## Results (1-50 of 193 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
56.1.h.a $$1$$ $$0.028$$ $$\Q$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-14})$$ $$\Q(\sqrt{2})$$ $$-1$$ $$0$$ $$0$$ $$-1$$ $$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots$$
56.2.a.a $$1$$ $$0.447$$ $$\Q$$ None None $$0$$ $$0$$ $$2$$ $$-1$$ $$-$$ $$q+2q^{5}-q^{7}-3q^{9}-4q^{11}+2q^{13}+\cdots$$
56.2.a.b $$1$$ $$0.447$$ $$\Q$$ None None $$0$$ $$2$$ $$-4$$ $$1$$ $$-$$ $$q+2q^{3}-4q^{5}+q^{7}+q^{9}-8q^{15}+\cdots$$
56.2.b.a $$2$$ $$0.447$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta q^{2}+\beta q^{3}-2q^{4}-\beta q^{5}-2q^{6}+\cdots$$
56.2.b.b $$4$$ $$0.447$$ 4.0.2312.1 None None $$-1$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
56.2.e.a $$2$$ $$0.447$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}+(-2+\beta )q^{4}+(1-2\beta )q^{7}+\cdots$$
56.2.e.b $$4$$ $$0.447$$ $$\Q(i, \sqrt{6})$$ None None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+\cdots$$
56.2.i.a $$2$$ $$0.447$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$1$$ $$4$$ $$q-3\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
56.2.i.b $$2$$ $$0.447$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$1$$ $$-4$$ $$q+\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$
56.2.m.a $$12$$ $$0.447$$ 12.0.$$\cdots$$.2 None None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{8})q^{2}+(-1-\beta _{10})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$$
56.2.p.a $$12$$ $$0.447$$ 12.0.$$\cdots$$.1 None None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{1}+\beta _{5})q^{2}+\beta _{6}q^{3}-\beta _{3}q^{4}+\cdots$$
56.3.c.a $$4$$ $$1.526$$ 4.0.2048.2 None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
56.3.g.a $$4$$ $$1.526$$ $$\Q(\sqrt{2}, \sqrt{-7})$$ None None $$0$$ $$8$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(2-\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots$$
56.3.g.b $$8$$ $$1.526$$ 8.0.$$\cdots$$.3 None None $$1$$ $$-8$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+(-1+\beta _{3}-\beta _{4})q^{3}+(1+\beta _{6}+\cdots)q^{4}+\cdots$$
56.3.h.a $$2$$ $$1.526$$ $$\Q(\sqrt{7})$$ $$\Q(\sqrt{-14})$$ None $$-4$$ $$0$$ $$0$$ $$14$$ $$q-2q^{2}+\beta q^{3}+4q^{4}-\beta q^{5}-2\beta q^{6}+\cdots$$
56.3.h.b $$2$$ $$1.526$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$3$$ $$0$$ $$0$$ $$14$$ $$q+(1+\beta )q^{2}+(-1+3\beta )q^{4}+7q^{7}+\cdots$$
56.3.h.c $$2$$ $$1.526$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-14})$$ None $$4$$ $$0$$ $$0$$ $$-14$$ $$q+2q^{2}+\beta q^{3}+4q^{4}-3\beta q^{5}+2\beta q^{6}+\cdots$$
56.3.h.d $$8$$ $$1.526$$ 8.0.$$\cdots$$.51 None None $$-4$$ $$0$$ $$0$$ $$-16$$ $$q+(-1-\beta _{2})q^{2}+\beta _{6}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots$$
56.3.j.a $$28$$ $$1.526$$ None None $$-2$$ $$0$$ $$0$$ $$-4$$
56.3.k.a $$2$$ $$1.526$$ $$\Q(\sqrt{-3})$$ None None $$-4$$ $$-1$$ $$-9$$ $$-2$$ $$q-2q^{2}-\zeta_{6}q^{3}+4q^{4}+(-3-3\zeta_{6})q^{5}+\cdots$$
56.3.k.b $$2$$ $$1.526$$ $$\Q(\sqrt{-3})$$ None None $$2$$ $$-1$$ $$9$$ $$2$$ $$q+2\zeta_{6}q^{2}-\zeta_{6}q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$$
56.3.k.c $$12$$ $$1.526$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$6$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}+(1+\beta _{1}+\beta _{4}+\beta _{8})q^{3}+(-1+\cdots)q^{4}+\cdots$$
56.3.k.d $$12$$ $$1.526$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$2$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(\beta _{8}-\beta _{9}-\beta _{10})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$$
56.3.o.a $$8$$ $$1.526$$ 8.0.$$\cdots$$.2 None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{5}q^{3}+\beta _{4}q^{5}+(1-3\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$
56.4.a.a $$1$$ $$3.304$$ $$\Q$$ None None $$0$$ $$-2$$ $$-16$$ $$-7$$ $$-$$ $$q-2q^{3}-2^{4}q^{5}-7q^{7}-23q^{9}+24q^{11}+\cdots$$
56.4.a.b $$1$$ $$3.304$$ $$\Q$$ None None $$0$$ $$6$$ $$8$$ $$-7$$ $$+$$ $$q+6q^{3}+8q^{5}-7q^{7}+9q^{9}+56q^{11}+\cdots$$
56.4.a.c $$2$$ $$3.304$$ $$\Q(\sqrt{57})$$ None None $$0$$ $$-2$$ $$22$$ $$14$$ $$+$$ $$q+(-1-\beta )q^{3}+(11+\beta )q^{5}+7q^{7}+\cdots$$
56.4.b.a $$8$$ $$3.304$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$-2$$ $$0$$ $$0$$ $$-56$$ $$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
56.4.b.b $$10$$ $$3.304$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$3$$ $$0$$ $$0$$ $$70$$ $$q+\beta _{1}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots$$
56.4.e.a $$2$$ $$3.304$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$-5$$ $$0$$ $$0$$ $$0$$ $$q+(-2-\beta )q^{2}+(2+5\beta )q^{4}+(-7+14\beta )q^{7}+\cdots$$
56.4.e.b $$4$$ $$3.304$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(-6-2\beta _{2}+\cdots)q^{4}+\cdots$$
56.4.e.c $$16$$ $$3.304$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$8$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}+\beta _{12}q^{5}+\cdots$$
56.4.i.a $$6$$ $$3.304$$ 6.0.11163123.4 None None $$0$$ $$-1$$ $$-13$$ $$-20$$ $$q+\beta _{3}q^{3}+(-5+5\beta _{1}-\beta _{3}-\beta _{4}-2\beta _{5})q^{5}+\cdots$$
56.4.i.b $$6$$ $$3.304$$ 6.0.11163123.4 None None $$0$$ $$7$$ $$3$$ $$-4$$ $$q+(2-2\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots$$
56.4.m.a $$44$$ $$3.304$$ None None $$-2$$ $$-6$$ $$0$$ $$0$$
56.4.p.a $$44$$ $$3.304$$ None None $$0$$ $$0$$ $$0$$ $$-4$$
56.5.c.a $$8$$ $$5.789$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$56$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(7-\beta _{5})q^{7}+(-31+\cdots)q^{9}+\cdots$$
56.5.g.a $$2$$ $$5.789$$ $$\Q(\sqrt{-7})$$ None None $$6$$ $$-12$$ $$0$$ $$0$$ $$q+(3+\beta )q^{2}-6q^{3}+(2+6\beta )q^{4}+4\beta q^{5}+\cdots$$
56.5.g.b $$22$$ $$5.789$$ None None $$-9$$ $$12$$ $$0$$ $$0$$
56.5.h.a $$1$$ $$5.789$$ $$\Q$$ $$\Q(\sqrt{-14})$$ None $$4$$ $$-10$$ $$22$$ $$49$$ $$q+4q^{2}-10q^{3}+2^{4}q^{4}+22q^{5}-40q^{6}+\cdots$$
56.5.h.b $$1$$ $$5.789$$ $$\Q$$ $$\Q(\sqrt{-14})$$ None $$4$$ $$10$$ $$-22$$ $$49$$ $$q+4q^{2}+10q^{3}+2^{4}q^{4}-22q^{5}+40q^{6}+\cdots$$
56.5.h.c $$2$$ $$5.789$$ $$\Q(\sqrt{14})$$ $$\Q(\sqrt{-14})$$ None $$-8$$ $$0$$ $$0$$ $$-98$$ $$q-4q^{2}+\beta q^{3}+2^{4}q^{4}+3\beta q^{5}-4\beta q^{6}+\cdots$$
56.5.h.d $$2$$ $$5.789$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$-98$$ $$q-\beta q^{2}+(-2^{4}+\beta )q^{4}-7^{2}q^{7}+(2^{4}+\cdots)q^{8}+\cdots$$
56.5.h.e $$24$$ $$5.789$$ None None $$-4$$ $$0$$ $$0$$ $$96$$
56.5.j.a $$60$$ $$5.789$$ None None $$2$$ $$0$$ $$0$$ $$-4$$
56.5.k.a $$60$$ $$5.789$$ None None $$-4$$ $$-2$$ $$0$$ $$0$$
56.5.o.a $$16$$ $$5.789$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-56$$ $$q+(\beta _{2}-\beta _{6})q^{3}+\beta _{4}q^{5}+(-5-3\beta _{1}+\cdots)q^{7}+\cdots$$
56.6.a.a $$1$$ $$8.981$$ $$\Q$$ None None $$0$$ $$-6$$ $$4$$ $$49$$ $$+$$ $$q-6q^{3}+4q^{5}+7^{2}q^{7}-207q^{9}-240q^{11}+\cdots$$
56.6.a.b $$1$$ $$8.981$$ $$\Q$$ None None $$0$$ $$30$$ $$32$$ $$49$$ $$-$$ $$q+30q^{3}+2^{5}q^{5}+7^{2}q^{7}+657q^{9}+\cdots$$
56.6.a.c $$2$$ $$8.981$$ $$\Q(\sqrt{177})$$ None None $$0$$ $$-26$$ $$-62$$ $$98$$ $$-$$ $$q+(-13-\beta )q^{3}+(-31-5\beta )q^{5}+7^{2}q^{7}+\cdots$$