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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
165.1.l.a \(2\) \(0.082\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+iq^{4}+iq^{5}+q^{9}-iq^{11}+\cdots\)
165.1.l.b \(2\) \(0.082\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{4}-iq^{5}-q^{9}+iq^{11}+\cdots\)
165.2.a.a \(2\) \(1.318\) \(\Q(\sqrt{2}) \) None None \(-2\) \(-2\) \(-2\) \(-4\) \(+\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
165.2.a.b \(2\) \(1.318\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(4\) \(-\) \(q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}+2q^{7}+\cdots\)
165.2.a.c \(3\) \(1.318\) 3.3.148.1 None None \(-1\) \(3\) \(3\) \(0\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
165.2.c.a \(6\) \(1.318\) 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}+\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
165.2.c.b \(6\) \(1.318\) 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{4}q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
165.2.d.a \(2\) \(1.318\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(3\) \(0\) \(q-\beta q^{3}+2q^{4}+(1+\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
165.2.d.b \(2\) \(1.318\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-3\) \(0\) \(q+\beta q^{3}+2q^{4}+(-2+\beta )q^{5}+(-3+\cdots)q^{9}+\cdots\)
165.2.d.c \(16\) \(1.318\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
165.2.f.a \(8\) \(1.318\) 8.0.619810816.2 None None \(0\) \(-2\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots\)
165.2.f.b \(8\) \(1.318\) 8.0.619810816.2 None None \(0\) \(-2\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
165.2.j.a \(24\) \(1.318\) None None \(0\) \(0\) \(8\) \(0\)
165.2.k.a \(4\) \(1.318\) \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-8\) \(-8\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
165.2.k.b \(4\) \(1.318\) \(\Q(\zeta_{8})\) None None \(4\) \(0\) \(8\) \(-8\) \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
165.2.k.c \(16\) \(1.318\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(-2\) \(-8\) \(8\) \(q+\beta _{3}q^{2}-\beta _{15}q^{3}+(-\beta _{1}-\beta _{3}-\beta _{13}+\cdots)q^{4}+\cdots\)
165.2.k.d \(16\) \(1.318\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(4\) \(4\) \(8\) \(8\) \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(\beta _{1}+\beta _{3}+\beta _{13}+\cdots)q^{4}+\cdots\)
165.2.m.a \(8\) \(1.318\) 8.0.13140625.1 None None \(0\) \(-2\) \(2\) \(1\) \(q+(1-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6})q^{2}+(-1+\cdots)q^{3}+\cdots\)
165.2.m.b \(8\) \(1.318\) 8.0.819390625.1 None None \(2\) \(2\) \(2\) \(9\) \(q+\beta _{4}q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
165.2.m.c \(8\) \(1.318\) \(\Q(\zeta_{15})\) None None \(2\) \(2\) \(-2\) \(-5\) \(q+(-1+2\zeta_{15}-\zeta_{15}^{3}+\zeta_{15}^{4}-\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
165.2.m.d \(8\) \(1.318\) 8.0.13140625.1 None None \(4\) \(-2\) \(-2\) \(3\) \(q+(1+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots\)
165.2.p.a \(16\) \(1.318\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(8\) \(0\) \(-10\) \(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{2}-\beta _{5}+\beta _{6}-\beta _{8}+\cdots)q^{3}+\cdots\)
165.2.p.b \(48\) \(1.318\) None None \(0\) \(-4\) \(0\) \(10\)
165.2.r.a \(80\) \(1.318\) None None \(0\) \(0\) \(0\) \(0\)
165.2.s.a \(48\) \(1.318\) None None \(0\) \(0\) \(-4\) \(0\)
165.2.v.a \(160\) \(1.318\) None None \(0\) \(-8\) \(0\) \(-20\)
165.2.w.a \(96\) \(1.318\) None None \(0\) \(0\) \(-8\) \(-20\)
165.3.b.a \(16\) \(4.496\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
165.3.e.a \(28\) \(4.496\) None None \(0\) \(0\) \(0\) \(24\)
165.3.g.a \(2\) \(4.496\) \(\Q(\sqrt{-11}) \) None None \(-2\) \(-5\) \(-10\) \(0\) \(q-q^{2}+(-2-\beta )q^{3}-3q^{4}-5q^{5}+\cdots\)
165.3.g.b \(2\) \(4.496\) \(\Q(\sqrt{-11}) \) None None \(2\) \(5\) \(10\) \(0\) \(q+q^{2}+(3-\beta )q^{3}-3q^{4}+5q^{5}+(3+\cdots)q^{6}+\cdots\)
165.3.g.c \(36\) \(4.496\) None None \(0\) \(0\) \(0\) \(0\)
165.3.h.a \(24\) \(4.496\) None None \(0\) \(0\) \(4\) \(0\)
165.3.i.a \(40\) \(4.496\) None None \(8\) \(0\) \(16\) \(0\)
165.3.l.a \(4\) \(4.496\) \(\Q(i, \sqrt{10})\) None None \(0\) \(-12\) \(-16\) \(0\) \(q+\beta _{1}q^{2}-3q^{3}+\beta _{2}q^{4}+(-4-3\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.b \(4\) \(4.496\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}-\beta _{2}q^{4}+5\beta _{2}q^{5}+\cdots\)
165.3.l.c \(4\) \(4.496\) \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-3\beta _{2})q^{3}-4\beta _{2}q^{4}+(3\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.d \(4\) \(4.496\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(16\) \(0\) \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+\beta _{2}q^{4}+(4+3\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.e \(4\) \(4.496\) \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(10\) \(0\) \(0\) \(q+(3+\beta _{3})q^{3}+4\beta _{2}q^{4}+(-3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.f \(4\) \(4.496\) \(\Q(i, \sqrt{6})\) None None \(0\) \(12\) \(0\) \(0\) \(q+\beta _{1}q^{2}+3q^{3}-\beta _{2}q^{4}-5\beta _{2}q^{5}+\cdots\)
165.3.l.g \(64\) \(4.496\) None None \(0\) \(-16\) \(0\) \(0\)
165.3.n.a \(96\) \(4.496\) None None \(0\) \(0\) \(-4\) \(0\)
165.3.o.a \(176\) \(4.496\) None None \(0\) \(0\) \(0\) \(0\)
165.3.q.a \(128\) \(4.496\) None None \(0\) \(8\) \(0\) \(0\)
165.3.t.a \(32\) \(4.496\) None None \(0\) \(0\) \(40\) \(20\)
165.3.t.b \(32\) \(4.496\) None None \(0\) \(0\) \(-40\) \(-20\)
165.3.u.a \(352\) \(4.496\) None None \(0\) \(-4\) \(0\) \(-20\)
165.3.x.a \(192\) \(4.496\) None None \(0\) \(0\) \(-8\) \(52\)
165.4.a.a \(1\) \(9.735\) \(\Q\) None None \(0\) \(-3\) \(-5\) \(2\) \(+\) \(q-3q^{3}-8q^{4}-5q^{5}+2q^{7}+9q^{9}+\cdots\)
165.4.a.b \(1\) \(9.735\) \(\Q\) None None \(1\) \(3\) \(-5\) \(36\) \(+\) \(q+q^{2}+3q^{3}-7q^{4}-5q^{5}+3q^{6}+\cdots\)
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