## Results (displaying matches 1-50 of 356) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
225.1.g.a $$2$$ $$0.112$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-15})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots$$
225.2.a.a $$1$$ $$1.797$$ $$\Q$$ None None $$-2$$ $$0$$ $$0$$ $$-3$$ $$+$$ $$q-2q^{2}+2q^{4}-3q^{7}-2q^{11}+q^{13}+\cdots$$
225.2.a.b $$1$$ $$1.797$$ $$\Q$$ None None $$-1$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q-q^{2}-q^{4}+3q^{8}+4q^{11}+2q^{13}+\cdots$$
225.2.a.c $$1$$ $$1.797$$ $$\Q$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-5$$ $$+$$ $$q-2q^{4}-5q^{7}-5q^{13}+4q^{16}-q^{19}+\cdots$$
225.2.a.d $$1$$ $$1.797$$ $$\Q$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$5$$ $$-$$ $$q-2q^{4}+5q^{7}+5q^{13}+4q^{16}-q^{19}+\cdots$$
225.2.a.e $$1$$ $$1.797$$ $$\Q$$ None None $$2$$ $$0$$ $$0$$ $$3$$ $$-$$ $$q+2q^{2}+2q^{4}+3q^{7}-2q^{11}-q^{13}+\cdots$$
225.2.a.f $$2$$ $$1.797$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q-\beta q^{2}+3q^{4}-\beta q^{8}-q^{16}+2\beta q^{17}+\cdots$$
225.2.b.a $$2$$ $$1.797$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-2q^{4}+3iq^{7}-2q^{11}+iq^{13}+\cdots$$
225.2.b.b $$2$$ $$1.797$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+3iq^{8}+4q^{11}+2iq^{13}+\cdots$$
225.2.b.c $$2$$ $$1.797$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+iq^{7}-iq^{13}+4q^{16}+q^{19}+\cdots$$
225.2.e.a $$2$$ $$1.797$$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$3$$ $$0$$ $$-3$$ $$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
225.2.e.b $$6$$ $$1.797$$ 6.0.954288.1 None None $$1$$ $$-1$$ $$0$$ $$5$$ $$q+(\beta _{1}-\beta _{2}+\beta _{4}+\beta _{5})q^{2}-\beta _{4}q^{3}+\cdots$$
225.2.e.c $$8$$ $$1.797$$ 8.0.1223810289.2 None None $$-2$$ $$1$$ $$0$$ $$1$$ $$q-\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$$
225.2.e.d $$8$$ $$1.797$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{7}q^{2}+(\zeta_{24}^{6}-\zeta_{24}^{7})q^{3}-\zeta_{24}^{2}q^{4}+\cdots$$
225.2.e.e $$8$$ $$1.797$$ 8.0.1223810289.2 None None $$2$$ $$-1$$ $$0$$ $$-1$$ $$q+\beta _{1}q^{2}+(\beta _{4}-\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$$
225.2.f.a $$4$$ $$1.797$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(2-2\zeta_{8}^{2})q^{7}+\cdots$$
225.2.f.b $$8$$ $$1.797$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{6}q^{2}-4\zeta_{24}^{2}q^{4}+\zeta_{24}q^{7}+\cdots$$
225.2.h.a $$4$$ $$1.797$$ $$\Q(\zeta_{10})$$ None None $$1$$ $$0$$ $$-5$$ $$0$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots$$
225.2.h.b $$4$$ $$1.797$$ $$\Q(\zeta_{10})$$ None None $$2$$ $$0$$ $$5$$ $$-2$$ $$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\zeta_{10}^{3})q^{4}+\cdots$$
225.2.h.c $$8$$ $$1.797$$ 8.0.26265625.1 None None $$1$$ $$0$$ $$5$$ $$4$$ $$q+(\beta _{3}+\beta _{7})q^{2}+(-1+2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots$$
225.2.h.d $$12$$ $$1.797$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$6$$ $$-12$$ $$q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{5}-2\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots$$
225.2.h.e $$16$$ $$1.797$$ 16.0.$$\cdots$$.3 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{10}+\beta _{12}-\beta _{14})q^{2}+(-\beta _{8}+\cdots)q^{4}+\cdots$$
225.2.k.a $$4$$ $$1.797$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
225.2.k.b $$12$$ $$1.797$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{6}-\beta _{7})q^{2}+\beta _{6}q^{3}+(2+2\beta _{8}+\cdots)q^{4}+\cdots$$
225.2.k.c $$16$$ $$1.797$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{10}+\beta _{14})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$$
225.2.m.a $$8$$ $$1.797$$ 8.0.58140625.2 None None $$5$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$
225.2.m.b $$16$$ $$1.797$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{3}+\beta _{4}-\beta _{10}+\beta _{15})q^{2}+\cdots$$
225.2.m.c $$24$$ $$1.797$$ None None $$0$$ $$0$$ $$0$$ $$0$$
225.2.p.a $$16$$ $$1.797$$ 16.0.$$\cdots$$.9 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{6}-\beta _{13})q^{2}+\beta _{1}q^{3}+(-\beta _{9}+\cdots)q^{4}+\cdots$$
225.2.p.b $$16$$ $$1.797$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$6$$ $$6$$ $$0$$ $$2$$ $$q+\beta _{5}q^{2}+(1-\beta _{9}+\beta _{11}+\beta _{12}+\beta _{13}+\cdots)q^{3}+\cdots$$
225.2.p.c $$32$$ $$1.797$$ None None $$0$$ $$0$$ $$0$$ $$0$$
225.2.q.a $$224$$ $$1.797$$ None None $$-3$$ $$-8$$ $$-8$$ $$-8$$
225.2.s.a $$80$$ $$1.797$$ None None $$0$$ $$0$$ $$0$$ $$8$$
225.2.u.a $$224$$ $$1.797$$ None None $$-5$$ $$-10$$ $$0$$ $$0$$
225.2.w.a $$448$$ $$1.797$$ None None $$-24$$ $$-14$$ $$-24$$ $$-8$$
225.3.c.a $$2$$ $$6.131$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$-18$$ $$q+\beta q^{2}+2q^{4}-9q^{7}+6\beta q^{8}+13\beta q^{11}+\cdots$$
225.3.c.b $$2$$ $$6.131$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$18$$ $$q+\beta q^{2}+2q^{4}+9q^{7}+6\beta q^{8}-13\beta q^{11}+\cdots$$
225.3.c.c $$4$$ $$6.131$$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+\beta _{2}q^{2}+(-3-2\beta _{1})q^{4}+(-4-\beta _{1}+\cdots)q^{7}+\cdots$$
225.3.c.d $$4$$ $$6.131$$ $$\Q(\sqrt{-2}, \sqrt{-7})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-3q^{4}-\beta _{1}q^{7}-\beta _{2}q^{8}-\beta _{3}q^{11}+\cdots$$
225.3.d.a $$4$$ $$6.131$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{3}q^{2}-2q^{4}+9\zeta_{8}q^{7}-6\zeta_{8}^{3}q^{8}+\cdots$$
225.3.d.b $$8$$ $$6.131$$ 8.0.40960000.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(3-\beta _{6})q^{4}+(2\beta _{1}-\beta _{3})q^{7}+\cdots$$
225.3.g.a $$4$$ $$6.131$$ $$\Q(i, \sqrt{6})$$ None None $$-4$$ $$0$$ $$0$$ $$-4$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
225.3.g.b $$4$$ $$6.131$$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{1}q^{2}+8\beta _{2}q^{4}+5\beta _{1}q^{7}+8\beta _{3}q^{8}+\cdots$$
225.3.g.c $$4$$ $$6.131$$ $$\Q(i, \sqrt{30})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+11\beta _{2}q^{4}+7\beta _{3}q^{8}-61q^{16}+\cdots$$
225.3.g.d $$4$$ $$6.131$$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-4\beta _{2}q^{4}+\beta _{1}q^{7}-3\beta _{3}q^{13}-2^{4}q^{16}+\cdots$$
225.3.g.e $$4$$ $$6.131$$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{4}+4\beta _{1}q^{7}-5\beta _{3}q^{8}+\cdots$$
225.3.g.f $$4$$ $$6.131$$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{4}-6\beta _{1}q^{7}-5\beta _{3}q^{8}+\cdots$$
225.3.g.g $$4$$ $$6.131$$ $$\Q(i, \sqrt{10})$$ None None $$0$$ $$0$$ $$0$$ $$20$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(5+5\beta _{2})q^{7}-3\beta _{3}q^{8}+\cdots$$
225.3.i.a $$4$$ $$6.131$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{3}+\cdots$$
225.3.i.b $$32$$ $$6.131$$ None None $$0$$ $$0$$ $$0$$ $$0$$
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