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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1064.1.p.a 1064.p 1064.p $2$ $0.531$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-266}) \) None \(-2\) \(-1\) \(1\) \(-2\) \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
1064.1.p.b 1064.p 1064.p $2$ $0.531$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-266}) \) None \(-2\) \(1\) \(-1\) \(2\) \(q-q^{2}+(1-\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
1064.1.p.c 1064.p 1064.p $2$ $0.531$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-266}) \) None \(2\) \(-1\) \(-1\) \(2\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
1064.1.p.d 1064.p 1064.p $2$ $0.531$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-266}) \) None \(2\) \(1\) \(1\) \(-2\) \(q+q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(1-\beta )q^{6}+\cdots\)
1064.1.bg.a 1064.bg 1064.ag $2$ $0.531$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(-1\) \(-2\) \(1\) \(2\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1064.1.bg.b 1064.bg 1064.ag $2$ $0.531$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(-1\) \(2\) \(-1\) \(2\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
1064.1.bg.c 1064.bg 1064.ag $4$ $0.531$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-14}) \) None \(2\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
1064.1.br.a 1064.br 1064.ar $6$ $0.531$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-38}) \) None \(-3\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{6}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}-\zeta_{18}^{3}q^{4}+\cdots\)
1064.1.br.b 1064.br 1064.ar $6$ $0.531$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-38}) \) None \(3\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{6}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots\)
1064.1.br.c 1064.br 1064.ar $8$ $0.531$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{24}^{5}q^{2}+(-\zeta_{24}-\zeta_{24}^{7})q^{3}+\zeta_{24}^{10}q^{4}+\cdots\)
1064.1.cd.a 1064.cd 133.r $4$ $0.531$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-2\) \(q+(\beta _{1}-\beta _{3})q^{3}-\beta _{2}q^{7}+(1-\beta _{2})q^{9}+\cdots\)
1064.1.ef.a 1064.ef 1064.df $6$ $0.531$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(-3\) \(-3\) \(q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots\)
1064.1.ef.b 1064.ef 1064.df $6$ $0.531$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(3\) \(-3\) \(q-\zeta_{18}^{5}q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+(\zeta_{18}^{3}+\cdots)q^{5}+\cdots\)
1064.1.ef.c 1064.ef 1064.df $12$ $0.531$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(6\) \(q+\zeta_{36}^{10}q^{2}+(-\zeta_{36}-\zeta_{36}^{7})q^{3}+\cdots\)
1064.2.a.a 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{5}) \) None None \(0\) \(-3\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(1-2\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
1064.2.a.b 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{13}) \) None None \(0\) \(-1\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}-q^{7}+\beta q^{9}+(-1+\beta )q^{11}+\cdots\)
1064.2.a.c 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+2\beta )q^{5}+q^{7}+(-2+\cdots)q^{9}+\cdots\)
1064.2.a.d 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-q^{7}+(-2+\beta )q^{9}+(1+\cdots)q^{11}+\cdots\)
1064.2.a.e 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{5}) \) None None \(0\) \(3\) \(5\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
1064.2.a.f 1064.a 1.a $3$ $8.496$ 3.3.1101.1 None None \(0\) \(-1\) \(2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
1064.2.a.g 1064.a 1.a $4$ $8.496$ 4.4.18097.1 None None \(0\) \(0\) \(-3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots\)
1064.2.a.h 1064.a 1.a $4$ $8.496$ 4.4.25857.1 None None \(0\) \(2\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots\)
1064.2.a.i 1064.a 1.a $5$ $8.496$ 5.5.10463409.1 None None \(0\) \(0\) \(3\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{4})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
1064.2.m.a 1064.m 133.c $16$ $8.496$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{3}+(-\beta _{14}-\beta _{15})q^{5}+(\beta _{2}+\beta _{15})q^{7}+\cdots\)
1064.2.m.b 1064.m 133.c $24$ $8.496$ None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$
1064.2.q.a 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1064.2.q.b 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1064.2.q.c 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1064.2.q.d 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
1064.2.q.e 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(-5+\cdots)q^{11}+\cdots\)
1064.2.q.f 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
1064.2.q.g 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
1064.2.q.h 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1064.2.q.i 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1064.2.q.j 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1064.2.q.k 1064.q 7.c $4$ $8.496$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-4\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2})q^{5}+\cdots\)
1064.2.q.l 1064.q 7.c $4$ $8.496$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(4\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{2}q^{3}+(1-\beta _{2})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
1064.2.q.m 1064.q 7.c $6$ $8.496$ 6.0.31259952.1 None None \(0\) \(0\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots\)
1064.2.q.n 1064.q 7.c $16$ $8.496$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+\beta _{10}q^{5}+\beta _{11}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
1064.2.q.o 1064.q 7.c $22$ $8.496$ None None \(0\) \(0\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{3}]$
1064.2.r.a 1064.r 19.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+q^{7}+\cdots\)
1064.2.r.b 1064.r 19.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-q^{7}+\cdots\)
1064.2.r.c 1064.r 19.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+q^{7}+\cdots\)
1064.2.r.d 1064.r 19.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{5}+q^{7}+3\zeta_{6}q^{9}+2q^{11}+\cdots\)
1064.2.r.e 1064.r 19.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-q^{7}+\cdots\)
1064.2.r.f 1064.r 19.c $4$ $8.496$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(-1\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+\beta _{2}q^{5}-q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1064.2.r.g 1064.r 19.c $8$ $8.496$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(0\) \(-2\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{3}+(\beta _{1}-\beta _{4})q^{5}+q^{7}+(-2+\cdots)q^{9}+\cdots\)
1064.2.r.h 1064.r 19.c $8$ $8.496$ 8.0.3098592225.1 None None \(0\) \(2\) \(1\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{3}+(-\beta _{4}-\beta _{7})q^{5}-q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
1064.2.r.i 1064.r 19.c $14$ $8.496$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(2\) \(-3\) \(-14\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{4})q^{3}+(-\beta _{7}+\beta _{9})q^{5}+\cdots\)
1064.2.r.j 1064.r 19.c $16$ $8.496$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(3\) \(-5\) \(16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{7}-\beta _{13})q^{5}+q^{7}+\cdots\)
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