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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.2.a.a 21.a 1.a $1$ $0.168$ \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
21.2.e.a 21.e 7.c $2$ $0.168$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots\)
21.2.g.a 21.g 21.g $2$ $0.168$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(1\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots\)
21.3.b.a 21.b 3.b $4$ $0.572$ 4.0.65856.1 None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
21.3.d.a 21.d 7.b $2$ $0.572$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
21.3.f.a 21.f 7.d $2$ $0.572$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(9\) \(13\) $\mathrm{SU}(2)[C_{6}]$ \(q-3\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
21.3.f.b 21.f 7.d $2$ $0.572$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-9\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
21.3.f.c 21.f 7.d $2$ $0.572$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-6\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots\)
21.3.h.a 21.h 21.h $2$ $0.572$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-13\) $\mathrm{U}(1)[D_{6}]$ \(q+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-5-3\zeta_{6})q^{7}+\cdots\)
21.3.h.b 21.h 21.h $4$ $0.572$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(-4\) \(0\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
21.4.a.a 21.a 1.a $1$ $1.239$ \(\Q\) None \(-3\) \(-3\) \(-18\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}-3q^{3}+q^{4}-18q^{5}+9q^{6}+\cdots\)
21.4.a.b 21.a 1.a $1$ $1.239$ \(\Q\) None \(4\) \(-3\) \(-4\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-3q^{3}+8q^{4}-4q^{5}-12q^{6}+\cdots\)
21.4.a.c 21.a 1.a $2$ $1.239$ \(\Q(\sqrt{57}) \) None \(-3\) \(6\) \(6\) \(14\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3q^{3}+(7+3\beta )q^{4}+\cdots\)
21.4.c.a 21.c 21.c $2$ $1.239$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-20\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}+8q^{4}+(-10+3\zeta_{6})q^{7}+\cdots\)
21.4.c.b 21.c 21.c $4$ $1.239$ \(\Q(\sqrt{-6}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(28\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{3}q^{3}-9q^{4}+(-\beta _{1}-2\beta _{3})q^{5}+\cdots\)
21.4.e.a 21.e 7.c $2$ $1.239$ \(\Q(\sqrt{-3}) \) None \(3\) \(-3\) \(3\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{2}-3\zeta_{6}q^{3}-\zeta_{6}q^{4}+(3+\cdots)q^{5}+\cdots\)
21.4.e.b 21.e 7.c $6$ $1.239$ 6.0.9924270768.1 None \(-1\) \(9\) \(-11\) \(-13\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(3-3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots\)
21.4.g.a 21.g 21.g $12$ $1.239$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(0\) \(-56\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{6})q^{2}+(\beta _{7}+\beta _{8})q^{3}+(-2\beta _{4}+\cdots)q^{4}+\cdots\)
21.5.b.a 21.b 3.b $8$ $2.171$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-5+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
21.5.d.a 21.d 7.b $6$ $2.171$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(-6\) \(0\) \(0\) \(-22\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(10-\beta _{4}+\cdots)q^{4}+\cdots\)
21.5.f.a 21.f 7.d $2$ $2.171$ \(\Q(\sqrt{-3}) \) None \(-2\) \(9\) \(18\) \(77\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{6}q^{2}+(3+3\zeta_{6})q^{3}+(12-12\zeta_{6})q^{4}+\cdots\)
21.5.f.b 21.f 7.d $2$ $2.171$ \(\Q(\sqrt{-3}) \) None \(5\) \(9\) \(-3\) \(-91\) $\mathrm{SU}(2)[C_{6}]$ \(q+5\zeta_{6}q^{2}+(3+3\zeta_{6})q^{3}+(-9+9\zeta_{6})q^{4}+\cdots\)
21.5.f.c 21.f 7.d $6$ $2.171$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(3\) \(-27\) \(39\) \(23\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(-3-3\beta _{2})q^{3}+\cdots\)
21.5.h.a 21.h 21.h $2$ $2.171$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-9\) \(0\) \(71\) $\mathrm{U}(1)[D_{6}]$ \(q-9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+(55-39\zeta_{6})q^{7}+\cdots\)
21.5.h.b 21.h 21.h $16$ $2.171$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(8\) \(0\) \(-168\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(-10\beta _{2}+\cdots)q^{4}+\cdots\)
21.6.a.a 21.a 1.a $1$ $3.368$ \(\Q\) None \(-6\) \(-9\) \(78\) \(49\) $-$ $\mathrm{SU}(2)$ \(q-6q^{2}-9q^{3}+4q^{4}+78q^{5}+54q^{6}+\cdots\)
21.6.a.b 21.a 1.a $1$ $3.368$ \(\Q\) None \(1\) \(-9\) \(-34\) \(-49\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-9q^{3}-31q^{4}-34q^{5}-9q^{6}+\cdots\)
21.6.a.c 21.a 1.a $1$ $3.368$ \(\Q\) None \(5\) \(9\) \(94\) \(-49\) $-$ $\mathrm{SU}(2)$ \(q+5q^{2}+9q^{3}-7q^{4}+94q^{5}+45q^{6}+\cdots\)
21.6.a.d 21.a 1.a $1$ $3.368$ \(\Q\) None \(10\) \(9\) \(-106\) \(-49\) $-$ $\mathrm{SU}(2)$ \(q+10q^{2}+9q^{3}+68q^{4}-106q^{5}+\cdots\)
21.6.c.a 21.c 21.c $12$ $3.368$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(112\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2^{4}-\beta _{1})q^{4}+\cdots\)
21.6.e.a 21.e 7.c $2$ $3.368$ \(\Q(\sqrt{-3}) \) None \(2\) \(9\) \(-11\) \(259\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+9\zeta_{6}q^{3}+28\zeta_{6}q^{4}+\cdots\)
21.6.e.b 21.e 7.c $4$ $3.368$ \(\Q(\sqrt{-3}, \sqrt{-83})\) None \(3\) \(18\) \(33\) \(-350\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}-\beta _{3})q^{2}-9\beta _{1}q^{3}+(31\beta _{1}+\cdots)q^{4}+\cdots\)
21.6.e.c 21.e 7.c $8$ $3.368$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-3\) \(-36\) \(0\) \(258\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+9\beta _{2}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
21.6.g.a 21.g 21.g $2$ $3.368$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(27\) \(0\) \(211\) $\mathrm{U}(1)[D_{6}]$ \(q+(9+9\zeta_{6})q^{3}+(-2^{5}+2^{5}\zeta_{6})q^{4}+\cdots\)
21.6.g.b 21.g 21.g $4$ $3.368$ \(\Q(\sqrt{-3}, \sqrt{-17})\) None \(0\) \(-48\) \(0\) \(490\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\beta _{1}q^{2}+(-2^{4}+\beta _{1}+8\beta _{2}+\beta _{3})q^{3}+\cdots\)
21.6.g.c 21.g 21.g $16$ $3.368$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(18\) \(0\) \(-616\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{6})q^{3}+(12+\cdots)q^{4}+\cdots\)
21.7.b.a 21.b 3.b $12$ $4.831$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(52\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(4-\beta _{3})q^{3}+(-43+\beta _{2}+\cdots)q^{4}+\cdots\)
21.7.d.a 21.d 7.b $8$ $4.831$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(10\) \(0\) \(0\) \(28\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(44+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
21.7.f.a 21.f 7.d $8$ $4.831$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-5\) \(-108\) \(-294\) \(-656\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{1}+\beta _{2})q^{2}+(-18+9\beta _{2}+\cdots)q^{3}+\cdots\)
21.7.f.b 21.f 7.d $8$ $4.831$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-5\) \(108\) \(-42\) \(748\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(9+9\beta _{2})q^{3}+(-43+\cdots)q^{4}+\cdots\)
21.7.h.a 21.h 21.h $28$ $4.831$ None \(0\) \(-1\) \(0\) \(1120\) $\mathrm{SU}(2)[C_{6}]$
21.8.a.a 21.a 1.a $1$ $6.560$ \(\Q\) None \(2\) \(27\) \(-278\) \(-343\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3^{3}q^{3}-124q^{4}-278q^{5}+\cdots\)
21.8.a.b 21.a 1.a $2$ $6.560$ \(\Q(\sqrt{1065}) \) None \(-9\) \(-54\) \(-360\) \(686\) $-$ $\mathrm{SU}(2)$ \(q+(-4-\beta )q^{2}-3^{3}q^{3}+(154+9\beta )q^{4}+\cdots\)
21.8.a.c 21.a 1.a $2$ $6.560$ \(\Q(\sqrt{67}) \) None \(12\) \(-54\) \(-24\) \(-686\) $+$ $\mathrm{SU}(2)$ \(q+(6+\beta )q^{2}-3^{3}q^{3}+(176+12\beta )q^{4}+\cdots\)
21.8.a.d 21.a 1.a $3$ $6.560$ 3.3.2910828.1 None \(-3\) \(81\) \(-114\) \(1029\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3^{3}q^{3}+(75+\beta _{2})q^{4}+\cdots\)
21.8.c.a 21.c 21.c $16$ $6.560$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-1288\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-48+\beta _{3})q^{4}+\cdots\)
21.8.e.a 21.e 7.c $8$ $6.560$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-108\) \(-196\) \(154\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{2}+3^{3}\beta _{4}q^{3}+(-2\beta _{1}+5^{2}\beta _{4}+\cdots)q^{4}+\cdots\)
21.8.e.b 21.e 7.c $10$ $6.560$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-15\) \(135\) \(198\) \(-859\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3-\beta _{1}+3\beta _{4})q^{2}+3^{3}\beta _{4}q^{3}+\cdots\)
21.8.g.a 21.g 21.g $2$ $6.560$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(81\) \(0\) \(-1763\) $\mathrm{U}(1)[D_{6}]$ \(q+(3^{3}+3^{3}\zeta_{6})q^{3}+(-2^{7}+2^{7}\zeta_{6})q^{4}+\cdots\)
21.8.g.b 21.g 21.g $32$ $6.560$ None \(0\) \(-84\) \(0\) \(2464\) $\mathrm{SU}(2)[C_{6}]$
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