Results (displaying matches 1-50 of 138) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
539.1.c.a $$1$$ $$0.269$$ $$\Q$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-11})$$ $$\Q(\sqrt{77})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{4}-q^{9}+q^{11}+q^{16}-2q^{23}+\cdots$$
539.1.c.b $$2$$ $$0.269$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{3}+q^{4}+\beta q^{5}+q^{9}-q^{11}-\beta q^{12}+\cdots$$
539.1.h.a $$2$$ $$0.269$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-11})$$ $$\Q(\sqrt{77})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}-\zeta_{6}q^{16}+\cdots$$
539.1.h.b $$4$$ $$0.269$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$$
539.1.l.a $$4$$ $$0.269$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{10}+\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$$
539.1.t.a $$8$$ $$0.269$$ $$\Q(\zeta_{15})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{30}^{4}-\zeta_{30}^{13})q^{2}+(-\zeta_{30}^{2}+\cdots)q^{4}+\cdots$$
539.1.u.a $$8$$ $$0.269$$ $$\Q(\zeta_{15})$$ $$\Q(\sqrt{-7})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{30}^{8}-\zeta_{30}^{11})q^{2}+(-\zeta_{30}+\zeta_{30}^{4}+\cdots)q^{4}+\cdots$$
539.2.a.a $$1$$ $$4.304$$ $$\Q$$ None None $$-2$$ $$1$$ $$-1$$ $$0$$ $$+$$ $$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-2q^{9}+\cdots$$
539.2.a.b $$1$$ $$4.304$$ $$\Q$$ None None $$0$$ $$-1$$ $$-3$$ $$0$$ $$-$$ $$q-q^{3}-2q^{4}-3q^{5}-2q^{9}-q^{11}+\cdots$$
539.2.a.c $$1$$ $$4.304$$ $$\Q$$ None None $$0$$ $$3$$ $$1$$ $$0$$ $$-$$ $$q+3q^{3}-2q^{4}+q^{5}+6q^{9}-q^{11}+\cdots$$
539.2.a.d $$1$$ $$4.304$$ $$\Q$$ None None $$1$$ $$-2$$ $$2$$ $$0$$ $$+$$ $$q+q^{2}-2q^{3}-q^{4}+2q^{5}-2q^{6}-3q^{8}+\cdots$$
539.2.a.e $$2$$ $$4.304$$ $$\Q(\sqrt{2})$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q-q^{2}+\beta q^{3}-q^{4}-\beta q^{5}-\beta q^{6}+3q^{8}+\cdots$$
539.2.a.f $$2$$ $$4.304$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-2$$ $$4$$ $$0$$ $$-$$ $$q-\beta q^{2}+(-1-\beta )q^{3}+3q^{4}+2q^{5}+\cdots$$
539.2.a.g $$3$$ $$4.304$$ $$\Q(\zeta_{18})^+$$ None None $$0$$ $$-3$$ $$-6$$ $$0$$ $$+$$ $$q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$$
539.2.a.h $$3$$ $$4.304$$ 3.3.257.1 None None $$0$$ $$-1$$ $$-2$$ $$0$$ $$+$$ $$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$$
539.2.a.i $$3$$ $$4.304$$ 3.3.257.1 None None $$0$$ $$1$$ $$2$$ $$0$$ $$-$$ $$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$$
539.2.a.j $$3$$ $$4.304$$ $$\Q(\zeta_{18})^+$$ None None $$0$$ $$3$$ $$6$$ $$0$$ $$-$$ $$q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$$
539.2.a.k $$4$$ $$4.304$$ 4.4.9248.1 None None $$2$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q-\beta _{3}q^{2}+\beta _{2}q^{3}+(2-\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
539.2.a.l $$10$$ $$4.304$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q+\beta _{5}q^{2}+\beta _{1}q^{3}+(2+\beta _{9})q^{4}+\beta _{7}q^{5}+\cdots$$
539.2.b.a $$8$$ $$4.304$$ 8.0.$$\cdots$$.1 $$\Q(\sqrt{-11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+2q^{4}+\beta _{5}q^{5}+(-3+\beta _{3}+\cdots)q^{9}+\cdots$$
539.2.b.b $$12$$ $$4.304$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots$$
539.2.b.c $$16$$ $$4.304$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{8}q^{2}-\beta _{7}q^{3}+(-2+\beta _{6})q^{4}-\beta _{4}q^{5}+\cdots$$
539.2.e.a $$2$$ $$4.304$$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$-2$$ $$2$$ $$0$$ $$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
539.2.e.b $$2$$ $$4.304$$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$2$$ $$-2$$ $$0$$ $$q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
539.2.e.c $$2$$ $$4.304$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$-1$$ $$0$$ $$q+(-3+3\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$$
539.2.e.d $$2$$ $$4.304$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-3$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots$$
539.2.e.e $$2$$ $$4.304$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$3$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots$$
539.2.e.f $$2$$ $$4.304$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$1$$ $$0$$ $$q+(3-3\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$$
539.2.e.g $$2$$ $$4.304$$ $$\Q(\sqrt{-3})$$ None None $$2$$ $$-1$$ $$1$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
539.2.e.h $$2$$ $$4.304$$ $$\Q(\sqrt{-3})$$ None None $$2$$ $$1$$ $$-1$$ $$0$$ $$q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
539.2.e.i $$4$$ $$4.304$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$0$$ $$-2$$ $$4$$ $$0$$ $$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+3\beta _{1}q^{4}+\cdots$$
539.2.e.j $$4$$ $$4.304$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$0$$ $$2$$ $$-4$$ $$0$$ $$q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+3\beta _{1}q^{4}+\cdots$$
539.2.e.k $$4$$ $$4.304$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
539.2.e.l $$6$$ $$4.304$$ 6.0.1783323.2 None None $$0$$ $$-1$$ $$-2$$ $$0$$ $$q+(-\beta _{3}+\beta _{5})q^{2}-\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$$
539.2.e.m $$6$$ $$4.304$$ $$\Q(\zeta_{18})$$ None None $$0$$ $$3$$ $$6$$ $$0$$ $$q+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots$$
539.2.e.n $$8$$ $$4.304$$ 8.0.6927565824.3 None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{3}-\beta _{4}-\beta _{5})q^{2}+\beta _{2}q^{3}+\cdots$$
539.2.e.o $$20$$ $$4.304$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{8}q^{2}+(-\beta _{1}+\beta _{10})q^{3}+(-2\beta _{2}+\cdots)q^{4}+\cdots$$
539.2.f.a $$4$$ $$4.304$$ $$\Q(\zeta_{10})$$ None None $$2$$ $$-1$$ $$5$$ $$0$$ $$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots$$
539.2.f.b $$4$$ $$4.304$$ $$\Q(\zeta_{10})$$ None None $$2$$ $$1$$ $$-5$$ $$0$$ $$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots$$
539.2.f.c $$8$$ $$4.304$$ 8.0.37515625.1 $$\Q(\sqrt{-7})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{1}+2\beta _{2}-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$$
539.2.f.d $$8$$ $$4.304$$ 8.0.159390625.1 None None $$-1$$ $$4$$ $$-3$$ $$0$$ $$q+\beta _{4}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
539.2.f.e $$16$$ $$4.304$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-3$$ $$2$$ $$5$$ $$0$$ $$q+(-\beta _{5}-\beta _{6})q^{2}+(-\beta _{9}+\beta _{11}-\beta _{13}+\cdots)q^{3}+\cdots$$
539.2.f.f $$16$$ $$4.304$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\beta _{2}+\beta _{5}-\beta _{7})q^{2}+(\beta _{11}-\beta _{12}+\cdots)q^{3}+\cdots$$
539.2.f.g $$20$$ $$4.304$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$3$$ $$-4$$ $$4$$ $$0$$ $$q+\beta _{6}q^{2}+(-\beta _{1}-\beta _{7}-\beta _{18}+\beta _{19})q^{3}+\cdots$$
539.2.f.h $$20$$ $$4.304$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$3$$ $$4$$ $$-4$$ $$0$$ $$q+\beta _{6}q^{2}+(\beta _{1}+\beta _{7}+\beta _{18}-\beta _{19})q^{3}+\cdots$$
539.2.f.i $$48$$ $$4.304$$ None None $$0$$ $$0$$ $$0$$ $$0$$
539.2.i.a $$4$$ $$4.304$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+5\beta _{2}q^{4}+(3\beta _{1}-3\beta _{3})q^{8}+\cdots$$
539.2.i.b $$8$$ $$4.304$$ 8.0.3317760000.8 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{4})q^{2}+\beta _{5}q^{3}-\beta _{1}q^{5}+(\beta _{6}+\cdots)q^{6}+\cdots$$
539.2.i.c $$12$$ $$4.304$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$6$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{7})q^{2}+(1-\beta _{2}+\beta _{8}+\beta _{9}+\cdots)q^{3}+\cdots$$
539.2.i.d $$16$$ $$4.304$$ 16.0.$$\cdots$$.7 $$\Q(\sqrt{-11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{8})q^{3}-2\beta _{7}q^{4}+\beta _{5}q^{5}+(3+\cdots)q^{9}+\cdots$$
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