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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2800.1.f.a $1$ $1.397$ \(\Q\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-1\) $-$ \(q-q^{7}+q^{9}+q^{11}+q^{23}-q^{29}-q^{37}+\cdots\)
2800.1.f.b $1$ $1.397$ \(\Q\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(1\) $-$ \(q+q^{7}+q^{9}+q^{11}-q^{23}-q^{29}+q^{37}+\cdots\)
2800.1.f.c $2$ $1.397$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+iq^{3}+iq^{7}+q^{11}-iq^{13}+iq^{17}+\cdots\)
2800.1.p.a $2$ $1.397$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-iq^{7}-q^{9}+q^{11}-iq^{23}+q^{29}+\cdots\)
2800.1.u.a $4$ $1.397$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\)
2800.1.u.b $8$ $1.397$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots\)
2800.1.v.a $4$ $1.397$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{7}) \) \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{7}+3\zeta_{8}^{2}q^{9}+2q^{21}+\cdots\)
2800.1.v.b $8$ $1.397$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{24}^{9}q^{3}+\zeta_{24}^{3}q^{7}+(-\zeta_{24}^{4}-\zeta_{24}^{8}+\cdots)q^{11}+\cdots\)
2800.1.z.a $2$ $1.397$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+iq^{9}+\cdots\)
2800.1.z.b $4$ $1.397$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{7}+\cdots\)
2800.1.z.c $4$ $1.397$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
2800.1.bf.a $2$ $1.397$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-2\) $-$ \(q-q^{2}+q^{4}-q^{7}-q^{8}+iq^{9}+(-1+\cdots)q^{11}+\cdots\)
2800.1.bf.b $2$ $1.397$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(2\) $-$ \(q+q^{2}+q^{4}+q^{7}+q^{8}+iq^{9}+(-1+\cdots)q^{11}+\cdots\)
2800.1.bf.c $4$ $1.397$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(4\) $-$ \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+q^{7}+q^{8}+\cdots\)
2800.1.bf.d $4$ $1.397$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(-4\) $-$ \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-q^{7}-q^{8}+\cdots\)
2800.1.bm.a $4$ $1.397$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
2800.1.bm.b $8$ $1.397$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{9}q^{7}-\zeta_{24}^{3}q^{8}+\cdots\)
2800.1.ce.a $2$ $1.397$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-3\) \(0\) \(1\) $-$ \(q+(-1+\zeta_{6}^{2})q^{3}+\zeta_{6}q^{7}+(1-\zeta_{6}+\cdots)q^{9}+\cdots\)
2800.1.ce.b $2$ $1.397$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(3\) \(0\) \(-1\) $-$ \(q+(1-\zeta_{6}^{2})q^{3}-\zeta_{6}q^{7}+(1-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{9}+\cdots\)
2800.1.dc.a $4$ $1.397$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(2\) $-$ \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{7}+\cdots\)
2800.1.dc.b $4$ $1.397$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(-2\) $-$ \(q+\zeta_{12}^{5}q^{2}+(-\zeta_{12}+\zeta_{12}^{4})q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
2800.1.dc.c $4$ $1.397$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(2\) $-$ \(q-\zeta_{12}^{5}q^{2}+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
2800.1.dc.d $4$ $1.397$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(-2\) $-$ \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{7}+\cdots\)
2800.1.di.a $4$ $1.397$ \(\Q(\zeta_{12})\) None None \(-2\) \(-2\) \(0\) \(0\) $-$ \(q-\zeta_{12}^{2}q^{2}+(\zeta_{12}+\zeta_{12}^{4})q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
2800.1.di.b $4$ $1.397$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{7}+\cdots\)
2800.1.di.c $4$ $1.397$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{7}+\cdots\)
2800.1.di.d $4$ $1.397$ \(\Q(\zeta_{12})\) None None \(2\) \(2\) \(0\) \(0\) $-$ \(q+\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{4})q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
2800.1.dm.a $8$ $1.397$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{24}^{7}q^{3}+\zeta_{24}q^{7}-\zeta_{24}^{8}q^{21}+\cdots\)
2800.2.a.a $1$ $22.358$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-1\) $+$ \(q-3q^{3}-q^{7}+6q^{9}-3q^{11}+q^{13}+\cdots\)
2800.2.a.b $1$ $22.358$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-1\) $-$ \(q-3q^{3}-q^{7}+6q^{9}+5q^{11}+6q^{13}+\cdots\)
2800.2.a.c $1$ $22.358$ \(\Q\) None None \(0\) \(-3\) \(0\) \(1\) $-$ \(q-3q^{3}+q^{7}+6q^{9}+5q^{11}+5q^{13}+\cdots\)
2800.2.a.d $1$ $22.358$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-1\) $+$ \(q-2q^{3}-q^{7}+q^{9}-5q^{11}+8q^{17}+\cdots\)
2800.2.a.e $1$ $22.358$ \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) $+$ \(q-2q^{3}+q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
2800.2.a.f $1$ $22.358$ \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) $+$ \(q-2q^{3}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
2800.2.a.g $1$ $22.358$ \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) $+$ \(q-2q^{3}+q^{7}+q^{9}+4q^{13}-6q^{17}+\cdots\)
2800.2.a.h $1$ $22.358$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $+$ \(q-q^{3}-q^{7}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
2800.2.a.i $1$ $22.358$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $+$ \(q-q^{3}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots\)
2800.2.a.j $1$ $22.358$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $+$ \(q-q^{3}+q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots\)
2800.2.a.k $1$ $22.358$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $+$ \(q-q^{3}+q^{7}-2q^{9}+q^{11}-q^{13}-3q^{17}+\cdots\)
2800.2.a.l $1$ $22.358$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $-$ \(q-q^{3}+q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
2800.2.a.m $1$ $22.358$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $-$ \(q-q^{7}-3q^{9}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
2800.2.a.n $1$ $22.358$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $-$ \(q-q^{7}-3q^{9}-q^{11}-2q^{13}-4q^{17}+\cdots\)
2800.2.a.o $1$ $22.358$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ \(q-q^{7}-3q^{9}+4q^{13}+4q^{17}-4q^{19}+\cdots\)
2800.2.a.p $1$ $22.358$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $+$ \(q-q^{7}-3q^{9}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
2800.2.a.q $1$ $22.358$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $-$ \(q-q^{7}-3q^{9}+5q^{11}-6q^{13}+4q^{17}+\cdots\)
2800.2.a.r $1$ $22.358$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ \(q+q^{7}-3q^{9}-q^{11}+2q^{13}+4q^{17}+\cdots\)
2800.2.a.s $1$ $22.358$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ \(q+q^{7}-3q^{9}-4q^{13}-4q^{17}-4q^{19}+\cdots\)
2800.2.a.t $1$ $22.358$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ \(q+q^{7}-3q^{9}+5q^{11}+6q^{13}-4q^{17}+\cdots\)
2800.2.a.u $1$ $22.358$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $-$ \(q+q^{3}-q^{7}-2q^{9}+q^{11}+q^{13}+3q^{17}+\cdots\)
2800.2.a.v $1$ $22.358$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $+$ \(q+q^{3}-q^{7}-2q^{9}+q^{11}+6q^{13}+\cdots\)
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