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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
666.2.a.a 666.a 1.a $1$ $5.318$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-q^{13}+\cdots\)
666.2.a.b 666.a 1.a $1$ $5.318$ \(\Q\) None \(-1\) \(0\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{7}-q^{8}-q^{11}+q^{13}+\cdots\)
666.2.a.c 666.a 1.a $1$ $5.318$ \(\Q\) None \(-1\) \(0\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-3q^{7}-q^{8}-2q^{10}+\cdots\)
666.2.a.d 666.a 1.a $1$ $5.318$ \(\Q\) None \(1\) \(0\) \(-4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}-q^{7}+q^{8}-4q^{10}+\cdots\)
666.2.a.e 666.a 1.a $1$ $5.318$ \(\Q\) None \(1\) \(0\) \(-2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-3q^{7}+q^{8}-2q^{10}+\cdots\)
666.2.a.f 666.a 1.a $1$ $5.318$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+4q^{11}+\cdots\)
666.2.a.g 666.a 1.a $1$ $5.318$ \(\Q\) None \(1\) \(0\) \(4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}+3q^{7}+q^{8}+4q^{10}+\cdots\)
666.2.a.h 666.a 1.a $2$ $5.318$ \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+(1-\beta )q^{7}-q^{8}+\cdots\)
666.2.a.i 666.a 1.a $2$ $5.318$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1-3\beta )q^{5}-2\beta q^{7}-q^{8}+\cdots\)
666.2.a.j 666.a 1.a $2$ $5.318$ \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+(2-2\beta )q^{7}+q^{8}+\cdots\)
666.2.a.k 666.a 1.a $2$ $5.318$ \(\Q(\sqrt{17}) \) None \(2\) \(0\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+(1-\beta )q^{7}+q^{8}+\cdots\)
666.2.c.a 666.c 37.b $2$ $5.318$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{5}+3q^{7}-iq^{8}+\cdots\)
666.2.c.b 666.c 37.b $4$ $5.318$ \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{5}-2q^{7}+\cdots\)
666.2.c.c 666.c 37.b $4$ $5.318$ \(\Q(i, \sqrt{65})\) None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+2\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
666.2.c.d 666.c 37.b $4$ $5.318$ \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}+q^{7}+\beta _{1}q^{8}-\beta _{3}q^{11}+\cdots\)
666.2.e.a 666.e 9.c $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
666.2.e.b 666.e 9.c $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
666.2.e.c 666.e 9.c $12$ $5.318$ 12.0.\(\cdots\).1 None \(-6\) \(2\) \(5\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{9}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{11})q^{3}+\cdots\)
666.2.e.d 666.e 9.c $14$ $5.318$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(7\) \(-1\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{10})q^{2}+\beta _{2}q^{3}+\beta _{10}q^{4}-\beta _{12}q^{5}+\cdots\)
666.2.e.e 666.e 9.c $20$ $5.318$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-10\) \(2\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{11}q^{2}+\beta _{7}q^{3}+(-1+\beta _{11})q^{4}+\cdots\)
666.2.e.f 666.e 9.c $22$ $5.318$ None \(11\) \(-4\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$
666.2.f.a 666.f 37.c $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots\)
666.2.f.b 666.f 37.c $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+q^{8}+\cdots\)
666.2.f.c 666.f 37.c $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)
666.2.f.d 666.f 37.c $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
666.2.f.e 666.f 37.c $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{7}-q^{8}+\cdots\)
666.2.f.f 666.f 37.c $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}-3\zeta_{6}q^{7}+\cdots\)
666.2.f.g 666.f 37.c $4$ $5.318$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(0\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
666.2.f.h 666.f 37.c $4$ $5.318$ \(\Q(\sqrt{-3}, \sqrt{11})\) None \(-2\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
666.2.f.i 666.f 37.c $4$ $5.318$ \(\Q(\sqrt{-3}, \sqrt{11})\) None \(2\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
666.2.f.j 666.f 37.c $6$ $5.318$ 6.0.4406832.1 None \(3\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{3})q^{2}+\beta _{3}q^{4}-\beta _{5}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
666.2.g.a 666.g 333.g $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
666.2.g.b 666.g 333.g $36$ $5.318$ None \(18\) \(-2\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{3}]$
666.2.g.c 666.g 333.g $38$ $5.318$ None \(-19\) \(1\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$
666.2.h.a 666.h 333.h $2$ $5.318$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+2q^{5}+\cdots\)
666.2.h.b 666.h 333.h $36$ $5.318$ None \(-36\) \(-2\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{3}]$
666.2.h.c 666.h 333.h $38$ $5.318$ None \(38\) \(-2\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$
666.2.j.a 666.j 111.g $4$ $5.318$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2+2\zeta_{8}^{2})q^{5}+\cdots\)
666.2.j.b 666.j 111.g $4$ $5.318$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-4q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
666.2.j.c 666.j 111.g $4$ $5.318$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2+2\zeta_{8}^{2})q^{5}+\cdots\)
666.2.j.d 666.j 111.g $8$ $5.318$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{4}+(1-\beta _{2}+\beta _{7})q^{7}+\cdots\)
666.2.k.a 666.k 333.k $76$ $5.318$ None \(0\) \(4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
666.2.q.a 666.q 333.q $4$ $5.318$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-1+2\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
666.2.q.b 666.q 333.q $72$ $5.318$ None \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$
666.2.s.a 666.s 37.e $4$ $5.318$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
666.2.s.b 666.s 37.e $4$ $5.318$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{8}+\cdots\)
666.2.s.c 666.s 37.e $4$ $5.318$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{5}+\cdots\)
666.2.s.d 666.s 37.e $4$ $5.318$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
666.2.s.e 666.s 37.e $4$ $5.318$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(6\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}^{2})q^{5}+\cdots\)
666.2.s.f 666.s 37.e $8$ $5.318$ 8.0.303595776.1 None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{5}q^{2}+(1+\beta _{4})q^{4}+(-2\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
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