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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
770.2.a.a \(1\) \(6.148\) \(\Q\) None \(-1\) \(-2\) \(-1\) \(1\) \(-\) \(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
770.2.a.b \(1\) \(6.148\) \(\Q\) None \(-1\) \(-2\) \(1\) \(-1\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
770.2.a.c \(1\) \(6.148\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
770.2.a.d \(1\) \(6.148\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
770.2.a.e \(1\) \(6.148\) \(\Q\) None \(-1\) \(2\) \(-1\) \(1\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
770.2.a.f \(1\) \(6.148\) \(\Q\) None \(1\) \(-2\) \(-1\) \(1\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
770.2.a.g \(1\) \(6.148\) \(\Q\) None \(1\) \(-2\) \(1\) \(1\) \(-\) \(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
770.2.a.h \(2\) \(6.148\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(2\) \(-\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
770.2.a.i \(2\) \(6.148\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(-2\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{7}+\cdots\)
770.2.a.j \(2\) \(6.148\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-2\) \(2\) \(-\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(1+\beta )q^{6}+\cdots\)
770.2.a.k \(2\) \(6.148\) \(\Q(\sqrt{33}) \) None \(2\) \(4\) \(2\) \(2\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
770.2.a.l \(3\) \(6.148\) 3.3.892.1 None \(-3\) \(0\) \(-3\) \(-3\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
770.2.a.m \(3\) \(6.148\) 3.3.316.1 None \(3\) \(2\) \(3\) \(-3\) \(-\) \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+q^{5}+(1+\beta _{2})q^{6}+\cdots\)
770.2.c.a \(2\) \(6.148\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{2}-q^{4}+(-2+i)q^{5}-iq^{7}+\cdots\)
770.2.c.b \(2\) \(6.148\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-q^{4}+(1-2i)q^{5}-iq^{7}+iq^{8}+\cdots\)
770.2.c.c \(2\) \(6.148\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}-q^{4}+(2-i)q^{5}+iq^{7}-iq^{8}+\cdots\)
770.2.c.d \(4\) \(6.148\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-1-2\beta _{1}+\cdots)q^{5}+\cdots\)
770.2.c.e \(8\) \(6.148\) 8.0.1698758656.6 None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{5}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
770.2.c.f \(10\) \(6.148\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{4}q^{2}+\beta _{7}q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)
770.2.e.a \(16\) \(6.148\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{10}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{10}q^{5}+\cdots\)
770.2.e.b \(16\) \(6.148\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{10}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{10}q^{5}+\cdots\)
770.2.g.a \(24\) \(6.148\) None \(-24\) \(0\) \(0\) \(2\)
770.2.g.b \(24\) \(6.148\) None \(24\) \(0\) \(0\) \(-2\)
770.2.i.a \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.b \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.c \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.d \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.e \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.f \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.g \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.h \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.i \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.j \(6\) \(6.148\) \(\Q(\zeta_{18})\) None \(3\) \(0\) \(-3\) \(0\) \(q+(1-\zeta_{18}^{3})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
770.2.i.k \(6\) \(6.148\) 6.0.64827.1 None \(3\) \(0\) \(3\) \(0\) \(q+(1-\beta _{5})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
770.2.i.l \(8\) \(6.148\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(1\) \(4\) \(3\) \(q+(-1-\beta _{5})q^{2}+\beta _{1}q^{3}+\beta _{5}q^{4}+(1+\cdots)q^{5}+\cdots\)
770.2.i.m \(10\) \(6.148\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-5\) \(0\) \(-5\) \(0\) \(q+(-1+\beta _{6})q^{2}+(\beta _{1}-\beta _{2})q^{3}-\beta _{6}q^{4}+\cdots\)
770.2.l.a \(16\) \(6.148\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}+\beta _{1}q^{3}-\beta _{8}q^{4}+(\beta _{2}+\beta _{13}+\cdots)q^{5}+\cdots\)
770.2.l.b \(24\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)
770.2.l.c \(40\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)
770.2.m.a \(4\) \(6.148\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-2-\zeta_{8}^{2})q^{5}+\cdots\)
770.2.m.b \(4\) \(6.148\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+2\zeta_{8}^{2})q^{5}+\cdots\)
770.2.m.c \(4\) \(6.148\) \(\Q(\zeta_{8})\) None \(0\) \(8\) \(-4\) \(0\) \(q+\zeta_{8}q^{2}+(2+2\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
770.2.m.d \(8\) \(6.148\) 8.0.40960000.1 None \(0\) \(-4\) \(16\) \(0\) \(q-\beta _{7}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots\)
770.2.m.e \(16\) \(6.148\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-8\) \(-8\) \(0\) \(q-\beta _{10}q^{2}+(-1-\beta _{3}+\beta _{7}-\beta _{15})q^{3}+\cdots\)
770.2.m.f \(36\) \(6.148\) None \(0\) \(-4\) \(0\) \(0\)
770.2.n.a \(4\) \(6.148\) \(\Q(\zeta_{10})\) None \(-1\) \(-3\) \(-1\) \(-1\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
770.2.n.b \(4\) \(6.148\) \(\Q(\zeta_{10})\) None \(1\) \(-4\) \(1\) \(1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
770.2.n.c \(4\) \(6.148\) \(\Q(\zeta_{10})\) None \(1\) \(-2\) \(1\) \(-1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
770.2.n.d \(4\) \(6.148\) \(\Q(\zeta_{10})\) None \(1\) \(2\) \(1\) \(-1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots\)
770.2.n.e \(8\) \(6.148\) 8.0.682515625.5 None \(2\) \(-1\) \(2\) \(2\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{4}-\beta _{6})q^{3}+\beta _{3}q^{4}+\cdots\)
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