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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
70.2.a.a 70.a 1.a $1$ $0.559$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
70.2.c.a 70.c 5.b $4$ $0.559$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
70.2.e.a 70.e 7.c $2$ $0.559$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.e.b 70.e 7.c $2$ $0.559$ \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.e.c 70.e 7.c $2$ $0.559$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.e.d 70.e 7.c $2$ $0.559$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
70.2.g.a 70.g 35.f $8$ $0.559$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{16}^{6}q^{2}+(\zeta_{16}-\zeta_{16}^{3})q^{3}-\zeta_{16}^{4}q^{4}+\cdots\)
70.2.i.a 70.i 35.j $4$ $0.559$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{3}+\cdots\)
70.2.i.b 70.i 35.j $4$ $0.559$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
70.2.k.a 70.k 35.k $16$ $0.559$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-12\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{7}-\beta _{15})q^{2}+(-\beta _{4}+\beta _{13})q^{3}+\cdots\)
70.3.b.a 70.b 7.b $8$ $1.907$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+2q^{4}-\beta _{2}q^{5}+\cdots\)
70.3.d.a 70.d 35.c $8$ $1.907$ 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{5}q^{3}-2q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
70.3.f.a 70.f 5.c $4$ $1.907$ \(\Q(i, \sqrt{14})\) None \(-4\) \(4\) \(12\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{2})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
70.3.f.b 70.f 5.c $8$ $1.907$ 8.0.\(\cdots\).20 None \(8\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{3})q^{2}+(1+\beta _{1}-\beta _{3})q^{3}+2\beta _{3}q^{4}+\cdots\)
70.3.h.a 70.h 35.i $16$ $1.907$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{10}q^{2}+\beta _{1}q^{3}+2\beta _{4}q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
70.3.j.a 70.j 7.d $8$ $1.907$ 8.0.3317760000.3 None \(0\) \(12\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{5})q^{2}+(1-\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
70.3.l.a 70.l 35.l $8$ $1.907$ 8.0.3317760000.2 None \(4\) \(-4\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\beta _{2}-\beta _{4})q^{2}+(-\beta _{2}+2\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
70.3.l.b 70.l 35.l $8$ $1.907$ 8.0.303595776.1 None \(4\) \(2\) \(-6\) \(-12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\beta _{3}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
70.3.l.c 70.l 35.l $16$ $1.907$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-8\) \(2\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\beta _{4}+\beta _{8})q^{2}+(-\beta _{3}-\beta _{10}+\cdots)q^{3}+\cdots\)
70.4.a.a 70.a 1.a $1$ $4.130$ \(\Q\) None \(-2\) \(-8\) \(-5\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-8q^{3}+4q^{4}-5q^{5}+2^{4}q^{6}+\cdots\)
70.4.a.b 70.a 1.a $1$ $4.130$ \(\Q\) None \(-2\) \(-3\) \(5\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
70.4.a.c 70.a 1.a $1$ $4.130$ \(\Q\) None \(-2\) \(-1\) \(-5\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+4q^{4}-5q^{5}+2q^{6}+\cdots\)
70.4.a.d 70.a 1.a $1$ $4.130$ \(\Q\) None \(-2\) \(4\) \(5\) \(7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots\)
70.4.a.e 70.a 1.a $1$ $4.130$ \(\Q\) None \(2\) \(5\) \(5\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+5q^{3}+4q^{4}+5q^{5}+10q^{6}+\cdots\)
70.4.a.f 70.a 1.a $1$ $4.130$ \(\Q\) None \(2\) \(7\) \(-5\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+7q^{3}+4q^{4}-5q^{5}+14q^{6}+\cdots\)
70.4.c.a 70.c 5.b $2$ $4.130$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+7iq^{3}-4q^{4}+(10+5i)q^{5}+\cdots\)
70.4.c.b 70.c 5.b $6$ $4.130$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{3}q^{2}+(-2\beta _{3}+\beta _{5})q^{3}-4q^{4}+\cdots\)
70.4.e.a 70.e 7.c $2$ $4.130$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(5\) \(35\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
70.4.e.b 70.e 7.c $2$ $4.130$ \(\Q(\sqrt{-3}) \) None \(2\) \(-10\) \(5\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-10+10\zeta_{6})q^{3}+(-4+\cdots)q^{4}+\cdots\)
70.4.e.c 70.e 7.c $2$ $4.130$ \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(5\) \(17\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
70.4.e.d 70.e 7.c $4$ $4.130$ \(\Q(\sqrt{-3}, \sqrt{46})\) None \(4\) \(2\) \(-10\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
70.4.e.e 70.e 7.c $6$ $4.130$ 6.0.\(\cdots\).2 None \(-6\) \(-4\) \(-15\) \(14\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\beta _{3})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\cdots\)
70.4.g.a 70.g 35.f $24$ $4.130$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$
70.4.i.a 70.i 35.j $24$ $4.130$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{6}]$
70.4.k.a 70.k 35.k $48$ $4.130$ None \(0\) \(0\) \(48\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
70.5.b.a 70.b 7.b $8$ $7.236$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(132\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(\beta _{2}-\beta _{4}-\beta _{5})q^{3}+8q^{4}+\cdots\)
70.5.d.a 70.d 35.c $16$ $7.236$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-\beta _{4}q^{3}-8q^{4}-\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots\)
70.5.f.a 70.f 5.c $12$ $7.236$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-24\) \(-20\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2\beta _{1})q^{2}+(-2+2\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
70.5.f.b 70.f 5.c $12$ $7.236$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(24\) \(-20\) \(40\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2\beta _{1})q^{2}+(-2+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
70.5.h.a 70.h 35.i $32$ $7.236$ None \(0\) \(0\) \(54\) \(0\) $\mathrm{SU}(2)[C_{6}]$
70.5.j.a 70.j 7.d $24$ $7.236$ None \(0\) \(36\) \(0\) \(76\) $\mathrm{SU}(2)[C_{6}]$
70.5.l.a 70.l 35.l $32$ $7.236$ None \(-32\) \(-8\) \(-10\) \(-34\) $\mathrm{SU}(2)[C_{12}]$
70.5.l.b 70.l 35.l $32$ $7.236$ None \(32\) \(8\) \(-26\) \(14\) $\mathrm{SU}(2)[C_{12}]$
70.6.a.a 70.a 1.a $1$ $11.227$ \(\Q\) None \(-4\) \(-23\) \(25\) \(49\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-23q^{3}+2^{4}q^{4}+5^{2}q^{5}+92q^{6}+\cdots\)
70.6.a.b 70.a 1.a $1$ $11.227$ \(\Q\) None \(-4\) \(-9\) \(25\) \(-49\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+5^{2}q^{5}+6^{2}q^{6}+\cdots\)
70.6.a.c 70.a 1.a $1$ $11.227$ \(\Q\) None \(-4\) \(-3\) \(-25\) \(49\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-3q^{3}+2^{4}q^{4}-5^{2}q^{5}+12q^{6}+\cdots\)
70.6.a.d 70.a 1.a $1$ $11.227$ \(\Q\) None \(-4\) \(11\) \(-25\) \(-49\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+11q^{3}+2^{4}q^{4}-5^{2}q^{5}-44q^{6}+\cdots\)
70.6.a.e 70.a 1.a $1$ $11.227$ \(\Q\) None \(4\) \(-17\) \(25\) \(-49\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-17q^{3}+2^{4}q^{4}+5^{2}q^{5}-68q^{6}+\cdots\)
70.6.a.f 70.a 1.a $1$ $11.227$ \(\Q\) None \(4\) \(-11\) \(-25\) \(49\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-11q^{3}+2^{4}q^{4}-5^{2}q^{5}-44q^{6}+\cdots\)
70.6.a.g 70.a 1.a $2$ $11.227$ \(\Q(\sqrt{3369}) \) None \(8\) \(3\) \(-50\) \(-98\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(2-\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
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