## Results (displaying all 29 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1003.1.b.a $$1$$ $$0.501$$ $$\Q$$ $$\Q(\sqrt{-59})$$, $$\Q(\sqrt{-1003})$$ $$\Q(\sqrt{17})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots$$
1003.1.b.b $$2$$ $$0.501$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots$$
1003.1.f.a $$2$$ $$0.501$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$-2$$ $$-2$$ $$-2$$ $$q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots$$
1003.1.f.b $$4$$ $$0.501$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$2$$ $$2$$ $$2$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots$$
1003.1.h.a $$4$$ $$0.501$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$$
1003.1.h.b $$8$$ $$0.501$$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots$$
1003.2.a.a $$1$$ $$8.009$$ $$\Q$$ None None $$-1$$ $$3$$ $$1$$ $$1$$ $$-$$ $$q-q^{2}+3q^{3}-q^{4}+q^{5}-3q^{6}+q^{7}+\cdots$$
1003.2.a.b $$1$$ $$8.009$$ $$\Q$$ None None $$0$$ $$2$$ $$-2$$ $$2$$ $$+$$ $$q+2q^{3}-2q^{4}-2q^{5}+2q^{7}+q^{9}+\cdots$$
1003.2.a.c $$1$$ $$8.009$$ $$\Q$$ None None $$1$$ $$1$$ $$1$$ $$3$$ $$-$$ $$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+3q^{7}+\cdots$$
1003.2.a.d $$1$$ $$8.009$$ $$\Q$$ None None $$2$$ $$0$$ $$-2$$ $$-2$$ $$+$$ $$q+2q^{2}+2q^{4}-2q^{5}-2q^{7}-3q^{9}+\cdots$$
1003.2.a.e $$3$$ $$8.009$$ 3.3.229.1 None None $$-3$$ $$2$$ $$-4$$ $$-2$$ $$+$$ $$q-q^{2}+(1+\beta _{2})q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$$
1003.2.a.f $$4$$ $$8.009$$ 4.4.2225.1 None None $$-3$$ $$-2$$ $$1$$ $$8$$ $$+$$ $$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
1003.2.a.g $$10$$ $$8.009$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$-1$$ $$-7$$ $$-12$$ $$-9$$ $$+$$ $$q-\beta _{8}q^{2}+(-1+\beta _{1})q^{3}+(2-\beta _{5})q^{4}+\cdots$$
1003.2.a.h $$16$$ $$8.009$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-6$$ $$-7$$ $$-21$$ $$-11$$ $$+$$ $$q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$$
1003.2.a.i $$18$$ $$8.009$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$5$$ $$1$$ $$21$$ $$-1$$ $$-$$ $$q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$$
1003.2.a.j $$22$$ $$8.009$$ None None $$5$$ $$7$$ $$19$$ $$3$$ $$-$$
1003.2.d.a $$2$$ $$8.009$$ $$\Q(\sqrt{-2})$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-q^{4}-3q^{8}+3q^{9}-\beta q^{11}+\cdots$$
1003.2.d.b $$4$$ $$8.009$$ $$\Q(i, \sqrt{5})$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots$$
1003.2.d.c $$38$$ $$8.009$$ None None $$2$$ $$0$$ $$0$$ $$0$$
1003.2.d.d $$44$$ $$8.009$$ None None $$-8$$ $$0$$ $$0$$ $$0$$
1003.4.a.a $$3$$ $$59.179$$ 3.3.75845.1 None None $$-3$$ $$-5$$ $$17$$ $$-2$$ $$-$$ $$q-q^{2}+(-2-\beta _{2})q^{3}-7q^{4}+(6+\beta _{2})q^{5}+\cdots$$
1003.4.a.b $$52$$ $$59.179$$ None None $$-8$$ $$-19$$ $$-95$$ $$-50$$ $$-$$
1003.4.a.c $$57$$ $$59.179$$ None None $$-11$$ $$-18$$ $$-132$$ $$-52$$ $$-$$
1003.4.a.d $$59$$ $$59.179$$ None None $$13$$ $$12$$ $$102$$ $$-24$$ $$+$$
1003.4.a.e $$61$$ $$59.179$$ None None $$13$$ $$30$$ $$128$$ $$116$$ $$+$$
1003.6.a.a $$94$$ $$160.865$$ None None $$-23$$ $$-99$$ $$-759$$ $$-929$$ $$+$$
1003.6.a.b $$96$$ $$160.865$$ None None $$-23$$ $$-45$$ $$-391$$ $$51$$ $$+$$
1003.6.a.c $$98$$ $$160.865$$ None None $$25$$ $$45$$ $$541$$ $$247$$ $$-$$
1003.6.a.d $$100$$ $$160.865$$ None None $$25$$ $$63$$ $$509$$ $$247$$ $$-$$