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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.1.d.a 63.d 7.b $1$ $0.031$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(-1\) \(q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots\)
63.2.a.a 63.a 1.a $1$ $0.503$ \(\Q\) None None \(1\) \(0\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots\)
63.2.a.b 63.a 1.a $2$ $0.503$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-2\beta q^{5}+q^{7}-\beta q^{8}+\cdots\)
63.2.c.a 63.c 21.c $4$ $0.503$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
63.2.e.a 63.e 7.c $2$ $0.503$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) $\mathrm{U}(1)[D_{3}]$ \(q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots\)
63.2.e.b 63.e 7.c $2$ $0.503$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)
63.2.f.a 63.f 9.c $6$ $0.503$ \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
63.2.f.b 63.f 9.c $6$ $0.503$ 6.0.309123.1 None None \(1\) \(-4\) \(5\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
63.2.g.a 63.g 63.g $2$ $0.503$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
63.2.g.b 63.g 63.g $10$ $0.503$ 10.0.\(\cdots\).1 None None \(2\) \(2\) \(-8\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
63.2.h.a 63.h 63.h $2$ $0.503$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots\)
63.2.h.b 63.h 63.h $10$ $0.503$ 10.0.\(\cdots\).1 None None \(-4\) \(-1\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
63.2.i.a 63.i 63.i $2$ $0.503$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\cdots\)
63.2.i.b 63.i 63.i $10$ $0.503$ 10.0.\(\cdots\).1 None None \(0\) \(-3\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots\)
63.2.o.a 63.o 63.o $12$ $0.503$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-6\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{4}+\beta _{7})q^{4}+\cdots\)
63.2.p.a 63.p 21.g $4$ $0.503$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+2\beta _{3})q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots\)
63.2.s.a 63.s 63.s $2$ $0.503$ \(\Q(\sqrt{-3}) \) None None \(-3\) \(-3\) \(-6\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
63.2.s.b 63.s 63.s $10$ $0.503$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
63.3.b.a 63.b 3.b $4$ $1.717$ \(\Q(\sqrt{-2}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+2\beta _{1}q^{5}+\beta _{2}q^{7}+\cdots\)
63.3.d.a 63.d 7.b $1$ $1.717$ \(\Q\) \(\Q(\sqrt{-7}) \) None \(3\) \(0\) \(0\) \(-7\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{2}+5q^{4}-7q^{7}+3q^{8}+6q^{11}+\cdots\)
63.3.d.b 63.d 7.b $2$ $1.717$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-3q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
63.3.d.c 63.d 7.b $2$ $1.717$ \(\Q(\sqrt{7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(14\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+3q^{4}+7q^{7}-\beta q^{8}-8\beta q^{11}+\cdots\)
63.3.j.a 63.j 63.j $6$ $1.717$ 6.0.63369648.1 None None \(0\) \(18\) \(-15\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{4}-\beta _{5})q^{2}+3q^{3}+(-4+\cdots)q^{4}+\cdots\)
63.3.j.b 63.j 63.j $22$ $1.717$ None None \(0\) \(-19\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$
63.3.k.a 63.k 63.k $28$ $1.717$ None None \(1\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
63.3.l.a 63.l 63.l $28$ $1.717$ None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
63.3.m.a 63.m 7.d $2$ $1.717$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(6\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{6}q^{2}+(4-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots\)
63.3.m.b 63.m 7.d $2$ $1.717$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(13\) $\mathrm{U}(1)[D_{6}]$ \(q+(4-4\zeta_{6})q^{4}+(8-3\zeta_{6})q^{7}+(-7+\cdots)q^{13}+\cdots\)
63.3.m.c 63.m 7.d $2$ $1.717$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(9\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{4}+(6-3\zeta_{6})q^{5}+\cdots\)
63.3.m.d 63.m 7.d $2$ $1.717$ \(\Q(\sqrt{-3}) \) None None \(3\) \(0\) \(-9\) \(13\) $\mathrm{SU}(2)[C_{6}]$ \(q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}+(-6+3\zeta_{6})q^{5}+\cdots\)
63.3.m.e 63.m 7.d $4$ $1.717$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(-26\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(-9+9\beta _{1})q^{4}+(\beta _{2}+2\beta _{3})q^{5}+\cdots\)
63.3.n.a 63.n 63.n $6$ $1.717$ 6.0.63369648.1 None None \(3\) \(-9\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{5})q^{2}+3\beta _{2}q^{3}+(\beta _{1}-4\beta _{2}+\cdots)q^{4}+\cdots\)
63.3.n.b 63.n 63.n $22$ $1.717$ None None \(-6\) \(8\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$
63.3.q.a 63.q 21.h $12$ $1.717$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-3\beta _{8}+\beta _{9})q^{4}-\beta _{6}q^{5}+\cdots\)
63.3.r.a 63.r 9.d $24$ $1.717$ None None \(0\) \(2\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{6}]$
63.3.t.a 63.t 63.t $28$ $1.717$ None None \(-2\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$
63.4.a.a 63.a 1.a $1$ $3.717$ \(\Q\) None None \(-4\) \(0\) \(4\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+8q^{4}+4q^{5}-7q^{7}-2^{4}q^{10}+\cdots\)
63.4.a.b 63.a 1.a $1$ $3.717$ \(\Q\) None None \(1\) \(0\) \(-16\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-7q^{4}-2^{4}q^{5}-7q^{7}-15q^{8}+\cdots\)
63.4.a.c 63.a 1.a $1$ $3.717$ \(\Q\) None None \(3\) \(0\) \(18\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+3q^{2}+q^{4}+18q^{5}+7q^{7}-21q^{8}+\cdots\)
63.4.a.d 63.a 1.a $2$ $3.717$ \(\Q(\sqrt{19}) \) None None \(0\) \(0\) \(0\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+11q^{4}+2\beta q^{5}-7q^{7}+3\beta q^{8}+\cdots\)
63.4.a.e 63.a 1.a $2$ $3.717$ \(\Q(\sqrt{57}) \) None None \(3\) \(0\) \(-6\) \(14\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(7+3\beta )q^{4}+(-2-2\beta )q^{5}+\cdots\)
63.4.c.a 63.c 21.c $4$ $3.717$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(-8-5\beta _{3})q^{4}-7\beta _{3}q^{7}+\cdots\)
63.4.c.b 63.c 21.c $4$ $3.717$ \(\Q(\sqrt{-2}, \sqrt{111})\) None None \(0\) \(0\) \(0\) \(-44\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{1}q^{2}+\beta _{3}q^{5}+(-11-\beta _{2})q^{7}+\cdots\)
63.4.e.a 63.e 7.c $2$ $3.717$ \(\Q(\sqrt{-3}) \) None None \(-3\) \(0\) \(-3\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
63.4.e.b 63.e 7.c $2$ $3.717$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(7\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots\)
63.4.e.c 63.e 7.c $6$ $3.717$ 6.0.9924270768.1 None None \(1\) \(0\) \(11\) \(-13\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-8+\beta _{1}+\beta _{2}+8\beta _{4}+\beta _{5})q^{4}+\cdots\)
63.4.e.d 63.e 7.c $8$ $3.717$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{2}-\beta _{6})q^{4}+\cdots\)
63.4.f.a 63.f 9.c $2$ $3.717$ \(\Q(\sqrt{-3}) \) None None \(1\) \(-9\) \(14\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-6+3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
63.4.f.b 63.f 9.c $16$ $3.717$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(2\) \(-30\) \(56\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{3}-\beta _{7})q^{3}+(5\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
63.4.f.c 63.f 9.c $18$ $3.717$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(6\) \(9\) \(24\) \(-63\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2}-\beta _{3}-\beta _{5})q^{2}+(1+\beta _{8})q^{3}+\cdots\)
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