## Results (1-50 of 206 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
585.1.o.a $8$ $0.292$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{2}+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\cdots)q^{4}+\cdots$$
585.2.a.a $1$ $4.671$ $$\Q$$ None None $$-2$$ $$0$$ $$-1$$ $$-3$$ $+$ $$q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots$$
585.2.a.b $1$ $4.671$ $$\Q$$ None None $$-2$$ $$0$$ $$-1$$ $$3$$ $-$ $$q-2q^{2}+2q^{4}-q^{5}+3q^{7}+2q^{10}+\cdots$$
585.2.a.c $1$ $4.671$ $$\Q$$ None None $$-2$$ $$0$$ $$1$$ $$-1$$ $+$ $$q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots$$
585.2.a.d $1$ $4.671$ $$\Q$$ None None $$-1$$ $$0$$ $$-1$$ $$2$$ $+$ $$q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots$$
585.2.a.e $1$ $4.671$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-1$$ $-$ $$q-2q^{4}-q^{5}-q^{7}+3q^{11}+q^{13}+\cdots$$
585.2.a.f $1$ $4.671$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-1$$ $+$ $$q-2q^{4}+q^{5}-q^{7}-3q^{11}+q^{13}+\cdots$$
585.2.a.g $1$ $4.671$ $$\Q$$ None None $$1$$ $$0$$ $$-1$$ $$0$$ $+$ $$q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-4q^{11}+\cdots$$
585.2.a.h $1$ $4.671$ $$\Q$$ None None $$1$$ $$0$$ $$1$$ $$-4$$ $+$ $$q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots$$
585.2.a.i $1$ $4.671$ $$\Q$$ None None $$1$$ $$0$$ $$1$$ $$2$$ $-$ $$q+q^{2}-q^{4}+q^{5}+2q^{7}-3q^{8}+q^{10}+\cdots$$
585.2.a.j $2$ $4.671$ $$\Q(\sqrt{17})$$ None None $$-1$$ $$0$$ $$-2$$ $$-5$$ $+$ $$q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(-3+\beta )q^{7}+\cdots$$
585.2.a.k $2$ $4.671$ $$\Q(\sqrt{3})$$ None None $$0$$ $$0$$ $$2$$ $$4$$ $-$ $$q+\beta q^{2}+q^{4}+q^{5}+2q^{7}-\beta q^{8}+\beta q^{10}+\cdots$$
585.2.a.l $2$ $4.671$ $$\Q(\sqrt{17})$$ None None $$1$$ $$0$$ $$2$$ $$-5$$ $-$ $$q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(-3+\beta )q^{7}+\cdots$$
585.2.a.m $2$ $4.671$ $$\Q(\sqrt{2})$$ None None $$2$$ $$0$$ $$-2$$ $$4$$ $-$ $$q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(2+2\beta )q^{7}+\cdots$$
585.2.a.n $3$ $4.671$ 3.3.316.1 None None $$0$$ $$0$$ $$3$$ $$1$$ $-$ $$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+q^{5}-\beta _{2}q^{7}+\cdots$$
585.2.b.a $2$ $4.671$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+iq^{5}+2iq^{7}+3iq^{8}+\cdots$$
585.2.b.b $2$ $4.671$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+iq^{5}+4iq^{7}+3iq^{8}+\cdots$$
585.2.b.c $2$ $4.671$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+iq^{5}-4iq^{7}+3iq^{8}+\cdots$$
585.2.b.d $2$ $4.671$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+iq^{5}-3iq^{7}-3iq^{11}+(2+\cdots)q^{13}+\cdots$$
585.2.b.e $4$ $4.671$ $$\Q(i, \sqrt{17})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
585.2.b.f $4$ $4.671$ $$\Q(i, \sqrt{13})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\beta _{1}q^{2}-2q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots$$
585.2.b.g $6$ $4.671$ 6.0.5089536.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$
585.2.c.a $2$ $4.671$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+2q^{4}+(1+2i)q^{5}-iq^{7}+q^{11}+\cdots$$
585.2.c.b $6$ $4.671$ 6.0.350464.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2})q^{4}+\cdots$$
585.2.c.c $10$ $4.671$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{7})q^{4}+\cdots$$
585.2.c.d $12$ $4.671$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{8}q^{2}+(-1-\beta _{9})q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots$$
585.2.h.a $2$ $4.671$ $$\Q(\sqrt{-1})$$ None None $$-4$$ $$0$$ $$-4$$ $$-6$$ $$q-2q^{2}+2q^{4}+(-2+i)q^{5}-3q^{7}+\cdots$$
585.2.h.b $2$ $4.671$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$0$$ $$-2$$ $$0$$ $$q-q^{2}-q^{4}+(-1-i)q^{5}+3q^{8}+(1+\cdots)q^{10}+\cdots$$
585.2.h.c $2$ $4.671$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$0$$ $$2$$ $$0$$ $$q+q^{2}-q^{4}+(1+i)q^{5}-3q^{8}+(1+i)q^{10}+\cdots$$
585.2.h.d $2$ $4.671$ $$\Q(\sqrt{-1})$$ None None $$4$$ $$0$$ $$4$$ $$6$$ $$q+2q^{2}+2q^{4}+(2-i)q^{5}+3q^{7}+(4+\cdots)q^{10}+\cdots$$
585.2.h.e $4$ $4.671$ $$\Q(\sqrt{-5}, \sqrt{13})$$ $$\Q(\sqrt{-195})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2q^{4}-\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{11}+\cdots$$
585.2.h.f $8$ $4.671$ 8.0.$$\cdots$$.21 $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(2-\beta _{2})q^{4}+\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots$$
585.2.h.g $12$ $4.671$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{10}q^{2}+(1+\beta _{5}-\beta _{11})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
585.2.i.a $2$ $4.671$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$-1$$ $$4$$ $$q+(2-\zeta_{6})q^{3}+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$$
585.2.i.b $2$ $4.671$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$0$$ $$1$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
585.2.i.c $2$ $4.671$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$3$$ $$1$$ $$1$$ $$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
585.2.i.d $2$ $4.671$ $$\Q(\sqrt{-3})$$ None None $$2$$ $$-3$$ $$1$$ $$0$$ $$q+(2-2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$$
585.2.i.e $16$ $4.671$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-3$$ $$1$$ $$8$$ $$11$$ $$q-\beta _{6}q^{2}+(-\beta _{7}+\beta _{14})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$$
585.2.i.f $16$ $4.671$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$1$$ $$-2$$ $$-8$$ $$6$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots$$
585.2.i.g $26$ $4.671$ None None $$1$$ $$1$$ $$-13$$ $$-10$$
585.2.i.h $30$ $4.671$ None None $$1$$ $$1$$ $$15$$ $$-10$$
585.2.j.a $2$ $4.671$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$2$$ $$1$$ $$q+2\zeta_{6}q^{4}+q^{5}+\zeta_{6}q^{7}+(6-6\zeta_{6})q^{11}+\cdots$$
585.2.j.b $2$ $4.671$ $$\Q(\sqrt{-3})$$ None None $$2$$ $$0$$ $$2$$ $$-5$$ $$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+q^{5}-5\zeta_{6}q^{7}+\cdots$$
585.2.j.c $4$ $4.671$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$0$$ $$-4$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots$$
585.2.j.d $4$ $4.671$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None None $$-1$$ $$0$$ $$4$$ $$2$$ $$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$$
585.2.j.e $4$ $4.671$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$1$$ $$0$$ $$-4$$ $$-4$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}-q^{5}+\cdots$$
585.2.j.f $6$ $4.671$ 6.0.1714608.1 None None $$0$$ $$0$$ $$-6$$ $$-3$$ $$q+(\beta _{3}-\beta _{5})q^{2}+(-2\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$
585.2.j.g $6$ $4.671$ 6.0.591408.1 None None $$0$$ $$0$$ $$6$$ $$5$$ $$q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$$
585.2.j.h $10$ $4.671$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$-2$$ $$0$$ $$10$$ $$-1$$ $$q+(\beta _{1}+\beta _{3})q^{2}+(-1+\beta _{4}-\beta _{8})q^{4}+\cdots$$
585.2.j.i $10$ $4.671$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$2$$ $$0$$ $$-10$$ $$-1$$ $$q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$$