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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
672.1.ba.a 672.ba 168.s $2$ $0.335$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(-1\) \(-1\) \(1\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
672.1.ba.b 672.ba 168.s $2$ $0.335$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(1\) \(1\) \(1\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
672.2.a.a 672.a 1.a $1$ $5.366$ \(\Q\) None None \(0\) \(-1\) \(-4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
672.2.a.b 672.a 1.a $1$ $5.366$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
672.2.a.c 672.a 1.a $1$ $5.366$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
672.2.a.d 672.a 1.a $1$ $5.366$ \(\Q\) None None \(0\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
672.2.a.e 672.a 1.a $1$ $5.366$ \(\Q\) None None \(0\) \(1\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
672.2.a.f 672.a 1.a $1$ $5.366$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
672.2.a.g 672.a 1.a $1$ $5.366$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
672.2.a.h 672.a 1.a $1$ $5.366$ \(\Q\) None None \(0\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
672.2.a.i 672.a 1.a $2$ $5.366$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
672.2.a.j 672.a 1.a $2$ $5.366$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
672.2.b.a 672.b 28.d $8$ $5.366$ 8.0.836829184.2 None None \(0\) \(-8\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.b.b 672.b 28.d $8$ $5.366$ 8.0.836829184.2 None None \(0\) \(8\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.c.a 672.c 8.b $4$ $5.366$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}+q^{7}+\cdots\)
672.2.c.b 672.c 8.b $8$ $5.366$ 8.0.386672896.3 None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}-q^{7}-q^{9}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.h.a 672.h 12.b $4$ $5.366$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.b 672.h 12.b $4$ $5.366$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-3\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.c 672.h 12.b $4$ $5.366$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.d 672.h 12.b $4$ $5.366$ \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.e 672.h 12.b $8$ $5.366$ 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(-2+\beta _{6}+\cdots)q^{9}+\cdots\)
672.2.i.a 672.i 168.i $4$ $5.366$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
672.2.i.b 672.i 168.i $4$ $5.366$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{3}+2\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
672.2.i.c 672.i 168.i $4$ $5.366$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
672.2.i.d 672.i 168.i $8$ $5.366$ 8.0.3317760000.1 None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{2}-\beta _{3})q^{3}-\beta _{3}q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
672.2.i.e 672.i 168.i $8$ $5.366$ 8.0.\(\cdots\).11 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{6}-\beta _{7})q^{5}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)
672.2.j.a 672.j 24.f $4$ $5.366$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{8}^{2})q^{3}-2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.j.b 672.j 24.f $4$ $5.366$ \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
672.2.j.c 672.j 24.f $4$ $5.366$ \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
672.2.j.d 672.j 24.f $12$ $5.366$ 12.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\beta _{1}q^{7}+\cdots\)
672.2.k.a 672.k 21.c $8$ $5.366$ 8.0.342102016.5 None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
672.2.k.b 672.k 21.c $8$ $5.366$ 8.0.49787136.1 \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}-3q^{9}+\beta _{3}q^{11}+\cdots\)
672.2.k.c 672.k 21.c $8$ $5.366$ 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{4}+\beta _{5})q^{3}+\beta _{7}q^{5}+(-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
672.2.k.d 672.k 21.c $8$ $5.366$ 8.0.342102016.5 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
672.2.p.a 672.p 56.e $16$ $5.366$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+\beta _{2}q^{5}+\beta _{7}q^{7}-q^{9}+\beta _{3}q^{11}+\cdots\)
672.2.q.a 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
672.2.q.b 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
672.2.q.c 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.d 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.e 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(4\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
672.2.q.f 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
672.2.q.g 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
672.2.q.h 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.i 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.j 672.q 7.c $2$ $5.366$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
672.2.q.k 672.q 7.c $6$ $5.366$ 6.0.1156923.1 None None \(0\) \(-3\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
672.2.q.l 672.q 7.c $6$ $5.366$ 6.0.1156923.1 None None \(0\) \(3\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
672.2.bb.a 672.bb 56.m $32$ $5.366$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
672.2.bc.a 672.bc 21.g $4$ $5.366$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
672.2.bc.b 672.bc 21.g $4$ $5.366$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}+(2\zeta_{12}+\cdots)q^{7}+\cdots\)
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