## Results (displaying matches 1-50 of 256) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
72.1.p.a $$2$$ $$0.036$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-2})$$ None $$-1$$ $$-1$$ $$0$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$$
72.2.a.a $$1$$ $$0.575$$ $$\Q$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$-$$ $$q+2q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots$$
72.2.d.a $$2$$ $$0.575$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta q^{2}-2q^{4}+2\beta q^{5}+2q^{7}-2\beta q^{8}+\cdots$$
72.2.d.b $$2$$ $$0.575$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$0$$ $$0$$ $$-4$$ $$q+(1+i)q^{2}+2iq^{4}-2iq^{5}-2q^{7}+\cdots$$
72.2.f.a $$4$$ $$0.575$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
72.2.i.a $$2$$ $$0.575$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$1$$ $$3$$ $$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots$$
72.2.i.b $$4$$ $$0.575$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$1$$ $$1$$ $$-3$$ $$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$$
72.2.l.a $$4$$ $$0.575$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$$
72.2.l.b $$16$$ $$0.575$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-3$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$$
72.2.n.a $$4$$ $$0.575$$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$0$$ $$0$$ $$-8$$ $$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$$
72.2.n.b $$16$$ $$0.575$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$1$$ $$0$$ $$0$$ $$6$$ $$q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots$$
72.3.b.a $$1$$ $$1.962$$ $$\Q$$ $$\Q(\sqrt{-2})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+2q^{2}+4q^{4}+8q^{8}-14q^{11}+2^{4}q^{16}+\cdots$$
72.3.b.b $$4$$ $$1.962$$ 4.0.4752.1 None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(-2+\beta _{1}-\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$$
72.3.b.c $$4$$ $$1.962$$ $$\Q(\sqrt{-6}, \sqrt{10})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots$$
72.3.e.a $$2$$ $$1.962$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$24$$ $$q+5\beta q^{5}+12q^{7}-4\beta q^{11}-8q^{13}+\cdots$$
72.3.h.a $$8$$ $$1.962$$ 8.0.$$\cdots$$.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(1+\beta _{5})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$$
72.3.j.a $$44$$ $$1.962$$ None None $$-3$$ $$0$$ $$0$$ $$-2$$
72.3.m.a $$4$$ $$1.962$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$-12$$ $$6$$ $$-6$$ $$q-3q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots$$
72.3.m.b $$8$$ $$1.962$$ 8.0.$$\cdots$$.9 None None $$0$$ $$10$$ $$-6$$ $$6$$ $$q+(1-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
72.3.p.a $$4$$ $$1.962$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ None $$4$$ $$2$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots$$
72.3.p.b $$40$$ $$1.962$$ None None $$-5$$ $$-6$$ $$0$$ $$0$$
72.4.a.a $$1$$ $$4.248$$ $$\Q$$ None None $$0$$ $$0$$ $$-16$$ $$-12$$ $$-$$ $$q-2^{4}q^{5}-12q^{7}-2^{6}q^{11}+58q^{13}+\cdots$$
72.4.a.b $$1$$ $$4.248$$ $$\Q$$ None None $$0$$ $$0$$ $$-14$$ $$-24$$ $$-$$ $$q-14q^{5}-24q^{7}+28q^{11}-74q^{13}+\cdots$$
72.4.a.c $$1$$ $$4.248$$ $$\Q$$ None None $$0$$ $$0$$ $$2$$ $$24$$ $$+$$ $$q+2q^{5}+24q^{7}+44q^{11}+22q^{13}+\cdots$$
72.4.a.d $$1$$ $$4.248$$ $$\Q$$ None None $$0$$ $$0$$ $$16$$ $$-12$$ $$+$$ $$q+2^{4}q^{5}-12q^{7}+2^{6}q^{11}+58q^{13}+\cdots$$
72.4.d.a $$2$$ $$4.248$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$-68$$ $$q+\beta q^{2}-8q^{4}-7\beta q^{5}-34q^{7}-8\beta q^{8}+\cdots$$
72.4.d.b $$2$$ $$4.248$$ $$\Q(\sqrt{-7})$$ None None $$2$$ $$0$$ $$0$$ $$-16$$ $$q+(1+\beta )q^{2}+(-6+2\beta )q^{4}+4\beta q^{5}+\cdots$$
72.4.d.c $$4$$ $$4.248$$ $$\Q(\sqrt{-10}, \sqrt{22})$$ None None $$0$$ $$0$$ $$0$$ $$40$$ $$q+\beta _{1}q^{2}+(3+\beta _{3})q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots$$
72.4.d.d $$6$$ $$4.248$$ 6.0.8248384.1 None None $$-2$$ $$0$$ $$0$$ $$28$$ $$q+\beta _{1}q^{2}+(3+\beta _{5})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
72.4.f.a $$12$$ $$4.248$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(-1+\beta _{6})q^{4}-\beta _{5}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$$
72.4.i.a $$8$$ $$4.248$$ 8.0.5206055409.1 None None $$0$$ $$-3$$ $$-5$$ $$3$$ $$q-\beta _{5}q^{3}+(2\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$$
72.4.i.b $$10$$ $$4.248$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$4$$ $$-5$$ $$-3$$ $$q-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{8})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots$$
72.4.l.a $$4$$ $$4.248$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-10$$ $$0$$ $$0$$ $$q+2\beta _{1}q^{2}+(-5+\beta _{1}+5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots$$
72.4.l.b $$64$$ $$4.248$$ None None $$-3$$ $$6$$ $$0$$ $$0$$
72.4.n.a $$68$$ $$4.248$$ None None $$-1$$ $$0$$ $$0$$ $$-2$$
72.5.b.a $$1$$ $$7.443$$ $$\Q$$ $$\Q(\sqrt{-2})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-4q^{2}+2^{4}q^{4}-2^{6}q^{8}+46q^{11}+\cdots$$
72.5.b.b $$2$$ $$7.443$$ $$\Q(\sqrt{-15})$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta )q^{2}+(-14+2\beta )q^{4}-8\beta q^{5}+\cdots$$
72.5.b.c $$8$$ $$7.443$$ 8.0.$$\cdots$$.5 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(3-\beta _{4})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
72.5.b.d $$8$$ $$7.443$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None None $$6$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{1})q^{2}+(1+\beta _{1}+\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots$$
72.5.e.a $$2$$ $$7.443$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$-120$$ $$q+11\beta q^{5}-60q^{7}+44\beta q^{11}-176q^{13}+\cdots$$
72.5.e.b $$2$$ $$7.443$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$72$$ $$q+5\beta q^{5}+6^{2}q^{7}+116\beta q^{11}+304q^{13}+\cdots$$
72.5.h.a $$16$$ $$7.443$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{4}+\beta _{5}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$$
72.5.j.a $$92$$ $$7.443$$ None None $$-3$$ $$0$$ $$0$$ $$-2$$
72.5.m.a $$24$$ $$7.443$$ None None $$0$$ $$4$$ $$0$$ $$0$$
72.5.p.a $$4$$ $$7.443$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ None $$-8$$ $$14$$ $$0$$ $$0$$ $$q-4\beta _{2}q^{2}+(\beta _{1}+7\beta _{2}-\beta _{3})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$$
72.5.p.b $$88$$ $$7.443$$ None None $$7$$ $$-18$$ $$0$$ $$0$$
72.6.a.a $$1$$ $$11.548$$ $$\Q$$ None None $$0$$ $$0$$ $$-94$$ $$144$$ $$-$$ $$q-94q^{5}+12^{2}q^{7}+380q^{11}+814q^{13}+\cdots$$
72.6.a.b $$1$$ $$11.548$$ $$\Q$$ None None $$0$$ $$0$$ $$-38$$ $$120$$ $$+$$ $$q-38q^{5}+120q^{7}-524q^{11}-962q^{13}+\cdots$$
72.6.a.c $$1$$ $$11.548$$ $$\Q$$ None None $$0$$ $$0$$ $$-16$$ $$12$$ $$+$$ $$q-2^{4}q^{5}+12q^{7}-448q^{11}-206q^{13}+\cdots$$
72.6.a.d $$1$$ $$11.548$$ $$\Q$$ None None $$0$$ $$0$$ $$16$$ $$12$$ $$-$$ $$q+2^{4}q^{5}+12q^{7}+448q^{11}-206q^{13}+\cdots$$
Next