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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1008.1.f.a 1008.f 7.b $1$ $0.503$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots\)
1008.1.u.a 1008.u 112.l $2$ $0.503$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+iq^{7}-q^{8}+(1-i)q^{11}+\cdots\)
1008.1.u.b 1008.u 112.l $2$ $0.503$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+(1-i+\cdots)q^{11}+\cdots\)
1008.1.u.c 1008.u 112.l $2$ $0.503$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+iq^{7}+q^{8}+(-1+i+\cdots)q^{11}+\cdots\)
1008.1.y.a 1008.y 336.v $4$ $0.503$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
1008.1.y.b 1008.y 336.v $4$ $0.503$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{7}-\zeta_{8}q^{8}+\cdots\)
1008.1.bw.a 1008.bw 252.u $4$ $0.503$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1008.1.cd.a 1008.cd 28.g $2$ $0.503$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}+q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots\)
1008.1.cd.b 1008.cd 28.g $2$ $0.503$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{7}+q^{13}+(-1-\zeta_{6})q^{19}+\cdots\)
1008.1.cg.a 1008.cg 7.d $2$ $0.503$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1008.1.dc.a 1008.dc 21.h $4$ $0.503$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)
1008.1.dd.a 1008.dd 252.al $4$ $0.503$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots\)
1008.1.dt.a 1008.dt 112.u $8$ $0.503$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots\)
1008.1.ed.a 1008.ed 336.at $8$ $0.503$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}q^{5}+\zeta_{24}^{2}q^{7}+\cdots\)
1008.2.a.a 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(-4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+q^{7}+2q^{11}-6q^{13}+4q^{17}+\cdots\)
1008.2.a.b 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
1008.2.a.c 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+6q^{11}-6q^{13}+2q^{17}+\cdots\)
1008.2.a.d 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots\)
1008.2.a.e 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
1008.2.a.f 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+2q^{11}+2q^{13}-6q^{17}+\cdots\)
1008.2.a.g 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-6q^{11}+2q^{13}+4q^{19}-6q^{23}+\cdots\)
1008.2.a.h 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-4q^{13}-6q^{17}-2q^{19}-5q^{25}+\cdots\)
1008.2.a.i 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-6q^{11}-6q^{13}-2q^{17}+\cdots\)
1008.2.a.j 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
1008.2.a.k 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-2q^{11}+2q^{13}+6q^{17}+\cdots\)
1008.2.a.l 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
1008.2.a.m 1008.a 1.a $1$ $8.049$ \(\Q\) None None \(0\) \(0\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}+2q^{17}+2q^{19}+8q^{23}+\cdots\)
1008.2.a.n 1008.a 1.a $2$ $8.049$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+\beta q^{11}+2q^{13}-\beta q^{17}+\cdots\)
1008.2.b.a 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}-4\zeta_{6}q^{17}+\cdots\)
1008.2.b.b 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
1008.2.b.c 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{2}]$ \(q+(-2+\zeta_{6})q^{7}-4\zeta_{6}q^{13}+8q^{19}+\cdots\)
1008.2.b.d 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-6}) \) None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+(-1-\beta )q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.e 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-6}) \) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+(1+\beta )q^{7}+\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.f 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) $\mathrm{U}(1)[D_{2}]$ \(q+(2-\zeta_{6})q^{7}-4\zeta_{6}q^{13}-8q^{19}+5q^{25}+\cdots\)
1008.2.b.g 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
1008.2.b.h 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}+4\zeta_{6}q^{17}+\cdots\)
1008.2.b.i 1008.b 28.d $4$ $8.049$ \(\Q(\sqrt{-6}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{11}+3\beta _{1}q^{17}+\cdots\)
1008.2.h.a 1008.h 12.b $4$ $8.049$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+4\zeta_{8}^{3}q^{11}-4q^{13}+\cdots\)
1008.2.h.b 1008.h 12.b $8$ $8.049$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{24}^{2}+\zeta_{24}^{7})q^{5}-\zeta_{24}q^{7}+(-\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)
1008.2.k.a 1008.k 21.c $4$ $8.049$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}+(\beta _{1}+\beta _{3})q^{23}+\cdots\)
1008.2.k.b 1008.k 21.c $4$ $8.049$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+(1+\beta _{1})q^{7}-\beta _{2}q^{11}-2\beta _{1}q^{13}+\cdots\)
1008.2.k.c 1008.k 21.c $8$ $8.049$ \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}^{7}q^{5}+(-1-\zeta_{16}^{6})q^{7}+(\zeta_{16}+\cdots)q^{11}+\cdots\)
1008.2.q.a 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
1008.2.q.b 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1008.2.q.c 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1008.2.q.d 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1008.2.q.e 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1008.2.q.f 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1008.2.q.g 1008.q 63.h $6$ $8.049$ 6.0.309123.1 None None \(0\) \(-2\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{4})q^{3}+(1-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
1008.2.q.h 1008.q 63.h $6$ $8.049$ 6.0.309123.1 None None \(0\) \(2\) \(-5\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+2\beta _{4}+\cdots)q^{5}+\cdots\)
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