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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.1.h.a 192.h 24.h $2$ $0.096$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{9}+iq^{19}-q^{25}+iq^{27}+\cdots\)
192.2.a.a 192.a 1.a $1$ $1.533$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
192.2.a.b 192.a 1.a $1$ $1.533$ \(\Q\) None None \(0\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
192.2.a.c 192.a 1.a $1$ $1.533$ \(\Q\) None None \(0\) \(1\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
192.2.a.d 192.a 1.a $1$ $1.533$ \(\Q\) None None \(0\) \(1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
192.2.c.a 192.c 12.b $2$ $1.533$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}-2\zeta_{6}q^{7}-3q^{9}+2q^{13}+\cdots\)
192.2.c.b 192.c 12.b $4$ $1.533$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}+(\zeta_{8}-\zeta_{8}^{2})q^{7}+\cdots\)
192.2.d.a 192.d 8.b $4$ $1.533$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}-q^{9}+\cdots\)
192.2.f.a 192.f 24.f $4$ $1.533$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}-3q^{9}+\cdots\)
192.2.f.b 192.f 24.f $4$ $1.533$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{12}q^{3}-\zeta_{12}^{3}q^{7}+3q^{9}-\zeta_{12}^{2}q^{13}+\cdots\)
192.2.j.a 192.j 16.e $8$ $1.533$ 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(-\beta _{3}+\beta _{5})q^{5}+(\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
192.2.k.a 192.k 48.k $12$ $1.533$ 12.0.\(\cdots\).2 None None \(0\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{10}q^{3}+\beta _{7}q^{5}+(1-\beta _{11})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
192.2.r.a 192.r 64.i $128$ $1.533$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
192.2.s.a 192.s 192.s $240$ $1.533$ None None \(0\) \(-8\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{16}]$
192.3.b.a 192.b 8.d $4$ $5.232$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+3q^{9}+\cdots\)
192.3.b.b 192.b 8.d $4$ $5.232$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+5\zeta_{12}^{3}q^{7}+\cdots\)
192.3.e.a 192.e 3.b $1$ $5.232$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(-2\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots\)
192.3.e.b 192.e 3.b $1$ $5.232$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(2\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}+2q^{7}+9q^{9}+22q^{13}-26q^{19}+\cdots\)
192.3.e.c 192.e 3.b $2$ $5.232$ \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+\cdots)q^{9}+\cdots\)
192.3.e.d 192.e 3.b $2$ $5.232$ \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+2\beta )q^{9}+\cdots\)
192.3.e.e 192.e 3.b $4$ $5.232$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots\)
192.3.e.f 192.e 3.b $4$ $5.232$ \(\Q(\sqrt{-2}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots\)
192.3.g.a 192.g 4.b $2$ $5.232$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-6q^{5}+4\zeta_{6}q^{7}-3q^{9}+12\zeta_{6}q^{11}+\cdots\)
192.3.g.b 192.g 4.b $2$ $5.232$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+2q^{5}-4\zeta_{6}q^{7}-3q^{9}-4\zeta_{6}q^{11}+\cdots\)
192.3.g.c 192.g 4.b $4$ $5.232$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{3}+(2-\zeta_{12}^{3})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
192.3.h.a 192.h 24.h $4$ $5.232$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3\zeta_{12}q^{3}-\zeta_{12}^{3}q^{7}-9q^{9}-\zeta_{12}^{2}q^{13}+\cdots\)
192.3.h.b 192.h 24.h $4$ $5.232$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{8}^{2}q^{3}+(7-\zeta_{8}^{3})q^{9}+(-3\zeta_{8}-6\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
192.3.h.c 192.h 24.h $8$ $5.232$ 8.0.12960000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{4}q^{5}-\beta _{1}q^{7}+(1-\beta _{5}+\cdots)q^{9}+\cdots\)
192.3.i.a 192.i 48.i $8$ $5.232$ 8.0.629407744.1 None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
192.3.i.b 192.i 48.i $20$ $5.232$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}-\beta _{6}q^{7}+\cdots\)
192.3.l.a 192.l 16.f $16$ $5.232$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}-\beta _{9}q^{5}+\beta _{5}q^{7}-3\beta _{4}q^{9}+\cdots\)
192.3.q.a 192.q 192.q $496$ $5.232$ None None \(0\) \(-8\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{16}]$
192.3.t.a 192.t 64.j $256$ $5.232$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
192.4.a.a 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(-3\) \(-14\) \(-24\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-14q^{5}-24q^{7}+9q^{9}+28q^{11}+\cdots\)
192.4.a.b 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(-3\) \(-10\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-10q^{5}+4q^{7}+9q^{9}+20q^{11}+\cdots\)
192.4.a.c 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(-3\) \(-6\) \(16\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-6q^{5}+2^{4}q^{7}+9q^{9}+12q^{11}+\cdots\)
192.4.a.d 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(-3\) \(-2\) \(12\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{5}+12q^{7}+9q^{9}-60q^{11}+\cdots\)
192.4.a.e 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(-3\) \(14\) \(-36\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+14q^{5}-6^{2}q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
192.4.a.f 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(-3\) \(18\) \(8\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+18q^{5}+8q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
192.4.a.g 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(3\) \(-14\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-14q^{5}+24q^{7}+9q^{9}-28q^{11}+\cdots\)
192.4.a.h 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(3\) \(-10\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-10q^{5}-4q^{7}+9q^{9}-20q^{11}+\cdots\)
192.4.a.i 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(3\) \(-6\) \(-16\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-6q^{5}-2^{4}q^{7}+9q^{9}-12q^{11}+\cdots\)
192.4.a.j 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(3\) \(-2\) \(-12\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{5}-12q^{7}+9q^{9}+60q^{11}+\cdots\)
192.4.a.k 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(3\) \(14\) \(36\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+14q^{5}+6^{2}q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
192.4.a.l 192.a 1.a $1$ $11.328$ \(\Q\) None None \(0\) \(3\) \(18\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+18q^{5}-8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
192.4.c.a 192.c 12.b $2$ $11.328$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{6}q^{3}-6\zeta_{6}q^{7}-3^{3}q^{9}-70q^{13}+\cdots\)
192.4.c.b 192.c 12.b $4$ $11.328$ \(\Q(\sqrt{3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots\)
192.4.c.c 192.c 12.b $4$ $11.328$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{3}q^{5}-5\beta _{1}q^{7}+(21-\beta _{3})q^{9}+\cdots\)
192.4.c.d 192.c 12.b $12$ $11.328$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+\beta _{8}q^{5}+\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\)
192.4.d.a 192.d 8.b $4$ $11.328$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\zeta_{12}q^{3}-3\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
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