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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
147.1.l.a \(6\) \(0.073\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots\)
147.2.a.a \(1\) \(1.174\) \(\Q\) None None \(-1\) \(-1\) \(2\) \(0\) \(-\) \(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+3q^{8}+\cdots\)
147.2.a.b \(1\) \(1.174\) \(\Q\) None None \(2\) \(-1\) \(2\) \(0\) \(-\) \(q+2q^{2}-q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots\)
147.2.a.c \(1\) \(1.174\) \(\Q\) None None \(2\) \(1\) \(-2\) \(0\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots\)
147.2.a.d \(2\) \(1.174\) \(\Q(\sqrt{2}) \) None None \(-2\) \(-2\) \(-4\) \(0\) \(+\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
147.2.a.e \(2\) \(1.174\) \(\Q(\sqrt{2}) \) None None \(-2\) \(2\) \(4\) \(0\) \(-\) \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(2+\cdots)q^{5}+\cdots\)
147.2.c.a \(2\) \(1.174\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{3}+2q^{4}-3q^{9}-2\zeta_{6}q^{12}+\cdots\)
147.2.c.b \(8\) \(1.174\) 8.0.3288334336.2 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
147.2.e.a \(2\) \(1.174\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(1\) \(-2\) \(0\) \(q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
147.2.e.b \(2\) \(1.174\) \(\Q(\sqrt{-3}) \) None None \(1\) \(-1\) \(2\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
147.2.e.c \(2\) \(1.174\) \(\Q(\sqrt{-3}) \) None None \(1\) \(1\) \(-2\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
147.2.e.d \(4\) \(1.174\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(2\) \(-2\) \(-4\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
147.2.e.e \(4\) \(1.174\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(2\) \(2\) \(4\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{2}-\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
147.2.g.a \(2\) \(1.174\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{9}+\cdots\)
147.2.g.b \(16\) \(1.174\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{13}q^{2}+(\beta _{7}-\beta _{9})q^{3}+(1-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
147.2.i.a \(24\) \(1.174\) None None \(1\) \(4\) \(0\) \(0\)
147.2.i.b \(36\) \(1.174\) None None \(-1\) \(-6\) \(-4\) \(-6\)
147.2.k.a \(96\) \(1.174\) None None \(0\) \(-7\) \(0\) \(-14\)
147.2.m.a \(48\) \(1.174\) None None \(-1\) \(-4\) \(0\) \(0\)
147.2.m.b \(60\) \(1.174\) None None \(1\) \(5\) \(-2\) \(5\)
147.2.o.a \(12\) \(1.174\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-1\) \(q+(2\zeta_{21}+\zeta_{21}^{8})q^{3}+(-2\zeta_{21}^{3}-2\zeta_{21}^{10}+\cdots)q^{4}+\cdots\)
147.2.o.b \(192\) \(1.174\) None None \(0\) \(-14\) \(0\) \(-28\)
147.3.b.a \(1\) \(4.005\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(0\) \(q-3q^{3}+4q^{4}+9q^{9}-12q^{12}+23q^{13}+\cdots\)
147.3.b.b \(1\) \(4.005\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(0\) \(q+3q^{3}+4q^{4}+9q^{9}+12q^{12}-23q^{13}+\cdots\)
147.3.b.c \(2\) \(4.005\) \(\Q(\sqrt{-5}) \) None None \(0\) \(-4\) \(0\) \(0\) \(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}+\beta q^{5}+\cdots\)
147.3.b.d \(2\) \(4.005\) \(\Q(\sqrt{-5}) \) None None \(0\) \(4\) \(0\) \(0\) \(q+\beta q^{2}+(2+\beta )q^{3}-q^{4}-\beta q^{5}+(-5+\cdots)q^{6}+\cdots\)
147.3.b.e \(4\) \(4.005\) \(\Q(\sqrt{-5}, \sqrt{-6})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
147.3.b.f \(4\) \(4.005\) 4.0.65856.1 None None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
147.3.b.g \(8\) \(4.005\) 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{5}-\beta _{7})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)
147.3.d.a \(2\) \(4.005\) \(\Q(\sqrt{-3}) \) None None \(-4\) \(0\) \(0\) \(0\) \(q-2q^{2}-\zeta_{6}q^{3}+2\zeta_{6}q^{5}+2\zeta_{6}q^{6}+\cdots\)
147.3.d.b \(2\) \(4.005\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+\zeta_{6}q^{3}-3q^{4}+3\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
147.3.d.c \(2\) \(4.005\) \(\Q(\sqrt{-3}) \) None None \(6\) \(0\) \(0\) \(0\) \(q+3q^{2}+\zeta_{6}q^{3}+5q^{4}+3\zeta_{6}q^{5}+3\zeta_{6}q^{6}+\cdots\)
147.3.d.d \(8\) \(4.005\) 8.0.339738624.1 None None \(-8\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{3}q^{3}+(5-\beta _{5})q^{4}+\cdots\)
147.3.f.a \(2\) \(4.005\) \(\Q(\sqrt{-3}) \) None None \(-3\) \(3\) \(-9\) \(0\) \(q-3\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
147.3.f.b \(2\) \(4.005\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(-12\) \(0\) \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
147.3.f.c \(2\) \(4.005\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(9\) \(0\) \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
147.3.f.d \(2\) \(4.005\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(3\) \(12\) \(0\) \(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
147.3.f.e \(2\) \(4.005\) \(\Q(\sqrt{-3}) \) None None \(2\) \(3\) \(6\) \(0\) \(q+2\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+\cdots\)
147.3.f.f \(8\) \(4.005\) 8.0.339738624.1 None None \(4\) \(-12\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{7})q^{2}+(-1+\beta _{3})q^{3}+(-5+\cdots)q^{4}+\cdots\)
147.3.f.g \(8\) \(4.005\) 8.0.339738624.1 None None \(4\) \(12\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{7})q^{2}+(1-\beta _{3})q^{3}+(-5+\cdots)q^{4}+\cdots\)
147.3.h.a \(2\) \(4.005\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(0\) \(q-3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-9+9\zeta_{6})q^{9}+\cdots\)
147.3.h.b \(4\) \(4.005\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
147.3.h.c \(8\) \(4.005\) 8.0.\(\cdots\).8 None None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(\beta _{2}-\beta _{6})q^{3}+(2\beta _{2}-3\beta _{4}+\cdots)q^{4}+\cdots\)
147.3.h.d \(8\) \(4.005\) 8.0.3317760000.3 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{6})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
147.3.h.e \(8\) \(4.005\) 8.0.\(\cdots\).8 None None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-\beta _{2}+\beta _{6})q^{3}+(2\beta _{2}-3\beta _{4}+\cdots)q^{4}+\cdots\)
147.3.h.f \(16\) \(4.005\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{8}-\beta _{9}+\beta _{12})q^{3}+(1+\cdots)q^{4}+\cdots\)
147.3.j.a \(108\) \(4.005\) None None \(0\) \(0\) \(0\) \(-2\)
147.3.l.a \(216\) \(4.005\) None None \(0\) \(-5\) \(0\) \(-14\)
147.3.n.a \(12\) \(4.005\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(13\) \(q+(3\zeta_{21}^{2}+3\zeta_{21}^{9})q^{3}+(-4+4\zeta_{21}^{2}+\cdots)q^{4}+\cdots\)
147.3.n.b \(408\) \(4.005\) None None \(0\) \(-10\) \(0\) \(-42\)
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