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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1089.1.c.a 1089.c 11.b $2$ $0.543$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-\beta q^{7}+\beta q^{13}+q^{16}-\beta q^{19}+\cdots\)
1089.1.h.a 1089.h 99.h $4$ $0.543$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(2\) \(2\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
1089.1.i.a 1089.i 9.d $2$ $0.543$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(3\) \(0\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1089.1.k.a 1089.k 11.d $8$ $0.543$ 8.0.64000000.1 \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{4}-\beta _{7}q^{7}-\beta _{1}q^{13}+\beta _{4}q^{16}+\cdots\)
1089.1.r.a 1089.r 99.n $8$ $0.543$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-3\) \(0\) \(q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{11}+\cdots)q^{5}+\cdots\)
1089.1.s.a 1089.s 99.o $8$ $0.543$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-1\) \(0\) \(q-\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+\zeta_{30}q^{5}+\cdots\)
1089.1.s.b 1089.s 99.o $16$ $0.543$ 16.0.\(\cdots\).1 None None \(0\) \(-2\) \(-2\) \(0\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots\)
1089.2.a.a 1089.a 1.a $1$ $8.696$ \(\Q\) None None \(-2\) \(0\) \(-4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots\)
1089.2.a.b 1089.a 1.a $1$ $8.696$ \(\Q\) None None \(-2\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+2q^{7}+2q^{10}+\cdots\)
1089.2.a.c 1089.a 1.a $1$ $8.696$ \(\Q\) None None \(-1\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
1089.2.a.d 1089.a 1.a $1$ $8.696$ \(\Q\) None None \(-1\) \(0\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{5}+2q^{7}+3q^{8}-4q^{10}+\cdots\)
1089.2.a.e 1089.a 1.a $1$ $8.696$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-5q^{7}-2q^{13}+4q^{16}+7q^{19}+\cdots\)
1089.2.a.f 1089.a 1.a $1$ $8.696$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+5q^{7}+2q^{13}+4q^{16}-7q^{19}+\cdots\)
1089.2.a.g 1089.a 1.a $1$ $8.696$ \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(3\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+3q^{5}+4q^{16}-6q^{20}+9q^{23}+\cdots\)
1089.2.a.h 1089.a 1.a $1$ $8.696$ \(\Q\) None None \(1\) \(0\) \(-4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}+2q^{7}-3q^{8}-4q^{10}+\cdots\)
1089.2.a.i 1089.a 1.a $1$ $8.696$ \(\Q\) None None \(1\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}+2q^{7}-3q^{8}-q^{10}+\cdots\)
1089.2.a.j 1089.a 1.a $1$ $8.696$ \(\Q\) None None \(1\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}-4q^{7}-3q^{8}+2q^{10}+\cdots\)
1089.2.a.k 1089.a 1.a $1$ $8.696$ \(\Q\) None None \(2\) \(0\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-4q^{5}+q^{7}-8q^{10}+\cdots\)
1089.2.a.l 1089.a 1.a $2$ $8.696$ \(\Q(\sqrt{5}) \) None None \(-3\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots\)
1089.2.a.m 1089.a 1.a $2$ $8.696$ \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(3\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+3q^{7}+\cdots\)
1089.2.a.n 1089.a 1.a $2$ $8.696$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-\beta q^{7}+4\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots\)
1089.2.a.o 1089.a 1.a $2$ $8.696$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(6\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots\)
1089.2.a.p 1089.a 1.a $2$ $8.696$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{4}-2q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
1089.2.a.q 1089.a 1.a $2$ $8.696$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}+\beta q^{5}-2q^{7}+3\beta q^{8}+\cdots\)
1089.2.a.r 1089.a 1.a $2$ $8.696$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}-\beta q^{5}+2q^{7}+3\beta q^{8}+\cdots\)
1089.2.a.s 1089.a 1.a $2$ $8.696$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(3\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}-3q^{7}+\cdots\)
1089.2.a.t 1089.a 1.a $2$ $8.696$ \(\Q(\sqrt{5}) \) None None \(3\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots\)
1089.2.a.u 1089.a 1.a $4$ $8.696$ \(\Q(\sqrt{3}, \sqrt{11})\) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1089.2.a.v 1089.a 1.a $4$ $8.696$ 4.4.4400.1 None None \(0\) \(0\) \(0\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1089.2.a.w 1089.a 1.a $4$ $8.696$ 4.4.4400.1 None None \(0\) \(0\) \(0\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{1}q^{5}+(3+2\beta _{2}+\cdots)q^{7}+\cdots\)
1089.2.d.a 1089.d 33.d $2$ $8.696$ \(\Q(\sqrt{-2}) \) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-q^{4}-\beta q^{5}-2\beta q^{7}+3q^{8}+\cdots\)
1089.2.d.b 1089.d 33.d $2$ $8.696$ \(\Q(\sqrt{-2}) \) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-q^{4}+\beta q^{5}-2\beta q^{7}-3q^{8}+\cdots\)
1089.2.d.c 1089.d 33.d $4$ $8.696$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots\)
1089.2.d.d 1089.d 33.d $4$ $8.696$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots\)
1089.2.d.e 1089.d 33.d $4$ $8.696$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+q^{4}+(2\beta _{1}-\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots\)
1089.2.d.f 1089.d 33.d $4$ $8.696$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots\)
1089.2.d.g 1089.d 33.d $16$ $8.696$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{15}q^{2}+(1+\beta _{4})q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
1089.2.e.a 1089.e 9.c $2$ $8.696$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
1089.2.e.b 1089.e 9.c $2$ $8.696$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
1089.2.e.c 1089.e 9.c $2$ $8.696$ \(\Q(\sqrt{-3}) \) None None \(1\) \(-3\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
1089.2.e.d 1089.e 9.c $4$ $8.696$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-3\) \(-6\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots\)
1089.2.e.e 1089.e 9.c $4$ $8.696$ \(\Q(\zeta_{12})\) None None \(0\) \(-6\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-1-\zeta_{12})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1089.2.e.f 1089.e 9.c $4$ $8.696$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-3\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q-\beta _{3}q^{3}+2\beta _{2}q^{4}+(1-2\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1089.2.e.g 1089.e 9.c $4$ $8.696$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(3\) \(-6\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots\)
1089.2.e.h 1089.e 9.c $6$ $8.696$ \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
1089.2.e.i 1089.e 9.c $8$ $8.696$ 8.0.508277025.1 None None \(1\) \(5\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{7})q^{2}+(1+\beta _{7})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
1089.2.e.j 1089.e 9.c $12$ $8.696$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{7}q^{2}+(1+\beta _{2}-\beta _{6})q^{3}+(-1-2\beta _{4}+\cdots)q^{4}+\cdots\)
1089.2.e.k 1089.e 9.c $16$ $8.696$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{6})q^{2}-\beta _{13}q^{3}+(2\beta _{5}+\cdots)q^{4}+\cdots\)
1089.2.e.l 1089.e 9.c $20$ $8.696$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-1\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots\)
1089.2.e.m 1089.e 9.c $20$ $8.696$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots\)
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