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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
660.1.v.a \(4\) \(0.329\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{3}q^{11}+\cdots\)
660.1.v.b \(4\) \(0.329\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{9}+\cdots\)
660.2.a.a \(1\) \(5.270\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(-2\) \(-\) \(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
660.2.a.b \(1\) \(5.270\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(q-q^{3}-q^{5}+q^{9}+q^{11}-4q^{13}+q^{15}+\cdots\)
660.2.a.c \(1\) \(5.270\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-4\) \(+\) \(q+q^{3}-q^{5}-4q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
660.2.a.d \(1\) \(5.270\) \(\Q\) None None \(0\) \(1\) \(-1\) \(2\) \(-\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
660.2.a.e \(2\) \(5.270\) \(\Q(\sqrt{13}) \) None None \(0\) \(-2\) \(2\) \(2\) \(-\) \(q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+q^{11}+\cdots\)
660.2.a.f \(2\) \(5.270\) \(\Q(\sqrt{13}) \) None None \(0\) \(2\) \(2\) \(2\) \(-\) \(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}-q^{11}+\cdots\)
660.2.c.a \(2\) \(5.270\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1+2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
660.2.c.b \(2\) \(5.270\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1-2i)q^{5}-q^{9}+q^{11}-4iq^{13}+\cdots\)
660.2.c.c \(4\) \(5.270\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{2})q^{7}-q^{9}+\cdots\)
660.2.d.a \(16\) \(5.270\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{5}q^{3}+\beta _{10}q^{5}+\beta _{2}q^{7}+(-1-\beta _{6}+\cdots)q^{9}+\cdots\)
660.2.f.a \(40\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.f.b \(40\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.i.a \(36\) \(5.270\) None None \(0\) \(-36\) \(0\) \(0\)
660.2.i.b \(36\) \(5.270\) None None \(0\) \(36\) \(0\) \(0\)
660.2.k.a \(4\) \(5.270\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-2q^{4}-q^{5}+\zeta_{8}^{3}q^{6}+\cdots\)
660.2.k.b \(4\) \(5.270\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}+2q^{4}+q^{5}+\zeta_{8}^{2}q^{6}+\cdots\)
660.2.k.c \(20\) \(5.270\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(20\) \(0\) \(q-\beta _{9}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
660.2.k.d \(20\) \(5.270\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(-20\) \(0\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}-q^{5}+\beta _{17}q^{6}+\cdots\)
660.2.l.a \(60\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.l.b \(60\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.n.a \(4\) \(5.270\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(3\) \(0\) \(q-\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
660.2.n.b \(4\) \(5.270\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-3\) \(0\) \(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
660.2.n.c \(16\) \(5.270\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{8}q^{3}+(\beta _{2}-\beta _{4})q^{5}+\beta _{9}q^{7}+(-1+\cdots)q^{9}+\cdots\)
660.2.q.a \(272\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.t.a \(20\) \(5.270\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{9}q^{3}-\beta _{11}q^{5}+(-\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{7}+\cdots\)
660.2.t.b \(20\) \(5.270\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{10}q^{5}+(1+\beta _{2}-\beta _{14}+\cdots)q^{7}+\cdots\)
660.2.u.a \(60\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.u.b \(60\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.x.a \(24\) \(5.270\) None None \(0\) \(0\) \(8\) \(0\)
660.2.y.a \(8\) \(5.270\) 8.0.13140625.1 None None \(0\) \(-2\) \(-2\) \(3\) \(q+(-1+\beta _{3}-\beta _{4}-\beta _{7})q^{3}+\beta _{7}q^{5}+\cdots\)
660.2.y.b \(8\) \(5.270\) 8.0.159390625.1 None None \(0\) \(-2\) \(2\) \(-3\) \(q-\beta _{3}q^{3}+\beta _{6}q^{5}+(1-2\beta _{2}-2\beta _{3}+\cdots)q^{7}+\cdots\)
660.2.y.c \(8\) \(5.270\) 8.0.819390625.1 None None \(0\) \(2\) \(-2\) \(3\) \(q+(1+\beta _{2}+\beta _{3}-\beta _{6})q^{3}-\beta _{6}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
660.2.y.d \(8\) \(5.270\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(2\) \(2\) \(-3\) \(q-\beta _{6}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
660.2.bb.a \(96\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.bd.a \(544\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.be.a \(96\) \(5.270\) None None \(0\) \(0\) \(-24\) \(0\)
660.2.be.b \(96\) \(5.270\) None None \(0\) \(0\) \(24\) \(0\)
660.2.bg.a \(144\) \(5.270\) None None \(0\) \(-36\) \(0\) \(0\)
660.2.bg.b \(144\) \(5.270\) None None \(0\) \(36\) \(0\) \(0\)
660.2.bj.a \(384\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.bl.a \(16\) \(5.270\) 16.0.\(\cdots\).1 None None \(0\) \(-8\) \(0\) \(10\) \(q+(-1+\beta _{2}-\beta _{8}+\beta _{10}-\beta _{12})q^{3}+\cdots\)
660.2.bl.b \(48\) \(5.270\) None None \(0\) \(4\) \(0\) \(-10\)
660.2.bm.a \(48\) \(5.270\) None None \(0\) \(0\) \(-4\) \(0\)
660.2.bo.a \(96\) \(5.270\) None None \(0\) \(0\) \(-8\) \(-20\)
660.2.br.a \(576\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.2.bs.a \(192\) \(5.270\) None None \(0\) \(-2\) \(0\) \(8\)
660.2.bv.a \(1088\) \(5.270\) None None \(0\) \(0\) \(0\) \(0\)
660.3.b.a \(16\) \(17.984\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{7}q^{7}+3q^{9}+(-1+\cdots)q^{11}+\cdots\)
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