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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
117.1.j.a 117.j 13.d $2$ $0.058$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots\)
117.2.a.a 117.a 1.a $1$ $0.934$ \(\Q\) None None \(-1\) \(0\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}-4q^{7}+3q^{8}+2q^{10}+\cdots\)
117.2.a.b 117.a 1.a $2$ $0.934$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+2q^{7}-\beta q^{8}-2\beta q^{11}+\cdots\)
117.2.a.c 117.a 1.a $2$ $0.934$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{5}-2\beta q^{7}+\cdots\)
117.2.b.a 117.b 13.b $2$ $0.934$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}-q^{4}-2\zeta_{6}q^{7}-\zeta_{6}q^{8}+2\zeta_{6}q^{11}+\cdots\)
117.2.b.b 117.b 13.b $4$ $0.934$ 4.0.8112.1 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}-\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)
117.2.e.a 117.e 9.c $2$ $0.934$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(-3\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
117.2.e.b 117.e 9.c $10$ $0.934$ 10.0.\(\cdots\).1 None None \(-2\) \(1\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{9}q^{2}+(\beta _{1}-\beta _{5}+\beta _{9})q^{3}+(\beta _{1}-\beta _{6}+\cdots)q^{4}+\cdots\)
117.2.e.c 117.e 9.c $12$ $0.934$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(2\) \(-2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}-\beta _{7}-\beta _{8}+\beta _{10}-\beta _{11})q^{2}+\cdots\)
117.2.f.a 117.f 117.f $24$ $0.934$ None None \(1\) \(-1\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$
117.2.g.a 117.g 13.c $2$ $0.934$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) $\mathrm{U}(1)[D_{3}]$ \(q+2\zeta_{6}q^{4}+\zeta_{6}q^{7}+(4-3\zeta_{6})q^{13}+\cdots\)
117.2.g.b 117.g 13.c $2$ $0.934$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots\)
117.2.g.c 117.g 13.c $4$ $0.934$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(1\) \(0\) \(6\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{1}+2\beta _{2}+\beta _{3})q^{4}+\cdots\)
117.2.h.a 117.h 117.h $24$ $0.934$ None None \(-2\) \(-1\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$
117.2.i.a 117.i 39.f $12$ $0.934$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{9}q^{2}+(\beta _{3}-2\beta _{4})q^{4}-\beta _{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
117.2.l.a 117.l 117.l $2$ $0.934$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+\cdots\)
117.2.l.b 117.l 117.l $22$ $0.934$ None None \(0\) \(-1\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{6}]$
117.2.q.a 117.q 13.e $2$ $0.934$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{6}q^{4}+(2-4\zeta_{6})q^{5}+(-2+\zeta_{6})q^{7}+\cdots\)
117.2.q.b 117.q 13.e $2$ $0.934$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(9\) $\mathrm{U}(1)[D_{6}]$ \(q-2\zeta_{6}q^{4}+(6-3\zeta_{6})q^{7}+(-4+3\zeta_{6})q^{13}+\cdots\)
117.2.q.c 117.q 13.e $2$ $0.934$ \(\Q(\sqrt{-3}) \) None None \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+(-1+2\zeta_{6})q^{5}+\cdots\)
117.2.q.d 117.q 13.e $4$ $0.934$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}-\beta _{3}q^{5}+(-4+2\beta _{2}+\cdots)q^{7}+\cdots\)
117.2.r.a 117.r 117.r $2$ $0.934$ \(\Q(\sqrt{-3}) \) None None \(-3\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
117.2.r.b 117.r 117.r $22$ $0.934$ None None \(0\) \(2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$
117.2.t.a 117.t 117.t $2$ $0.934$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-2+\cdots)q^{5}+\cdots\)
117.2.t.b 117.t 117.t $2$ $0.934$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots\)
117.2.t.c 117.t 117.t $20$ $0.934$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{17}q^{2}+\beta _{10}q^{3}+(1-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots\)
117.2.x.a 117.x 117.x $48$ $0.934$ None None \(-6\) \(-2\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
117.2.z.a 117.z 117.z $4$ $0.934$ \(\Q(\zeta_{12})\) None None \(-6\) \(-6\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{2}+\cdots\)
117.2.z.b 117.z 117.z $44$ $0.934$ None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
117.2.ba.a 117.ba 39.k $8$ $0.934$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{24}^{4}-\zeta_{24}^{5})q^{2}-2\zeta_{24}q^{4}+(\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
117.2.ba.b 117.ba 39.k $8$ $0.934$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}+2\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
117.2.bc.a 117.bc 117.ac $48$ $0.934$ None None \(-6\) \(-2\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{12}]$
117.3.c.a 117.c 3.b $8$ $3.188$ 8.0.\(\cdots\).15 None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
117.3.d.a 117.d 39.d $8$ $3.188$ 8.0.\(\cdots\).5 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}-\beta _{4}q^{7}+\cdots\)
117.3.j.a 117.j 13.d $4$ $3.188$ \(\Q(i, \sqrt{10})\) None None \(4\) \(0\) \(-8\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+3\beta _{2}+2\beta _{3})q^{4}+\cdots\)
117.3.j.b 117.j 13.d $8$ $3.188$ 8.0.\(\cdots\).10 None None \(-4\) \(0\) \(20\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}+(-1-\beta _{1}-\beta _{4}-\beta _{7})q^{4}+\cdots\)
117.3.j.c 117.j 13.d $8$ $3.188$ 8.0.897122304.10 None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(\beta _{3}+\beta _{7})q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots\)
117.3.k.a 117.k 117.k $52$ $3.188$ None None \(0\) \(-1\) \(-6\) \(-1\) $\mathrm{SU}(2)[C_{6}]$
117.3.m.a 117.m 117.m $52$ $3.188$ None None \(-3\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
117.3.n.a 117.n 117.n $52$ $3.188$ None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
117.3.o.a 117.o 39.h $20$ $3.188$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(42\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-2\beta _{5}+\beta _{10})q^{4}+(\beta _{12}+\cdots)q^{5}+\cdots\)
117.3.p.a 117.p 39.i $20$ $3.188$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+(2\beta _{3}-\beta _{4})q^{4}+(\beta _{8}-\beta _{15}+\cdots)q^{5}+\cdots\)
117.3.s.a 117.s 9.d $48$ $3.188$ None None \(0\) \(2\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{6}]$
117.3.u.a 117.u 117.u $52$ $3.188$ None None \(-3\) \(-1\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{6}]$
117.3.v.a 117.v 117.v $52$ $3.188$ None None \(-6\) \(-1\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{6}]$
117.3.w.a 117.w 117.w $104$ $3.188$ None None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$
117.3.y.a 117.y 117.y $104$ $3.188$ None None \(-2\) \(-8\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$
117.3.bb.a 117.bb 117.ab $104$ $3.188$ None None \(-2\) \(-2\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
117.3.bd.a 117.bd 13.f $4$ $3.188$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-22\) $\mathrm{U}(1)[D_{12}]$ \(q-4\zeta_{12}q^{4}+(-8-8\zeta_{12}+5\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
117.3.bd.b 117.bd 13.f $4$ $3.188$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(14\) \(16\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1-2\zeta_{12}+\cdots)q^{4}+\cdots\)
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