## Results (1-50 of 187 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
416.1.h.a $$1$$ $$0.208$$ $$\Q$$ $$\Q(\sqrt{-26})$$ None $$0$$ $$1$$ $$-1$$ $$1$$ $$q+q^{3}-q^{5}+q^{7}+q^{13}-q^{15}-q^{17}+\cdots$$
416.1.h.b $$1$$ $$0.208$$ $$\Q$$ $$\Q(\sqrt{-26})$$ None $$0$$ $$1$$ $$1$$ $$-1$$ $$q+q^{3}+q^{5}-q^{7}-q^{13}+q^{15}-q^{17}+\cdots$$
416.1.t.a $$2$$ $$0.208$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+i)q^{5}-q^{9}+iq^{13}-iq^{17}+\cdots$$
416.1.bb.a $$4$$ $$0.208$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{7}-\zeta_{12}q^{11}+q^{13}+\cdots$$
416.1.bl.a $$4$$ $$0.208$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}q^{13}+\cdots$$
416.2.a.a $$1$$ $$3.322$$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$-3$$ $$+$$ $$q-q^{3}+q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$$
416.2.a.b $$1$$ $$3.322$$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$3$$ $$-$$ $$q+q^{3}+q^{5}+3q^{7}-2q^{9}+2q^{11}+\cdots$$
416.2.a.c $$2$$ $$3.322$$ $$\Q(\sqrt{17})$$ None None $$0$$ $$-1$$ $$-3$$ $$-3$$ $$+$$ $$q-\beta q^{3}+(-2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots$$
416.2.a.d $$2$$ $$3.322$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$0$$ $$6$$ $$0$$ $$-$$ $$q-\beta q^{3}+3q^{5}-\beta q^{7}+2q^{9}+2\beta q^{11}+\cdots$$
416.2.a.e $$2$$ $$3.322$$ $$\Q(\sqrt{17})$$ None None $$0$$ $$1$$ $$-3$$ $$3$$ $$-$$ $$q+\beta q^{3}+(-2+\beta )q^{5}+(2-\beta )q^{7}+(1+\cdots)q^{9}+\cdots$$
416.2.a.f $$4$$ $$3.322$$ 4.4.13448.1 None None $$0$$ $$0$$ $$-2$$ $$0$$ $$-$$ $$q-\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots$$
416.2.b.a $$2$$ $$3.322$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$-6$$ $$q+iq^{3}+3iq^{5}-3q^{7}+2q^{9}+iq^{13}+\cdots$$
416.2.b.b $$4$$ $$3.322$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$12$$ $$q+2\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{5}+(3-\zeta_{12}^{3})q^{7}+\cdots$$
416.2.b.c $$6$$ $$3.322$$ 6.0.399424.1 None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\beta _{5}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}+(-2+\beta _{1}+\cdots)q^{9}+\cdots$$
416.2.e.a $$2$$ $$3.322$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}-q^{5}-3iq^{7}+2q^{9}+2q^{11}+\cdots$$
416.2.e.b $$2$$ $$3.322$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+q^{5}+3iq^{7}+2q^{9}-2q^{11}+\cdots$$
416.2.e.c $$8$$ $$3.322$$ 8.0.4521217600.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+(-3-\beta _{5}+\cdots)q^{9}+\cdots$$
416.2.f.a $$2$$ $$3.322$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-3q^{3}+3iq^{5}-iq^{7}+6q^{9}+4iq^{11}+\cdots$$
416.2.f.b $$2$$ $$3.322$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{5}-3q^{9}+(-3+i)q^{13}-2q^{17}+\cdots$$
416.2.f.c $$2$$ $$3.322$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$6$$ $$0$$ $$0$$ $$q+3q^{3}+3iq^{5}+iq^{7}+6q^{9}-4iq^{11}+\cdots$$
416.2.f.d $$4$$ $$3.322$$ $$\Q(i, \sqrt{13})$$ $$\Q(\sqrt{-13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{7}-3q^{9}+(\beta _{1}+\beta _{2})q^{11}-\beta _{3}q^{13}+\cdots$$
416.2.f.e $$4$$ $$3.322$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}-\beta _{1}q^{5}-\beta _{2}q^{7}+2q^{9}+(2+\cdots)q^{13}+\cdots$$
416.2.i.a $$2$$ $$3.322$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-2$$ $$2$$ $$0$$ $$q+(-2+2\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots$$
416.2.i.b $$2$$ $$3.322$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$2$$ $$2$$ $$0$$ $$q+(2-2\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots$$
416.2.i.c $$4$$ $$3.322$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$-2$$ $$0$$ $$6$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+2\beta _{3}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$
416.2.i.d $$4$$ $$3.322$$ $$\Q(\sqrt{-3}, \sqrt{11})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+8\beta _{2}q^{9}+\cdots$$
416.2.i.e $$4$$ $$3.322$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(1-2\zeta_{12}+\zeta_{12}^{3})q^{5}+3\zeta_{12}^{2}q^{9}+\cdots$$
416.2.i.f $$4$$ $$3.322$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$2$$ $$0$$ $$-6$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}-2\beta _{3}q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots$$
416.2.i.g $$8$$ $$3.322$$ 8.0.6927565824.3 None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-\beta _{2}-\beta _{7})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$
416.2.k.a $$2$$ $$3.322$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$-2$$ $$q-2iq^{3}+(-1-i)q^{5}+(-1-i)q^{7}+\cdots$$
416.2.k.b $$2$$ $$3.322$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$2$$ $$q+2iq^{3}+(-1-i)q^{5}+(1+i)q^{7}+\cdots$$
416.2.k.c $$4$$ $$3.322$$ $$\Q(i, \sqrt{10})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{1}q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots$$
416.2.k.d $$4$$ $$3.322$$ $$\Q(i, \sqrt{10})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{9}+(1+\cdots)q^{11}+\cdots$$
416.2.k.e $$8$$ $$3.322$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-\beta _{4}q^{3}+\beta _{7}q^{5}+(-\beta _{3}+\beta _{7})q^{7}+\cdots$$
416.2.k.f $$8$$ $$3.322$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q-\beta _{4}q^{3}-\beta _{6}q^{5}+(-\beta _{2}+\beta _{6})q^{7}+\cdots$$
416.2.u.a $$4$$ $$3.322$$ $$\Q(i, \sqrt{26})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots$$
416.2.u.b $$20$$ $$3.322$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{15}q^{5}+(\beta _{4}-\beta _{9})q^{7}+(1+\cdots)q^{9}+\cdots$$
416.2.w.a $$4$$ $$3.322$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2+4\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
416.2.w.b $$4$$ $$3.322$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-1+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+(3-3\zeta_{12}^{2}+\cdots)q^{9}+\cdots$$
416.2.w.c $$8$$ $$3.322$$ 8.0.56070144.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+\beta _{3}q^{7}+\cdots$$
416.2.w.d $$12$$ $$3.322$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{3}+(-2\beta _{4}-\beta _{5}+\beta _{6})q^{5}-\beta _{3}q^{7}+\cdots$$
416.2.z.a $$24$$ $$3.322$$ None None $$0$$ $$0$$ $$0$$ $$2$$
416.2.ba.a $$4$$ $$3.322$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$-6$$ $$8$$ $$12$$ $$q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{3}+(2+2\zeta_{12}+\cdots)q^{5}+\cdots$$
416.2.ba.b $$4$$ $$3.322$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$6$$ $$-8$$ $$12$$ $$q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots$$
416.2.ba.c $$16$$ $$3.322$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-18$$ $$q+(-\beta _{1}+\beta _{8}+\beta _{12})q^{3}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
416.2.bd.a $$216$$ $$3.322$$ None None $$-4$$ $$-8$$ $$-4$$ $$0$$
416.2.bf.a $$192$$ $$3.322$$ None None $$0$$ $$0$$ $$0$$ $$0$$
416.2.bg.a $$216$$ $$3.322$$ None None $$0$$ $$-8$$ $$0$$ $$0$$
416.2.bi.a $$216$$ $$3.322$$ None None $$-4$$ $$-8$$ $$-4$$ $$-8$$
416.2.bk.a $$48$$ $$3.322$$ None None $$0$$ $$4$$ $$0$$ $$0$$