## Results (1-50 of 69 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
639.1.d.a $$3$$ $$0.319$$ $$\Q(\zeta_{14})^+$$ $$\Q(\sqrt{-71})$$ None $$1$$ $$0$$ $$1$$ $$0$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+(1+\beta _{2})q^{8}+\cdots$$
639.1.g.a $$2$$ $$0.319$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-71})$$ None $$1$$ $$-1$$ $$-2$$ $$0$$ $$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{5}-q^{6}+q^{8}+\cdots$$
639.1.g.b $$12$$ $$0.319$$ $$\Q(\zeta_{21})$$ $$\Q(\sqrt{-71})$$ None $$-1$$ $$1$$ $$2$$ $$0$$ $$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}-\zeta_{42}^{19}q^{3}+\cdots$$
639.2.a.a $$1$$ $$5.102$$ $$\Q$$ None None $$-1$$ $$0$$ $$-2$$ $$2$$ $$+$$ $$q-q^{2}-q^{4}-2q^{5}+2q^{7}+3q^{8}+2q^{10}+\cdots$$
639.2.a.b $$2$$ $$5.102$$ $$\Q(\sqrt{2})$$ None None $$-2$$ $$0$$ $$0$$ $$-4$$ $$+$$ $$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots$$
639.2.a.c $$2$$ $$5.102$$ $$\Q(\sqrt{13})$$ None None $$-1$$ $$0$$ $$1$$ $$-2$$ $$+$$ $$q-\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}-q^{7}-3q^{8}+\cdots$$
639.2.a.d $$2$$ $$5.102$$ $$\Q(\sqrt{5})$$ None None $$1$$ $$0$$ $$-1$$ $$-6$$ $$+$$ $$q+\beta q^{2}+(-1+\beta )q^{4}-\beta q^{5}-3q^{7}+\cdots$$
639.2.a.e $$2$$ $$5.102$$ $$\Q(\sqrt{2})$$ None None $$2$$ $$0$$ $$0$$ $$-4$$ $$-$$ $$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(-2+\cdots)q^{7}+\cdots$$
639.2.a.f $$2$$ $$5.102$$ $$\Q(\sqrt{5})$$ None None $$3$$ $$0$$ $$5$$ $$-4$$ $$-$$ $$q+(1+\beta )q^{2}+3\beta q^{4}+(3-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$$
639.2.a.g $$3$$ $$5.102$$ 3.3.257.1 None None $$0$$ $$0$$ $$3$$ $$2$$ $$-$$ $$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$$
639.2.a.h $$3$$ $$5.102$$ 3.3.257.1 None None $$1$$ $$0$$ $$-5$$ $$2$$ $$-$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2+\beta _{1}+\beta _{2})q^{5}+\cdots$$
639.2.a.i $$4$$ $$5.102$$ 4.4.2225.1 None None $$-3$$ $$0$$ $$3$$ $$6$$ $$-$$ $$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$$
639.2.a.j $$4$$ $$5.102$$ 4.4.8112.1 None None $$0$$ $$0$$ $$-8$$ $$2$$ $$+$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2-\beta _{1})q^{5}+\cdots$$
639.2.a.k $$4$$ $$5.102$$ 4.4.8112.1 None None $$0$$ $$0$$ $$8$$ $$2$$ $$-$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots$$
639.2.b.a $$24$$ $$5.102$$ None None $$0$$ $$0$$ $$0$$ $$0$$
639.2.e.a $$4$$ $$5.102$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$-3$$ $$0$$ $$-4$$ $$4$$ $$q+(-1-\beta _{1}-\beta _{3})q^{2}+(-1-2\beta _{3})q^{3}+\cdots$$
639.2.e.b $$56$$ $$5.102$$ None None $$-1$$ $$-1$$ $$-2$$ $$11$$
639.2.e.c $$80$$ $$5.102$$ None None $$2$$ $$-1$$ $$2$$ $$-17$$
639.2.f.a $$4$$ $$5.102$$ $$\Q(\zeta_{10})$$ None None $$-3$$ $$0$$ $$8$$ $$3$$ $$q+(-1+\zeta_{10}^{3})q^{2}+(1-\zeta_{10})q^{4}+(3\zeta_{10}+\cdots)q^{5}+\cdots$$
639.2.f.b $$20$$ $$5.102$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None None $$0$$ $$0$$ $$-10$$ $$-3$$ $$q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{13}+\beta _{15}+\cdots)q^{4}+\cdots$$
639.2.f.c $$20$$ $$5.102$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$6$$ $$0$$ $$1$$ $$-1$$ $$q+\beta _{14}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$$
639.2.f.d $$24$$ $$5.102$$ None None $$-3$$ $$0$$ $$2$$ $$-4$$
639.2.f.e $$48$$ $$5.102$$ None None $$0$$ $$0$$ $$0$$ $$4$$
639.2.i.a $$28$$ $$5.102$$ $$\Q(\sqrt{-71})$$ None $$0$$ $$0$$ $$0$$ $$0$$
639.2.i.b $$112$$ $$5.102$$ None None $$-6$$ $$-2$$ $$0$$ $$0$$
639.2.j.a $$6$$ $$5.102$$ $$\Q(\zeta_{14})$$ None None $$-3$$ $$0$$ $$6$$ $$-8$$ $$q+(\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4})q^{2}+(1-\zeta_{14}^{2}+\cdots)q^{4}+\cdots$$
639.2.j.b $$6$$ $$5.102$$ $$\Q(\zeta_{14})$$ None None $$3$$ $$0$$ $$-6$$ $$-8$$ $$q+(-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4})q^{2}+(1+\cdots)q^{4}+\cdots$$
639.2.j.c $$30$$ $$5.102$$ None None $$3$$ $$0$$ $$10$$ $$-3$$
639.2.j.d $$36$$ $$5.102$$ None None $$2$$ $$0$$ $$-2$$ $$0$$
639.2.j.e $$36$$ $$5.102$$ None None $$2$$ $$0$$ $$2$$ $$-4$$
639.2.j.f $$60$$ $$5.102$$ None None $$0$$ $$0$$ $$0$$ $$20$$
639.2.m.a $$96$$ $$5.102$$ None None $$0$$ $$0$$ $$0$$ $$0$$
639.2.p.a $$144$$ $$5.102$$ None None $$0$$ $$0$$ $$0$$ $$0$$
639.2.q.a $$560$$ $$5.102$$ None None $$-3$$ $$-8$$ $$-1$$ $$-3$$
639.2.r.a $$840$$ $$5.102$$ None None $$-5$$ $$-5$$ $$-10$$ $$-5$$
639.2.s.a $$560$$ $$5.102$$ None None $$-9$$ $$-8$$ $$-15$$ $$-5$$
639.2.v.a $$120$$ $$5.102$$ None None $$22$$ $$0$$ $$20$$ $$-27$$
639.2.v.b $$144$$ $$5.102$$ None None $$3$$ $$0$$ $$-2$$ $$4$$
639.2.v.c $$144$$ $$5.102$$ None None $$3$$ $$0$$ $$2$$ $$0$$
639.2.v.d $$288$$ $$5.102$$ None None $$0$$ $$0$$ $$0$$ $$-4$$
639.2.w.a $$840$$ $$5.102$$ None None $$-15$$ $$-5$$ $$-42$$ $$-7$$
639.2.z.a $$576$$ $$5.102$$ None None $$0$$ $$0$$ $$0$$ $$0$$
639.2.bc.a $$3360$$ $$5.102$$ None None $$-25$$ $$-55$$ $$-20$$ $$-25$$
639.2.bf.a $$3360$$ $$5.102$$ None None $$-75$$ $$-55$$ $$-48$$ $$-23$$
639.3.c.a $$48$$ $$17.411$$ None None $$0$$ $$0$$ $$0$$ $$0$$
639.3.d.a $$4$$ $$17.411$$ 4.0.2836736.1 None None $$4$$ $$0$$ $$8$$ $$0$$ $$q+(1+\beta _{1})q^{2}+(-1+2\beta _{1})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$$
639.3.d.b $$7$$ $$17.411$$ 7.7.$$\cdots$$.1 $$\Q(\sqrt{-71})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(4+\beta _{3})q^{4}+(\beta _{3}+\beta _{4})q^{5}+\cdots$$
639.3.d.c $$24$$ $$17.411$$ None None $$-4$$ $$0$$ $$0$$ $$0$$
639.3.d.d $$24$$ $$17.411$$ None None $$0$$ $$0$$ $$0$$ $$0$$
639.4.a.a $$1$$ $$37.702$$ $$\Q$$ None None $$-5$$ $$0$$ $$-13$$ $$-7$$ $$+$$ $$q-5q^{2}+17q^{4}-13q^{5}-7q^{7}-45q^{8}+\cdots$$