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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2070.2.a.a 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
2070.2.a.b 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
2070.2.a.c 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots\)
2070.2.a.d 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.e 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.f 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.g 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
2070.2.a.h 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+6q^{13}+\cdots\)
2070.2.a.i 2070.a 1.a $1$ $16.529$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
2070.2.a.j 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.k 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.l 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.m 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-4q^{11}+\cdots\)
2070.2.a.n 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.o 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
2070.2.a.p 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.q 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.r 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots\)
2070.2.a.s 2070.a 1.a $1$ $16.529$ \(\Q\) None \(1\) \(0\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.t 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots\)
2070.2.a.u 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
2070.2.a.v 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+(2+\beta )q^{7}-q^{8}+\cdots\)
2070.2.a.w 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(-2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
2070.2.a.x 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{21}) \) None \(2\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+q^{10}+\cdots\)
2070.2.a.y 2070.a 1.a $2$ $16.529$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(2+\beta )q^{7}+q^{8}+\cdots\)
2070.2.a.z 2070.a 1.a $3$ $16.529$ 3.3.1101.1 None \(-3\) \(0\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2070.2.d.a 2070.d 5.b $4$ $16.529$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}-2\zeta_{8}^{2}q^{7}+\cdots\)
2070.2.d.b 2070.d 5.b $4$ $16.529$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}-\beta _{3}q^{5}-4\beta _{1}q^{7}-\beta _{1}q^{8}+\cdots\)
2070.2.d.c 2070.d 5.b $4$ $16.529$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-q^{4}+(1+2\beta _{2})q^{5}+3\beta _{1}q^{7}+\cdots\)
2070.2.d.d 2070.d 5.b $6$ $16.529$ 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-q^{4}+\beta _{4}q^{5}+2\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots\)
2070.2.d.e 2070.d 5.b $6$ $16.529$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
2070.2.d.f 2070.d 5.b $8$ $16.529$ 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+(\beta _{3}+\beta _{6})q^{5}+(\beta _{2}-\beta _{5}+\cdots)q^{7}+\cdots\)
2070.2.d.g 2070.d 5.b $8$ $16.529$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}q^{2}-q^{4}+\zeta_{24}^{5}q^{5}-\zeta_{24}q^{8}+\cdots\)
2070.2.d.h 2070.d 5.b $16$ $16.529$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}-q^{4}-\beta _{11}q^{5}+\beta _{12}q^{7}+\cdots\)
2070.2.e.a 2070.e 69.c $16$ $16.529$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{8}q^{2}-q^{4}-q^{5}-\beta _{5}q^{7}+\beta _{8}q^{8}+\cdots\)
2070.2.e.b 2070.e 69.c $16$ $16.529$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{2}-q^{4}+q^{5}-\beta _{5}q^{7}-\beta _{8}q^{8}+\cdots\)
2070.2.h.a 2070.h 345.h $24$ $16.529$ None \(-24\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2070.2.h.b 2070.h 345.h $24$ $16.529$ None \(24\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2070.2.j.a 2070.j 15.e $4$ $16.529$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2-\zeta_{8}^{2})q^{5}+\cdots\)
2070.2.j.b 2070.j 15.e $4$ $16.529$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
2070.2.j.c 2070.j 15.e $4$ $16.529$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
2070.2.j.d 2070.j 15.e $4$ $16.529$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
2070.2.j.e 2070.j 15.e $4$ $16.529$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
2070.2.j.f 2070.j 15.e $4$ $16.529$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2-\zeta_{8}^{2})q^{5}+\cdots\)
2070.2.j.g 2070.j 15.e $12$ $16.529$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{7}q^{4}-\beta _{11}q^{5}+(-2+2\beta _{7}+\cdots)q^{7}+\cdots\)
2070.2.j.h 2070.j 15.e $16$ $16.529$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}-\beta _{7}q^{4}+(-\beta _{4}+\beta _{10})q^{5}+\cdots\)
2070.2.j.i 2070.j 15.e $16$ $16.529$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{7}q^{2}-\beta _{10}q^{4}+\beta _{15}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2070.2.j.j 2070.j 15.e $20$ $16.529$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{13}q^{2}+\beta _{5}q^{4}+(-\beta _{12}-\beta _{16}+\cdots)q^{5}+\cdots\)
2070.3.b.a 2070.b 15.d $88$ $56.403$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2070.3.c.a 2070.c 23.b $16$ $56.403$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+2q^{4}-\beta _{2}q^{5}+(\beta _{1}+\beta _{7}+\cdots)q^{7}+\cdots\)
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