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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.2.a.a 105.a 1.a $1$ $0.838$ \(\Q\) None \(1\) \(1\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
105.2.a.b 105.a 1.a $2$ $0.838$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+3q^{4}-q^{5}+\beta q^{6}+q^{7}+\cdots\)
105.2.b.a 105.b 21.c $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-q^{5}-3q^{6}+\cdots\)
105.2.b.b 105.b 21.c $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+q^{5}+3q^{6}+\cdots\)
105.2.b.c 105.b 21.c $4$ $0.838$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)
105.2.b.d 105.b 21.c $4$ $0.838$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)
105.2.d.a 105.d 5.b $2$ $0.838$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}+(1-2i)q^{5}-q^{6}+\cdots\)
105.2.d.b 105.d 5.b $6$ $0.838$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots\)
105.2.g.a 105.g 105.g $4$ $0.838$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
105.2.g.b 105.g 105.g $4$ $0.838$ \(\Q(\sqrt{-5}, \sqrt{7})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{3}-2q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
105.2.g.c 105.g 105.g $4$ $0.838$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
105.2.i.a 105.i 7.c $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
105.2.i.b 105.i 7.c $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
105.2.i.c 105.i 7.c $4$ $0.838$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{5}-\beta _{3}q^{6}+\cdots\)
105.2.i.d 105.i 7.c $4$ $0.838$ \(\Q(\zeta_{12})\) None \(2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
105.2.j.a 105.j 15.e $24$ $0.838$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
105.2.m.a 105.m 35.f $16$ $0.838$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}+\beta _{10}q^{3}+(-\beta _{2}+\beta _{9}-\beta _{11}+\cdots)q^{4}+\cdots\)
105.2.p.a 105.p 105.p $24$ $0.838$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
105.2.q.a 105.q 35.j $16$ $0.838$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{5}+\beta _{6}-\beta _{15})q^{2}+\beta _{3}q^{3}+(1+\cdots)q^{4}+\cdots\)
105.2.s.a 105.s 21.g $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
105.2.s.b 105.s 21.g $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
105.2.s.c 105.s 21.g $8$ $0.838$ 8.0.856615824.2 None \(-3\) \(1\) \(4\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(1-\beta _{1}+\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
105.2.s.d 105.s 21.g $8$ $0.838$ 8.0.856615824.2 None \(3\) \(2\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}+(1+\beta _{3}+\beta _{6})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
105.2.u.a 105.u 35.k $32$ $0.838$ None \(0\) \(0\) \(-12\) \(8\) $\mathrm{SU}(2)[C_{12}]$
105.2.x.a 105.x 105.x $48$ $0.838$ None \(0\) \(-2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{12}]$
105.3.c.a 105.c 3.b $16$ $2.861$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(-2+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots\)
105.3.e.a 105.e 35.c $16$ $2.861$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{4})q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots\)
105.3.f.a 105.f 15.d $24$ $2.861$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
105.3.h.a 105.h 7.b $12$ $2.861$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{3}q^{3}+(4-\beta _{1})q^{4}+\beta _{8}q^{5}+\cdots\)
105.3.k.a 105.k 105.k $4$ $2.861$ \(\Q(\zeta_{8})\) None \(0\) \(-8\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-2-\zeta_{8}+2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots\)
105.3.k.b 105.k 105.k $4$ $2.861$ \(\Q(\zeta_{8})\) None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(2+\zeta_{8}-2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots\)
105.3.k.c 105.k 105.k $16$ $2.861$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(32\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+(\beta _{7}+\beta _{10}-\beta _{13}+\beta _{15})q^{3}+\cdots\)
105.3.k.d 105.k 105.k $32$ $2.861$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
105.3.l.a 105.l 5.c $24$ $2.861$ None \(8\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{4}]$
105.3.n.a 105.n 7.d $8$ $2.861$ 8.0.\(\cdots\).16 None \(2\) \(-12\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
105.3.n.b 105.n 7.d $12$ $2.861$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(18\) \(0\) \(22\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{10})q^{2}+(2+\beta _{3})q^{3}+(4\beta _{3}+\cdots)q^{4}+\cdots\)
105.3.o.a 105.o 105.o $16$ $2.861$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{9}+\beta _{13})q^{3}+(-1+\cdots)q^{4}+\cdots\)
105.3.o.b 105.o 105.o $40$ $2.861$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
105.3.r.a 105.r 35.i $32$ $2.861$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
105.3.t.a 105.t 21.h $8$ $2.861$ 8.0.3317760000.8 None \(0\) \(-4\) \(0\) \(56\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{4}-\beta _{5})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
105.3.t.b 105.t 21.h $36$ $2.861$ None \(0\) \(4\) \(0\) \(-58\) $\mathrm{SU}(2)[C_{6}]$
105.3.v.a 105.v 35.l $64$ $2.861$ None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
105.3.w.a 105.w 105.w $112$ $2.861$ None \(0\) \(-6\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{12}]$
105.4.a.a 105.a 1.a $1$ $6.195$ \(\Q\) None \(0\) \(-3\) \(5\) \(7\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-8q^{4}+5q^{5}+7q^{7}+9q^{9}+\cdots\)
105.4.a.b 105.a 1.a $1$ $6.195$ \(\Q\) None \(5\) \(-3\) \(5\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+5q^{2}-3q^{3}+17q^{4}+5q^{5}-15q^{6}+\cdots\)
105.4.a.c 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{17}) \) None \(-7\) \(-6\) \(-10\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q+(-3-\beta )q^{2}-3q^{3}+(5+7\beta )q^{4}+\cdots\)
105.4.a.d 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{5}) \) None \(-4\) \(6\) \(-10\) \(-14\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots\)
105.4.a.e 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{2}) \) None \(-2\) \(-6\) \(10\) \(-14\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots\)
105.4.a.f 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{65}) \) None \(1\) \(6\) \(10\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+(8+\beta )q^{4}+5q^{5}+3\beta q^{6}+\cdots\)
105.4.a.g 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{41}) \) None \(3\) \(6\) \(-10\) \(14\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3q^{3}+(3+3\beta )q^{4}-5q^{5}+\cdots\)
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