## Results (displaying matches 1-50 of 103) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
308.1.g.a $$1$$ $$0.154$$ $$\Q$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-77})$$ $$\Q(\sqrt{11})$$ $$-1$$ $$0$$ $$0$$ $$1$$ $$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{9}+q^{11}+\cdots$$
308.1.g.b $$1$$ $$0.154$$ $$\Q$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-77})$$ $$\Q(\sqrt{11})$$ $$1$$ $$0$$ $$0$$ $$-1$$ $$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}-q^{11}+\cdots$$
308.1.s.a $$4$$ $$0.154$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$1$$ $$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{7}+\cdots$$
308.1.s.b $$4$$ $$0.154$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$-1$$ $$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}^{4}q^{8}+\cdots$$
308.2.a.a $$1$$ $$2.459$$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$-1$$ $$+$$ $$q-q^{3}-q^{5}-q^{7}-2q^{9}+q^{11}-4q^{13}+\cdots$$
308.2.a.b $$2$$ $$2.459$$ $$\Q(\sqrt{6})$$ None None $$0$$ $$0$$ $$4$$ $$-2$$ $$-$$ $$q+\beta q^{3}+2q^{5}-q^{7}+3q^{9}-q^{11}+\cdots$$
308.2.a.c $$3$$ $$2.459$$ 3.3.1016.1 None None $$0$$ $$-1$$ $$-1$$ $$3$$ $$-$$ $$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots$$
308.2.c.a $$4$$ $$2.459$$ $$\Q(\sqrt{2}, \sqrt{-5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}-2q^{9}+\cdots$$
308.2.c.b $$4$$ $$2.459$$ $$\Q(\sqrt{-2}, \sqrt{-7})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}-2\beta _{2}q^{5}-\beta _{3}q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots$$
308.2.d.a $$18$$ $$2.459$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$-1$$ $$0$$ $$0$$ $$18$$ $$q+\beta _{12}q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}-\beta _{10}q^{5}+\cdots$$
308.2.d.b $$18$$ $$2.459$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$1$$ $$0$$ $$0$$ $$-18$$ $$q-\beta _{12}q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}-\beta _{10}q^{5}+\cdots$$
308.2.f.a $$40$$ $$2.459$$ None None $$0$$ $$0$$ $$0$$ $$0$$
308.2.i.a $$6$$ $$2.459$$ 6.0.309123.1 None None $$0$$ $$-1$$ $$2$$ $$4$$ $$q-\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots$$
308.2.i.b $$6$$ $$2.459$$ 6.0.1783323.2 None None $$0$$ $$3$$ $$2$$ $$2$$ $$q+(1-\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots$$
308.2.j.a $$4$$ $$2.459$$ $$\Q(\zeta_{10})$$ None None $$0$$ $$4$$ $$-2$$ $$1$$ $$q+(2\zeta_{10}+2\zeta_{10}^{3})q^{3}-2\zeta_{10}q^{5}+\zeta_{10}^{3}q^{7}+\cdots$$
308.2.j.b $$8$$ $$2.459$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$0$$ $$-8$$ $$-1$$ $$2$$ $$q+(-2-2\beta _{2}-\beta _{3}-\beta _{6})q^{3}+\beta _{7}q^{5}+\cdots$$
308.2.j.c $$12$$ $$2.459$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$6$$ $$1$$ $$-3$$ $$q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{8}-\beta _{9}+\beta _{11})q^{3}+\cdots$$
308.2.l.a $$80$$ $$2.459$$ None None $$0$$ $$0$$ $$0$$ $$0$$
308.2.n.a $$4$$ $$2.459$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None None $$-1$$ $$0$$ $$0$$ $$-2$$ $$q-\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$$
308.2.n.b $$4$$ $$2.459$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None None $$1$$ $$0$$ $$0$$ $$2$$ $$q+\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$$
308.2.n.c $$80$$ $$2.459$$ None None $$0$$ $$0$$ $$-4$$ $$0$$
308.2.q.a $$16$$ $$2.459$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$6$$ $$0$$ $$q-\beta _{3}q^{3}+\beta _{5}q^{5}+\beta _{9}q^{7}+\beta _{7}q^{9}+\cdots$$
308.2.t.a $$8$$ $$2.459$$ 8.0.37515625.1 $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$$
308.2.t.b $$8$$ $$2.459$$ 8.0.37515625.1 $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$$
308.2.t.c $$160$$ $$2.459$$ None None $$-10$$ $$0$$ $$0$$ $$0$$
308.2.v.a $$72$$ $$2.459$$ None None $$-1$$ $$0$$ $$0$$ $$18$$
308.2.v.b $$72$$ $$2.459$$ None None $$1$$ $$0$$ $$0$$ $$-18$$
308.2.w.a $$32$$ $$2.459$$ None None $$0$$ $$0$$ $$0$$ $$-5$$
308.2.y.a $$16$$ $$2.459$$ 16.0.$$\cdots$$.1 None None $$0$$ $$1$$ $$-5$$ $$14$$ $$q+(-\beta _{3}+\beta _{6}+\beta _{7}+\beta _{12}-\beta _{15})q^{3}+\cdots$$
308.2.y.b $$48$$ $$2.459$$ None None $$0$$ $$-1$$ $$7$$ $$-7$$
308.2.z.a $$64$$ $$2.459$$ None None $$0$$ $$0$$ $$-6$$ $$5$$
308.2.bc.a $$352$$ $$2.459$$ None None $$-5$$ $$0$$ $$-6$$ $$0$$
308.2.be.a $$352$$ $$2.459$$ None None $$-1$$ $$0$$ $$-18$$ $$0$$
308.3.b.a $$12$$ $$8.392$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-6$$ $$q+\beta _{1}q^{3}-\beta _{5}q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots$$
308.3.e.a $$60$$ $$8.392$$ None None $$0$$ $$0$$ $$8$$ $$0$$
308.3.g.a $$2$$ $$8.392$$ $$\Q(\sqrt{14})$$ $$\Q(\sqrt{-77})$$ None $$-4$$ $$0$$ $$0$$ $$-14$$ $$q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}-7q^{7}+\cdots$$
308.3.g.b $$2$$ $$8.392$$ $$\Q(\sqrt{22})$$ $$\Q(\sqrt{-77})$$ None $$-4$$ $$0$$ $$0$$ $$14$$ $$q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}+7q^{7}+\cdots$$
308.3.g.c $$2$$ $$8.392$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$-3$$ $$0$$ $$0$$ $$14$$ $$q+(-1-\beta )q^{2}+(-1+3\beta )q^{4}+7q^{7}+\cdots$$
308.3.g.d $$2$$ $$8.392$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$3$$ $$0$$ $$0$$ $$-14$$ $$q+(1+\beta )q^{2}+(-1+3\beta )q^{4}-7q^{7}+\cdots$$
308.3.g.e $$2$$ $$8.392$$ $$\Q(\sqrt{22})$$ $$\Q(\sqrt{-77})$$ None $$4$$ $$0$$ $$0$$ $$-14$$ $$q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}-7q^{7}+\cdots$$
308.3.g.f $$2$$ $$8.392$$ $$\Q(\sqrt{14})$$ $$\Q(\sqrt{-77})$$ None $$4$$ $$0$$ $$0$$ $$14$$ $$q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}+7q^{7}+\cdots$$
308.3.g.g $$80$$ $$8.392$$ None None $$0$$ $$0$$ $$0$$ $$0$$
308.3.h.a $$12$$ $$8.392$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-10$$ $$-6$$ $$0$$ $$q+(-1+\beta _{3})q^{3}+(-1+\beta _{4})q^{5}+\beta _{5}q^{7}+\cdots$$
308.3.k.a $$32$$ $$8.392$$ None None $$0$$ $$0$$ $$-2$$ $$0$$
308.3.m.a $$184$$ $$8.392$$ None None $$0$$ $$0$$ $$-12$$ $$0$$
308.3.o.a $$160$$ $$8.392$$ None None $$0$$ $$0$$ $$0$$ $$0$$
308.3.p.a $$28$$ $$8.392$$ None None $$0$$ $$-6$$ $$0$$ $$14$$
308.3.r.a $$48$$ $$8.392$$ None None $$0$$ $$10$$ $$6$$ $$0$$
308.3.s.a $$8$$ $$8.392$$ 8.0.37515625.1 $$\Q(\sqrt{-7})$$ None $$-3$$ $$0$$ $$0$$ $$14$$ $$q+(-\beta _{4}+\beta _{5})q^{2}+(3\beta _{2}+\beta _{7})q^{4}-7\beta _{3}q^{7}+\cdots$$
308.3.s.b $$8$$ $$8.392$$ 8.0.37515625.1 $$\Q(\sqrt{-7})$$ None $$3$$ $$0$$ $$0$$ $$-14$$ $$q+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots$$
Next