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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
111.1.d.a \(1\) \(0.055\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) \(\Q(\sqrt{37}) \) \(0\) \(1\) \(0\) \(-2\) \(q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\)
111.1.d.b \(2\) \(0.055\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-111}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots\)
111.1.h.a \(2\) \(0.055\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
111.1.i.a \(2\) \(0.055\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
111.2.a.a \(3\) \(0.886\) 3.3.148.1 None None \(3\) \(-3\) \(4\) \(-4\) \(-\) \(q+(1+\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
111.2.a.b \(4\) \(0.886\) 4.4.6224.1 None None \(0\) \(4\) \(-2\) \(4\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
111.2.c.a \(2\) \(0.886\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots\)
111.2.c.b \(4\) \(0.886\) 4.0.27648.1 None None \(0\) \(4\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
111.2.e.a \(6\) \(0.886\) 6.0.1415907.1 None None \(0\) \(3\) \(2\) \(-2\) \(q+(-\beta _{1}-\beta _{2})q^{2}+(1+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
111.2.e.b \(10\) \(0.886\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(-5\) \(2\) \(0\) \(q+\beta _{3}q^{2}+(-1+\beta _{6})q^{3}+(-2+2\beta _{6}+\cdots)q^{4}+\cdots\)
111.2.g.a \(20\) \(0.886\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+\beta _{13}q^{3}+(-\beta _{6}+\beta _{8})q^{4}+\cdots\)
111.2.j.a \(2\) \(0.886\) \(\Q(\sqrt{-3}) \) None None \(-3\) \(-1\) \(-6\) \(-1\) \(q+(-1-\zeta_{6})q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{4}+(-4+\cdots)q^{5}+\cdots\)
111.2.j.b \(4\) \(0.886\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(-3\) \(2\) \(3\) \(6\) \(q+(-1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
111.2.j.c \(6\) \(0.886\) 6.0.16553403.1 None None \(0\) \(-3\) \(9\) \(-3\) \(q-\beta _{3}q^{2}+(-1+\beta _{2})q^{3}+(2-2\beta _{2}+\cdots)q^{4}+\cdots\)
111.2.k.a \(18\) \(0.886\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-3\) \(0\) \(-6\) \(6\) \(q-\beta _{7}q^{2}+(\beta _{9}+\beta _{13})q^{3}+(\beta _{13}+\beta _{16}+\cdots)q^{4}+\cdots\)
111.2.k.b \(24\) \(0.886\) None None \(-3\) \(0\) \(-6\) \(-9\)
111.2.m.a \(40\) \(0.886\) None None \(0\) \(-6\) \(0\) \(-4\)
111.2.o.a \(12\) \(0.886\) 12.0.\(\cdots\).1 None None \(3\) \(0\) \(-3\) \(-6\) \(q+\beta _{3}q^{2}+\beta _{9}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
111.2.o.b \(18\) \(0.886\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(3\) \(0\) \(-3\) \(9\) \(q-\beta _{16}q^{2}+(-\beta _{10}+\beta _{17})q^{3}+(-\beta _{9}+\cdots)q^{4}+\cdots\)
111.2.q.a \(12\) \(0.886\) \(\Q(\zeta_{36})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{36}^{4}-2\zeta_{36}^{10})q^{3}+2\zeta_{36}q^{4}+\cdots\)
111.2.q.b \(120\) \(0.886\) None None \(0\) \(-12\) \(0\) \(-24\)
111.3.b.a \(24\) \(3.025\) None None \(0\) \(-4\) \(0\) \(8\)
111.3.d.a \(4\) \(3.025\) 4.4.65712.1 \(\Q(\sqrt{-111}) \) None \(0\) \(-12\) \(0\) \(0\) \(q-\beta _{2}q^{2}-3q^{3}+(4-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
111.3.d.b \(4\) \(3.025\) 4.4.85248.1 \(\Q(\sqrt{-111}) \) None \(0\) \(12\) \(0\) \(0\) \(q+\beta _{1}q^{2}+3q^{3}+(4+3\beta _{2})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
111.3.d.c \(16\) \(3.025\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(-16\) \(q+\beta _{8}q^{2}+\beta _{5}q^{3}+(1+\beta _{6})q^{4}-\beta _{2}q^{5}+\cdots\)
111.3.f.a \(24\) \(3.025\) None None \(8\) \(0\) \(20\) \(0\)
111.3.h.a \(48\) \(3.025\) None None \(0\) \(0\) \(0\) \(-8\)
111.3.i.a \(48\) \(3.025\) None None \(0\) \(-2\) \(0\) \(4\)
111.3.l.a \(24\) \(3.025\) None None \(-4\) \(-36\) \(8\) \(0\)
111.3.l.b \(24\) \(3.025\) None None \(-4\) \(36\) \(8\) \(0\)
111.3.n.a \(6\) \(3.025\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(39\) \(q-3\zeta_{18}^{4}q^{3}+4\zeta_{18}q^{4}+(5-3\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
111.3.n.b \(132\) \(3.025\) None None \(0\) \(-9\) \(0\) \(-54\)
111.3.p.a \(6\) \(3.025\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-39\) \(q+(3\zeta_{18}^{2}-3\zeta_{18}^{5})q^{3}+4\zeta_{18}^{2}q^{4}+\cdots\)
111.3.p.b \(132\) \(3.025\) None None \(0\) \(-3\) \(0\) \(30\)
111.3.r.a \(72\) \(3.025\) None None \(0\) \(0\) \(-18\) \(0\)
111.3.r.b \(84\) \(3.025\) None None \(0\) \(0\) \(-18\) \(0\)
111.4.a.a \(1\) \(6.549\) \(\Q\) None None \(-4\) \(3\) \(2\) \(-28\) \(-\) \(q-4q^{2}+3q^{3}+8q^{4}+2q^{5}-12q^{6}+\cdots\)
111.4.a.b \(1\) \(6.549\) \(\Q\) None None \(-1\) \(-3\) \(-4\) \(-1\) \(+\) \(q-q^{2}-3q^{3}-7q^{4}-4q^{5}+3q^{6}+\cdots\)
111.4.a.c \(1\) \(6.549\) \(\Q\) None None \(1\) \(3\) \(-8\) \(-13\) \(-\) \(q+q^{2}+3q^{3}-7q^{4}-8q^{5}+3q^{6}+\cdots\)
111.4.a.d \(3\) \(6.549\) 3.3.2700.1 None None \(-3\) \(-9\) \(-6\) \(15\) \(-\) \(q+(-1-\beta _{2})q^{2}-3q^{3}+(3-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
111.4.a.e \(5\) \(6.549\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(4\) \(-15\) \(18\) \(-12\) \(+\) \(q+(1-\beta _{1})q^{2}-3q^{3}+(7+\beta _{2}+\beta _{4})q^{4}+\cdots\)
111.4.a.f \(7\) \(6.549\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(3\) \(21\) \(14\) \(43\) \(+\) \(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{1}+\beta _{2})q^{4}+\cdots\)
111.4.c.a \(10\) \(6.549\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(-30\) \(0\) \(26\) \(q+\beta _{1}q^{2}-3q^{3}+(-3+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
111.4.c.b \(10\) \(6.549\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(30\) \(0\) \(-30\) \(q+\beta _{1}q^{2}+3q^{3}+(-4+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
111.4.e.a \(18\) \(6.549\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-3\) \(-27\) \(4\) \(43\) \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{4}q^{3}+(-\beta _{1}+3\beta _{4}+\cdots)q^{4}+\cdots\)
111.4.e.b \(18\) \(6.549\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-3\) \(27\) \(4\) \(1\) \(q+(\beta _{1}+\beta _{2})q^{2}+(3+3\beta _{5})q^{3}+(-2+\cdots)q^{4}+\cdots\)
111.4.g.a \(4\) \(6.549\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}+8\zeta_{12}q^{4}-6\zeta_{12}^{3}q^{7}+\cdots\)
111.4.g.b \(68\) \(6.549\) None None \(0\) \(0\) \(0\) \(-8\)
111.4.j.a \(20\) \(6.549\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(3\) \(-30\) \(-21\) \(-15\) \(q+\beta _{2}q^{2}+(-3+3\beta _{7})q^{3}+(5-\beta _{1}+\cdots)q^{4}+\cdots\)
111.4.j.b \(20\) \(6.549\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(3\) \(30\) \(-21\) \(-29\) \(q+\beta _{3}q^{2}+3\beta _{6}q^{3}+(-\beta _{2}+5\beta _{6}+\beta _{13}+\cdots)q^{4}+\cdots\)
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