## Results (1-50 of 323 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
624.1.l.a $1$ $0.311$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-39})$$ $$\Q(\sqrt{13})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q+q^{3}+q^{9}-q^{13}-q^{25}+q^{27}-q^{39}+\cdots$$
624.1.bd.a $2$ $0.311$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+(-1-i)q^{7}-q^{9}-iq^{13}+\cdots$$
624.1.bd.b $2$ $0.311$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+(1+i)q^{7}-q^{9}-iq^{13}+(-1+\cdots)q^{19}+\cdots$$
624.1.bi.a $8$ $0.311$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$$
624.1.bs.a $2$ $0.311$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-1$$ $$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$$
624.1.cb.a $2$ $0.311$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$3$$ $$q-\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$$
624.1.cp.a $4$ $0.311$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\zeta_{12}q^{3}+(-\zeta_{12}^{3}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
624.1.cp.b $4$ $0.311$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-\zeta_{12}q^{3}+(\zeta_{12}^{3}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
624.2.a.a $1$ $4.983$ $$\Q$$ None None $$0$$ $$-1$$ $$-4$$ $$4$$ $+$ $$q-q^{3}-4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots$$
624.2.a.b $1$ $4.983$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$-2$$ $+$ $$q-q^{3}-2q^{7}+q^{9}+q^{13}-6q^{17}+\cdots$$
624.2.a.c $1$ $4.983$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$0$$ $+$ $$q-q^{3}+q^{9}-6q^{11}-q^{13}+2q^{17}+\cdots$$
624.2.a.d $1$ $4.983$ $$\Q$$ None None $$0$$ $$-1$$ $$2$$ $$0$$ $-$ $$q-q^{3}+2q^{5}+q^{9}+q^{13}-2q^{15}+\cdots$$
624.2.a.e $1$ $4.983$ $$\Q$$ None None $$0$$ $$1$$ $$-4$$ $$2$$ $-$ $$q+q^{3}-4q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$$
624.2.a.f $1$ $4.983$ $$\Q$$ None None $$0$$ $$1$$ $$-2$$ $$-4$$ $+$ $$q+q^{3}-2q^{5}-4q^{7}+q^{9}+q^{13}-2q^{15}+\cdots$$
624.2.a.g $1$ $4.983$ $$\Q$$ None None $$0$$ $$1$$ $$0$$ $$4$$ $-$ $$q+q^{3}+4q^{7}+q^{9}+2q^{11}-q^{13}+\cdots$$
624.2.a.h $1$ $4.983$ $$\Q$$ None None $$0$$ $$1$$ $$2$$ $$-4$$ $-$ $$q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$$
624.2.a.i $1$ $4.983$ $$\Q$$ None None $$0$$ $$1$$ $$2$$ $$4$$ $-$ $$q+q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$$
624.2.a.j $1$ $4.983$ $$\Q$$ None None $$0$$ $$1$$ $$4$$ $$0$$ $-$ $$q+q^{3}+4q^{5}+q^{9}+2q^{11}-q^{13}+\cdots$$
624.2.a.k $2$ $4.983$ $$\Q(\sqrt{2})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $-$ $$q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots$$
624.2.c.a $2$ $4.983$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{5}+iq^{7}+q^{9}+(-3-i)q^{13}+\cdots$$
624.2.c.b $2$ $4.983$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots$$
624.2.c.c $2$ $4.983$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+2iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots$$
624.2.c.d $2$ $4.983$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{5}-2iq^{7}+q^{9}+3iq^{11}+\cdots$$
624.2.c.e $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots$$
624.2.c.f $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots$$
624.2.c.g $2$ $4.983$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{7}+q^{9}+iq^{11}+(3-i)q^{13}+\cdots$$
624.2.d.a $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$0$$ $$0$$ $$q+(-1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots$$
624.2.d.b $2$ $4.983$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-1+\beta )q^{3}-\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots$$
624.2.d.c $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots$$
624.2.d.d $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots$$
624.2.d.e $2$ $4.983$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1+2\beta )q^{9}+\cdots$$
624.2.d.f $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$0$$ $$0$$ $$q+(1+\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$$
624.2.d.g $4$ $4.983$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$-1$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$
624.2.d.h $4$ $4.983$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+3q^{9}+2\beta _{2}q^{11}+\cdots$$
624.2.d.i $4$ $4.983$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$1$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
624.2.n.a $2$ $4.983$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\zeta_{6}q^{3}-4q^{7}-3q^{9}+(1+2\zeta_{6})q^{13}+\cdots$$
624.2.n.b $2$ $4.983$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\zeta_{6}q^{3}+4q^{7}-3q^{9}+(1-2\zeta_{6})q^{13}+\cdots$$
624.2.n.c $4$ $4.983$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1+\beta _{1})q^{3}+\beta _{2}q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots$$
624.2.n.d $4$ $4.983$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots$$
624.2.n.e $8$ $4.983$ 8.0.170772624.1 None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\beta _{4}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+(\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots$$
624.2.n.f $8$ $4.983$ 8.0.170772624.1 None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}+(\beta _{3}+\beta _{5})q^{5}+(\beta _{3}+\beta _{5})q^{7}+\cdots$$
624.2.q.a $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-4$$ $$1$$ $$q+(-1+\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$$
624.2.q.b $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-2$$ $$-2$$ $$q+(-1+\zeta_{6})q^{3}-q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$$
624.2.q.c $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-2$$ $$2$$ $$q+(-1+\zeta_{6})q^{3}-q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$$
624.2.q.d $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$4$$ $$1$$ $$q+(-1+\zeta_{6})q^{3}+2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$$
624.2.q.e $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$6$$ $$-4$$ $$q+(-1+\zeta_{6})q^{3}+3q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$$
624.2.q.f $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$6$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+3q^{5}-\zeta_{6}q^{9}+(3+\zeta_{6})q^{13}+\cdots$$
624.2.q.g $2$ $4.983$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$6$$ $$2$$ $$q+(1-\zeta_{6})q^{3}+3q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$$
624.2.q.h $4$ $4.983$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None None $$0$$ $$2$$ $$-6$$ $$-3$$ $$q+(1-\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$$
624.2.q.i $4$ $4.983$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None None $$0$$ $$2$$ $$-4$$ $$2$$ $$q+(1-\beta _{1})q^{3}-q^{5}+(\beta _{1}+\beta _{2})q^{7}-\beta _{1}q^{9}+\cdots$$