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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1638.2.a.a 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots\)
1638.2.a.b 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
1638.2.a.c 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
1638.2.a.d 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
1638.2.a.e 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{13}-q^{14}+\cdots\)
1638.2.a.f 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
1638.2.a.g 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
1638.2.a.h 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1638.2.a.i 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
1638.2.a.j 1638.a 1.a $1$ $13.079$ \(\Q\) None \(-1\) \(0\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
1638.2.a.k 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(-4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}-q^{7}+q^{8}-4q^{10}+\cdots\)
1638.2.a.l 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
1638.2.a.m 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
1638.2.a.n 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1638.2.a.o 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1638.2.a.p 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{13}+q^{14}+\cdots\)
1638.2.a.q 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}-q^{13}+\cdots\)
1638.2.a.r 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1638.2.a.s 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
1638.2.a.t 1638.a 1.a $1$ $13.079$ \(\Q\) None \(1\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
1638.2.a.u 1638.a 1.a $2$ $13.079$ \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{7}-q^{8}+\cdots\)
1638.2.a.v 1638.a 1.a $2$ $13.079$ \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta q^{5}-q^{7}-q^{8}+\beta q^{10}+\cdots\)
1638.2.a.w 1638.a 1.a $2$ $13.079$ \(\Q(\sqrt{41}) \) None \(-2\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
1638.2.a.x 1638.a 1.a $2$ $13.079$ \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
1638.2.a.y 1638.a 1.a $2$ $13.079$ \(\Q(\sqrt{57}) \) None \(2\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
1638.2.c.a 1638.c 13.b $2$ $13.079$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots\)
1638.2.c.b 1638.c 13.b $2$ $13.079$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots\)
1638.2.c.c 1638.c 13.b $2$ $13.079$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{5}+iq^{7}-iq^{8}+\cdots\)
1638.2.c.d 1638.c 13.b $2$ $13.079$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots\)
1638.2.c.e 1638.c 13.b $2$ $13.079$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{5}-iq^{7}+iq^{8}+\cdots\)
1638.2.c.f 1638.c 13.b $2$ $13.079$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{5}+iq^{7}+iq^{8}+\cdots\)
1638.2.c.g 1638.c 13.b $2$ $13.079$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+3iq^{5}+iq^{7}+iq^{8}+\cdots\)
1638.2.c.h 1638.c 13.b $4$ $13.079$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots\)
1638.2.c.i 1638.c 13.b $6$ $13.079$ 6.0.30647296.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots\)
1638.2.c.j 1638.c 13.b $6$ $13.079$ 6.0.3356224.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\beta _{1}q^{7}+\cdots\)
1638.2.c.k 1638.c 13.b $6$ $13.079$ 6.0.3356224.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}-\beta _{1}q^{7}+\cdots\)
1638.2.e.a 1638.e 273.g $16$ $13.079$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{7}-q^{8}+\cdots\)
1638.2.e.b 1638.e 273.g $16$ $13.079$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+\beta _{6}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots\)
1638.2.g.a 1638.g 21.c $8$ $13.079$ 8.0.40960000.1 None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+(-1-\beta _{3})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
1638.2.g.b 1638.g 21.c $8$ $13.079$ 8.0.836829184.2 None \(0\) \(0\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-q^{4}+(-2-\beta _{1}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
1638.2.g.c 1638.g 21.c $8$ $13.079$ 8.0.40960000.1 None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}+(1-\beta _{3})q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
1638.2.g.d 1638.g 21.c $8$ $13.079$ 8.0.836829184.2 None \(0\) \(0\) \(8\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-q^{4}+(2+\beta _{1}+\beta _{6}-\beta _{7})q^{5}+\cdots\)
1638.2.j.a 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1638.2.j.b 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1638.2.j.c 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
1638.2.j.d 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1638.2.j.e 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1638.2.j.f 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1638.2.j.g 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1638.2.j.h 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
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