## Results (36 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
667.1.b.a $$1$$ $$0.333$$ $$\Q$$ $$\Q(\sqrt{-23})$$, $$\Q(\sqrt{-667})$$ $$\Q(\sqrt{29})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{4}+q^{9}-2q^{13}+q^{16}-q^{23}+\cdots$$
667.1.b.b $$2$$ $$0.333$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-23})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots$$
667.1.i.a $$6$$ $$0.333$$ $$\Q(\zeta_{14})$$ $$\Q(\sqrt{-23})$$ None $$5$$ $$-2$$ $$0$$ $$0$$ $$q+(1+\zeta_{14}^{4})q^{2}+(-\zeta_{14}-\zeta_{14}^{5})q^{3}+\cdots$$
667.1.i.b $$12$$ $$0.333$$ $$\Q(\zeta_{21})$$ $$\Q(\sqrt{-23})$$ None $$-5$$ $$2$$ $$0$$ $$0$$ $$q+(-\zeta_{42}+\zeta_{42}^{14})q^{2}+(\zeta_{42}^{16}-\zeta_{42}^{17}+\cdots)q^{3}+\cdots$$
667.1.k.a $$6$$ $$0.333$$ $$\Q(\zeta_{14})$$ $$\Q(\sqrt{-23})$$ None $$-7$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\zeta_{14}^{4})q^{2}+(-\zeta_{14}+\zeta_{14}^{5}+\cdots)q^{3}+\cdots$$
667.1.k.b $$12$$ $$0.333$$ $$\Q(\zeta_{21})$$ $$\Q(\sqrt{-23})$$ None $$7$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{42}^{7}+\zeta_{42}^{8})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{10}+\cdots)q^{3}+\cdots$$
667.2.a.a $$10$$ $$5.326$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$-3$$ $$-9$$ $$-10$$ $$1$$ $$+$$ $$q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
667.2.a.b $$12$$ $$5.326$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$-3$$ $$-3$$ $$-16$$ $$-7$$ $$+$$ $$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{4}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots$$
667.2.a.c $$13$$ $$5.326$$ $$\mathbb{Q}[x]/(x^{13} - \cdots)$$ None None $$4$$ $$3$$ $$16$$ $$1$$ $$-$$ $$q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$$
667.2.a.d $$16$$ $$5.326$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$3$$ $$5$$ $$16$$ $$1$$ $$-$$ $$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$$
667.2.c.a $$24$$ $$5.326$$ None None $$0$$ $$0$$ $$6$$ $$-14$$
667.2.c.b $$30$$ $$5.326$$ None None $$0$$ $$0$$ $$-2$$ $$6$$
667.2.f.a $$12$$ $$5.326$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-23})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{9}-\beta _{10})q^{2}+(-\beta _{3}+\beta _{8}+\cdots)q^{3}+\cdots$$
667.2.f.b $$104$$ $$5.326$$ None None $$-8$$ $$-4$$ $$0$$ $$0$$
667.2.g.a $$6$$ $$5.326$$ $$\Q(\zeta_{14})$$ None None $$-2$$ $$1$$ $$2$$ $$-13$$ $$q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$$
667.2.g.b $$144$$ $$5.326$$ None None $$1$$ $$-1$$ $$-2$$ $$19$$
667.2.g.c $$186$$ $$5.326$$ None None $$-1$$ $$0$$ $$-8$$ $$-14$$
667.2.h.a $$280$$ $$5.326$$ None None $$0$$ $$-2$$ $$-8$$ $$-10$$
667.2.h.b $$280$$ $$5.326$$ None None $$0$$ $$-2$$ $$0$$ $$6$$
667.2.j.a $$144$$ $$5.326$$ None None $$0$$ $$0$$ $$-6$$ $$14$$
667.2.j.b $$180$$ $$5.326$$ None None $$0$$ $$0$$ $$2$$ $$-6$$
667.2.m.a $$580$$ $$5.326$$ None None $$0$$ $$0$$ $$-14$$ $$-22$$
667.2.o.a $$72$$ $$5.326$$ $$\Q(\sqrt{-23})$$ None $$0$$ $$0$$ $$0$$ $$0$$
667.2.o.b $$624$$ $$5.326$$ None None $$-20$$ $$-24$$ $$0$$ $$0$$
667.2.q.a $$1160$$ $$5.326$$ None None $$-14$$ $$-18$$ $$0$$ $$-44$$
667.2.s.a $$3480$$ $$5.326$$ None None $$-49$$ $$-45$$ $$-49$$ $$-49$$
667.2.u.a $$3480$$ $$5.326$$ None None $$-63$$ $$-63$$ $$-49$$ $$-41$$
667.2.x.a $$6960$$ $$5.326$$ None None $$-112$$ $$-108$$ $$-154$$ $$-110$$
667.4.a.a $$35$$ $$39.354$$ None None $$-6$$ $$-22$$ $$-80$$ $$-38$$ $$-$$
667.4.a.b $$38$$ $$39.354$$ None None $$-8$$ $$-16$$ $$-80$$ $$-38$$ $$-$$
667.4.a.c $$39$$ $$39.354$$ None None $$6$$ $$2$$ $$80$$ $$18$$ $$+$$
667.4.a.d $$42$$ $$39.354$$ None None $$12$$ $$32$$ $$80$$ $$18$$ $$+$$
667.6.a.a $$61$$ $$106.976$$ None None $$-24$$ $$-97$$ $$-400$$ $$-243$$ $$+$$
667.6.a.b $$64$$ $$106.976$$ None None $$-12$$ $$-7$$ $$-400$$ $$-243$$ $$+$$
667.6.a.c $$65$$ $$106.976$$ None None $$16$$ $$47$$ $$400$$ $$149$$ $$-$$
667.6.a.d $$68$$ $$106.976$$ None None $$12$$ $$65$$ $$400$$ $$149$$ $$-$$