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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.2.a.a 33.a 1.a $1$ $0.264$ \(\Q\) None \(1\) \(-1\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)
33.2.d.a 33.d 33.d $2$ $0.264$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
33.2.e.a 33.e 11.c $4$ $0.264$ \(\Q(\zeta_{10})\) None \(-3\) \(-1\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots\)
33.2.e.b 33.e 11.c $4$ $0.264$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
33.2.f.a 33.f 33.f $8$ $0.264$ \(\Q(\zeta_{20})\) None \(0\) \(-6\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(-1+\zeta_{20}+\cdots)q^{3}+\cdots\)
33.3.b.a 33.b 3.b $2$ $0.899$ \(\Q(\sqrt{-11}) \) None \(0\) \(6\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}+3q^{3}-7q^{4}+2\beta q^{5}-3\beta q^{6}+\cdots\)
33.3.b.b 33.b 3.b $4$ $0.899$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-5\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\cdots)q^{3}+\cdots\)
33.3.c.a 33.c 11.b $4$ $0.899$ 4.0.39744.5 None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+(-5-2\beta _{1})q^{4}+\cdots\)
33.3.g.a 33.g 11.d $16$ $0.899$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-4\) \(-30\) $\mathrm{SU}(2)[C_{10}]$ \(q+(1+\beta _{2}-\beta _{5}+\beta _{7}+\beta _{8})q^{2}-\beta _{14}q^{3}+\cdots\)
33.3.h.a 33.h 33.h $8$ $0.899$ \(\Q(\zeta_{20})\) None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{10}]$ \(q+\zeta_{20}q^{2}+(2+2\zeta_{20}-2\zeta_{20}^{2}-\zeta_{20}^{3}+\cdots)q^{3}+\cdots\)
33.3.h.b 33.h 33.h $16$ $0.899$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-10\) \(0\) \(6\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{6}+\beta _{9})q^{3}+(-1+\cdots)q^{4}+\cdots\)
33.4.a.a 33.a 1.a $1$ $1.947$ \(\Q\) None \(-5\) \(3\) \(-14\) \(-32\) $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+3q^{3}+17q^{4}-14q^{5}-15q^{6}+\cdots\)
33.4.a.b 33.a 1.a $1$ $1.947$ \(\Q\) None \(-1\) \(-3\) \(-4\) \(-26\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-7q^{4}-4q^{5}+3q^{6}+\cdots\)
33.4.a.c 33.a 1.a $2$ $1.947$ \(\Q(\sqrt{97}) \) None \(1\) \(-6\) \(-14\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-3q^{3}+(2^{4}+\beta )q^{4}+(-6-2\beta )q^{5}+\cdots\)
33.4.a.d 33.a 1.a $2$ $1.947$ \(\Q(\sqrt{33}) \) None \(1\) \(6\) \(16\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+\beta q^{4}+(10-4\beta )q^{5}+\cdots\)
33.4.d.a 33.d 33.d $2$ $1.947$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-8\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-4-\beta )q^{3}-8q^{4}-4\beta q^{5}+(5+8\beta )q^{9}+\cdots\)
33.4.d.b 33.d 33.d $8$ $1.947$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(1-\beta _{3})q^{3}+(5+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
33.4.e.a 33.e 11.c $4$ $1.947$ \(\Q(\zeta_{10})\) None \(10\) \(-3\) \(-21\) \(37\) $\mathrm{SU}(2)[C_{5}]$ \(q+(4-2\zeta_{10}+4\zeta_{10}^{2})q^{2}-3\zeta_{10}^{3}q^{3}+\cdots\)
33.4.e.b 33.e 11.c $8$ $1.947$ 8.0.682515625.5 None \(-6\) \(-6\) \(9\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-2\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+\cdots\)
33.4.e.c 33.e 11.c $12$ $1.947$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(9\) \(28\) \(12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\beta _{3}-\beta _{5}-\beta _{6}-\beta _{7})q^{2}-3\beta _{6}q^{3}+\cdots\)
33.4.f.a 33.f 33.f $40$ $1.947$ None \(0\) \(-3\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$
33.5.b.a 33.b 3.b $14$ $3.411$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(-5\) \(0\) \(76\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-7+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
33.5.c.a 33.c 11.b $8$ $3.411$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-36\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-10-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
33.5.g.a 33.g 11.d $32$ $3.411$ None \(0\) \(0\) \(36\) \(150\) $\mathrm{SU}(2)[C_{10}]$
33.5.h.a 33.h 33.h $56$ $3.411$ None \(0\) \(0\) \(0\) \(-86\) $\mathrm{SU}(2)[C_{10}]$
33.6.a.a 33.a 1.a $1$ $5.293$ \(\Q\) None \(-2\) \(-9\) \(46\) \(148\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-9q^{3}-28q^{4}+46q^{5}+18q^{6}+\cdots\)
33.6.a.b 33.a 1.a $1$ $5.293$ \(\Q\) None \(1\) \(9\) \(-92\) \(-26\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+9q^{3}-31q^{4}-92q^{5}+9q^{6}+\cdots\)
33.6.a.c 33.a 1.a $2$ $5.293$ \(\Q(\sqrt{177}) \) None \(-5\) \(-18\) \(58\) \(-286\) $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}-9q^{3}+(2^{4}+5\beta )q^{4}+\cdots\)
33.6.a.d 33.a 1.a $2$ $5.293$ \(\Q(\sqrt{313}) \) None \(1\) \(-18\) \(-38\) \(-18\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-9q^{3}+(46+\beta )q^{4}+(-24+\cdots)q^{5}+\cdots\)
33.6.a.e 33.a 1.a $2$ $5.293$ \(\Q(\sqrt{33}) \) None \(13\) \(18\) \(58\) \(146\) $-$ $\mathrm{SU}(2)$ \(q+(7-\beta )q^{2}+9q^{3}+(5^{2}-13\beta )q^{4}+\cdots\)
33.6.d.a 33.d 33.d $2$ $5.293$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(31\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(2^{4}-\beta )q^{3}-2^{5}q^{4}+(29-58\beta )q^{5}+\cdots\)
33.6.d.b 33.d 33.d $16$ $5.293$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-54\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(-3-\beta _{2})q^{3}+(20+\beta _{9}+\cdots)q^{4}+\cdots\)
33.6.e.a 33.e 11.c $20$ $5.293$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(-45\) \(-33\) \(-335\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}+\beta _{7})q^{2}-9\beta _{9}q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots\)
33.6.e.b 33.e 11.c $20$ $5.293$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(6\) \(45\) \(-11\) \(-139\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{5}+\beta _{6})q^{2}+9\beta _{7}q^{3}+(-12+\cdots)q^{4}+\cdots\)
33.6.f.a 33.f 33.f $72$ $5.293$ None \(0\) \(18\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$
33.7.b.a 33.b 3.b $20$ $7.592$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(16\) \(0\) \(160\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(-39+\beta _{2}+\cdots)q^{4}+\cdots\)
33.7.c.a 33.c 11.b $12$ $7.592$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(224\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-17+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
33.7.g.a 33.g 11.d $48$ $7.592$ None \(0\) \(0\) \(-224\) \(720\) $\mathrm{SU}(2)[C_{10}]$
33.7.h.a 33.h 33.h $88$ $7.592$ None \(0\) \(33\) \(0\) \(402\) $\mathrm{SU}(2)[C_{10}]$
33.8.a.a 33.a 1.a $1$ $10.309$ \(\Q\) None \(10\) \(27\) \(-410\) \(-1028\) $-$ $\mathrm{SU}(2)$ \(q+10q^{2}+3^{3}q^{3}-28q^{4}-410q^{5}+\cdots\)
33.8.a.b 33.a 1.a $2$ $10.309$ \(\Q(\sqrt{177}) \) None \(-19\) \(54\) \(-34\) \(-166\) $-$ $\mathrm{SU}(2)$ \(q+(-9-\beta )q^{2}+3^{3}q^{3}+(-3+19\beta )q^{4}+\cdots\)
33.8.a.c 33.a 1.a $2$ $10.309$ \(\Q(\sqrt{97}) \) None \(1\) \(-54\) \(-194\) \(-418\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-3^{3}q^{3}+(90+\beta )q^{4}+(-90+\cdots)q^{5}+\cdots\)
33.8.a.d 33.a 1.a $3$ $10.309$ 3.3.115512.1 None \(9\) \(-81\) \(-444\) \(1614\) $+$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{2}-3^{3}q^{3}+(-5+13\beta _{1}+\cdots)q^{4}+\cdots\)
33.8.a.e 33.a 1.a $4$ $10.309$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(15\) \(108\) \(306\) \(890\) $+$ $\mathrm{SU}(2)$ \(q+(4-\beta _{1})q^{2}+3^{3}q^{3}+(142-2\beta _{1}+\cdots)q^{4}+\cdots\)
33.8.d.a 33.d 33.d $2$ $10.309$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-83\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-35-13\beta )q^{3}-2^{7}q^{4}+(71-142\beta )q^{5}+\cdots\)
33.8.d.b 33.d 33.d $24$ $10.309$ None \(0\) \(120\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
33.8.e.a 33.e 11.c $28$ $10.309$ None \(-22\) \(189\) \(-777\) \(-83\) $\mathrm{SU}(2)[C_{5}]$
33.8.e.b 33.e 11.c $28$ $10.309$ None \(-6\) \(-189\) \(773\) \(1289\) $\mathrm{SU}(2)[C_{5}]$
33.8.f.a 33.f 33.f $104$ $10.309$ None \(0\) \(-42\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$
33.9.b.a 33.b 3.b $26$ $13.443$ None \(0\) \(-35\) \(0\) \(7156\) $\mathrm{SU}(2)[C_{2}]$
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