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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
676.1.b.a $2$ $0.337$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-iq^{2}-q^{4}+iq^{5}+iq^{8}+q^{9}+q^{10}+\cdots\)
676.1.c.a $1$ $0.337$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) $-$ \(q-q^{2}+q^{4}+q^{5}-q^{8}+q^{9}-q^{10}+\cdots\)
676.1.c.b $1$ $0.337$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-1\) \(0\) $-$ \(q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots\)
676.1.i.a $4$ $0.337$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
676.1.j.a $2$ $0.337$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(2\) \(0\) $-$ \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}-\zeta_{6}q^{9}+\cdots\)
676.1.o.a $12$ $0.337$ \(\Q(\zeta_{26})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-2\) \(0\) $-$ \(q+\zeta_{26}^{8}q^{2}-\zeta_{26}^{3}q^{4}+(\zeta_{26}^{2}+\zeta_{26}^{12}+\cdots)q^{5}+\cdots\)
676.1.t.a $24$ $0.337$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(2\) \(0\) $-$ \(q+\zeta_{78}^{8}q^{2}+\zeta_{78}^{16}q^{4}+(\zeta_{78}^{28}+\zeta_{78}^{38}+\cdots)q^{5}+\cdots\)
676.2.a.a $1$ $5.398$ \(\Q\) None None \(0\) \(-2\) \(-3\) \(-4\) $-$ \(q-2q^{3}-3q^{5}-4q^{7}+q^{9}+6q^{15}+\cdots\)
676.2.a.b $1$ $5.398$ \(\Q\) None None \(0\) \(-2\) \(3\) \(4\) $-$ \(q-2q^{3}+3q^{5}+4q^{7}+q^{9}-6q^{15}+\cdots\)
676.2.a.c $1$ $5.398$ \(\Q\) None None \(0\) \(0\) \(-2\) \(2\) $-$ \(q-2q^{5}+2q^{7}-3q^{9}+2q^{11}+6q^{17}+\cdots\)
676.2.a.d $1$ $5.398$ \(\Q\) None None \(0\) \(3\) \(-2\) \(-1\) $-$ \(q+3q^{3}-2q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots\)
676.2.a.e $1$ $5.398$ \(\Q\) None None \(0\) \(3\) \(2\) \(1\) $-$ \(q+3q^{3}+2q^{5}+q^{7}+6q^{9}-5q^{11}+\cdots\)
676.2.a.f $2$ $5.398$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(0\) $+$ \(q-q^{3}+\beta q^{7}-2q^{9}-3\beta q^{11}-3q^{17}+\cdots\)
676.2.a.g $3$ $5.398$ \(\Q(\zeta_{14})^+\) None None \(0\) \(0\) \(-8\) \(1\) $+$ \(q+(-\beta _{1}-\beta _{2})q^{3}+(-2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
676.2.a.h $3$ $5.398$ \(\Q(\zeta_{14})^+\) None None \(0\) \(0\) \(8\) \(-1\) $-$ \(q+(-\beta _{1}-\beta _{2})q^{3}+(2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
676.2.d.a $2$ $5.398$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(0\) \(0\) $-$ \(q-2q^{3}+3iq^{5}-4iq^{7}+q^{9}-6iq^{15}+\cdots\)
676.2.d.b $2$ $5.398$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(0\) $-$ \(q-q^{3}-\zeta_{6}q^{7}-2q^{9}+3\zeta_{6}q^{11}+3q^{17}+\cdots\)
676.2.d.c $2$ $5.398$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+iq^{5}+iq^{7}-3q^{9}+iq^{11}-6q^{17}+\cdots\)
676.2.d.d $2$ $5.398$ \(\Q(\sqrt{-1}) \) None None \(0\) \(6\) \(0\) \(0\) $-$ \(q+3q^{3}+2iq^{5}-iq^{7}+6q^{9}+5iq^{11}+\cdots\)
676.2.d.e $6$ $5.398$ 6.0.153664.1 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(1-2\beta _{2}-\beta _{4})q^{3}+(-\beta _{1}+3\beta _{5})q^{5}+\cdots\)
676.2.e.a $2$ $5.398$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-4\) \(1\) $-$ \(q+(-3+3\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
676.2.e.b $2$ $5.398$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(-2\) $-$ \(q-2q^{5}-2\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-2+2\zeta_{6})q^{11}+\cdots\)
676.2.e.c $2$ $5.398$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(4\) \(2\) $-$ \(q+2q^{5}+2\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
676.2.e.d $2$ $5.398$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(6\) \(-4\) $-$ \(q+(2-2\zeta_{6})q^{3}+3q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
676.2.e.e $4$ $5.398$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) $-$ \(q+(1-\zeta_{12})q^{3}-\zeta_{12}^{2}q^{7}+2\zeta_{12}q^{9}+\cdots\)
676.2.e.f $6$ $5.398$ 6.0.64827.1 None None \(0\) \(0\) \(-16\) \(-1\) $-$ \(q+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
676.2.e.g $6$ $5.398$ 6.0.64827.1 None None \(0\) \(0\) \(16\) \(1\) $-$ \(q+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+(2+\beta _{2}+\cdots)q^{5}+\cdots\)
676.2.f.a $2$ $5.398$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-13}) \) None \(-2\) \(0\) \(0\) \(-2\) $-$ \(q+(-1+i)q^{2}-2iq^{4}+(-1-i)q^{7}+\cdots\)
676.2.f.b $2$ $5.398$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(6\) \(0\) $-$ \(q+(-1-i)q^{2}+2iq^{4}+(3+3i)q^{5}+\cdots\)
676.2.f.c $2$ $5.398$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-13}) \) None \(2\) \(0\) \(0\) \(2\) $-$ \(q+(1-i)q^{2}-2iq^{4}+(1+i)q^{7}+(-2+\cdots)q^{8}+\cdots\)
676.2.f.d $4$ $5.398$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(-6\) \(0\) $-$ \(q+(-1+\zeta_{12}^{2})q^{2}-2\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
676.2.f.e $4$ $5.398$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(6\) \(0\) $-$ \(q+(1-\zeta_{12}^{2})q^{2}-2\zeta_{12}^{2}q^{4}+(1-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
676.2.f.f $8$ $5.398$ 8.0.157351936.1 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(\beta _{6}-\beta _{7})q^{2}+(1-2\beta _{1})q^{3}+(-2\beta _{3}+\cdots)q^{4}+\cdots\)
676.2.f.g $8$ $5.398$ 8.0.18939904.2 None None \(4\) \(0\) \(0\) \(0\) $-$ \(q+(-\beta _{3}+\beta _{6}+\beta _{7})q^{2}+(-1+2\beta _{1}+\cdots)q^{3}+\cdots\)
676.2.f.h $16$ $5.398$ 16.0.\(\cdots\).1 None None \(-2\) \(0\) \(-12\) \(0\) $-$ \(q-\beta _{2}q^{2}+(-\beta _{3}-\beta _{6})q^{3}+(-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots\)
676.2.f.i $16$ $5.398$ 16.0.\(\cdots\).1 None None \(2\) \(0\) \(12\) \(0\) $-$ \(q+\beta _{2}q^{2}+(-\beta _{3}-\beta _{6})q^{3}+(-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots\)
676.2.f.j $72$ $5.398$ None None \(0\) \(0\) \(0\) \(0\) $-$
676.2.h.a $2$ $5.398$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(3\) $-$ \(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
676.2.h.b $4$ $5.398$ \(\Q(\zeta_{12})\) None None \(0\) \(-6\) \(0\) \(0\) $-$ \(q+(-3+3\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)
676.2.h.c $4$ $5.398$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{12}^{3}q^{5}-\zeta_{12}q^{7}+(3-3\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
676.2.h.d $4$ $5.398$ \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(0\) \(0\) $-$ \(q+(2-2\zeta_{12}^{2})q^{3}+3\zeta_{12}^{3}q^{5}+(-4\zeta_{12}+\cdots)q^{7}+\cdots\)
676.2.h.e $12$ $5.398$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(1+\beta _{4}-\beta _{7}+2\beta _{9})q^{3}+(-3\beta _{6}+\cdots)q^{5}+\cdots\)
676.2.l.a $4$ $5.398$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-12\) \(0\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
676.2.l.b $4$ $5.398$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-13}) \) None \(-2\) \(0\) \(0\) \(-2\) $-$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
676.2.l.c $4$ $5.398$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(6\) \(0\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
676.2.l.d $4$ $5.398$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-6\) \(0\) $-$ \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
676.2.l.e $4$ $5.398$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-6\) \(0\) $-$ \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
676.2.l.f $4$ $5.398$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-13}) \) None \(2\) \(0\) \(0\) \(2\) $-$ \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
676.2.l.g $4$ $5.398$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(12\) \(0\) $-$ \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
676.2.l.h $16$ $5.398$ 16.0.\(\cdots\).2 None None \(-4\) \(0\) \(0\) \(0\) $-$ \(q+(-\beta _{2}+\beta _{9})q^{2}+(-2\beta _{1}-\beta _{11}-\beta _{13}+\cdots)q^{3}+\cdots\)
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