## Results (1-50 of 160 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
684.1.h.a $$1$$ $$0.341$$ $$\Q$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$-1$$ $$q+q^{5}-q^{7}+q^{11}+q^{17}+q^{19}-2q^{23}+\cdots$$
684.1.h.b $$2$$ $$0.341$$ $$\Q(\sqrt{3})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-\beta q^{5}+q^{7}+\beta q^{11}+\beta q^{17}-q^{19}+\cdots$$
684.1.q.a $$8$$ $$0.341$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{11}+\cdots)q^{5}+\cdots$$
684.1.x.a $$4$$ $$0.341$$ $$\Q(\zeta_{12})$$ None None $$-4$$ $$0$$ $$2$$ $$0$$ $$q-q^{2}-\zeta_{12}^{3}q^{3}+q^{4}+\zeta_{12}^{2}q^{5}+\cdots$$
684.1.bm.a $$4$$ $$0.341$$ $$\Q(\zeta_{12})$$ None None $$2$$ $$0$$ $$-4$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$$
684.1.bx.a $$6$$ $$0.341$$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{18}^{5}+\zeta_{18}^{7})q^{7}+(\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{13}+\cdots$$
684.2.a.a $$1$$ $$5.462$$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$+$$ $$q-2q^{5}-2q^{11}+2q^{13}-6q^{17}-q^{19}+\cdots$$
684.2.a.b $$1$$ $$5.462$$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-3$$ $$+$$ $$q+q^{5}-3q^{7}-5q^{11}-4q^{13}+3q^{17}+\cdots$$
684.2.a.c $$1$$ $$5.462$$ $$\Q$$ None None $$0$$ $$0$$ $$3$$ $$1$$ $$-$$ $$q+3q^{5}+q^{7}+5q^{11}-6q^{13}+5q^{17}+\cdots$$
684.2.a.d $$2$$ $$5.462$$ $$\Q(\sqrt{33})$$ None None $$0$$ $$0$$ $$-3$$ $$1$$ $$-$$ $$q+(-1-\beta )q^{5}+(1-\beta )q^{7}+(1+\beta )q^{11}+\cdots$$
684.2.a.e $$2$$ $$5.462$$ $$\Q(\sqrt{7})$$ None None $$0$$ $$0$$ $$0$$ $$6$$ $$-$$ $$q+\beta q^{5}+3q^{7}+\beta q^{11}+2q^{13}-3\beta q^{17}+\cdots$$
684.2.c.a $$4$$ $$5.462$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}^{2}q^{5}+4\zeta_{8}q^{7}+\cdots$$
684.2.c.b $$32$$ $$5.462$$ None None $$0$$ $$0$$ $$0$$ $$0$$
684.2.d.a $$8$$ $$5.462$$ 8.0.$$\cdots$$.4 $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}-\beta _{2}q^{7}-\beta _{6}q^{11}+(\beta _{3}-\beta _{5}+\cdots)q^{17}+\cdots$$
684.2.f.a $$4$$ $$5.462$$ $$\Q(\sqrt{-2}, \sqrt{19})$$ $$\Q(\sqrt{-57})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-2q^{4}+2\beta _{1}q^{8}-\beta _{2}q^{11}+\cdots$$
684.2.f.b $$8$$ $$5.462$$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(1-\beta _{2}+\beta _{6}+\cdots)q^{5}+\cdots$$
684.2.f.c $$10$$ $$5.462$$ 10.0.$$\cdots$$.1 None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{4}q^{5}-\beta _{5}q^{7}+\cdots$$
684.2.f.d $$10$$ $$5.462$$ 10.0.$$\cdots$$.1 None None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{4}q^{5}-\beta _{5}q^{7}+\cdots$$
684.2.f.e $$16$$ $$5.462$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}-\beta _{11}q^{5}+(\beta _{7}+\cdots)q^{7}+\cdots$$
684.2.i.a $$2$$ $$5.462$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-3$$ $$5$$ $$q+(1-2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(5-5\zeta_{6})q^{7}+\cdots$$
684.2.i.b $$2$$ $$5.462$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$1$$ $$-3$$ $$q+(1-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots$$
684.2.i.c $$16$$ $$5.462$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$-1$$ $$2$$ $$3$$ $$q-\beta _{1}q^{3}-\beta _{13}q^{5}+(-\beta _{3}+\beta _{8}+\beta _{11}+\cdots)q^{7}+\cdots$$
684.2.i.d $$16$$ $$5.462$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$-1$$ $$6$$ $$-5$$ $$q+(\beta _{2}+\beta _{13})q^{3}+(\beta _{7}+\beta _{8})q^{5}+(-1+\cdots)q^{7}+\cdots$$
684.2.j.a $$40$$ $$5.462$$ None None $$0$$ $$-2$$ $$0$$ $$-1$$
684.2.k.a $$2$$ $$5.462$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-4$$ $$-6$$ $$q+(-4+4\zeta_{6})q^{5}-3q^{7}+4q^{11}-5\zeta_{6}q^{13}+\cdots$$
684.2.k.b $$2$$ $$5.462$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$0$$ $$q+(-1+\zeta_{6})q^{5}+4q^{11}+\zeta_{6}q^{13}+\cdots$$
684.2.k.c $$2$$ $$5.462$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-q^{7}+7\zeta_{6}q^{13}+(5-2\zeta_{6})q^{19}+5\zeta_{6}q^{25}+\cdots$$
684.2.k.d $$2$$ $$5.462$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$10$$ $$q+5q^{7}-5\zeta_{6}q^{13}+(3+2\zeta_{6})q^{19}+\cdots$$
684.2.k.e $$2$$ $$5.462$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$4$$ $$-6$$ $$q+(4-4\zeta_{6})q^{5}-3q^{7}-4q^{11}-5\zeta_{6}q^{13}+\cdots$$
684.2.k.f $$4$$ $$5.462$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{5}+(-1+\beta _{3})q^{7}-\beta _{3}q^{11}+\cdots$$
684.2.k.g $$4$$ $$5.462$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None None $$0$$ $$0$$ $$2$$ $$8$$ $$q+(1+\beta _{1}+\beta _{2})q^{5}+(2-\beta _{3})q^{7}+(-3+\cdots)q^{11}+\cdots$$
684.2.l.a $$40$$ $$5.462$$ None None $$0$$ $$1$$ $$0$$ $$-1$$
684.2.n.a $$2$$ $$5.462$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}-3q^{9}+\cdots$$
684.2.n.b $$38$$ $$5.462$$ None None $$0$$ $$3$$ $$0$$ $$2$$
684.2.o.a $$232$$ $$5.462$$ None None $$-3$$ $$0$$ $$0$$ $$0$$
684.2.r.a $$16$$ $$5.462$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$3$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{12}q^{2}+(-1-\beta _{1}+\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots$$
684.2.r.b $$20$$ $$5.462$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$-1$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{4})q^{2}+(-\beta _{2}-\beta _{9})q^{4}+\cdots$$
684.2.r.c $$20$$ $$5.462$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$1$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{16}q^{2}+(\beta _{14}-\beta _{17})q^{4}-\beta _{6}q^{5}+\cdots$$
684.2.r.d $$40$$ $$5.462$$ None None $$0$$ $$0$$ $$0$$ $$0$$
684.2.u.a $$232$$ $$5.462$$ None None $$0$$ $$0$$ $$2$$ $$0$$
684.2.w.a $$232$$ $$5.462$$ None None $$0$$ $$0$$ $$-4$$ $$0$$
684.2.z.a $$8$$ $$5.462$$ 8.0.$$\cdots$$.3 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-2\beta _{4}q^{4}-2\beta _{3}q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots$$
684.2.z.b $$72$$ $$5.462$$ None None $$0$$ $$0$$ $$0$$ $$0$$
684.2.bb.a $$2$$ $$5.462$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$0$$ $$-1$$ $$q+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{7}+(3-3\zeta_{6})q^{9}+\cdots$$
684.2.bb.b $$38$$ $$5.462$$ None None $$0$$ $$3$$ $$0$$ $$2$$
684.2.bd.a $$40$$ $$5.462$$ None None $$0$$ $$0$$ $$0$$ $$-2$$
684.2.bg.a $$4$$ $$5.462$$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$0$$ $$-6$$ $$-12$$ $$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
684.2.bg.b $$4$$ $$5.462$$ $$\Q(\zeta_{12})$$ None None $$2$$ $$0$$ $$-6$$ $$12$$ $$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1+2\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
684.2.bg.c $$208$$ $$5.462$$ None None $$0$$ $$0$$ $$12$$ $$0$$
684.2.bi.a $$232$$ $$5.462$$ None None $$0$$ $$0$$ $$-6$$ $$0$$