## Results (1-50 of 155 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
507.1.c.a $1$ $0.253$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-39})$$ $$\Q(\sqrt{13})$$ $$0$$ $$-1$$ $$0$$ $$0$$ $$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{25}+\cdots$$
507.1.h.a $2$ $0.253$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-39})$$ $$\Q(\sqrt{13})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+q^{12}+\cdots$$
507.1.i.a $2$ $0.253$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-39})$$ $$\Q(\sqrt{13})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}-q^{12}+\cdots$$
507.1.n.a $12$ $0.253$ $$\Q(\zeta_{26})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$0$$ $$q+\zeta_{26}^{7}q^{3}-\zeta_{26}^{2}q^{4}+(\zeta_{26}^{9}+\zeta_{26}^{10}+\cdots)q^{7}+\cdots$$
507.1.o.a $12$ $0.253$ $$\Q(\zeta_{26})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-2$$ $$q-\zeta_{26}^{7}q^{3}+\zeta_{26}^{2}q^{4}+(-\zeta_{26}^{9}+\zeta_{26}^{10}+\cdots)q^{7}+\cdots$$
507.2.a.a $1$ $4.048$ $$\Q$$ None None $$-1$$ $$-1$$ $$-2$$ $$4$$ $+$ $$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+4q^{7}+\cdots$$
507.2.a.b $1$ $4.048$ $$\Q$$ None None $$-1$$ $$-1$$ $$1$$ $$-2$$ $+$ $$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$$
507.2.a.c $1$ $4.048$ $$\Q$$ None None $$1$$ $$-1$$ $$-1$$ $$2$$ $+$ $$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$$
507.2.a.d $2$ $4.048$ $$\Q(\sqrt{17})$$ None None $$-1$$ $$2$$ $$3$$ $$3$$ $-$ $$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(2-\beta )q^{5}+\cdots$$
507.2.a.e $2$ $4.048$ $$\Q(\sqrt{3})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $-$ $$q-q^{3}-2q^{4}+2\beta q^{5}+\beta q^{7}+q^{9}+\cdots$$
507.2.a.f $2$ $4.048$ $$\Q(\sqrt{3})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $-$ $$q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+2\beta q^{7}+\cdots$$
507.2.a.g $2$ $4.048$ $$\Q(\sqrt{17})$$ None None $$1$$ $$2$$ $$-3$$ $$-3$$ $-$ $$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-2+\beta )q^{5}+\cdots$$
507.2.a.h $2$ $4.048$ $$\Q(\sqrt{2})$$ None None $$2$$ $$2$$ $$0$$ $$0$$ $-$ $$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-2\beta q^{5}+\cdots$$
507.2.a.i $3$ $4.048$ $$\Q(\zeta_{14})^+$$ None None $$-3$$ $$-3$$ $$-6$$ $$-2$$ $+$ $$q+(-1+\beta _{1}+\beta _{2})q^{2}-q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$$
507.2.a.j $3$ $4.048$ $$\Q(\zeta_{14})^+$$ None None $$-1$$ $$3$$ $$-4$$ $$-10$$ $+$ $$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$$
507.2.a.k $3$ $4.048$ $$\Q(\zeta_{14})^+$$ None None $$1$$ $$3$$ $$4$$ $$10$$ $-$ $$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots$$
507.2.a.l $3$ $4.048$ $$\Q(\zeta_{14})^+$$ None None $$3$$ $$-3$$ $$6$$ $$2$$ $-$ $$q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(4-\beta _{1})q^{4}+\cdots$$
507.2.b.a $2$ $4.048$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots$$
507.2.b.b $2$ $4.048$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}+q^{4}-iq^{5}-iq^{6}-2iq^{7}+\cdots$$
507.2.b.c $2$ $4.048$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+2q^{4}+2\zeta_{6}q^{5}-\zeta_{6}q^{7}+q^{9}+\cdots$$
507.2.b.d $4$ $4.048$ $$\Q(i, \sqrt{17})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
507.2.b.e $4$ $4.048$ $$\Q(\zeta_{8})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+q^{3}+(-1-\zeta_{8}^{3})q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$$
507.2.b.f $6$ $4.048$ 6.0.153664.1 None None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{3}+\beta _{5})q^{2}-q^{3}+(-3-\beta _{2}+\cdots)q^{4}+\cdots$$
507.2.b.g $6$ $4.048$ 6.0.153664.1 None None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots$$
507.2.e.a $2$ $4.048$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$1$$ $$4$$ $$4$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
507.2.e.b $2$ $4.048$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$1$$ $$-4$$ $$-4$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
507.2.e.c $2$ $4.048$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$1$$ $$2$$ $$2$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
507.2.e.d $4$ $4.048$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$-2$$ $$-2$$ $$0$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\cdots$$
507.2.e.e $4$ $4.048$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots$$
507.2.e.f $4$ $4.048$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+(2-2\zeta_{12})q^{4}-2\zeta_{12}^{3}q^{5}+\cdots$$
507.2.e.g $4$ $4.048$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None None $$1$$ $$-2$$ $$6$$ $$-3$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$$
507.2.e.h $4$ $4.048$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$2$$ $$-2$$ $$0$$ $$0$$ $$q+(1+\beta _{1}+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\cdots$$
507.2.e.i $6$ $4.048$ 6.0.64827.1 None None $$-3$$ $$3$$ $$12$$ $$-2$$ $$q+(-2+2\beta _{1}+\beta _{4}+2\beta _{5})q^{2}+(1-\beta _{5})q^{3}+\cdots$$
507.2.e.j $6$ $4.048$ 6.0.64827.1 None None $$-1$$ $$-3$$ $$8$$ $$-10$$ $$q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
507.2.e.k $6$ $4.048$ 6.0.64827.1 None None $$1$$ $$-3$$ $$-8$$ $$10$$ $$q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
507.2.e.l $6$ $4.048$ 6.0.64827.1 None None $$3$$ $$3$$ $$-12$$ $$2$$ $$q+(2-2\beta _{1}-\beta _{4}-2\beta _{5})q^{2}+(1-\beta _{5})q^{3}+\cdots$$
507.2.f.a $4$ $4.048$ $$\Q(\zeta_{8})$$ None None $$0$$ $$-4$$ $$0$$ $$-4$$ $$q+\zeta_{8}q^{2}+(-1-\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$$
507.2.f.b $4$ $4.048$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots$$
507.2.f.c $4$ $4.048$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots$$
507.2.f.d $8$ $4.048$ 8.0.56070144.2 $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-2\beta _{2}-\beta _{5})q^{4}+\cdots$$
507.2.f.e $8$ $4.048$ 8.0.56070144.2 None None $$0$$ $$4$$ $$0$$ $$-8$$ $$q+(\beta _{1}+\beta _{2}+\beta _{4})q^{2}+(\beta _{4}+\beta _{5})q^{3}+\cdots$$
507.2.f.f $8$ $4.048$ 8.0.56070144.2 None None $$0$$ $$4$$ $$0$$ $$8$$ $$q+(\beta _{1}+\beta _{2}+\beta _{4})q^{2}+(1-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots$$
507.2.f.g $48$ $4.048$ None None $$0$$ $$0$$ $$0$$ $$0$$
507.2.j.a $2$ $4.048$ $$\Q(\sqrt{-3})$$ None None $$-3$$ $$1$$ $$0$$ $$-6$$ $$q+(-1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
507.2.j.b $2$ $4.048$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$0$$ $$3$$ $$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(2-4\zeta_{6})q^{5}+\cdots$$
507.2.j.c $2$ $4.048$ $$\Q(\sqrt{-3})$$ None None $$3$$ $$1$$ $$0$$ $$6$$ $$q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
507.2.j.d $4$ $4.048$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
507.2.j.e $4$ $4.048$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
507.2.j.f $8$ $4.048$ $$\Q(\zeta_{24})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+(1-\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{4}+\cdots$$
507.2.j.g $8$ $4.048$ 8.0.1731891456.1 None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(2+3\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$$