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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
891.1.c.a 891.c 11.b $1$ $0.445$ \(\Q\) \(\Q(\sqrt{-11}) \) None 99.1.h.a \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}+q^{11}+q^{16}-q^{20}+2q^{23}+\cdots\)
891.1.c.b 891.c 11.b $1$ $0.445$ \(\Q\) \(\Q(\sqrt{-11}) \) None 99.1.h.a \(0\) \(0\) \(1\) \(0\) \(q+q^{4}+q^{5}-q^{11}+q^{16}+q^{20}-2q^{23}+\cdots\)
891.1.q.a 891.q 297.q $6$ $0.445$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-11}) \) None 297.1.q.a \(0\) \(0\) \(3\) \(0\) \(q-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}-\zeta_{18}^{4})q^{5}+\zeta_{18}q^{11}+\cdots\)
891.1.w.a 891.w 891.w $18$ $0.445$ \(\Q(\zeta_{54})\) \(\Q(\sqrt{-11}) \) None 891.1.w.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{54}^{13}q^{3}+\zeta_{54}^{10}q^{4}+(\zeta_{54}^{6}+\zeta_{54}^{8}+\cdots)q^{5}+\cdots\)
891.2.a.a 891.a 1.a $1$ $7.115$ \(\Q\) None None 99.2.e.c \(-2\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-2q^{5}+4q^{7}+4q^{10}+\cdots\)
891.2.a.b 891.a 1.a $1$ $7.115$ \(\Q\) None None 891.2.a.b \(-1\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
891.2.a.c 891.a 1.a $1$ $7.115$ \(\Q\) None None 99.2.e.a \(-1\) \(0\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
891.2.a.d 891.a 1.a $1$ $7.115$ \(\Q\) None None 99.2.e.b \(0\) \(0\) \(-3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{5}-4q^{7}+q^{11}+2q^{13}+\cdots\)
891.2.a.e 891.a 1.a $1$ $7.115$ \(\Q\) None None 99.2.e.b \(0\) \(0\) \(3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}-4q^{7}-q^{11}+2q^{13}+\cdots\)
891.2.a.f 891.a 1.a $1$ $7.115$ \(\Q\) None None 891.2.a.b \(1\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
891.2.a.g 891.a 1.a $1$ $7.115$ \(\Q\) None None 99.2.e.a \(1\) \(0\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
891.2.a.h 891.a 1.a $1$ $7.115$ \(\Q\) None None 99.2.e.c \(2\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+2q^{5}+4q^{7}+4q^{10}+\cdots\)
891.2.a.i 891.a 1.a $2$ $7.115$ \(\Q(\sqrt{13}) \) None None 891.2.a.i \(-1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
891.2.a.j 891.a 1.a $2$ $7.115$ \(\Q(\sqrt{13}) \) None None 891.2.a.i \(1\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
891.2.a.k 891.a 1.a $3$ $7.115$ \(\Q(\zeta_{18})^+\) None None 99.2.e.d \(0\) \(0\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
891.2.a.l 891.a 1.a $3$ $7.115$ \(\Q(\zeta_{18})^+\) None None 99.2.e.d \(0\) \(0\) \(3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
891.2.a.m 891.a 1.a $3$ $7.115$ 3.3.837.1 None None 891.2.a.m \(0\) \(0\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
891.2.a.n 891.a 1.a $3$ $7.115$ 3.3.837.1 None None 891.2.a.m \(0\) \(0\) \(6\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots\)
891.2.a.o 891.a 1.a $4$ $7.115$ 4.4.4752.1 None None 891.2.a.o \(-2\) \(0\) \(-8\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots\)
891.2.a.p 891.a 1.a $4$ $7.115$ 4.4.22545.1 None None 99.2.e.e \(-1\) \(0\) \(-4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
891.2.a.q 891.a 1.a $4$ $7.115$ 4.4.22545.1 None None 99.2.e.e \(1\) \(0\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots\)
891.2.a.r 891.a 1.a $4$ $7.115$ 4.4.4752.1 None None 891.2.a.o \(2\) \(0\) \(8\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
891.2.d.a 891.d 33.d $4$ $7.115$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None 99.2.g.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{4}+\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+4q^{16}+\cdots\)
891.2.d.b 891.d 33.d $16$ $7.115$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 99.2.g.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(2-\beta _{3})q^{4}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)
891.2.d.c 891.d 33.d $24$ $7.115$ None None 891.2.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
891.2.e.a 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 297.2.a.a \(-2\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
891.2.e.b 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 11.2.a.a \(-2\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
891.2.e.c 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 99.2.a.a \(-1\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots\)
891.2.e.d 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 891.2.a.b \(-1\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.e 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 33.2.a.a \(-1\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.f 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 297.2.a.b \(-1\) \(0\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.g 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 33.2.a.a \(1\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
891.2.e.h 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 297.2.a.b \(1\) \(0\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots\)
891.2.e.i 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 891.2.a.b \(1\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
891.2.e.j 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 99.2.a.a \(1\) \(0\) \(4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.k 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 11.2.a.a \(2\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.l 891.e 9.c $2$ $7.115$ \(\Q(\sqrt{-3}) \) None None 297.2.a.a \(2\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.m 891.e 9.c $4$ $7.115$ \(\Q(\zeta_{12})\) None None 297.2.a.e \(-2\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta_{2}-\beta_1)q^{2}+(2\beta_{3}-2\beta_{2}+2\beta_1-2)q^{4}+\cdots\)
891.2.e.n 891.e 9.c $4$ $7.115$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None 891.2.a.i \(-1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
891.2.e.o 891.e 9.c $4$ $7.115$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None 891.2.a.i \(1\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
891.2.e.p 891.e 9.c $4$ $7.115$ \(\Q(\zeta_{12})\) None None 297.2.a.e \(2\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta_{2}+\beta_1)q^{2}+(2\beta_{3}-2\beta_{2}+2\beta_1-2)q^{4}+\cdots\)
891.2.e.q 891.e 9.c $6$ $7.115$ 6.0.954288.1 None None 297.2.a.g \(-1\) \(0\) \(2\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
891.2.e.r 891.e 9.c $6$ $7.115$ 6.0.2101707.2 None None 891.2.a.m \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots\)
891.2.e.s 891.e 9.c $6$ $7.115$ 6.0.2101707.2 None None 891.2.a.m \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots\)
891.2.e.t 891.e 9.c $6$ $7.115$ 6.0.954288.1 None None 297.2.a.g \(1\) \(0\) \(-2\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
891.2.e.u 891.e 9.c $8$ $7.115$ 8.0.22581504.2 None None 891.2.a.o \(-2\) \(0\) \(-8\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
891.2.e.v 891.e 9.c $8$ $7.115$ 8.0.22581504.2 None None 891.2.a.o \(2\) \(0\) \(8\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots\)
891.2.f.a 891.f 11.c $4$ $7.115$ \(\Q(\zeta_{10})\) None None 99.2.m.a \(-4\) \(0\) \(6\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
891.2.f.b 891.f 11.c $4$ $7.115$ \(\Q(\zeta_{10})\) None None 99.2.m.a \(4\) \(0\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+(3+\cdots)q^{4}+\cdots\)
891.2.f.c 891.f 11.c $24$ $7.115$ None None 891.2.f.c \(-2\) \(0\) \(4\) \(7\) $\mathrm{SU}(2)[C_{5}]$
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