## Results (1-50 of 350 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
720.1.j.a $1$ $0.359$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$1$$ $$0$$ $$q+q^{5}+q^{25}-2q^{29}+2q^{41}-q^{49}+\cdots$$
720.1.r.a $4$ $0.359$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$$
720.1.bk.a $4$ $0.359$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{5}+(1-\zeta_{8}^{2})q^{13}-\zeta_{8}^{3}q^{17}+\cdots$$
720.1.bu.a $4$ $0.359$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{5}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{7}+\cdots$$
720.2.a.a $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-2$$ $+$ $$q-q^{5}-2q^{7}-2q^{11}+4q^{13}-2q^{17}+\cdots$$
720.2.a.b $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-2$$ $-$ $$q-q^{5}-2q^{7}+6q^{11}-4q^{13}+6q^{17}+\cdots$$
720.2.a.c $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$0$$ $+$ $$q-q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots$$
720.2.a.d $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$0$$ $-$ $$q-q^{5}-4q^{11}+6q^{13}+6q^{17}+4q^{19}+\cdots$$
720.2.a.e $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$4$$ $-$ $$q-q^{5}+4q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots$$
720.2.a.f $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-4$$ $+$ $$q+q^{5}-4q^{7}-6q^{13}+2q^{17}-4q^{19}+\cdots$$
720.2.a.g $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-2$$ $+$ $$q+q^{5}-2q^{7}-6q^{11}-4q^{13}-6q^{17}+\cdots$$
720.2.a.h $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-2$$ $-$ $$q+q^{5}-2q^{7}+2q^{13}+6q^{17}+4q^{19}+\cdots$$
720.2.a.i $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-2$$ $-$ $$q+q^{5}-2q^{7}+2q^{11}+4q^{13}+2q^{17}+\cdots$$
720.2.a.j $1$ $5.749$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$4$$ $-$ $$q+q^{5}+4q^{7}+2q^{13}-6q^{17}+4q^{19}+\cdots$$
720.2.f.a $2$ $5.749$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}+4iq^{7}-4q^{11}-4iq^{13}+\cdots$$
720.2.f.b $2$ $5.749$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}-2iq^{7}+2q^{11}+2iq^{13}+\cdots$$
720.2.f.c $2$ $5.749$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+i)q^{5}-2iq^{7}-4q^{11}-2iq^{17}+\cdots$$
720.2.f.d $2$ $5.749$ $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{5}+2\beta q^{17}+4q^{19}+4\beta q^{23}+\cdots$$
720.2.f.e $2$ $5.749$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+i)q^{5}+iq^{7}-4q^{11}+2iq^{13}+\cdots$$
720.2.f.f $2$ $5.749$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}-2iq^{7}+2q^{11}-6iq^{13}+\cdots$$
720.2.f.g $2$ $5.749$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}-4iq^{7}+4q^{11}+4iq^{13}+\cdots$$
720.2.h.a $8$ $5.749$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{5}+\zeta_{24}^{5}q^{7}+(\zeta_{24}^{2}-\zeta_{24}^{4}+\cdots)q^{11}+\cdots$$
720.2.o.a $4$ $5.749$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{3}q^{5}+2\zeta_{8}q^{13}+(\zeta_{8}^{2}-2\zeta_{8}^{3})q^{17}+\cdots$$
720.2.o.b $8$ $5.749$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}-\zeta_{24}^{2})q^{5}-\zeta_{24}^{6}q^{7}+\zeta_{24}^{3}q^{11}+\cdots$$
720.2.q.a $2$ $5.749$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$-1$$ $$-1$$ $$q+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$$
720.2.q.b $2$ $5.749$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$1$$ $$-1$$ $$q+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$$
720.2.q.c $2$ $5.749$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$-1$$ $$-4$$ $$q+(1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\cdots$$
720.2.q.d $2$ $5.749$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$1$$ $$-3$$ $$q+(2-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots$$
720.2.q.e $2$ $5.749$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$1$$ $$0$$ $$q+(1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-5+\cdots)q^{11}+\cdots$$
720.2.q.f $4$ $5.749$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$-2$$ $$2$$ $$1$$ $$q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$$
720.2.q.g $4$ $5.749$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$-2$$ $$2$$ $$2$$ $$q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$$
720.2.q.h $4$ $5.749$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$2$$ $$4$$ $$q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(2-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots$$
720.2.q.i $6$ $5.749$ 6.0.954288.1 None None $$0$$ $$-1$$ $$-3$$ $$5$$ $$q-\beta _{4}q^{3}+\beta _{3}q^{5}+(2-\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots$$
720.2.q.j $6$ $5.749$ 6.0.954288.1 None None $$0$$ $$1$$ $$-3$$ $$-5$$ $$q+(\beta _{2}-\beta _{5})q^{3}+\beta _{3}q^{5}+(-2-2\beta _{3}+\cdots)q^{7}+\cdots$$
720.2.q.k $6$ $5.749$ 6.0.954288.1 None None $$0$$ $$1$$ $$3$$ $$3$$ $$q-\beta _{4}q^{3}+(1+\beta _{2})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
720.2.q.l $8$ $5.749$ 8.0.856615824.2 None None $$0$$ $$0$$ $$-4$$ $$-1$$ $$q+\beta _{4}q^{3}-\beta _{1}q^{5}+(\beta _{2}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$$
720.2.t.a $4$ $5.749$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+\zeta_{8}q^{5}+\cdots$$
720.2.t.b $8$ $5.749$ 8.0.18939904.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}-\beta _{5})q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots$$
720.2.t.c $16$ $5.749$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{9}q^{2}+(\beta _{1}-\beta _{5}-\beta _{14})q^{4}-\beta _{4}q^{5}+\cdots$$
720.2.t.d $20$ $5.749$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{3}q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots$$
720.2.t.e $32$ $5.749$ None None $$0$$ $$0$$ $$0$$ $$0$$
720.2.u.a $96$ $5.749$ None None $$0$$ $$0$$ $$0$$ $$0$$
720.2.w.a $4$ $5.749$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-2-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$$
720.2.w.b $4$ $5.749$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$$
720.2.w.c $4$ $5.749$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-4\zeta_{8}-4\zeta_{8}^{3})q^{11}+\cdots$$
720.2.w.d $4$ $5.749$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(2+2\zeta_{8}^{2})q^{7}+(2\zeta_{8}+\cdots)q^{11}+\cdots$$
720.2.w.e $8$ $5.749$ 8.0.40960000.1 None None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{7}q^{5}+(1+\beta _{2}+\beta _{5})q^{7}+(\beta _{1}+\beta _{6}+\cdots)q^{11}+\cdots$$
720.2.x.a $2$ $5.749$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2-i)q^{5}+(-5+5i)q^{13}+(5+\cdots)q^{17}+\cdots$$
720.2.x.b $2$ $5.749$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-2i)q^{5}+(1-i)q^{13}+(-5+\cdots)q^{17}+\cdots$$
720.2.x.c $2$ $5.749$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+2i)q^{5}+(1-i)q^{13}+(5+5i)q^{17}+\cdots$$