Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 3 5 89
4005.2.a.r $$10$$ $$31.980$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-6$$ $$0$$ $$-10$$ $$7$$ $$-$$ $$+$$ $$+$$ $$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$$
4005.2.a.s $$10$$ $$31.980$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-1$$ $$0$$ $$-10$$ $$-1$$ $$-$$ $$+$$ $$-$$ $$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{6}q^{7}+\cdots$$
4005.2.a.t $$10$$ $$31.980$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$0$$ $$10$$ $$9$$ $$-$$ $$-$$ $$-$$ $$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$$