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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
348.2.a.a \(1\) \(2.779\) \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) \(-\) \(q-q^{3}-2q^{5}+q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots\)
348.2.a.b \(1\) \(2.779\) \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) \(+\) \(q-q^{3}-3q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots\)
348.2.a.c \(1\) \(2.779\) \(\Q\) None \(0\) \(1\) \(-4\) \(-3\) \(+\) \(q+q^{3}-4q^{5}-3q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
348.2.a.d \(1\) \(2.779\) \(\Q\) None \(0\) \(1\) \(2\) \(1\) \(-\) \(q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
348.2.b.a \(8\) \(2.779\) 8.0.12960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
348.2.b.b \(12\) \(2.779\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) \(\Q(\sqrt{-29}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{11}q^{3}-2q^{4}+\beta _{9}q^{5}+\cdots\)
348.2.b.c \(12\) \(2.779\) 12.0.\(\cdots\).3 \(\Q(\sqrt{-87}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+\beta _{4}q^{3}+\beta _{5}q^{4}-\beta _{3}q^{6}+\cdots\)
348.2.b.d \(24\) \(2.779\) None \(0\) \(0\) \(0\) \(0\)
348.2.c.a \(16\) \(2.779\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+\beta _{1}q^{3}+(\beta _{2}+\beta _{9}+\beta _{11}+\cdots)q^{4}+\cdots\)
348.2.c.b \(40\) \(2.779\) None \(0\) \(0\) \(0\) \(0\)
348.2.h.a \(2\) \(2.779\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(-6\) \(q+iq^{3}-2q^{5}-3q^{7}-q^{9}-3iq^{11}+\cdots\)
348.2.h.b \(2\) \(2.779\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(8\) \(q+iq^{3}-2q^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots\)
348.2.h.c \(2\) \(2.779\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(8\) \(2\) \(q+iq^{3}+4q^{5}+q^{7}-q^{9}-5iq^{11}+\cdots\)
348.2.i.a \(60\) \(2.779\) None \(4\) \(0\) \(0\) \(0\)
348.2.l.a \(20\) \(2.779\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{14}q^{3}+\beta _{19}q^{5}-\beta _{8}q^{7}-\beta _{3}q^{9}+\cdots\)
348.2.m.a \(12\) \(2.779\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-2\) \(-5\) \(2\) \(q+\beta _{11}q^{3}+(-1+\beta _{2}-\beta _{3}+\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
348.2.m.b \(12\) \(2.779\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(2\) \(9\) \(2\) \(q+\beta _{8}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
348.2.n.a \(36\) \(2.779\) None \(0\) \(0\) \(0\) \(-4\)
348.2.s.a \(336\) \(2.779\) None \(0\) \(0\) \(0\) \(0\)
348.2.t.a \(336\) \(2.779\) None \(0\) \(0\) \(0\) \(0\)
348.2.u.a \(120\) \(2.779\) None \(0\) \(0\) \(0\) \(0\)
348.2.x.a \(360\) \(2.779\) None \(-4\) \(0\) \(0\) \(0\)
348.3.d.a \(4\) \(9.482\) \(\Q(\sqrt{-5}, \sqrt{-29})\) None \(0\) \(8\) \(0\) \(-22\) \(q+(2+\beta _{2})q^{3}-2\beta _{2}q^{5}+(-6+\beta _{3})q^{7}+\cdots\)
348.3.d.b \(14\) \(9.482\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2\) \(0\) \(26\) \(q-\beta _{1}q^{3}-\beta _{11}q^{5}+(2+\beta _{4})q^{7}+\beta _{2}q^{9}+\cdots\)
348.3.e.a \(4\) \(9.482\) \(\Q(i, \sqrt{29})\) None \(0\) \(0\) \(0\) \(-20\) \(q-3\beta _{1}q^{3}-\beta _{2}q^{5}-5q^{7}-9q^{9}-2\beta _{3}q^{11}+\cdots\)
348.3.e.b \(16\) \(9.482\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(12\) \(q-\beta _{8}q^{3}-\beta _{5}q^{5}+(1+\beta _{4})q^{7}+(1-\beta _{7}+\cdots)q^{9}+\cdots\)
348.3.f.a \(56\) \(9.482\) None \(0\) \(0\) \(0\) \(0\)
348.3.g.a \(60\) \(9.482\) None \(0\) \(0\) \(-8\) \(0\)
348.3.j.a \(20\) \(9.482\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+(-\beta _{1}+\beta _{6}-\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots\)
348.3.k.a \(232\) \(9.482\) None \(0\) \(0\) \(0\) \(0\)
348.3.o.a \(360\) \(9.482\) None \(0\) \(0\) \(8\) \(0\)
348.3.p.a \(360\) \(9.482\) None \(4\) \(0\) \(8\) \(0\)
348.3.q.a \(120\) \(9.482\) None \(0\) \(0\) \(0\) \(8\)
348.3.r.a \(120\) \(9.482\) None \(0\) \(0\) \(0\) \(-8\)
348.3.v.a \(1392\) \(9.482\) None \(0\) \(0\) \(0\) \(0\)
348.3.w.a \(120\) \(9.482\) None \(0\) \(0\) \(0\) \(0\)
348.4.a.a \(1\) \(20.533\) \(\Q\) None \(0\) \(3\) \(-9\) \(21\) \(-\) \(q+3q^{3}-9q^{5}+21q^{7}+9q^{9}-66q^{11}+\cdots\)
348.4.a.b \(2\) \(20.533\) \(\Q(\sqrt{13}) \) None \(0\) \(6\) \(-2\) \(-40\) \(-\) \(q+3q^{3}+(-1-\beta )q^{5}+(-20+3\beta )q^{7}+\cdots\)
348.4.a.c \(3\) \(20.533\) 3.3.189021.1 None \(0\) \(9\) \(19\) \(9\) \(+\) \(q+3q^{3}+(6-\beta _{2})q^{5}+(3+\beta _{1}-\beta _{2})q^{7}+\cdots\)
348.4.a.d \(4\) \(20.533\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-12\) \(-1\) \(17\) \(+\) \(q-3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(4+\beta _{1}+\cdots)q^{7}+\cdots\)
348.4.a.e \(4\) \(20.533\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-12\) \(9\) \(-11\) \(-\) \(q-3q^{3}+(2-\beta _{2})q^{5}+(-3+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
348.4.h.a \(14\) \(20.533\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(24\) \(-12\) \(q+\beta _{8}q^{3}+(2+\beta _{2})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
348.4.l.a \(60\) \(20.533\) None \(0\) \(0\) \(0\) \(0\)
348.4.m.a \(48\) \(20.533\) None \(0\) \(-24\) \(-21\) \(-6\)
348.4.m.b \(48\) \(20.533\) None \(0\) \(24\) \(41\) \(-6\)
348.4.n.a \(84\) \(20.533\) None \(0\) \(0\) \(-24\) \(12\)
348.5.d.a \(38\) \(35.973\) None \(0\) \(-18\) \(0\) \(108\)
348.5.e.a \(40\) \(35.973\) None \(0\) \(0\) \(0\) \(80\)
348.5.j.a \(40\) \(35.973\) None \(0\) \(0\) \(0\) \(0\)
348.6.a.a \(6\) \(55.814\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-54\) \(-36\) \(117\) \(-\) \(q-9q^{3}+(-6-\beta _{2})q^{5}+(20-\beta _{5})q^{7}+\cdots\)
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