## Results (1-50 of 51 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
712.1.c.a $$1$$ $$0.355$$ $$\Q$$ $$\Q(\sqrt{-2})$$, $$\Q(\sqrt{-178})$$ $$\Q(\sqrt{89})$$ $$1$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}+q^{8}+q^{9}-2q^{11}+q^{16}+\cdots$$
712.1.c.b $$2$$ $$0.355$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-178})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-\beta q^{7}-q^{8}+q^{9}+\beta q^{13}+\cdots$$
712.1.l.a $$2$$ $$0.355$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$2$$ $$0$$ $$0$$ $$q-q^{2}+(1-i)q^{3}+q^{4}+(-1+i)q^{6}+\cdots$$
712.1.s.a $$10$$ $$0.355$$ $$\Q(\zeta_{22})$$ $$\Q(\sqrt{-2})$$ None $$-1$$ $$-2$$ $$0$$ $$0$$ $$q-\zeta_{22}^{5}q^{2}+(\zeta_{22}^{4}-\zeta_{22}^{9})q^{3}+\zeta_{22}^{10}q^{4}+\cdots$$
712.1.w.a $$10$$ $$0.355$$ $$\Q(\zeta_{22})$$ $$\Q(\sqrt{-2})$$ None $$-1$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{22}^{9}q^{2}+(\zeta_{22}^{3}-\zeta_{22}^{5})q^{3}-\zeta_{22}^{7}q^{4}+\cdots$$
712.1.y.a $$20$$ $$0.355$$ $$\Q(\zeta_{44})$$ $$\Q(\sqrt{-2})$$ None $$2$$ $$-2$$ $$0$$ $$0$$ $$q-\zeta_{44}^{20}q^{2}+(-\zeta_{44}^{3}+\zeta_{44}^{16})q^{3}+\cdots$$
712.2.a.a $$1$$ $$5.685$$ $$\Q$$ None None $$0$$ $$-2$$ $$2$$ $$-4$$ $$-$$ $$q-2q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{13}+\cdots$$
712.2.a.b $$3$$ $$5.685$$ 3.3.148.1 None None $$0$$ $$-1$$ $$-3$$ $$-2$$ $$+$$ $$q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$$
712.2.a.c $$5$$ $$5.685$$ 5.5.758752.1 None None $$0$$ $$3$$ $$1$$ $$2$$ $$-$$ $$q+(1-\beta _{1})q^{3}+(-\beta _{1}+\beta _{3}+\beta _{4})q^{5}+\cdots$$
712.2.a.d $$6$$ $$5.685$$ 6.6.20603984.1 None None $$0$$ $$-5$$ $$-3$$ $$-2$$ $$+$$ $$q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{5})q^{5}+\cdots$$
712.2.a.e $$7$$ $$5.685$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$0$$ $$3$$ $$3$$ $$6$$ $$-$$ $$q+\beta _{1}q^{3}+\beta _{5}q^{5}+(1+\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots$$
712.2.b.a $$2$$ $$5.685$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta q^{2}+\beta q^{3}-2q^{4}+2\beta q^{5}-2q^{6}+\cdots$$
712.2.b.b $$2$$ $$5.685$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}-\beta q^{3}-2q^{4}-2\beta q^{5}+2q^{6}+\cdots$$
712.2.b.c $$4$$ $$5.685$$ 4.0.2312.1 None None $$-1$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
712.2.b.d $$36$$ $$5.685$$ None None $$0$$ $$0$$ $$0$$ $$-16$$
712.2.b.e $$44$$ $$5.685$$ None None $$-1$$ $$0$$ $$0$$ $$20$$
712.2.e.a $$2$$ $$5.685$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$6$$ $$0$$ $$q+iq^{3}+3q^{5}+4iq^{7}+2q^{9}+4q^{11}+\cdots$$
712.2.e.b $$10$$ $$5.685$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{8})q^{7}+\cdots$$
712.2.e.c $$10$$ $$5.685$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{8}q^{7}+(-1-\beta _{5}+\cdots)q^{9}+\cdots$$
712.2.f.a $$88$$ $$5.685$$ None None $$-2$$ $$0$$ $$0$$ $$0$$
712.2.j.a $$2$$ $$5.685$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$0$$ $$2$$ $$q+(-1-i)q^{3}+(1+i)q^{7}-iq^{9}+4q^{11}+\cdots$$
712.2.j.b $$22$$ $$5.685$$ None None $$0$$ $$-4$$ $$0$$ $$4$$
712.2.j.c $$22$$ $$5.685$$ None None $$0$$ $$4$$ $$0$$ $$-6$$
712.2.k.a $$4$$ $$5.685$$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$-2$$ $$-12$$ $$4$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
712.2.k.b $$4$$ $$5.685$$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$2$$ $$12$$ $$4$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}+(\zeta_{12}+\cdots)q^{4}+\cdots$$
712.2.k.c $$168$$ $$5.685$$ None None $$0$$ $$0$$ $$0$$ $$-12$$
712.2.m.a $$4$$ $$5.685$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-8$$ $$0$$ $$0$$ $$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+(-2-2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$$
712.2.m.b $$4$$ $$5.685$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$$
712.2.m.c $$344$$ $$5.685$$ None None $$-8$$ $$0$$ $$0$$ $$0$$
712.2.q.a $$110$$ $$5.685$$ None None $$0$$ $$0$$ $$-2$$ $$0$$
712.2.q.b $$110$$ $$5.685$$ None None $$0$$ $$2$$ $$2$$ $$0$$
712.2.t.a $$880$$ $$5.685$$ None None $$-9$$ $$0$$ $$0$$ $$-22$$
712.2.u.a $$100$$ $$5.685$$ None None $$0$$ $$0$$ $$0$$ $$0$$
712.2.u.b $$120$$ $$5.685$$ None None $$0$$ $$0$$ $$-4$$ $$0$$
712.2.x.a $$880$$ $$5.685$$ None None $$-9$$ $$0$$ $$0$$ $$-18$$
712.2.z.a $$1760$$ $$5.685$$ None None $$-18$$ $$0$$ $$0$$ $$-40$$
712.2.ba.a $$220$$ $$5.685$$ None None $$0$$ $$4$$ $$0$$ $$-4$$
712.2.ba.b $$240$$ $$5.685$$ None None $$0$$ $$-2$$ $$0$$ $$4$$
712.2.bf.a $$40$$ $$5.685$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$
712.2.bf.b $$40$$ $$5.685$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$8$$ $$0$$ $$0$$
712.2.bf.c $$3440$$ $$5.685$$ None None $$-36$$ $$-88$$ $$0$$ $$0$$
712.4.a.a $$14$$ $$42.009$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None None $$0$$ $$-3$$ $$-17$$ $$-28$$ $$-$$ $$q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+(-2-\beta _{6}+\cdots)q^{7}+\cdots$$
712.4.a.b $$16$$ $$42.009$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$15$$ $$7$$ $$4$$ $$+$$ $$q+(1-\beta _{1})q^{3}-\beta _{4}q^{5}+\beta _{6}q^{7}+(10+\cdots)q^{9}+\cdots$$
712.4.a.c $$17$$ $$42.009$$ $$\mathbb{Q}[x]/(x^{17} - \cdots)$$ None None $$0$$ $$-9$$ $$-13$$ $$-24$$ $$-$$ $$q+(-1+\beta _{1})q^{3}+(-1+\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots$$
712.4.a.d $$19$$ $$42.009$$ $$\mathbb{Q}[x]/(x^{19} - \cdots)$$ None None $$0$$ $$3$$ $$23$$ $$0$$ $$+$$ $$q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}-\beta _{3}q^{7}+(12+\cdots)q^{9}+\cdots$$
712.4.e.a $$34$$ $$42.009$$ None None $$0$$ $$0$$ $$-16$$ $$0$$
712.4.e.b $$34$$ $$42.009$$ None None $$0$$ $$0$$ $$-8$$ $$0$$
712.6.a.a $$25$$ $$114.193$$ None None $$0$$ $$-9$$ $$-131$$ $$-48$$ $$+$$
712.6.a.b $$27$$ $$114.193$$ None None $$0$$ $$27$$ $$81$$ $$72$$ $$-$$
712.6.a.c $$28$$ $$114.193$$ None None $$0$$ $$-45$$ $$-19$$ $$-124$$ $$+$$