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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1053.1.k.a 1053.k 117.k $2$ $0.526$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}+q^{16}+\cdots\)
1053.1.m.a 1053.m 117.m $2$ $0.526$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{4}+\zeta_{6}q^{13}-\zeta_{6}q^{16}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1053.1.n.a 1053.n 117.n $2$ $0.526$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-39}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{5}-q^{8}+q^{10}-\zeta_{6}^{2}q^{11}+\cdots\)
1053.1.n.b 1053.n 117.n $2$ $0.526$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+\zeta_{6}q^{13}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{25}+\cdots\)
1053.1.n.c 1053.n 117.n $2$ $0.526$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-39}) \) None \(1\) \(0\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{5}+q^{8}+q^{10}+\zeta_{6}^{2}q^{11}+\cdots\)
1053.1.n.d 1053.n 117.n $4$ $0.526$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
1053.1.u.a 1053.u 117.u $2$ $0.526$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{6}^{2}q^{4}+q^{7}-\zeta_{6}q^{13}-\zeta_{6}q^{16}+\cdots\)
1053.1.v.a 1053.v 117.v $2$ $0.526$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-\zeta_{6}^{2}q^{13}+q^{16}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1053.1.z.a 1053.z 117.w $4$ $0.526$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{3}q^{4}+(\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}q^{13}+\cdots\)
1053.1.bb.a 1053.bb 117.y $4$ $0.526$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{5}q^{4}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}-\zeta_{12}^{5}q^{13}+\cdots\)
1053.1.be.a 1053.be 117.ab $4$ $0.526$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{12}q^{4}+(-1+\zeta_{12}^{3})q^{7}-\zeta_{12}^{5}q^{13}+\cdots\)
1053.2.a.a 1053.a 1.a $1$ $8.408$ \(\Q\) None None \(-2\) \(0\) \(-4\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-4q^{5}+2q^{7}+8q^{10}+\cdots\)
1053.2.a.b 1053.a 1.a $1$ $8.408$ \(\Q\) None None \(-1\) \(0\) \(-2\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+5q^{7}+3q^{8}+2q^{10}+\cdots\)
1053.2.a.c 1053.a 1.a $1$ $8.408$ \(\Q\) None None \(1\) \(0\) \(2\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}+5q^{7}-3q^{8}+2q^{10}+\cdots\)
1053.2.a.d 1053.a 1.a $1$ $8.408$ \(\Q\) None None \(2\) \(0\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+4q^{5}+2q^{7}+8q^{10}+\cdots\)
1053.2.a.e 1053.a 1.a $2$ $8.408$ \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
1053.2.a.f 1053.a 1.a $2$ $8.408$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
1053.2.a.g 1053.a 1.a $3$ $8.408$ 3.3.621.1 None None \(0\) \(0\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1053.2.a.h 1053.a 1.a $3$ $8.408$ 3.3.621.1 None None \(0\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
1053.2.a.i 1053.a 1.a $4$ $8.408$ \(\Q(\sqrt{3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(-10\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-\beta _{2}q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
1053.2.a.j 1053.a 1.a $5$ $8.408$ 5.5.403137.1 None None \(-2\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{3}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1053.2.a.k 1053.a 1.a $5$ $8.408$ 5.5.403137.1 None None \(2\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{3}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1053.2.a.l 1053.a 1.a $6$ $8.408$ 6.6.22931361.1 None None \(-2\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}-\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1053.2.a.m 1053.a 1.a $6$ $8.408$ 6.6.22931361.1 None None \(2\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{4}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
1053.2.a.n 1053.a 1.a $8$ $8.408$ 8.8.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{7})q^{5}+\cdots\)
1053.2.b.a 1053.b 13.b $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-2\zeta_{6})q^{2}-q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
1053.2.b.b 1053.b 13.b $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-2\zeta_{6})q^{2}-q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
1053.2.b.c 1053.b 13.b $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}-q^{4}+2\zeta_{6}q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{8}+\cdots\)
1053.2.b.d 1053.b 13.b $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}-q^{4}+2\zeta_{6}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{8}+\cdots\)
1053.2.b.e 1053.b 13.b $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{11}+\cdots\)
1053.2.b.f 1053.b 13.b $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}+\zeta_{6}q^{5}+\zeta_{6}q^{7}+\zeta_{6}q^{11}+\cdots\)
1053.2.b.g 1053.b 13.b $4$ $8.408$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}-\beta _{1}q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
1053.2.b.h 1053.b 13.b $4$ $8.408$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}-\beta _{1}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
1053.2.b.i 1053.b 13.b $10$ $8.408$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{7}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1053.2.b.j 1053.b 13.b $10$ $8.408$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{7}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1053.2.b.k 1053.b 13.b $12$ $8.408$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots\)
1053.2.e.a 1053.e 9.c $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
1053.2.e.b 1053.e 9.c $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
1053.2.e.c 1053.e 9.c $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots\)
1053.2.e.d 1053.e 9.c $2$ $8.408$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
1053.2.e.e 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1053.2.e.f 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(-1\) \(0\) \(-5\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
1053.2.e.g 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-1\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1053.2.e.h 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-1\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1053.2.e.i 1053.e 9.c $4$ $8.408$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}-2\zeta_{12}q^{7}+\cdots\)
1053.2.e.j 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(1\) \(0\) \(5\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
1053.2.e.k 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(1\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1053.2.e.l 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(1\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1053.2.e.m 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots\)
1053.2.e.n 1053.e 9.c $6$ $8.408$ 6.0.1156923.1 None None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
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