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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1216.1.e.a 1216.e 19.b $1$ $0.607$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(-1\) \(q+q^{5}-q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
1216.1.e.b 1216.e 19.b $1$ $0.607$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(1\) \(q+q^{5}+q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
1216.1.g.a 1216.g 152.g $2$ $0.607$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{38}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}-iq^{11}+q^{17}-iq^{19}+q^{25}+\cdots\)
1216.1.g.b 1216.g 152.g $4$ $0.607$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{5}+(\zeta_{12}-\zeta_{12}^{5}+\cdots)q^{7}+\cdots\)
1216.1.p.a 1216.p 152.l $4$ $0.607$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
1216.1.q.a 1216.q 76.g $4$ $0.607$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{13}+\cdots\)
1216.1.bi.a 1216.bi 152.s $12$ $0.607$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{36}^{13}+\zeta_{36}^{15})q^{3}+(-\zeta_{36}^{8}-\zeta_{36}^{10}+\cdots)q^{9}+\cdots\)
1216.2.a.a 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{7}+6q^{9}-2q^{11}+q^{13}+\cdots\)
1216.2.a.b 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(-2\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-3q^{5}+q^{7}+q^{9}+3q^{11}+\cdots\)
1216.2.a.c 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(-2\) \(1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}+\cdots\)
1216.2.a.d 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(-2\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots\)
1216.2.a.e 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}+6q^{11}-5q^{13}+\cdots\)
1216.2.a.f 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(-1\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots\)
1216.2.a.g 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(-1\) \(4\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}-3q^{7}-2q^{9}+2q^{11}+\cdots\)
1216.2.a.h 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(0\) \(-3\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-5q^{7}-3q^{9}+5q^{11}+4q^{13}+\cdots\)
1216.2.a.i 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(0\) \(-3\) \(5\) $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+5q^{7}-3q^{9}-5q^{11}+4q^{13}+\cdots\)
1216.2.a.j 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-3q^{9}-3q^{11}+4q^{13}+\cdots\)
1216.2.a.k 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(0\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-3q^{9}+3q^{11}+4q^{13}+\cdots\)
1216.2.a.l 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots\)
1216.2.a.m 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}-2q^{9}-6q^{11}-5q^{13}+\cdots\)
1216.2.a.n 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(1\) \(4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+3q^{7}-2q^{9}-2q^{11}+\cdots\)
1216.2.a.o 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(2\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-3q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
1216.2.a.p 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(2\) \(1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
1216.2.a.q 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(2\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+3q^{7}+q^{9}+5q^{11}+\cdots\)
1216.2.a.r 1216.a 1.a $1$ $9.710$ \(\Q\) None None \(0\) \(3\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{7}+6q^{9}+2q^{11}+q^{13}+\cdots\)
1216.2.a.s 1216.a 1.a $2$ $9.710$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(1\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}+3q^{7}+(1+\beta )q^{9}+\cdots\)
1216.2.a.t 1216.a 1.a $2$ $9.710$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(1\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}-3q^{7}+(1+\beta )q^{9}+\cdots\)
1216.2.a.u 1216.a 1.a $3$ $9.710$ 3.3.961.1 None None \(0\) \(-1\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
1216.2.a.v 1216.a 1.a $3$ $9.710$ 3.3.961.1 None None \(0\) \(1\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
1216.2.a.w 1216.a 1.a $4$ $9.710$ 4.4.15317.1 None None \(0\) \(-2\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)
1216.2.a.x 1216.a 1.a $4$ $9.710$ 4.4.15317.1 None None \(0\) \(2\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+\cdots\)
1216.2.b.a 1216.b 152.b $4$ $9.710$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\zeta_{12}q^{3}+\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}-q^{9}+\cdots\)
1216.2.b.b 1216.b 152.b $4$ $9.710$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-q^{9}+\cdots\)
1216.2.b.c 1216.b 152.b $4$ $9.710$ \(\Q(i, \sqrt{19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{5}-3\beta _{1}q^{7}+3q^{9}+\beta _{2}q^{11}+\cdots\)
1216.2.b.d 1216.b 152.b $8$ $9.710$ 8.0.49787136.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-4q^{9}-\beta _{7}q^{13}+\cdots\)
1216.2.b.e 1216.b 152.b $8$ $9.710$ 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{5}+\beta _{6}q^{7}+3q^{9}+(-2\beta _{1}+\beta _{5}+\cdots)q^{11}+\cdots\)
1216.2.b.f 1216.b 152.b $12$ $9.710$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) \(\Q(\sqrt{-38}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{4}q^{3}+\beta _{7}q^{7}+(-3+\beta _{2})q^{9}+\beta _{5}q^{13}+\cdots\)
1216.2.c.a 1216.c 8.b $2$ $9.710$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-3q^{7}+2q^{9}-3iq^{13}+3q^{17}+\cdots\)
1216.2.c.b 1216.c 8.b $2$ $9.710$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-4iq^{5}-q^{7}-6q^{9}+5iq^{13}+\cdots\)
1216.2.c.c 1216.c 8.b $2$ $9.710$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+4iq^{5}+q^{7}-6q^{9}-5iq^{13}+\cdots\)
1216.2.c.d 1216.c 8.b $2$ $9.710$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+3q^{7}+2q^{9}+3iq^{13}+3q^{17}+\cdots\)
1216.2.c.e 1216.c 8.b $4$ $9.710$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1216.2.c.f 1216.c 8.b $4$ $9.710$ \(\Q(i, \sqrt{11})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-q^{9}-5\beta _{1}q^{11}+\cdots\)
1216.2.c.g 1216.c 8.b $4$ $9.710$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1216.2.c.h 1216.c 8.b $8$ $9.710$ 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{3}+2\beta _{6})q^{7}+\cdots\)
1216.2.c.i 1216.c 8.b $8$ $9.710$ 8.0.2702336256.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+\beta _{5}q^{7}+3q^{9}+(-\beta _{2}-2\beta _{4}+\cdots)q^{11}+\cdots\)
1216.2.h.a 1216.h 76.d $2$ $9.710$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+q^{5}+\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
1216.2.h.b 1216.h 76.d $4$ $9.710$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
1216.2.h.c 1216.h 76.d $4$ $9.710$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
1216.2.h.d 1216.h 76.d $8$ $9.710$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(1+\beta _{1})q^{5}-\beta _{7}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
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