Results (displaying all 31 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2015.1.h.a $$4$$ $$1.006$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-155})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+q^{9}+\cdots$$
2015.1.h.b $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$\Q(\sqrt{-2015})$$ None $$-1$$ $$-1$$ $$6$$ $$-1$$ $$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$$
2015.1.h.c $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$\Q(\sqrt{-2015})$$ None $$-1$$ $$1$$ $$6$$ $$-1$$ $$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$$
2015.1.h.d $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$\Q(\sqrt{-2015})$$ None $$1$$ $$-1$$ $$-6$$ $$1$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$$
2015.1.h.e $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$\Q(\sqrt{-2015})$$ None $$1$$ $$1$$ $$-6$$ $$1$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$$
2015.1.bf.a $$8$$ $$1.006$$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-155})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{3}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{6}q^{5}+\cdots$$
2015.1.bq.a $$2$$ $$1.006$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-155})$$ None $$0$$ $$-2$$ $$2$$ $$0$$ $$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots$$
2015.1.bq.b $$2$$ $$1.006$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-155})$$ None $$0$$ $$2$$ $$2$$ $$0$$ $$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots$$
2015.1.bq.c $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$$
2015.1.bq.d $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-155})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\zeta_{12}^{2}q^{4}-q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots$$
2015.1.bq.e $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$$
2015.2.a.a $$1$$ $$16.090$$ $$\Q$$ None None $$-2$$ $$-3$$ $$1$$ $$-4$$ $$-$$ $$q-2q^{2}-3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots$$
2015.2.a.b $$1$$ $$16.090$$ $$\Q$$ None None $$0$$ $$-2$$ $$-1$$ $$-4$$ $$+$$ $$q-2q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}+3q^{11}+\cdots$$
2015.2.a.c $$1$$ $$16.090$$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$2$$ $$+$$ $$q+q^{3}-2q^{4}-q^{5}+2q^{7}-2q^{9}-2q^{12}+\cdots$$
2015.2.a.d $$3$$ $$16.090$$ 3.3.316.1 None None $$0$$ $$0$$ $$-3$$ $$0$$ $$+$$ $$q+\beta _{1}q^{3}-2q^{4}-q^{5}+(2+\beta _{2})q^{9}+\cdots$$
2015.2.a.e $$6$$ $$16.090$$ 6.6.2501557.1 None None $$0$$ $$-1$$ $$-6$$ $$-1$$ $$+$$ $$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(2-\beta _{5})q^{4}-q^{5}+\cdots$$
2015.2.a.f $$7$$ $$16.090$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$-2$$ $$-2$$ $$-7$$ $$-5$$ $$+$$ $$q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1+\beta _{4})q^{4}-q^{5}+\cdots$$
2015.2.a.g $$8$$ $$16.090$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$-2$$ $$-1$$ $$8$$ $$-7$$ $$+$$ $$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$$
2015.2.a.h $$8$$ $$16.090$$ 8.8.1299600812.1 None None $$0$$ $$-3$$ $$8$$ $$-1$$ $$+$$ $$q+\beta _{2}q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$$
2015.2.a.i $$20$$ $$16.090$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$3$$ $$7$$ $$-20$$ $$1$$ $$-$$ $$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$$
2015.2.a.j $$20$$ $$16.090$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$5$$ $$1$$ $$-20$$ $$11$$ $$-$$ $$q+\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$$
2015.2.a.k $$22$$ $$16.090$$ None None $$2$$ $$3$$ $$22$$ $$3$$ $$-$$
2015.2.a.l $$22$$ $$16.090$$ None None $$5$$ $$4$$ $$22$$ $$5$$ $$-$$
2015.4.a.a $$37$$ $$118.889$$ None None $$-9$$ $$-17$$ $$185$$ $$-64$$ $$-$$
2015.4.a.b $$37$$ $$118.889$$ None None $$-5$$ $$1$$ $$185$$ $$-20$$ $$-$$
2015.4.a.c $$40$$ $$118.889$$ None None $$-9$$ $$1$$ $$-200$$ $$-64$$ $$-$$
2015.4.a.d $$40$$ $$118.889$$ None None $$-5$$ $$-17$$ $$-200$$ $$-20$$ $$-$$
2015.4.a.e $$51$$ $$118.889$$ None None $$1$$ $$7$$ $$-255$$ $$-6$$ $$+$$
2015.4.a.f $$51$$ $$118.889$$ None None $$5$$ $$13$$ $$-255$$ $$62$$ $$+$$
2015.4.a.g $$52$$ $$118.889$$ None None $$1$$ $$13$$ $$260$$ $$-6$$ $$+$$
2015.4.a.h $$52$$ $$118.889$$ None None $$5$$ $$7$$ $$260$$ $$62$$ $$+$$