## Results (45 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
471.1.d.a $$1$$ $$0.235$$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-471})$$ $$\Q(\sqrt{157})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q+q^{3}-q^{4}+q^{9}-q^{12}+2q^{13}+q^{16}+\cdots$$
471.1.d.b $$2$$ $$0.235$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-471})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\beta q^{2}+q^{3}+q^{4}+\beta q^{5}-\beta q^{6}+q^{9}+\cdots$$
471.1.d.c $$4$$ $$0.235$$ $$\Q(\zeta_{16})^+$$ $$\Q(\sqrt{-471})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$$
471.1.n.a $$12$$ $$0.235$$ $$\Q(\zeta_{26})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$0$$ $$q+\zeta_{26}^{2}q^{3}+\zeta_{26}^{11}q^{4}+(\zeta_{26}^{5}+\zeta_{26}^{12}+\cdots)q^{7}+\cdots$$
471.1.o.a $$12$$ $$0.235$$ $$\Q(\zeta_{26})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-2$$ $$q-\zeta_{26}^{3}q^{3}+\zeta_{26}^{10}q^{4}+(-\zeta_{26}-\zeta_{26}^{5}+\cdots)q^{7}+\cdots$$
471.2.a.a $$1$$ $$3.761$$ $$\Q$$ None None $$-1$$ $$-1$$ $$-2$$ $$3$$ $$+$$ $$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{7}+\cdots$$
471.2.a.b $$2$$ $$3.761$$ $$\Q(\sqrt{5})$$ None None $$-1$$ $$2$$ $$-2$$ $$-6$$ $$+$$ $$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$$
471.2.a.c $$3$$ $$3.761$$ 3.3.229.1 None None $$0$$ $$-3$$ $$-2$$ $$-3$$ $$+$$ $$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$$
471.2.a.d $$9$$ $$3.761$$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$2$$ $$-9$$ $$8$$ $$-2$$ $$-$$ $$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$$
471.2.a.e $$12$$ $$3.761$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$-1$$ $$12$$ $$4$$ $$8$$ $$-$$ $$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots$$
471.2.b.a $$12$$ $$3.761$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$-12$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
471.2.b.b $$14$$ $$3.761$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None None $$0$$ $$14$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$$
471.2.e.a $$4$$ $$3.761$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$2$$ $$0$$ $$-8$$ $$q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-2\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$$
471.2.e.b $$22$$ $$3.761$$ None None $$2$$ $$11$$ $$-4$$ $$4$$
471.2.e.c $$28$$ $$3.761$$ None None $$2$$ $$-14$$ $$-2$$ $$4$$
471.2.f.a $$100$$ $$3.761$$ None None $$0$$ $$0$$ $$0$$ $$-12$$
471.2.h.a $$24$$ $$3.761$$ None None $$0$$ $$12$$ $$0$$ $$0$$
471.2.h.b $$26$$ $$3.761$$ None None $$0$$ $$-13$$ $$-6$$ $$0$$
471.2.l.a $$4$$ $$3.761$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$6$$ $$0$$ $$-8$$ $$q+(2-\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{4}+(-3+\cdots)q^{7}+\cdots$$
471.2.l.b $$200$$ $$3.761$$ None None $$0$$ $$-6$$ $$0$$ $$0$$
471.2.m.a $$156$$ $$3.761$$ None None $$-1$$ $$13$$ $$-4$$ $$2$$
471.2.m.b $$180$$ $$3.761$$ None None $$-1$$ $$-15$$ $$-8$$ $$-10$$
471.2.p.a $$144$$ $$3.761$$ None None $$0$$ $$12$$ $$0$$ $$0$$
471.2.p.b $$168$$ $$3.761$$ None None $$0$$ $$-14$$ $$0$$ $$0$$
471.2.q.a $$312$$ $$3.761$$ None None $$-2$$ $$-13$$ $$4$$ $$4$$
471.2.q.b $$336$$ $$3.761$$ None None $$-2$$ $$14$$ $$2$$ $$-4$$
471.2.s.a $$1200$$ $$3.761$$ None None $$0$$ $$-26$$ $$0$$ $$-40$$
471.2.v.a $$288$$ $$3.761$$ None None $$0$$ $$-12$$ $$0$$ $$0$$
471.2.v.b $$312$$ $$3.761$$ None None $$0$$ $$13$$ $$6$$ $$0$$
471.2.w.a $$48$$ $$3.761$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-6$$ $$0$$ $$8$$
471.2.w.b $$2400$$ $$3.761$$ None None $$0$$ $$-46$$ $$0$$ $$-104$$
471.4.a.a $$14$$ $$27.790$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None None $$-2$$ $$42$$ $$-32$$ $$-60$$ $$-$$ $$q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$$
471.4.a.b $$17$$ $$27.790$$ $$\mathbb{Q}[x]/(x^{17} - \cdots)$$ None None $$-2$$ $$-51$$ $$-28$$ $$10$$ $$-$$ $$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$$
471.4.a.c $$22$$ $$27.790$$ None None $$4$$ $$-66$$ $$32$$ $$-4$$ $$+$$
471.4.a.d $$25$$ $$27.790$$ None None $$4$$ $$75$$ $$28$$ $$94$$ $$+$$
471.4.b.a $$40$$ $$27.790$$ None None $$0$$ $$-120$$ $$0$$ $$0$$
471.4.b.b $$40$$ $$27.790$$ None None $$0$$ $$120$$ $$0$$ $$0$$
471.6.a.a $$27$$ $$75.541$$ None None $$-2$$ $$243$$ $$-164$$ $$-618$$ $$+$$
471.6.a.b $$30$$ $$75.541$$ None None $$-8$$ $$-270$$ $$-136$$ $$68$$ $$+$$
471.6.a.c $$35$$ $$75.541$$ None None $$4$$ $$-315$$ $$164$$ $$-30$$ $$-$$
471.6.a.d $$38$$ $$75.541$$ None None $$10$$ $$342$$ $$136$$ $$460$$ $$-$$
471.8.a.a $$40$$ $$147.133$$ None None $$-16$$ $$1080$$ $$-428$$ $$-3424$$ $$-$$
471.8.a.b $$43$$ $$147.133$$ None None $$-22$$ $$-1161$$ $$-1072$$ $$6$$ $$-$$
471.8.a.c $$48$$ $$147.133$$ None None $$2$$ $$-1296$$ $$428$$ $$-680$$ $$+$$
471.8.a.d $$51$$ $$147.133$$ None None $$8$$ $$1377$$ $$1072$$ $$4122$$ $$+$$