Results (1-50 of 106 matches)

Label Dim. $$A$$ Field CM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
69.2.a.a $$1$$ $$0.551$$ $$\Q$$ None $$1$$ $$1$$ $$0$$ $$-2$$ $$-$$ $$q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots$$
69.2.a.b $$2$$ $$0.551$$ $$\Q(\sqrt{5})$$ None $$0$$ $$-2$$ $$-2$$ $$2$$ $$-$$ $$q-\beta q^{2}-q^{3}+3q^{4}+(-1+\beta )q^{5}+\cdots$$
69.2.c.a $$6$$ $$0.551$$ 6.0.8869743.1 $$\Q(\sqrt{-23})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$$
69.2.e.a $$10$$ $$0.551$$ $$\Q(\zeta_{22})$$ None $$-4$$ $$1$$ $$5$$ $$-8$$ $$q+(-1+\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots$$
69.2.e.b $$10$$ $$0.551$$ $$\Q(\zeta_{22})$$ None $$4$$ $$1$$ $$-3$$ $$6$$ $$q+(-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{8}+\zeta_{22}^{9})q^{2}+\cdots$$
69.2.e.c $$20$$ $$0.551$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-4$$ $$-2$$ $$-6$$ $$-6$$ $$q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+2\beta _{6}+2\beta _{7}+\cdots)q^{2}+\cdots$$
69.2.g.a $$60$$ $$0.551$$ None $$0$$ $$-11$$ $$0$$ $$-22$$
69.3.b.a $$14$$ $$1.880$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$-4$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$$
69.3.d.a $$8$$ $$1.880$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
69.3.f.a $$80$$ $$1.880$$ None $$4$$ $$0$$ $$0$$ $$0$$
69.3.h.a $$140$$ $$1.880$$ None $$0$$ $$-7$$ $$0$$ $$-18$$
69.4.a.a $$2$$ $$4.071$$ $$\Q(\sqrt{5})$$ None $$-4$$ $$6$$ $$-26$$ $$-10$$ $$-$$ $$q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots$$
69.4.a.b $$2$$ $$4.071$$ $$\Q(\sqrt{2})$$ None $$-2$$ $$-6$$ $$8$$ $$-28$$ $$-$$ $$q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots$$
69.4.a.c $$4$$ $$4.071$$ 4.4.1140200.1 None $$-2$$ $$-12$$ $$-2$$ $$32$$ $$+$$ $$q+\beta _{1}q^{2}-3q^{3}+(6-\beta _{1}-2\beta _{2})q^{4}+\cdots$$
69.4.a.d $$4$$ $$4.071$$ 4.4.2009704.1 None $$4$$ $$12$$ $$4$$ $$-14$$ $$+$$ $$q+(1-\beta _{1})q^{2}+3q^{3}+(7-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
69.4.c.a $$2$$ $$4.071$$ $$\Q(\sqrt{-23})$$ $$\Q(\sqrt{-23})$$ $$0$$ $$4$$ $$0$$ $$0$$ $$q-\beta q^{2}+(2-\beta )q^{3}-15q^{4}+(-23+\cdots)q^{6}+\cdots$$
69.4.c.b $$4$$ $$4.071$$ $$\Q(\sqrt{-3}, \sqrt{-23})$$ $$\Q(\sqrt{-23})$$ $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\beta _{2}-\beta _{3})q^{2}+(-1+2\beta _{1}+\cdots)q^{3}+\cdots$$
69.4.c.c $$16$$ $$4.071$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{11}q^{2}-\beta _{10}q^{3}+(-2+\beta _{1})q^{4}+\cdots$$
69.4.e.a $$60$$ $$4.071$$ None $$0$$ $$-18$$ $$22$$ $$24$$
69.4.e.b $$60$$ $$4.071$$ None $$4$$ $$18$$ $$-6$$ $$-4$$
69.4.g.a $$220$$ $$4.071$$ None $$0$$ $$-5$$ $$0$$ $$-22$$
69.5.b.a $$30$$ $$7.133$$ None $$0$$ $$8$$ $$0$$ $$-4$$
69.5.d.a $$16$$ $$7.133$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$12$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{2}+\beta _{3}q^{3}+(9+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$$
69.5.f.a $$160$$ $$7.133$$ None $$-12$$ $$0$$ $$0$$ $$0$$
69.5.h.a $$300$$ $$7.133$$ None $$0$$ $$-19$$ $$0$$ $$-18$$
69.6.a.a $$2$$ $$11.066$$ $$\Q(\sqrt{29})$$ None $$0$$ $$-18$$ $$94$$ $$-118$$ $$-$$ $$q-2\beta q^{2}-9q^{3}+84q^{4}+(47-\beta )q^{5}+\cdots$$
69.6.a.b $$3$$ $$11.066$$ 3.3.5333.1 None $$-8$$ $$27$$ $$-56$$ $$-114$$ $$+$$ $$q+(-3+\beta _{2})q^{2}+9q^{3}+(9-4\beta _{1}-9\beta _{2})q^{4}+\cdots$$
69.6.a.c $$4$$ $$11.066$$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None $$4$$ $$-36$$ $$-122$$ $$62$$ $$-$$ $$q+(1+\beta _{1})q^{2}-9q^{3}+(-12+4\beta _{1}+\cdots)q^{4}+\cdots$$
69.6.a.d $$4$$ $$11.066$$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None $$4$$ $$-36$$ $$22$$ $$-62$$ $$+$$ $$q+(1-\beta _{1})q^{2}-9q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots$$
69.6.a.e $$5$$ $$11.066$$ $$\mathbb{Q}[x]/(x^{5} - \cdots)$$ None $$8$$ $$45$$ $$94$$ $$272$$ $$-$$ $$q+(2-\beta _{2})q^{2}+9q^{3}+(24-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$
69.6.c.a $$6$$ $$11.066$$ 6.0.8869743.1 $$\Q(\sqrt{-23})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}-3\beta _{2}-2\beta _{3}+\beta _{4}+\beta _{5})q^{2}+\cdots$$
69.6.c.b $$32$$ $$11.066$$ None $$0$$ $$0$$ $$0$$ $$0$$
69.6.e.a $$100$$ $$11.066$$ None $$-8$$ $$90$$ $$6$$ $$118$$
69.6.e.b $$100$$ $$11.066$$ None $$12$$ $$-90$$ $$-50$$ $$-78$$
69.6.g.a $$380$$ $$11.066$$ None $$0$$ $$-11$$ $$0$$ $$-22$$
69.7.b.a $$44$$ $$15.874$$ None $$0$$ $$20$$ $$0$$ $$568$$
69.7.d.a $$24$$ $$15.874$$ None $$-20$$ $$0$$ $$0$$ $$0$$
69.7.f.a $$240$$ $$15.874$$ None $$20$$ $$0$$ $$0$$ $$0$$
69.7.h.a $$460$$ $$15.874$$ None $$0$$ $$23$$ $$0$$ $$-18$$
69.8.a.a $$5$$ $$21.555$$ $$\mathbb{Q}[x]/(x^{5} - \cdots)$$ None $$0$$ $$-135$$ $$-266$$ $$-496$$ $$-$$ $$q+\beta _{1}q^{2}-3^{3}q^{3}+(54+2\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$$
69.8.a.b $$6$$ $$21.555$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$-8$$ $$162$$ $$-372$$ $$-1104$$ $$-$$ $$q+(-1-\beta _{1})q^{2}+3^{3}q^{3}+(29+3\beta _{1}+\cdots)q^{4}+\cdots$$
69.8.a.c $$7$$ $$21.555$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None $$0$$ $$-189$$ $$-516$$ $$1018$$ $$+$$ $$q+\beta _{1}q^{2}-3^{3}q^{3}+(93+\beta _{1}+\beta _{2})q^{4}+\cdots$$
69.8.a.d $$8$$ $$21.555$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$24$$ $$216$$ $$378$$ $$126$$ $$+$$ $$q+(3-\beta _{1})q^{2}+3^{3}q^{3}+(70-4\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
69.8.c.a $$6$$ $$21.555$$ 6.0.8869743.1 $$\Q(\sqrt{-23})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-2\beta _{1}-6\beta _{2}+3\beta _{3}+2\beta _{4}+2\beta _{5})q^{2}+\cdots$$
69.8.c.b $$48$$ $$21.555$$ None $$0$$ $$24$$ $$0$$ $$0$$
69.8.e.a $$140$$ $$21.555$$ None $$-16$$ $$-378$$ $$-6$$ $$978$$
69.8.e.b $$140$$ $$21.555$$ None $$-12$$ $$378$$ $$2$$ $$-394$$
69.8.g.a $$540$$ $$21.555$$ None $$0$$ $$-35$$ $$0$$ $$-22$$
69.9.b.a $$58$$ $$28.109$$ None $$0$$ $$-112$$ $$0$$ $$6996$$
69.9.d.a $$32$$ $$28.109$$ None $$12$$ $$0$$ $$0$$ $$0$$