## Results (1-50 of 323 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
80.1.h.a $$1$$ $$0.040$$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$-1$$ $$0$$ $$q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots$$
80.2.a.a $$1$$ $$0.639$$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$4$$ $$-$$ $$q+q^{5}+4q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots$$
80.2.a.b $$1$$ $$0.639$$ $$\Q$$ None None $$0$$ $$2$$ $$-1$$ $$-2$$ $$-$$ $$q+2q^{3}-q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots$$
80.2.c.a $$2$$ $$0.639$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1+i)q^{5}-iq^{7}-q^{9}+\cdots$$
80.2.j.a $$2$$ $$0.639$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$0$$ $$2$$ $$-6$$ $$q+(1-i)q^{2}+2iq^{3}-2iq^{4}+(1+2i)q^{5}+\cdots$$
80.2.j.b $$18$$ $$0.639$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$-4$$ $$0$$ $$-4$$ $$2$$ $$q+\beta _{6}q^{2}-\beta _{16}q^{3}-\beta _{13}q^{4}+(-1+\cdots)q^{5}+\cdots$$
80.2.l.a $$16$$ $$0.639$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{2}+(\beta _{3}-\beta _{6}+\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$$
80.2.n.a $$2$$ $$0.639$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}-3iq^{9}+(-5+5i)q^{13}+\cdots$$
80.2.n.b $$4$$ $$0.639$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}+(-1-2\zeta_{12})q^{5}+\zeta_{12}^{3}q^{7}+\cdots$$
80.2.q.a $$2$$ $$0.639$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$2$$ $$2$$ $$0$$ $$q+(-1-i)q^{2}+(1+i)q^{3}+2iq^{4}+\cdots$$
80.2.q.b $$2$$ $$0.639$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$-2$$ $$4$$ $$0$$ $$q+(1+i)q^{2}+(-1-i)q^{3}+2iq^{4}+\cdots$$
80.2.q.c $$16$$ $$0.639$$ 16.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\beta _{12}q^{2}+(-\beta _{3}-\beta _{11}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots$$
80.2.s.a $$2$$ $$0.639$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-4$$ $$-4$$ $$-6$$ $$q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots$$
80.2.s.b $$18$$ $$0.639$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$0$$ $$0$$ $$2$$ $$2$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{13}q^{4}+\beta _{17}q^{5}+\cdots$$
80.3.b.a $$4$$ $$2.180$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+(-9+6\beta _{1}+\cdots)q^{9}+\cdots$$
80.3.h.a $$2$$ $$2.180$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$10$$ $$0$$ $$q-\beta q^{3}+5q^{5}+3\beta q^{7}+11q^{9}-5\beta q^{15}+\cdots$$
80.3.h.b $$4$$ $$2.180$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+3\beta _{1}q^{7}+\cdots$$
80.3.i.a $$44$$ $$2.180$$ None None $$-2$$ $$0$$ $$-2$$ $$0$$
80.3.k.a $$44$$ $$2.180$$ None None $$0$$ $$0$$ $$-2$$ $$0$$
80.3.p.a $$2$$ $$2.180$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$-6$$ $$14$$ $$q+(-1+i)q^{3}+(-3+4i)q^{5}+(7+7i)q^{7}+\cdots$$
80.3.p.b $$2$$ $$2.180$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$10$$ $$6$$ $$q+(-1+i)q^{3}+5q^{5}+(3+3i)q^{7}+\cdots$$
80.3.p.c $$2$$ $$2.180$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$4$$ $$0$$ $$-4$$ $$q+(2-2i)q^{3}-5iq^{5}+(-2-2i)q^{7}+\cdots$$
80.3.p.d $$4$$ $$2.180$$ $$\Q(i, \sqrt{41})$$ None None $$0$$ $$2$$ $$-6$$ $$-14$$ $$q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
80.3.r.a $$32$$ $$2.180$$ None None $$0$$ $$0$$ $$0$$ $$0$$
80.3.t.a $$44$$ $$2.180$$ None None $$-2$$ $$-4$$ $$-2$$ $$0$$
80.4.a.a $$1$$ $$4.720$$ $$\Q$$ None None $$0$$ $$-10$$ $$-5$$ $$18$$ $$+$$ $$q-10q^{3}-5q^{5}+18q^{7}+73q^{9}+2^{4}q^{11}+\cdots$$
80.4.a.b $$1$$ $$4.720$$ $$\Q$$ None None $$0$$ $$-4$$ $$5$$ $$-16$$ $$-$$ $$q-4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-6^{2}q^{11}+\cdots$$
80.4.a.c $$1$$ $$4.720$$ $$\Q$$ None None $$0$$ $$-4$$ $$5$$ $$16$$ $$+$$ $$q-4q^{3}+5q^{5}+2^{4}q^{7}-11q^{9}+60q^{11}+\cdots$$
80.4.a.d $$1$$ $$4.720$$ $$\Q$$ None None $$0$$ $$-2$$ $$-5$$ $$-6$$ $$-$$ $$q-2q^{3}-5q^{5}-6q^{7}-23q^{9}-2^{5}q^{11}+\cdots$$
80.4.a.e $$1$$ $$4.720$$ $$\Q$$ None None $$0$$ $$6$$ $$-5$$ $$34$$ $$+$$ $$q+6q^{3}-5q^{5}+34q^{7}+9q^{9}-2^{4}q^{11}+\cdots$$
80.4.a.f $$1$$ $$4.720$$ $$\Q$$ None None $$0$$ $$8$$ $$5$$ $$4$$ $$+$$ $$q+8q^{3}+5q^{5}+4q^{7}+37q^{9}-12q^{11}+\cdots$$
80.4.c.a $$2$$ $$4.720$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-10$$ $$0$$ $$q+iq^{3}+(-5-5i)q^{5}-13iq^{7}+23q^{9}+\cdots$$
80.4.c.b $$2$$ $$4.720$$ $$\Q(\sqrt{-19})$$ None None $$0$$ $$0$$ $$14$$ $$0$$ $$q-\beta q^{3}+(7-\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots$$
80.4.c.c $$4$$ $$4.720$$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$$
80.4.j.a $$68$$ $$4.720$$ None None $$-2$$ $$0$$ $$-2$$ $$-4$$
80.4.l.a $$48$$ $$4.720$$ None None $$0$$ $$0$$ $$0$$ $$0$$
80.4.n.a $$2$$ $$4.720$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-11i)q^{5}-3^{3}iq^{9}+(55-55i)q^{13}+\cdots$$
80.4.n.b $$4$$ $$4.720$$ $$\Q(i, \sqrt{35})$$ None None $$0$$ $$0$$ $$-20$$ $$0$$ $$q-\beta _{2}q^{3}+(-5+10\beta _{1})q^{5}+\beta _{3}q^{7}+\cdots$$
80.4.n.c $$12$$ $$4.720$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$16$$ $$0$$ $$q-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+(-2\beta _{2}+\cdots)q^{7}+\cdots$$
80.4.q.a $$68$$ $$4.720$$ None None $$0$$ $$0$$ $$-2$$ $$0$$
80.4.s.a $$68$$ $$4.720$$ None None $$-2$$ $$-4$$ $$-2$$ $$-4$$
80.5.b.a $$4$$ $$8.270$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-9-6\beta _{2}+\cdots)q^{9}+\cdots$$
80.5.b.b $$4$$ $$8.270$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}-5\beta _{1}q^{5}+(2\beta _{2}+7\beta _{3})q^{7}+\cdots$$
80.5.h.a $$2$$ $$8.270$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$-50$$ $$0$$ $$q-\beta q^{3}-5^{2}q^{5}-3\beta q^{7}+239q^{9}+\cdots$$
80.5.h.b $$2$$ $$8.270$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$14$$ $$0$$ $$q+(7+i)q^{5}-3^{4}q^{9}+10iq^{13}+20iq^{17}+\cdots$$
80.5.h.c $$8$$ $$8.270$$ 8.0.$$\cdots$$.10 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+\beta _{4}q^{5}+(2\beta _{3}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots$$
80.5.i.a $$92$$ $$8.270$$ None None $$-2$$ $$0$$ $$-2$$ $$0$$
80.5.k.a $$92$$ $$8.270$$ None None $$0$$ $$0$$ $$-2$$ $$0$$
80.5.p.a $$2$$ $$8.270$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-20$$ $$40$$ $$84$$ $$q+(-10+10i)q^{3}+(20+15i)q^{5}+\cdots$$
80.5.p.b $$2$$ $$8.270$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-18$$ $$-30$$ $$-58$$ $$q+(-9+9i)q^{3}+(-15+20i)q^{5}+\cdots$$