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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
185.2.a.a \(1\) \(1.477\) \(\Q\) None \(-2\) \(1\) \(-1\) \(-5\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-5q^{7}+\cdots\)
185.2.a.b \(1\) \(1.477\) \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) \(+\) \(q-q^{3}-2q^{4}+q^{5}-3q^{7}-2q^{9}-5q^{11}+\cdots\)
185.2.a.c \(1\) \(1.477\) \(\Q\) None \(1\) \(-2\) \(-1\) \(-2\) \(+\) \(q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}-2q^{7}+\cdots\)
185.2.a.d \(5\) \(1.477\) 5.5.368464.1 None \(0\) \(-1\) \(5\) \(7\) \(-\) \(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(2-\beta _{1}-\beta _{4})q^{4}+\cdots\)
185.2.a.e \(5\) \(1.477\) 5.5.973904.1 None \(2\) \(3\) \(-5\) \(11\) \(-\) \(q+\beta _{4}q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{3})q^{4}+\cdots\)
185.2.b.a \(18\) \(1.477\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q+(\beta _{1}+\beta _{13})q^{2}+(\beta _{12}-\beta _{13})q^{3}+(-2+\cdots)q^{4}+\cdots\)
185.2.c.a \(2\) \(1.477\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(2\) \(q+q^{3}+2q^{4}+iq^{5}+q^{7}-2q^{9}-3q^{11}+\cdots\)
185.2.c.b \(12\) \(1.477\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(2\) \(0\) \(-18\) \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{9}+\beta _{10}+\cdots)q^{4}+\cdots\)
185.2.d.a \(16\) \(1.477\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}-\beta _{9}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
185.2.e.a \(14\) \(1.477\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(-2\) \(-7\) \(0\) \(q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{6}q^{3}+(\beta _{2}+\beta _{9}+\cdots)q^{4}+\cdots\)
185.2.e.b \(14\) \(1.477\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(-2\) \(7\) \(2\) \(q+\beta _{8}q^{2}+\beta _{6}q^{3}+(-1+\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
185.2.f.a \(2\) \(1.477\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-6\) \(q-iq^{2}+(-1-i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
185.2.f.b \(2\) \(1.477\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-4\) \(0\) \(q-iq^{2}+(2+2i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
185.2.f.c \(6\) \(1.477\) 6.0.350464.1 None \(0\) \(-2\) \(2\) \(-4\) \(q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
185.2.f.d \(24\) \(1.477\) None \(0\) \(4\) \(0\) \(6\)
185.2.k.a \(2\) \(1.477\) \(\Q(\sqrt{-1}) \) None \(-2\) \(-4\) \(-2\) \(0\) \(q-q^{2}+(-2+2i)q^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
185.2.k.b \(2\) \(1.477\) \(\Q(\sqrt{-1}) \) None \(-2\) \(2\) \(-2\) \(-6\) \(q-q^{2}+(1-i)q^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
185.2.k.c \(6\) \(1.477\) 6.0.350464.1 None \(-2\) \(2\) \(0\) \(-4\) \(q+\beta _{3}q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
185.2.k.d \(24\) \(1.477\) None \(4\) \(-4\) \(8\) \(6\)
185.2.l.a \(32\) \(1.477\) None \(0\) \(0\) \(3\) \(0\)
185.2.m.a \(28\) \(1.477\) None \(-6\) \(-4\) \(0\) \(-2\)
185.2.n.a \(36\) \(1.477\) None \(0\) \(0\) \(-2\) \(0\)
185.2.o.a \(36\) \(1.477\) None \(-3\) \(0\) \(0\) \(6\)
185.2.o.b \(36\) \(1.477\) None \(-3\) \(0\) \(0\) \(0\)
185.2.p.a \(68\) \(1.477\) None \(-4\) \(-8\) \(-10\) \(-2\)
185.2.u.a \(68\) \(1.477\) None \(-6\) \(-4\) \(0\) \(-2\)
185.2.v.a \(96\) \(1.477\) None \(0\) \(0\) \(-12\) \(0\)
185.2.w.a \(72\) \(1.477\) None \(6\) \(0\) \(0\) \(-6\)
185.2.x.a \(108\) \(1.477\) None \(0\) \(0\) \(-9\) \(0\)
185.2.z.a \(204\) \(1.477\) None \(-12\) \(-6\) \(-12\) \(-12\)
185.2.bc.a \(204\) \(1.477\) None \(-12\) \(-18\) \(-12\) \(-12\)
185.3.g.a \(48\) \(5.041\) None \(4\) \(0\) \(0\) \(0\)
185.3.h.a \(72\) \(5.041\) None \(0\) \(-8\) \(0\) \(-4\)
185.3.i.a \(72\) \(5.041\) None \(0\) \(0\) \(4\) \(-4\)
185.3.j.a \(72\) \(5.041\) None \(0\) \(0\) \(-6\) \(0\)
185.3.q.a \(144\) \(5.041\) None \(0\) \(0\) \(18\) \(0\)
185.3.r.a \(144\) \(5.041\) None \(-6\) \(-4\) \(-18\) \(-2\)
185.3.s.a \(144\) \(5.041\) None \(-6\) \(0\) \(2\) \(-2\)
185.3.t.a \(96\) \(5.041\) None \(-4\) \(0\) \(0\) \(0\)
185.3.y.a \(432\) \(5.041\) None \(-12\) \(-6\) \(0\) \(-12\)
185.3.ba.a \(432\) \(5.041\) None \(0\) \(0\) \(-30\) \(0\)
185.3.bb.a \(312\) \(5.041\) None \(0\) \(0\) \(0\) \(0\)
185.3.bd.a \(432\) \(5.041\) None \(-12\) \(-18\) \(-24\) \(-12\)
185.4.a.a \(7\) \(10.915\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-5\) \(-6\) \(35\) \(-49\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
185.4.a.b \(7\) \(10.915\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(-8\) \(-35\) \(-77\) \(-\) \(q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(2+\beta _{5}-\beta _{6})q^{4}+\cdots\)
185.4.a.c \(10\) \(10.915\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(7\) \(4\) \(-50\) \(49\) \(+\) \(q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(5-\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots\)
185.4.a.d \(12\) \(10.915\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(6\) \(60\) \(77\) \(+\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(7+\beta _{2}-\beta _{3})q^{4}+\cdots\)
185.4.b.a \(54\) \(10.915\) None \(0\) \(0\) \(-8\) \(0\)
185.4.c.a \(38\) \(10.915\) None \(0\) \(0\) \(0\) \(-12\)
185.4.d.a \(56\) \(10.915\) None \(0\) \(0\) \(0\) \(0\)
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