## Results (1-50 of 276 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
819.1.d.a $$1$$ $$0.409$$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-91})$$ $$\Q(\sqrt{273})$$ $$0$$ $$0$$ $$0$$ $$-1$$ $$q+q^{4}-q^{7}+q^{13}+q^{16}+2q^{19}+\cdots$$
819.1.d.b $$1$$ $$0.409$$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-91})$$ $$\Q(\sqrt{273})$$ $$0$$ $$0$$ $$0$$ $$1$$ $$q+q^{4}+q^{7}-q^{13}+q^{16}-2q^{19}+\cdots$$
819.1.bd.a $$2$$ $$0.409$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+q^{4}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}+q^{16}+\zeta_{6}^{2}q^{19}+\cdots$$
819.1.bj.a $$4$$ $$0.409$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q-\beta _{3}q^{2}-q^{4}+\beta _{2}q^{7}+(1-\beta _{2})q^{13}+\cdots$$
819.1.cg.a $$2$$ $$0.409$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q-\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots$$
819.1.cj.a $$4$$ $$0.409$$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}+\zeta_{12}q^{6}+\cdots$$
819.1.cx.a $$2$$ $$0.409$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots$$
819.1.dp.a $$4$$ $$0.409$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{2})q^{7}+\beta _{2}q^{13}+\cdots$$
819.1.ef.a $$2$$ $$0.409$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q-q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}+q^{16}+(1+\cdots)q^{19}+\cdots$$
819.1.ek.a $$4$$ $$0.409$$ $$\Q(\zeta_{12})$$ None None $$4$$ $$0$$ $$0$$ $$-2$$ $$q+q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}q^{6}+\cdots$$
819.1.eu.a $$4$$ $$0.409$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}-\zeta_{12}^{5}q^{13}+\cdots$$
819.1.ff.a $$4$$ $$0.409$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{7}+\zeta_{12}q^{13}+\zeta_{12}^{2}q^{16}+\cdots$$
819.2.a.a $$1$$ $$6.540$$ $$\Q$$ None None $$-2$$ $$0$$ $$-1$$ $$-1$$ $$-$$ $$q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots$$
819.2.a.b $$1$$ $$6.540$$ $$\Q$$ None None $$-1$$ $$0$$ $$0$$ $$-1$$ $$+$$ $$q-q^{2}-q^{4}-q^{7}+3q^{8}-q^{13}+q^{14}+\cdots$$
819.2.a.c $$1$$ $$6.540$$ $$\Q$$ None None $$0$$ $$0$$ $$3$$ $$1$$ $$-$$ $$q-2q^{4}+3q^{5}+q^{7}+q^{13}+4q^{16}+\cdots$$
819.2.a.d $$1$$ $$6.540$$ $$\Q$$ None None $$1$$ $$0$$ $$0$$ $$-1$$ $$+$$ $$q+q^{2}-q^{4}-q^{7}-3q^{8}-q^{13}-q^{14}+\cdots$$
819.2.a.e $$1$$ $$6.540$$ $$\Q$$ None None $$2$$ $$0$$ $$1$$ $$1$$ $$-$$ $$q+2q^{2}+2q^{4}+q^{5}+q^{7}+2q^{10}+\cdots$$
819.2.a.f $$1$$ $$6.540$$ $$\Q$$ None None $$2$$ $$0$$ $$3$$ $$-1$$ $$-$$ $$q+2q^{2}+2q^{4}+3q^{5}-q^{7}+6q^{10}+\cdots$$
819.2.a.g $$2$$ $$6.540$$ $$\Q(\sqrt{2})$$ None None $$-2$$ $$0$$ $$0$$ $$2$$ $$+$$ $$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots$$
819.2.a.h $$2$$ $$6.540$$ $$\Q(\sqrt{2})$$ None None $$0$$ $$0$$ $$-6$$ $$2$$ $$+$$ $$q+\beta q^{2}+(-3+\beta )q^{5}+q^{7}-2\beta q^{8}+\cdots$$
819.2.a.i $$3$$ $$6.540$$ 3.3.316.1 None None $$-1$$ $$0$$ $$-2$$ $$-3$$ $$+$$ $$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1})q^{5}+\cdots$$
819.2.a.j $$3$$ $$6.540$$ 3.3.316.1 None None $$2$$ $$0$$ $$3$$ $$-3$$ $$-$$ $$q+(1-\beta _{1})q^{2}+(2-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$$
819.2.a.k $$4$$ $$6.540$$ 4.4.17428.1 None None $$-1$$ $$0$$ $$3$$ $$4$$ $$-$$ $$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$$
819.2.a.l $$4$$ $$6.540$$ $$\Q(\sqrt{3}, \sqrt{11})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$-$$ $$q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$$
819.2.a.m $$6$$ $$6.540$$ 6.6.199374400.1 None None $$0$$ $$0$$ $$0$$ $$-6$$ $$-$$ $$q+\beta _{4}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}-q^{7}+\cdots$$
819.2.c.a $$2$$ $$6.540$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-2q^{4}+3iq^{5}+iq^{7}-6q^{10}+\cdots$$
819.2.c.b $$6$$ $$6.540$$ 6.0.350464.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}+\beta _{4})q^{2}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
819.2.c.c $$6$$ $$6.540$$ 6.0.350464.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots$$
819.2.c.d $$8$$ $$6.540$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\beta _{7})q^{5}+\cdots$$
819.2.c.e $$12$$ $$6.540$$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(-1+\beta _{10})q^{4}-\beta _{1}q^{5}+\cdots$$
819.2.e.a $$32$$ $$6.540$$ None None $$0$$ $$0$$ $$0$$ $$-8$$
819.2.g.a $$8$$ $$6.540$$ 8.0.$$\cdots$$.5 $$\Q(\sqrt{-91})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2q^{4}+\beta _{5}q^{5}+\beta _{1}q^{7}+\beta _{3}q^{13}+\cdots$$
819.2.g.b $$8$$ $$6.540$$ 8.0.40960000.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+3q^{4}-2\beta _{1}q^{5}+(\beta _{2}+2\beta _{7})q^{7}+\cdots$$
819.2.g.c $$12$$ $$6.540$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$-12$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{5})q^{2}+(2-\beta _{1}-\beta _{5})q^{4}+\cdots$$
819.2.g.d $$12$$ $$6.540$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$12$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{5})q^{2}+(2-\beta _{1}-\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots$$
819.2.i.a $$84$$ $$6.540$$ None None $$-4$$ $$1$$ $$-8$$ $$84$$
819.2.i.b $$84$$ $$6.540$$ None None $$4$$ $$-1$$ $$8$$ $$-84$$
819.2.j.a $$2$$ $$6.540$$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$0$$ $$4$$ $$-5$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$$
819.2.j.b $$2$$ $$6.540$$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$0$$ $$0$$ $$1$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots$$
819.2.j.c $$4$$ $$6.540$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$-3$$ $$0$$ $$0$$ $$-8$$ $$q+(-1-\beta _{1}-\beta _{3})q^{2}+(3\beta _{1}+3\beta _{2}+\cdots)q^{4}+\cdots$$
819.2.j.d $$6$$ $$6.540$$ 6.0.64827.1 None None $$-2$$ $$0$$ $$-3$$ $$0$$ $$q+(-1+\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
819.2.j.e $$6$$ $$6.540$$ $$\Q(\zeta_{18})$$ None None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$$
819.2.j.f $$8$$ $$6.540$$ 8.0.4868829729.1 None None $$-1$$ $$0$$ $$3$$ $$9$$ $$q+(\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(\beta _{3}+2\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$$
819.2.j.g $$10$$ $$6.540$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$0$$ $$-3$$ $$4$$ $$q+(-\beta _{4}+\beta _{8})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
819.2.j.h $$10$$ $$6.540$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$4$$ $$0$$ $$2$$ $$1$$ $$q+(-\beta _{1}+\beta _{7})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
819.2.j.i $$12$$ $$6.540$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(\beta _{1}+\beta _{6})q^{2}+(-1-\beta _{5}-\beta _{9})q^{4}+\cdots$$
819.2.j.j $$20$$ $$6.540$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{4}q^{2}+(-2-2\beta _{3}-\beta _{14})q^{4}-\beta _{10}q^{5}+\cdots$$
819.2.k.a $$216$$ $$6.540$$ None None $$-1$$ $$1$$ $$2$$ $$-6$$
819.2.l.a $$216$$ $$6.540$$ None None $$-1$$ $$-2$$ $$2$$ $$3$$
819.2.m.a $$2$$ $$6.540$$ $$\Q(\sqrt{-3})$$ None None $$2$$ $$3$$ $$-2$$ $$1$$ $$q+(2-2\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$$