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Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
504.1.e.a $$4$$ $$0.252$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$$
504.1.l.a $$1$$ $$0.252$$ $$\Q$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-14})$$ $$\Q(\sqrt{2})$$ $$1$$ $$0$$ $$0$$ $$-1$$ $$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{14}+q^{16}+\cdots$$
504.1.l.b $$2$$ $$0.252$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{42})$$ $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{2}-q^{4}+q^{7}+iq^{8}-iq^{11}+\cdots$$
504.1.ba.a $$4$$ $$0.252$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$$
504.1.bn.a $$2$$ $$0.252$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-14})$$ None $$-1$$ $$-2$$ $$-1$$ $$-1$$ $$q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$$
504.1.bn.b $$2$$ $$0.252$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-14})$$ None $$-1$$ $$2$$ $$1$$ $$-1$$ $$q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots$$
504.1.bn.c $$4$$ $$0.252$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-14})$$ None $$2$$ $$0$$ $$0$$ $$2$$ $$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$$
504.1.bw.a $$4$$ $$0.252$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots$$
504.1.ce.a $$4$$ $$0.252$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}+\zeta_{12}^{3}q^{6}+\cdots$$
504.1.cu.a $$4$$ $$0.252$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}-\beta _{1}q^{11}-q^{13}+\cdots$$
504.2.a.a $$1$$ $$4.024$$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$-1$$ $$+$$ $$q-2q^{5}-q^{7}-2q^{11}+2q^{13}-6q^{17}+\cdots$$
504.2.a.b $$1$$ $$4.024$$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$-1$$ $$+$$ $$q-2q^{5}-q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots$$
504.2.a.c $$1$$ $$4.024$$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$-1$$ $$-$$ $$q-2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots$$
504.2.a.d $$1$$ $$4.024$$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$1$$ $$+$$ $$q-2q^{5}+q^{7}-6q^{11}-6q^{13}+2q^{17}+\cdots$$
504.2.a.e $$1$$ $$4.024$$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$1$$ $$-$$ $$q-2q^{5}+q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots$$
504.2.a.f $$1$$ $$4.024$$ $$\Q$$ None None $$0$$ $$0$$ $$2$$ $$-1$$ $$-$$ $$q+2q^{5}-q^{7}+2q^{11}+2q^{13}+6q^{17}+\cdots$$
504.2.a.g $$1$$ $$4.024$$ $$\Q$$ None None $$0$$ $$0$$ $$2$$ $$1$$ $$-$$ $$q+2q^{5}+q^{7}+6q^{11}-6q^{13}-2q^{17}+\cdots$$
504.2.a.h $$1$$ $$4.024$$ $$\Q$$ None None $$0$$ $$0$$ $$4$$ $$1$$ $$-$$ $$q+4q^{5}+q^{7}+2q^{17}-2q^{19}-8q^{23}+\cdots$$
504.2.c.a $$2$$ $$4.024$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta q^{2}-2q^{4}-\beta q^{5}+q^{7}-2\beta q^{8}+\cdots$$
504.2.c.b $$4$$ $$4.024$$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots$$
504.2.c.c $$4$$ $$4.024$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+\beta _{2}q^{5}+q^{7}+\cdots$$
504.2.c.d $$4$$ $$4.024$$ 4.0.2312.1 None None $$1$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}-q^{7}+\cdots$$
504.2.c.e $$8$$ $$4.024$$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}-q^{7}+\beta _{3}q^{8}+\cdots$$
504.2.c.f $$8$$ $$4.024$$ 8.0.386672896.3 None None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{3}q^{2}-\beta _{2}q^{4}+(-\beta _{2}+\beta _{6})q^{5}+\cdots$$
504.2.i.a $$8$$ $$4.024$$ 8.0.157351936.1 $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{7}+\beta _{3}q^{8}+\cdots$$
504.2.i.b $$24$$ $$4.024$$ None None $$0$$ $$0$$ $$0$$ $$0$$
504.2.j.a $$24$$ $$4.024$$ None None $$0$$ $$0$$ $$0$$ $$0$$
504.2.k.a $$8$$ $$4.024$$ $$\Q(\zeta_{16})$$ None None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\zeta_{16}^{7}q^{5}+(1+\zeta_{16}^{4})q^{7}+(\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{11}+\cdots$$
504.2.p.a $$2$$ $$4.024$$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta )q^{2}+(-1-\beta )q^{4}+(-1+\cdots)q^{7}+\cdots$$
504.2.p.b $$4$$ $$4.024$$ $$\Q(\zeta_{12})$$ None None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\zeta_{12})q^{2}-2\zeta_{12}q^{4}+2\zeta_{12}^{3}q^{5}+\cdots$$
504.2.p.c $$4$$ $$4.024$$ $$\Q(\sqrt{-2}, \sqrt{7})$$ $$\Q(\sqrt{-42})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots$$
504.2.p.d $$4$$ $$4.024$$ $$\Q(i, \sqrt{7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(2-\beta _{2})q^{4}+(-1+2\beta _{2}+\cdots)q^{7}+\cdots$$
504.2.p.e $$4$$ $$4.024$$ $$\Q(\zeta_{12})$$ None None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1+\zeta_{12})q^{2}+2\zeta_{12}q^{4}-2\zeta_{12}^{3}q^{5}+\cdots$$
504.2.p.f $$4$$ $$4.024$$ $$\Q(i, \sqrt{6})$$ None None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}+\beta _{3}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$
504.2.p.g $$16$$ $$4.024$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+\beta _{3}q^{4}+\beta _{5}q^{5}+\beta _{8}q^{7}+\cdots$$
504.2.q.a $$2$$ $$4.024$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$4$$ $$q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
504.2.q.b $$2$$ $$4.024$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$1$$ $$-4$$ $$q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
504.2.q.c $$22$$ $$4.024$$ None None $$0$$ $$-2$$ $$1$$ $$5$$
504.2.q.d $$22$$ $$4.024$$ None None $$0$$ $$2$$ $$3$$ $$-5$$
504.2.r.a $$2$$ $$4.024$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$1$$ $$-1$$ $$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots$$
504.2.r.b $$2$$ $$4.024$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$-2$$ $$-1$$ $$q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots$$
504.2.r.c $$6$$ $$4.024$$ $$\Q(\zeta_{18})$$ None None $$0$$ $$0$$ $$3$$ $$-3$$ $$q+(-\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{5}+\cdots$$
504.2.r.d $$8$$ $$4.024$$ 8.0.508277025.1 None None $$0$$ $$-4$$ $$4$$ $$-4$$ $$q+(-\beta _{4}-\beta _{6})q^{3}+(1+\beta _{1}+2\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$$
504.2.r.e $$8$$ $$4.024$$ 8.0.2091141441.1 None None $$0$$ $$-1$$ $$-3$$ $$4$$ $$q+\beta _{4}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$$
504.2.r.f $$10$$ $$4.024$$ 10.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$-3$$ $$5$$ $$q+\beta _{6}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$$
504.2.s.a $$2$$ $$4.024$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-4$$ $$5$$ $$q+(-4+4\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}-3q^{13}+\cdots$$
504.2.s.b $$2$$ $$4.024$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$-5$$ $$q+(-1+\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+5\zeta_{6}q^{11}+\cdots$$
504.2.s.c $$2$$ $$4.024$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$-4$$ $$q+(-1+\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots$$
504.2.s.d $$2$$ $$4.024$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$1$$ $$q+(-1+\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots$$
504.2.s.e $$2$$ $$4.024$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$4$$ $$q+(-1+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-\zeta_{6}q^{11}+\cdots$$
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