## Results (1-50 of 87 matches)

Label Dim $A$ Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
289.2.a.a $1$ $2.308$ $$\Q$$ None $$-1$$ $$0$$ $$2$$ $$-4$$ $+$ $$q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots$$
289.2.a.b $2$ $2.308$ $$\Q(\sqrt{13})$$ None $$-1$$ $$-1$$ $$-1$$ $$-3$$ $+$ $$q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots$$
289.2.a.c $2$ $2.308$ $$\Q(\sqrt{13})$$ None $$-1$$ $$1$$ $$1$$ $$3$$ $-$ $$q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots$$
289.2.a.d $3$ $2.308$ $$\Q(\zeta_{18})^+$$ None $$0$$ $$-3$$ $$-6$$ $$0$$ $+$ $$q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots$$
289.2.a.e $3$ $2.308$ $$\Q(\zeta_{18})^+$$ None $$0$$ $$3$$ $$6$$ $$0$$ $-$ $$q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$$
289.2.a.f $4$ $2.308$ $$\Q(\zeta_{16})^+$$ None $$4$$ $$0$$ $$0$$ $$0$$ $-$ $$q+(1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots$$
289.2.b.a $2$ $2.308$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-q^{4}+iq^{5}+2iq^{7}-3q^{8}+\cdots$$
289.2.b.b $4$ $2.308$ 4.0.2048.2 None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots$$
289.2.b.c $4$ $2.308$ $$\Q(i, \sqrt{13})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
289.2.b.d $6$ $2.308$ 6.0.419904.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{2}-\beta _{4})q^{4}+\cdots$$
289.2.c.a $4$ $2.308$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}+q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{3}q^{7}+\cdots$$
289.2.c.b $8$ $2.308$ 8.0.1871773696.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
289.2.c.c $8$ $2.308$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{16}^{2}-\zeta_{16}^{3})q^{2}+(-\zeta_{16}+\zeta_{16}^{7})q^{3}+\cdots$$
289.2.c.d $12$ $2.308$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}-\beta _{9})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots$$
289.2.d.a $4$ $2.308$ $$\Q(\zeta_{8})$$ None $$-4$$ $$4$$ $$0$$ $$4$$ $$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$$
289.2.d.b $4$ $2.308$ $$\Q(\zeta_{8})$$ None $$4$$ $$-4$$ $$-4$$ $$-4$$ $$q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$$
289.2.d.c $4$ $2.308$ $$\Q(\zeta_{8})$$ None $$4$$ $$4$$ $$4$$ $$4$$ $$q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots$$
289.2.d.d $8$ $2.308$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots$$
289.2.d.e $16$ $2.308$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{5})q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-2\beta _{8}+\cdots)q^{4}+\cdots$$
289.2.d.f $24$ $2.308$ None $$0$$ $$0$$ $$0$$ $$0$$
289.2.f.a $384$ $2.308$ None $$-13$$ $$-13$$ $$-43$$ $$-13$$
289.2.g.a $384$ $2.308$ None $$-17$$ $$-17$$ $$17$$ $$-17$$
289.2.h.a $768$ $2.308$ None $$-34$$ $$-34$$ $$-34$$ $$-34$$
289.2.i.a $1600$ $2.308$ None $$-64$$ $$-64$$ $$-68$$ $$-64$$
289.3.e.a $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$-8$$ $$-16$$ $$-8$$ $$-16$$ $$q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-2-2\zeta_{16}+\cdots)q^{3}+\cdots$$
289.3.e.b $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$-8$$ $$-8$$ $$0$$ $$-8$$ $$q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots$$
289.3.e.c $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$-8$$ $$8$$ $$-16$$ $$-8$$ $$q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots$$
289.3.e.d $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$-8$$ $$8$$ $$0$$ $$8$$ $$q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots$$
289.3.e.e $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$-8$$ $$16$$ $$8$$ $$16$$ $$q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(2+2\zeta_{16}+\cdots)q^{3}+\cdots$$
289.3.e.f $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$0$$ $$-8$$ $$-8$$ $$8$$ $$q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots$$
289.3.e.g $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$24$$ $$16$$ $$q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-2\zeta_{16}^{2}+\cdots)q^{3}+\cdots$$
289.3.e.h $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$0$$ $$8$$ $$8$$ $$-8$$ $$q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots$$
289.3.e.i $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$8$$ $$-8$$ $$-16$$ $$8$$ $$q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots$$
289.3.e.j $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$8$$ $$-8$$ $$16$$ $$-8$$ $$q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots$$
289.3.e.k $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$8$$ $$0$$ $$-16$$ $$40$$ $$q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots$$
289.3.e.l $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$8$$ $$0$$ $$16$$ $$-40$$ $$q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots$$
289.3.e.m $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$8$$ $$8$$ $$16$$ $$-8$$ $$q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots$$
289.3.e.n $8$ $7.875$ $$\Q(\zeta_{16})$$ None $$8$$ $$8$$ $$-16$$ $$8$$ $$q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots$$
289.3.e.o $16$ $7.875$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+\beta _{11}q^{3}+3\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots$$
289.3.e.p $32$ $7.875$ None $$0$$ $$0$$ $$0$$ $$0$$
289.3.e.q $48$ $7.875$ None $$0$$ $$0$$ $$0$$ $$0$$
289.3.e.r $96$ $7.875$ None $$0$$ $$0$$ $$0$$ $$0$$
289.3.j.a $6400$ $7.875$ None $$-128$$ $$-128$$ $$-128$$ $$-128$$
289.4.a.a $1$ $17.052$ $$\Q$$ None $$-3$$ $$8$$ $$-6$$ $$28$$ $+$ $$q-3q^{2}+8q^{3}+q^{4}-6q^{5}-24q^{6}+\cdots$$
289.4.a.b $3$ $17.052$ 3.3.2636.1 None $$1$$ $$-4$$ $$8$$ $$-22$$ $+$ $$q+(\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}-2\beta _{2})q^{3}+\cdots$$
289.4.a.c $4$ $17.052$ 4.4.2555057.1 None $$1$$ $$-2$$ $$14$$ $$36$$ $+$ $$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots$$
289.4.a.d $4$ $17.052$ 4.4.2555057.1 None $$1$$ $$2$$ $$-14$$ $$-36$$ $-$ $$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots$$
289.4.a.e $4$ $17.052$ 4.4.4669632.2 None $$2$$ $$0$$ $$0$$ $$0$$ $+$ $$q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+\cdots$$
289.4.a.f $8$ $17.052$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$8$$ $$0$$ $$0$$ $$0$$ $+$ $$q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(5-\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots$$
289.4.a.g $12$ $17.052$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $-$ $$q+(-1+\beta _{5})q^{2}+\beta _{7}q^{3}+(2+2\beta _{1}+\cdots)q^{4}+\cdots$$