## Results (1-50 of 181 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
816.1.m.a $$1$$ $$0.407$$ $$\Q$$ $$\Q(\sqrt{-51})$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q-q^{3}-q^{5}+q^{9}+q^{11}-q^{13}+q^{15}+\cdots$$
816.1.m.b $$1$$ $$0.407$$ $$\Q$$ $$\Q(\sqrt{-51})$$ None $$0$$ $$1$$ $$1$$ $$0$$ $$q+q^{3}+q^{5}+q^{9}-q^{11}-q^{13}+q^{15}+\cdots$$
816.1.bc.a $$4$$ $$0.407$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots$$
816.2.a.a $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$-1$$ $$-3$$ $$4$$ $$-$$ $$q-q^{3}-3q^{5}+4q^{7}+q^{9}-q^{11}-5q^{13}+\cdots$$
816.2.a.b $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$-1$$ $$-2$$ $$0$$ $$+$$ $$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$$
816.2.a.c $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$-2$$ $$+$$ $$q-q^{3}-2q^{7}+q^{9}+2q^{13}-q^{17}+\cdots$$
816.2.a.d $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$-2$$ $$-$$ $$q-q^{3}-2q^{7}+q^{9}+2q^{13}-q^{17}+\cdots$$
816.2.a.e $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$0$$ $$+$$ $$q-q^{3}+q^{5}+q^{9}-5q^{11}-5q^{13}+\cdots$$
816.2.a.f $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$-1$$ $$2$$ $$4$$ $$-$$ $$q-q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$$
816.2.a.g $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$-1$$ $$3$$ $$4$$ $$-$$ $$q-q^{3}+3q^{5}+4q^{7}+q^{9}+3q^{11}+\cdots$$
816.2.a.h $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$1$$ $$-4$$ $$2$$ $$+$$ $$q+q^{3}-4q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots$$
816.2.a.i $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$-4$$ $$+$$ $$q+q^{3}-q^{5}-4q^{7}+q^{9}-3q^{11}+3q^{13}+\cdots$$
816.2.a.j $$1$$ $$6.516$$ $$\Q$$ None None $$0$$ $$1$$ $$3$$ $$0$$ $$-$$ $$q+q^{3}+3q^{5}+q^{9}+q^{11}+3q^{13}+\cdots$$
816.2.a.k $$2$$ $$6.516$$ $$\Q(\sqrt{57})$$ None None $$0$$ $$-2$$ $$-1$$ $$-8$$ $$-$$ $$q-q^{3}-\beta q^{5}-4q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$$
816.2.a.l $$2$$ $$6.516$$ $$\Q(\sqrt{17})$$ None None $$0$$ $$2$$ $$-1$$ $$2$$ $$-$$ $$q+q^{3}-\beta q^{5}+(2-2\beta )q^{7}+q^{9}+(4+\cdots)q^{11}+\cdots$$
816.2.a.m $$2$$ $$6.516$$ $$\Q(\sqrt{17})$$ None None $$0$$ $$2$$ $$3$$ $$0$$ $$-$$ $$q+q^{3}+(1+\beta )q^{5}+q^{9}+(1-\beta )q^{11}+\cdots$$
816.2.c.a $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2iq^{5}+2iq^{7}-q^{9}-6q^{13}+\cdots$$
816.2.c.b $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{5}-2iq^{7}-q^{9}+5iq^{11}+\cdots$$
816.2.c.c $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-4iq^{7}-q^{9}+4iq^{11}+2q^{13}+\cdots$$
816.2.c.d $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{5}-2iq^{7}-q^{9}-3iq^{11}+\cdots$$
816.2.c.e $$4$$ $$6.516$$ $$\Q(i, \sqrt{33})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots$$
816.2.c.f $$6$$ $$6.516$$ 6.0.399424.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots$$
816.2.e.a $$4$$ $$6.516$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{3}q^{3}+3\zeta_{12}q^{5}+2\zeta_{12}^{2}q^{7}+\cdots$$
816.2.e.b $$8$$ $$6.516$$ 8.0.$$\cdots$$.8 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{3}+2\beta _{3}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots$$
816.2.e.c $$20$$ $$6.516$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{14}q^{3}-\beta _{15}q^{5}-\beta _{16}q^{7}+(\beta _{9}+\cdots)q^{9}+\cdots$$
816.2.o.a $$4$$ $$6.516$$ $$\Q(\sqrt{-3}, \sqrt{17})$$ $$\Q(\sqrt{-51})$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q-\beta _{2}q^{3}+(-1+\beta _{3})q^{5}-3q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$$
816.2.o.b $$4$$ $$6.516$$ $$\Q(\sqrt{-3}, \sqrt{17})$$ $$\Q(\sqrt{-51})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{2}q^{5}-3q^{9}-3\beta _{1}q^{11}+\cdots$$
816.2.o.c $$4$$ $$6.516$$ $$\Q(\sqrt{-3}, \sqrt{17})$$ $$\Q(\sqrt{-51})$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q+\beta _{2}q^{3}+(1-\beta _{3})q^{5}-3q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$$
816.2.o.d $$8$$ $$6.516$$ 8.0.$$\cdots$$.12 $$\Q(\sqrt{-17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3}-\beta _{6})q^{7}-\beta _{2}q^{9}+\cdots$$
816.2.o.e $$16$$ $$6.516$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}-\beta _{9}q^{5}+\beta _{10}q^{7}+(1+\beta _{7}+\cdots)q^{9}+\cdots$$
816.2.r.a $$4$$ $$6.516$$ $$\Q(i, \sqrt{5})$$ None None $$-4$$ $$2$$ $$0$$ $$0$$ $$q+(-1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-2\beta _{2}q^{4}+\cdots$$
816.2.r.b $$4$$ $$6.516$$ $$\Q(i, \sqrt{5})$$ None None $$4$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$$
816.2.r.c $$272$$ $$6.516$$ None None $$0$$ $$-8$$ $$0$$ $$-8$$
816.2.s.a $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$2$$ $$0$$ $$-2$$ $$q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots$$
816.2.s.b $$2$$ $$6.516$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$2$$ $$0$$ $$6$$ $$q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots$$
816.2.s.c $$68$$ $$6.516$$ None None $$-2$$ $$68$$ $$0$$ $$-4$$
816.2.s.d $$72$$ $$6.516$$ None None $$-2$$ $$-72$$ $$0$$ $$0$$
816.2.u.a $$64$$ $$6.516$$ None None $$0$$ $$0$$ $$0$$ $$0$$
816.2.u.b $$64$$ $$6.516$$ None None $$0$$ $$0$$ $$0$$ $$0$$
816.2.w.a $$280$$ $$6.516$$ None None $$0$$ $$0$$ $$0$$ $$0$$
816.2.bd.a $$4$$ $$6.516$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$-4$$ $$-8$$ $$q-\zeta_{8}q^{3}+(-1+2\zeta_{8}-\zeta_{8}^{2})q^{5}+(-2+\cdots)q^{7}+\cdots$$
816.2.bd.b $$4$$ $$6.516$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{8}q^{3}+\zeta_{8}q^{5}+(1-\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\cdots$$
816.2.bd.c $$4$$ $$6.516$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q-\zeta_{8}q^{3}+(1+2\zeta_{8}+\zeta_{8}^{2})q^{5}-2\zeta_{8}^{3}q^{7}+\cdots$$
816.2.bd.d $$4$$ $$6.516$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$8$$ $$4$$ $$q+\zeta_{8}q^{3}+(2+\zeta_{8}+2\zeta_{8}^{2})q^{5}+(1-\zeta_{8}^{2}+\cdots)q^{7}+\cdots$$
816.2.bd.e $$8$$ $$6.516$$ 8.0.836829184.2 None None $$0$$ $$0$$ $$-4$$ $$4$$ $$q+\beta _{3}q^{3}+(-1+\beta _{3}+\beta _{4}+\beta _{7})q^{5}+\cdots$$
816.2.bd.f $$12$$ $$6.516$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{3}q^{3}+\beta _{6}q^{5}+(\beta _{4}+\beta _{10})q^{7}-\beta _{5}q^{9}+\cdots$$
816.2.bf.a $$8$$ $$6.516$$ 8.0.12960000.1 None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-\beta _{2}+\beta _{5})q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+\cdots$$
816.2.bf.b $$8$$ $$6.516$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{7}q^{3}+\zeta_{24}q^{5}+(-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{7}+\cdots$$
816.2.bf.c $$8$$ $$6.516$$ 8.0.12960000.1 None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1-\beta _{1}+\beta _{5})q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}+\cdots$$
816.2.bf.d $$24$$ $$6.516$$ None None $$0$$ $$0$$ $$0$$ $$0$$