## Results (displaying matches 1-50 of 72) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
164.1.d.a $$1$$ $$0.082$$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-41})$$ $$\Q(\sqrt{41})$$ $$1$$ $$0$$ $$-2$$ $$0$$ $$q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots$$
164.1.d.b $$2$$ $$0.082$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-41})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots$$
164.1.j.a $$4$$ $$0.082$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-1})$$ None $$-1$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$$
164.1.l.a $$4$$ $$0.082$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-1})$$ None $$-1$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$$
164.2.a.a $$4$$ $$1.310$$ 4.4.25808.1 None None $$0$$ $$2$$ $$4$$ $$0$$ $$-$$ $$q+(-\beta _{1}+\beta _{2})q^{3}+(2-\beta _{2}+\beta _{3})q^{5}+\cdots$$
164.2.b.a $$4$$ $$1.310$$ 4.0.25088.1 None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-\beta _{3}q^{7}+\beta _{2}q^{9}+\cdots$$
164.2.f.a $$6$$ $$1.310$$ 6.0.5089536.1 None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
164.2.g.a $$16$$ $$1.310$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$-2$$ $$-4$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{3}+\beta _{4}-\beta _{6}+\beta _{7}-\beta _{9}+\cdots)q^{5}+\cdots$$
164.2.i.a $$4$$ $$1.310$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1+\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{4}+4\zeta_{8}^{3}q^{5}+\cdots$$
164.2.i.b $$72$$ $$1.310$$ None None $$-8$$ $$0$$ $$-8$$ $$0$$
164.2.k.a $$16$$ $$1.310$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{12}q^{5}+(-\beta _{9}+\beta _{14})q^{7}+\cdots$$
164.2.m.a $$24$$ $$1.310$$ None None $$0$$ $$-2$$ $$0$$ $$0$$
164.2.o.a $$16$$ $$1.310$$ $$\Q(\zeta_{40})$$ $$\Q(\sqrt{-1})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{40}^{2}-\zeta_{40}^{6}+\zeta_{40}^{8}+\zeta_{40}^{10}+\cdots)q^{2}+\cdots$$
164.2.o.b $$288$$ $$1.310$$ None None $$-12$$ $$0$$ $$-32$$ $$0$$
164.3.c.a $$40$$ $$4.469$$ None None $$-2$$ $$0$$ $$0$$ $$0$$
164.3.d.a $$4$$ $$4.469$$ 4.4.3442688.1 $$\Q(\sqrt{-41})$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q-2q^{2}-\beta _{2}q^{3}+4q^{4}+\beta _{3}q^{5}+2\beta _{2}q^{6}+\cdots$$
164.3.d.b $$4$$ $$4.469$$ 4.4.83968.1 $$\Q(\sqrt{-41})$$ None $$8$$ $$0$$ $$0$$ $$0$$ $$q+2q^{2}-\beta _{3}q^{3}+4q^{4}+3\beta _{2}q^{5}-2\beta _{3}q^{6}+\cdots$$
164.3.d.c $$32$$ $$4.469$$ None None $$-2$$ $$0$$ $$-8$$ $$0$$
164.3.e.a $$2$$ $$4.469$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2iq^{2}-4q^{4}-6iq^{5}+8iq^{8}-9iq^{9}+\cdots$$
164.3.e.b $$2$$ $$4.469$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-4q^{4}-6iq^{5}-8iq^{8}-9iq^{9}+\cdots$$
164.3.e.c $$76$$ $$4.469$$ None None $$0$$ $$0$$ $$0$$ $$0$$
164.3.h.a $$28$$ $$4.469$$ None None $$0$$ $$-8$$ $$0$$ $$0$$
164.3.j.a $$160$$ $$4.469$$ None None $$-3$$ $$0$$ $$-10$$ $$0$$
164.3.l.a $$160$$ $$4.469$$ None None $$-3$$ $$0$$ $$-2$$ $$0$$
164.3.n.a $$8$$ $$4.469$$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\zeta_{20}^{3}q^{2}+4\zeta_{20}^{6}q^{4}+(-4+3\zeta_{20}+\cdots)q^{5}+\cdots$$
164.3.n.b $$8$$ $$4.469$$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{20}^{3}q^{2}+4\zeta_{20}^{6}q^{4}+(4+3\zeta_{20}+\cdots)q^{5}+\cdots$$
164.3.n.c $$304$$ $$4.469$$ None None $$-10$$ $$0$$ $$-20$$ $$0$$
164.3.p.a $$112$$ $$4.469$$ None None $$0$$ $$8$$ $$0$$ $$0$$
164.4.a.a $$3$$ $$9.676$$ 3.3.4344.1 None None $$0$$ $$-2$$ $$-10$$ $$0$$ $$-$$ $$q+(-1-\beta _{1})q^{3}+(-3+\beta _{1}-\beta _{2})q^{5}+\cdots$$
164.4.a.b $$7$$ $$9.676$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$0$$ $$4$$ $$10$$ $$0$$ $$+$$ $$q+(1-\beta _{2})q^{3}+(2-\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$$
164.4.b.a $$10$$ $$9.676$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$$
164.4.f.a $$22$$ $$9.676$$ None None $$0$$ $$2$$ $$0$$ $$0$$
164.4.g.a $$40$$ $$9.676$$ None None $$0$$ $$-2$$ $$0$$ $$0$$
164.4.i.a $$4$$ $$9.676$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q+(-2-2\zeta_{8}^{2})q^{2}+8\zeta_{8}^{2}q^{4}+4\zeta_{8}^{3}q^{5}+\cdots$$
164.4.i.b $$240$$ $$9.676$$ None None $$4$$ $$0$$ $$-8$$ $$0$$
164.4.k.a $$40$$ $$9.676$$ None None $$0$$ $$0$$ $$0$$ $$0$$
164.4.m.a $$88$$ $$9.676$$ None None $$0$$ $$-2$$ $$0$$ $$0$$
164.4.o.a $$16$$ $$9.676$$ $$\Q(\zeta_{40})$$ $$\Q(\sqrt{-1})$$ None $$8$$ $$0$$ $$0$$ $$0$$ $$q+(-2\zeta_{40}^{2}+2\zeta_{40}^{6}-2\zeta_{40}^{8}-2\zeta_{40}^{10}+\cdots)q^{2}+\cdots$$
164.4.o.b $$960$$ $$9.676$$ None None $$-24$$ $$0$$ $$-32$$ $$0$$
164.5.c.a $$80$$ $$16.953$$ None None $$6$$ $$0$$ $$0$$ $$0$$
164.5.d.a $$2$$ $$16.953$$ $$\Q(\sqrt{41})$$ $$\Q(\sqrt{-41})$$ None $$-8$$ $$-22$$ $$0$$ $$138$$ $$q-4q^{2}+(-11-\beta )q^{3}+2^{4}q^{4}+6\beta q^{5}+\cdots$$
164.5.d.b $$2$$ $$16.953$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$-8$$ $$0$$ $$28$$ $$0$$ $$q-4q^{2}+2^{4}q^{4}+14q^{5}-2^{6}q^{8}-3^{4}q^{9}+\cdots$$
164.5.d.c $$2$$ $$16.953$$ $$\Q(\sqrt{41})$$ $$\Q(\sqrt{-41})$$ None $$-8$$ $$22$$ $$0$$ $$-138$$ $$q-4q^{2}+(11-\beta )q^{3}+2^{4}q^{4}-6\beta q^{5}+\cdots$$
164.5.d.d $$2$$ $$16.953$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-41})$$ None $$8$$ $$0$$ $$-64$$ $$0$$ $$q+4q^{2}+11\beta q^{3}+2^{4}q^{4}-2^{5}q^{5}+\cdots$$
164.5.d.e $$2$$ $$16.953$$ $$\Q(\sqrt{82})$$ $$\Q(\sqrt{-41})$$ None $$8$$ $$0$$ $$64$$ $$0$$ $$q+4q^{2}+\beta q^{3}+2^{4}q^{4}+2^{5}q^{5}+4\beta q^{6}+\cdots$$
164.5.d.f $$72$$ $$16.953$$ None None $$6$$ $$0$$ $$-8$$ $$0$$
164.5.h.a $$56$$ $$16.953$$ None None $$0$$ $$16$$ $$0$$ $$0$$
164.6.a.a $$6$$ $$26.303$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None None $$0$$ $$-8$$ $$-68$$ $$88$$ $$+$$ $$q+(-1-\beta _{3})q^{3}+(-11+\beta _{2})q^{5}+(14+\cdots)q^{7}+\cdots$$
164.6.a.b $$10$$ $$26.303$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$10$$ $$32$$ $$88$$ $$-$$ $$q+(1+\beta _{1})q^{3}+(3+\beta _{3})q^{5}+(9+2\beta _{1}+\cdots)q^{7}+\cdots$$
164.6.b.a $$18$$ $$26.303$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$0$$ $$0$$ $$-72$$ $$0$$ $$q+\beta _{1}q^{3}+(-4-\beta _{3})q^{5}+(\beta _{1}+\beta _{12}+\cdots)q^{7}+\cdots$$
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