## Results (1-50 of 259 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
252.1.h.a $$4$$ $$0.126$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$$
252.1.z.a $$2$$ $$0.126$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+(-1-\zeta_{6}+\cdots)q^{19}+\cdots$$
252.2.a.a $$1$$ $$2.012$$ $$\Q$$ None None $$0$$ $$0$$ $$-4$$ $$-1$$ $$+$$ $$q-4q^{5}-q^{7}-2q^{11}-6q^{13}+4q^{17}+\cdots$$
252.2.a.b $$1$$ $$2.012$$ $$\Q$$ None None $$0$$ $$0$$ $$0$$ $$1$$ $$-$$ $$q+q^{7}+6q^{11}+2q^{13}-4q^{19}+6q^{23}+\cdots$$
252.2.b.a $$2$$ $$2.012$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots$$
252.2.b.b $$4$$ $$2.012$$ $$\Q(\sqrt{-2}, \sqrt{7})$$ $$\Q(\sqrt{-21})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots$$
252.2.b.c $$4$$ $$2.012$$ $$\Q(i, \sqrt{7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+2\beta _{2}+\cdots)q^{7}+\cdots$$
252.2.b.d $$4$$ $$2.012$$ 4.0.2312.1 None None $$1$$ $$0$$ $$0$$ $$-2$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$$
252.2.b.e $$4$$ $$2.012$$ 4.0.2312.1 None None $$1$$ $$0$$ $$0$$ $$2$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$$
252.2.e.a $$12$$ $$2.012$$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{7}-\beta _{9}-\beta _{10}+\cdots)q^{5}+\cdots$$
252.2.f.a $$4$$ $$2.012$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{3}q^{5}+(-1-\beta _{1})q^{7}-\beta _{2}q^{11}+\cdots$$
252.2.i.a $$2$$ $$2.012$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$-2$$ $$-5$$ $$q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$$
252.2.i.b $$14$$ $$2.012$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None None $$0$$ $$3$$ $$-2$$ $$6$$ $$q+(-\beta _{1}+\beta _{3})q^{3}-\beta _{9}q^{5}+\beta _{10}q^{7}+\cdots$$
252.2.j.a $$6$$ $$2.012$$ 6.0.309123.1 None None $$0$$ $$-2$$ $$-1$$ $$3$$ $$q+(\beta _{2}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots$$
252.2.j.b $$6$$ $$2.012$$ 6.0.309123.1 None None $$0$$ $$2$$ $$3$$ $$-3$$ $$q+(1+\beta _{3}+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$$
252.2.k.a $$2$$ $$2.012$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-2$$ $$1$$ $$q+(-2+2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$$
252.2.k.b $$2$$ $$2.012$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$5$$ $$q+(3-\zeta_{6})q^{7}+5q^{13}+(1-\zeta_{6})q^{19}+\cdots$$
252.2.k.c $$2$$ $$2.012$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$3$$ $$-4$$ $$q+(3-3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots$$
252.2.l.a $$2$$ $$2.012$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$4$$ $$4$$ $$q+(1-2\zeta_{6})q^{3}+2q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
252.2.l.b $$14$$ $$2.012$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None None $$0$$ $$0$$ $$4$$ $$-3$$ $$q+\beta _{1}q^{3}+(-\beta _{5}+\beta _{9})q^{5}+\beta _{6}q^{7}+\cdots$$
252.2.n.a $$4$$ $$2.012$$ $$\Q(\zeta_{12})$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+\cdots)q^{3}+\cdots$$
252.2.n.b $$84$$ $$2.012$$ None None $$-1$$ $$0$$ $$0$$ $$0$$
252.2.o.a $$88$$ $$2.012$$ None None $$-3$$ $$0$$ $$0$$ $$0$$
252.2.t.a $$4$$ $$2.012$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q-\beta _{2}q^{5}+(2-3\beta _{1})q^{7}+(-\beta _{2}-\beta _{3})q^{11}+\cdots$$
252.2.w.a $$16$$ $$2.012$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-1$$ $$q-\beta _{10}q^{3}+\beta _{7}q^{5}+(\beta _{3}-\beta _{8})q^{7}-\beta _{4}q^{9}+\cdots$$
252.2.x.a $$16$$ $$2.012$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(-\beta _{1}-\beta _{8})q^{3}+\beta _{15}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
252.2.ba.a $$72$$ $$2.012$$ None None $$0$$ $$0$$ $$0$$ $$0$$
252.2.bb.a $$88$$ $$2.012$$ None None $$0$$ $$0$$ $$-6$$ $$0$$
252.2.be.a $$32$$ $$2.012$$ None None $$0$$ $$0$$ $$0$$ $$0$$
252.2.bf.a $$4$$ $$2.012$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None None $$-1$$ $$0$$ $$6$$ $$0$$ $$q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots$$
252.2.bf.b $$4$$ $$2.012$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\beta _{3}q^{2}-2q^{4}-2\beta _{1}q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots$$
252.2.bf.c $$4$$ $$2.012$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(2\beta _{1}-2\beta _{3})q^{5}+\cdots$$
252.2.bf.d $$4$$ $$2.012$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None None $$1$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-2+\beta _{2}+\cdots)q^{5}+\cdots$$
252.2.bf.e $$4$$ $$2.012$$ $$\Q(\zeta_{12})$$ None None $$2$$ $$0$$ $$6$$ $$0$$ $$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$$
252.2.bf.f $$8$$ $$2.012$$ 8.0.562828176.1 None None $$-1$$ $$0$$ $$0$$ $$-2$$ $$q+\beta _{5}q^{2}+(-\beta _{4}+\beta _{6}-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
252.2.bf.g $$8$$ $$2.012$$ 8.0.562828176.1 None None $$-1$$ $$0$$ $$0$$ $$2$$ $$q+(-\beta _{1}-\beta _{5})q^{2}+(-\beta _{2}-\beta _{6}+\beta _{7})q^{4}+\cdots$$
252.2.bi.a $$4$$ $$2.012$$ $$\Q(\zeta_{12})$$ None None $$2$$ $$0$$ $$-6$$ $$0$$ $$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(2\zeta_{12}+\cdots)q^{3}+\cdots$$
252.2.bi.b $$4$$ $$2.012$$ $$\Q(\zeta_{12})$$ None None $$2$$ $$0$$ $$6$$ $$0$$ $$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+\cdots)q^{3}+\cdots$$
252.2.bi.c $$80$$ $$2.012$$ None None $$-6$$ $$0$$ $$0$$ $$0$$
252.2.bj.a $$4$$ $$2.012$$ $$\Q(\zeta_{12})$$ None None $$-4$$ $$0$$ $$-12$$ $$0$$ $$q+(-1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
252.2.bj.b $$84$$ $$2.012$$ None None $$2$$ $$0$$ $$6$$ $$0$$
252.2.bm.a $$16$$ $$2.012$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(-\beta _{5}-\beta _{10})q^{3}+(\beta _{7}-\beta _{11})q^{5}+\cdots$$
252.3.c.a $$4$$ $$6.867$$ $$\Q(\sqrt{-2}, \sqrt{7})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{5}+\beta _{3}q^{7}+(2\beta _{1}+\beta _{2})q^{11}+\cdots$$
252.3.d.a $$2$$ $$6.867$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$-14$$ $$q-\zeta_{6}q^{5}-7q^{7}-18q^{11}+3\zeta_{6}q^{13}+\cdots$$
252.3.d.b $$2$$ $$6.867$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+(-1-\zeta_{6})q^{7}-2\zeta_{6}q^{13}-4\zeta_{6}q^{19}+\cdots$$
252.3.d.c $$2$$ $$6.867$$ $$\Q(\sqrt{-6})$$ None None $$0$$ $$0$$ $$0$$ $$10$$ $$q+\beta q^{5}+(5-\beta )q^{7}+6q^{11}+\beta q^{13}+\cdots$$
252.3.g.a $$6$$ $$6.867$$ 6.0.1539727.2 None None $$1$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$$
252.3.g.b $$12$$ $$6.867$$ 12.0.$$\cdots$$.1 None None $$-2$$ $$0$$ $$-8$$ $$0$$ $$q-\beta _{3}q^{2}-\beta _{5}q^{4}+(-\beta _{3}+\beta _{8})q^{5}+\cdots$$
252.3.g.c $$12$$ $$6.867$$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-1-\beta _{6})q^{4}+(-\beta _{2}+\beta _{7}+\cdots)q^{5}+\cdots$$
252.3.h.a $$8$$ $$6.867$$ 8.0.157351936.1 $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{2}+(\beta _{3}+\beta _{6})q^{4}+7\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{8}+\cdots$$