## Results (displaying all 46 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1001.1.r.a $$4$$ $$0.500$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots$$
1001.1.y.a $$2$$ $$0.500$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-143})$$ None $$-1$$ $$1$$ $$0$$ $$1$$ $$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots$$
1001.1.y.b $$2$$ $$0.500$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-143})$$ None $$1$$ $$1$$ $$0$$ $$-1$$ $$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots$$
1001.1.y.c $$8$$ $$0.500$$ $$\Q(\zeta_{15})$$ $$\Q(\sqrt{-143})$$ None $$-1$$ $$-1$$ $$0$$ $$1$$ $$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$$
1001.1.y.d $$8$$ $$0.500$$ $$\Q(\zeta_{15})$$ $$\Q(\sqrt{-143})$$ None $$1$$ $$-1$$ $$0$$ $$-1$$ $$q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$$
1001.1.bo.a $$4$$ $$0.500$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$$
1001.2.a.a $$1$$ $$7.993$$ $$\Q$$ None None $$-2$$ $$-3$$ $$-3$$ $$-1$$ $$-$$ $$q-2q^{2}-3q^{3}+2q^{4}-3q^{5}+6q^{6}+\cdots$$
1001.2.a.b $$1$$ $$7.993$$ $$\Q$$ None None $$-1$$ $$0$$ $$-2$$ $$-1$$ $$-$$ $$q-q^{2}-q^{4}-2q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots$$
1001.2.a.c $$1$$ $$7.993$$ $$\Q$$ None None $$0$$ $$2$$ $$-1$$ $$-1$$ $$+$$ $$q+2q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-q^{11}+\cdots$$
1001.2.a.d $$2$$ $$7.993$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$3$$ $$3$$ $$2$$ $$-$$ $$q+(1-2\beta )q^{2}+(2-\beta )q^{3}+3q^{4}+(1+\cdots)q^{5}+\cdots$$
1001.2.a.e $$2$$ $$7.993$$ $$\Q(\sqrt{21})$$ None None $$2$$ $$1$$ $$-1$$ $$2$$ $$-$$ $$q+q^{2}+(1-\beta )q^{3}-q^{4}-\beta q^{5}+(1-\beta )q^{6}+\cdots$$
1001.2.a.f $$3$$ $$7.993$$ 3.3.1101.1 None None $$3$$ $$-1$$ $$1$$ $$-3$$ $$-$$ $$q+q^{2}-\beta _{1}q^{3}-q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$$
1001.2.a.g $$4$$ $$7.993$$ 4.4.23301.1 None None $$-2$$ $$-1$$ $$-5$$ $$4$$ $$-$$ $$q+(-1+\beta _{3})q^{2}-\beta _{1}q^{3}+(2-\beta _{2})q^{4}+\cdots$$
1001.2.a.h $$4$$ $$7.993$$ 4.4.1957.1 None None $$0$$ $$-1$$ $$5$$ $$-4$$ $$+$$ $$q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(\beta _{1}+\beta _{2})q^{3}+\cdots$$
1001.2.a.i $$5$$ $$7.993$$ 5.5.106069.1 None None $$-2$$ $$-3$$ $$0$$ $$5$$ $$+$$ $$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
1001.2.a.j $$5$$ $$7.993$$ 5.5.216637.1 None None $$-2$$ $$0$$ $$-4$$ $$-5$$ $$+$$ $$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$$
1001.2.a.k $$5$$ $$7.993$$ 5.5.81509.1 None None $$0$$ $$-4$$ $$-6$$ $$5$$ $$+$$ $$q+\beta _{4}q^{2}+(-1+\beta _{2})q^{3}+(1-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$
1001.2.a.l $$7$$ $$7.993$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$0$$ $$6$$ $$9$$ $$-7$$ $$-$$ $$q+\beta _{5}q^{2}+(1-\beta _{1})q^{3}+(4+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
1001.2.a.m $$8$$ $$7.993$$ 8.8.3212905625.1 None None $$2$$ $$-1$$ $$-5$$ $$-8$$ $$-$$ $$q+\beta _{7}q^{2}-\beta _{2}q^{3}+(2-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$$
1001.2.a.n $$11$$ $$7.993$$ $$\mathbb{Q}[x]/(x^{11} - \cdots)$$ None None $$-1$$ $$2$$ $$7$$ $$11$$ $$-$$ $$q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots$$
1001.2.b.a $$48$$ $$7.993$$ None None $$0$$ $$0$$ $$0$$ $$4$$
1001.2.b.b $$48$$ $$7.993$$ None None $$0$$ $$0$$ $$0$$ $$-4$$
1001.2.d.a $$2$$ $$7.993$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+iq^{2}-2q^{3}+q^{4}-2iq^{5}-2iq^{6}+\cdots$$
1001.2.d.b $$30$$ $$7.993$$ None None $$0$$ $$-8$$ $$0$$ $$0$$
1001.2.d.c $$40$$ $$7.993$$ None None $$0$$ $$12$$ $$0$$ $$0$$
1001.2.i.a $$8$$ $$7.993$$ 8.0.447703281.1 None None $$-2$$ $$-1$$ $$1$$ $$-16$$ $$q-\beta _{3}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$
1001.2.i.b $$22$$ $$7.993$$ None None $$2$$ $$-1$$ $$0$$ $$15$$
1001.2.i.c $$30$$ $$7.993$$ None None $$6$$ $$2$$ $$3$$ $$1$$
1001.2.i.d $$50$$ $$7.993$$ None None $$-6$$ $$2$$ $$1$$ $$1$$
1001.2.i.e $$50$$ $$7.993$$ None None $$0$$ $$-2$$ $$3$$ $$-1$$
1001.4.a.a $$18$$ $$59.061$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$-4$$ $$-12$$ $$-34$$ $$126$$ $$-$$ $$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots$$
1001.4.a.b $$18$$ $$59.061$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$0$$ $$0$$ $$-14$$ $$-126$$ $$-$$ $$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$$
1001.4.a.c $$22$$ $$59.061$$ None None $$-4$$ $$-2$$ $$16$$ $$-154$$ $$-$$
1001.4.a.d $$22$$ $$59.061$$ None None $$0$$ $$-14$$ $$0$$ $$154$$ $$-$$
1001.4.a.e $$25$$ $$59.061$$ None None $$0$$ $$-8$$ $$-42$$ $$-175$$ $$+$$
1001.4.a.f $$25$$ $$59.061$$ None None $$0$$ $$18$$ $$48$$ $$175$$ $$+$$
1001.4.a.g $$25$$ $$59.061$$ None None $$4$$ $$4$$ $$-2$$ $$175$$ $$+$$
1001.4.a.h $$25$$ $$59.061$$ None None $$4$$ $$6$$ $$44$$ $$-175$$ $$+$$
1001.6.a.a $$35$$ $$160.544$$ None None $$-8$$ $$-42$$ $$-2$$ $$1715$$ $$+$$
1001.6.a.b $$35$$ $$160.544$$ None None $$-8$$ $$7$$ $$-178$$ $$-1715$$ $$+$$
1001.6.a.c $$35$$ $$160.544$$ None None $$0$$ $$-29$$ $$-258$$ $$1715$$ $$+$$
1001.6.a.d $$35$$ $$160.544$$ None None $$0$$ $$-6$$ $$180$$ $$-1715$$ $$+$$
1001.6.a.e $$38$$ $$160.544$$ None None $$0$$ $$12$$ $$-51$$ $$1862$$ $$-$$
1001.6.a.f $$38$$ $$160.544$$ None None $$8$$ $$-24$$ $$-71$$ $$-1862$$ $$-$$
1001.6.a.g $$42$$ $$160.544$$ None None $$0$$ $$25$$ $$73$$ $$-2058$$ $$-$$
1001.6.a.h $$42$$ $$160.544$$ None None $$8$$ $$61$$ $$191$$ $$2058$$ $$-$$