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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
504.1.e.a 504.e 168.e $4$ $0.252$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
504.1.l.a 504.l 56.h $1$ $0.252$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(1\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{14}+q^{16}+\cdots\)
504.1.l.b 504.l 56.h $2$ $0.252$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(2\) \(q-iq^{2}-q^{4}+q^{7}+iq^{8}-iq^{11}+\cdots\)
504.1.ba.a 504.ba 504.aa $4$ $0.252$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
504.1.bn.a 504.bn 504.an $2$ $0.252$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(-1\) \(-2\) \(-1\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
504.1.bn.b 504.bn 504.an $2$ $0.252$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(-1\) \(2\) \(1\) \(-1\) \(q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
504.1.bn.c 504.bn 504.an $4$ $0.252$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-14}) \) None \(2\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
504.1.bw.a 504.bw 56.j $4$ $0.252$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)
504.1.ce.a 504.ce 504.be $4$ $0.252$ \(\Q(\zeta_{12})\) None None \(0\) \(-4\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}+\zeta_{12}^{3}q^{6}+\cdots\)
504.1.cu.a 504.cu 21.h $4$ $0.252$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(2\) \(q+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}-\beta _{1}q^{11}-q^{13}+\cdots\)
504.2.a.a 504.a 1.a $1$ $4.024$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-2q^{11}+2q^{13}-6q^{17}+\cdots\)
504.2.a.b 504.a 1.a $1$ $4.024$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
504.2.a.c 504.a 1.a $1$ $4.024$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
504.2.a.d 504.a 1.a $1$ $4.024$ \(\Q\) None None \(0\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-6q^{11}-6q^{13}+2q^{17}+\cdots\)
504.2.a.e 504.a 1.a $1$ $4.024$ \(\Q\) None None \(0\) \(0\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
504.2.a.f 504.a 1.a $1$ $4.024$ \(\Q\) None None \(0\) \(0\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+2q^{11}+2q^{13}+6q^{17}+\cdots\)
504.2.a.g 504.a 1.a $1$ $4.024$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+6q^{11}-6q^{13}-2q^{17}+\cdots\)
504.2.a.h 504.a 1.a $1$ $4.024$ \(\Q\) None None \(0\) \(0\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+q^{7}+2q^{17}-2q^{19}-8q^{23}+\cdots\)
504.2.c.a 504.c 8.b $2$ $4.024$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}-\beta q^{5}+q^{7}-2\beta q^{8}+\cdots\)
504.2.c.b 504.c 8.b $4$ $4.024$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
504.2.c.c 504.c 8.b $4$ $4.024$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+\beta _{2}q^{5}+q^{7}+\cdots\)
504.2.c.d 504.c 8.b $4$ $4.024$ 4.0.2312.1 None None \(1\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}-q^{7}+\cdots\)
504.2.c.e 504.c 8.b $8$ $4.024$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}-q^{7}+\beta _{3}q^{8}+\cdots\)
504.2.c.f 504.c 8.b $8$ $4.024$ 8.0.386672896.3 None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{2}q^{4}+(-\beta _{2}+\beta _{6})q^{5}+\cdots\)
504.2.i.a 504.i 168.i $8$ $4.024$ 8.0.157351936.1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{7}+\beta _{3}q^{8}+\cdots\)
504.2.i.b 504.i 168.i $24$ $4.024$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
504.2.j.a 504.j 24.f $24$ $4.024$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
504.2.k.a 504.k 21.c $8$ $4.024$ \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}^{7}q^{5}+(1+\zeta_{16}^{4})q^{7}+(\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{11}+\cdots\)
504.2.p.a 504.p 56.e $2$ $4.024$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+\beta )q^{2}+(-1-\beta )q^{4}+(-1+\cdots)q^{7}+\cdots\)
504.2.p.b 504.p 56.e $4$ $4.024$ \(\Q(\zeta_{12})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\zeta_{12})q^{2}-2\zeta_{12}q^{4}+2\zeta_{12}^{3}q^{5}+\cdots\)
504.2.p.c 504.p 56.e $4$ $4.024$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-42}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\)
504.2.p.d 504.p 56.e $4$ $4.024$ \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{2}+(2-\beta _{2})q^{4}+(-1+2\beta _{2}+\cdots)q^{7}+\cdots\)
504.2.p.e 504.p 56.e $4$ $4.024$ \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{12})q^{2}+2\zeta_{12}q^{4}-2\zeta_{12}^{3}q^{5}+\cdots\)
504.2.p.f 504.p 56.e $4$ $4.024$ \(\Q(i, \sqrt{6})\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}+\beta _{3}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
504.2.p.g 504.p 56.e $16$ $4.024$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+\beta _{3}q^{4}+\beta _{5}q^{5}+\beta _{8}q^{7}+\cdots\)
504.2.q.a 504.q 63.h $2$ $4.024$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
504.2.q.b 504.q 63.h $2$ $4.024$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
504.2.q.c 504.q 63.h $22$ $4.024$ None None \(0\) \(-2\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$
504.2.q.d 504.q 63.h $22$ $4.024$ None None \(0\) \(2\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$
504.2.r.a 504.r 9.c $2$ $4.024$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots\)
504.2.r.b 504.r 9.c $2$ $4.024$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots\)
504.2.r.c 504.r 9.c $6$ $4.024$ \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
504.2.r.d 504.r 9.c $8$ $4.024$ 8.0.508277025.1 None None \(0\) \(-4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}-\beta _{6})q^{3}+(1+\beta _{1}+2\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
504.2.r.e 504.r 9.c $8$ $4.024$ 8.0.2091141441.1 None None \(0\) \(-1\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
504.2.r.f 504.r 9.c $10$ $4.024$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
504.2.s.a 504.s 7.c $2$ $4.024$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}-3q^{13}+\cdots\)
504.2.s.b 504.s 7.c $2$ $4.024$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+5\zeta_{6}q^{11}+\cdots\)
504.2.s.c 504.s 7.c $2$ $4.024$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
504.2.s.d 504.s 7.c $2$ $4.024$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
504.2.s.e 504.s 7.c $2$ $4.024$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-\zeta_{6}q^{11}+\cdots\)
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