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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
855.1.g.a 855.g 95.d $1$ $0.427$ \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{4}-q^{5}+2q^{11}+q^{16}+q^{19}+\cdots\)
855.1.g.b 855.g 95.d $2$ $0.427$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{285}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-iq^{5}+q^{16}-iq^{17}-q^{19}+\cdots\)
855.1.g.c 855.g 95.d $2$ $0.427$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta q^{2}+q^{4}+q^{5}-\beta q^{10}+\beta q^{13}+\cdots\)
855.1.m.a 855.m 285.j $4$ $0.427$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+(-1-\zeta_{8}^{2})q^{7}+\cdots\)
855.1.m.b 855.m 285.j $4$ $0.427$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+(1+\zeta_{8}^{2})q^{7}+\cdots\)
855.1.u.a 855.u 285.n $8$ $0.427$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{5}-\zeta_{24}^{11})q^{2}-\zeta_{24}^{4}q^{4}+\cdots\)
855.1.v.a 855.v 95.h $4$ $0.427$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
855.1.z.a 855.z 855.z $2$ $0.427$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-95}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
855.1.z.b 855.z 855.z $2$ $0.427$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-95}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
855.1.z.c 855.z 855.z $4$ $0.427$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}-\zeta_{12}q^{3}+(-1+\cdots)q^{4}+\cdots\)
855.1.z.d 855.z 855.z $8$ $0.427$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{11}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
855.1.ck.a 855.ck 95.m $8$ $0.427$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{7}q^{5}+\zeta_{24}^{3}q^{8}-\zeta_{24}^{8}q^{10}+\cdots\)
855.1.cw.a 855.cw 95.o $12$ $0.427$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{36}^{7}+\zeta_{36}^{15})q^{2}+(\zeta_{36}^{4}-\zeta_{36}^{12}+\cdots)q^{4}+\cdots\)
855.2.a.a 855.a 1.a $1$ $6.827$ \(\Q\) None None \(-1\) \(0\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
855.2.a.b 855.a 1.a $1$ $6.827$ \(\Q\) None None \(-1\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}-2q^{7}+3q^{8}-q^{10}+\cdots\)
855.2.a.c 855.a 1.a $1$ $6.827$ \(\Q\) None None \(1\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
855.2.a.d 855.a 1.a $2$ $6.827$ \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+\beta q^{7}+\cdots\)
855.2.a.e 855.a 1.a $2$ $6.827$ \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)
855.2.a.f 855.a 1.a $2$ $6.827$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-\beta q^{8}+\cdots\)
855.2.a.g 855.a 1.a $2$ $6.827$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}-q^{5}+(-1+\beta )q^{7}+\cdots\)
855.2.a.h 855.a 1.a $3$ $6.827$ 3.3.148.1 None None \(-1\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}-\beta _{2}q^{7}+\cdots\)
855.2.a.i 855.a 1.a $3$ $6.827$ 3.3.148.1 None None \(-1\) \(0\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+2\beta _{2}q^{7}+\cdots\)
855.2.a.j 855.a 1.a $3$ $6.827$ 3.3.148.1 None None \(-1\) \(0\) \(3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
855.2.a.k 855.a 1.a $3$ $6.827$ 3.3.148.1 None None \(1\) \(0\) \(-3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-2+\cdots)q^{7}+\cdots\)
855.2.a.l 855.a 1.a $3$ $6.827$ 3.3.148.1 None None \(1\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}-\beta _{2}q^{7}+\cdots\)
855.2.a.m 855.a 1.a $4$ $6.827$ 4.4.11344.1 None None \(2\) \(0\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)
855.2.b.a 855.b 285.b $4$ $6.827$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
855.2.b.b 855.b 285.b $4$ $6.827$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+3\zeta_{8}^{2}q^{8}+\cdots\)
855.2.b.c 855.b 285.b $8$ $6.827$ 8.0.8540717056.1 \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+\beta _{6}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
855.2.b.d 855.b 285.b $24$ $6.827$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
855.2.c.a 855.c 5.b $2$ $6.827$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots\)
855.2.c.b 855.c 5.b $2$ $6.827$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(1+2i)q^{5}+2iq^{7}+\cdots\)
855.2.c.c 855.c 5.b $2$ $6.827$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(2-i)q^{5}-2iq^{7}+3iq^{8}+\cdots\)
855.2.c.d 855.c 5.b $6$ $6.827$ 6.0.16516096.1 None None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots\)
855.2.c.e 855.c 5.b $6$ $6.827$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
855.2.c.f 855.c 5.b $12$ $6.827$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}+(-1+\beta _{2})q^{4}-\beta _{8}q^{5}-\beta _{6}q^{7}+\cdots\)
855.2.c.g 855.c 5.b $14$ $6.827$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
855.2.h.a 855.h 57.d $24$ $6.827$ None None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$
855.2.i.a 855.i 9.c $26$ $6.827$ None None \(3\) \(-2\) \(-13\) \(10\) $\mathrm{SU}(2)[C_{3}]$
855.2.i.b 855.i 9.c $30$ $6.827$ None None \(-3\) \(2\) \(15\) \(2\) $\mathrm{SU}(2)[C_{3}]$
855.2.i.c 855.i 9.c $42$ $6.827$ None None \(-3\) \(-2\) \(-21\) \(-2\) $\mathrm{SU}(2)[C_{3}]$
855.2.i.d 855.i 9.c $46$ $6.827$ None None \(3\) \(2\) \(23\) \(-10\) $\mathrm{SU}(2)[C_{3}]$
855.2.j.a 855.j 171.g $80$ $6.827$ None None \(-2\) \(1\) \(-80\) \(1\) $\mathrm{SU}(2)[C_{3}]$
855.2.j.b 855.j 171.g $80$ $6.827$ None None \(-2\) \(1\) \(80\) \(1\) $\mathrm{SU}(2)[C_{3}]$
855.2.k.a 855.k 19.c $2$ $6.827$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
855.2.k.b 855.k 19.c $2$ $6.827$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}-4q^{7}-3q^{11}+\cdots\)
855.2.k.c 855.k 19.c $2$ $6.827$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+2q^{7}+3q^{11}+\cdots\)
855.2.k.d 855.k 19.c $2$ $6.827$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
855.2.k.e 855.k 19.c $4$ $6.827$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-1\) \(0\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
855.2.k.f 855.k 19.c $4$ $6.827$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(2\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots\)
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