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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
222.2.a.a 222.a 1.a $1$ $1.773$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+3q^{7}+\cdots\)
222.2.a.b 222.a 1.a $1$ $1.773$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
222.2.a.c 222.a 1.a $1$ $1.773$ \(\Q\) None \(-1\) \(1\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
222.2.a.d 222.a 1.a $1$ $1.773$ \(\Q\) None \(1\) \(-1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
222.2.a.e 222.a 1.a $1$ $1.773$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
222.2.c.a 222.c 37.b $2$ $1.773$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
222.2.c.b 222.c 37.b $4$ $1.773$ \(\Q(i, \sqrt{65})\) None \(0\) \(-4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{3}-q^{4}-2\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots\)
222.2.e.a 222.e 37.c $2$ $1.773$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+\cdots\)
222.2.e.b 222.e 37.c $2$ $1.773$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
222.2.e.c 222.e 37.c $4$ $1.773$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(2\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{4}-\beta _{3}q^{5}+\cdots\)
222.2.g.a 222.g 111.g $28$ $1.773$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
222.2.j.a 222.j 37.e $4$ $1.773$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots\)
222.2.j.b 222.j 37.e $8$ $1.773$ 8.0.303595776.1 None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}-\beta _{4}q^{3}-\beta _{4}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
222.2.k.a 222.k 37.f $6$ $1.773$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
222.2.k.b 222.k 37.f $6$ $1.773$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
222.2.k.c 222.k 37.f $6$ $1.773$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(9\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
222.2.k.d 222.k 37.f $6$ $1.773$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(9\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
222.2.k.e 222.k 37.f $12$ $1.773$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(-6\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{4}q^{2}-\beta _{2}q^{3}-\beta _{7}q^{4}+(-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
222.2.m.a 222.m 111.m $56$ $1.773$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
222.2.n.a 222.n 37.h $24$ $1.773$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
222.2.n.b 222.n 37.h $24$ $1.773$ None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{18}]$
222.2.q.a 222.q 111.q $144$ $1.773$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$
222.3.b.a 222.b 3.b $24$ $6.049$ None \(0\) \(4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$
222.3.d.a 222.d 111.d $24$ $6.049$ None \(0\) \(-4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$
222.3.f.a 222.f 37.d $4$ $6.049$ \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\zeta_{12})q^{2}-\zeta_{12}^{2}q^{3}-2\zeta_{12}q^{4}+\cdots\)
222.3.f.b 222.f 37.d $12$ $6.049$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{4})q^{2}-\beta _{5}q^{3}+2\beta _{4}q^{4}+\cdots\)
222.3.f.c 222.f 37.d $12$ $6.049$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(-12\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{3})q^{2}+\beta _{2}q^{3}+2\beta _{3}q^{4}+(-1+\cdots)q^{5}+\cdots\)
222.3.h.a 222.h 111.h $48$ $6.049$ None \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$
222.3.i.a 222.i 111.i $4$ $6.049$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(2\) \(0\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{2}-2\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
222.3.i.b 222.i 111.i $44$ $6.049$ None \(0\) \(0\) \(0\) \(-18\) $\mathrm{SU}(2)[C_{6}]$
222.3.l.a 222.l 37.g $12$ $6.049$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(-18\) \(6\) \(2\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\beta _{2}+\beta _{7})q^{2}+(-2+\beta _{7})q^{3}+\cdots\)
222.3.l.b 222.l 37.g $12$ $6.049$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(18\) \(-6\) \(14\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{4}-\beta _{5})q^{2}+(1+\beta _{4})q^{3}+2\beta _{6}q^{4}+\cdots\)
222.3.l.c 222.l 37.g $16$ $6.049$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(8\) \(-24\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1})q^{3}+2\beta _{4}q^{4}+\cdots\)
222.3.l.d 222.l 37.g $16$ $6.049$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(8\) \(24\) \(6\) \(-14\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{8}-\beta _{9})q^{2}+(1-\beta _{9})q^{3}+(2\beta _{5}+\cdots)q^{4}+\cdots\)
222.3.o.a 222.o 111.n $156$ $6.049$ None \(0\) \(6\) \(0\) \(30\) $\mathrm{SU}(2)[C_{18}]$
222.3.p.a 222.p 111.p $156$ $6.049$ None \(0\) \(-6\) \(0\) \(-30\) $\mathrm{SU}(2)[C_{18}]$
222.3.r.a 222.r 37.i $24$ $6.049$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{36}]$
222.3.r.b 222.r 37.i $36$ $6.049$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$
222.3.r.c 222.r 37.i $36$ $6.049$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{36}]$
222.3.r.d 222.r 37.i $48$ $6.049$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$
222.4.a.a 222.a 1.a $1$ $13.098$ \(\Q\) None \(-2\) \(-3\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-2q^{5}+6q^{6}+\cdots\)
222.4.a.b 222.a 1.a $1$ $13.098$ \(\Q\) None \(2\) \(-3\) \(0\) \(-16\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2^{4}q^{7}+\cdots\)
222.4.a.c 222.a 1.a $1$ $13.098$ \(\Q\) None \(2\) \(3\) \(-16\) \(-24\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-2^{4}q^{5}+6q^{6}+\cdots\)
222.4.a.d 222.a 1.a $2$ $13.098$ \(\Q(\sqrt{11}) \) None \(-4\) \(6\) \(-14\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(-7+3\beta )q^{5}+\cdots\)
222.4.a.e 222.a 1.a $2$ $13.098$ \(\Q(\sqrt{2}) \) None \(4\) \(-6\) \(-4\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-2+3\beta )q^{5}+\cdots\)
222.4.a.f 222.a 1.a $2$ $13.098$ \(\Q(\sqrt{97}) \) None \(4\) \(-6\) \(-4\) \(17\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-4\beta q^{5}-6q^{6}+\cdots\)
222.4.a.g 222.a 1.a $3$ $13.098$ 3.3.51992.1 None \(-6\) \(-9\) \(-12\) \(21\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(-4+3\beta _{1}+\cdots)q^{5}+\cdots\)
222.4.a.h 222.a 1.a $3$ $13.098$ 3.3.14013.1 None \(-6\) \(9\) \(6\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(2-\beta _{1})q^{5}+\cdots\)
222.4.a.i 222.a 1.a $3$ $13.098$ 3.3.576860.1 None \(6\) \(9\) \(14\) \(25\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(5-\beta _{1})q^{5}+\cdots\)
222.4.c.a 222.c 37.b $4$ $13.098$ \(\Q(i, \sqrt{21})\) None \(0\) \(-12\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-3q^{3}-4q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
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