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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.1.h.a 864.h 24.h $1$ $0.431$ \(\Q\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(-1\) \(1\) \(q-q^{5}+q^{7}+q^{11}+2q^{29}+q^{31}+\cdots\)
864.1.h.b 864.h 24.h $1$ $0.431$ \(\Q\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(1\) \(1\) \(q+q^{5}+q^{7}-q^{11}-2q^{29}+q^{31}+\cdots\)
864.1.o.a 864.o 36.f $4$ $0.431$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{5}q^{11}+\cdots\)
864.1.t.a 864.t 72.p $2$ $0.431$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{11}+q^{17}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
864.1.bd.a 864.bd 216.r $6$ $0.431$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}q^{3}+\zeta_{18}^{2}q^{9}+(\zeta_{18}^{5}-\zeta_{18}^{6}+\cdots)q^{11}+\cdots\)
864.2.a.a 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-3q^{7}+6q^{11}-3q^{13}+2q^{17}+\cdots\)
864.2.a.b 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+2q^{11}+q^{13}-6q^{17}+\cdots\)
864.2.a.c 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-2q^{11}+q^{13}-6q^{17}+\cdots\)
864.2.a.d 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(-2\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+3q^{7}-6q^{11}-3q^{13}+2q^{17}+\cdots\)
864.2.a.e 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+3q^{11}+4q^{17}-6q^{19}+\cdots\)
864.2.a.f 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-3q^{11}+4q^{17}+6q^{19}+\cdots\)
864.2.a.g 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}-3q^{11}-4q^{17}-6q^{19}+\cdots\)
864.2.a.h 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}+3q^{11}-4q^{17}+6q^{19}+\cdots\)
864.2.a.i 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-3q^{7}-6q^{11}-3q^{13}-2q^{17}+\cdots\)
864.2.a.j 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{11}+q^{13}+6q^{17}+\cdots\)
864.2.a.k 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+2q^{11}+q^{13}+6q^{17}+\cdots\)
864.2.a.l 864.a 1.a $1$ $6.899$ \(\Q\) None None \(0\) \(0\) \(2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+3q^{7}+6q^{11}-3q^{13}-2q^{17}+\cdots\)
864.2.a.m 864.a 1.a $2$ $6.899$ \(\Q(\sqrt{13}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+\beta q^{7}-q^{11}+4q^{13}-2\beta q^{19}+\cdots\)
864.2.a.n 864.a 1.a $2$ $6.899$ \(\Q(\sqrt{13}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-\beta q^{7}+q^{11}+4q^{13}+2\beta q^{19}+\cdots\)
864.2.c.a 864.c 12.b $8$ $6.899$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{3}q^{5}-\zeta_{24}^{7}q^{7}+(\zeta_{24}+\zeta_{24}^{5}+\cdots)q^{11}+\cdots\)
864.2.c.b 864.c 12.b $8$ $6.899$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}^{2}q^{5}+(-\zeta_{24}-\zeta_{24}^{3})q^{7}+\zeta_{24}^{6}q^{11}+\cdots\)
864.2.d.a 864.d 8.b $4$ $6.899$ \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}-q^{7}+3\beta _{1}q^{11}-\beta _{3}q^{13}+\cdots\)
864.2.d.b 864.d 8.b $4$ $6.899$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{5}+(1-\zeta_{8}^{3})q^{7}+(\zeta_{8}+\cdots)q^{11}+\cdots\)
864.2.d.c 864.d 8.b $8$ $6.899$ 8.0.629407744.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}-\beta _{7}q^{7}-\beta _{2}q^{11}+(\beta _{3}+\beta _{6}+\cdots)q^{13}+\cdots\)
864.2.f.a 864.f 24.f $8$ $6.899$ 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}-\beta _{4}q^{7}-\beta _{6}q^{11}+(\beta _{4}+\beta _{7})q^{13}+\cdots\)
864.2.f.b 864.f 24.f $8$ $6.899$ 8.0.170772624.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{6}q^{11}+\beta _{7}q^{13}+\cdots\)
864.2.i.a 864.i 9.c $2$ $6.899$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
864.2.i.b 864.i 9.c $2$ $6.899$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
864.2.i.c 864.i 9.c $4$ $6.899$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{5}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
864.2.i.d 864.i 9.c $4$ $6.899$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
864.2.i.e 864.i 9.c $4$ $6.899$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{5}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+(1+\cdots)q^{11}+\cdots\)
864.2.i.f 864.i 9.c $8$ $6.899$ 8.0.170772624.1 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{5}+(\beta _{1}-\beta _{7})q^{7}-\beta _{3}q^{11}+(-2\beta _{4}+\cdots)q^{13}+\cdots\)
864.2.p.a 864.p 72.l $4$ $6.899$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-6+\beta _{1}+3\beta _{2}-\beta _{3})q^{11}+(-3+\cdots)q^{17}+\cdots\)
864.2.p.b 864.p 72.l $16$ $6.899$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{6}q^{5}+(-\beta _{4}-\beta _{11})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
864.2.r.a 864.r 72.n $4$ $6.899$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{5}+4\zeta_{12}^{2}q^{7}+(3\zeta_{12}-3\zeta_{12}^{3})q^{11}+\cdots\)
864.2.r.b 864.r 72.n $16$ $6.899$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}-\beta _{5}-\beta _{11})q^{5}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
864.2.s.a 864.s 36.h $24$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
864.2.v.a 864.v 32.g $128$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
864.2.v.b 864.v 32.g $128$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
864.2.w.a 864.w 96.o $128$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
864.2.w.b 864.w 96.o $128$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
864.2.y.a 864.y 27.e $48$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
864.2.y.b 864.y 27.e $54$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
864.2.y.c 864.y 27.e $54$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
864.2.y.d 864.y 27.e $60$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
864.2.bf.a 864.bf 216.t $204$ $6.899$ None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{18}]$
864.2.bh.a 864.bh 216.v $12$ $6.899$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q+(-\beta _{4}-\beta _{7}+\beta _{10})q^{3}+(-\beta _{2}+2\beta _{5}+\cdots)q^{9}+\cdots\)
864.2.bh.b 864.bh 216.v $192$ $6.899$ None None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
864.2.bi.a 864.bi 108.l $216$ $6.899$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
864.2.bk.a 864.bk 288.ac $368$ $6.899$ None None \(4\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{24}]$
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