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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
840.1.bp.a 840.bp 840.ap $4$ $0.419$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots\)
840.1.bp.b 840.bp 840.ap $4$ $0.419$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots\)
840.1.bp.c 840.bp 840.ap $8$ $0.419$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{5}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
840.1.bp.d 840.bp 840.ap $8$ $0.419$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
840.1.cg.a 840.cg 840.bg $4$ $0.419$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
840.1.cg.b 840.cg 840.bg $4$ $0.419$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
840.1.dh.a 840.dh 840.ch $8$ $0.419$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots\)
840.1.dh.b 840.dh 840.ch $8$ $0.419$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots\)
840.2.a.a 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
840.2.a.b 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
840.2.a.c 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
840.2.a.d 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(-1\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
840.2.a.e 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(-1\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
840.2.a.f 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(-1\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
840.2.a.g 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
840.2.a.h 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
840.2.a.i 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
840.2.a.j 840.a 1.a $1$ $6.707$ \(\Q\) None None \(0\) \(1\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
840.2.a.k 840.a 1.a $2$ $6.707$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}+\beta q^{11}+2q^{13}+\cdots\)
840.2.e.a 840.e 24.f $4$ $6.707$ \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}-2\zeta_{8}q^{4}+\cdots\)
840.2.e.b 840.e 24.f $4$ $6.707$ \(\Q(\zeta_{8})\) None None \(4\) \(-4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}+2\zeta_{8}q^{4}+\cdots\)
840.2.e.c 840.e 24.f $44$ $6.707$ None None \(-2\) \(4\) \(44\) \(0\) $\mathrm{SU}(2)[C_{2}]$
840.2.e.d 840.e 24.f $44$ $6.707$ None None \(2\) \(4\) \(-44\) \(0\) $\mathrm{SU}(2)[C_{2}]$
840.2.f.a 840.f 21.c $16$ $6.707$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-16\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-q^{5}+\beta _{4}q^{7}-\beta _{1}q^{9}+\beta _{8}q^{11}+\cdots\)
840.2.f.b 840.f 21.c $16$ $6.707$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(16\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+q^{5}+\beta _{9}q^{7}-\beta _{1}q^{9}+\beta _{8}q^{11}+\cdots\)
840.2.g.a 840.g 8.b $8$ $6.707$ \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{16}^{5}q^{2}+\zeta_{16}^{2}q^{3}-\zeta_{16}q^{4}+\zeta_{16}^{2}q^{5}+\cdots\)
840.2.g.b 840.g 8.b $12$ $6.707$ 12.0.\(\cdots\).1 None None \(-2\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{4}q^{3}-\beta _{7}q^{4}-\beta _{4}q^{5}+\cdots\)
840.2.g.c 840.g 8.b $12$ $6.707$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+\beta _{7}q^{4}-\beta _{4}q^{5}+\cdots\)
840.2.g.d 840.g 8.b $16$ $6.707$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-2\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{5}q^{3}-\beta _{2}q^{4}+\beta _{5}q^{5}+\cdots\)
840.2.j.a 840.j 40.f $2$ $6.707$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-i)q^{2}-q^{3}+2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
840.2.j.b 840.j 40.f $2$ $6.707$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}+q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
840.2.j.c 840.j 40.f $2$ $6.707$ \(\Q(\sqrt{-1}) \) None None \(2\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}-q^{3}+2iq^{4}+(2+i)q^{5}+\cdots\)
840.2.j.d 840.j 40.f $2$ $6.707$ \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+q^{3}+2iq^{4}+(2+i)q^{5}+\cdots\)
840.2.j.e 840.j 40.f $32$ $6.707$ None None \(-2\) \(-32\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
840.2.j.f 840.j 40.f $32$ $6.707$ None None \(2\) \(32\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
840.2.k.a 840.k 105.g $24$ $6.707$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
840.2.k.b 840.k 105.g $24$ $6.707$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
840.2.p.a 840.p 120.m $72$ $6.707$ None None \(0\) \(0\) \(0\) \(-72\) $\mathrm{SU}(2)[C_{2}]$
840.2.p.b 840.p 120.m $72$ $6.707$ None None \(0\) \(0\) \(0\) \(72\) $\mathrm{SU}(2)[C_{2}]$
840.2.t.a 840.t 5.b $2$ $6.707$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(-1-2i)q^{5}-iq^{7}-q^{9}+\cdots\)
840.2.t.b 840.t 5.b $2$ $6.707$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(-1+2i)q^{5}-iq^{7}-q^{9}+\cdots\)
840.2.t.c 840.t 5.b $4$ $6.707$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}-q^{9}-2q^{11}+\cdots\)
840.2.t.d 840.t 5.b $6$ $6.707$ 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
840.2.t.e 840.t 5.b $6$ $6.707$ 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
840.2.u.a 840.u 840.u $4$ $6.707$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}-2q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
840.2.u.b 840.u 840.u $4$ $6.707$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}-2q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
840.2.u.c 840.u 840.u $8$ $6.707$ 8.0.2517630976.5 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}-\beta _{6}q^{5}+(\beta _{3}+\cdots)q^{6}+\cdots\)
840.2.u.d 840.u 840.u $8$ $6.707$ 8.0.2517630976.5 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+2q^{4}+\beta _{6}q^{5}+(\beta _{2}+\cdots)q^{6}+\cdots\)
840.2.u.e 840.u 840.u $160$ $6.707$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
840.2.w.a 840.w 280.n $48$ $6.707$ None None \(0\) \(-48\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
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