## Results (1-50 of 83 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1000.1.e.a $$2$$ $$0.499$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-10})$$ None $$-2$$ $$0$$ $$0$$ $$1$$ $$q-q^{2}+q^{4}+(1-\beta )q^{7}-q^{8}+q^{9}+\cdots$$
1000.1.e.b $$2$$ $$0.499$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-10})$$ None $$2$$ $$0$$ $$0$$ $$-1$$ $$q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+q^{9}+\cdots$$
1000.1.g.a $$4$$ $$0.499$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}-q^{4}-\beta _{1}q^{7}+\beta _{3}q^{8}-q^{9}+\cdots$$
1000.2.a.a $$2$$ $$7.985$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-1$$ $$0$$ $$-1$$ $$+$$ $$q-\beta q^{3}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots$$
1000.2.a.b $$2$$ $$7.985$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-1$$ $$0$$ $$4$$ $$+$$ $$q-\beta q^{3}+(1+2\beta )q^{7}+(-2+\beta )q^{9}+\cdots$$
1000.2.a.c $$2$$ $$7.985$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$1$$ $$0$$ $$-4$$ $$+$$ $$q+\beta q^{3}+(-1-2\beta )q^{7}+(-2+\beta )q^{9}+\cdots$$
1000.2.a.d $$2$$ $$7.985$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$1$$ $$0$$ $$1$$ $$-$$ $$q+\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}+2\beta q^{11}+\cdots$$
1000.2.a.e $$4$$ $$7.985$$ 4.4.4400.1 None None $$0$$ $$-4$$ $$0$$ $$-6$$ $$+$$ $$q+(-1+\beta _{1})q^{3}+(-2-\beta _{2}-\beta _{3})q^{7}+\cdots$$
1000.2.a.f $$4$$ $$7.985$$ 4.4.10025.1 None None $$0$$ $$-1$$ $$0$$ $$-9$$ $$-$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots$$
1000.2.a.g $$4$$ $$7.985$$ 4.4.10025.1 None None $$0$$ $$1$$ $$0$$ $$9$$ $$-$$ $$q+\beta _{1}q^{3}+(2+\beta _{3})q^{7}+(2-\beta _{2}+\beta _{3})q^{9}+\cdots$$
1000.2.a.h $$4$$ $$7.985$$ 4.4.4400.1 None None $$0$$ $$4$$ $$0$$ $$6$$ $$-$$ $$q+(1+\beta _{1})q^{3}+(2+\beta _{2}-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$$
1000.2.c.a $$4$$ $$7.985$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(2\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$$
1000.2.c.b $$4$$ $$7.985$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$$
1000.2.c.c $$8$$ $$7.985$$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(3\beta _{2}+\beta _{3}-\beta _{7})q^{7}+(-3+\cdots)q^{9}+\cdots$$
1000.2.c.d $$8$$ $$7.985$$ 8.0.309760000.3 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{5}+\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots$$
1000.2.d.a $$4$$ $$7.985$$ $$\Q(i, \sqrt{5})$$ None None $$-4$$ $$0$$ $$0$$ $$2$$ $$q+(-1+\beta _{3})q^{2}+2\beta _{1}q^{3}-2\beta _{3}q^{4}+\cdots$$
1000.2.d.b $$4$$ $$7.985$$ $$\Q(i, \sqrt{5})$$ None None $$4$$ $$0$$ $$0$$ $$-2$$ $$q+(1+\beta _{3})q^{2}+2\beta _{1}q^{3}+2\beta _{3}q^{4}+(2\beta _{1}+\cdots)q^{6}+\cdots$$
1000.2.d.c $$40$$ $$7.985$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1000.2.d.d $$48$$ $$7.985$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1000.2.f.a $$4$$ $$7.985$$ $$\Q(i, \sqrt{5})$$ None None $$-4$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\beta _{3})q^{2}+(-2-2\beta _{2})q^{3}+2\beta _{3}q^{4}+\cdots$$
1000.2.f.b $$4$$ $$7.985$$ $$\Q(i, \sqrt{5})$$ None None $$4$$ $$4$$ $$0$$ $$0$$ $$q+(1-\beta _{3})q^{2}+(2+2\beta _{2})q^{3}-2\beta _{3}q^{4}+\cdots$$
1000.2.f.c $$20$$ $$7.985$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$-3$$ $$4$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{14}q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$$
1000.2.f.d $$20$$ $$7.985$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$3$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{14}q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$$
1000.2.f.e $$48$$ $$7.985$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1000.2.k.a $$8$$ $$7.985$$ 8.0.1024000000.2 $$\Q(\sqrt{-10})$$ None $$-8$$ $$0$$ $$0$$ $$4$$ $$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+\beta _{3}q^{7}+\cdots$$
1000.2.k.b $$8$$ $$7.985$$ 8.0.1024000000.2 $$\Q(\sqrt{-10})$$ None $$8$$ $$0$$ $$0$$ $$-4$$ $$q+(1+\beta _{1})q^{2}+2\beta _{1}q^{4}-\beta _{3}q^{7}+(-2+\cdots)q^{8}+\cdots$$
1000.2.k.c $$16$$ $$7.985$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-4$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{7}+\beta _{12})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1000.2.k.d $$16$$ $$7.985$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{15}q^{2}+(\beta _{1}+\beta _{14})q^{3}+(-\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$$
1000.2.k.e $$16$$ $$7.985$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$4$$ $$-4$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+(\beta _{3}+\beta _{7}-\beta _{12})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1000.2.k.f $$64$$ $$7.985$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1000.2.k.g $$64$$ $$7.985$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1000.2.m.a $$4$$ $$7.985$$ $$\Q(\zeta_{10})$$ None None $$0$$ $$-5$$ $$0$$ $$-6$$ $$q+(-2+2\zeta_{10}+\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$$
1000.2.m.b $$8$$ $$7.985$$ 8.0.58140625.2 None None $$0$$ $$6$$ $$0$$ $$-4$$ $$q+(1-\beta _{2})q^{3}+(-\beta _{1}+\beta _{4}+\beta _{5})q^{7}+\cdots$$
1000.2.m.c $$16$$ $$7.985$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$-1$$ $$0$$ $$6$$ $$q-\beta _{1}q^{3}-\beta _{10}q^{7}+(\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots$$
1000.2.m.d $$32$$ $$7.985$$ None None $$0$$ $$-2$$ $$0$$ $$16$$
1000.2.m.e $$32$$ $$7.985$$ None None $$0$$ $$2$$ $$0$$ $$-16$$
1000.2.o.a $$112$$ $$7.985$$ None None $$5$$ $$0$$ $$0$$ $$0$$
1000.2.o.b $$224$$ $$7.985$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1000.2.q.a $$8$$ $$7.985$$ $$\Q(\zeta_{20})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+\cdots$$
1000.2.q.b $$16$$ $$7.985$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{9}+\beta _{10})q^{3}+(-\beta _{5}+\beta _{9}+\beta _{11}+\cdots)q^{7}+\cdots$$
1000.2.q.c $$32$$ $$7.985$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1000.2.q.d $$32$$ $$7.985$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1000.2.t.a $$112$$ $$7.985$$ None None $$3$$ $$0$$ $$0$$ $$16$$
1000.2.t.b $$224$$ $$7.985$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1000.2.v.a $$8$$ $$7.985$$ $$\Q(\zeta_{20})$$ None None $$-8$$ $$0$$ $$0$$ $$4$$ $$q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$
1000.2.v.b $$8$$ $$7.985$$ $$\Q(\zeta_{20})$$ None None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$
1000.2.v.c $$8$$ $$7.985$$ $$\Q(\zeta_{20})$$ None None $$2$$ $$0$$ $$0$$ $$4$$ $$q+(\zeta_{20}+\zeta_{20}^{6})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$
1000.2.v.d $$8$$ $$7.985$$ $$\Q(\zeta_{20})$$ None None $$2$$ $$0$$ $$0$$ $$4$$ $$q+(\zeta_{20}+\zeta_{20}^{6})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$
1000.2.v.e $$8$$ $$7.985$$ $$\Q(\zeta_{20})$$ None None $$8$$ $$0$$ $$0$$ $$-4$$ $$q+(1-\zeta_{20}^{5})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$
1000.2.v.f $$8$$ $$7.985$$ $$\Q(\zeta_{20})$$ None None $$8$$ $$0$$ $$0$$ $$-4$$ $$q+(1-\zeta_{20}^{5})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$