## Results (1-50 of 77 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1053.1.k.a $2$ $0.526$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}+q^{16}+\cdots$$
1053.1.m.a $2$ $0.526$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}^{2}q^{4}+\zeta_{6}q^{13}-\zeta_{6}q^{16}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$$
1053.1.n.a $2$ $0.526$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-39})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{5}-q^{8}+q^{10}-\zeta_{6}^{2}q^{11}+\cdots$$
1053.1.n.b $2$ $0.526$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-39})$$ $$\Q(\sqrt{13})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{4}+\zeta_{6}q^{13}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{25}+\cdots$$
1053.1.n.c $2$ $0.526$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-39})$$ None $$1$$ $$0$$ $$1$$ $$0$$ $$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{5}+q^{8}+q^{10}+\zeta_{6}^{2}q^{11}+\cdots$$
1053.1.n.d $4$ $0.526$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots$$
1053.1.u.a $2$ $0.526$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{6}^{2}q^{4}+q^{7}-\zeta_{6}q^{13}-\zeta_{6}q^{16}+\cdots$$
1053.1.v.a $2$ $0.526$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-q^{4}-\zeta_{6}^{2}q^{13}+q^{16}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$$
1053.1.z.a $4$ $0.526$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\zeta_{12}^{3}q^{4}+(\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}q^{13}+\cdots$$
1053.1.bb.a $4$ $0.526$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\zeta_{12}^{5}q^{4}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}-\zeta_{12}^{5}q^{13}+\cdots$$
1053.1.be.a $4$ $0.526$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\zeta_{12}q^{4}+(-1+\zeta_{12}^{3})q^{7}-\zeta_{12}^{5}q^{13}+\cdots$$
1053.2.a.a $1$ $8.408$ $$\Q$$ None None $$-2$$ $$0$$ $$-4$$ $$2$$ $+$ $$q-2q^{2}+2q^{4}-4q^{5}+2q^{7}+8q^{10}+\cdots$$
1053.2.a.b $1$ $8.408$ $$\Q$$ None None $$-1$$ $$0$$ $$-2$$ $$5$$ $-$ $$q-q^{2}-q^{4}-2q^{5}+5q^{7}+3q^{8}+2q^{10}+\cdots$$
1053.2.a.c $1$ $8.408$ $$\Q$$ None None $$1$$ $$0$$ $$2$$ $$5$$ $-$ $$q+q^{2}-q^{4}+2q^{5}+5q^{7}-3q^{8}+2q^{10}+\cdots$$
1053.2.a.d $1$ $8.408$ $$\Q$$ None None $$2$$ $$0$$ $$4$$ $$2$$ $-$ $$q+2q^{2}+2q^{4}+4q^{5}+2q^{7}+8q^{10}+\cdots$$
1053.2.a.e $2$ $8.408$ $$\Q(\sqrt{5})$$ None None $$-1$$ $$0$$ $$3$$ $$-3$$ $+$ $$q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$$
1053.2.a.f $2$ $8.408$ $$\Q(\sqrt{5})$$ None None $$1$$ $$0$$ $$-3$$ $$-3$$ $+$ $$q+\beta q^{2}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots$$
1053.2.a.g $3$ $8.408$ 3.3.621.1 None None $$0$$ $$0$$ $$-3$$ $$0$$ $-$ $$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$$
1053.2.a.h $3$ $8.408$ 3.3.621.1 None None $$0$$ $$0$$ $$3$$ $$0$$ $-$ $$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$$
1053.2.a.i $4$ $8.408$ $$\Q(\sqrt{3}, \sqrt{7})$$ None None $$0$$ $$0$$ $$0$$ $$-10$$ $+$ $$q+\beta _{3}q^{2}-\beta _{2}q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots$$
1053.2.a.j $5$ $8.408$ 5.5.403137.1 None None $$-2$$ $$0$$ $$-1$$ $$-2$$ $+$ $$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{3}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$
1053.2.a.k $5$ $8.408$ 5.5.403137.1 None None $$2$$ $$0$$ $$1$$ $$-2$$ $-$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{3}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$
1053.2.a.l $6$ $8.408$ 6.6.22931361.1 None None $$-2$$ $$0$$ $$-3$$ $$0$$ $+$ $$q-\beta _{1}q^{2}+(1+\beta _{1}-\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots$$
1053.2.a.m $6$ $8.408$ 6.6.22931361.1 None None $$2$$ $$0$$ $$3$$ $$0$$ $-$ $$q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{4}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$$
1053.2.a.n $8$ $8.408$ 8.8.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$6$$ $-$ $$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{7})q^{5}+\cdots$$
1053.2.b.a $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(1-2\zeta_{6})q^{2}-q^{4}+(1-2\zeta_{6})q^{5}+\cdots$$
1053.2.b.b $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(1-2\zeta_{6})q^{2}-q^{4}+(1-2\zeta_{6})q^{5}+\cdots$$
1053.2.b.c $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{2}-q^{4}+2\zeta_{6}q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{8}+\cdots$$
1053.2.b.d $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{2}-q^{4}+2\zeta_{6}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{8}+\cdots$$
1053.2.b.e $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{11}+\cdots$$
1053.2.b.f $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+\zeta_{6}q^{5}+\zeta_{6}q^{7}+\zeta_{6}q^{11}+\cdots$$
1053.2.b.g $4$ $8.408$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}-\beta _{1}q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$$
1053.2.b.h $4$ $8.408$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}-\beta _{1}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$$
1053.2.b.i $10$ $8.408$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{7}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$
1053.2.b.j $10$ $8.408$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{7}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1053.2.b.k $12$ $8.408$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots$$
1053.2.e.a $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$0$$ $$-2$$ $$-5$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$$
1053.2.e.b $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$0$$ $$-2$$ $$4$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$$
1053.2.e.c $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$0$$ $$2$$ $$-5$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots$$
1053.2.e.d $2$ $8.408$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$0$$ $$2$$ $$4$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$$
1053.2.e.e $4$ $8.408$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
1053.2.e.f $4$ $8.408$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None None $$-1$$ $$0$$ $$-5$$ $$2$$ $$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$$
1053.2.e.g $4$ $8.408$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$-1$$ $$0$$ $$-3$$ $$0$$ $$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
1053.2.e.h $4$ $8.408$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$-1$$ $$0$$ $$3$$ $$3$$ $$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
1053.2.e.i $4$ $8.408$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}-2\zeta_{12}q^{7}+\cdots$$
1053.2.e.j $4$ $8.408$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None None $$1$$ $$0$$ $$5$$ $$2$$ $$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$$
1053.2.e.k $4$ $8.408$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$1$$ $$0$$ $$-3$$ $$3$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
1053.2.e.l $4$ $8.408$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$1$$ $$0$$ $$3$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
1053.2.e.m $4$ $8.408$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots$$
1053.2.e.n $6$ $8.408$ 6.0.1156923.1 None None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$$