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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
310.2.a.a 310.a 1.a $1$ $2.475$ \(\Q\) None \(1\) \(-2\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}-4q^{7}+\cdots\)
310.2.a.b 310.a 1.a $1$ $2.475$ \(\Q\) None \(1\) \(2\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots\)
310.2.a.c 310.a 1.a $2$ $2.475$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
310.2.a.d 310.a 1.a $2$ $2.475$ \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-2q^{7}+\cdots\)
310.2.a.e 310.a 1.a $3$ $2.475$ 3.3.148.1 None \(3\) \(2\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
310.2.b.a 310.b 5.b $8$ $2.475$ 8.0.619810816.2 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
310.2.b.b 310.b 5.b $8$ $2.475$ 8.0.2058981376.2 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+\beta _{6}q^{3}-q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
310.2.e.a 310.e 31.c $6$ $2.475$ 6.0.309123.1 None \(-6\) \(-1\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{2}q^{6}+\cdots\)
310.2.e.b 310.e 31.c $6$ $2.475$ 6.0.49572675.1 None \(-6\) \(1\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
310.2.e.c 310.e 31.c $6$ $2.475$ 6.0.309123.1 None \(6\) \(-1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(\beta _{1}-\beta _{5})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
310.2.e.d 310.e 31.c $6$ $2.475$ 6.0.771147.1 None \(6\) \(1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+\beta _{4}q^{5}+\cdots\)
310.2.f.a 310.f 155.f $32$ $2.475$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$
310.2.h.a 310.h 31.d $4$ $2.475$ \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(4\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots\)
310.2.h.b 310.h 31.d $4$ $2.475$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\cdots\)
310.2.h.c 310.h 31.d $8$ $2.475$ 8.0.484000000.9 None \(-2\) \(0\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{1}-\beta _{6}+\cdots)q^{3}+\cdots\)
310.2.h.d 310.h 31.d $8$ $2.475$ 8.0.64000000.2 None \(-2\) \(2\) \(8\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)
310.2.h.e 310.h 31.d $8$ $2.475$ 8.0.64000000.2 None \(2\) \(2\) \(-8\) \(10\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\beta _{2}+\beta _{4}+\beta _{6})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
310.2.k.a 310.k 155.j $32$ $2.475$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
310.2.n.a 310.n 155.n $64$ $2.475$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{10}]$
310.2.p.a 310.p 155.p $64$ $2.475$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{12}]$
310.2.q.a 310.q 31.g $8$ $2.475$ \(\Q(\zeta_{15})\) None \(-2\) \(-8\) \(-4\) \(-16\) $\mathrm{SU}(2)[C_{15}]$ \(q+\zeta_{15}^{3}q^{2}+(-2+\zeta_{15}+\zeta_{15}^{2}-2\zeta_{15}^{3}+\cdots)q^{3}+\cdots\)
310.2.q.b 310.q 31.g $8$ $2.475$ \(\Q(\zeta_{15})\) None \(-2\) \(3\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{15}]$ \(q+\zeta_{15}^{3}q^{2}+(1-\zeta_{15}^{4}+\zeta_{15}^{5})q^{3}+\cdots\)
310.2.q.c 310.q 31.g $8$ $2.475$ \(\Q(\zeta_{15})\) None \(-2\) \(4\) \(-4\) \(9\) $\mathrm{SU}(2)[C_{15}]$ \(q+\zeta_{15}^{3}q^{2}+(1-\zeta_{15}-\zeta_{15}^{2}+2\zeta_{15}^{3}+\cdots)q^{3}+\cdots\)
310.2.q.d 310.q 31.g $8$ $2.475$ \(\Q(\zeta_{15})\) None \(2\) \(-8\) \(4\) \(-7\) $\mathrm{SU}(2)[C_{15}]$ \(q-\zeta_{15}^{3}q^{2}+(-1-\zeta_{15}+\zeta_{15}^{2}+\zeta_{15}^{5}+\cdots)q^{3}+\cdots\)
310.2.q.e 310.q 31.g $8$ $2.475$ \(\Q(\zeta_{15})\) None \(2\) \(1\) \(4\) \(12\) $\mathrm{SU}(2)[C_{15}]$ \(q-\zeta_{15}^{3}q^{2}+(1-\zeta_{15}^{4}+\zeta_{15}^{5}-2\zeta_{15}^{7})q^{3}+\cdots\)
310.2.q.f 310.q 31.g $8$ $2.475$ \(\Q(\zeta_{15})\) None \(2\) \(6\) \(4\) \(2\) $\mathrm{SU}(2)[C_{15}]$ \(q-\zeta_{15}^{3}q^{2}+(\zeta_{15}-\zeta_{15}^{2}+\zeta_{15}^{4}+\cdots)q^{3}+\cdots\)
310.2.q.g 310.q 31.g $24$ $2.475$ None \(-6\) \(1\) \(12\) \(-11\) $\mathrm{SU}(2)[C_{15}]$
310.2.q.h 310.q 31.g $24$ $2.475$ None \(6\) \(1\) \(-12\) \(13\) $\mathrm{SU}(2)[C_{15}]$
310.2.s.a 310.s 155.r $128$ $2.475$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{20}]$
310.2.t.a 310.t 155.u $128$ $2.475$ None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{30}]$
310.2.w.a 310.w 155.x $256$ $2.475$ None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{60}]$
310.3.c.a 310.c 31.b $24$ $8.447$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$
310.3.d.a 310.d 155.c $32$ $8.447$ None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$
310.3.g.a 310.g 5.c $28$ $8.447$ None \(-28\) \(4\) \(8\) \(-16\) $\mathrm{SU}(2)[C_{4}]$
310.3.g.b 310.g 5.c $32$ $8.447$ None \(32\) \(-4\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
310.3.i.a 310.i 155.i $64$ $8.447$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
310.3.j.a 310.j 31.e $40$ $8.447$ None \(0\) \(12\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$
310.3.l.a 310.l 155.m $128$ $8.447$ None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{10}]$
310.3.m.a 310.m 31.f $48$ $8.447$ None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{10}]$
310.3.m.b 310.m 31.f $48$ $8.447$ None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{10}]$
310.3.o.a 310.o 155.o $4$ $8.447$ \(\Q(\zeta_{12})\) None \(-4\) \(-6\) \(-6\) \(18\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}-3\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
310.3.o.b 310.o 155.o $4$ $8.447$ \(\Q(\zeta_{12})\) None \(4\) \(6\) \(8\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}^{3})q^{2}+(3\zeta_{12}+3\zeta_{12}^{2}-3\zeta_{12}^{3})q^{3}+\cdots\)
310.3.o.c 310.o 155.o $60$ $8.447$ None \(-60\) \(10\) \(-2\) \(-22\) $\mathrm{SU}(2)[C_{12}]$
310.3.o.d 310.o 155.o $60$ $8.447$ None \(60\) \(-2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{12}]$
310.3.r.a 310.r 155.s $128$ $8.447$ None \(-32\) \(4\) \(8\) \(-12\) $\mathrm{SU}(2)[C_{20}]$
310.3.r.b 310.r 155.s $128$ $8.447$ None \(32\) \(4\) \(-8\) \(-12\) $\mathrm{SU}(2)[C_{20}]$
310.3.u.a 310.u 31.h $80$ $8.447$ None \(0\) \(-6\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{30}]$
310.3.u.b 310.u 31.h $80$ $8.447$ None \(0\) \(-6\) \(0\) \(16\) $\mathrm{SU}(2)[C_{30}]$
310.3.v.a 310.v 155.v $256$ $8.447$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{30}]$
310.3.x.a 310.x 155.w $256$ $8.447$ None \(-64\) \(-4\) \(-8\) \(24\) $\mathrm{SU}(2)[C_{60}]$
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