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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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