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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1584.1.j.a $1$ $0.791$ \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(1\) \(0\) $-$ \(q+q^{5}+q^{11}-q^{23}+q^{31}-q^{37}+\cdots\)
1584.1.bf.a $2$ $0.791$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ \(q-q^{3}+\zeta_{6}^{2}q^{5}+q^{9}+\zeta_{6}q^{11}-2\zeta_{6}^{2}q^{15}+\cdots\)
1584.1.bf.b $2$ $0.791$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(1\) \(0\) $-$ \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\zeta_{6}q^{11}+\cdots\)
1584.1.bf.c $2$ $0.791$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(1\) \(0\) $-$ \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots\)
1584.1.bk.a $2$ $0.791$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ \(q-q^{3}+q^{9}-\zeta_{6}q^{11}-\zeta_{6}^{2}q^{23}-\zeta_{6}q^{25}+\cdots\)
1584.1.bk.b $2$ $0.791$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-3\) \(0\) $-$ \(q+\zeta_{6}^{2}q^{3}+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1584.1.bk.c $2$ $0.791$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(3\) \(0\) $-$ \(q-\zeta_{6}q^{3}+(1+\zeta_{6})q^{5}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots\)
1584.1.bk.d $2$ $0.791$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-3\) \(0\) $-$ \(q-\zeta_{6}^{2}q^{3}+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1584.1.bk.e $2$ $0.791$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(3\) \(0\) $-$ \(q+\zeta_{6}q^{3}+(1+\zeta_{6})q^{5}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots\)
1584.1.bk.f $2$ $0.791$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) $-$ \(q+q^{3}+q^{9}+\zeta_{6}q^{11}+\zeta_{6}^{2}q^{23}-\zeta_{6}q^{25}+\cdots\)
1584.2.a.a $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(-4\) \(2\) $-$ \(q-4q^{5}+2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
1584.2.a.b $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(-4\) \(2\) $+$ \(q-4q^{5}+2q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
1584.2.a.c $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-2\) $+$ \(q-2q^{5}-2q^{7}-q^{11}+6q^{13}+4q^{17}+\cdots\)
1584.2.a.d $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) $+$ \(q-2q^{5}+q^{11}+2q^{13}-6q^{17}+4q^{23}+\cdots\)
1584.2.a.e $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(-2\) \(2\) $-$ \(q-2q^{5}+2q^{7}+q^{11}-2q^{13}-4q^{17}+\cdots\)
1584.2.a.f $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(-2\) \(4\) $+$ \(q-2q^{5}+4q^{7}-q^{11}-6q^{13}-2q^{17}+\cdots\)
1584.2.a.g $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) $-$ \(q-q^{5}+2q^{7}+q^{11}+4q^{13}+2q^{17}+\cdots\)
1584.2.a.h $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ \(q-2q^{7}-q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots\)
1584.2.a.i $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ \(q-2q^{7}-q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\)
1584.2.a.j $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ \(q-2q^{7}+q^{11}+2q^{17}-8q^{19}-2q^{23}+\cdots\)
1584.2.a.k $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ \(q-2q^{7}+q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\)
1584.2.a.l $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ \(q+2q^{7}-q^{11}-6q^{13}-6q^{17}+2q^{19}+\cdots\)
1584.2.a.m $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ \(q+2q^{7}+q^{11}-6q^{13}+6q^{17}+2q^{19}+\cdots\)
1584.2.a.n $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(2\) \(-4\) $-$ \(q+2q^{5}-4q^{7}-q^{11}+6q^{13}-6q^{17}+\cdots\)
1584.2.a.o $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(2\) \(-4\) $-$ \(q+2q^{5}-4q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
1584.2.a.p $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(3\) \(-2\) $+$ \(q+3q^{5}-2q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots\)
1584.2.a.q $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(3\) \(2\) $-$ \(q+3q^{5}+2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
1584.2.a.r $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(4\) \(2\) $-$ \(q+4q^{5}+2q^{7}-q^{11}-2q^{13}-2q^{17}+\cdots\)
1584.2.a.s $1$ $12.648$ \(\Q\) None None \(0\) \(0\) \(4\) \(2\) $-$ \(q+4q^{5}+2q^{7}+q^{11}+4q^{13}+2q^{17}+\cdots\)
1584.2.a.t $2$ $12.648$ \(\Q(\sqrt{17}) \) None None \(0\) \(0\) \(-3\) \(2\) $-$ \(q+(-1-\beta )q^{5}+(2-2\beta )q^{7}-q^{11}+\cdots\)
1584.2.a.u $2$ $12.648$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(-4\) $+$ \(q+\beta q^{5}+(-2-\beta )q^{7}-q^{11}+(2-\beta )q^{13}+\cdots\)
1584.2.a.v $2$ $12.648$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(-4\) $-$ \(q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(2+\beta )q^{13}+\cdots\)
1584.2.b.a $2$ $12.648$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+2\beta q^{5}+(-3-\beta )q^{11}-3\beta q^{13}+\cdots\)
1584.2.b.b $2$ $12.648$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta q^{5}+3\beta q^{7}+(-3+\beta )q^{11}+6q^{17}+\cdots\)
1584.2.b.c $2$ $12.648$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta q^{5}-3\beta q^{7}+(3+\beta )q^{11}-6q^{17}+\cdots\)
1584.2.b.d $2$ $12.648$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+2\beta q^{5}+(3-\beta )q^{11}+3\beta q^{13}+6q^{17}+\cdots\)
1584.2.b.e $4$ $12.648$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{5}+\beta _{3}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots\)
1584.2.b.f $6$ $12.648$ 6.0.12781568.1 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}+\beta _{4})q^{11}+\cdots\)
1584.2.b.g $6$ $12.648$ 6.0.12781568.1 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
1584.2.d.a $2$ $12.648$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta q^{5}-2\beta q^{7}-q^{11}+\beta q^{17}-2\beta q^{19}+\cdots\)
1584.2.d.b $2$ $12.648$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta q^{5}+2\beta q^{7}+q^{11}+\beta q^{17}+2\beta q^{19}+\cdots\)
1584.2.d.c $8$ $12.648$ 8.0.1768034304.5 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{4}q^{5}-\beta _{4}q^{7}-q^{11}+(-1+\beta _{3}+\cdots)q^{13}+\cdots\)
1584.2.d.d $8$ $12.648$ 8.0.1768034304.5 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{4}q^{5}+\beta _{4}q^{7}+q^{11}+(-1+\beta _{3}+\cdots)q^{13}+\cdots\)
1584.2.o.a $2$ $12.648$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-6\) \(0\) $-$ \(q-3q^{5}-\beta q^{11}+\beta q^{23}+4q^{25}+3\beta q^{31}+\cdots\)
1584.2.o.b $4$ $12.648$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{2}q^{5}+\beta _{2}q^{7}+(-3+\beta _{1})q^{11}+\cdots\)
1584.2.o.c $4$ $12.648$ \(\Q(\sqrt{6}, \sqrt{-11})\) \(\Q(\sqrt{-33}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{7}-\beta _{3}q^{11}+\beta _{2}q^{17}+3\beta _{1}q^{19}+\cdots\)
1584.2.o.d $4$ $12.648$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{2}q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{11}-3\beta _{1}q^{13}+\cdots\)
1584.2.o.e $4$ $12.648$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(6\) \(0\) $-$ \(q+(1+\beta _{3})q^{5}+(2\beta _{1}-\beta _{2})q^{11}+(\beta _{1}+\cdots)q^{23}+\cdots\)
1584.2.o.f $4$ $12.648$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(8\) \(0\) $-$ \(q+2q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\cdots\)
1584.2.o.g $8$ $12.648$ 8.0.454201344.7 None None \(0\) \(0\) \(-8\) \(0\) $-$ \(q+(-1-\beta _{1})q^{5}+\beta _{6}q^{7}+(\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots\)
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