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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.1.l.a 112.l 112.l $2$ $0.056$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots\)
112.2.a.a 112.a 1.a $1$ $0.894$ \(\Q\) None None \(0\) \(-2\) \(-4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots\)
112.2.a.b 112.a 1.a $1$ $0.894$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-3q^{9}+4q^{11}+2q^{13}+\cdots\)
112.2.a.c 112.a 1.a $1$ $0.894$ \(\Q\) None None \(0\) \(2\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{7}+q^{9}-4q^{13}+6q^{17}+\cdots\)
112.2.f.a 112.f 28.d $2$ $0.894$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{3}-2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots\)
112.2.f.b 112.f 28.d $2$ $0.894$ \(\Q(\sqrt{-3}) \) None None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{3}+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots\)
112.2.i.a 112.i 7.c $2$ $0.894$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
112.2.i.b 112.i 7.c $2$ $0.894$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
112.2.i.c 112.i 7.c $2$ $0.894$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
112.2.j.a 112.j 112.j $4$ $0.894$ \(\Q(i, \sqrt{6})\) None None \(-4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(-\beta _{2}-\beta _{3})q^{5}+\cdots\)
112.2.j.b 112.j 112.j $4$ $0.894$ \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots\)
112.2.j.c 112.j 112.j $4$ $0.894$ \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\zeta_{12})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
112.2.j.d 112.j 112.j $16$ $0.894$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{9}q^{2}+\beta _{15}q^{3}+(-1-\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots\)
112.2.m.a 112.m 16.e $2$ $0.894$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}+(-2+2i)q^{3}-2iq^{4}+\cdots\)
112.2.m.b 112.m 16.e $2$ $0.894$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(2+2i)q^{5}+\cdots\)
112.2.m.c 112.m 16.e $8$ $0.894$ 8.0.214798336.3 None None \(2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
112.2.m.d 112.m 16.e $12$ $0.894$ 12.0.\(\cdots\).1 None None \(2\) \(4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{10})q^{3}+\beta _{1}q^{4}+\cdots\)
112.2.p.a 112.p 28.f $2$ $0.894$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(3\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
112.2.p.b 112.p 28.f $2$ $0.894$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
112.2.p.c 112.p 28.f $4$ $0.894$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+(-2-\beta _{2})q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
112.2.v.a 112.v 112.v $56$ $0.894$ None None \(-2\) \(-6\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{12}]$
112.2.w.a 112.w 112.w $4$ $0.894$ \(\Q(\zeta_{12})\) None None \(-2\) \(-4\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots\)
112.2.w.b 112.w 112.w $4$ $0.894$ \(\Q(\zeta_{12})\) None None \(4\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
112.2.w.c 112.w 112.w $48$ $0.894$ None None \(-4\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$
112.3.c.a 112.c 7.b $1$ $3.052$ \(\Q\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(7\) $\mathrm{U}(1)[D_{2}]$ \(q+7q^{7}+9q^{9}+6q^{11}-18q^{23}+5^{2}q^{25}+\cdots\)
112.3.c.b 112.c 7.b $2$ $3.052$ \(\Q(\sqrt{-6}) \) None None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+\beta q^{5}+(-5-\beta )q^{7}-15q^{9}+\cdots\)
112.3.c.c 112.c 7.b $4$ $3.052$ 4.0.2048.2 None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
112.3.d.a 112.d 4.b $2$ $3.052$ \(\Q(\sqrt{-7}) \) None None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta q^{3}+8q^{5}+\beta q^{7}-19q^{9}-4\beta q^{11}+\cdots\)
112.3.d.b 112.d 4.b $4$ $3.052$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+\cdots\)
112.3.k.a 112.k 16.f $48$ $3.052$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
112.3.l.a 112.l 112.l $4$ $3.052$ \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(-2+3\beta _{2})q^{4}+7\beta _{3}q^{7}+\cdots\)
112.3.l.b 112.l 112.l $56$ $3.052$ None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
112.3.r.a 112.r 28.g $4$ $3.052$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(3\beta _{1}-\beta _{3})q^{7}-2\beta _{2}q^{9}+\cdots\)
112.3.r.b 112.r 28.g $6$ $3.052$ 6.0.259470000.1 None None \(0\) \(-3\) \(-1\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{5})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
112.3.r.c 112.r 28.g $6$ $3.052$ 6.0.259470000.1 None None \(0\) \(3\) \(-1\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{5})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
112.3.s.a 112.s 7.d $2$ $3.052$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(3\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+7q^{7}+\cdots\)
112.3.s.b 112.s 7.d $4$ $3.052$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(6\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2+\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
112.3.s.c 112.s 7.d $8$ $3.052$ 8.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{3}-\beta _{7}q^{5}+(2-3\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
112.3.u.a 112.u 112.u $120$ $3.052$ None None \(-2\) \(-2\) \(-2\) \(-8\) $\mathrm{SU}(2)[C_{12}]$
112.3.x.a 112.x 112.x $120$ $3.052$ None None \(-2\) \(-6\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{12}]$
112.4.a.a 112.a 1.a $1$ $6.608$ \(\Q\) None None \(0\) \(-8\) \(-14\) \(7\) $+$ $\mathrm{SU}(2)$ \(q-8q^{3}-14q^{5}+7q^{7}+37q^{9}+28q^{11}+\cdots\)
112.4.a.b 112.a 1.a $1$ $6.608$ \(\Q\) None None \(0\) \(-6\) \(8\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-6q^{3}+8q^{5}+7q^{7}+9q^{9}-56q^{11}+\cdots\)
112.4.a.c 112.a 1.a $1$ $6.608$ \(\Q\) None None \(0\) \(-4\) \(6\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-4q^{3}+6q^{5}-7q^{7}-11q^{9}+12q^{11}+\cdots\)
112.4.a.d 112.a 1.a $1$ $6.608$ \(\Q\) None None \(0\) \(2\) \(-16\) \(7\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2^{4}q^{5}+7q^{7}-23q^{9}-24q^{11}+\cdots\)
112.4.a.e 112.a 1.a $1$ $6.608$ \(\Q\) None None \(0\) \(2\) \(-12\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-12q^{5}-7q^{7}-23q^{9}-48q^{11}+\cdots\)
112.4.a.f 112.a 1.a $1$ $6.608$ \(\Q\) None None \(0\) \(2\) \(16\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+2^{4}q^{5}+7q^{7}-23q^{9}+8q^{11}+\cdots\)
112.4.a.g 112.a 1.a $1$ $6.608$ \(\Q\) None None \(0\) \(10\) \(-8\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+10q^{3}-8q^{5}+7q^{7}+73q^{9}+40q^{11}+\cdots\)
112.4.a.h 112.a 1.a $2$ $6.608$ \(\Q(\sqrt{57}) \) None None \(0\) \(2\) \(22\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(11+\beta )q^{5}-7q^{7}+(31+\cdots)q^{9}+\cdots\)
112.4.f.a 112.f 28.d $4$ $6.608$ \(\Q(\sqrt{-5}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
112.4.f.b 112.f 28.d $8$ $6.608$ 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+2\beta _{3}-\beta _{7})q^{7}+\cdots\)
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