## Results (displaying matches 1-50 of 203) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
224.1.h.a $$1$$ $$0.112$$ $$\Q$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-14})$$ $$\Q(\sqrt{2})$$ $$0$$ $$0$$ $$0$$ $$1$$ $$q+q^{7}-q^{9}-2q^{23}-q^{25}+q^{49}+\cdots$$
224.1.r.a $$4$$ $$0.112$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$$
224.1.v.a $$4$$ $$0.112$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$$
224.2.a.a $$1$$ $$1.789$$ $$\Q$$ None None $$0$$ $$-2$$ $$0$$ $$-1$$ $$+$$ $$q-2q^{3}-q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$$
224.2.a.b $$1$$ $$1.789$$ $$\Q$$ None None $$0$$ $$2$$ $$0$$ $$1$$ $$-$$ $$q+2q^{3}+q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots$$
224.2.a.c $$2$$ $$1.789$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-2$$ $$2$$ $$2$$ $$-$$ $$q+(-1-\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots$$
224.2.a.d $$2$$ $$1.789$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$2$$ $$2$$ $$-2$$ $$-$$ $$q+(1+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots$$
224.2.b.a $$2$$ $$1.789$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\beta q^{3}+\beta q^{5}-q^{7}+q^{9}+2\beta q^{11}+\cdots$$
224.2.b.b $$4$$ $$1.789$$ 4.0.2312.1 None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+q^{7}+(-2+\beta _{3})q^{9}+\cdots$$
224.2.e.a $$2$$ $$1.789$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{7}+3q^{9}+4q^{11}+2\beta q^{23}-5q^{25}+\cdots$$
224.2.e.b $$4$$ $$1.789$$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots$$
224.2.f.a $$8$$ $$1.789$$ $$\Q(\zeta_{16})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{6}q^{7}+\cdots$$
224.2.i.a $$4$$ $$1.789$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$-2$$ $$-2$$ $$-4$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
224.2.i.b $$4$$ $$1.789$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
224.2.i.c $$4$$ $$1.789$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None None $$0$$ $$0$$ $$6$$ $$0$$ $$q+\beta _{1}q^{3}-3\beta _{2}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$$
224.2.i.d $$4$$ $$1.789$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$2$$ $$-2$$ $$4$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots$$
224.2.p.a $$16$$ $$1.789$$ 16.0.$$\cdots$$.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{14}q^{3}-\beta _{13}q^{5}-\beta _{9}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots$$
224.2.q.a $$12$$ $$1.789$$ 12.0.$$\cdots$$.2 None None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{8}q^{3}+(-\beta _{4}-\beta _{7})q^{5}+(\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots$$
224.2.t.a $$12$$ $$1.789$$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{10}q^{3}+(-\beta _{4}+\beta _{7})q^{5}+(\beta _{8}-\beta _{9}+\cdots)q^{7}+\cdots$$
224.2.u.a $$4$$ $$1.789$$ $$\Q(\zeta_{8})$$ None None $$-4$$ $$-4$$ $$-8$$ $$0$$ $$q+(-1+\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots$$
224.2.u.b $$40$$ $$1.789$$ None None $$4$$ $$4$$ $$8$$ $$0$$
224.2.u.c $$52$$ $$1.789$$ None None $$0$$ $$0$$ $$0$$ $$0$$
224.2.x.a $$8$$ $$1.789$$ 8.0.157351936.1 $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(2\beta _{2}+\cdots)q^{7}+\cdots$$
224.2.x.b $$112$$ $$1.789$$ None None $$-8$$ $$0$$ $$0$$ $$-4$$
224.2.bd.a $$240$$ $$1.789$$ None None $$-4$$ $$-4$$ $$-4$$ $$-8$$
224.2.be.a $$240$$ $$1.789$$ None None $$-4$$ $$-12$$ $$-12$$ $$-8$$
224.3.c.a $$8$$ $$6.104$$ 8.0.$$\cdots$$.3 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{3}+\beta _{7}q^{5}+\beta _{2}q^{7}+(-7-\beta _{5}+\cdots)q^{9}+\cdots$$
224.3.c.b $$8$$ $$6.104$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{5}q^{5}+\beta _{7}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$$
224.3.d.a $$4$$ $$6.104$$ $$\Q(i, \sqrt{7})$$ None None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+\beta _{1}q^{3}+(-2+\beta _{2})q^{5}-\beta _{3}q^{7}+5q^{9}+\cdots$$
224.3.d.b $$8$$ $$6.104$$ 8.0.1997017344.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{3}q^{7}+(-5+\beta _{2}+\cdots)q^{9}+\cdots$$
224.3.g.a $$4$$ $$6.104$$ $$\Q(\sqrt{2}, \sqrt{-7})$$ None None $$0$$ $$-8$$ $$0$$ $$0$$ $$q+(-2+\beta _{1})q^{3}+(-\beta _{2}+2\beta _{3})q^{5}+\cdots$$
224.3.g.b $$8$$ $$6.104$$ 8.0.$$\cdots$$.3 None None $$0$$ $$8$$ $$0$$ $$0$$ $$q+(1+\beta _{3})q^{3}+(-\beta _{1}+\beta _{2}+\beta _{4})q^{5}+\cdots$$
224.3.h.a $$2$$ $$6.104$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$-14$$ $$q-7q^{7}-9q^{9}-\beta q^{11}-18q^{23}-5^{2}q^{25}+\cdots$$
224.3.h.b $$2$$ $$6.104$$ $$\Q(\sqrt{7})$$ $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$-14$$ $$q+\beta q^{3}+\beta q^{5}-7q^{7}+19q^{9}+\beta q^{13}+\cdots$$
224.3.h.c $$2$$ $$6.104$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$14$$ $$q+\beta q^{3}+3\beta q^{5}+7q^{7}-q^{9}-9\beta q^{13}+\cdots$$
224.3.h.d $$8$$ $$6.104$$ 8.0.$$\cdots$$.51 None None $$0$$ $$0$$ $$0$$ $$16$$ $$q-\beta _{3}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots$$
224.3.n.a $$28$$ $$6.104$$ None None $$0$$ $$0$$ $$0$$ $$4$$
224.3.o.a $$2$$ $$6.104$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-9$$ $$2$$ $$q+\zeta_{6}q^{3}+(-3-3\zeta_{6})q^{5}+(-3+8\zeta_{6})q^{7}+\cdots$$
224.3.o.b $$2$$ $$6.104$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$9$$ $$-2$$ $$q+\zeta_{6}q^{3}+(3+3\zeta_{6})q^{5}+(3-8\zeta_{6})q^{7}+\cdots$$
224.3.o.c $$12$$ $$6.104$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+(-1+\beta _{2}-\beta _{8})q^{3}+(\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$$
224.3.o.d $$12$$ $$6.104$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$6$$ $$0$$ $$0$$ $$q+(1-\beta _{3}+\beta _{6}+\beta _{7}-\beta _{10})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
224.3.r.a $$4$$ $$6.104$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-18$$ $$0$$ $$q+5\zeta_{12}q^{3}-9\zeta_{12}^{2}q^{5}+(8\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots$$
224.3.r.b $$4$$ $$6.104$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-7\zeta_{12}^{3}q^{7}+\cdots$$
224.3.r.c $$12$$ $$6.104$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{1}q^{3}+(\beta _{5}+\beta _{11})q^{5}+(\beta _{3}-\beta _{6}+\cdots)q^{7}+\cdots$$
224.3.r.d $$12$$ $$6.104$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$18$$ $$0$$ $$q+(\beta _{7}+\beta _{9}-\beta _{10})q^{3}+(-3\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots$$
224.3.s.a $$16$$ $$6.104$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+\beta _{10}q^{5}-\beta _{13}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$$
224.3.s.b $$16$$ $$6.104$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}-\beta _{5}q^{5}+(\beta _{2}+\beta _{12})q^{7}+(-5\beta _{7}+\cdots)q^{9}+\cdots$$
224.3.v.a $$8$$ $$6.104$$ 8.0.157351936.1 $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\beta _{6}-\beta _{7})q^{2}+(-\beta _{3}+3\beta _{5})q^{4}+\cdots$$
224.3.v.b $$240$$ $$6.104$$ None None $$-8$$ $$0$$ $$0$$ $$-4$$
224.3.w.a $$192$$ $$6.104$$ None None $$0$$ $$0$$ $$0$$ $$0$$
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