## Results (1-50 of 212 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
640.1.e.a $1$ $0.319$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-10})$$ $$\Q(\sqrt{10})$$ $$0$$ $$0$$ $$-1$$ $$0$$ $$q-q^{5}+q^{9}+2q^{13}+q^{25}-2q^{37}+\cdots$$
640.1.e.b $1$ $0.319$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-10})$$ $$\Q(\sqrt{10})$$ $$0$$ $$0$$ $$1$$ $$0$$ $$q+q^{5}+q^{9}-2q^{13}+q^{25}+2q^{37}+\cdots$$
640.1.e.c $4$ $0.319$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$$
640.1.m.a $2$ $0.319$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{5}-iq^{9}+(-1-i)q^{13}+(1+i+\cdots)q^{17}+\cdots$$
640.1.m.b $2$ $0.319$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}-iq^{9}+(1+i)q^{13}+(1+i+\cdots)q^{17}+\cdots$$
640.2.a.a $1$ $5.110$ $$\Q$$ None None $$0$$ $$-2$$ $$-1$$ $$0$$ $-$ $$q-2q^{3}-q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots$$
640.2.a.b $1$ $5.110$ $$\Q$$ None None $$0$$ $$-2$$ $$1$$ $$0$$ $+$ $$q-2q^{3}+q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots$$
640.2.a.c $1$ $5.110$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-2$$ $+$ $$q-q^{5}-2q^{7}-3q^{9}+6q^{11}-2q^{13}+\cdots$$
640.2.a.d $1$ $5.110$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$2$$ $+$ $$q-q^{5}+2q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots$$
640.2.a.e $1$ $5.110$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-2$$ $+$ $$q+q^{5}-2q^{7}-3q^{9}-6q^{11}+2q^{13}+\cdots$$
640.2.a.f $1$ $5.110$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$2$$ $-$ $$q+q^{5}+2q^{7}-3q^{9}+6q^{11}+2q^{13}+\cdots$$
640.2.a.g $1$ $5.110$ $$\Q$$ None None $$0$$ $$2$$ $$-1$$ $$0$$ $-$ $$q+2q^{3}-q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots$$
640.2.a.h $1$ $5.110$ $$\Q$$ None None $$0$$ $$2$$ $$1$$ $$0$$ $-$ $$q+2q^{3}+q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots$$
640.2.a.i $2$ $5.110$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-2$$ $$-2$$ $$-2$$ $+$ $$q+(-1-\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+\cdots$$
640.2.a.j $2$ $5.110$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-2$$ $$2$$ $$2$$ $-$ $$q+(-1-\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots$$
640.2.a.k $2$ $5.110$ $$\Q(\sqrt{5})$$ None None $$0$$ $$2$$ $$-2$$ $$2$$ $-$ $$q+(1+\beta )q^{3}-q^{5}+(1-\beta )q^{7}+(3+2\beta )q^{9}+\cdots$$
640.2.a.l $2$ $5.110$ $$\Q(\sqrt{5})$$ None None $$0$$ $$2$$ $$2$$ $$-2$$ $-$ $$q+(1+\beta )q^{3}+q^{5}+(-1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots$$
640.2.c.a $6$ $5.110$ 6.0.350464.1 None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{2}+\beta _{5})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$$
640.2.c.b $6$ $5.110$ 6.0.350464.1 None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$$
640.2.c.c $6$ $5.110$ 6.0.350464.1 None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$
640.2.c.d $6$ $5.110$ 6.0.350464.1 None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$
640.2.d.a $4$ $5.110$ $$\Q(i, \sqrt{10})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}-7q^{9}-6\beta _{1}q^{13}+\cdots$$
640.2.d.b $4$ $5.110$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}+3\zeta_{8}^{3}q^{7}+q^{9}+\cdots$$
640.2.d.c $4$ $5.110$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+q^{9}+\cdots$$
640.2.d.d $4$ $5.110$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}-3\zeta_{8}^{3}q^{7}+q^{9}+\cdots$$
640.2.f.a $2$ $5.110$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+i)q^{5}-3q^{9}-6q^{13}-4iq^{17}+\cdots$$
640.2.f.b $2$ $5.110$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+i)q^{5}-3q^{9}+6q^{13}+4iq^{17}+\cdots$$
640.2.f.c $4$ $5.110$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\beta _{3}q^{3}+(-2-\beta _{1})q^{5}+\beta _{2}q^{7}+3q^{9}+\cdots$$
640.2.f.d $4$ $5.110$ $$\Q(\sqrt{-2}, \sqrt{5})$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}-\beta _{1}q^{7}-3q^{9}-\beta _{2}q^{11}+\cdots$$
640.2.f.e $4$ $5.110$ $$\Q(\sqrt{2}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-q^{9}+\beta _{2}q^{15}+\cdots$$
640.2.f.f $4$ $5.110$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}-\beta _{2}q^{5}-3\beta _{1}q^{7}+7q^{9}+\cdots$$
640.2.f.g $4$ $5.110$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\beta _{3}q^{3}+(2+\beta _{1})q^{5}+\beta _{2}q^{7}+3q^{9}+\cdots$$
640.2.j.a $2$ $5.110$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$-6$$ $$q-2iq^{3}+(-1-2i)q^{5}+(-3-3i)q^{7}+\cdots$$
640.2.j.b $2$ $5.110$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$6$$ $$q+2iq^{3}+(-1-2i)q^{5}+(3+3i)q^{7}+\cdots$$
640.2.j.c $18$ $5.110$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$0$$ $$0$$ $$4$$ $$-2$$ $$q-\beta _{12}q^{3}-\beta _{6}q^{5}-\beta _{11}q^{7}+(-1+\cdots)q^{9}+\cdots$$
640.2.j.d $18$ $5.110$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$0$$ $$0$$ $$4$$ $$2$$ $$q-\beta _{12}q^{3}+\beta _{4}q^{5}-\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots$$
640.2.l.a $16$ $5.110$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{5}-\beta _{7})q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{4}-\beta _{7}+\cdots)q^{7}+\cdots$$
640.2.l.b $16$ $5.110$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{5}+\beta _{7})q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$$
640.2.n.a $12$ $5.110$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{2}q^{3}+\beta _{9}q^{5}+(-1-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots$$
640.2.n.b $12$ $5.110$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{3}q^{3}-\beta _{8}q^{5}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$$
640.2.n.c $12$ $5.110$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\beta _{3}q^{3}+\beta _{8}q^{5}+(1+\beta _{2}-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots$$
640.2.n.d $12$ $5.110$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{2}q^{3}-\beta _{9}q^{5}+(1+\beta _{3}+\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots$$
640.2.o.a $2$ $5.110$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-4$$ $$-4$$ $$-4$$ $$q+(-2+2i)q^{3}+(-2+i)q^{5}+(-2+\cdots)q^{7}+\cdots$$
640.2.o.b $2$ $5.110$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-4$$ $$4$$ $$4$$ $$q+(-2+2i)q^{3}+(2-i)q^{5}+(2-2i)q^{7}+\cdots$$
640.2.o.c $2$ $5.110$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}+3iq^{9}+(-5-5i)q^{13}+\cdots$$
640.2.o.d $2$ $5.110$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2-i)q^{5}+3iq^{9}+(1+i)q^{13}+\cdots$$
640.2.o.e $2$ $5.110$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}+3iq^{9}+(-1-i)q^{13}+\cdots$$
640.2.o.f $2$ $5.110$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-i)q^{5}+3iq^{9}+(5+5i)q^{13}+\cdots$$
640.2.o.g $2$ $5.110$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$4$$ $$-4$$ $$4$$ $$q+(2-2i)q^{3}+(-2+i)q^{5}+(2-2i)q^{7}+\cdots$$
640.2.o.h $2$ $5.110$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$4$$ $$4$$ $$-4$$ $$q+(2-2i)q^{3}+(2-i)q^{5}+(-2+2i)q^{7}+\cdots$$