.s.f \(8\) \(5.318\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{5}q^{2}+(1+\beta _{4})q^{4}+(-2\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
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