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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
156.1.o.a \(2\) \(0.078\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots\)
156.1.s.a \(2\) \(0.078\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-3\) \(q+\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
156.2.a.a \(1\) \(1.246\) \(\Q\) None None \(0\) \(-1\) \(-4\) \(-2\) \(+\) \(q-q^{3}-4q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
156.2.a.b \(1\) \(1.246\) \(\Q\) None None \(0\) \(1\) \(0\) \(2\) \(-\) \(q+q^{3}+2q^{7}+q^{9}+q^{13}-6q^{17}+\cdots\)
156.2.b.a \(2\) \(1.246\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots\)
156.2.b.b \(2\) \(1.246\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+iq^{5}+2iq^{7}+q^{9}-3iq^{11}+\cdots\)
156.2.c.a \(2\) \(1.246\) \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}-\beta q^{5}+\cdots\)
156.2.c.b \(2\) \(1.246\) \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+\beta q^{2}+(1+\beta )q^{3}-2q^{4}-\beta q^{5}+(-2+\cdots)q^{6}+\cdots\)
156.2.c.c \(8\) \(1.246\) 8.0.121550625.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(1+\beta _{1}-\beta _{6})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
156.2.c.d \(12\) \(1.246\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}-\beta _{6}q^{3}-\beta _{8}q^{4}+(-\beta _{9}+\cdots)q^{5}+\cdots\)
156.2.h.a \(8\) \(1.246\) 8.0.592240896.6 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{3}q^{3}-\beta _{4}q^{4}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)
156.2.h.b \(16\) \(1.246\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}+\beta _{6}q^{3}-\beta _{12}q^{4}-\beta _{4}q^{5}+\cdots\)
156.2.i.a \(2\) \(1.246\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(4\) \(-1\) \(q+(1-\zeta_{6})q^{3}+2q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
156.2.k.a \(2\) \(1.246\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(-2\) \(-4\) \(q+(-1-i)q^{2}-iq^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
156.2.k.b \(2\) \(1.246\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(-2\) \(4\) \(q+(-1-i)q^{2}+iq^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
156.2.k.c \(2\) \(1.246\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(4\) \(0\) \(q+(-1+i)q^{2}+iq^{3}-2iq^{4}+(2+2i)q^{5}+\cdots\)
156.2.k.d \(2\) \(1.246\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(4\) \(0\) \(q+(1-i)q^{2}-iq^{3}-2iq^{4}+(2+2i)q^{5}+\cdots\)
156.2.k.e \(10\) \(1.246\) 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(\beta _{5}+\beta _{7})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
156.2.k.f \(10\) \(1.246\) 10.0.\(\cdots\).1 None None \(4\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{6}q^{3}+(-\beta _{7}-\beta _{8})q^{4}+\cdots\)
156.2.m.a \(4\) \(1.246\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
156.2.m.b \(4\) \(1.246\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{12}^{3}q^{3}+(2-2\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{7}+\cdots\)
156.2.p.a \(8\) \(1.246\) 8.0.3317760000.3 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}-\beta _{6}q^{3}-2\beta _{4}q^{4}+(\beta _{2}-\beta _{7})q^{5}+\cdots\)
156.2.p.b \(40\) \(1.246\) None None \(0\) \(0\) \(0\) \(0\)
156.2.q.a \(2\) \(1.246\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(6\) \(q+(1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(4-2\zeta_{6})q^{7}+\cdots\)
156.2.q.b \(4\) \(1.246\) \(\Q(\sqrt{-3}, \sqrt{-43})\) None None \(0\) \(-2\) \(0\) \(-3\) \(q+(-1+\beta _{2})q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
156.2.r.a \(4\) \(1.246\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-6\) \(0\) \(6\) \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
156.2.r.b \(4\) \(1.246\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(6\) \(0\) \(-6\) \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{3}+2q^{4}-2\beta _{3}q^{5}+\cdots\)
156.2.r.c \(40\) \(1.246\) None None \(0\) \(0\) \(0\) \(0\)
156.2.u.a \(4\) \(1.246\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}-3\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
156.2.u.b \(16\) \(1.246\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) \(q+(-\beta _{9}-\beta _{13}-\beta _{15})q^{3}+(-\beta _{3}-\beta _{9}+\cdots)q^{5}+\cdots\)
156.2.w.a \(4\) \(1.246\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(-4\) \(-6\) \(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
156.2.w.b \(4\) \(1.246\) \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(-4\) \(6\) \(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
156.2.w.c \(24\) \(1.246\) None None \(-4\) \(0\) \(2\) \(-2\)
156.2.w.d \(24\) \(1.246\) None None \(-2\) \(0\) \(2\) \(2\)
156.3.d.a \(8\) \(4.251\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(6\) \(0\) \(-8\) \(q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
156.3.e.a \(2\) \(4.251\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(0\) \(-12\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
156.3.e.b \(2\) \(4.251\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(0\) \(12\) \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
156.3.e.c \(24\) \(4.251\) None None \(0\) \(0\) \(0\) \(0\)
156.3.f.a \(24\) \(4.251\) None None \(4\) \(0\) \(0\) \(0\)
156.3.g.a \(2\) \(4.251\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(6\) \(0\) \(0\) \(q+3q^{3}+2\zeta_{6}q^{7}+9q^{9}+(11-\zeta_{6})q^{13}+\cdots\)
156.3.g.b \(4\) \(4.251\) \(\Q(i, \sqrt{11})\) None None \(0\) \(-10\) \(0\) \(0\) \(q+(-2+\beta _{3})q^{3}+(-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
156.3.g.c \(4\) \(4.251\) \(\Q(\sqrt{-2}, \sqrt{15})\) None None \(0\) \(4\) \(0\) \(0\) \(q+(1-\beta _{1})q^{3}-\beta _{3}q^{5}+(-7-2\beta _{1}+\cdots)q^{9}+\cdots\)
156.3.j.a \(8\) \(4.251\) 8.0.\(\cdots\).10 None None \(0\) \(0\) \(12\) \(-8\) \(q+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots\)
156.3.l.a \(4\) \(4.251\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-12\) \(q+\zeta_{8}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+4\zeta_{8}^{2}q^{4}+\cdots\)
156.3.l.b \(4\) \(4.251\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(12\) \(q+\zeta_{8}q^{2}+(\zeta_{8}-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+4\zeta_{8}^{2}q^{4}+\cdots\)
156.3.l.c \(96\) \(4.251\) None None \(0\) \(0\) \(0\) \(0\)
156.3.n.a \(2\) \(4.251\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(3\) \(0\) \(0\) \(q+(-2+2\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
156.3.n.b \(2\) \(4.251\) \(\Q(\sqrt{-3}) \) None None \(2\) \(-3\) \(0\) \(0\) \(q+(2-2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
156.3.n.c \(4\) \(4.251\) \(\Q(\sqrt{-3}, \sqrt{142})\) None None \(-8\) \(6\) \(0\) \(-4\) \(q-2q^{2}+(2+\beta _{2})q^{3}+4q^{4}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots\)
156.3.n.d \(4\) \(4.251\) \(\Q(\sqrt{-3}, \sqrt{142})\) None None \(-4\) \(-6\) \(0\) \(4\) \(q+(-2-2\beta _{2})q^{2}+(-2-\beta _{2})q^{3}+4\beta _{2}q^{4}+\cdots\)
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