## Results (1-50 of 176 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
168.1.s.a $$2$$ $$0.084$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-6})$$ None $$-1$$ $$-1$$ $$1$$ $$-1$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$$
168.1.s.b $$2$$ $$0.084$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-6})$$ None $$1$$ $$1$$ $$-1$$ $$-1$$ $$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$$
168.2.a.a $$1$$ $$1.341$$ $$\Q$$ None None $$0$$ $$-1$$ $$2$$ $$1$$ $$-$$ $$q-q^{3}+2q^{5}+q^{7}+q^{9}+6q^{13}-2q^{15}+\cdots$$
168.2.a.b $$1$$ $$1.341$$ $$\Q$$ None None $$0$$ $$1$$ $$2$$ $$-1$$ $$-$$ $$q+q^{3}+2q^{5}-q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots$$
168.2.c.a $$4$$ $$1.341$$ $$\Q(\zeta_{12})$$ None None $$2$$ $$0$$ $$0$$ $$-4$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+\zeta_{12}^{2}q^{3}+(\zeta_{12}+\cdots)q^{4}+\cdots$$
168.2.c.b $$8$$ $$1.341$$ 8.0.386672896.3 None None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{4}q^{2}-\beta _{2}q^{3}+\beta _{1}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
168.2.i.a $$4$$ $$1.341$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$-4$$ $$0$$ $$-8$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots$$
168.2.i.b $$4$$ $$1.341$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+2\beta _{2}q^{5}+\cdots$$
168.2.i.c $$4$$ $$1.341$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$4$$ $$0$$ $$-8$$ $$q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots$$
168.2.i.d $$8$$ $$1.341$$ 8.0.$$\cdots$$.11 $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}+(\beta _{6}-\beta _{7})q^{5}+\cdots$$
168.2.i.e $$8$$ $$1.341$$ 8.0.3317760000.1 None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\beta _{5}q^{2}+(-\beta _{4}-\beta _{6})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$$
168.2.j.a $$4$$ $$1.341$$ $$\Q(i, \sqrt{5})$$ None None $$-4$$ $$-2$$ $$4$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$$
168.2.j.b $$4$$ $$1.341$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+2q^{4}+2\zeta_{8}^{3}q^{5}+\cdots$$
168.2.j.c $$4$$ $$1.341$$ $$\Q(i, \sqrt{5})$$ None None $$4$$ $$-2$$ $$-4$$ $$0$$ $$q+(1+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$$
168.2.j.d $$12$$ $$1.341$$ 12.0.$$\cdots$$.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots$$
168.2.k.a $$8$$ $$1.341$$ 8.0.342102016.5 None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-1-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots$$
168.2.p.a $$16$$ $$1.341$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{6}-\beta _{11}+\cdots)q^{5}+\cdots$$
168.2.q.a $$2$$ $$1.341$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$1$$ $$1$$ $$q-\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots$$
168.2.q.b $$2$$ $$1.341$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-2$$ $$5$$ $$q+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+\cdots$$
168.2.q.c $$4$$ $$1.341$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None None $$0$$ $$2$$ $$1$$ $$-6$$ $$q+(1-\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$$
168.2.t.a $$32$$ $$1.341$$ None None $$-2$$ $$0$$ $$0$$ $$0$$
168.2.u.a $$16$$ $$1.341$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(\beta _{3}+\beta _{9})q^{3}+\beta _{14}q^{5}-\beta _{10}q^{7}+\cdots$$
168.2.v.a $$56$$ $$1.341$$ None None $$0$$ $$-2$$ $$0$$ $$0$$
168.2.ba.a $$4$$ $$1.341$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$-6$$ $$6$$ $$-2$$ $$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$$
168.2.ba.b $$4$$ $$1.341$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$6$$ $$-6$$ $$-2$$ $$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
168.2.ba.c $$48$$ $$1.341$$ None None $$0$$ $$0$$ $$0$$ $$-4$$
168.2.bc.a $$32$$ $$1.341$$ None None $$2$$ $$0$$ $$0$$ $$0$$
168.3.d.a $$12$$ $$4.578$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+(-\beta _{3}-\beta _{11})q^{5}+\beta _{1}q^{7}+\cdots$$
168.3.e.a $$1$$ $$4.578$$ $$\Q$$ $$\Q(\sqrt{-42})$$ None $$-2$$ $$-3$$ $$0$$ $$-7$$ $$q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-7q^{7}+\cdots$$
168.3.e.b $$1$$ $$4.578$$ $$\Q$$ $$\Q(\sqrt{-42})$$ None $$-2$$ $$3$$ $$0$$ $$7$$ $$q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+7q^{7}+\cdots$$
168.3.e.c $$1$$ $$4.578$$ $$\Q$$ $$\Q(\sqrt{-42})$$ None $$2$$ $$-3$$ $$0$$ $$7$$ $$q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+7q^{7}+\cdots$$
168.3.e.d $$1$$ $$4.578$$ $$\Q$$ $$\Q(\sqrt{-42})$$ None $$2$$ $$3$$ $$0$$ $$-7$$ $$q+2q^{2}+3q^{3}+4q^{4}+6q^{6}-7q^{7}+\cdots$$
168.3.e.e $$8$$ $$4.578$$ 8.0.$$\cdots$$.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{3})q^{2}+(\beta _{2}+\beta _{6})q^{3}+(3-\beta _{7})q^{4}+\cdots$$
168.3.e.f $$48$$ $$4.578$$ None None $$0$$ $$0$$ $$0$$ $$0$$
168.3.f.a $$8$$ $$4.578$$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$$
168.3.g.a $$24$$ $$4.578$$ None None $$-2$$ $$0$$ $$0$$ $$0$$
168.3.l.a $$32$$ $$4.578$$ None None $$-2$$ $$0$$ $$0$$ $$0$$
168.3.n.a $$48$$ $$4.578$$ None None $$0$$ $$0$$ $$0$$ $$0$$
168.3.s.a $$4$$ $$4.578$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ None $$-4$$ $$6$$ $$-2$$ $$10$$ $$q+(-2-2\beta _{1})q^{2}-3\beta _{1}q^{3}+4\beta _{1}q^{4}+\cdots$$
168.3.s.b $$4$$ $$4.578$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ None $$4$$ $$-6$$ $$2$$ $$10$$ $$q+(2+2\beta _{1})q^{2}+3\beta _{1}q^{3}+4\beta _{1}q^{4}+\cdots$$
168.3.s.c $$112$$ $$4.578$$ None None $$0$$ $$0$$ $$0$$ $$-28$$
168.3.x.a $$4$$ $$4.578$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$-26$$ $$q+2\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+4\zeta_{12}^{2}q^{4}+\cdots$$
168.3.x.b $$60$$ $$4.578$$ None None $$2$$ $$0$$ $$0$$ $$26$$
168.3.y.a $$64$$ $$4.578$$ None None $$-2$$ $$0$$ $$0$$ $$0$$
168.3.z.a $$8$$ $$4.578$$ 8.0.$$\cdots$$.2 None None $$0$$ $$-12$$ $$6$$ $$-4$$ $$q+(-2+\beta _{4})q^{3}+(1+\beta _{6})q^{5}+(1-3\beta _{4}+\cdots)q^{7}+\cdots$$
168.3.z.b $$8$$ $$4.578$$ 8.0.$$\cdots$$.9 None None $$0$$ $$12$$ $$-6$$ $$8$$ $$q+(1-\beta _{2})q^{3}+(-1+\beta _{7})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$$
168.3.be.a $$120$$ $$4.578$$ None None $$0$$ $$-6$$ $$0$$ $$0$$
168.3.bf.a $$32$$ $$4.578$$ None None $$0$$ $$0$$ $$0$$ $$12$$
168.4.a.a $$1$$ $$9.912$$ $$\Q$$ None None $$0$$ $$-3$$ $$-10$$ $$7$$ $$+$$ $$q-3q^{3}-10q^{5}+7q^{7}+9q^{9}-12q^{11}+\cdots$$
168.4.a.b $$1$$ $$9.912$$ $$\Q$$ None None $$0$$ $$-3$$ $$-2$$ $$7$$ $$-$$ $$q-3q^{3}-2q^{5}+7q^{7}+9q^{9}+12q^{11}+\cdots$$