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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
805.1.t.a 805.t 805.t $2$ $0.402$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
805.1.t.b 805.t 805.t $2$ $0.402$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(1\) \(1\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
805.2.a.a 805.a 1.a $1$ $6.428$ \(\Q\) None None \(-1\) \(0\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
805.2.a.b 805.a 1.a $1$ $6.428$ \(\Q\) None None \(-1\) \(0\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
805.2.a.c 805.a 1.a $1$ $6.428$ \(\Q\) None None \(2\) \(-1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
805.2.a.d 805.a 1.a $1$ $6.428$ \(\Q\) None None \(2\) \(3\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+2q^{4}-q^{5}+6q^{6}+\cdots\)
805.2.a.e 805.a 1.a $2$ $6.428$ \(\Q(\sqrt{5}) \) None None \(3\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots\)
805.2.a.f 805.a 1.a $3$ $6.428$ \(\Q(\zeta_{14})^+\) None None \(-2\) \(0\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-1+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
805.2.a.g 805.a 1.a $4$ $6.428$ 4.4.2777.1 None None \(-2\) \(-5\) \(4\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(-1-\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots\)
805.2.a.h 805.a 1.a $4$ $6.428$ 4.4.22545.1 None None \(-1\) \(0\) \(-4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots\)
805.2.a.i 805.a 1.a $4$ $6.428$ 4.4.7537.1 None None \(1\) \(4\) \(-4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.a.j 805.a 1.a $4$ $6.428$ 4.4.2777.1 None None \(3\) \(6\) \(4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
805.2.a.k 805.a 1.a $5$ $6.428$ 5.5.122821.1 None None \(-3\) \(-6\) \(5\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
805.2.a.l 805.a 1.a $5$ $6.428$ 5.5.255877.1 None None \(-1\) \(-4\) \(-5\) \(5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.a.m 805.a 1.a $8$ $6.428$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(7\) \(8\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.c.a 805.c 5.b $2$ $6.428$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{4}+(2-i)q^{5}+iq^{7}+2q^{9}+\cdots\)
805.2.c.b 805.c 5.b $24$ $6.428$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$
805.2.c.c 805.c 5.b $42$ $6.428$ None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$
805.2.d.a 805.d 805.d $4$ $6.428$ \(\Q(\sqrt{-5}, \sqrt{23})\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}-3q^{9}+\cdots\)
805.2.d.b 805.d 805.d $8$ $6.428$ 8.0.40960000.1 None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{4}-\beta _{5})q^{2}-q^{3}-\beta _{2}q^{4}+(\beta _{3}+2\beta _{7})q^{5}+\cdots\)
805.2.d.c 805.d 805.d $8$ $6.428$ 8.0.40960000.1 None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}+q^{3}-\beta _{2}q^{4}+(-2\beta _{3}+\cdots)q^{5}+\cdots\)
805.2.d.d 805.d 805.d $12$ $6.428$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-q^{3}+(-2-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
805.2.d.e 805.d 805.d $12$ $6.428$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+q^{3}+(-2-\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots\)
805.2.d.f 805.d 805.d $48$ $6.428$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
805.2.f.a 805.f 161.c $32$ $6.428$ None None \(-2\) \(0\) \(-32\) \(-3\) $\mathrm{SU}(2)[C_{2}]$
805.2.f.b 805.f 161.c $32$ $6.428$ None None \(-2\) \(0\) \(32\) \(3\) $\mathrm{SU}(2)[C_{2}]$
805.2.i.a 805.i 7.c $2$ $6.428$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(-2\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
805.2.i.b 805.i 7.c $4$ $6.428$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
805.2.i.c 805.i 7.c $24$ $6.428$ None None \(7\) \(2\) \(12\) \(3\) $\mathrm{SU}(2)[C_{3}]$
805.2.i.d 805.i 7.c $26$ $6.428$ None None \(5\) \(2\) \(-13\) \(0\) $\mathrm{SU}(2)[C_{3}]$
805.2.i.e 805.i 7.c $30$ $6.428$ None None \(-5\) \(0\) \(15\) \(-3\) $\mathrm{SU}(2)[C_{3}]$
805.2.i.f 805.i 7.c $34$ $6.428$ None None \(-5\) \(2\) \(-17\) \(-1\) $\mathrm{SU}(2)[C_{3}]$
805.2.k.a 805.k 35.f $176$ $6.428$ None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
805.2.l.a 805.l 115.e $144$ $6.428$ None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
805.2.p.a 805.p 161.g $64$ $6.428$ None None \(2\) \(0\) \(-32\) \(3\) $\mathrm{SU}(2)[C_{6}]$
805.2.p.b 805.p 161.g $64$ $6.428$ None None \(2\) \(0\) \(32\) \(-3\) $\mathrm{SU}(2)[C_{6}]$
805.2.r.a 805.r 805.r $8$ $6.428$ 8.0.\(\cdots\).4 \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+2\beta _{3}q^{4}+(\beta _{4}+\beta _{5})q^{5}+\beta _{1}q^{7}+(3+\cdots)q^{9}+\cdots\)
805.2.r.b 805.r 805.r $176$ $6.428$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
805.2.s.a 805.s 35.j $4$ $6.428$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{12}q^{3}+(-2+2\zeta_{12}^{2})q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots\)
805.2.s.b 805.s 35.j $4$ $6.428$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
805.2.s.c 805.s 35.j $4$ $6.428$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
805.2.s.d 805.s 35.j $164$ $6.428$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
805.2.u.a 805.u 23.c $110$ $6.428$ None None \(0\) \(-2\) \(11\) \(-11\) $\mathrm{SU}(2)[C_{11}]$
805.2.u.b 805.u 23.c $110$ $6.428$ None None \(4\) \(2\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{11}]$
805.2.u.c 805.u 23.c $130$ $6.428$ None None \(-2\) \(-2\) \(13\) \(13\) $\mathrm{SU}(2)[C_{11}]$
805.2.u.d 805.u 23.c $130$ $6.428$ None None \(2\) \(2\) \(-13\) \(13\) $\mathrm{SU}(2)[C_{11}]$
805.2.v.a 805.v 35.k $352$ $6.428$ None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{12}]$
805.2.y.a 805.y 805.y $368$ $6.428$ None None \(-4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
805.2.bb.a 805.bb 161.k $320$ $6.428$ None None \(2\) \(0\) \(-32\) \(-3\) $\mathrm{SU}(2)[C_{22}]$
805.2.bb.b 805.bb 161.k $320$ $6.428$ None None \(2\) \(0\) \(32\) \(3\) $\mathrm{SU}(2)[C_{22}]$
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