## Results (1-50 of 195 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
420.1.o.a $$2$$ $$0.210$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-5})$$, $$\Q(\sqrt{-21})$$ $$\Q(\sqrt{105})$$ $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}-iq^{7}+\cdots$$
420.1.o.b $$2$$ $$0.210$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-5})$$, $$\Q(\sqrt{-21})$$ $$\Q(\sqrt{105})$$ $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{5}+q^{6}-iq^{7}+\cdots$$
420.1.be.a $$4$$ $$0.210$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{5}+\cdots$$
420.1.be.b $$4$$ $$0.210$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$$
420.2.a.a $$1$$ $$3.354$$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$-1$$ $$-$$ $$q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$$
420.2.a.b $$1$$ $$3.354$$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$1$$ $$-$$ $$q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots$$
420.2.a.c $$1$$ $$3.354$$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$1$$ $$-$$ $$q+q^{3}-q^{5}+q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$$
420.2.a.d $$1$$ $$3.354$$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$-1$$ $$-$$ $$q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$$
420.2.c.a $$16$$ $$3.354$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$2$$ $$-16$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots$$
420.2.c.b $$16$$ $$3.354$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$2$$ $$16$$ $$0$$ $$4$$ $$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots$$
420.2.d.a $$2$$ $$3.354$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$-2$$ $$4$$ $$q+(-1-\zeta_{6})q^{3}-q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
420.2.d.b $$2$$ $$3.354$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$2$$ $$4$$ $$q+(1+\zeta_{6})q^{3}+q^{5}+(3-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
420.2.d.c $$4$$ $$3.354$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$-2$$ $$4$$ $$-6$$ $$q+(-1+\beta _{3})q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
420.2.d.d $$4$$ $$3.354$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$2$$ $$-4$$ $$-6$$ $$q+(1+\beta _{1})q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
420.2.f.a $$8$$ $$3.354$$ 8.0.$$\cdots$$.2 $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}-\beta _{6})q^{7}+\cdots$$
420.2.f.b $$8$$ $$3.354$$ 8.0.40960000.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}-\beta _{2}q^{5}+(\beta _{5}+\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots$$
420.2.i.a $$48$$ $$3.354$$ None None $$0$$ $$0$$ $$0$$ $$0$$
420.2.k.a $$2$$ $$3.354$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{3}+(-2-i)q^{5}+iq^{7}-q^{9}+\cdots$$
420.2.k.b $$2$$ $$3.354$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2-i)q^{5}+iq^{7}-q^{9}+4q^{11}+\cdots$$
420.2.l.a $$4$$ $$3.354$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$-4$$ $$0$$ $$4$$ $$q-\zeta_{8}^{2}q^{2}+(-1+\zeta_{8}^{2})q^{3}-2q^{4}+\cdots$$
420.2.l.b $$4$$ $$3.354$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$4$$ $$0$$ $$-4$$ $$q+\zeta_{8}^{2}q^{2}+(1-\zeta_{8}^{2})q^{3}-2q^{4}+(\zeta_{8}^{2}+\cdots)q^{5}+\cdots$$
420.2.l.c $$8$$ $$3.354$$ 8.0.386672896.3 None None $$0$$ $$-2$$ $$-8$$ $$-8$$ $$q-\beta _{3}q^{2}+\beta _{2}q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+\cdots$$
420.2.l.d $$8$$ $$3.354$$ 8.0.386672896.3 None None $$0$$ $$-2$$ $$8$$ $$-8$$ $$q+\beta _{3}q^{2}-\beta _{6}q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+\cdots$$
420.2.l.e $$8$$ $$3.354$$ 8.0.386672896.3 None None $$0$$ $$2$$ $$-8$$ $$8$$ $$q-\beta _{3}q^{2}+\beta _{6}q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+\cdots$$
420.2.l.f $$8$$ $$3.354$$ 8.0.386672896.3 None None $$0$$ $$2$$ $$8$$ $$8$$ $$q+\beta _{3}q^{2}-\beta _{2}q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+\cdots$$
420.2.l.g $$16$$ $$3.354$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+\beta _{3}q^{2}+\beta _{4}q^{3}+\beta _{11}q^{4}+\beta _{5}q^{5}+\cdots$$
420.2.l.h $$16$$ $$3.354$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$16$$ $$q+\beta _{3}q^{2}+\beta _{6}q^{3}+\beta _{11}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$$
420.2.n.a $$24$$ $$3.354$$ None None $$0$$ $$0$$ $$0$$ $$0$$
420.2.n.b $$24$$ $$3.354$$ None None $$0$$ $$0$$ $$0$$ $$0$$
420.2.q.a $$2$$ $$3.354$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-1$$ $$5$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
420.2.q.b $$2$$ $$3.354$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$1$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
420.2.q.c $$4$$ $$3.354$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None None $$0$$ $$-2$$ $$-2$$ $$0$$ $$q+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+\beta _{1}q^{7}+(-1+\cdots)q^{9}+\cdots$$
420.2.q.d $$4$$ $$3.354$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$-2$$ $$2$$ $$-2$$ $$q+(-1-\beta _{1})q^{3}-\beta _{1}q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$$
420.2.s.a $$24$$ $$3.354$$ None None $$0$$ $$-4$$ $$0$$ $$0$$
420.2.t.a $$4$$ $$3.354$$ $$\Q(\zeta_{8})$$ None None $$4$$ $$0$$ $$-8$$ $$0$$ $$q+(1+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+2\zeta_{8}^{2}q^{4}+\cdots$$
420.2.t.b $$4$$ $$3.354$$ $$\Q(\zeta_{8})$$ None None $$4$$ $$0$$ $$8$$ $$0$$ $$q+(1+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+2\zeta_{8}^{2}q^{4}+\cdots$$
420.2.t.c $$32$$ $$3.354$$ None None $$-4$$ $$0$$ $$-8$$ $$0$$
420.2.t.d $$32$$ $$3.354$$ None None $$-4$$ $$0$$ $$8$$ $$0$$
420.2.w.a $$8$$ $$3.354$$ 8.0.$$\cdots$$.1 $$\Q(\sqrt{-21})$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$$
420.2.w.b $$8$$ $$3.354$$ 8.0.$$\cdots$$.1 $$\Q(\sqrt{-21})$$ None $$8$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$$
420.2.w.c $$160$$ $$3.354$$ None None $$0$$ $$0$$ $$0$$ $$0$$
420.2.x.a $$16$$ $$3.354$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots$$
420.2.ba.a $$8$$ $$3.354$$ 8.0.3317760000.8 $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+(\beta _{5}+\beta _{7})q^{3}+2\beta _{3}q^{4}-\beta _{6}q^{5}+\cdots$$
420.2.ba.b $$8$$ $$3.354$$ 8.0.3317760000.8 $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}-\beta _{5})q^{2}+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+\cdots$$
420.2.ba.c $$160$$ $$3.354$$ None None $$0$$ $$0$$ $$0$$ $$0$$
420.2.bb.a $$16$$ $$3.354$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{6}q^{3}+(\beta _{1}+\beta _{14})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$$
420.2.bf.a $$128$$ $$3.354$$ None None $$0$$ $$0$$ $$0$$ $$0$$
420.2.bh.a $$10$$ $$3.354$$ 10.0.$$\cdots$$.1 None None $$0$$ $$-1$$ $$-5$$ $$-5$$ $$q+\beta _{5}q^{3}+(-1-\beta _{7})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots$$
420.2.bh.b $$10$$ $$3.354$$ 10.0.$$\cdots$$.1 None None $$0$$ $$1$$ $$5$$ $$-5$$ $$q+\beta _{6}q^{3}+(1+\beta _{7})q^{5}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$
420.2.bi.a $$4$$ $$3.354$$ $$\Q(\zeta_{12})$$ None None $$-4$$ $$2$$ $$0$$ $$-2$$ $$q+(-1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{3}+\cdots$$