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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
630.2.a.a 630.a 1.a $1$ $5.031$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.b 630.a 1.a $1$ $5.031$ \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.c 630.a 1.a $1$ $5.031$ \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.d 630.a 1.a $1$ $5.031$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.e 630.a 1.a $1$ $5.031$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.f 630.a 1.a $1$ $5.031$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.g 630.a 1.a $1$ $5.031$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
630.2.a.h 630.a 1.a $1$ $5.031$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
630.2.a.i 630.a 1.a $1$ $5.031$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
630.2.a.j 630.a 1.a $1$ $5.031$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
630.2.b.a 630.b 21.c $8$ $5.031$ 8.0.7442857984.4 None \(0\) \(0\) \(-8\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-q^{4}-q^{5}+\beta _{6}q^{7}-\beta _{3}q^{8}+\cdots\)
630.2.b.b 630.b 21.c $8$ $5.031$ 8.0.7442857984.4 None \(0\) \(0\) \(8\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-q^{4}+q^{5}+\beta _{6}q^{7}+\beta _{3}q^{8}+\cdots\)
630.2.d.a 630.d 105.g $4$ $5.031$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.d.b 630.d 105.g $4$ $5.031$ \(\Q(\sqrt{-2}, \sqrt{5})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.c 630.d 105.g $4$ $5.031$ \(\Q(\sqrt{-2}, \sqrt{5})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.d 630.d 105.g $4$ $5.031$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.g.a 630.g 5.b $2$ $5.031$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2-i)q^{5}+iq^{7}+\cdots\)
630.2.g.b 630.g 5.b $2$ $5.031$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-1+2i)q^{5}-iq^{7}+\cdots\)
630.2.g.c 630.g 5.b $2$ $5.031$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots\)
630.2.g.d 630.g 5.b $2$ $5.031$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(1+2i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.e 630.g 5.b $2$ $5.031$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots\)
630.2.g.f 630.g 5.b $2$ $5.031$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(2-i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.g 630.g 5.b $4$ $5.031$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
630.2.i.a 630.i 63.h $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.b 630.i 63.h $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.c 630.i 63.h $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.d 630.i 63.h $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.e 630.i 63.h $4$ $5.031$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(-6\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-2-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
630.2.i.f 630.i 63.h $12$ $5.031$ 12.0.\(\cdots\).1 None \(-12\) \(2\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(\beta _{4}-\beta _{7})q^{3}+q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots\)
630.2.i.g 630.i 63.h $12$ $5.031$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}-\beta _{8}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
630.2.i.h 630.i 63.h $12$ $5.031$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(2\) \(6\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-\beta _{2}+\beta _{6})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
630.2.i.i 630.i 63.h $16$ $5.031$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(2\) \(8\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-\beta _{1}+\beta _{7})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
630.2.j.a 630.j 9.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.b 630.j 9.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.c 630.j 9.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.d 630.j 9.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.e 630.j 9.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.f 630.j 9.c $4$ $5.031$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
630.2.j.g 630.j 9.c $4$ $5.031$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(1\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots\)
630.2.j.h 630.j 9.c $4$ $5.031$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
630.2.j.i 630.j 9.c $6$ $5.031$ 6.0.954288.1 None \(-3\) \(-1\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
630.2.j.j 630.j 9.c $6$ $5.031$ 6.0.954288.1 None \(-3\) \(-1\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
630.2.j.k 630.j 9.c $6$ $5.031$ 6.0.954288.1 None \(-3\) \(1\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+\beta _{3}q^{4}+\beta _{3}q^{5}+\cdots\)
630.2.j.l 630.j 9.c $8$ $5.031$ 8.0.856615824.2 None \(-4\) \(-3\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots\)
630.2.k.a 630.k 7.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
630.2.k.b 630.k 7.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
630.2.k.c 630.k 7.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
630.2.k.d 630.k 7.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
630.2.k.e 630.k 7.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
630.2.k.f 630.k 7.c $2$ $5.031$ \(\Q(\sqrt{-3}) \) 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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