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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 11
847.2.a.c \(1\) \(6.763\) \(\Q\) None \(0\) \(1\) \(3\) \(-1\) \(+\) \(-\) \(q+q^{3}-2q^{4}+3q^{5}-q^{7}-2q^{9}-2q^{12}+\cdots\)
847.2.a.f \(2\) \(6.763\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-4\) \(-2\) \(+\) \(-\) \(q-\beta q^{2}+(1-\beta )q^{3}+3q^{4}-2q^{5}+(5+\cdots)q^{6}+\cdots\)
847.2.a.g \(2\) \(6.763\) \(\Q(\sqrt{13}) \) None \(1\) \(-1\) \(0\) \(-2\) \(+\) \(-\) \(q+\beta q^{2}-\beta q^{3}+(1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
847.2.a.h \(2\) \(6.763\) \(\Q(\sqrt{5}) \) None \(3\) \(-1\) \(2\) \(-2\) \(+\) \(-\) \(q+(1+\beta )q^{2}+(-1+\beta )q^{3}+3\beta q^{4}+\cdots\)
847.2.a.o \(8\) \(6.763\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(4\) \(10\) \(-8\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1-\beta _{4}-\beta _{7})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)
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