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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
221.2.a.a 221.a 1.a $1$ $1.765$ \(\Q\) None \(-1\) \(0\) \(4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{5}-2q^{7}+3q^{8}-3q^{9}+\cdots\)
221.2.a.b 221.a 1.a $1$ $1.765$ \(\Q\) None \(1\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+2q^{5}+2q^{6}+2q^{7}+\cdots\)
221.2.a.c 221.a 1.a $2$ $1.765$ \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
221.2.a.d 221.a 1.a $2$ $1.765$ \(\Q(\sqrt{21}) \) None \(-1\) \(1\) \(-2\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1-\beta )q^{3}+(3+\beta )q^{4}-q^{5}+\cdots\)
221.2.a.e 221.a 1.a $2$ $1.765$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{3}+3q^{4}+(-1-\beta )q^{5}+\cdots\)
221.2.a.f 221.a 1.a $3$ $1.765$ 3.3.229.1 None \(0\) \(-3\) \(-2\) \(-9\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
221.2.a.g 221.a 1.a $6$ $1.765$ 6.6.28134208.1 None \(1\) \(1\) \(-2\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+\beta _{1}q^{3}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots\)
221.2.b.a 221.b 221.b $4$ $1.765$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-\beta _{3}q^{6}+\cdots\)
221.2.b.b 221.b 221.b $4$ $1.765$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+q^{4}-\zeta_{8}^{3}q^{6}+\cdots\)
221.2.b.c 221.b 221.b $6$ $1.765$ 6.0.111756112.1 None \(0\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
221.2.b.d 221.b 221.b $6$ $1.765$ 6.0.111756112.1 None \(0\) \(0\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
221.2.c.a 221.c 13.b $2$ $1.765$ \(\Q(\sqrt{-3}) \) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}+2q^{3}-q^{4}-2\zeta_{6}q^{5}-2\zeta_{6}q^{6}+\cdots\)
221.2.c.b 221.c 13.b $4$ $1.765$ 4.0.8112.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
221.2.c.c 221.c 13.b $4$ $1.765$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{3}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
221.2.c.d 221.c 13.b $10$ $1.765$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-2+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
221.2.d.a 221.d 17.b $2$ $1.765$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}-q^{4}+iq^{5}+iq^{6}-3q^{8}+\cdots\)
221.2.d.b 221.d 17.b $4$ $1.765$ 4.0.2312.1 None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
221.2.d.c 221.d 17.b $6$ $1.765$ 6.0.839056.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
221.2.d.d 221.d 17.b $6$ $1.765$ 6.0.49362048.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(2-\beta _{2}-\beta _{3})q^{4}+\cdots\)
221.2.e.a 221.e 13.c $14$ $1.765$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(3\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}-\beta _{12}q^{3}+(-\beta _{2}-\beta _{10})q^{4}+\cdots\)
221.2.e.b 221.e 13.c $22$ $1.765$ None \(0\) \(-5\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$
221.2.f.a 221.f 17.c $4$ $1.765$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-\zeta_{8})q^{3}+(-1+\cdots)q^{4}+\cdots\)
221.2.f.b 221.f 17.c $4$ $1.765$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
221.2.f.c 221.f 17.c $4$ $1.765$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(1-\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
221.2.f.d 221.f 17.c $8$ $1.765$ 8.0.1052872704.3 None \(0\) \(2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{4}-\beta _{5}+\beta _{7})q^{2}+(\beta _{3}+\beta _{4}-\beta _{7})q^{3}+\cdots\)
221.2.f.e 221.f 17.c $16$ $1.765$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-6\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{14}q^{3}+(-1-\beta _{3}+\beta _{9}+\cdots)q^{4}+\cdots\)
221.2.k.a 221.k 221.k $40$ $1.765$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
221.2.l.a 221.l 221.l $36$ $1.765$ None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
221.2.m.a 221.m 13.e $2$ $1.765$ \(\Q(\sqrt{-3}) \) None \(3\) \(1\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
221.2.m.b 221.m 13.e $12$ $1.765$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-3\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
221.2.m.c 221.m 13.e $22$ $1.765$ None \(0\) \(-3\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{6}]$
221.2.n.a 221.n 221.n $40$ $1.765$ None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
221.2.p.a 221.p 221.p $4$ $1.765$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{8}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
221.2.p.b 221.p 221.p $4$ $1.765$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(4\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q-\zeta_{8}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
221.2.p.c 221.p 221.p $64$ $1.765$ None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
221.2.q.a 221.q 17.d $32$ $1.765$ None \(0\) \(0\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{8}]$
221.2.q.b 221.q 17.d $40$ $1.765$ None \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{8}]$
221.2.s.a 221.s 221.s $80$ $1.765$ None \(0\) \(-2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
221.2.x.a 221.x 221.x $72$ $1.765$ None \(0\) \(-2\) \(-16\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
221.2.z.a 221.z 221.z $152$ $1.765$ None \(-8\) \(-16\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
221.2.ba.a 221.ba 221.aa $152$ $1.765$ None \(-8\) \(-16\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
221.2.bd.a 221.bd 221.ad $144$ $1.765$ None \(-12\) \(-4\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{24}]$
221.2.be.a 221.be 221.ae $160$ $1.765$ None \(-4\) \(-4\) \(-16\) \(-4\) $\mathrm{SU}(2)[C_{24}]$
221.2.bh.a 221.bh 221.ah $304$ $1.765$ None \(-16\) \(-8\) \(-16\) \(-16\) $\mathrm{SU}(2)[C_{48}]$
221.2.bi.a 221.bi 221.ai $304$ $1.765$ None \(-16\) \(-8\) \(-16\) \(-16\) $\mathrm{SU}(2)[C_{48}]$
221.3.g.a 221.g 221.g $80$ $6.022$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
221.3.h.a 221.h 221.h $80$ $6.022$ None \(4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
221.3.i.a 221.i 221.i $80$ $6.022$ None \(-4\) \(-4\) \(-24\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
221.3.j.a 221.j 13.d $72$ $6.022$ None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{4}]$
221.3.o.a 221.o 221.o $160$ $6.022$ None \(0\) \(-8\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
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