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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
120.1.i.a 120.i 120.i $2$ $0.060$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots\)
120.2.a.a 120.a 1.a $1$ $0.958$ \(\Q\) None None \(0\) \(1\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+4q^{7}+q^{9}-6q^{13}-q^{15}+\cdots\)
120.2.a.b 120.a 1.a $1$ $0.958$ \(\Q\) None None \(0\) \(1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
120.2.b.a 120.b 24.f $8$ $0.958$ 8.0.1649659456.5 None None \(-1\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
120.2.b.b 120.b 24.f $8$ $0.958$ 8.0.1649659456.5 None None \(1\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
120.2.d.a 120.d 40.f $6$ $0.958$ 6.0.839056.1 None None \(-1\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+q^{3}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
120.2.d.b 120.d 40.f $6$ $0.958$ 6.0.839056.1 None None \(1\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{3}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
120.2.f.a 120.f 5.b $2$ $0.958$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}+2q^{11}+\cdots\)
120.2.k.a 120.k 8.b $2$ $0.958$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}-iq^{3}+2iq^{4}+iq^{5}+\cdots\)
120.2.k.b 120.k 8.b $6$ $0.958$ 6.0.399424.1 None None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{4}+\beta _{1}q^{5}+\cdots\)
120.2.m.a 120.m 120.m $4$ $0.958$ \(\Q(\sqrt{3}, \sqrt{-5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
120.2.m.b 120.m 120.m $16$ $0.958$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{13}q^{3}-\beta _{11}q^{4}+\beta _{7}q^{5}+\cdots\)
120.2.r.a 120.r 15.e $4$ $0.958$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
120.2.r.b 120.r 15.e $4$ $0.958$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1+2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)
120.2.r.c 120.r 15.e $4$ $0.958$ \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)
120.2.v.a 120.v 40.k $24$ $0.958$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
120.2.w.a 120.w 120.w $4$ $0.958$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) None \(-4\) \(0\) \(4\) \(-4\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
120.2.w.b 120.w 120.w $4$ $0.958$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) None \(4\) \(0\) \(-4\) \(-4\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
120.2.w.c 120.w 120.w $32$ $0.958$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
120.3.c.a 120.c 15.d $12$ $3.270$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{8}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)
120.3.g.a 120.g 8.d $16$ $3.270$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
120.3.i.a 120.i 120.i $1$ $3.270$ \(\Q\) \(\Q(\sqrt{-30}) \) None \(-2\) \(-3\) \(-5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
120.3.i.b 120.i 120.i $1$ $3.270$ \(\Q\) \(\Q(\sqrt{-30}) \) None \(-2\) \(3\) \(5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
120.3.i.c 120.i 120.i $1$ $3.270$ \(\Q\) \(\Q(\sqrt{-30}) \) None \(2\) \(-3\) \(5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
120.3.i.d 120.i 120.i $1$ $3.270$ \(\Q\) \(\Q(\sqrt{-30}) \) None \(2\) \(3\) \(-5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
120.3.i.e 120.i 120.i $4$ $3.270$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2\beta _{1}q^{2}+3\beta _{1}q^{3}-4q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
120.3.i.f 120.i 120.i $4$ $3.270$ \(\Q(i, \sqrt{15})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}+(4+\beta _{3})q^{4}-5\beta _{2}q^{5}+\cdots\)
120.3.i.g 120.i 120.i $32$ $3.270$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
120.3.l.a 120.l 3.b $8$ $3.270$ 8.0.\(\cdots\).5 None None \(0\) \(-4\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{6}q^{5}+(1+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
120.3.n.a 120.n 24.h $32$ $3.270$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
120.3.p.a 120.p 40.e $24$ $3.270$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
120.3.q.a 120.q 120.q $88$ $3.270$ None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
120.3.t.a 120.t 40.i $48$ $3.270$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
120.3.u.a 120.u 5.c $4$ $3.270$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(4\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(1+\beta _{1}+3\beta _{2}-2\beta _{3})q^{5}+\cdots\)
120.3.u.b 120.u 5.c $8$ $3.270$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(0\) \(-12\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
120.4.a.a 120.a 1.a $1$ $7.080$ \(\Q\) None None \(0\) \(-3\) \(-5\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+4q^{7}+9q^{9}+72q^{11}+\cdots\)
120.4.a.b 120.a 1.a $1$ $7.080$ \(\Q\) None None \(0\) \(-3\) \(-5\) \(20\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+20q^{7}+9q^{9}-56q^{11}+\cdots\)
120.4.a.c 120.a 1.a $1$ $7.080$ \(\Q\) None None \(0\) \(-3\) \(5\) \(-16\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}-2^{4}q^{7}+9q^{9}-28q^{11}+\cdots\)
120.4.a.d 120.a 1.a $1$ $7.080$ \(\Q\) None None \(0\) \(-3\) \(5\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+9q^{9}+4q^{11}+54q^{13}+\cdots\)
120.4.a.e 120.a 1.a $1$ $7.080$ \(\Q\) None None \(0\) \(3\) \(-5\) \(20\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}+20q^{7}+9q^{9}+2^{4}q^{11}+\cdots\)
120.4.a.f 120.a 1.a $1$ $7.080$ \(\Q\) None None \(0\) \(3\) \(5\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+8q^{7}+9q^{9}+20q^{11}+\cdots\)
120.4.b.a 120.b 24.f $24$ $7.080$ None None \(-3\) \(0\) \(120\) \(0\) $\mathrm{SU}(2)[C_{2}]$
120.4.b.b 120.b 24.f $24$ $7.080$ None None \(3\) \(0\) \(-120\) \(0\) $\mathrm{SU}(2)[C_{2}]$
120.4.d.a 120.d 40.f $18$ $7.080$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-1\) \(54\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+3q^{3}+\beta _{2}q^{4}+\beta _{10}q^{5}+\cdots\)
120.4.d.b 120.d 40.f $18$ $7.080$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(1\) \(-54\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-3q^{3}-\beta _{7}q^{4}+\beta _{11}q^{5}+\cdots\)
120.4.f.a 120.f 5.b $2$ $7.080$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(-10+5i)q^{5}-10iq^{7}+\cdots\)
120.4.f.b 120.f 5.b $2$ $7.080$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(-2-11i)q^{5}-10iq^{7}+\cdots\)
120.4.f.c 120.f 5.b $2$ $7.080$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(5+10i)q^{5}+4iq^{7}-9q^{9}+\cdots\)
120.4.f.d 120.f 5.b $4$ $7.080$ \(\Q(i, \sqrt{129})\) None None \(0\) \(0\) \(22\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}+(6+5\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
120.4.k.a 120.k 8.b $2$ $7.080$ \(\Q(\sqrt{-1}) \) None None \(-4\) \(0\) \(0\) \(52\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+2i)q^{2}+3iq^{3}-8iq^{4}+5iq^{5}+\cdots\)
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