## Results (1-50 of 252 matches)

Label Dim $A$ Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
390.2.a.a $1$ $3.114$ $$\Q$$ None $$-1$$ $$-1$$ $$-1$$ $$0$$ $+$ $$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$$
390.2.a.b $1$ $3.114$ $$\Q$$ None $$-1$$ $$-1$$ $$1$$ $$-2$$ $-$ $$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$$
390.2.a.c $1$ $3.114$ $$\Q$$ None $$-1$$ $$1$$ $$-1$$ $$4$$ $-$ $$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$$
390.2.a.d $1$ $3.114$ $$\Q$$ None $$-1$$ $$1$$ $$1$$ $$2$$ $-$ $$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$$
390.2.a.e $1$ $3.114$ $$\Q$$ None $$1$$ $$-1$$ $$-1$$ $$2$$ $-$ $$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$$
390.2.a.f $1$ $3.114$ $$\Q$$ None $$1$$ $$-1$$ $$1$$ $$0$$ $-$ $$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$$
390.2.a.g $1$ $3.114$ $$\Q$$ None $$1$$ $$1$$ $$-1$$ $$2$$ $-$ $$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$$
390.2.a.h $2$ $3.114$ $$\Q(\sqrt{2})$$ None $$2$$ $$2$$ $$2$$ $$0$$ $-$ $$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots$$
390.2.b.a $2$ $3.114$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+iq^{8}+\cdots$$
390.2.b.b $2$ $3.114$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+iq^{8}+\cdots$$
390.2.b.c $4$ $3.114$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$$
390.2.b.d $4$ $3.114$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$$
390.2.e.a $2$ $3.114$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}+(-2-i)q^{5}+\cdots$$
390.2.e.b $2$ $3.114$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}-q^{6}+\cdots$$
390.2.e.c $2$ $3.114$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+(2+i)q^{5}+q^{6}+\cdots$$
390.2.e.d $2$ $3.114$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+(2-i)q^{5}+q^{6}+\cdots$$
390.2.e.e $4$ $3.114$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{2}q^{5}-q^{6}+\cdots$$
390.2.f.a $6$ $3.114$ 6.0.350464.1 None $$-6$$ $$0$$ $$-2$$ $$4$$ $$q-q^{2}-\beta _{4}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$$
390.2.f.b $6$ $3.114$ 6.0.350464.1 None $$6$$ $$0$$ $$2$$ $$-4$$ $$q+q^{2}+\beta _{4}q^{3}+q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots$$
390.2.i.a $2$ $3.114$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$-2$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
390.2.i.b $2$ $3.114$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$2$$ $$3$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
390.2.i.c $2$ $3.114$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-2$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
390.2.i.d $2$ $3.114$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-2$$ $$5$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
390.2.i.e $2$ $3.114$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$-2$$ $$-3$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
390.2.i.f $2$ $3.114$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$2$$ $$2$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
390.2.i.g $4$ $3.114$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$-2$$ $$-2$$ $$4$$ $$-3$$ $$q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$$
390.2.j.a $12$ $3.114$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$-12$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-\beta _{2}q^{3}+q^{4}+(\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$$
390.2.j.b $16$ $3.114$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$16$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+\beta _{8}q^{3}+q^{4}+\beta _{14}q^{5}+\beta _{8}q^{6}+\cdots$$
390.2.l.a $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.l.b $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}+(1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.l.c $20$ $3.114$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{9}q^{2}+\beta _{1}q^{3}-\beta _{11}q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots$$
390.2.l.d $20$ $3.114$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$4$$ $$0$$ $$-4$$ $$q+\beta _{4}q^{2}+\beta _{12}q^{3}+\beta _{11}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots$$
390.2.n.a $56$ $3.114$ None $$0$$ $$0$$ $$0$$ $$0$$
390.2.p.a $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$12$$ $$q+\zeta_{8}q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.b $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$-12$$ $$q+\zeta_{8}q^{2}+(-1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.c $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}+(-1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.d $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+(1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.e $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.f $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.g $8$ $3.114$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}-\beta _{6}q^{3}-\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots$$
390.2.s.a $8$ $3.114$ 8.0.40960000.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$$
390.2.s.b $24$ $3.114$ None $$0$$ $$-8$$ $$0$$ $$0$$
390.2.s.c $24$ $3.114$ None $$0$$ $$4$$ $$0$$ $$0$$
390.2.t.a $12$ $3.114$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\beta _{4}q^{2}-\beta _{7}q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$$
390.2.t.b $16$ $3.114$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+\beta _{8}q^{3}-q^{4}-\beta _{10}q^{5}+\beta _{5}q^{6}+\cdots$$
390.2.x.a $12$ $3.114$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-6$$ $$0$$ $$-2$$ $$-2$$ $$q+(-1-\beta _{6})q^{2}+\beta _{4}q^{3}+\beta _{6}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$$
390.2.x.b $12$ $3.114$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$6$$ $$0$$ $$2$$ $$2$$ $$q+(1+\beta _{6})q^{2}-\beta _{4}q^{3}+\beta _{6}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$$
390.2.y.a $4$ $3.114$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
390.2.y.b $4$ $3.114$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$-6$$ $$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
390.2.y.c $4$ $3.114$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$6$$ $$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}+\cdots)q^{5}+\cdots$$