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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.1.s.a 228.s 57.l $6$ $0.114$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{8}q^{3}+(\zeta_{18}^{2}+\zeta_{18}^{4})q^{7}-\zeta_{18}^{7}q^{9}+\cdots\)
228.2.a.a 228.a 1.a $1$ $1.821$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+q^{7}+q^{9}-5q^{11}-6q^{13}+\cdots\)
228.2.a.b 228.a 1.a $1$ $1.821$ \(\Q\) None None \(0\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
228.2.a.c 228.a 1.a $2$ $1.821$ \(\Q(\sqrt{33}) \) None None \(0\) \(2\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
228.2.c.a 228.c 12.b $36$ $1.821$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
228.2.d.a 228.d 57.d $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(8\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}+4q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
228.2.d.b 228.d 57.d $4$ $1.821$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
228.2.f.a 228.f 76.d $10$ $1.821$ 10.0.\(\cdots\).1 None None \(-2\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
228.2.f.b 228.f 76.d $10$ $1.821$ 10.0.\(\cdots\).1 None None \(2\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
228.2.i.a 228.i 19.c $4$ $1.821$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
228.2.i.b 228.i 19.c $4$ $1.821$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(2\) \(-2\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(2-\beta _{3})q^{7}+\cdots\)
228.2.k.a 228.k 76.f $20$ $1.821$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-1\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{4}q^{2}-\beta _{12}q^{3}+\beta _{9}q^{4}+(\beta _{6}-\beta _{17}+\cdots)q^{5}+\cdots\)
228.2.k.b 228.k 76.f $20$ $1.821$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(1\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{8}-\beta _{16})q^{2}-\beta _{11}q^{3}+\beta _{17}q^{4}+\cdots\)
228.2.m.a 228.m 228.m $72$ $1.821$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
228.2.p.a 228.p 57.f $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(-10\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}-5q^{7}+3\zeta_{6}q^{9}+(-6+\cdots)q^{13}+\cdots\)
228.2.p.b 228.p 57.f $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(2\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+q^{7}+3\zeta_{6}q^{9}+(2-\zeta_{6})q^{13}+\cdots\)
228.2.p.c 228.p 57.f $4$ $1.821$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-2\) \(9\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
228.2.p.d 228.p 57.f $4$ $1.821$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-1\) \(-9\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{3}+(-3+2\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
228.2.q.a 228.q 19.e $6$ $1.821$ \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(6\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+\zeta_{18}^{4}q^{3}+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{5}+\cdots\)
228.2.q.b 228.q 19.e $12$ $1.821$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-6\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{7}q^{3}+(-1+\beta _{2}-\beta _{5}+\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)
228.2.t.a 228.t 57.j $6$ $1.821$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q+(\zeta_{18}^{2}-2\zeta_{18}^{5})q^{3}+(-\zeta_{18}-2\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
228.2.t.b 228.t 57.j $36$ $1.821$ None None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
228.2.v.a 228.v 228.v $216$ $1.821$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
228.2.w.a 228.w 76.k $60$ $1.821$ None None \(-3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
228.2.w.b 228.w 76.k $60$ $1.821$ None None \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
228.3.b.a 228.b 228.b $1$ $6.213$ \(\Q\) \(\Q(\sqrt{-57}) \) None \(-2\) \(-3\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-8q^{8}+\cdots\)
228.3.b.b 228.b 228.b $1$ $6.213$ \(\Q\) \(\Q(\sqrt{-57}) \) None \(-2\) \(3\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-8q^{8}+\cdots\)
228.3.b.c 228.b 228.b $1$ $6.213$ \(\Q\) \(\Q(\sqrt{-57}) \) None \(2\) \(-3\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+8q^{8}+\cdots\)
228.3.b.d 228.b 228.b $1$ $6.213$ \(\Q\) \(\Q(\sqrt{-57}) \) None \(2\) \(3\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+8q^{8}+\cdots\)
228.3.b.e 228.b 228.b $72$ $6.213$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
228.3.e.a 228.e 3.b $12$ $6.213$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{10}q^{5}+(-1-\beta _{7}+\beta _{8}+\cdots)q^{7}+\cdots\)
228.3.g.a 228.g 4.b $36$ $6.213$ None None \(4\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$
228.3.h.a 228.h 19.b $6$ $6.213$ 6.0.219615408.1 None None \(0\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}-3q^{9}+(-4+\cdots)q^{11}+\cdots\)
228.3.j.a 228.j 76.g $2$ $6.213$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(-3\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
228.3.j.b 228.j 76.g $2$ $6.213$ \(\Q(\sqrt{-3}) \) None None \(4\) \(3\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2q^{2}+(2-\zeta_{6})q^{3}+4q^{4}-4\zeta_{6}q^{5}+\cdots\)
228.3.j.c 228.j 76.g $38$ $6.213$ None None \(-1\) \(-57\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
228.3.j.d 228.j 76.g $38$ $6.213$ None None \(-1\) \(57\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
228.3.l.a 228.l 19.d $2$ $6.213$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-6\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{3}+(-6+6\zeta_{6})q^{5}-5q^{7}+\cdots\)
228.3.l.b 228.l 19.d $2$ $6.213$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}+\cdots\)
228.3.l.c 228.l 19.d $2$ $6.213$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(2\) \(22\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}+11q^{7}+\cdots\)
228.3.l.d 228.l 19.d $6$ $6.213$ 6.0.954288.1 None None \(0\) \(-9\) \(4\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{2})q^{3}+(2-2\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots\)
228.3.n.a 228.n 228.n $152$ $6.213$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
228.3.o.a 228.o 57.h $2$ $6.213$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-26\) $\mathrm{U}(1)[D_{6}]$ \(q+3\zeta_{6}q^{3}-13q^{7}+(-9+9\zeta_{6})q^{9}+\cdots\)
228.3.o.b 228.o 57.h $2$ $6.213$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(22\) $\mathrm{U}(1)[D_{6}]$ \(q+3\zeta_{6}q^{3}+11q^{7}+(-9+9\zeta_{6})q^{9}+\cdots\)
228.3.o.c 228.o 57.h $24$ $6.213$ None None \(0\) \(-8\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$
228.3.r.a 228.r 19.f $18$ $6.213$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-2\beta _{3}-\beta _{7})q^{3}+(-1-\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)
228.3.r.b 228.r 19.f $24$ $6.213$ None None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$
228.3.s.a 228.s 57.l $6$ $6.213$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q-3\zeta_{18}^{4}q^{3}+(-5\zeta_{18}-3\zeta_{18}^{2}+8\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
228.3.s.b 228.s 57.l $72$ $6.213$ None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
228.3.u.a 228.u 228.u $456$ $6.213$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
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