## Results (displaying matches 1-50 of 265) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
315.1.bg.a $$2$$ $$0.157$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$-2$$ $$1$$ $$1$$ $$q-q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$$
315.1.bg.b $$2$$ $$0.157$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$2$$ $$-1$$ $$-1$$ $$q+q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$$
315.2.a.a $$1$$ $$2.515$$ $$\Q$$ None None $$-1$$ $$0$$ $$-1$$ $$1$$ $$+$$ $$q-q^{2}-q^{4}-q^{5}+q^{7}+3q^{8}+q^{10}+\cdots$$
315.2.a.b $$1$$ $$2.515$$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$1$$ $$-$$ $$q-2q^{4}+q^{5}+q^{7}+3q^{11}+5q^{13}+\cdots$$
315.2.a.c $$2$$ $$2.515$$ $$\Q(\sqrt{2})$$ None None $$-2$$ $$0$$ $$-2$$ $$-2$$ $$+$$ $$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}-q^{7}+\cdots$$
315.2.a.d $$2$$ $$2.515$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$0$$ $$2$$ $$2$$ $$-$$ $$q-\beta q^{2}+3q^{4}+q^{5}+q^{7}-\beta q^{8}-\beta q^{10}+\cdots$$
315.2.a.e $$2$$ $$2.515$$ $$\Q(\sqrt{17})$$ None None $$1$$ $$0$$ $$-2$$ $$-2$$ $$-$$ $$q+\beta q^{2}+(2+\beta )q^{4}-q^{5}-q^{7}+(4+\beta )q^{8}+\cdots$$
315.2.a.f $$2$$ $$2.515$$ $$\Q(\sqrt{2})$$ None None $$2$$ $$0$$ $$2$$ $$-2$$ $$-$$ $$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}-q^{7}+\cdots$$
315.2.b.a $$4$$ $$2.515$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None None $$0$$ $$0$$ $$-4$$ $$4$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots$$
315.2.b.b $$4$$ $$2.515$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None None $$0$$ $$0$$ $$4$$ $$4$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+\cdots$$
315.2.d.a $$2$$ $$2.515$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+2iq^{2}-2q^{4}+(2-i)q^{5}+iq^{7}+\cdots$$
315.2.d.b $$2$$ $$2.515$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}+q^{4}+(-2+i)q^{5}+iq^{7}+\cdots$$
315.2.d.c $$2$$ $$2.515$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}+q^{4}+(-1-2i)q^{5}-iq^{7}+\cdots$$
315.2.d.d $$2$$ $$2.515$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}+q^{4}+(2+i)q^{5}-iq^{7}+3iq^{8}+\cdots$$
315.2.d.e $$6$$ $$2.515$$ 6.0.350464.1 None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{1}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
315.2.g.a $$16$$ $$2.515$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(1+\beta _{14})q^{4}-\beta _{4}q^{5}-\beta _{12}q^{7}+\cdots$$
315.2.i.a $$2$$ $$2.515$$ $$\Q(\sqrt{-3})$$ None None $$-2$$ $$-3$$ $$1$$ $$-1$$ $$q+(-2+2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$$
315.2.i.b $$2$$ $$2.515$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$1$$ $$-1$$ $$q+(2-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$$
315.2.i.c $$8$$ $$2.515$$ 8.0.142635249.1 None None $$1$$ $$-1$$ $$-4$$ $$-4$$ $$q+\beta _{7}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{4}+\beta _{6})q^{3}+\cdots$$
315.2.i.d $$8$$ $$2.515$$ $$\Q(\zeta_{15})$$ None None $$1$$ $$3$$ $$4$$ $$4$$ $$q+(1+\zeta_{15}-\zeta_{15}^{2}+\zeta_{15}^{3})q^{2}+(1+\cdots)q^{3}+\cdots$$
315.2.i.e $$12$$ $$2.515$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$3$$ $$1$$ $$6$$ $$-6$$ $$q+(1-\beta _{2}-\beta _{4})q^{2}+\beta _{9}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$$
315.2.i.f $$16$$ $$2.515$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$1$$ $$1$$ $$-8$$ $$8$$ $$q+(\beta _{2}+\beta _{13})q^{2}+\beta _{5}q^{3}+(-2-2\beta _{3}+\cdots)q^{4}+\cdots$$
315.2.j.a $$2$$ $$2.515$$ $$\Q(\sqrt{-3})$$ None None $$-2$$ $$0$$ $$1$$ $$-1$$ $$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$$
315.2.j.b $$2$$ $$2.515$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$5$$ $$q+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
315.2.j.c $$4$$ $$2.515$$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$0$$ $$2$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots$$
315.2.j.d $$4$$ $$2.515$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$-2$$ $$-2$$ $$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$$
315.2.j.e $$4$$ $$2.515$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$2$$ $$0$$ $$2$$ $$2$$ $$q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots$$
315.2.j.f $$6$$ $$2.515$$ 6.0.4406832.1 None None $$-2$$ $$0$$ $$-3$$ $$1$$ $$q+(-\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$$
315.2.j.g $$6$$ $$2.515$$ 6.0.4406832.1 None None $$2$$ $$0$$ $$3$$ $$1$$ $$q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$$
315.2.k.a $$4$$ $$2.515$$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None None $$1$$ $$0$$ $$-4$$ $$-8$$ $$q+\beta _{1}q^{2}+(1+2\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$$
315.2.k.b $$24$$ $$2.515$$ None None $$-1$$ $$1$$ $$-24$$ $$7$$
315.2.k.c $$36$$ $$2.515$$ None None $$0$$ $$-1$$ $$36$$ $$-1$$
315.2.l.a $$4$$ $$2.515$$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None None $$-2$$ $$6$$ $$2$$ $$10$$ $$q+(-1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(2-\beta _{3})q^{4}+\cdots$$
315.2.l.b $$24$$ $$2.515$$ None None $$2$$ $$-5$$ $$12$$ $$-11$$
315.2.l.c $$36$$ $$2.515$$ None None $$0$$ $$-1$$ $$-18$$ $$-1$$
315.2.m.a $$12$$ $$2.515$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{2}q^{2}+(\beta _{5}+\beta _{6}-\beta _{8})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$$
315.2.m.b $$12$$ $$2.515$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(\beta _{1}+\beta _{8}+\beta _{9})q^{2}+(-\beta _{5}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots$$
315.2.p.a $$4$$ $$2.515$$ $$\Q(i, \sqrt{10})$$ None None $$0$$ $$0$$ $$-8$$ $$4$$ $$q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(-2+\beta _{2})q^{5}+\cdots$$
315.2.p.b $$4$$ $$2.515$$ $$\Q(i, \sqrt{10})$$ None None $$0$$ $$0$$ $$8$$ $$4$$ $$q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(2-\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots$$
315.2.p.c $$4$$ $$2.515$$ $$\Q(i, \sqrt{10})$$ None None $$4$$ $$0$$ $$0$$ $$4$$ $$q+(1+\beta _{2})q^{2}+\beta _{1}q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots$$
315.2.p.d $$8$$ $$2.515$$ 8.0.40960000.1 None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{4}+\beta _{5}q^{5}+(-1-\beta _{3}+\cdots)q^{7}+\cdots$$
315.2.p.e $$16$$ $$2.515$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{2}q^{2}+(-\beta _{6}-\beta _{7}+\beta _{13})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
315.2.r.a $$4$$ $$2.515$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{12}^{3}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+q^{4}+\cdots$$
315.2.r.b $$84$$ $$2.515$$ None None $$0$$ $$0$$ $$3$$ $$0$$
315.2.t.a $$2$$ $$2.515$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$1$$ $$4$$ $$q+(1-2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-q^{4}+\cdots$$
315.2.t.b $$30$$ $$2.515$$ None None $$0$$ $$4$$ $$15$$ $$-3$$
315.2.t.c $$32$$ $$2.515$$ None None $$0$$ $$-1$$ $$-16$$ $$1$$
315.2.u.a $$88$$ $$2.515$$ None None $$0$$ $$0$$ $$-6$$ $$0$$
315.2.z.a $$8$$ $$2.515$$ 8.0.$$\cdots$$.2 $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{3}+(2+2\beta _{4})q^{4}+(\beta _{1}-\beta _{6})q^{5}+\cdots$$
315.2.z.b $$80$$ $$2.515$$ None None $$0$$ $$0$$ $$0$$ $$0$$
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