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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
189.1.m.a \(2\) \(0.094\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{6}q^{4}-q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots\)
189.1.q.a \(2\) \(0.094\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{6}^{2}q^{4}+q^{7}-q^{13}-\zeta_{6}q^{16}-\zeta_{6}q^{19}+\cdots\)
189.2.a.a \(1\) \(1.509\) \(\Q\) None None \(-2\) \(0\) \(-1\) \(-1\) \(+\) \(q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots\)
189.2.a.b \(1\) \(1.509\) \(\Q\) None None \(0\) \(0\) \(-3\) \(1\) \(+\) \(q-2q^{4}-3q^{5}+q^{7}-6q^{11}-4q^{13}+\cdots\)
189.2.a.c \(1\) \(1.509\) \(\Q\) None None \(0\) \(0\) \(3\) \(1\) \(-\) \(q-2q^{4}+3q^{5}+q^{7}+6q^{11}-4q^{13}+\cdots\)
189.2.a.d \(1\) \(1.509\) \(\Q\) None None \(2\) \(0\) \(1\) \(-1\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}-q^{7}+2q^{10}+\cdots\)
189.2.a.e \(2\) \(1.509\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(2\) \(-\) \(q+\beta q^{2}+q^{4}+\beta q^{5}+q^{7}-\beta q^{8}+3q^{10}+\cdots\)
189.2.a.f \(2\) \(1.509\) \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(-2\) \(-\) \(q+\beta q^{2}+5q^{4}-\beta q^{5}-q^{7}+3\beta q^{8}+\cdots\)
189.2.c.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+2q^{4}+\zeta_{6}q^{7}+(1-2\zeta_{6})q^{13}+4q^{16}+\cdots\)
189.2.c.b \(4\) \(1.509\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}-3q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
189.2.c.c \(4\) \(1.509\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{2}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}-2\beta _{1}q^{8}+\cdots\)
189.2.e.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(4\) \(4\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.b \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+(2-2\zeta_{6})q^{4}+(1-3\zeta_{6})q^{7}+2q^{13}+\cdots\)
189.2.e.c \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-4\) \(4\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.d \(4\) \(1.509\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}-\beta _{2}q^{5}+\cdots\)
189.2.e.e \(6\) \(1.509\) 6.0.309123.1 None None \(-2\) \(0\) \(-1\) \(2\) \(q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
189.2.e.f \(6\) \(1.509\) 6.0.309123.1 None None \(2\) \(0\) \(1\) \(2\) \(q+(1-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
189.2.f.a \(6\) \(1.509\) 6.0.309123.1 None None \(-1\) \(0\) \(-5\) \(3\) \(q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
189.2.f.b \(6\) \(1.509\) \(\Q(\zeta_{18})\) None None \(3\) \(0\) \(3\) \(-3\) \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
189.2.g.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(2\) \(1\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.g.b \(10\) \(1.509\) 10.0.\(\cdots\).1 None None \(-2\) \(0\) \(8\) \(-1\) \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)
189.2.h.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(4\) \(q-q^{2}-q^{4}+(-1+\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
189.2.h.b \(10\) \(1.509\) 10.0.\(\cdots\).1 None None \(4\) \(0\) \(-4\) \(-4\) \(q+(\beta _{1}-\beta _{5})q^{2}+(1+\beta _{3})q^{4}+(\beta _{6}-\beta _{9})q^{5}+\cdots\)
189.2.i.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(4\) \(q+(-1+2\zeta_{6})q^{2}-q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
189.2.i.b \(10\) \(1.509\) 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(-6\) \(q+(-\beta _{3}-\beta _{5})q^{2}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
189.2.o.a \(12\) \(1.509\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(6\) \(0\) \(0\) \(-2\) \(q+(\beta _{1}-\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots\)
189.2.p.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+(-2+2\zeta_{6})q^{4}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.p.b \(4\) \(1.509\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(10\) \(q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{3})q^{5}+(2+\beta _{2})q^{7}+\cdots\)
189.2.p.c \(4\) \(1.509\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(-3+2\beta _{2})q^{7}+\cdots\)
189.2.p.d \(12\) \(1.509\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}+(1-\beta _{3}-\beta _{7}+\beta _{9})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
189.2.s.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None None \(3\) \(0\) \(6\) \(-5\) \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+3q^{5}+(-3+\cdots)q^{7}+\cdots\)
189.2.s.b \(10\) \(1.509\) 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(3\) \(q+(-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7}-\beta _{8})q^{2}+\cdots\)
189.2.u.a \(132\) \(1.509\) None None \(-3\) \(-3\) \(-3\) \(-6\)
189.2.v.a \(54\) \(1.509\) None None \(0\) \(-3\) \(-3\) \(0\)
189.2.v.b \(54\) \(1.509\) None None \(0\) \(3\) \(-3\) \(0\)
189.2.w.a \(132\) \(1.509\) None None \(-3\) \(-3\) \(-3\) \(-6\)
189.2.ba.a \(132\) \(1.509\) None None \(-3\) \(-9\) \(-9\) \(-6\)
189.2.bd.a \(132\) \(1.509\) None None \(-3\) \(-9\) \(-9\) \(-6\)
189.2.be.a \(132\) \(1.509\) None None \(-12\) \(0\) \(0\) \(-6\)
189.3.b.a \(4\) \(5.150\) 4.0.1166592.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-6+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
189.3.b.b \(4\) \(5.150\) \(\Q(\sqrt{-2}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{5}+\beta _{2}q^{7}+\cdots\)
189.3.b.c \(8\) \(5.150\) 8.0.1997017344.2 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(-1-\beta _{2}-\beta _{3})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
189.3.d.a \(2\) \(5.150\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(0\) \(-7\) \(q-q^{2}-3q^{4}+(1-2\zeta_{6})q^{5}+(-7+7\zeta_{6})q^{7}+\cdots\)
189.3.d.b \(2\) \(5.150\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(13\) \(q-4q^{4}+(6+\zeta_{6})q^{7}+(-5+10\zeta_{6})q^{13}+\cdots\)
189.3.d.c \(2\) \(5.150\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(0\) \(-7\) \(q+q^{2}-3q^{4}+(1-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots\)
189.3.d.d \(8\) \(5.150\) 8.0.\(\cdots\).6 None None \(0\) \(0\) \(0\) \(-16\) \(q-\beta _{2}q^{2}+(3+\beta _{5})q^{4}-\beta _{3}q^{5}+(-2+\cdots)q^{7}+\cdots\)
189.3.d.e \(8\) \(5.150\) 8.0.\(\cdots\).14 None None \(0\) \(0\) \(0\) \(12\) \(q-\beta _{4}q^{2}+(5-\beta _{1})q^{4}+\beta _{2}q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
189.3.j.a \(6\) \(5.150\) 6.0.63369648.1 None None \(0\) \(0\) \(15\) \(-2\) \(q+(-1-\beta _{4}-\beta _{5})q^{2}+(-4-\beta _{1})q^{4}+\cdots\)
189.3.j.b \(22\) \(5.150\) None None \(0\) \(0\) \(-12\) \(0\)
189.3.k.a \(28\) \(5.150\) None None \(-1\) \(0\) \(0\) \(0\)
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