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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 41
2009.2.a.b \(2\) \(16.042\) \(\Q(\sqrt{5}) \) None \(-1\) \(3\) \(1\) \(0\) \(-\) \(+\) \(q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
2009.2.a.g \(3\) \(16.042\) 3.3.148.1 None \(-1\) \(0\) \(2\) \(0\) \(-\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
2009.2.a.h \(3\) \(16.042\) 3.3.257.1 None \(0\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
2009.2.a.k \(3\) \(16.042\) \(\Q(\zeta_{14})^+\) None \(4\) \(-5\) \(-2\) \(0\) \(-\) \(+\) \(q+(1+\beta _{1})q^{2}+(-2+\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
2009.2.a.o \(6\) \(16.042\) 6.6.185257757.1 None \(-1\) \(4\) \(1\) \(0\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
2009.2.a.q \(7\) \(16.042\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(7\) \(4\) \(0\) \(-\) \(+\) \(q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
2009.2.a.r \(17\) \(16.042\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(3\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots\)
2009.2.a.s \(17\) \(16.042\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(3\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots\)
2009.2.a.u \(20\) \(16.042\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(8\) \(8\) \(0\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{18}q^{5}+\cdots\)
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