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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1050.2.a.a 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
1050.2.a.b 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
1050.2.a.c 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
1050.2.a.d 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
1050.2.a.e 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
1050.2.a.f 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
1050.2.a.g 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
1050.2.a.h 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
1050.2.a.i 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
1050.2.a.j 1050.a 1.a $1$ $8.384$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
1050.2.a.k 1050.a 1.a $1$ $8.384$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
1050.2.a.l 1050.a 1.a $1$ $8.384$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
1050.2.a.m 1050.a 1.a $1$ $8.384$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
1050.2.a.n 1050.a 1.a $1$ $8.384$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
1050.2.a.o 1050.a 1.a $1$ $8.384$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
1050.2.a.p 1050.a 1.a $1$ $8.384$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
1050.2.a.q 1050.a 1.a $1$ $8.384$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
1050.2.a.r 1050.a 1.a $1$ $8.384$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
1050.2.b.a 1050.b 21.c $4$ $8.384$ \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
1050.2.b.b 1050.b 21.c $4$ $8.384$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{1}q^{6}+(1+\cdots)q^{7}+\cdots\)
1050.2.b.c 1050.b 21.c $4$ $8.384$ \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(1-\beta _{3})q^{3}-q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{6}+\cdots\)
1050.2.b.d 1050.b 21.c $12$ $8.384$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{9}q^{3}-q^{4}+\beta _{8}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1050.2.b.e 1050.b 21.c $12$ $8.384$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{9}q^{3}-q^{4}-\beta _{8}q^{6}+(\beta _{7}+\cdots)q^{7}+\cdots\)
1050.2.b.f 1050.b 21.c $16$ $8.384$ 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}-\beta _{7}q^{3}-q^{4}-\beta _{2}q^{6}+\beta _{9}q^{7}+\cdots\)
1050.2.d.a 1050.d 105.g $4$ $8.384$ \(\Q(i, \sqrt{5})\) None \(-4\) \(-2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-\beta _{2}-\beta _{3})q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots\)
1050.2.d.b 1050.d 105.g $4$ $8.384$ \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{3}q^{6}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1050.2.d.c 1050.d 105.g $4$ $8.384$ \(\Q(i, \sqrt{5})\) None \(-4\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+(-\beta _{2}-\beta _{3})q^{6}+\cdots\)
1050.2.d.d 1050.d 105.g $4$ $8.384$ \(\Q(i, \sqrt{5})\) None \(4\) \(-2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(-\beta _{2}-\beta _{3})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
1050.2.d.e 1050.d 105.g $4$ $8.384$ \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{3}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1050.2.d.f 1050.d 105.g $4$ $8.384$ \(\Q(i, \sqrt{5})\) None \(4\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots\)
1050.2.d.g 1050.d 105.g $12$ $8.384$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{10}q^{3}+q^{4}-\beta _{10}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1050.2.d.h 1050.d 105.g $12$ $8.384$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{10}q^{3}+q^{4}-\beta _{10}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1050.2.g.a 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{7}-iq^{8}+\cdots\)
1050.2.g.b 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.c 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
1050.2.g.d 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.e 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{7}-iq^{8}+\cdots\)
1050.2.g.f 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.g 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots\)
1050.2.g.h 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.i 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.j 1050.g 5.b $2$ $8.384$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots\)
1050.2.i.a 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.b 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.c 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.d 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.e 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.f 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.g 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.h 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
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