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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
136.1.e.a 136.e 136.e $1$ $0.068$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots\)
136.1.j.a 136.j 136.j $2$ $0.068$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}+(-1-i)q^{3}-q^{4}+(-1+i+\cdots)q^{6}+\cdots\)
136.1.p.a 136.p 136.p $4$ $0.068$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
136.2.a.a 136.a 1.a $1$ $1.086$ \(\Q\) None None \(0\) \(-2\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
136.2.a.b 136.a 1.a $1$ $1.086$ \(\Q\) None None \(0\) \(2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}+2q^{11}-6q^{13}-q^{17}+\cdots\)
136.2.a.c 136.a 1.a $2$ $1.086$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+2q^{5}+(1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
136.2.b.a 136.b 17.b $2$ $1.086$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}+iq^{11}-2q^{13}+\cdots\)
136.2.b.b 136.b 17.b $2$ $1.086$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+\beta q^{7}+3q^{9}-2\beta q^{11}+2q^{13}+\cdots\)
136.2.c.a 136.c 8.b $8$ $1.086$ 8.0.1649659456.5 None None \(-1\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
136.2.c.b 136.c 8.b $8$ $1.086$ 8.0.4469724736.1 None None \(-1\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{6})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
136.2.h.a 136.h 136.h $16$ $1.086$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{12}q^{3}-\beta _{3}q^{4}-\beta _{6}q^{5}+\cdots\)
136.2.i.a 136.i 136.i $8$ $1.086$ 8.0.342102016.5 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+(-\beta _{2}+\beta _{6})q^{3}+\beta _{7}q^{4}+\cdots\)
136.2.i.b 136.i 136.i $24$ $1.086$ None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
136.2.k.a 136.k 17.c $2$ $1.086$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(-3-3i)q^{5}+(-3+\cdots)q^{7}+\cdots\)
136.2.k.b 136.k 17.c $2$ $1.086$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(2+2i)q^{5}+(2-2i)q^{7}+\cdots\)
136.2.k.c 136.k 17.c $2$ $1.086$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(1+i)q^{5}+(-1+i)q^{7}+\cdots\)
136.2.k.d 136.k 17.c $2$ $1.086$ \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{3}+(-1-i)q^{5}+(2-2i)q^{7}+\cdots\)
136.2.n.a 136.n 17.d $4$ $1.086$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1-\zeta_{8})q^{3}+(1-\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)
136.2.n.b 136.n 17.d $4$ $1.086$ \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(1+\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}+\cdots)q^{5}+\cdots\)
136.2.n.c 136.n 17.d $12$ $1.086$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{2}q^{3}+\beta _{8}q^{5}+(1-\beta _{3}-\beta _{6}-\beta _{8}+\cdots)q^{7}+\cdots\)
136.2.o.a 136.o 136.o $64$ $1.086$ None None \(-4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{8}]$
136.2.s.a 136.s 136.s $8$ $1.086$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-8\) \(0\) \(0\) $\mathrm{U}(1)[D_{16}]$ \(q+(-\zeta_{16}+\zeta_{16}^{5})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots\)
136.2.s.b 136.s 136.s $8$ $1.086$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) None \(0\) \(8\) \(0\) \(0\) $\mathrm{U}(1)[D_{16}]$ \(q+(\zeta_{16}-\zeta_{16}^{5})q^{2}+(1+\zeta_{16}-\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
136.2.s.c 136.s 136.s $112$ $1.086$ None None \(-8\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
136.3.e.a 136.e 136.e $2$ $3.706$ \(\Q(\sqrt{17}) \) \(\Q(\sqrt{-34}) \) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}+\beta q^{5}-\beta q^{7}-8q^{8}+\cdots\)
136.3.e.b 136.e 136.e $2$ $3.706$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}+8q^{8}+\cdots\)
136.3.e.c 136.e 136.e $2$ $3.706$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-34}) \) None \(4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}+\beta q^{5}-2\beta q^{7}+8q^{8}+\cdots\)
136.3.e.d 136.e 136.e $28$ $3.706$ None None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
136.3.f.a 136.f 8.d $32$ $3.706$ None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
136.3.j.a 136.j 136.j $4$ $3.706$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+2\zeta_{8}^{2}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}-4q^{4}+\cdots\)
136.3.j.b 136.j 136.j $64$ $3.706$ None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
136.3.p.a 136.p 136.p $4$ $3.706$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-8\) \(0\) \(0\) $\mathrm{U}(1)[D_{8}]$ \(q-2\zeta_{8}^{3}q^{2}+(-2-2\zeta_{8}-3\zeta_{8}^{2}+3\zeta_{8}^{3})q^{3}+\cdots\)
136.3.p.b 136.p 136.p $4$ $3.706$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(8\) \(0\) \(0\) $\mathrm{U}(1)[D_{8}]$ \(q-2\zeta_{8}^{3}q^{2}+(2+2\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
136.3.p.c 136.p 136.p $128$ $3.706$ None None \(-4\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
136.3.q.a 136.q 136.q $272$ $3.706$ None None \(-8\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{16}]$
136.3.t.a 136.t 17.e $32$ $3.706$ None None \(0\) \(-8\) \(0\) \(8\) $\mathrm{SU}(2)[C_{16}]$
136.3.t.b 136.t 17.e $40$ $3.706$ None None \(0\) \(8\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
136.4.a.a 136.a 1.a $2$ $8.024$ \(\Q(\sqrt{3}) \) None None \(0\) \(4\) \(-12\) \(-36\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(-6-2\beta )q^{5}+(-18+\cdots)q^{7}+\cdots\)
136.4.a.b 136.a 1.a $3$ $8.024$ 3.3.8396.1 None None \(0\) \(-4\) \(-8\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{3}+(-3+\beta _{1}-2\beta _{2})q^{5}+\cdots\)
136.4.a.c 136.a 1.a $3$ $8.024$ 3.3.1556.1 None None \(0\) \(8\) \(2\) \(12\) $+$ $\mathrm{SU}(2)$ \(q+(3-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(4-\beta _{1}+\cdots)q^{7}+\cdots\)
136.4.a.d 136.a 1.a $4$ $8.024$ 4.4.550476.1 None None \(0\) \(-2\) \(8\) \(-22\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+\cdots\)
136.4.b.a 136.b 17.b $6$ $8.024$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
136.4.b.b 136.b 17.b $8$ $8.024$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{4}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
136.4.c.a 136.c 8.b $24$ $8.024$ None None \(1\) \(0\) \(0\) \(-56\) $\mathrm{SU}(2)[C_{2}]$
136.4.c.b 136.c 8.b $24$ $8.024$ None None \(1\) \(0\) \(0\) \(84\) $\mathrm{SU}(2)[C_{2}]$
136.4.h.a 136.h 136.h $52$ $8.024$ None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
136.4.i.a 136.i 136.i $104$ $8.024$ None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
136.4.k.a 136.k 17.c $14$ $8.024$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(-4\) \(8\) \(-10\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(1-\beta _{5}+\beta _{7})q^{5}+(-1-\beta _{5}+\cdots)q^{7}+\cdots\)
136.4.k.b 136.k 17.c $14$ $8.024$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(6\) \(6\) \(10\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{3}-\beta _{7}q^{5}+(1-\beta _{5}-\beta _{8})q^{7}+\cdots\)
136.4.n.a 136.n 17.d $24$ $8.024$ None None \(0\) \(0\) \(-28\) \(0\) $\mathrm{SU}(2)[C_{8}]$
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