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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
270.2.a.a $1$ $2.156$ \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) $-$ \(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
270.2.a.b $1$ $2.156$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $-$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
270.2.a.c $1$ $2.156$ \(\Q\) None \(1\) \(0\) \(-1\) \(2\) $-$ \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
270.2.a.d $1$ $2.156$ \(\Q\) None \(1\) \(0\) \(1\) \(2\) $-$ \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
270.2.c.a $2$ $2.156$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ \(q+iq^{2}-q^{4}+(-1-2i)q^{5}-4iq^{7}+\cdots\)
270.2.c.b $2$ $2.156$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $-$ \(q+iq^{2}-q^{4}+(1-2i)q^{5}+4iq^{7}+\cdots\)
270.2.c.c $4$ $2.156$ \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+(1+2\beta _{3})q^{7}+\cdots\)
270.2.e.a $2$ $2.156$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(4\) $-$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
270.2.e.b $2$ $2.156$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) $-$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
270.2.e.c $4$ $2.156$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(0\) \(-2\) \(-1\) $-$ \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
270.2.f.a $8$ $2.156$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-8\) $-$ \(q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
270.2.f.b $8$ $2.156$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) $-$ \(q+(\zeta_{24}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{6}q^{4}+(2\zeta_{24}+\cdots)q^{5}+\cdots\)
270.2.i.a $4$ $2.156$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) $-$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
270.2.i.b $8$ $2.156$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(4\) \(0\) $-$ \(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots\)
270.2.k.a $6$ $2.156$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(6\) $-$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}-2\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
270.2.k.b $12$ $2.156$ 12.0.\(\cdots\).1 None \(0\) \(3\) \(0\) \(-12\) $-$ \(q-\beta _{7}q^{2}+(1-\beta _{5}-\beta _{7}-\beta _{11})q^{3}+\cdots\)
270.2.k.c $12$ $2.156$ 12.0.\(\cdots\).1 None \(0\) \(3\) \(0\) \(6\) $-$ \(q+(-\beta _{7}-\beta _{10})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{7}+\cdots)q^{3}+\cdots\)
270.2.k.d $18$ $2.156$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-3\) \(0\) \(-3\) $-$ \(q+\beta _{2}q^{2}-\beta _{7}q^{3}+\beta _{3}q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots\)
270.2.k.e $24$ $2.156$ None \(0\) \(-3\) \(0\) \(3\) $-$
270.2.m.a $8$ $2.156$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-12\) \(-8\) $-$ \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-1+\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
270.2.m.b $16$ $2.156$ 16.0.\(\cdots\).9 None \(0\) \(0\) \(12\) \(8\) $-$ \(q+\beta _{5}q^{2}-\beta _{6}q^{4}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
270.2.p.a $108$ $2.156$ None \(0\) \(0\) \(6\) \(0\) $-$
270.2.r.a $216$ $2.156$ None \(0\) \(0\) \(0\) \(0\) $-$
270.3.b.a $4$ $7.357$ 4.0.31744.1 None \(0\) \(0\) \(-12\) \(0\) $-$ \(q-\beta _{2}q^{2}+2q^{4}+(-3-\beta _{1}-\beta _{2})q^{5}+\cdots\)
270.3.b.b $4$ $7.357$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(3\zeta_{8}-4\zeta_{8}^{3})q^{5}+\cdots\)
270.3.b.c $4$ $7.357$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}+5\zeta_{8}^{2}q^{7}+\cdots\)
270.3.b.d $4$ $7.357$ 4.0.31744.1 None \(0\) \(0\) \(12\) \(0\) $-$ \(q+\beta _{2}q^{2}+2q^{4}+(3-\beta _{1}+\beta _{2})q^{5}+\cdots\)
270.3.d.a $4$ $7.357$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-4\) $-$ \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-q^{7}+2\beta _{1}q^{8}+\cdots\)
270.3.d.b $8$ $7.357$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(-8\) $-$ \(q+\beta _{2}q^{2}-2q^{4}-\beta _{1}q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots\)
270.3.g.a $4$ $7.357$ \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(-12\) \(8\) $-$ \(q+(-1-\beta _{2})q^{2}+2\beta _{2}q^{4}+(-3-2\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.b $4$ $7.357$ \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(12\) \(-4\) $-$ \(q+(-1+\beta _{2})q^{2}-2\beta _{2}q^{4}+(3+2\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.c $4$ $7.357$ \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(-12\) \(-4\) $-$ \(q+(1-\beta _{2})q^{2}-2\beta _{2}q^{4}+(-3+2\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.d $4$ $7.357$ \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(12\) \(8\) $-$ \(q+(1+\beta _{2})q^{2}+2\beta _{2}q^{4}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
270.3.g.e $8$ $7.357$ 8.0.\(\cdots\).38 None \(-8\) \(0\) \(12\) \(-8\) $-$ \(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.f $8$ $7.357$ 8.0.\(\cdots\).38 None \(8\) \(0\) \(-12\) \(-8\) $-$ \(q+(1+\beta _{1})q^{2}+2\beta _{1}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.h.a $16$ $7.357$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $-$ \(q+\beta _{6}q^{2}-2\beta _{10}q^{4}+\beta _{12}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
270.3.j.a $8$ $7.357$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(12\) \(0\) $-$ \(q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}-2\zeta_{24}^{2}q^{4}+\cdots\)
270.3.j.b $16$ $7.357$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-30\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-2-2\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
270.3.l.a $24$ $7.357$ None \(-12\) \(0\) \(0\) \(6\) $-$
270.3.l.b $24$ $7.357$ None \(12\) \(0\) \(0\) \(-6\) $-$
270.3.n.a $216$ $7.357$ None \(0\) \(0\) \(-18\) \(0\) $-$
270.3.o.a $144$ $7.357$ None \(0\) \(0\) \(0\) \(0\) $-$
270.3.q.a $216$ $7.357$ None \(0\) \(0\) \(0\) \(18\) $-$
270.3.q.b $216$ $7.357$ None \(0\) \(0\) \(0\) \(-18\) $-$
270.4.a.a $1$ $15.931$ \(\Q\) None \(-2\) \(0\) \(-5\) \(-34\) $+$ \(q-2q^{2}+4q^{4}-5q^{5}-34q^{7}-8q^{8}+\cdots\)
270.4.a.b $1$ $15.931$ \(\Q\) None \(-2\) \(0\) \(-5\) \(8\) $-$ \(q-2q^{2}+4q^{4}-5q^{5}+8q^{7}-8q^{8}+\cdots\)
270.4.a.c $1$ $15.931$ \(\Q\) None \(-2\) \(0\) \(5\) \(-22\) $+$ \(q-2q^{2}+4q^{4}+5q^{5}-22q^{7}-8q^{8}+\cdots\)
270.4.a.d $1$ $15.931$ \(\Q\) None \(-2\) \(0\) \(5\) \(-13\) $-$ \(q-2q^{2}+4q^{4}+5q^{5}-13q^{7}-8q^{8}+\cdots\)
270.4.a.e $1$ $15.931$ \(\Q\) None \(-2\) \(0\) \(5\) \(-4\) $-$ \(q-2q^{2}+4q^{4}+5q^{5}-4q^{7}-8q^{8}+\cdots\)
270.4.a.f $1$ $15.931$ \(\Q\) None \(-2\) \(0\) \(5\) \(14\) $+$ \(q-2q^{2}+4q^{4}+5q^{5}+14q^{7}-8q^{8}+\cdots\)
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