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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
528.1.g.a $1$ $0.264$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-33}) \) \(\Q(\sqrt{3}) \) \(0\) \(-1\) \(0\) \(0\) $-$ \(q-q^{3}+q^{9}+q^{11}+2q^{23}+q^{25}+\cdots\)
528.1.g.b $1$ $0.264$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-33}) \) \(\Q(\sqrt{3}) \) \(0\) \(1\) \(0\) \(0\) $-$ \(q+q^{3}+q^{9}-q^{11}-2q^{23}+q^{25}+\cdots\)
528.1.g.c $2$ $0.264$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(0\) \(0\) $-$ \(q+\zeta_{6}^{2}q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots\)
528.1.g.d $2$ $0.264$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(0\) \(0\) $-$ \(q-\zeta_{6}^{2}q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots\)
528.2.a.a $1$ $4.216$ \(\Q\) None None \(0\) \(-1\) \(-4\) \(2\) $-$ \(q-q^{3}-4q^{5}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
528.2.a.b $1$ $4.216$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(-4\) $-$ \(q-q^{3}-2q^{5}-4q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
528.2.a.c $1$ $4.216$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $+$ \(q-q^{3}-2q^{7}+q^{9}-q^{11}-2q^{17}+\cdots\)
528.2.a.d $1$ $4.216$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $+$ \(q-q^{3}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
528.2.a.e $1$ $4.216$ \(\Q\) None None \(0\) \(-1\) \(2\) \(2\) $-$ \(q-q^{3}+2q^{5}+2q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
528.2.a.f $1$ $4.216$ \(\Q\) None None \(0\) \(-1\) \(4\) \(2\) $-$ \(q-q^{3}+4q^{5}+2q^{7}+q^{9}+q^{11}-4q^{15}+\cdots\)
528.2.a.g $1$ $4.216$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-4\) $+$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
528.2.a.h $1$ $4.216$ \(\Q\) None None \(0\) \(1\) \(2\) \(-2\) $-$ \(q+q^{3}+2q^{5}-2q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
528.2.a.i $1$ $4.216$ \(\Q\) None None \(0\) \(1\) \(2\) \(0\) $-$ \(q+q^{3}+2q^{5}+q^{9}-q^{11}+2q^{13}+\cdots\)
528.2.a.j $1$ $4.216$ \(\Q\) None None \(0\) \(1\) \(2\) \(4\) $-$ \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
528.2.b.a $2$ $4.216$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(0\) \(0\) $-$ \(q-\beta q^{3}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
528.2.b.b $2$ $4.216$ \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(0\) $-$ \(q+(1+\beta )q^{3}-\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.b.c $2$ $4.216$ \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(0\) $-$ \(q+(1+\beta )q^{3}-\beta q^{5}-3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.b.d $4$ $4.216$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{2})q^{9}+\cdots\)
528.2.b.e $6$ $4.216$ 6.0.7388168.1 None None \(0\) \(-1\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
528.2.b.f $6$ $4.216$ 6.0.7388168.1 None None \(0\) \(-1\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
528.2.d.a $2$ $4.216$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(0\) \(0\) $-$ \(q+(-1-\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
528.2.d.b $2$ $4.216$ \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(0\) \(0\) $-$ \(q+(-1+\beta )q^{3}-2\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
528.2.d.c $2$ $4.216$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-3q^{9}-q^{11}+4q^{13}+\cdots\)
528.2.d.d $2$ $4.216$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-3q^{9}+q^{11}+4q^{13}+\cdots\)
528.2.d.e $2$ $4.216$ \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(0\) $-$ \(q+(1+\beta )q^{3}+2\beta q^{5}+\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.d.f $2$ $4.216$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(0\) \(0\) $-$ \(q+(1+\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(2-4\zeta_{6})q^{7}+\cdots\)
528.2.d.g $4$ $4.216$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-1\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(-2\beta _{1}-2\beta _{3})q^{7}+\cdots\)
528.2.d.h $4$ $4.216$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(1\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+2\beta _{3})q^{7}+\cdots\)
528.2.o.a $4$ $4.216$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(-8\) \(0\) $-$ \(q+\beta _{1}q^{3}-2q^{5}-\beta _{3}q^{7}-q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
528.2.o.b $8$ $4.216$ 8.0.454201344.7 None None \(0\) \(0\) \(8\) \(0\) $-$ \(q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-\beta _{7}q^{7}-q^{9}+\cdots\)
528.2.q.a $96$ $4.216$ None None \(0\) \(0\) \(0\) \(0\) $-$
528.2.t.a $40$ $4.216$ None None \(0\) \(0\) \(0\) \(0\) $-$
528.2.t.b $40$ $4.216$ None None \(0\) \(0\) \(0\) \(0\) $-$
528.2.u.a $160$ $4.216$ None None \(0\) \(0\) \(0\) \(0\) $-$
528.2.x.a $184$ $4.216$ None None \(0\) \(-4\) \(0\) \(0\) $-$
528.2.y.a $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(-1\) \(-7\) \(-3\) $-$ \(q+\zeta_{10}^{2}q^{3}+(-3+2\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
528.2.y.b $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(-1\) \(-3\) \(-1\) $-$ \(q+\zeta_{10}^{2}q^{3}+(-1-\zeta_{10}^{2})q^{5}-\zeta_{10}^{3}q^{7}+\cdots\)
528.2.y.c $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(-1\) \(3\) \(-5\) $-$ \(q+\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots\)
528.2.y.d $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(-1\) \(8\) \(6\) $-$ \(q+\zeta_{10}^{2}q^{3}+(3-\zeta_{10}+3\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.e $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(-8\) \(-6\) $-$ \(q-\zeta_{10}^{2}q^{3}+(-3+\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
528.2.y.f $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(-1\) \(3\) $-$ \(q-\zeta_{10}^{2}q^{3}+(-1+2\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
528.2.y.g $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(0\) \(2\) $-$ \(q-\zeta_{10}^{2}q^{3}+(1-3\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.h $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(1\) \(3\) $-$ \(q-\zeta_{10}^{2}q^{3}+(1-2\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.i $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(3\) \(-7\) $-$ \(q-\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots\)
528.2.y.j $4$ $4.216$ \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(5\) \(7\) $-$ \(q-\zeta_{10}^{2}q^{3}+(1+2\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.k $8$ $4.216$ 8.0.185640625.1 None None \(0\) \(-2\) \(-1\) \(5\) $-$ \(q+\beta _{6}q^{3}+(-2\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
528.2.ba.a $8$ $4.216$ \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(-6\) \(0\) $-$ \(q+\zeta_{20}q^{3}+(-1+\zeta_{20}^{6})q^{5}+(-\zeta_{20}+\cdots)q^{7}+\cdots\)
528.2.ba.b $8$ $4.216$ \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(14\) \(0\) $-$ \(q+\zeta_{20}q^{3}+(1+2\zeta_{20}^{2}-2\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{5}+\cdots\)
528.2.ba.c $32$ $4.216$ None None \(0\) \(0\) \(-8\) \(0\) $-$
528.2.bl.a $32$ $4.216$ None None \(0\) \(0\) \(0\) \(0\) $-$
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