## Results (1-50 of 254 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
468.1.e.a $$1$$ $$0.234$$ $$\Q$$ $$\Q(\sqrt{-39})$$, $$\Q(\sqrt{-13})$$ $$\Q(\sqrt{3})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-q^{8}+2q^{11}-q^{13}+q^{16}+\cdots$$
468.1.e.b $$1$$ $$0.234$$ $$\Q$$ $$\Q(\sqrt{-39})$$, $$\Q(\sqrt{-13})$$ $$\Q(\sqrt{3})$$ $$1$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}+q^{8}-2q^{11}-q^{13}+q^{16}+\cdots$$
468.1.e.c $$2$$ $$0.234$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-39})$$ $$\Q(\sqrt{39})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+iq^{5}+iq^{8}+2q^{10}+\cdots$$
468.1.o.a $$4$$ $$0.234$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+q^{13}+\cdots$$
468.1.q.a $$4$$ $$0.234$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$$
468.1.r.a $$4$$ $$0.234$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$$
468.1.v.a $$4$$ $$0.234$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$$
468.1.y.a $$4$$ $$0.234$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}-\zeta_{12}^{4}q^{5}+\cdots$$
468.1.z.a $$2$$ $$0.234$$ $$\Q(\sqrt{-3})$$ None $$\Q(\sqrt{13})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-\zeta_{6}+\cdots)q^{17}+\cdots$$
468.1.br.a $$2$$ $$0.234$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-1})$$ None $$1$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{5}-q^{8}+\zeta_{6}q^{10}+\cdots$$
468.1.bx.a $$8$$ $$0.234$$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{5}+\cdots$$
468.1.cd.a $$4$$ $$0.234$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{7}-\zeta_{12}q^{13}+(\zeta_{12}+\cdots)q^{19}+\cdots$$
468.2.a.a $$1$$ $$3.737$$ $$\Q$$ None None $$0$$ $$0$$ $$-4$$ $$4$$ $$-$$ $$q-4q^{5}+4q^{7}+4q^{11}-q^{13}+8q^{23}+\cdots$$
468.2.a.b $$1$$ $$3.737$$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$-2$$ $$+$$ $$q-2q^{5}-2q^{7}+2q^{11}-q^{13}-6q^{17}+\cdots$$
468.2.a.c $$1$$ $$3.737$$ $$\Q$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$-$$ $$q+2q^{7}+q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots$$
468.2.a.d $$1$$ $$3.737$$ $$\Q$$ None None $$0$$ $$0$$ $$4$$ $$-2$$ $$-$$ $$q+4q^{5}-2q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots$$
468.2.a.e $$1$$ $$3.737$$ $$\Q$$ None None $$0$$ $$0$$ $$4$$ $$4$$ $$-$$ $$q+4q^{5}+4q^{7}-4q^{11}-q^{13}-8q^{23}+\cdots$$
468.2.b.a $$2$$ $$3.737$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{5}-\zeta_{6}q^{11}+(-1+\zeta_{6})q^{13}+\cdots$$
468.2.b.b $$2$$ $$3.737$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{7}+(-1-\zeta_{6})q^{13}-\zeta_{6}q^{19}+\cdots$$
468.2.b.c $$2$$ $$3.737$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}-2iq^{7}-3iq^{11}+(3+i)q^{13}+\cdots$$
468.2.c.a $$4$$ $$3.737$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{3}q^{2}+2q^{4}-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\cdots$$
468.2.c.b $$8$$ $$3.737$$ 8.0.157351936.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{4})q^{4}-\beta _{5}q^{5}+\cdots$$
468.2.c.c $$12$$ $$3.737$$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{3}+\beta _{10})q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots$$
468.2.h.a $$4$$ $$3.737$$ $$\Q(\sqrt{-2}, \sqrt{13})$$ $$\Q(\sqrt{-13})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{2}-2q^{4}+(-1-\beta _{3})q^{7}+2\beta _{2}q^{8}+\cdots$$
468.2.h.b $$4$$ $$3.737$$ $$\Q(\sqrt{-2}, \sqrt{13})$$ $$\Q(\sqrt{-13})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{2}q^{2}-2q^{4}+(1+\beta _{3})q^{7}+2\beta _{2}q^{8}+\cdots$$
468.2.h.c $$4$$ $$3.737$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{2}+2q^{4}-\zeta_{8}^{2}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots$$
468.2.h.d $$16$$ $$3.737$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{8})q^{4}+(-\beta _{6}-\beta _{12}+\cdots)q^{5}+\cdots$$
468.2.i.a $$2$$ $$3.737$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$0$$ $$-2$$ $$q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots$$
468.2.i.b $$10$$ $$3.737$$ 10.0.$$\cdots$$.1 None None $$0$$ $$-3$$ $$7$$ $$2$$ $$q-\beta _{1}q^{3}+(2-\beta _{1}-\beta _{2}+2\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$$
468.2.i.c $$12$$ $$3.737$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$-1$$ $$0$$ $$q+(-\beta _{5}-\beta _{7})q^{3}+\beta _{1}q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$$
468.2.j.a $$28$$ $$3.737$$ None None $$0$$ $$0$$ $$0$$ $$2$$
468.2.k.a $$28$$ $$3.737$$ None None $$0$$ $$0$$ $$0$$ $$-4$$
468.2.l.a $$2$$ $$3.737$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-4$$ $$-1$$ $$q-2q^{5}-\zeta_{6}q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$$
468.2.l.b $$2$$ $$3.737$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-4$$ $$-1$$ $$q-2q^{5}-\zeta_{6}q^{7}+(2-2\zeta_{6})q^{11}+(4+\cdots)q^{13}+\cdots$$
468.2.l.c $$2$$ $$3.737$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-5$$ $$q-5\zeta_{6}q^{7}+(-4+\zeta_{6})q^{13}-8\zeta_{6}q^{19}+\cdots$$
468.2.l.d $$2$$ $$3.737$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$6$$ $$4$$ $$q+3q^{5}+4\zeta_{6}q^{7}+(-3-\zeta_{6})q^{13}+\cdots$$
468.2.l.e $$4$$ $$3.737$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{3}q^{5}+(2+2\beta _{2})q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots$$
468.2.n.a $$2$$ $$3.737$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$-6$$ $$0$$ $$q+(-1-i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots$$
468.2.n.b $$2$$ $$3.737$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$0$$ $$-4$$ $$0$$ $$q+(-1+i)q^{2}-2iq^{4}+(-2-2i)q^{5}+\cdots$$
468.2.n.c $$2$$ $$3.737$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$6$$ $$0$$ $$q+(-1-i)q^{2}+2iq^{4}+(3+3i)q^{5}+\cdots$$
468.2.n.d $$2$$ $$3.737$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$0$$ $$-4$$ $$0$$ $$q+(1-i)q^{2}-2iq^{4}+(-2-2i)q^{5}+\cdots$$
468.2.n.e $$2$$ $$3.737$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$0$$ $$2$$ $$-4$$ $$q+(1+i)q^{2}+2iq^{4}+(1+i)q^{5}+(-2+\cdots)q^{7}+\cdots$$
468.2.n.f $$2$$ $$3.737$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$0$$ $$2$$ $$4$$ $$q+(1+i)q^{2}+2iq^{4}+(1+i)q^{5}+(2+\cdots)q^{7}+\cdots$$
468.2.n.g $$2$$ $$3.737$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$6$$ $$0$$ $$q+(1+i)q^{2}+2iq^{4}+(3+3i)q^{5}+(-2+\cdots)q^{8}+\cdots$$
468.2.n.h $$8$$ $$3.737$$ 8.0.157351936.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$$
468.2.n.i $$8$$ $$3.737$$ 8.0.18939904.2 None None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{2}+\beta _{5}-\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$
468.2.n.j $$10$$ $$3.737$$ 10.0.$$\cdots$$.1 None None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(-\beta _{5}-\beta _{7})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
468.2.n.k $$10$$ $$3.737$$ 10.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(\beta _{7}+\beta _{8})q^{4}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$$
468.2.n.l $$16$$ $$3.737$$ 16.0.$$\cdots$$.7 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{11}q^{2}+\beta _{7}q^{4}-\beta _{2}q^{5}+(\beta _{7}-\beta _{9}+\cdots)q^{7}+\cdots$$
468.2.p.a $$12$$ $$3.737$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{8}q^{5}-\beta _{4}q^{7}+(\beta _{6}+\beta _{9})q^{11}+(-1+\cdots)q^{13}+\cdots$$