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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
124.1.i.a 124.i 124.i $4$ $0.062$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
124.2.a.a 124.a 1.a $1$ $0.990$ \(\Q\) None None \(0\) \(-2\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-3q^{5}-q^{7}+q^{9}-6q^{11}+\cdots\)
124.2.a.b 124.a 1.a $1$ $0.990$ \(\Q\) None None \(0\) \(0\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}-3q^{9}+6q^{11}-4q^{13}+\cdots\)
124.2.d.a 124.d 124.d $4$ $0.990$ \(\Q(i, \sqrt{6})\) None None \(-4\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}-2\beta _{1}q^{4}+\cdots\)
124.2.d.b 124.d 124.d $4$ $0.990$ \(\Q(\sqrt{6}, \sqrt{-7})\) None None \(2\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-2-\beta _{1})q^{4}-2q^{5}+\cdots\)
124.2.d.c 124.d 124.d $6$ $0.990$ 6.0.21717639.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{5}q^{2}-\beta _{3}q^{4}+(\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
124.2.e.a 124.e 31.c $6$ $0.990$ 6.0.954288.1 None None \(0\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
124.2.f.a 124.f 31.d $4$ $0.990$ \(\Q(\zeta_{10})\) None None \(0\) \(-3\) \(8\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}^{3})q^{3}+2q^{5}+(\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
124.2.f.b 124.f 31.d $4$ $0.990$ \(\Q(\zeta_{10})\) None None \(0\) \(5\) \(-6\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)
124.2.g.a 124.g 124.g $28$ $0.990$ None None \(-4\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
124.2.j.a 124.j 124.j $8$ $0.990$ \(\Q(\zeta_{20})\) None None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
124.2.j.b 124.j 124.j $48$ $0.990$ None None \(-1\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{10}]$
124.2.m.a 124.m 31.g $24$ $0.990$ None None \(0\) \(-1\) \(1\) \(-9\) $\mathrm{SU}(2)[C_{15}]$
124.2.p.a 124.p 124.p $112$ $0.990$ None None \(-6\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{30}]$
124.3.b.a 124.b 4.b $30$ $3.379$ None None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
124.3.c.a 124.c 31.b $2$ $3.379$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-12\) \(-20\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-6q^{5}-10q^{7}-3q^{9}+5\zeta_{6}q^{11}+\cdots\)
124.3.c.b 124.c 31.b $4$ $3.379$ 4.0.63368.1 None None \(0\) \(0\) \(18\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(4+\beta _{3})q^{5}+(2-\beta _{3})q^{7}+\cdots\)
124.3.h.a 124.h 31.e $10$ $3.379$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(3\) \(3\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{5}q^{3}+(-\beta _{1}-\beta _{6})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
124.3.i.a 124.i 124.i $60$ $3.379$ None None \(-4\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
124.3.k.a 124.k 31.f $24$ $3.379$ None None \(0\) \(0\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{10}]$
124.3.l.a 124.l 124.l $120$ $3.379$ None None \(-3\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{10}]$
124.3.n.a 124.n 124.n $240$ $3.379$ None None \(-6\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{30}]$
124.3.o.a 124.o 31.h $40$ $3.379$ None None \(0\) \(-3\) \(-3\) \(19\) $\mathrm{SU}(2)[C_{30}]$
124.4.a.a 124.a 1.a $4$ $7.316$ 4.4.841724.1 None None \(0\) \(-4\) \(-14\) \(-12\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{3}+(-3-\beta _{1}-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
124.4.a.b 124.a 1.a $4$ $7.316$ 4.4.4000044.1 None None \(0\) \(2\) \(6\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(4+\beta _{1}+\cdots)q^{7}+\cdots\)
124.4.d.a 124.d 124.d $2$ $7.316$ \(\Q(\sqrt{-31}) \) \(\Q(\sqrt{-31}) \) None \(1\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+(-8+\beta )q^{4}-2q^{5}+(6-12\beta )q^{7}+\cdots\)
124.4.d.b 124.d 124.d $4$ $7.316$ \(\Q(\sqrt{-3}, \sqrt{-31})\) \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(4+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
124.4.d.c 124.d 124.d $40$ $7.316$ None None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
124.4.e.a 124.e 31.c $2$ $7.316$ \(\Q(\sqrt{-3}) \) None None \(0\) \(5\) \(15\) \(-29\) $\mathrm{SU}(2)[C_{3}]$ \(q+(5-5\zeta_{6})q^{3}+15\zeta_{6}q^{5}+(-29+29\zeta_{6})q^{7}+\cdots\)
124.4.e.b 124.e 31.c $6$ $7.316$ 6.0.\(\cdots\).1 None None \(0\) \(-9\) \(-3\) \(45\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3-\beta _{1}-\beta _{2}+3\beta _{3})q^{3}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
124.4.e.c 124.e 31.c $8$ $7.316$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(0\) \(-16\) \(-32\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{3}+(-\beta _{3}-4\beta _{4}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
124.4.f.a 124.f 31.d $32$ $7.316$ None None \(0\) \(2\) \(8\) \(-34\) $\mathrm{SU}(2)[C_{5}]$
124.4.g.a 124.g 124.g $92$ $7.316$ None None \(-4\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
124.4.j.a 124.j 124.j $184$ $7.316$ None None \(-3\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{10}]$
124.4.m.a 124.m 31.g $64$ $7.316$ None None \(0\) \(4\) \(4\) \(46\) $\mathrm{SU}(2)[C_{15}]$
124.4.p.a 124.p 124.p $368$ $7.316$ None None \(-6\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{30}]$
124.5.b.a 124.b 4.b $60$ $12.818$ None None \(6\) \(0\) \(24\) \(0\) $\mathrm{SU}(2)[C_{2}]$
124.5.c.a 124.c 31.b $10$ $12.818$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}-\beta _{4}q^{7}+(-15+\cdots)q^{9}+\cdots\)
124.5.h.a 124.h 31.e $22$ $12.818$ None None \(0\) \(9\) \(-3\) \(15\) $\mathrm{SU}(2)[C_{6}]$
124.5.i.a 124.i 124.i $124$ $12.818$ None None \(-4\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
124.5.k.a 124.k 31.f $40$ $12.818$ None None \(0\) \(0\) \(6\) \(202\) $\mathrm{SU}(2)[C_{10}]$
124.5.l.a 124.l 124.l $248$ $12.818$ None None \(-3\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{10}]$
124.5.n.a 124.n 124.n $496$ $12.818$ None None \(-6\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{30}]$
124.5.o.a 124.o 31.h $88$ $12.818$ None None \(0\) \(-9\) \(3\) \(-215\) $\mathrm{SU}(2)[C_{30}]$
124.6.a.a 124.a 1.a $6$ $19.888$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(2\) \(-75\) \(-157\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-12+\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots\)
124.6.a.b 124.a 1.a $6$ $19.888$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(20\) \(25\) \(39\) $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{3}+(4+\beta _{1}-\beta _{5})q^{5}+(6+\cdots)q^{7}+\cdots\)
124.6.d.a 124.d 124.d $6$ $19.888$ 6.0.21717639.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2}+2\beta _{4}-2\beta _{5})q^{2}+(-4\beta _{1}+\cdots)q^{4}+\cdots\)
124.6.d.b 124.d 124.d $72$ $19.888$ None None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
124.6.e.a 124.e 31.c $26$ $19.888$ None None \(0\) \(-7\) \(29\) \(-85\) $\mathrm{SU}(2)[C_{3}]$
124.6.f.a 124.f 31.d $56$ $19.888$ None None \(0\) \(2\) \(-58\) \(104\) $\mathrm{SU}(2)[C_{5}]$
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