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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
528.1.g.a 528.g 132.d $1$ $0.264$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-33}) \) \(\Q(\sqrt{3}) \) 528.1.g.a \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+q^{11}+2q^{23}+q^{25}+\cdots\)
528.1.g.b 528.g 132.d $1$ $0.264$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-33}) \) \(\Q(\sqrt{3}) \) 528.1.g.a \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}-q^{11}-2q^{23}+q^{25}+\cdots\)
528.1.g.c 528.g 132.d $2$ $0.264$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None 528.1.g.c \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots\)
528.1.g.d 528.g 132.d $2$ $0.264$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None 528.1.g.c \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots\)
528.2.a.a 528.a 1.a $1$ $4.216$ \(\Q\) None None 66.2.a.c \(0\) \(-1\) \(-4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
528.2.a.b 528.a 1.a $1$ $4.216$ \(\Q\) None None 264.2.a.b \(0\) \(-1\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-4q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
528.2.a.c 528.a 1.a $1$ $4.216$ \(\Q\) None None 264.2.a.c \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}-q^{11}-2q^{17}+\cdots\)
528.2.a.d 528.a 1.a $1$ $4.216$ \(\Q\) None None 66.2.a.a \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
528.2.a.e 528.a 1.a $1$ $4.216$ \(\Q\) None None 132.2.a.b \(0\) \(-1\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+2q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
528.2.a.f 528.a 1.a $1$ $4.216$ \(\Q\) None None 264.2.a.d \(0\) \(-1\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+2q^{7}+q^{9}+q^{11}-4q^{15}+\cdots\)
528.2.a.g 528.a 1.a $1$ $4.216$ \(\Q\) None None 33.2.a.a \(0\) \(1\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
528.2.a.h 528.a 1.a $1$ $4.216$ \(\Q\) None None 132.2.a.a \(0\) \(1\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-2q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
528.2.a.i 528.a 1.a $1$ $4.216$ \(\Q\) None None 264.2.a.a \(0\) \(1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}-q^{11}+2q^{13}+\cdots\)
528.2.a.j 528.a 1.a $1$ $4.216$ \(\Q\) None None 66.2.a.b \(0\) \(1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
528.2.b.a 528.b 33.d $2$ $4.216$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None 33.2.d.a \(0\) \(-1\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{3}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
528.2.b.b 528.b 33.d $2$ $4.216$ \(\Q(\sqrt{-2}) \) None None 66.2.b.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{3}-\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.b.c 528.b 33.d $2$ $4.216$ \(\Q(\sqrt{-2}) \) None None 66.2.b.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{3}-\beta q^{5}-3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.b.d 528.b 33.d $4$ $4.216$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None 132.2.b.a \(0\) \(1\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{2})q^{9}+\cdots\)
528.2.b.e 528.b 33.d $6$ $4.216$ 6.0.7388168.1 None None 264.2.b.a \(0\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
528.2.b.f 528.b 33.d $6$ $4.216$ 6.0.7388168.1 None None 264.2.b.a \(0\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
528.2.d.a 528.d 12.b $2$ $4.216$ \(\Q(\sqrt{-3}) \) None None 528.2.d.a \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
528.2.d.b 528.d 12.b $2$ $4.216$ \(\Q(\sqrt{-2}) \) None None 528.2.d.b \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta )q^{3}-2\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
528.2.d.c 528.d 12.b $2$ $4.216$ \(\Q(\sqrt{-3}) \) None None 528.2.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-3q^{9}-q^{11}+4q^{13}+\cdots\)
528.2.d.d 528.d 12.b $2$ $4.216$ \(\Q(\sqrt{-3}) \) None None 528.2.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-3q^{9}+q^{11}+4q^{13}+\cdots\)
528.2.d.e 528.d 12.b $2$ $4.216$ \(\Q(\sqrt{-2}) \) None None 528.2.d.b \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{3}+2\beta q^{5}+\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.d.f 528.d 12.b $2$ $4.216$ \(\Q(\sqrt{-3}) \) None None 528.2.d.a \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(2-4\zeta_{6})q^{7}+\cdots\)
528.2.d.g 528.d 12.b $4$ $4.216$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None 528.2.d.g \(0\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(-2\beta _{1}-2\beta _{3})q^{7}+\cdots\)
528.2.d.h 528.d 12.b $4$ $4.216$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None 528.2.d.g \(0\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+2\beta _{3})q^{7}+\cdots\)
528.2.o.a 528.o 44.c $4$ $4.216$ \(\Q(i, \sqrt{10})\) None None 528.2.o.a \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-2q^{5}-\beta _{3}q^{7}-q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
528.2.o.b 528.o 44.c $8$ $4.216$ 8.0.454201344.7 None None 528.2.o.b \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-\beta _{7}q^{7}-q^{9}+\cdots\)
528.2.q.a 528.q 176.i $96$ $4.216$ None None 528.2.q.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
528.2.t.a 528.t 16.e $40$ $4.216$ None None 528.2.t.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
528.2.t.b 528.t 16.e $40$ $4.216$ None None 528.2.t.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
528.2.u.a 528.u 48.k $160$ $4.216$ None None 528.2.u.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
528.2.x.a 528.x 528.x $184$ $4.216$ None None 528.2.x.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
528.2.y.a 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 132.2.i.b \(0\) \(-1\) \(-7\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(-3+2\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
528.2.y.b 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 33.2.e.b \(0\) \(-1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(-1-\zeta_{10}^{2})q^{5}-\zeta_{10}^{3}q^{7}+\cdots\)
528.2.y.c 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 264.2.q.d \(0\) \(-1\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots\)
528.2.y.d 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 66.2.e.a \(0\) \(-1\) \(8\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(3-\zeta_{10}+3\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.e 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 264.2.q.a \(0\) \(1\) \(-8\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(-3+\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
528.2.y.f 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 33.2.e.a \(0\) \(1\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(-1+2\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
528.2.y.g 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 66.2.e.b \(0\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(1-3\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.h 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 264.2.q.b \(0\) \(1\) \(1\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(1-2\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.i 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 132.2.i.a \(0\) \(1\) \(3\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots\)
528.2.y.j 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None 264.2.q.c \(0\) \(1\) \(5\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(1+2\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.k 528.y 11.c $8$ $4.216$ 8.0.185640625.1 None None 264.2.q.e \(0\) \(-2\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{6}q^{3}+(-2\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
528.2.ba.a 528.ba 44.g $8$ $4.216$ \(\Q(\zeta_{20})\) None None 528.2.ba.a \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\zeta_{20}q^{3}+(-1+\zeta_{20}^{6})q^{5}+(-\zeta_{20}+\cdots)q^{7}+\cdots\)
528.2.ba.b 528.ba 44.g $8$ $4.216$ \(\Q(\zeta_{20})\) None None 528.2.ba.b \(0\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\zeta_{20}q^{3}+(1+2\zeta_{20}^{2}-2\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{5}+\cdots\)
528.2.ba.c 528.ba 44.g $32$ $4.216$ None None 528.2.ba.c \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{10}]$
528.2.bl.a 528.bl 132.o $32$ $4.216$ None None 528.2.bl.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
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