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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
342.2.a.a \(1\) \(2.731\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-2q^{11}+\cdots\)
342.2.a.b \(1\) \(2.731\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots\)
342.2.a.c \(1\) \(2.731\) \(\Q\) None \(-1\) \(0\) \(0\) \(-4\) \(+\) \(q-q^{2}+q^{4}-4q^{7}-q^{8}-4q^{13}+4q^{14}+\cdots\)
342.2.a.d \(1\) \(2.731\) \(\Q\) None \(-1\) \(0\) \(4\) \(3\) \(-\) \(q-q^{2}+q^{4}+4q^{5}+3q^{7}-q^{8}-4q^{10}+\cdots\)
342.2.a.e \(1\) \(2.731\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}+5q^{13}+\cdots\)
342.2.a.f \(1\) \(2.731\) \(\Q\) None \(1\) \(0\) \(0\) \(4\) \(-\) \(q+q^{2}+q^{4}+4q^{7}+q^{8}-4q^{11}+4q^{14}+\cdots\)
342.2.a.g \(1\) \(2.731\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+2q^{11}+\cdots\)
342.2.b.a \(2\) \(2.731\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(4\) \(q-q^{2}+q^{4}+\beta q^{5}+2q^{7}-q^{8}-\beta q^{10}+\cdots\)
342.2.b.b \(2\) \(2.731\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(4\) \(q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots\)
342.2.e.a \(6\) \(2.731\) 6.0.309123.1 None \(-3\) \(2\) \(0\) \(4\) \(q+(-1-\beta _{4})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots\)
342.2.e.b \(6\) \(2.731\) \(\Q(\zeta_{18})\) None \(3\) \(0\) \(0\) \(6\) \(q+(1-\zeta_{18})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+\cdots\)
342.2.e.c \(12\) \(2.731\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(2\) \(0\) \(-6\) \(q+(-1+\beta _{6})q^{2}+\beta _{10}q^{3}-\beta _{6}q^{4}+\cdots\)
342.2.e.d \(12\) \(2.731\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(0\) \(-4\) \(q+(1-\beta _{7})q^{2}+(\beta _{1}-\beta _{9})q^{3}-\beta _{7}q^{4}+\cdots\)
342.2.f.a \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(0\) \(-4\) \(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1-\zeta_{6})q^{6}+\cdots\)
342.2.f.b \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(1\) \(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}-3\zeta_{6}q^{5}+\cdots\)
342.2.f.c \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(1\) \(3\) \(q+q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+\cdots\)
342.2.f.d \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-2\) \(0\) \(q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}-2\zeta_{6}q^{5}+\cdots\)
342.2.f.e \(4\) \(2.731\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(4\) \(-4\) \(6\) \(2\) \(q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+3\beta _{2}q^{5}+\cdots\)
342.2.f.f \(10\) \(2.731\) 10.0.\(\cdots\).1 None \(10\) \(2\) \(-2\) \(-5\) \(q+q^{2}+(\beta _{1}+\beta _{8})q^{3}+q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
342.2.f.g \(18\) \(2.731\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-18\) \(0\) \(0\) \(5\) \(q-q^{2}-\beta _{9}q^{3}+q^{4}+(\beta _{4}-\beta _{16})q^{5}+\cdots\)
342.2.g.a \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(6\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)
342.2.g.b \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-8\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{7}+q^{8}+\cdots\)
342.2.g.c \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{7}+q^{8}+\cdots\)
342.2.g.d \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-4\) \(-6\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
342.2.g.e \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(6\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(2-2\zeta_{6})q^{5}+\cdots\)
342.2.g.f \(4\) \(2.731\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(2\) \(4\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
342.2.h.a \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-2\) \(3\) \(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
342.2.h.b \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(4\) \(0\) \(q-\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
342.2.h.c \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(0\) \(-4\) \(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
342.2.h.d \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(6\) \(1\) \(q-\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
342.2.h.e \(4\) \(2.731\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(2\) \(-12\) \(2\) \(q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
342.2.h.f \(10\) \(2.731\) 10.0.\(\cdots\).1 None \(-5\) \(-4\) \(4\) \(-5\) \(q+\beta _{4}q^{2}-\beta _{3}q^{3}+(-1-\beta _{4})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
342.2.h.g \(18\) \(2.731\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(9\) \(0\) \(0\) \(5\) \(q+\beta _{8}q^{2}+(\beta _{1}+\beta _{9})q^{3}+(-1+\beta _{8}+\cdots)q^{4}+\cdots\)
342.2.j.a \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(0\) \(-1\) \(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
342.2.j.b \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(0\) \(5\) \(q+\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
342.2.j.c \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-4\) \(q+\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
342.2.j.d \(8\) \(2.731\) 8.0.764411904.5 None \(4\) \(0\) \(0\) \(-8\) \(q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{6})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
342.2.j.e \(8\) \(2.731\) 8.0.152695449.1 None \(4\) \(5\) \(0\) \(6\) \(q+(1+\beta _{6})q^{2}+(1-\beta _{1}+\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots\)
342.2.j.f \(18\) \(2.731\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-9\) \(4\) \(0\) \(0\) \(q+\beta _{9}q^{2}+(\beta _{1}+\beta _{14})q^{3}+(-1-\beta _{9}+\cdots)q^{4}+\cdots\)
342.2.n.a \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-3\) \(-1\) \(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(-2+\zeta_{6})q^{5}+\cdots\)
342.2.n.b \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-6\) \(-4\) \(q+q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-4+2\zeta_{6})q^{5}+\cdots\)
342.2.n.c \(2\) \(2.731\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(5\) \(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{5}+\cdots\)
342.2.n.d \(8\) \(2.731\) 8.0.764411904.5 None \(8\) \(0\) \(12\) \(-8\) \(q+q^{2}+(-\beta _{1}+\beta _{4})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
342.2.n.e \(8\) \(2.731\) 8.0.152695449.1 None \(8\) \(4\) \(-9\) \(6\) \(q+q^{2}+(\beta _{3}-\beta _{6})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
342.2.n.f \(18\) \(2.731\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-18\) \(-1\) \(3\) \(0\) \(q-q^{2}+\beta _{14}q^{3}+q^{4}-\beta _{10}q^{5}-\beta _{14}q^{6}+\cdots\)
342.2.p.a \(20\) \(2.731\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-10\) \(1\) \(0\) \(2\) \(q+\beta _{5}q^{2}+(-\beta _{1}+\beta _{9})q^{3}+(-1-\beta _{5}+\cdots)q^{4}+\cdots\)
342.2.p.b \(20\) \(2.731\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(10\) \(-1\) \(0\) \(2\) \(q-\beta _{5}q^{2}+(\beta _{1}-\beta _{9})q^{3}+(-1-\beta _{5}+\cdots)q^{4}+\cdots\)
342.2.s.a \(4\) \(2.731\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(-4\) \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
342.2.s.b \(4\) \(2.731\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(-4\) \(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
342.2.u.a \(6\) \(2.731\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-9\) \(3\) \(q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(-1+\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
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