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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
338.2.a.a $1$ $2.699$ \(\Q\) None \(-1\) \(-3\) \(1\) \(-1\) $+$ \(q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{7}+\cdots\)
338.2.a.b $1$ $2.699$ \(\Q\) None \(-1\) \(-1\) \(3\) \(3\) $-$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots\)
338.2.a.c $1$ $2.699$ \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) $+$ \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-3q^{9}+\cdots\)
338.2.a.d $1$ $2.699$ \(\Q\) None \(1\) \(-1\) \(-3\) \(-3\) $+$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
338.2.a.e $1$ $2.699$ \(\Q\) None \(1\) \(0\) \(-1\) \(4\) $-$ \(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots\)
338.2.a.f $1$ $2.699$ \(\Q\) None \(1\) \(1\) \(3\) \(1\) $-$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
338.2.a.g $3$ $2.699$ \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(-2\) \(4\) $-$ \(q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots\)
338.2.a.h $3$ $2.699$ \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(2\) \(-4\) $-$ \(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
338.2.b.a $2$ $2.699$ \(\Q(\sqrt{-1}) \) None \(0\) \(-6\) \(0\) \(0\) $-$ \(q+iq^{2}-3q^{3}-q^{4}-iq^{5}-3iq^{6}+\cdots\)
338.2.b.b $2$ $2.699$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+iq^{2}-q^{4}-iq^{5}-4iq^{7}-iq^{8}+\cdots\)
338.2.b.c $2$ $2.699$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $-$ \(q+iq^{2}+q^{3}-q^{4}+3iq^{5}+iq^{6}+\cdots\)
338.2.b.d $6$ $2.699$ 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) $-$ \(q-\beta _{5}q^{2}+(1+\beta _{2}-\beta _{4})q^{3}-q^{4}-2\beta _{1}q^{5}+\cdots\)
338.2.c.a $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(6\) \(-1\) $-$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.b $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-6\) \(3\) $-$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.c $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-2\) \(-1\) $-$ \(q+(-1+\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.d $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-6\) \(1\) $-$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.e $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(4\) $-$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+4\zeta_{6}q^{7}+\cdots\)
338.2.c.f $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(6\) \(-3\) $-$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.g $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(2\) \(1\) $-$ \(q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.h $6$ $2.699$ 6.0.64827.1 None \(-3\) \(-3\) \(4\) \(4\) $-$ \(q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
338.2.c.i $6$ $2.699$ 6.0.64827.1 None \(3\) \(-3\) \(-4\) \(-4\) $-$ \(q+(1-\beta _{5})q^{2}+(-1-\beta _{1}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
338.2.e.a $4$ $2.699$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) $-$ \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
338.2.e.b $4$ $2.699$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+(4\zeta_{12}+\cdots)q^{7}+\cdots\)
338.2.e.c $4$ $2.699$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $-$ \(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
338.2.e.d $4$ $2.699$ \(\Q(\zeta_{12})\) None \(0\) \(6\) \(0\) \(0\) $-$ \(q+\zeta_{12}q^{2}+(3-3\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
338.2.e.e $12$ $2.699$ 12.0.\(\cdots\).1 None \(0\) \(-6\) \(0\) \(0\) $-$ \(q+\beta _{6}q^{2}+(\beta _{4}+2\beta _{9})q^{3}+\beta _{7}q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)
338.2.g.a $96$ $2.699$ None \(8\) \(-1\) \(3\) \(-13\) $-$
338.2.g.b $108$ $2.699$ None \(-9\) \(-1\) \(-5\) \(5\) $-$
338.2.h.a $192$ $2.699$ None \(0\) \(2\) \(0\) \(0\) $-$
338.2.i.a $168$ $2.699$ None \(-7\) \(0\) \(0\) \(14\) $-$
338.2.i.b $192$ $2.699$ None \(8\) \(0\) \(2\) \(-10\) $-$
338.2.k.a $336$ $2.699$ None \(0\) \(0\) \(0\) \(0\) $-$
338.3.d.a $2$ $9.210$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(6\) \(-4\) $-$ \(q+(-1-i)q^{2}+2iq^{4}+(3+3i)q^{5}+\cdots\)
338.3.d.b $2$ $9.210$ \(\Q(\sqrt{-1}) \) None \(-2\) \(8\) \(-8\) \(-10\) $-$ \(q+(-1-i)q^{2}+4q^{3}+2iq^{4}+(-4+\cdots)q^{5}+\cdots\)
338.3.d.c $2$ $9.210$ \(\Q(\sqrt{-1}) \) None \(2\) \(8\) \(8\) \(10\) $-$ \(q+(1+i)q^{2}+4q^{3}+2iq^{4}+(4+4i)q^{5}+\cdots\)
338.3.d.d $4$ $9.210$ \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(0\) \(2\) $-$ \(q+(-1-\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
338.3.d.e $4$ $9.210$ \(\Q(\zeta_{12})\) None \(4\) \(0\) \(0\) \(-2\) $-$ \(q+(1+\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
338.3.d.f $8$ $9.210$ 8.0.\(\cdots\).1 None \(-8\) \(0\) \(-6\) \(-10\) $-$ \(q+(-1+\beta _{5})q^{2}+(-1+\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
338.3.d.g $8$ $9.210$ 8.0.\(\cdots\).1 None \(8\) \(0\) \(6\) \(10\) $-$ \(q+(1-\beta _{5})q^{2}+(-1+\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
338.3.d.h $12$ $9.210$ 12.0.\(\cdots\).2 None \(-12\) \(-8\) \(8\) \(24\) $-$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{4}+\beta _{7}-\beta _{9}+\cdots)q^{3}+\cdots\)
338.3.d.i $12$ $9.210$ 12.0.\(\cdots\).2 None \(12\) \(-8\) \(-8\) \(-24\) $-$ \(q+(1-\beta _{1})q^{2}+(-1+\beta _{4}+\beta _{7}-\beta _{9}+\cdots)q^{3}+\cdots\)
338.3.f.a $4$ $9.210$ \(\Q(\zeta_{12})\) None \(-2\) \(-8\) \(16\) \(-10\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-4\zeta_{12}^{2}q^{3}+\cdots\)
338.3.f.b $4$ $9.210$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-12\) \(-4\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
338.3.f.c $4$ $9.210$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-20\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)
338.3.f.d $4$ $9.210$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(22\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
338.3.f.e $4$ $9.210$ \(\Q(\zeta_{12})\) None \(2\) \(-8\) \(-16\) \(10\) $-$ \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}-4\zeta_{12}^{2}q^{3}+\cdots\)
338.3.f.f $4$ $9.210$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(20\) $-$ \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
338.3.f.g $4$ $9.210$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(12\) \(4\) $-$ \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
338.3.f.h $8$ $9.210$ 8.0.\(\cdots\).1 None \(-4\) \(0\) \(6\) \(-8\) $-$ \(q+(-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}-\beta _{5})q^{3}-2\beta _{5}q^{4}+\cdots\)
338.3.f.i $8$ $9.210$ 8.0.\(\cdots\).1 None \(4\) \(0\) \(-6\) \(2\) $-$ \(q+(\beta _{3}+\beta _{4})q^{2}+(\beta _{2}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots\)
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