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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1170.2.a.a 1170.a 1.a $1$ $9.342$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
1170.2.a.b 1170.a 1.a $1$ $9.342$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{13}+\cdots\)
1170.2.a.c 1170.a 1.a $1$ $9.342$ \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
1170.2.a.d 1170.a 1.a $1$ $9.342$ \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
1170.2.a.e 1170.a 1.a $1$ $9.342$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
1170.2.a.f 1170.a 1.a $1$ $9.342$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
1170.2.a.g 1170.a 1.a $1$ $9.342$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
1170.2.a.h 1170.a 1.a $1$ $9.342$ \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
1170.2.a.i 1170.a 1.a $1$ $9.342$ \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
1170.2.a.j 1170.a 1.a $1$ $9.342$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1170.2.a.k 1170.a 1.a $1$ $9.342$ \(\Q\) None \(1\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
1170.2.a.l 1170.a 1.a $1$ $9.342$ \(\Q\) None \(1\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
1170.2.a.m 1170.a 1.a $1$ $9.342$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{13}+\cdots\)
1170.2.a.n 1170.a 1.a $1$ $9.342$ \(\Q\) None \(1\) \(0\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
1170.2.a.o 1170.a 1.a $2$ $9.342$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
1170.2.a.p 1170.a 1.a $2$ $9.342$ \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}-q^{8}+\cdots\)
1170.2.a.q 1170.a 1.a $2$ $9.342$ \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
1170.2.b.a 1170.b 13.b $2$ $9.342$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}-iq^{8}-q^{10}+\cdots\)
1170.2.b.b 1170.b 13.b $2$ $9.342$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{5}-iq^{8}+q^{10}+\cdots\)
1170.2.b.c 1170.b 13.b $2$ $9.342$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{5}+iq^{8}+q^{10}+\cdots\)
1170.2.b.d 1170.b 13.b $4$ $9.342$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.b.e 1170.b 13.b $4$ $9.342$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}q^{8}+\cdots\)
1170.2.b.f 1170.b 13.b $4$ $9.342$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.b.g 1170.b 13.b $8$ $9.342$ 8.0.3057647616.6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}-\beta _{7}q^{7}+\beta _{1}q^{8}+\cdots\)
1170.2.e.a 1170.e 5.b $2$ $9.342$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots\)
1170.2.e.b 1170.e 5.b $2$ $9.342$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-2+i)q^{5}+4iq^{7}+\cdots\)
1170.2.e.c 1170.e 5.b $2$ $9.342$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2-i)q^{5}+4iq^{7}+\cdots\)
1170.2.e.d 1170.e 5.b $2$ $9.342$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(2+i)q^{5}+iq^{8}+(1+\cdots)q^{10}+\cdots\)
1170.2.e.e 1170.e 5.b $4$ $9.342$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.e.f 1170.e 5.b $6$ $9.342$ 6.0.3534400.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-q^{4}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
1170.2.e.g 1170.e 5.b $6$ $9.342$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-q^{4}+(-\beta _{2}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1170.2.e.h 1170.e 5.b $6$ $9.342$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-q^{4}+(\beta _{2}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1170.2.f.a 1170.f 65.d $4$ $9.342$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-4\) \(0\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.f.b 1170.f 65.d $4$ $9.342$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(4\) \(0\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1170.2.f.c 1170.f 65.d $6$ $9.342$ 6.0.350464.1 None \(-6\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1170.2.f.d 1170.f 65.d $6$ $9.342$ 6.0.350464.1 None \(6\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.f.e 1170.f 65.d $8$ $9.342$ 8.0.\(\cdots\).15 None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+\beta _{5}q^{5}-\beta _{4}q^{7}-q^{8}+\cdots\)
1170.2.f.f 1170.f 65.d $8$ $9.342$ 8.0.\(\cdots\).15 None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}-\beta _{5}q^{5}-\beta _{4}q^{7}+q^{8}+\cdots\)
1170.2.i.a 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+2\zeta_{6}q^{7}+\cdots\)
1170.2.i.b 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+4\zeta_{6}q^{7}+\cdots\)
1170.2.i.c 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-3\zeta_{6}q^{7}+\cdots\)
1170.2.i.d 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots\)
1170.2.i.e 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+q^{8}+\cdots\)
1170.2.i.f 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+\zeta_{6}q^{7}+\cdots\)
1170.2.i.g 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+5\zeta_{6}q^{7}+\cdots\)
1170.2.i.h 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
1170.2.i.i 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+3\zeta_{6}q^{7}+\cdots\)
1170.2.i.j 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+3\zeta_{6}q^{7}+\cdots\)
1170.2.i.k 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots\)
1170.2.i.l 1170.i 13.c $2$ $9.342$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+4\zeta_{6}q^{7}+\cdots\)
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