## Results (displaying matches 1-50 of 63) Next

Label Dim. $$A$$ Field CM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
670.2.a.a $$1$$ $$5.350$$ $$\Q$$ None $$-1$$ $$-2$$ $$1$$ $$-1$$ $$+$$ $$q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{7}+\cdots$$
670.2.a.b $$1$$ $$5.350$$ $$\Q$$ None $$-1$$ $$0$$ $$1$$ $$1$$ $$+$$ $$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-3q^{9}+\cdots$$
670.2.a.c $$1$$ $$5.350$$ $$\Q$$ None $$1$$ $$-2$$ $$-1$$ $$1$$ $$+$$ $$q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots$$
670.2.a.d $$1$$ $$5.350$$ $$\Q$$ None $$1$$ $$0$$ $$-1$$ $$-5$$ $$+$$ $$q+q^{2}+q^{4}-q^{5}-5q^{7}+q^{8}-3q^{9}+\cdots$$
670.2.a.e $$2$$ $$5.350$$ $$\Q(\sqrt{2})$$ None $$-2$$ $$0$$ $$-2$$ $$2$$ $$+$$ $$q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots$$
670.2.a.f $$2$$ $$5.350$$ $$\Q(\sqrt{2})$$ None $$2$$ $$-4$$ $$2$$ $$-6$$ $$+$$ $$q+q^{2}+(-2+\beta )q^{3}+q^{4}+q^{5}+(-2+\cdots)q^{6}+\cdots$$
670.2.a.g $$3$$ $$5.350$$ 3.3.148.1 None $$-3$$ $$4$$ $$3$$ $$1$$ $$-$$ $$q-q^{2}+(1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$$
670.2.a.h $$3$$ $$5.350$$ 3.3.756.1 None $$3$$ $$0$$ $$-3$$ $$3$$ $$-$$ $$q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$$
670.2.a.i $$3$$ $$5.350$$ 3.3.404.1 None $$3$$ $$2$$ $$3$$ $$1$$ $$-$$ $$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots$$
670.2.a.j $$4$$ $$5.350$$ 4.4.15188.1 None $$-4$$ $$-2$$ $$-4$$ $$-5$$ $$-$$ $$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots$$
670.2.c.a $$10$$ $$5.350$$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{8}q^{3}-q^{4}+(\beta _{1}-\beta _{7})q^{5}+\cdots$$
670.2.c.b $$24$$ $$5.350$$ None $$0$$ $$0$$ $$-2$$ $$0$$
670.2.e.a $$2$$ $$5.350$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-6$$ $$-2$$ $$2$$ $$q+(-1+\zeta_{6})q^{2}-3q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots$$
670.2.e.b $$2$$ $$5.350$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-6$$ $$2$$ $$-4$$ $$q+(-1+\zeta_{6})q^{2}-3q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots$$
670.2.e.c $$2$$ $$5.350$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$2$$ $$-2$$ $$5$$ $$q+(-1+\zeta_{6})q^{2}+q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots$$
670.2.e.d $$2$$ $$5.350$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$2$$ $$-2$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}+q^{3}-\zeta_{6}q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots$$
670.2.e.e $$4$$ $$5.350$$ $$\Q(\sqrt{-3}, \sqrt{193})$$ None $$-2$$ $$4$$ $$-4$$ $$-4$$ $$q-\beta _{2}q^{2}+q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots$$
670.2.e.f $$4$$ $$5.350$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-2$$ $$4$$ $$-4$$ $$-4$$ $$q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(-1+\beta _{1})q^{4}+\cdots$$
670.2.e.g $$6$$ $$5.350$$ 6.0.954288.1 None $$3$$ $$-2$$ $$6$$ $$-2$$ $$q+(1-\beta _{3})q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}+q^{5}+\cdots$$
670.2.e.h $$6$$ $$5.350$$ 6.0.2696112.1 None $$3$$ $$2$$ $$6$$ $$2$$ $$q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+q^{5}+\cdots$$
670.2.e.i $$8$$ $$5.350$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-4$$ $$8$$ $$8$$ $$0$$ $$q+(-1+\beta _{2})q^{2}+(1+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$$
670.2.e.j $$12$$ $$5.350$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$6$$ $$-4$$ $$-12$$ $$3$$ $$q-\beta _{5}q^{2}-\beta _{2}q^{3}+(-1-\beta _{5})q^{4}-q^{5}+\cdots$$
670.2.f.a $$68$$ $$5.350$$ None $$0$$ $$0$$ $$0$$ $$0$$
670.2.h.a $$4$$ $$5.350$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
670.2.h.b $$12$$ $$5.350$$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$24$$ $$0$$ $$q+(\beta _{3}+\beta _{4})q^{2}+(-\beta _{4}-\beta _{9})q^{3}+(1+\cdots)q^{4}+\cdots$$
670.2.h.c $$52$$ $$5.350$$ None $$0$$ $$0$$ $$-16$$ $$0$$
670.2.k.a $$40$$ $$5.350$$ None $$-4$$ $$6$$ $$-4$$ $$13$$
670.2.k.b $$50$$ $$5.350$$ None $$-5$$ $$2$$ $$5$$ $$1$$
670.2.k.c $$50$$ $$5.350$$ None $$5$$ $$-2$$ $$-5$$ $$-1$$
670.2.k.d $$60$$ $$5.350$$ None $$6$$ $$2$$ $$6$$ $$3$$
670.2.m.a $$136$$ $$5.350$$ None $$0$$ $$0$$ $$0$$ $$0$$
670.2.o.a $$340$$ $$5.350$$ None $$0$$ $$0$$ $$4$$ $$0$$
670.2.q.a $$100$$ $$5.350$$ None $$5$$ $$-2$$ $$-10$$ $$4$$
670.2.q.b $$120$$ $$5.350$$ None $$-6$$ $$0$$ $$-12$$ $$0$$
670.2.q.c $$120$$ $$5.350$$ None $$6$$ $$-4$$ $$12$$ $$1$$
670.2.q.d $$140$$ $$5.350$$ None $$-7$$ $$2$$ $$14$$ $$-1$$
670.2.s.a $$680$$ $$5.350$$ None $$0$$ $$0$$ $$0$$ $$0$$
670.2.v.a $$680$$ $$5.350$$ None $$0$$ $$0$$ $$-4$$ $$0$$
670.2.w.a $$1360$$ $$5.350$$ None $$0$$ $$0$$ $$0$$ $$0$$
670.3.b.a $$48$$ $$18.256$$ None $$0$$ $$0$$ $$0$$ $$0$$
670.3.d.a $$68$$ $$18.256$$ None $$0$$ $$0$$ $$0$$ $$0$$
670.3.i.a $$88$$ $$18.256$$ None $$0$$ $$0$$ $$0$$ $$-36$$
670.4.a.a $$1$$ $$39.531$$ $$\Q$$ None $$-2$$ $$-6$$ $$-5$$ $$31$$ $$-$$ $$q-2q^{2}-6q^{3}+4q^{4}-5q^{5}+12q^{6}+\cdots$$
670.4.a.b $$1$$ $$39.531$$ $$\Q$$ None $$-2$$ $$7$$ $$-5$$ $$31$$ $$+$$ $$q-2q^{2}+7q^{3}+4q^{4}-5q^{5}-14q^{6}+\cdots$$
670.4.a.c $$6$$ $$39.531$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$-12$$ $$7$$ $$-30$$ $$-10$$ $$-$$ $$q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$$
670.4.a.d $$7$$ $$39.531$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None $$14$$ $$-13$$ $$35$$ $$-49$$ $$-$$ $$q+2q^{2}+(-2+\beta _{5})q^{3}+4q^{4}+5q^{5}+\cdots$$
670.4.a.e $$8$$ $$39.531$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-16$$ $$-12$$ $$-40$$ $$-59$$ $$+$$ $$q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$$
670.4.a.f $$8$$ $$39.531$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-16$$ $$-7$$ $$40$$ $$-1$$ $$-$$ $$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots$$
670.4.a.g $$8$$ $$39.531$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$16$$ $$-5$$ $$-40$$ $$-27$$ $$-$$ $$q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$$
670.4.a.h $$9$$ $$39.531$$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None $$-18$$ $$11$$ $$45$$ $$6$$ $$+$$ $$q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots$$
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