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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.2.a.a 54.a 1.a $1$ $0.431$ \(\Q\) None \(-1\) \(0\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots\)
54.2.a.b 54.a 1.a $1$ $0.431$ \(\Q\) None \(1\) \(0\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)
54.2.c.a 54.c 9.c $2$ $0.431$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
54.2.e.a 54.e 27.e $6$ $0.431$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+\cdots\)
54.2.e.b 54.e 27.e $12$ $0.431$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{11}q^{3}+\beta _{3}q^{4}+\cdots\)
54.3.b.a 54.b 3.b $2$ $1.471$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}+6\beta q^{5}+5q^{7}-2\beta q^{8}+\cdots\)
54.3.d.a 54.d 9.d $4$ $1.471$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(18\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(6-3\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
54.3.f.a 54.f 27.f $36$ $1.471$ None \(0\) \(0\) \(18\) \(0\) $\mathrm{SU}(2)[C_{18}]$
54.4.a.a 54.a 1.a $1$ $3.186$ \(\Q\) None \(-2\) \(0\) \(-12\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-12q^{5}-7q^{7}-8q^{8}+\cdots\)
54.4.a.b 54.a 1.a $1$ $3.186$ \(\Q\) None \(-2\) \(0\) \(-3\) \(29\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-3q^{5}+29q^{7}-8q^{8}+\cdots\)
54.4.a.c 54.a 1.a $1$ $3.186$ \(\Q\) None \(2\) \(0\) \(3\) \(29\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+3q^{5}+29q^{7}+8q^{8}+\cdots\)
54.4.a.d 54.a 1.a $1$ $3.186$ \(\Q\) None \(2\) \(0\) \(12\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+12q^{5}-7q^{7}+8q^{8}+\cdots\)
54.4.c.a 54.c 9.c $2$ $3.186$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-9\) \(31\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-9\zeta_{6}q^{5}+\cdots\)
54.4.c.b 54.c 9.c $4$ $3.186$ \(\Q(\sqrt{-3}, \sqrt{-35})\) None \(-4\) \(0\) \(-9\) \(-19\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{1}q^{2}+(-4-4\beta _{1})q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots\)
54.4.e.a 54.e 27.e $24$ $3.186$ None \(0\) \(0\) \(-12\) \(-33\) $\mathrm{SU}(2)[C_{9}]$
54.4.e.b 54.e 27.e $30$ $3.186$ None \(0\) \(0\) \(-12\) \(33\) $\mathrm{SU}(2)[C_{9}]$
54.5.b.a 54.b 3.b $2$ $5.582$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-146\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-8q^{4}-12\beta q^{5}-73q^{7}-8\beta q^{8}+\cdots\)
54.5.b.b 54.b 3.b $4$ $5.582$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(68\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}-8q^{4}+(\zeta_{8}-3\zeta_{8}^{2})q^{5}+\cdots\)
54.5.d.a 54.d 9.d $8$ $5.582$ 8.0.\(\cdots\).4 None \(0\) \(0\) \(-18\) \(-26\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+8\beta _{2}q^{4}+(-3-\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
54.5.f.a 54.f 27.f $72$ $5.582$ None \(0\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{18}]$
54.6.a.a 54.a 1.a $1$ $8.661$ \(\Q\) None \(-4\) \(0\) \(-33\) \(59\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+2^{4}q^{4}-33q^{5}+59q^{7}-2^{6}q^{8}+\cdots\)
54.6.a.b 54.a 1.a $1$ $8.661$ \(\Q\) None \(-4\) \(0\) \(-24\) \(77\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+2^{4}q^{4}-24q^{5}+77q^{7}-2^{6}q^{8}+\cdots\)
54.6.a.c 54.a 1.a $1$ $8.661$ \(\Q\) None \(-4\) \(0\) \(84\) \(-193\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+2^{4}q^{4}+84q^{5}-193q^{7}+\cdots\)
54.6.a.d 54.a 1.a $1$ $8.661$ \(\Q\) None \(4\) \(0\) \(-84\) \(-193\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+2^{4}q^{4}-84q^{5}-193q^{7}+\cdots\)
54.6.a.e 54.a 1.a $1$ $8.661$ \(\Q\) None \(4\) \(0\) \(24\) \(77\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+2^{4}q^{4}+24q^{5}+77q^{7}+2^{6}q^{8}+\cdots\)
54.6.a.f 54.a 1.a $1$ $8.661$ \(\Q\) None \(4\) \(0\) \(33\) \(59\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+2^{4}q^{4}+33q^{5}+59q^{7}+2^{6}q^{8}+\cdots\)
54.6.c.a 54.c 9.c $4$ $8.661$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-8\) \(0\) \(54\) \(74\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\beta _{1})q^{2}-2^{4}\beta _{1}q^{4}+(3^{3}\beta _{1}+\cdots)q^{5}+\cdots\)
54.6.c.b 54.c 9.c $6$ $8.661$ 6.0.\(\cdots\).3 None \(12\) \(0\) \(54\) \(-132\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{1}q^{2}+(-2^{4}+2^{4}\beta _{1})q^{4}+(18+\cdots)q^{5}+\cdots\)
54.6.e.a 54.e 27.e $42$ $8.661$ None \(0\) \(0\) \(87\) \(-15\) $\mathrm{SU}(2)[C_{9}]$
54.6.e.b 54.e 27.e $48$ $8.661$ None \(0\) \(0\) \(87\) \(15\) $\mathrm{SU}(2)[C_{9}]$
54.7.b.a 54.b 3.b $2$ $12.423$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-410\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2^{5}q^{4}+6\beta q^{5}-205q^{7}+\cdots\)
54.7.b.b 54.b 3.b $2$ $12.423$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(778\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{2}-2^{5}q^{4}-15\beta q^{5}+389q^{7}+\cdots\)
54.7.b.c 54.b 3.b $4$ $12.423$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(836\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}-2^{5}q^{4}+(5\zeta_{8}+15\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
54.7.d.a 54.d 9.d $12$ $12.423$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-432\) \(240\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}-2^{5}\beta _{2}q^{4}+(-48-24\beta _{2}+\cdots)q^{5}+\cdots\)
54.7.f.a 54.f 27.f $108$ $12.423$ None \(0\) \(0\) \(-432\) \(0\) $\mathrm{SU}(2)[C_{18}]$
54.8.a.a 54.a 1.a $1$ $16.869$ \(\Q\) None \(-8\) \(0\) \(-120\) \(377\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+2^{6}q^{4}-120q^{5}+377q^{7}+\cdots\)
54.8.a.b 54.a 1.a $1$ $16.869$ \(\Q\) None \(-8\) \(0\) \(105\) \(-937\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+2^{6}q^{4}+105q^{5}-937q^{7}+\cdots\)
54.8.a.c 54.a 1.a $1$ $16.869$ \(\Q\) None \(-8\) \(0\) \(312\) \(323\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+2^{6}q^{4}+312q^{5}+323q^{7}+\cdots\)
54.8.a.d 54.a 1.a $1$ $16.869$ \(\Q\) None \(8\) \(0\) \(-312\) \(323\) $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+2^{6}q^{4}-312q^{5}+323q^{7}+\cdots\)
54.8.a.e 54.a 1.a $1$ $16.869$ \(\Q\) None \(8\) \(0\) \(-105\) \(-937\) $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+2^{6}q^{4}-105q^{5}-937q^{7}+\cdots\)
54.8.a.f 54.a 1.a $1$ $16.869$ \(\Q\) None \(8\) \(0\) \(120\) \(377\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+2^{6}q^{4}+120q^{5}+377q^{7}+\cdots\)
54.8.a.g 54.a 1.a $2$ $16.869$ \(\Q(\sqrt{329}) \) None \(-16\) \(0\) \(48\) \(880\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+2^{6}q^{4}+(24+\beta )q^{5}+(440+\cdots)q^{7}+\cdots\)
54.8.a.h 54.a 1.a $2$ $16.869$ \(\Q(\sqrt{329}) \) None \(16\) \(0\) \(-48\) \(880\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+2^{6}q^{4}+(-24-\beta )q^{5}+(440+\cdots)q^{7}+\cdots\)
54.8.c.a 54.c 9.c $6$ $16.869$ 6.0.\(\cdots\).1 None \(24\) \(0\) \(-54\) \(210\) $\mathrm{SU}(2)[C_{3}]$ \(q+8\beta _{1}q^{2}+(-2^{6}+2^{6}\beta _{1})q^{4}+(-18+\cdots)q^{5}+\cdots\)
54.8.c.b 54.c 9.c $8$ $16.869$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-32\) \(0\) \(-54\) \(-44\) $\mathrm{SU}(2)[C_{3}]$ \(q-8\beta _{1}q^{2}+(-2^{6}+2^{6}\beta _{1})q^{4}+(-14+\cdots)q^{5}+\cdots\)
54.8.e.a 54.e 27.e $60$ $16.869$ None \(0\) \(0\) \(213\) \(1677\) $\mathrm{SU}(2)[C_{9}]$
54.8.e.b 54.e 27.e $66$ $16.869$ None \(0\) \(0\) \(213\) \(-1677\) $\mathrm{SU}(2)[C_{9}]$
54.9.b.a 54.b 3.b $2$ $21.998$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-4130\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2^{7}q^{4}+60\beta q^{5}-2065q^{7}+\cdots\)
54.9.b.b 54.b 3.b $4$ $21.998$ \(\Q(\sqrt{-2}, \sqrt{79})\) None \(0\) \(0\) \(0\) \(164\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-2^{7}q^{4}+(-21\beta _{1}+\beta _{2})q^{5}+\cdots\)
54.9.b.c 54.b 3.b $4$ $21.998$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(308\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{8}^{2}q^{2}-2^{7}q^{4}+(-11\zeta_{8}+51\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
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