Results (1-50 of 123 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
68.1.d.a $$1$$ $$0.034$$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-17})$$ $$\Q(\sqrt{17})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots$$
68.1.f.a $$2$$ $$0.034$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$$
68.2.a.a $$2$$ $$0.543$$ $$\Q(\sqrt{3})$$ None None $$0$$ $$2$$ $$0$$ $$-2$$ $$-$$ $$q+(1+\beta )q^{3}-2\beta q^{5}+(-1-\beta )q^{7}+\cdots$$
68.2.b.a $$2$$ $$0.543$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}+2\beta q^{5}-3\beta q^{7}+q^{9}-\beta q^{11}+\cdots$$
68.2.e.a $$4$$ $$0.543$$ $$\Q(i, \sqrt{13})$$ None None $$0$$ $$-2$$ $$-4$$ $$2$$ $$q+(-1+\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots$$
68.2.h.a $$4$$ $$0.543$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(1-\zeta_{8})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots$$
68.2.i.a $$8$$ $$0.543$$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{16}+\zeta_{16}^{5})q^{2}-2\zeta_{16}^{6}q^{4}+\cdots$$
68.2.i.b $$48$$ $$0.543$$ None None $$-8$$ $$0$$ $$-16$$ $$0$$
68.3.c.a $$16$$ $$1.853$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}-\beta _{12}q^{3}+\beta _{10}q^{4}-\beta _{2}q^{5}+\cdots$$
68.3.d.a $$2$$ $$1.853$$ $$\Q(\sqrt{34})$$ $$\Q(\sqrt{-17})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}-\beta q^{7}+\cdots$$
68.3.d.b $$2$$ $$1.853$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-17})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}-9\beta q^{7}+\cdots$$
68.3.d.c $$12$$ $$1.853$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(-1-\beta _{3})q^{4}-\beta _{6}q^{5}+\cdots$$
68.3.f.a $$32$$ $$1.853$$ None None $$0$$ $$0$$ $$-8$$ $$0$$
68.3.g.a $$4$$ $$1.853$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-2\zeta_{8}^{2}q^{2}+(-2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{3}+\cdots$$
68.3.g.b $$4$$ $$1.853$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-16$$ $$0$$ $$q-2\zeta_{8}^{3}q^{2}-4\zeta_{8}^{2}q^{4}+(-4+4\zeta_{8}+\cdots)q^{5}+\cdots$$
68.3.g.c $$4$$ $$1.853$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$16$$ $$0$$ $$q+2\zeta_{8}^{3}q^{2}-4\zeta_{8}^{2}q^{4}+(4-4\zeta_{8}-3\zeta_{8}^{2}+\cdots)q^{5}+\cdots$$
68.3.g.d $$4$$ $$1.853$$ $$\Q(\zeta_{8})$$ None None $$8$$ $$0$$ $$-8$$ $$0$$ $$q+2q^{2}+(2\zeta_{8}^{2}+2\zeta_{8}^{3})q^{3}+4q^{4}+\cdots$$
68.3.g.e $$48$$ $$1.853$$ None None $$-12$$ $$0$$ $$8$$ $$0$$
68.3.j.a $$24$$ $$1.853$$ None None $$0$$ $$0$$ $$0$$ $$0$$
68.4.a.a $$1$$ $$4.012$$ $$\Q$$ None None $$0$$ $$-2$$ $$-8$$ $$-12$$ $$-$$ $$q-2q^{3}-8q^{5}-12q^{7}-23q^{9}-10q^{11}+\cdots$$
68.4.a.b $$3$$ $$4.012$$ 3.3.1524.1 None None $$0$$ $$4$$ $$26$$ $$8$$ $$+$$ $$q+(1+\beta _{2})q^{3}+(9-\beta _{1})q^{5}+(2+3\beta _{1}+\cdots)q^{7}+\cdots$$
68.4.b.a $$4$$ $$4.012$$ 4.0.1499912.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-15+\cdots)q^{9}+\cdots$$
68.4.e.a $$2$$ $$4.012$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-8$$ $$-2$$ $$-40$$ $$q+(-4-4i)q^{3}+(-1-i)q^{5}+(-20+\cdots)q^{7}+\cdots$$
68.4.e.b $$6$$ $$4.012$$ 6.0.27793984.1 None None $$0$$ $$6$$ $$0$$ $$44$$ $$q+(1+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{2}+\beta _{3}-3\beta _{5})q^{5}+\cdots$$
68.4.h.a $$20$$ $$4.012$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None None $$0$$ $$0$$ $$-16$$ $$0$$ $$q+\beta _{6}q^{3}+(-1-\beta _{8}-\beta _{9}+\beta _{10}+\beta _{14}+\cdots)q^{5}+\cdots$$
68.4.i.a $$8$$ $$4.012$$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\zeta_{16}-2\zeta_{16}^{5})q^{2}-8\zeta_{16}^{6}q^{4}+\cdots$$
68.4.i.b $$192$$ $$4.012$$ None None $$-8$$ $$0$$ $$-16$$ $$0$$
68.5.c.a $$32$$ $$7.029$$ None None $$6$$ $$0$$ $$0$$ $$0$$
68.5.d.a $$1$$ $$7.029$$ $$\Q$$ $$\Q(\sqrt{-17})$$ None $$4$$ $$-16$$ $$0$$ $$64$$ $$q+4q^{2}-2^{4}q^{3}+2^{4}q^{4}-2^{6}q^{6}+2^{6}q^{7}+\cdots$$
68.5.d.b $$1$$ $$7.029$$ $$\Q$$ $$\Q(\sqrt{-17})$$ None $$4$$ $$16$$ $$0$$ $$-64$$ $$q+4q^{2}+2^{4}q^{3}+2^{4}q^{4}+2^{6}q^{6}-2^{6}q^{7}+\cdots$$
68.5.d.c $$2$$ $$7.029$$ $$\Q(\sqrt{17})$$ $$\Q(\sqrt{-17})$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q-4q^{2}-\beta q^{3}+2^{4}q^{4}+4\beta q^{6}-9\beta q^{7}+\cdots$$
68.5.d.d $$2$$ $$7.029$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$8$$ $$0$$ $$0$$ $$0$$ $$q+4q^{2}+2^{4}q^{4}+iq^{5}+2^{6}q^{8}-3^{4}q^{9}+\cdots$$
68.5.d.e $$28$$ $$7.029$$ None None $$-10$$ $$0$$ $$0$$ $$0$$
68.5.f.a $$2$$ $$7.029$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-34$$ $$0$$ $$q-4iq^{2}-2^{4}q^{4}+(-17-17i)q^{5}+\cdots$$
68.5.f.b $$2$$ $$7.029$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$62$$ $$0$$ $$q-4iq^{2}-2^{4}q^{4}+(31+31i)q^{5}+2^{6}iq^{8}+\cdots$$
68.5.f.c $$64$$ $$7.029$$ None None $$0$$ $$0$$ $$-8$$ $$0$$
68.5.g.a $$136$$ $$7.029$$ None None $$-4$$ $$0$$ $$-8$$ $$0$$
68.5.j.a $$48$$ $$7.029$$ None None $$0$$ $$0$$ $$0$$ $$0$$
68.6.a.a $$2$$ $$10.906$$ $$\Q(\sqrt{13})$$ None None $$0$$ $$-8$$ $$-20$$ $$128$$ $$+$$ $$q+(-4-\beta )q^{3}+(-10+2\beta )q^{5}+(2^{6}+\cdots)q^{7}+\cdots$$
68.6.a.b $$4$$ $$10.906$$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None None $$0$$ $$10$$ $$-88$$ $$166$$ $$-$$ $$q+(2-\beta _{3})q^{3}+(-22+\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$$
68.6.b.a $$8$$ $$10.906$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{4}q^{5}+(-2\beta _{1}-\beta _{6})q^{7}+\cdots$$
68.6.e.a $$16$$ $$10.906$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$22$$ $$-44$$ $$-118$$ $$q+(1+\beta _{1}+\beta _{5})q^{3}+(-3-3\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots$$
68.6.h.a $$28$$ $$10.906$$ None None $$0$$ $$0$$ $$44$$ $$0$$
68.6.i.a $$8$$ $$10.906$$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(4\zeta_{16}-4\zeta_{16}^{5})q^{2}-2^{5}\zeta_{16}^{6}q^{4}+\cdots$$
68.6.i.b $$336$$ $$10.906$$ None None $$-8$$ $$0$$ $$-16$$ $$0$$
68.7.c.a $$48$$ $$15.644$$ None None $$-10$$ $$0$$ $$0$$ $$0$$
68.7.d.a $$2$$ $$15.644$$ $$\Q(\sqrt{34})$$ $$\Q(\sqrt{-17})$$ None $$-16$$ $$0$$ $$0$$ $$0$$ $$q-8q^{2}+7\beta q^{3}+2^{6}q^{4}-56\beta q^{6}+\cdots$$
68.7.d.b $$2$$ $$15.644$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-17})$$ None $$16$$ $$0$$ $$0$$ $$0$$ $$q+8q^{2}+5\beta q^{3}+2^{6}q^{4}+40\beta q^{6}+\cdots$$
68.7.d.c $$48$$ $$15.644$$ None None $$-2$$ $$0$$ $$0$$ $$0$$
68.7.f.a $$104$$ $$15.644$$ None None $$0$$ $$0$$ $$-48$$ $$0$$