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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
570.2.a.a 570.a 1.a $1$ $4.551$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.b 570.a 1.a $1$ $4.551$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.c 570.a 1.a $1$ $4.551$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.d 570.a 1.a $1$ $4.551$ \(\Q\) None \(-1\) \(1\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
570.2.a.e 570.a 1.a $1$ $4.551$ \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
570.2.a.f 570.a 1.a $1$ $4.551$ \(\Q\) None \(-1\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
570.2.a.g 570.a 1.a $1$ $4.551$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
570.2.a.h 570.a 1.a $1$ $4.551$ \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
570.2.a.i 570.a 1.a $1$ $4.551$ \(\Q\) None \(1\) \(-1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
570.2.a.j 570.a 1.a $1$ $4.551$ \(\Q\) None \(1\) \(1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.k 570.a 1.a $1$ $4.551$ \(\Q\) None \(1\) \(1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.l 570.a 1.a $1$ $4.551$ \(\Q\) None \(1\) \(1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.m 570.a 1.a $1$ $4.551$ \(\Q\) None \(1\) \(1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
570.2.c.a 570.c 285.b $4$ $4.551$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.b 570.c 285.b $4$ $4.551$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.c 570.c 285.b $8$ $4.551$ 8.0.1499238400.2 None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.c.d 570.c 285.b $8$ $4.551$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}-q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
570.2.c.e 570.c 285.b $8$ $4.551$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}q^{2}+(-\zeta_{24}-\zeta_{24}^{6})q^{3}-q^{4}+\cdots\)
570.2.c.f 570.c 285.b $8$ $4.551$ 8.0.1499238400.2 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.d.a 570.d 5.b $2$ $4.551$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
570.2.d.b 570.d 5.b $2$ $4.551$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
570.2.d.c 570.d 5.b $6$ $4.551$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots\)
570.2.d.d 570.d 5.b $6$ $4.551$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots\)
570.2.f.a 570.f 57.d $4$ $4.551$ \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-1-\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.b 570.f 57.d $4$ $4.551$ \(\Q(\zeta_{8})\) None \(4\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(1+\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.c 570.f 57.d $8$ $4.551$ 8.0.7278137344.1 None \(-8\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.f.d 570.f 57.d $8$ $4.551$ 8.0.7278137344.1 None \(8\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.i.a 570.i 19.c $2$ $4.551$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.b 570.i 19.c $2$ $4.551$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.c 570.i 19.c $2$ $4.551$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(1\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.d 570.i 19.c $2$ $4.551$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.e 570.i 19.c $2$ $4.551$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.f 570.i 19.c $4$ $4.551$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(2\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
570.2.i.g 570.i 19.c $4$ $4.551$ \(\Q(\sqrt{-3}, \sqrt{73})\) None \(2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
570.2.i.h 570.i 19.c $4$ $4.551$ \(\Q(\sqrt{-3}, \sqrt{19})\) None \(2\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.i 570.i 19.c $4$ $4.551$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.j 570.i 19.c $6$ $4.551$ 6.0.29654208.1 None \(-3\) \(-3\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
570.2.k.a 570.k 15.e $36$ $4.551$ None \(0\) \(4\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{4}]$
570.2.k.b 570.k 15.e $36$ $4.551$ None \(0\) \(4\) \(0\) \(20\) $\mathrm{SU}(2)[C_{4}]$
570.2.m.a 570.m 95.g $20$ $4.551$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots\)
570.2.m.b 570.m 95.g $20$ $4.551$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
570.2.n.a 570.n 285.q $80$ $4.551$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
570.2.q.a 570.q 95.i $8$ $4.551$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}-\zeta_{24}^{4})q^{3}+\cdots\)
570.2.q.b 570.q 95.i $12$ $4.551$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+\cdots\)
570.2.q.c 570.q 95.i $20$ $4.551$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{11}q^{2}+\beta _{11}q^{3}+(1-\beta _{12})q^{4}+\cdots\)
570.2.s.a 570.s 57.f $24$ $4.551$ None \(-12\) \(4\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$
570.2.s.b 570.s 57.f $24$ $4.551$ None \(12\) \(2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$
570.2.u.a 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.b 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.c 570.u 19.e $6$ $4.551$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
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