## Results (1-50 of 122 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.1.o.a $1$ $0.220$ $$\Q$$ $$\Q(\sqrt{-110})$$ None $$-1$$ $$-1$$ $$1$$ $$1$$ $$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$$
440.1.o.b $1$ $0.220$ $$\Q$$ $$\Q(\sqrt{-110})$$ None $$-1$$ $$1$$ $$-1$$ $$1$$ $$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$$
440.1.o.c $1$ $0.220$ $$\Q$$ $$\Q(\sqrt{-110})$$ None $$1$$ $$-1$$ $$1$$ $$-1$$ $$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$$
440.1.o.d $1$ $0.220$ $$\Q$$ $$\Q(\sqrt{-110})$$ None $$1$$ $$1$$ $$-1$$ $$-1$$ $$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$$
440.1.o.e $4$ $0.220$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-55})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$$
440.1.bh.a $4$ $0.220$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-10})$$ None $$-1$$ $$0$$ $$-1$$ $$3$$ $$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(1+\cdots)q^{7}+\cdots$$
440.1.bh.b $4$ $0.220$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-10})$$ None $$1$$ $$0$$ $$1$$ $$-3$$ $$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+(-1+\cdots)q^{7}+\cdots$$
440.2.a.a $1$ $3.513$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-2$$ $+$ $$q-q^{5}-2q^{7}-3q^{9}-q^{11}-8q^{19}+\cdots$$
440.2.a.b $1$ $3.513$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-2$$ $+$ $$q-q^{5}-2q^{7}-3q^{9}+q^{11}-4q^{13}+\cdots$$
440.2.a.c $1$ $3.513$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$4$$ $-$ $$q+q^{5}+4q^{7}-3q^{9}-q^{11}+6q^{13}+\cdots$$
440.2.a.d $1$ $3.513$ $$\Q$$ None None $$0$$ $$3$$ $$1$$ $$1$$ $-$ $$q+3q^{3}+q^{5}+q^{7}+6q^{9}-q^{11}-6q^{13}+\cdots$$
440.2.a.e $2$ $3.513$ $$\Q(\sqrt{17})$$ None None $$0$$ $$-1$$ $$2$$ $$-1$$ $-$ $$q-\beta q^{3}+q^{5}-\beta q^{7}+(1+\beta )q^{9}+q^{11}+\cdots$$
440.2.a.f $2$ $3.513$ $$\Q(\sqrt{17})$$ None None $$0$$ $$1$$ $$-2$$ $$3$$ $-$ $$q+\beta q^{3}-q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots$$
440.2.a.g $2$ $3.513$ $$\Q(\sqrt{17})$$ None None $$0$$ $$1$$ $$-2$$ $$5$$ $-$ $$q+\beta q^{3}-q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots$$
440.2.b.a $2$ $3.513$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1+i)q^{5}+iq^{7}-q^{9}+\cdots$$
440.2.b.b $2$ $3.513$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-i)q^{5}-2iq^{7}-q^{9}+q^{11}+\cdots$$
440.2.b.c $2$ $3.513$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}-q^{11}+\cdots$$
440.2.b.d $8$ $3.513$ 8.0.$$\cdots$$.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots$$
440.2.c.a $4$ $3.513$ $$\Q(\sqrt{-2}, \sqrt{5})$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-2q^{4}+\beta _{3}q^{5}-2\beta _{1}q^{7}+\cdots$$
440.2.c.b $8$ $3.513$ 8.0.$$\cdots$$.19 $$\Q(\sqrt{-55})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{2}-\beta _{5})q^{5}+\cdots$$
440.2.c.c $56$ $3.513$ None None $$0$$ $$0$$ $$0$$ $$0$$
440.2.g.a $4$ $3.513$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\zeta_{8}^{3}q^{2}+(-\zeta_{8}+\zeta_{8}^{2})q^{3}+2q^{4}+\cdots$$
440.2.g.b $12$ $3.513$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{9}q^{2}+(\beta _{1}+\beta _{3})q^{3}-\beta _{5}q^{4}-\beta _{8}q^{5}+\cdots$$
440.2.g.c $24$ $3.513$ None None $$0$$ $$0$$ $$0$$ $$0$$
440.2.l.a $2$ $3.513$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-4$$ $$-2$$ $$0$$ $$q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-1+\cdots)q^{5}+\cdots$$
440.2.l.b $2$ $3.513$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$4$$ $$2$$ $$0$$ $$q+(1+i)q^{2}+2q^{3}+2iq^{4}+(1+2i)q^{5}+\cdots$$
440.2.l.c $56$ $3.513$ None None $$0$$ $$0$$ $$0$$ $$0$$
440.2.p.a $48$ $3.513$ None None $$0$$ $$0$$ $$0$$ $$0$$
440.2.r.a $2$ $3.513$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$-4$$ $$-4$$ $$q+(-1+i)q^{2}+(-1+i)q^{3}-2iq^{4}+\cdots$$
440.2.r.b $2$ $3.513$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$-4$$ $$0$$ $$q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots$$
440.2.r.c $2$ $3.513$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$4$$ $$0$$ $$q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots$$
440.2.r.d $2$ $3.513$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$-2$$ $$4$$ $$4$$ $$q+(1-i)q^{2}+(-1+i)q^{3}-2iq^{4}+\cdots$$
440.2.r.e $4$ $3.513$ $$\Q(\zeta_{8})$$ None None $$0$$ $$-4$$ $$0$$ $$4$$ $$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$$
440.2.r.f $4$ $3.513$ $$\Q(\zeta_{8})$$ None None $$0$$ $$-4$$ $$0$$ $$-4$$ $$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots$$
440.2.r.g $48$ $3.513$ None None $$0$$ $$12$$ $$0$$ $$0$$
440.2.r.h $56$ $3.513$ None None $$4$$ $$4$$ $$0$$ $$0$$
440.2.t.a $4$ $3.513$ $$\Q(i, \sqrt{10})$$ None None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots$$
440.2.t.b $4$ $3.513$ $$\Q(i, \sqrt{10})$$ None None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$$
440.2.t.c $128$ $3.513$ None None $$0$$ $$0$$ $$0$$ $$0$$
440.2.v.a $4$ $3.513$ $$\Q(\zeta_{8})$$ None None $$0$$ $$4$$ $$-8$$ $$0$$ $$q+(1+\zeta_{8})q^{3}+(-2-\zeta_{8})q^{5}+(2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$$
440.2.v.b $32$ $3.513$ None None $$0$$ $$-4$$ $$8$$ $$0$$
440.2.y.a $8$ $3.513$ 8.0.13140625.1 None None $$0$$ $$1$$ $$-2$$ $$1$$ $$q+(\beta _{1}-\beta _{5})q^{3}+\beta _{7}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$$
440.2.y.b $12$ $3.513$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-1$$ $$3$$ $$-8$$ $$q+(\beta _{1}+\beta _{4})q^{3}+(1-\beta _{6}+\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots$$
440.2.y.c $12$ $3.513$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-1$$ $$3$$ $$-1$$ $$q+(\beta _{3}+\beta _{8})q^{3}-\beta _{6}q^{5}+(1+\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots$$
440.2.y.d $16$ $3.513$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$-3$$ $$-4$$ $$8$$ $$q-\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots$$
440.2.z.a $192$ $3.513$ None None $$0$$ $$0$$ $$0$$ $$0$$
440.2.bd.a $272$ $3.513$ None None $$0$$ $$0$$ $$0$$ $$0$$
440.2.bi.a $8$ $3.513$ $$\Q(\zeta_{20})$$ None None $$-2$$ $$0$$ $$0$$ $$-6$$ $$q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots$$
440.2.bi.b $8$ $3.513$ $$\Q(\zeta_{20})$$ None None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots$$
440.2.bi.c $176$ $3.513$ None None $$8$$ $$0$$ $$0$$ $$18$$