## Results (1-50 of 189 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
840.1.bp.a $$4$$ $$0.419$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots$$
840.1.bp.b $$4$$ $$0.419$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots$$
840.1.bp.c $$8$$ $$0.419$$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{5}q^{3}+\zeta_{16}^{4}q^{4}+\cdots$$
840.1.bp.d $$8$$ $$0.419$$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots$$
840.1.cg.a $$4$$ $$0.419$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots$$
840.1.cg.b $$4$$ $$0.419$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots$$
840.1.dh.a $$8$$ $$0.419$$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots$$
840.1.dh.b $$8$$ $$0.419$$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots$$
840.2.a.a $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$-1$$ $$+$$ $$q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$$
840.2.a.b $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$1$$ $$+$$ $$q-q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$$
840.2.a.c $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$1$$ $$-$$ $$q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots$$
840.2.a.d $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$-1$$ $$+$$ $$q-q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$$
840.2.a.e $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$-1$$ $$-$$ $$q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots$$
840.2.a.f $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$1$$ $$-$$ $$q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$$
840.2.a.g $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$-1$$ $$+$$ $$q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$$
840.2.a.h $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$-1$$ $$-$$ $$q+q^{3}-q^{5}-q^{7}+q^{9}+6q^{13}-q^{15}+\cdots$$
840.2.a.i $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$1$$ $$-$$ $$q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{13}-q^{15}+\cdots$$
840.2.a.j $$1$$ $$6.707$$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$-1$$ $$-$$ $$q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$$
840.2.a.k $$2$$ $$6.707$$ $$\Q(\sqrt{2})$$ None None $$0$$ $$2$$ $$2$$ $$2$$ $$-$$ $$q+q^{3}+q^{5}+q^{7}+q^{9}+\beta q^{11}+2q^{13}+\cdots$$
840.2.e.a $$4$$ $$6.707$$ $$\Q(\zeta_{8})$$ None None $$-4$$ $$-4$$ $$-4$$ $$0$$ $$q+(-1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}-2\zeta_{8}q^{4}+\cdots$$
840.2.e.b $$4$$ $$6.707$$ $$\Q(\zeta_{8})$$ None None $$4$$ $$-4$$ $$4$$ $$0$$ $$q+(1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}+2\zeta_{8}q^{4}+\cdots$$
840.2.e.c $$44$$ $$6.707$$ None None $$-2$$ $$4$$ $$44$$ $$0$$
840.2.e.d $$44$$ $$6.707$$ None None $$2$$ $$4$$ $$-44$$ $$0$$
840.2.f.a $$16$$ $$6.707$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$-16$$ $$2$$ $$q+\beta _{2}q^{3}-q^{5}+\beta _{4}q^{7}-\beta _{1}q^{9}+\beta _{8}q^{11}+\cdots$$
840.2.f.b $$16$$ $$6.707$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$16$$ $$2$$ $$q-\beta _{2}q^{3}+q^{5}+\beta _{9}q^{7}-\beta _{1}q^{9}+\beta _{8}q^{11}+\cdots$$
840.2.g.a $$8$$ $$6.707$$ $$\Q(\zeta_{16})$$ None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\zeta_{16}^{5}q^{2}+\zeta_{16}^{2}q^{3}-\zeta_{16}q^{4}+\zeta_{16}^{2}q^{5}+\cdots$$
840.2.g.b $$12$$ $$6.707$$ 12.0.$$\cdots$$.1 None None $$-2$$ $$0$$ $$0$$ $$-12$$ $$q+\beta _{2}q^{2}-\beta _{4}q^{3}-\beta _{7}q^{4}-\beta _{4}q^{5}+\cdots$$
840.2.g.c $$12$$ $$6.707$$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$12$$ $$q+\beta _{5}q^{2}+\beta _{4}q^{3}+\beta _{7}q^{4}-\beta _{4}q^{5}+\cdots$$
840.2.g.d $$16$$ $$6.707$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-2$$ $$0$$ $$0$$ $$-16$$ $$q-\beta _{4}q^{2}-\beta _{5}q^{3}-\beta _{2}q^{4}+\beta _{5}q^{5}+\cdots$$
840.2.j.a $$2$$ $$6.707$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$-4$$ $$0$$ $$q+(-1-i)q^{2}-q^{3}+2iq^{4}+(-2+\cdots)q^{5}+\cdots$$
840.2.j.b $$2$$ $$6.707$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$2$$ $$-4$$ $$0$$ $$q+(-1+i)q^{2}+q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots$$
840.2.j.c $$2$$ $$6.707$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$-2$$ $$4$$ $$0$$ $$q+(1+i)q^{2}-q^{3}+2iq^{4}+(2+i)q^{5}+\cdots$$
840.2.j.d $$2$$ $$6.707$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$2$$ $$4$$ $$0$$ $$q+(1+i)q^{2}+q^{3}+2iq^{4}+(2+i)q^{5}+\cdots$$
840.2.j.e $$32$$ $$6.707$$ None None $$-2$$ $$-32$$ $$0$$ $$0$$
840.2.j.f $$32$$ $$6.707$$ None None $$2$$ $$32$$ $$0$$ $$0$$
840.2.k.a $$24$$ $$6.707$$ None None $$0$$ $$0$$ $$0$$ $$0$$
840.2.k.b $$24$$ $$6.707$$ None None $$0$$ $$0$$ $$0$$ $$0$$
840.2.p.a $$72$$ $$6.707$$ None None $$0$$ $$0$$ $$0$$ $$-72$$
840.2.p.b $$72$$ $$6.707$$ None None $$0$$ $$0$$ $$0$$ $$72$$
840.2.t.a $$2$$ $$6.707$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{3}+(-1-2i)q^{5}-iq^{7}-q^{9}+\cdots$$
840.2.t.b $$2$$ $$6.707$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{3}+(-1+2i)q^{5}-iq^{7}-q^{9}+\cdots$$
840.2.t.c $$4$$ $$6.707$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}-q^{9}-2q^{11}+\cdots$$
840.2.t.d $$6$$ $$6.707$$ 6.0.350464.1 None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$$
840.2.t.e $$6$$ $$6.707$$ 6.0.350464.1 None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots$$
840.2.u.a $$4$$ $$6.707$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{1}q^{2}-\beta _{2}q^{3}-2q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
840.2.u.b $$4$$ $$6.707$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{3}-2q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
840.2.u.c $$8$$ $$6.707$$ 8.0.2517630976.5 $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}-\beta _{6}q^{5}+(\beta _{3}+\cdots)q^{6}+\cdots$$
840.2.u.d $$8$$ $$6.707$$ 8.0.2517630976.5 $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{7}q^{3}+2q^{4}+\beta _{6}q^{5}+(\beta _{2}+\cdots)q^{6}+\cdots$$
840.2.u.e $$160$$ $$6.707$$ None None $$0$$ $$0$$ $$0$$ $$0$$
840.2.w.a $$48$$ $$6.707$$ None None $$0$$ $$-48$$ $$0$$ $$0$$