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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
648.1.b.a 648.b 8.d $1$ $0.323$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}+q^{17}+\cdots\)
648.1.b.b 648.b 8.d $1$ $0.323$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}-q^{11}+q^{16}-q^{17}+\cdots\)
648.1.j.a 648.j 72.j $2$ $0.323$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(-1\) \(0\) \(1\) \(1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
648.1.j.b 648.j 72.j $2$ $0.323$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(1\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
648.1.r.a 648.r 216.r $6$ $0.323$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots\)
648.1.bf.a 648.bf 648.af $18$ $0.323$ \(\Q(\zeta_{54})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{54}^{7}q^{2}-\zeta_{54}^{19}q^{3}+\zeta_{54}^{14}q^{4}+\cdots\)
648.2.a.a 648.a 1.a $1$ $5.174$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+5q^{11}-5q^{13}-2q^{17}+\cdots\)
648.2.a.b 648.a 1.a $1$ $5.174$ \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{11}-5q^{13}-5q^{17}+8q^{19}+\cdots\)
648.2.a.c 648.a 1.a $1$ $5.174$ \(\Q\) None None \(0\) \(0\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}-5q^{11}-5q^{13}+2q^{17}+\cdots\)
648.2.a.d 648.a 1.a $1$ $5.174$ \(\Q\) None None \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}-5q^{13}+5q^{17}+8q^{19}+\cdots\)
648.2.a.e 648.a 1.a $2$ $5.174$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}-2\beta q^{7}-2q^{11}+(1+\cdots)q^{13}+\cdots\)
648.2.a.f 648.a 1.a $2$ $5.174$ \(\Q(\sqrt{33}) \) None None \(0\) \(0\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+(2-\beta )q^{7}+q^{11}+(2+\beta )q^{13}+\cdots\)
648.2.a.g 648.a 1.a $2$ $5.174$ \(\Q(\sqrt{33}) \) None None \(0\) \(0\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(2-\beta )q^{7}-q^{11}+(2+\beta )q^{13}+\cdots\)
648.2.a.h 648.a 1.a $2$ $5.174$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+2\beta q^{7}+2q^{11}+(1-2\beta )q^{13}+\cdots\)
648.2.d.a 648.d 8.b $2$ $5.174$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-2iq^{4}-2iq^{5}+4q^{7}+\cdots\)
648.2.d.b 648.d 8.b $2$ $5.174$ \(\Q(\sqrt{-7}) \) None None \(-1\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
648.2.d.c 648.d 8.b $2$ $5.174$ \(\Q(\sqrt{-7}) \) None None \(1\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-2+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
648.2.d.d 648.d 8.b $2$ $5.174$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+2iq^{4}-2iq^{5}+4q^{7}+\cdots\)
648.2.d.e 648.d 8.b $4$ $5.174$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
648.2.d.f 648.d 8.b $4$ $5.174$ \(\Q(\sqrt{3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}-4q^{7}+\cdots\)
648.2.d.g 648.d 8.b $4$ $5.174$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)
648.2.d.h 648.d 8.b $4$ $5.174$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(\beta _{2}+\beta _{3})q^{5}+\cdots\)
648.2.d.i 648.d 8.b $4$ $5.174$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
648.2.d.j 648.d 8.b $8$ $5.174$ 8.0.\(\cdots\).1 None None \(-1\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{5}q^{4}+(\beta _{1}+\beta _{4}-\beta _{7})q^{5}+\cdots\)
648.2.d.k 648.d 8.b $8$ $5.174$ 8.0.\(\cdots\).1 None None \(1\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{5}q^{4}+(-\beta _{1}-\beta _{4}+\beta _{7})q^{5}+\cdots\)
648.2.f.a 648.f 24.f $4$ $5.174$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
648.2.f.b 648.f 24.f $16$ $5.174$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(1-\beta _{9})q^{4}-\beta _{4}q^{5}+(-\beta _{7}+\cdots)q^{7}+\cdots\)
648.2.f.c 648.f 24.f $24$ $5.174$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
648.2.i.a 648.i 9.c $2$ $5.174$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
648.2.i.b 648.i 9.c $2$ $5.174$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
648.2.i.c 648.i 9.c $2$ $5.174$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
648.2.i.d 648.i 9.c $2$ $5.174$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
648.2.i.e 648.i 9.c $2$ $5.174$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
648.2.i.f 648.i 9.c $2$ $5.174$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
648.2.i.g 648.i 9.c $2$ $5.174$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
648.2.i.h 648.i 9.c $2$ $5.174$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(4\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
648.2.i.i 648.i 9.c $4$ $5.174$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
648.2.i.j 648.i 9.c $4$ $5.174$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\)
648.2.l.a 648.l 72.l $4$ $5.174$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}-2q^{4}+(-\beta _{1}+2\beta _{3})q^{5}+\cdots\)
648.2.l.b 648.l 72.l $4$ $5.174$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{3}q^{8}+2\beta _{1}q^{11}+\cdots\)
648.2.l.c 648.l 72.l $4$ $5.174$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-\beta _{1}+2\beta _{3})q^{5}+\cdots\)
648.2.l.d 648.l 72.l $8$ $5.174$ 8.0.170772624.1 None None \(-3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{2}+(-\beta _{2}-\beta _{7})q^{4}+\cdots\)
648.2.l.e 648.l 72.l $8$ $5.174$ 8.0.170772624.1 None None \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{3}+\beta _{7})q^{5}+(2+\cdots)q^{7}+\cdots\)
648.2.l.f 648.l 72.l $16$ $5.174$ 16.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{6}+\beta _{12})q^{2}+(1-\beta _{3}-\beta _{8})q^{4}+\cdots\)
648.2.l.g 648.l 72.l $48$ $5.174$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
648.2.n.a 648.n 72.n $4$ $5.174$ \(\Q(\zeta_{12})\) None None \(-4\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}^{3})q^{2}-2\zeta_{12}^{3}q^{4}+(-1+\cdots)q^{5}+\cdots\)
648.2.n.b 648.n 72.n $4$ $5.174$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
648.2.n.c 648.n 72.n $4$ $5.174$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
648.2.n.d 648.n 72.n $4$ $5.174$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(-1\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\)
648.2.n.e 648.n 72.n $4$ $5.174$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}-2q^{4}+(-2-\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
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