## Results (1-50 of 200 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1680.1.bb.a $1$ $0.838$ $$\Q$$ $$\Q(\sqrt{-5})$$, $$\Q(\sqrt{-105})$$ $$\Q(\sqrt{21})$$ $$0$$ $$-1$$ $$-1$$ $$-1$$ $-$ $$q-q^{3}-q^{5}-q^{7}+q^{9}+q^{15}+q^{21}+\cdots$$
1680.1.bb.b $1$ $0.838$ $$\Q$$ $$\Q(\sqrt{-5})$$, $$\Q(\sqrt{-105})$$ $$\Q(\sqrt{21})$$ $$0$$ $$-1$$ $$1$$ $$1$$ $-$ $$q-q^{3}+q^{5}+q^{7}+q^{9}-q^{15}-q^{21}+\cdots$$
1680.1.bb.c $1$ $0.838$ $$\Q$$ $$\Q(\sqrt{-5})$$, $$\Q(\sqrt{-105})$$ $$\Q(\sqrt{21})$$ $$0$$ $$1$$ $$-1$$ $$1$$ $-$ $$q+q^{3}-q^{5}+q^{7}+q^{9}-q^{15}+q^{21}+\cdots$$
1680.1.bb.d $1$ $0.838$ $$\Q$$ $$\Q(\sqrt{-5})$$, $$\Q(\sqrt{-105})$$ $$\Q(\sqrt{21})$$ $$0$$ $$1$$ $$1$$ $$-1$$ $-$ $$q+q^{3}+q^{5}-q^{7}+q^{9}+q^{15}-q^{21}+\cdots$$
1680.1.bb.e $2$ $0.838$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-35})$$, $$\Q(\sqrt{-21})$$ $$\Q(\sqrt{15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $-$ $$q+iq^{3}-iq^{5}-iq^{7}-q^{9}-q^{11}+\cdots$$
1680.1.bb.f $2$ $0.838$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-35})$$, $$\Q(\sqrt{-21})$$ $$\Q(\sqrt{15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $-$ $$q-iq^{3}-iq^{5}+iq^{7}-q^{9}+q^{11}+\cdots$$
1680.1.bb.g $4$ $0.838$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $-$ $$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$$
1680.1.bb.h $4$ $0.838$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $-$ $$q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
1680.1.dp.a $2$ $0.838$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$-2$$ $$-1$$ $$-1$$ $-$ $$q-q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+q^{9}+\zeta_{6}q^{15}+\cdots$$
1680.1.dp.b $2$ $0.838$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$-1$$ $$1$$ $$-1$$ $-$ $$q-\zeta_{6}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$$
1680.1.dp.c $2$ $0.838$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$1$$ $$1$$ $$1$$ $-$ $$q+\zeta_{6}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$$
1680.1.dp.d $2$ $0.838$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$2$$ $$-1$$ $$1$$ $-$ $$q+q^{3}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{9}-\zeta_{6}q^{15}+\cdots$$
1680.2.a.a $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$-1$$ $-$ $$q-q^{3}-q^{5}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots$$
1680.2.a.b $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$-1$$ $-$ $$q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$$
1680.2.a.c $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$-1$$ $+$ $$q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$$
1680.2.a.d $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$1$$ $-$ $$q-q^{3}-q^{5}+q^{7}+q^{9}+6q^{13}+q^{15}+\cdots$$
1680.2.a.e $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$1$$ $-$ $$q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$$
1680.2.a.f $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$-1$$ $+$ $$q-q^{3}+q^{5}-q^{7}+q^{9}-6q^{13}-q^{15}+\cdots$$
1680.2.a.g $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$-1$$ $+$ $$q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots$$
1680.2.a.h $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$1$$ $+$ $$q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$$
1680.2.a.i $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$1$$ $-$ $$q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots$$
1680.2.a.j $1$ $13.415$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$1$$ $-$ $$q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$$
1680.2.a.k $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$-1$$ $-$ $$q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$$
1680.2.a.l $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$-1$$ $-$ $$q+q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$$
1680.2.a.m $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$1$$ $+$ $$q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$$
1680.2.a.n $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$1$$ $-$ $$q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots$$
1680.2.a.o $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$1$$ $-$ $$q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$$
1680.2.a.p $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$-1$$ $+$ $$q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$$
1680.2.a.q $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$-1$$ $-$ $$q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$$
1680.2.a.r $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$-1$$ $-$ $$q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$$
1680.2.a.s $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$1$$ $-$ $$q+q^{3}+q^{5}+q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$$
1680.2.a.t $1$ $13.415$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$1$$ $-$ $$q+q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$$
1680.2.a.u $2$ $13.415$ $$\Q(\sqrt{2})$$ None None $$0$$ $$-2$$ $$2$$ $$-2$$ $-$ $$q-q^{3}+q^{5}-q^{7}+q^{9}+\beta q^{11}+2q^{13}+\cdots$$
1680.2.a.v $2$ $13.415$ $$\Q(\sqrt{5})$$ None None $$0$$ $$2$$ $$-2$$ $$-2$$ $+$ $$q+q^{3}-q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$$
1680.2.d.a $4$ $13.415$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $-$ $$q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots$$
1680.2.d.b $4$ $13.415$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $-$ $$q+q^{3}-\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots$$
1680.2.d.c $12$ $13.415$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-12$$ $$0$$ $$4$$ $-$ $$q-q^{3}-\beta _{1}q^{5}-\beta _{9}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots$$
1680.2.d.d $12$ $13.415$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$12$$ $$0$$ $$-4$$ $-$ $$q+q^{3}+\beta _{1}q^{5}+\beta _{8}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots$$
1680.2.f.a $2$ $13.415$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$2$$ $$-4$$ $-$ $$q+(-2+\zeta_{6})q^{3}+q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
1680.2.f.b $2$ $13.415$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-2$$ $$-4$$ $-$ $$q+\zeta_{6}q^{3}-q^{5}+(-2-\zeta_{6})q^{7}-3q^{9}+\cdots$$
1680.2.f.c $2$ $13.415$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$2$$ $$-4$$ $-$ $$q-\zeta_{6}q^{3}+q^{5}+(-2+\zeta_{6})q^{7}-3q^{9}+\cdots$$
1680.2.f.d $2$ $13.415$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$-2$$ $$-4$$ $-$ $$q+(2-\zeta_{6})q^{3}-q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$
1680.2.f.e $4$ $13.415$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$-2$$ $$-4$$ $$-6$$ $-$ $$q+(\beta _{1}+\beta _{2})q^{3}-q^{5}+(-1+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$$
1680.2.f.f $4$ $13.415$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$-2$$ $$-4$$ $$6$$ $-$ $$q+(-1-\beta _{1})q^{3}-q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
1680.2.f.g $4$ $13.415$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$-1$$ $$4$$ $$8$$ $-$ $$q-\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$$
1680.2.f.h $4$ $13.415$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$1$$ $$-4$$ $$8$$ $-$ $$q+\beta _{1}q^{3}-q^{5}+(2-\beta _{2})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$$
1680.2.f.i $4$ $13.415$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$2$$ $$4$$ $$-6$$ $-$ $$q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+(-1-2\beta _{2}+\cdots)q^{7}+\cdots$$
1680.2.f.j $4$ $13.415$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$2$$ $$4$$ $$6$$ $-$ $$q+(1+\beta _{1})q^{3}+q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots$$
1680.2.f.k $16$ $13.415$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$-16$$ $$-2$$ $-$ $$q+\beta _{3}q^{3}-q^{5}-\beta _{9}q^{7}+\beta _{7}q^{9}+\beta _{8}q^{11}+\cdots$$
1680.2.f.l $16$ $13.415$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$16$$ $$-2$$ $-$ $$q-\beta _{3}q^{3}+q^{5}-\beta _{4}q^{7}+\beta _{7}q^{9}+\beta _{8}q^{11}+\cdots$$