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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
104.1.h.a 104.h 104.h $1$ $0.052$ \(\Q\) \(\Q(\sqrt{-26}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
104.1.h.b 104.h 104.h $1$ $0.052$ \(\Q\) \(\Q(\sqrt{-26}) \) None \(1\) \(-1\) \(-1\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
104.2.a.a 104.a 1.a $1$ $0.830$ \(\Q\) None None \(0\) \(1\) \(-1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+5q^{7}-2q^{9}-2q^{11}+\cdots\)
104.2.a.b 104.a 1.a $2$ $0.830$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots\)
104.2.b.a 104.b 8.b $2$ $0.830$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+3iq^{5}+\cdots\)
104.2.b.b 104.b 8.b $4$ $0.830$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+2\zeta_{12}^{2}q^{3}+(\zeta_{12}+\cdots)q^{4}+\cdots\)
104.2.b.c 104.b 8.b $6$ $0.830$ 6.0.399424.1 None None \(-2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
104.2.e.a 104.e 104.e $2$ $0.830$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+q^{5}+\cdots\)
104.2.e.b 104.e 104.e $2$ $0.830$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+iq^{3}+2iq^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
104.2.e.c 104.e 104.e $8$ $0.830$ 8.0.4521217600.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{3}-\beta _{5}q^{4}-\beta _{6}q^{5}+\cdots\)
104.2.f.a 104.f 13.b $4$ $0.830$ \(\Q(i, \sqrt{17})\) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{3})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
104.2.i.a 104.i 13.c $2$ $0.830$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
104.2.i.b 104.i 13.c $4$ $0.830$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(-1\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
104.2.m.a 104.m 104.m $4$ $0.830$ \(\Q(i, \sqrt{26})\) None None \(-4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{2})q^{2}-q^{3}+2\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
104.2.m.b 104.m 104.m $20$ $0.830$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(2\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{14}q^{2}-\beta _{5}q^{3}-\beta _{2}q^{4}+\beta _{10}q^{5}+\cdots\)
104.2.o.a 104.o 13.e $8$ $0.830$ 8.0.195105024.2 None None \(0\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\)
104.2.r.a 104.r 104.r $24$ $0.830$ None None \(-1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
104.2.s.a 104.s 104.s $4$ $0.830$ \(\Q(\zeta_{12})\) None None \(-4\) \(-6\) \(-8\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
104.2.s.b 104.s 104.s $4$ $0.830$ \(\Q(\zeta_{12})\) None None \(-2\) \(6\) \(8\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\)
104.2.s.c 104.s 104.s $16$ $0.830$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(3\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{14})q^{2}+(\beta _{3}-\beta _{11})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
104.2.u.a 104.u 104.u $48$ $0.830$ None None \(-4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
104.3.g.a 104.g 8.d $24$ $2.834$ None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
104.3.h.a 104.h 104.h $3$ $2.834$ 3.3.2808.1 \(\Q(\sqrt{-26}) \) None \(-6\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+\beta _{2}q^{3}+4q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
104.3.h.b 104.h 104.h $3$ $2.834$ 3.3.2808.1 \(\Q(\sqrt{-26}) \) None \(6\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+\beta _{2}q^{3}+4q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
104.3.h.c 104.h 104.h $20$ $2.834$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{4})q^{4}+\beta _{11}q^{5}+\cdots\)
104.3.j.a 104.j 104.j $52$ $2.834$ None None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
104.3.l.a 104.l 13.d $2$ $2.834$ \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(10\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+2q^{3}+(5+5i)q^{5}+(-3+3i)q^{7}+\cdots\)
104.3.l.b 104.l 13.d $6$ $2.834$ 6.0.891380736.2 None None \(0\) \(-4\) \(-14\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
104.3.l.c 104.l 13.d $6$ $2.834$ 6.0.195552256.1 None None \(0\) \(0\) \(2\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}-\beta _{4}q^{5}+(2+\beta _{1}-2\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
104.3.n.a 104.n 104.n $4$ $2.834$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(4\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-2\beta _{1})q^{2}+(-4+4\beta _{1})q^{3}-4\beta _{1}q^{4}+\cdots\)
104.3.n.b 104.n 104.n $48$ $2.834$ None None \(-5\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
104.3.p.a 104.p 104.p $2$ $2.834$ \(\Q(\sqrt{-3}) \) None None \(-4\) \(-1\) \(4\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q-2q^{2}+(-1+\zeta_{6})q^{3}+4q^{4}+2q^{5}+\cdots\)
104.3.p.b 104.p 104.p $2$ $2.834$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(-1\) \(-4\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
104.3.p.c 104.p 104.p $4$ $2.834$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(3\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1})q^{2}+(2+2\beta _{2})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
104.3.p.d 104.p 104.p $44$ $2.834$ None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
104.3.v.a 104.v 13.f $4$ $2.834$ \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(3+6\zeta_{12}+\cdots)q^{5}+\cdots\)
104.3.v.b 104.v 13.f $4$ $2.834$ \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(6\) \(16\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-2\zeta_{12}+2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots\)
104.3.v.c 104.v 13.f $8$ $2.834$ 8.0.\(\cdots\).1 None None \(0\) \(-8\) \(-2\) \(-36\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-2-\beta _{2}-2\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
104.3.v.d 104.v 13.f $12$ $2.834$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{7}q^{3}+(-1+\beta _{2}-\beta _{3}+2\beta _{4}+2\beta _{5}+\cdots)q^{5}+\cdots\)
104.3.x.a 104.x 104.x $104$ $2.834$ None None \(-4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$
104.4.a.a 104.a 1.a $1$ $6.136$ \(\Q\) None None \(0\) \(1\) \(-7\) \(-21\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-7q^{5}-21q^{7}-26q^{9}+6q^{11}+\cdots\)
104.4.a.b 104.a 1.a $1$ $6.136$ \(\Q\) None None \(0\) \(5\) \(19\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+5q^{3}+19q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
104.4.a.c 104.a 1.a $2$ $6.136$ \(\Q(\sqrt{73}) \) None None \(0\) \(-3\) \(-3\) \(-25\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-3+3\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
104.4.a.d 104.a 1.a $2$ $6.136$ \(\Q(\sqrt{321}) \) None None \(0\) \(-1\) \(-11\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-6+\beta )q^{5}+(2-3\beta )q^{7}+\cdots\)
104.4.a.e 104.a 1.a $3$ $6.136$ 3.3.18257.1 None None \(0\) \(0\) \(-8\) \(36\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-3-2\beta _{1}-\beta _{2})q^{5}+(12+\cdots)q^{7}+\cdots\)
104.4.b.a 104.b 8.b $2$ $6.136$ \(\Q(\sqrt{-1}) \) None None \(4\) \(0\) \(0\) \(-58\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+2i)q^{2}-iq^{3}+8iq^{4}+11iq^{5}+\cdots\)
104.4.b.b 104.b 8.b $34$ $6.136$ None None \(-2\) \(0\) \(0\) \(86\) $\mathrm{SU}(2)[C_{2}]$
104.4.e.a 104.e 104.e $40$ $6.136$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
104.4.f.a 104.f 13.b $10$ $6.136$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{3}+\beta _{8}q^{5}-\beta _{7}q^{7}+(8-\beta _{1}+\cdots)q^{9}+\cdots\)
104.4.i.a 104.i 13.c $2$ $6.136$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-8\) \(-18\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-8+8\zeta_{6})q^{3}-9q^{5}+4\zeta_{6}q^{7}+\cdots\)
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