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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
381.1.f.a \(2\) \(0.190\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{12}+\cdots\)
381.1.m.a \(6\) \(0.190\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(5\) \(q+\zeta_{14}^{6}q^{3}-\zeta_{14}^{3}q^{4}+(1-\zeta_{14})q^{7}+\cdots\)
381.1.t.a \(12\) \(0.190\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-5\) \(q-\zeta_{42}^{11}q^{3}-\zeta_{42}^{9}q^{4}+(\zeta_{42}^{14}-\zeta_{42}^{17}+\cdots)q^{7}+\cdots\)
381.2.a.a \(1\) \(3.042\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-2\) \(+\) \(q+q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
381.2.a.b \(1\) \(3.042\) \(\Q\) None None \(2\) \(1\) \(3\) \(-4\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots\)
381.2.a.c \(5\) \(3.042\) 5.5.81509.1 None None \(-1\) \(-5\) \(-5\) \(0\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
381.2.a.d \(5\) \(3.042\) 5.5.246832.1 None None \(2\) \(-5\) \(1\) \(0\) \(-\) \(q+\beta _{2}q^{2}-q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
381.2.a.e \(9\) \(3.042\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(-2\) \(9\) \(-4\) \(10\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
381.2.c.a \(40\) \(3.042\) None None \(0\) \(0\) \(0\) \(0\)
381.2.e.a \(4\) \(3.042\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-2\) \(2\) \(-6\) \(-3\) \(q+(-1-\beta _{2})q^{2}+(1+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
381.2.e.b \(16\) \(3.042\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-2\) \(8\) \(4\) \(6\) \(q-\beta _{3}q^{2}+(1+\beta _{8})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
381.2.e.c \(24\) \(3.042\) None None \(0\) \(-12\) \(2\) \(-9\)
381.2.g.a \(4\) \(3.042\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-2\) \(-8\) \(-3\) \(q+(-1+2\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
381.2.g.b \(4\) \(3.042\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-1\) \(8\) \(-3\) \(q+(-1+2\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\)
381.2.g.c \(72\) \(3.042\) None None \(0\) \(0\) \(0\) \(-6\)
381.2.i.a \(60\) \(3.042\) None None \(6\) \(10\) \(4\) \(-14\)
381.2.i.b \(72\) \(3.042\) None None \(4\) \(-12\) \(-4\) \(16\)
381.2.j.a \(60\) \(3.042\) None None \(-6\) \(0\) \(6\) \(-3\)
381.2.j.b \(66\) \(3.042\) None None \(6\) \(0\) \(-6\) \(-3\)
381.2.l.a \(240\) \(3.042\) None None \(0\) \(-7\) \(0\) \(-42\)
381.2.n.a \(6\) \(3.042\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-2\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+2q^{4}+(-2\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
381.2.n.b \(240\) \(3.042\) None None \(0\) \(-6\) \(0\) \(-6\)
381.2.q.a \(120\) \(3.042\) None None \(-3\) \(-10\) \(2\) \(11\)
381.2.q.b \(144\) \(3.042\) None None \(-7\) \(12\) \(-2\) \(-19\)
381.2.s.a \(480\) \(3.042\) None None \(0\) \(-11\) \(0\) \(12\)
381.2.u.a \(360\) \(3.042\) None None \(6\) \(0\) \(-6\) \(3\)
381.2.u.b \(396\) \(3.042\) None None \(-6\) \(0\) \(6\) \(3\)
381.2.x.a \(36\) \(3.042\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\)
381.2.x.b \(1440\) \(3.042\) None None \(0\) \(-36\) \(0\) \(-78\)
381.3.b.a \(84\) \(10.381\) None None \(0\) \(-2\) \(0\) \(0\)
381.3.d.a \(2\) \(10.381\) \(\Q(\sqrt{-3}) \) None None \(-4\) \(0\) \(0\) \(0\) \(q-2q^{2}+\zeta_{6}q^{3}+5\zeta_{6}q^{5}-2\zeta_{6}q^{6}+\cdots\)
381.3.d.b \(40\) \(10.381\) None None \(0\) \(0\) \(0\) \(0\)
381.3.f.a \(168\) \(10.381\) None None \(0\) \(-1\) \(0\) \(-18\)
381.3.h.a \(42\) \(10.381\) None None \(2\) \(-63\) \(0\) \(30\)
381.3.h.b \(42\) \(10.381\) None None \(2\) \(63\) \(0\) \(-18\)
381.3.k.a \(252\) \(10.381\) None None \(-10\) \(0\) \(0\) \(-28\)
381.3.m.a \(504\) \(10.381\) None None \(0\) \(-5\) \(0\) \(28\)
381.3.o.a \(6\) \(10.381\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3\zeta_{18}q^{3}+4q^{4}+(2\zeta_{18}-2\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
381.3.o.b \(492\) \(10.381\) None None \(0\) \(-6\) \(0\) \(0\)
381.3.p.a \(126\) \(10.381\) None None \(0\) \(0\) \(18\) \(-6\)
381.3.p.b \(132\) \(10.381\) None None \(0\) \(0\) \(-18\) \(-6\)
381.3.r.a \(252\) \(10.381\) None None \(5\) \(-63\) \(0\) \(-52\)
381.3.r.b \(252\) \(10.381\) None None \(5\) \(63\) \(0\) \(68\)
381.3.t.a \(1008\) \(10.381\) None None \(0\) \(-13\) \(0\) \(-52\)
381.3.v.a \(756\) \(10.381\) None None \(0\) \(0\) \(-18\) \(6\)
381.3.v.b \(792\) \(10.381\) None None \(0\) \(0\) \(18\) \(6\)
381.3.w.a \(36\) \(10.381\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\)
381.3.w.b \(2952\) \(10.381\) None None \(0\) \(-36\) \(0\) \(-84\)
381.4.a.a \(11\) \(22.480\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-5\) \(33\) \(-10\) \(-51\) \(-\) \(q-\beta _{1}q^{2}+3q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
381.4.a.b \(16\) \(22.480\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(-48\) \(-20\) \(-9\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
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