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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
798.2.a.a \(1\) \(6.372\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
798.2.a.b \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
798.2.a.c \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(-2\) \(1\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
798.2.a.d \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
798.2.a.e \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(2\) \(-1\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
798.2.a.f \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(4\) \(1\) \(-\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}+q^{7}+\cdots\)
798.2.a.g \(1\) \(6.372\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
798.2.a.h \(1\) \(6.372\) \(\Q\) None \(1\) \(1\) \(-4\) \(-1\) \(+\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
798.2.a.i \(1\) \(6.372\) \(\Q\) None \(1\) \(1\) \(2\) \(-1\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
798.2.a.j \(2\) \(6.372\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(2\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
798.2.a.k \(2\) \(6.372\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(-2\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
798.2.a.l \(2\) \(6.372\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(2\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
798.2.a.m \(2\) \(6.372\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
798.2.b.a \(2\) \(6.372\) \(\Q(\sqrt{-2}) \) None \(-2\) \(-2\) \(0\) \(2\) \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
798.2.b.b \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(-2\) \(q-q^{2}+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{6}-q^{7}+\cdots\)
798.2.b.c \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}-q^{7}+\cdots\)
798.2.b.d \(2\) \(6.372\) \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(0\) \(2\) \(q+q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(1-\beta )q^{6}+\cdots\)
798.2.b.e \(8\) \(6.372\) 8.0.\(\cdots\).1 None \(-8\) \(-1\) \(0\) \(-8\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
798.2.b.f \(8\) \(6.372\) 8.0.5240022544.1 None \(-8\) \(1\) \(0\) \(8\) \(q-q^{2}+\beta _{5}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{5}q^{6}+\cdots\)
798.2.b.g \(8\) \(6.372\) 8.0.5240022544.1 None \(8\) \(-1\) \(0\) \(8\) \(q+q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{5}q^{6}+\cdots\)
798.2.b.h \(8\) \(6.372\) 8.0.\(\cdots\).1 None \(8\) \(1\) \(0\) \(-8\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
798.2.e.a \(12\) \(6.372\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(0\) \(0\) \(q+\beta _{4}q^{2}-q^{3}-q^{4}-\beta _{2}q^{5}-\beta _{4}q^{6}+\cdots\)
798.2.e.b \(12\) \(6.372\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(12\) \(0\) \(0\) \(q-\beta _{4}q^{2}+q^{3}-q^{4}-\beta _{2}q^{5}-\beta _{4}q^{6}+\cdots\)
798.2.f.a \(24\) \(6.372\) None \(0\) \(0\) \(0\) \(-2\)
798.2.f.b \(24\) \(6.372\) None \(0\) \(0\) \(0\) \(-2\)
798.2.i.a \(14\) \(6.372\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-7\) \(-14\) \(2\) \(4\) \(q+(-1-\beta _{8})q^{2}-q^{3}+\beta _{8}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
798.2.i.b \(14\) \(6.372\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-7\) \(14\) \(0\) \(6\) \(q+(-1-\beta _{3})q^{2}+q^{3}+\beta _{3}q^{4}-\beta _{1}q^{5}+\cdots\)
798.2.i.c \(14\) \(6.372\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(7\) \(-14\) \(-4\) \(0\) \(q-\beta _{4}q^{2}-q^{3}+(-1-\beta _{4})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
798.2.i.d \(14\) \(6.372\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(7\) \(14\) \(-2\) \(-6\) \(q+(1-\beta _{6})q^{2}+q^{3}-\beta _{6}q^{4}-\beta _{7}q^{5}+\cdots\)
798.2.j.a \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.b \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.c \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.d \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.e \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.f \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.g \(4\) \(6.372\) \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(-4\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(1-\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
798.2.j.h \(4\) \(6.372\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(6\) \(-2\) \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
798.2.j.i \(6\) \(6.372\) 6.0.4406832.1 None \(-3\) \(-3\) \(5\) \(-1\) \(q-\beta _{4}q^{2}+(-1+\beta _{4})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
798.2.j.j \(6\) \(6.372\) 6.0.4406832.1 None \(3\) \(3\) \(-1\) \(-1\) \(q+\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
798.2.j.k \(8\) \(6.372\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(-4\) \(-2\) \(-2\) \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
798.2.j.l \(8\) \(6.372\) 8.0.856615824.2 None \(4\) \(4\) \(0\) \(-2\) \(q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
798.2.k.a \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-3\) \(2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.b \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.c \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.d \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.e \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.f \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.g \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.h \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.i \(2\) \(6.372\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(3\) \(-2\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
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