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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.2.a.a 91.a 1.a $1$ $0.727$ \(\Q\) None \(-2\) \(0\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-3q^{5}-q^{7}-3q^{9}+\cdots\)
91.2.a.b 91.a 1.a $1$ $0.727$ \(\Q\) None \(0\) \(-2\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}+4q^{12}+\cdots\)
91.2.a.c 91.a 1.a $2$ $0.727$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(6\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+(3+\beta )q^{5}-2q^{6}+q^{7}+\cdots\)
91.2.a.d 91.a 1.a $3$ $0.727$ 3.3.316.1 None \(1\) \(-2\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
91.2.c.a 91.c 13.b $6$ $0.727$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
91.2.e.a 91.e 7.c $2$ $0.727$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
91.2.e.b 91.e 7.c $4$ $0.727$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(3\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots\)
91.2.e.c 91.e 7.c $10$ $0.727$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)
91.2.f.a 91.f 13.c $4$ $0.727$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(3\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots\)
91.2.f.b 91.f 13.c $4$ $0.727$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
91.2.f.c 91.f 13.c $8$ $0.727$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-1\) \(-14\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
91.2.g.a 91.g 91.g $2$ $0.727$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-6\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}-3q^{3}+(1-\zeta_{6})q^{4}+(-3+\cdots)q^{5}+\cdots\)
91.2.g.b 91.g 91.g $12$ $0.727$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-2\) \(1\) \(9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}+(\beta _{3}-\beta _{11})q^{3}+\cdots\)
91.2.h.a 91.h 91.h $2$ $0.727$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+3\zeta_{6}q^{3}-q^{4}-3\zeta_{6}q^{5}+3\zeta_{6}q^{6}+\cdots\)
91.2.h.b 91.h 91.h $12$ $0.727$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(1\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}+\beta _{5}-\beta _{11})q^{2}+\beta _{11}q^{3}+(1+\cdots)q^{4}+\cdots\)
91.2.i.a 91.i 91.i $12$ $0.727$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{8}q^{2}+\beta _{10}q^{3}+(-\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
91.2.k.a 91.k 91.k $2$ $0.727$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(2-\zeta_{6})q^{5}+\cdots\)
91.2.k.b 91.k 91.k $12$ $0.727$ 12.0.\(\cdots\).1 None \(0\) \(-3\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{9}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
91.2.q.a 91.q 13.e $12$ $0.727$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{4}-\beta _{6}+\beta _{10})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)
91.2.r.a 91.r 91.r $16$ $0.727$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{11}q^{2}+(-1+\beta _{3}+\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
91.2.u.a 91.u 91.u $2$ $0.727$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-2\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
91.2.u.b 91.u 91.u $12$ $0.727$ 12.0.\(\cdots\).1 None \(0\) \(6\) \(3\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{10}q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{8})q^{3}+\cdots\)
91.2.w.a 91.w 91.w $28$ $0.727$ None \(-2\) \(0\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{12}]$
91.2.ba.a 91.ba 91.aa $28$ $0.727$ None \(-2\) \(-6\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
91.2.bb.a 91.bb 91.ab $32$ $0.727$ None \(-2\) \(-12\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
91.2.bc.a 91.bc 91.ac $32$ $0.727$ None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
91.3.b.a 91.b 91.b $1$ $2.480$ \(\Q\) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(-3\) \(7\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}-3q^{5}+7q^{7}+9q^{9}-13q^{13}+\cdots\)
91.3.b.b 91.b 91.b $1$ $2.480$ \(\Q\) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(3\) \(-7\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}+3q^{5}-7q^{7}+9q^{9}+13q^{13}+\cdots\)
91.3.b.c 91.b 91.b $4$ $2.480$ \(\Q(i, \sqrt{26})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+3q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
91.3.b.d 91.b 91.b $6$ $2.480$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(-8\) \(7\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(-5+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
91.3.b.e 91.b 91.b $6$ $2.480$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(8\) \(-7\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(-5+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
91.3.d.a 91.d 7.b $16$ $2.480$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(2+\beta _{4})q^{4}+\beta _{3}q^{5}+\cdots\)
91.3.j.a 91.j 13.d $28$ $2.480$ None \(4\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{4}]$
91.3.l.a 91.l 91.l $34$ $2.480$ None \(0\) \(-6\) \(0\) \(-19\) $\mathrm{SU}(2)[C_{6}]$
91.3.m.a 91.m 91.m $34$ $2.480$ None \(1\) \(0\) \(-6\) \(14\) $\mathrm{SU}(2)[C_{6}]$
91.3.n.a 91.n 91.n $4$ $2.480$ \(\Q(\sqrt{-3}, \sqrt{-13})\) None \(-2\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{2})q^{2}-\beta _{1}q^{3}+3\beta _{2}q^{4}+\cdots\)
91.3.n.b 91.n 91.n $28$ $2.480$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{6}]$
91.3.o.a 91.o 7.d $32$ $2.480$ None \(-2\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
91.3.p.a 91.p 91.p $34$ $2.480$ None \(-3\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$
91.3.s.a 91.s 91.s $32$ $2.480$ None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
91.3.t.a 91.t 91.t $32$ $2.480$ None \(-6\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{6}]$
91.3.v.a 91.v 91.v $34$ $2.480$ None \(-2\) \(0\) \(-6\) \(-7\) $\mathrm{SU}(2)[C_{6}]$
91.3.x.a 91.x 91.x $68$ $2.480$ None \(-2\) \(2\) \(-2\) \(-26\) $\mathrm{SU}(2)[C_{12}]$
91.3.y.a 91.y 13.f $56$ $2.480$ None \(-4\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{12}]$
91.3.z.a 91.z 91.z $64$ $2.480$ None \(-2\) \(-4\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
91.3.bd.a 91.bd 91.ad $68$ $2.480$ None \(-2\) \(-4\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{12}]$
91.4.a.a 91.a 1.a $3$ $5.369$ 3.3.1384.1 None \(1\) \(1\) \(-22\) \(-21\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
91.4.a.b 91.a 1.a $4$ $5.369$ 4.4.5364412.1 None \(-4\) \(-5\) \(-36\) \(28\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
91.4.a.c 91.a 1.a $5$ $5.369$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(7\) \(-5\) \(16\) \(-35\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{4})q^{2}+(-1-\beta _{3})q^{3}+(10-\beta _{2}+\cdots)q^{4}+\cdots\)
91.4.a.d 91.a 1.a $6$ $5.369$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(2\) \(13\) \(26\) \(42\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
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