## Results (1-50 of 315 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.1.bm.a $4$ $0.120$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$$
240.2.a.a $1$ $1.916$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$-4$$ $+$ $$q-q^{3}-q^{5}-4q^{7}+q^{9}-6q^{13}+q^{15}+\cdots$$
240.2.a.b $1$ $1.916$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$4$$ $-$ $$q-q^{3}-q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$$
240.2.a.c $1$ $1.916$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$0$$ $-$ $$q-q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots$$
240.2.a.d $1$ $1.916$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$0$$ $-$ $$q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$$
240.2.f.a $2$ $1.916$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots$$
240.2.f.b $2$ $1.916$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-2i)q^{5}-4iq^{7}-q^{9}+\cdots$$
240.2.f.c $2$ $1.916$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2+i)q^{5}+2iq^{7}-q^{9}-2q^{11}+\cdots$$
240.2.h.a $4$ $1.916$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{3})q^{7}+3\beta _{2}q^{9}+\cdots$$
240.2.h.b $4$ $1.916$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}+2\zeta_{12}^{2}q^{7}+\cdots$$
240.2.o.a $4$ $1.916$ $$\Q(\sqrt{2}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(-2+\cdots)q^{9}+\cdots$$
240.2.o.b $8$ $1.916$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{2}q^{3}-\zeta_{24}q^{5}+(1-\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{9}+\cdots$$
240.2.s.a $4$ $1.916$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}+2q^{4}+\cdots$$
240.2.s.b $8$ $1.916$ 8.0.18939904.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{6}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
240.2.s.c $20$ $1.916$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+\beta _{5}q^{5}+\cdots$$
240.2.t.a $8$ $1.916$ 8.0.3317760000.5 $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+\beta _{2}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$$
240.2.t.b $80$ $1.916$ None None $$0$$ $$0$$ $$0$$ $$0$$
240.2.v.a $4$ $1.916$ $$\Q(\zeta_{8})$$ None None $$0$$ $$-4$$ $$4$$ $$4$$ $$q+(-1+\zeta_{8}^{2})q^{3}+(1+2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots$$
240.2.v.b $4$ $1.916$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$-2$$ $$0$$ $$4$$ $$q+(-1+\beta _{3})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots$$
240.2.v.c $4$ $1.916$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$-4$$ $$4$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1-2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots$$
240.2.v.d $4$ $1.916$ $$\Q(\zeta_{8})$$ None None $$0$$ $$4$$ $$0$$ $$-12$$ $$q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$$
240.2.v.e $4$ $1.916$ $$\Q(\zeta_{8})$$ None None $$0$$ $$4$$ $$0$$ $$4$$ $$q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$$
240.2.w.a $4$ $1.916$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+\zeta_{8}q^{3}+(-2+\zeta_{8}^{2})q^{5}+4\zeta_{8}^{3}q^{7}+\cdots$$
240.2.w.b $8$ $1.916$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\zeta_{24}^{5}q^{3}+(1+\zeta_{24}^{2}-\zeta_{24}^{3})q^{5}+\cdots$$
240.2.y.a $2$ $1.916$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$-2$$ $$-2$$ $$q+(-1-i)q^{2}-q^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots$$
240.2.y.b $2$ $1.916$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$2$$ $$-2$$ $$6$$ $$q+(-1-i)q^{2}+q^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots$$
240.2.y.c $2$ $1.916$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$-2$$ $$2$$ $$6$$ $$q+(1+i)q^{2}-q^{3}+2iq^{4}+(1-2i)q^{5}+\cdots$$
240.2.y.d $6$ $1.916$ 6.0.399424.1 None None $$0$$ $$6$$ $$6$$ $$-2$$ $$q+\beta _{3}q^{2}+q^{3}+(-\beta _{1}-\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$$
240.2.y.e $16$ $1.916$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$2$$ $$16$$ $$-4$$ $$-4$$ $$q+\beta _{7}q^{2}+q^{3}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$$
240.2.y.f $20$ $1.916$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$0$$ $$-20$$ $$0$$ $$-4$$ $$q+\beta _{13}q^{2}-q^{3}-\beta _{3}q^{4}+\beta _{7}q^{5}-\beta _{13}q^{6}+\cdots$$
240.2.bb.a $88$ $1.916$ None None $$0$$ $$0$$ $$0$$ $$0$$
240.2.bc.a $2$ $1.916$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$0$$ $$-4$$ $$6$$ $$q+(-1-i)q^{2}-iq^{3}+2iq^{4}+(-2+\cdots)q^{5}+\cdots$$
240.2.bc.b $2$ $1.916$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$0$$ $$-4$$ $$-2$$ $$q+(-1-i)q^{2}+iq^{3}+2iq^{4}+(-2+\cdots)q^{5}+\cdots$$
240.2.bc.c $2$ $1.916$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$0$$ $$-4$$ $$6$$ $$q+(1+i)q^{2}+iq^{3}+2iq^{4}+(-2-i)q^{5}+\cdots$$
240.2.bc.d $6$ $1.916$ 6.0.399424.1 None None $$-2$$ $$0$$ $$12$$ $$-2$$ $$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{2}-\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots$$
240.2.bc.e $16$ $1.916$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$2$$ $$0$$ $$-8$$ $$-4$$ $$q+\beta _{2}q^{2}-\beta _{5}q^{3}+(-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$
240.2.bc.f $20$ $1.916$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$2$$ $$0$$ $$8$$ $$-4$$ $$q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}-\beta _{15}q^{5}+\cdots$$
240.2.bf.a $88$ $1.916$ None None $$0$$ $$-4$$ $$0$$ $$0$$
240.2.bk.a $4$ $1.916$ $$\Q(\zeta_{8})$$ None None $$0$$ $$-4$$ $$0$$ $$-16$$ $$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots$$
240.2.bk.b $60$ $1.916$ None None $$0$$ $$4$$ $$0$$ $$16$$
240.2.bl.a $48$ $1.916$ None None $$0$$ $$0$$ $$0$$ $$0$$
240.3.c.a $1$ $6.540$ $$\Q$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$-3$$ $$-5$$ $$0$$ $$q-3q^{3}-5q^{5}+9q^{9}+15q^{15}+14q^{17}+\cdots$$
240.3.c.b $1$ $6.540$ $$\Q$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$3$$ $$5$$ $$0$$ $$q+3q^{3}+5q^{5}+9q^{9}+15q^{15}-14q^{17}+\cdots$$
240.3.c.c $4$ $6.540$ $$\Q(\sqrt{2}, \sqrt{-17})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(2\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
240.3.c.d $4$ $6.540$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots$$
240.3.c.e $12$ $6.540$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{7}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$$
240.3.e.a $4$ $6.540$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}-\beta _{1}q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots$$
240.3.e.b $4$ $6.540$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}-\beta _{1}q^{5}+(-2\beta _{2}-2\beta _{3})q^{7}+\cdots$$
240.3.j.a $4$ $6.540$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-20$$ $$0$$ $$q+\zeta_{12}q^{3}-5q^{5}-4\zeta_{12}q^{7}+3q^{9}+\cdots$$
240.3.j.b $4$ $6.540$ $$\Q(\sqrt{3}, \sqrt{-7})$$ None None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+\beta _{1}q^{3}+(-2+\beta _{2})q^{5}+2\beta _{1}q^{7}+\cdots$$