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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
210.2.a.a $1$ $1.677$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
210.2.a.b $1$ $1.677$ \(\Q\) None \(-1\) \(1\) \(1\) \(1\) $-$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
210.2.a.c $1$ $1.677$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
210.2.a.d $1$ $1.677$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
210.2.a.e $1$ $1.677$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
210.2.b.a $4$ $1.677$ \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(4\) \(6\) $-$ \(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+q^{5}+\cdots\)
210.2.b.b $4$ $1.677$ \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(-4\) \(6\) $-$ \(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}-q^{5}+\cdots\)
210.2.d.a $8$ $1.677$ 8.0.\(\cdots\).11 None \(-8\) \(0\) \(0\) \(0\) $-$ \(q-q^{2}-\beta _{7}q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
210.2.d.b $8$ $1.677$ 8.0.\(\cdots\).11 None \(8\) \(0\) \(0\) \(0\) $-$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
210.2.g.a $2$ $1.677$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ \(q+iq^{2}+iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
210.2.g.b $2$ $1.677$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $-$ \(q+iq^{2}-iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots\)
210.2.i.a $2$ $1.677$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-1\) \(4\) $-$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
210.2.i.b $2$ $1.677$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-4\) $-$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
210.2.i.c $2$ $1.677$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-4\) $-$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
210.2.i.d $2$ $1.677$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(4\) $-$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
210.2.j.a $12$ $1.677$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(4\) \(-4\) \(0\) $-$ \(q+\beta _{2}q^{2}+\beta _{11}q^{3}-\beta _{7}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
210.2.j.b $12$ $1.677$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(4\) \(4\) \(0\) $-$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{7}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
210.2.m.a $8$ $1.677$ 8.0.1698758656.6 None \(0\) \(0\) \(0\) \(4\) $-$ \(q+\beta _{3}q^{2}+\beta _{3}q^{3}-\beta _{5}q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
210.2.m.b $8$ $1.677$ 8.0.1698758656.6 None \(0\) \(0\) \(0\) \(8\) $-$ \(q+\beta _{3}q^{2}-\beta _{3}q^{3}-\beta _{5}q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
210.2.n.a $4$ $1.677$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $-$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
210.2.n.b $12$ $1.677$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{8})q^{3}+(1+\beta _{10})q^{4}+\cdots\)
210.2.r.a $12$ $1.677$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-2\) \(6\) \(8\) $-$ \(q+\beta _{4}q^{2}+(-\beta _{3}+\beta _{9})q^{3}-\beta _{6}q^{4}+\cdots\)
210.2.r.b $12$ $1.677$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(2\) \(-6\) \(8\) $-$ \(q-\beta _{4}q^{2}-\beta _{7}q^{3}-\beta _{6}q^{4}+(-1-\beta _{6}+\cdots)q^{5}+\cdots\)
210.2.t.a $4$ $1.677$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(-2\) \(-6\) \(-10\) $-$ \(q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
210.2.t.b $4$ $1.677$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(-1\) \(-3\) \(10\) $-$ \(q+(-1+\beta _{2})q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)
210.2.t.c $4$ $1.677$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(1\) \(6\) \(-10\) $-$ \(q+\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
210.2.t.d $4$ $1.677$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(2\) \(3\) \(10\) $-$ \(q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
210.2.t.e $8$ $1.677$ 8.0.3317760000.3 None \(-4\) \(0\) \(12\) \(0\) $-$ \(q-\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
210.2.t.f $8$ $1.677$ 8.0.3317760000.3 None \(4\) \(0\) \(-12\) \(0\) $-$ \(q+\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
210.2.u.a $16$ $1.677$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(-8\) $-$ \(q+\beta _{12}q^{2}-\beta _{6}q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
210.2.u.b $16$ $1.677$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(-4\) $-$ \(q+\beta _{2}q^{2}-\beta _{15}q^{3}-\beta _{5}q^{4}+(1+2\beta _{6}+\cdots)q^{5}+\cdots\)
210.2.x.a $64$ $1.677$ None \(0\) \(0\) \(0\) \(4\) $-$
210.3.c.a $24$ $5.722$ None \(0\) \(0\) \(0\) \(0\) $-$
210.3.e.a $16$ $5.722$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-8\) \(0\) \(0\) $-$ \(q-\beta _{4}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{9}q^{5}+(1+\cdots)q^{6}+\cdots\)
210.3.f.a $8$ $5.722$ 8.0.3317760000.3 None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+2q^{4}+\beta _{6}q^{5}+\beta _{3}q^{6}+\cdots\)
210.3.h.a $16$ $5.722$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{5}q^{2}-\beta _{1}q^{3}-2q^{4}+\beta _{8}q^{5}-\beta _{4}q^{6}+\cdots\)
210.3.k.a $32$ $5.722$ None \(-32\) \(0\) \(0\) \(-4\) $-$
210.3.k.b $32$ $5.722$ None \(32\) \(0\) \(0\) \(-4\) $-$
210.3.l.a $8$ $5.722$ 8.0.\(\cdots\).1 None \(8\) \(0\) \(0\) \(0\) $-$ \(q+(1+\beta _{2})q^{2}+\beta _{7}q^{3}+2\beta _{2}q^{4}+(-2\beta _{3}+\cdots)q^{5}+\cdots\)
210.3.l.b $16$ $5.722$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(0\) \(-16\) \(0\) $-$ \(q+(-1-\beta _{2})q^{2}+\beta _{3}q^{3}+2\beta _{2}q^{4}+\cdots\)
210.3.o.a $8$ $5.722$ 8.0.3317760000.3 None \(0\) \(12\) \(0\) \(0\) $-$ \(q+(\beta _{2}+\beta _{4})q^{2}+(1+\beta _{3})q^{3}+(-2+2\beta _{3}+\cdots)q^{4}+\cdots\)
210.3.o.b $16$ $5.722$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-24\) \(0\) \(4\) $-$ \(q+\beta _{9}q^{2}+(-1+\beta _{5})q^{3}+(-2-2\beta _{5}+\cdots)q^{4}+\cdots\)
210.3.p.a $32$ $5.722$ None \(0\) \(0\) \(12\) \(0\) $-$
210.3.q.a $64$ $5.722$ None \(0\) \(0\) \(0\) \(0\) $-$
210.3.s.a $40$ $5.722$ None \(0\) \(0\) \(0\) \(20\) $-$
210.3.v.a $32$ $5.722$ None \(-16\) \(0\) \(0\) \(-8\) $-$
210.3.v.b $32$ $5.722$ None \(16\) \(0\) \(-8\) \(24\) $-$
210.3.w.a $64$ $5.722$ None \(-32\) \(-6\) \(-12\) \(4\) $-$
210.3.w.b $64$ $5.722$ None \(32\) \(6\) \(12\) \(4\) $-$
210.4.a.a $1$ $12.390$ \(\Q\) None \(-2\) \(-3\) \(-5\) \(7\) $-$ \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
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