Results (displaying matches 1-50 of 217) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
160.1.p.a $$2$$ $$0.080$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots$$
160.2.a.a $$1$$ $$1.278$$ $$\Q$$ None None $$0$$ $$-2$$ $$-1$$ $$-2$$ $$+$$ $$q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$$
160.2.a.b $$1$$ $$1.278$$ $$\Q$$ None None $$0$$ $$2$$ $$-1$$ $$2$$ $$-$$ $$q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$$
160.2.a.c $$2$$ $$1.278$$ $$\Q(\sqrt{2})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$-$$ $$q+\beta q^{3}+q^{5}-\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots$$
160.2.c.a $$2$$ $$1.278$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+i)q^{5}+3q^{9}+2iq^{13}-4iq^{17}+\cdots$$
160.2.c.b $$4$$ $$1.278$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots$$
160.2.d.a $$4$$ $$1.278$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}q^{5}+(1+\zeta_{12}^{3})q^{7}+\cdots$$
160.2.f.a $$4$$ $$1.278$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots$$
160.2.n.a $$2$$ $$1.278$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-4$$ $$-4$$ $$-4$$ $$q+(-2-2i)q^{3}+(-2+i)q^{5}+(-2+\cdots)q^{7}+\cdots$$
160.2.n.b $$2$$ $$1.278$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$2$$ $$-2$$ $$q+(-1-i)q^{3}+(1-2i)q^{5}+(-1+i)q^{7}+\cdots$$
160.2.n.c $$2$$ $$1.278$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$2$$ $$6$$ $$q+(-1-i)q^{3}+(1+2i)q^{5}+(3-3i)q^{7}+\cdots$$
160.2.n.d $$2$$ $$1.278$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$2$$ $$-6$$ $$q+(1+i)q^{3}+(1+2i)q^{5}+(-3+3i)q^{7}+\cdots$$
160.2.n.e $$2$$ $$1.278$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$2$$ $$2$$ $$q+(1+i)q^{3}+(1-2i)q^{5}+(1-i)q^{7}+\cdots$$
160.2.n.f $$2$$ $$1.278$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$4$$ $$-4$$ $$4$$ $$q+(2+2i)q^{3}+(-2+i)q^{5}+(2-2i)q^{7}+\cdots$$
160.2.o.a $$8$$ $$1.278$$ $$\Q(\zeta_{20})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\zeta_{20}^{3}q^{3}+\zeta_{20}^{5}q^{5}-\zeta_{20}^{6}q^{7}+\cdots$$
160.2.u.a $$88$$ $$1.278$$ None None $$-4$$ $$-4$$ $$-4$$ $$0$$
160.2.x.a $$64$$ $$1.278$$ None None $$0$$ $$0$$ $$0$$ $$0$$
160.2.z.a $$88$$ $$1.278$$ None None $$0$$ $$0$$ $$-4$$ $$0$$
160.2.ba.a $$88$$ $$1.278$$ None None $$-4$$ $$-4$$ $$-4$$ $$-8$$
160.3.b.a $$4$$ $$4.360$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+4\beta _{2})q^{7}+\cdots$$
160.3.b.b $$4$$ $$4.360$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots$$
160.3.e.a $$1$$ $$4.360$$ $$\Q$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$-5$$ $$6$$ $$q-5q^{5}+6q^{7}+9q^{9}+18q^{11}+6q^{13}+\cdots$$
160.3.e.b $$1$$ $$4.360$$ $$\Q$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$5$$ $$-6$$ $$q+5q^{5}-6q^{7}+9q^{9}+18q^{11}-6q^{13}+\cdots$$
160.3.e.c $$8$$ $$4.360$$ 8.0.$$\cdots$$.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$$
160.3.g.a $$8$$ $$4.360$$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{6}q^{7}+(3+\beta _{3}+\cdots)q^{9}+\cdots$$
160.3.h.a $$6$$ $$4.360$$ 6.0.1827904.1 None None $$0$$ $$-4$$ $$-2$$ $$-12$$ $$q+(-1-\beta _{1})q^{3}-\beta _{4}q^{5}+(-2-\beta _{3}+\cdots)q^{7}+\cdots$$
160.3.h.b $$6$$ $$4.360$$ 6.0.1827904.1 None None $$0$$ $$4$$ $$-2$$ $$12$$ $$q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{4})q^{5}+\cdots$$
160.3.m.a $$20$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{8}q^{3}+\beta _{9}q^{5}-\beta _{4}q^{7}+(2\beta _{2}-\beta _{13}+\cdots)q^{9}+\cdots$$
160.3.p.a $$2$$ $$4.360$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+(-4+3i)q^{5}+9iq^{9}+(-17+17i)q^{13}+\cdots$$
160.3.p.b $$2$$ $$4.360$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+(4+3i)q^{5}+9iq^{9}+(7-7i)q^{13}+\cdots$$
160.3.p.c $$4$$ $$4.360$$ $$\Q(i, \sqrt{15})$$ None None $$0$$ $$0$$ $$-20$$ $$0$$ $$q-\beta _{2}q^{3}-5q^{5}+\beta _{3}q^{7}+21\beta _{1}q^{9}+\cdots$$
160.3.p.d $$4$$ $$4.360$$ $$\Q(i, \sqrt{7})$$ None None $$0$$ $$0$$ $$12$$ $$0$$ $$q-\beta _{2}q^{3}+(3+4\beta _{1})q^{5}-3\beta _{3}q^{7}+5\beta _{1}q^{9}+\cdots$$
160.3.p.e $$6$$ $$4.360$$ 6.0.3534400.1 None None $$0$$ $$0$$ $$4$$ $$-8$$ $$q+\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(-2-2\beta _{3}+\cdots)q^{7}+\cdots$$
160.3.p.f $$6$$ $$4.360$$ 6.0.3534400.1 None None $$0$$ $$0$$ $$4$$ $$8$$ $$q-\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(2+2\beta _{3}+\cdots)q^{7}+\cdots$$
160.3.v.a $$184$$ $$4.360$$ None None $$-4$$ $$-4$$ $$-4$$ $$0$$
160.3.w.a $$128$$ $$4.360$$ None None $$0$$ $$0$$ $$0$$ $$0$$
160.3.y.a $$184$$ $$4.360$$ None None $$0$$ $$0$$ $$-4$$ $$0$$
160.3.bb.a $$184$$ $$4.360$$ None None $$-4$$ $$-4$$ $$-4$$ $$-8$$
160.4.a.a $$1$$ $$9.440$$ $$\Q$$ None None $$0$$ $$-2$$ $$-5$$ $$6$$ $$+$$ $$q-2q^{3}-5q^{5}+6q^{7}-23q^{9}+60q^{11}+\cdots$$
160.4.a.b $$1$$ $$9.440$$ $$\Q$$ None None $$0$$ $$2$$ $$-5$$ $$-6$$ $$-$$ $$q+2q^{3}-5q^{5}-6q^{7}-23q^{9}-60q^{11}+\cdots$$
160.4.a.c $$2$$ $$9.440$$ $$\Q(\sqrt{6})$$ None None $$0$$ $$-8$$ $$10$$ $$-8$$ $$-$$ $$q+(-4+\beta )q^{3}+5q^{5}+(-4-5\beta )q^{7}+\cdots$$
160.4.a.d $$2$$ $$9.440$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$0$$ $$-10$$ $$0$$ $$-$$ $$q-\beta q^{3}-5q^{5}+7\beta q^{7}-7q^{9}+2\beta q^{11}+\cdots$$
160.4.a.e $$2$$ $$9.440$$ $$\Q(\sqrt{13})$$ None None $$0$$ $$0$$ $$-10$$ $$0$$ $$+$$ $$q-\beta q^{3}-5q^{5}-\beta q^{7}+5^{2}q^{9}-6\beta q^{11}+\cdots$$
160.4.a.f $$2$$ $$9.440$$ $$\Q(\sqrt{10})$$ None None $$0$$ $$0$$ $$10$$ $$0$$ $$+$$ $$q+\beta q^{3}+5q^{5}+3\beta q^{7}+13q^{9}-2\beta q^{11}+\cdots$$
160.4.a.g $$2$$ $$9.440$$ $$\Q(\sqrt{6})$$ None None $$0$$ $$8$$ $$10$$ $$8$$ $$+$$ $$q+(4+\beta )q^{3}+5q^{5}+(4-5\beta )q^{7}+(13+\cdots)q^{9}+\cdots$$
160.4.c.a $$2$$ $$9.440$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-22$$ $$0$$ $$q+(-11+i)q^{5}+3^{3}q^{9}-46iq^{13}+\cdots$$
160.4.c.b $$4$$ $$9.440$$ $$\Q(i, \sqrt{29})$$ None None $$0$$ $$0$$ $$-12$$ $$0$$ $$q+\beta _{2}q^{3}+(-3+\beta _{1})q^{5}+\beta _{2}q^{7}+11q^{9}+\cdots$$
160.4.c.c $$4$$ $$9.440$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+2\beta _{3})q^{3}-5\beta _{2}q^{5}+(-6\beta _{1}+\cdots)q^{7}+\cdots$$
160.4.c.d $$8$$ $$9.440$$ 8.0.$$\cdots$$.22 None None $$0$$ $$0$$ $$32$$ $$0$$ $$q+\beta _{1}q^{3}+(4-\beta _{4})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$$
160.4.d.a $$12$$ $$9.440$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-28$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-2+\beta _{4})q^{7}+(-9+\cdots)q^{9}+\cdots$$
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