## Results (45 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3072.1.e.a $2$ $1.533$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}-\beta q^{7}+q^{9}-\beta q^{13}+\beta q^{21}+\cdots$$
3072.1.e.b $2$ $1.533$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}-\beta q^{7}+q^{9}+\beta q^{13}-\beta q^{21}+\cdots$$
3072.1.h.a $4$ $1.533$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{13}+\cdots$$
3072.1.i.a $2$ $1.533$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+q^{9}+(-1+i)q^{11}-iq^{17}+\cdots$$
3072.1.i.b $2$ $1.533$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}+(-1+i)q^{11}+iq^{17}+\cdots$$
3072.1.i.c $2$ $1.533$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}+(1-i)q^{11}+iq^{17}+\cdots$$
3072.1.i.d $2$ $1.533$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+q^{9}+(1-i)q^{11}-iq^{17}+(-1+\cdots)q^{19}+\cdots$$
3072.1.i.e $4$ $1.533$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\zeta_{8}^{3}q^{3}+(-1-\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots$$
3072.1.i.f $4$ $1.533$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-2})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{9}-\zeta_{8}q^{11}-\zeta_{8}^{2}q^{25}+\cdots$$
3072.1.i.g $4$ $1.533$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{6})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}-\zeta_{8}q^{19}-\zeta_{8}^{2}q^{25}+\cdots$$
3072.1.i.h $4$ $1.533$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\zeta_{8}^{3}q^{3}+(1+\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$$
3072.1.p.a $8$ $1.533$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}q^{3}+(\zeta_{16}^{5}+\zeta_{16}^{7})q^{7}+\zeta_{16}^{2}q^{9}+\cdots$$
3072.1.p.b $8$ $1.533$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{16}q^{3}+(\zeta_{16}-\zeta_{16}^{3})q^{7}+\zeta_{16}^{2}q^{9}+\cdots$$
3072.1.p.c $8$ $1.533$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{16}q^{3}+(-\zeta_{16}+\zeta_{16}^{3})q^{7}+\zeta_{16}^{2}q^{9}+\cdots$$
3072.1.p.d $8$ $1.533$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}q^{3}+(-\zeta_{16}^{5}-\zeta_{16}^{7})q^{7}+\zeta_{16}^{2}q^{9}+\cdots$$
3072.2.a.a $2$ $24.530$ $$\Q(\sqrt{2})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $+$ $$q-q^{3}+\beta q^{7}+q^{9}+\beta q^{13}-6q^{17}+\cdots$$
3072.2.a.b $2$ $24.530$ $$\Q(\sqrt{2})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $+$ $$q-q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-3\beta q^{13}+\cdots$$
3072.2.a.c $2$ $24.530$ $$\Q(\sqrt{2})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $-$ $$q-q^{3}+\beta q^{5}+q^{9}+4q^{11}-\beta q^{13}+\cdots$$
3072.2.a.d $2$ $24.530$ $$\Q(\sqrt{2})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $-$ $$q-q^{3}+2\beta q^{5}-3\beta q^{7}+q^{9}+4q^{11}+\cdots$$
3072.2.a.e $2$ $24.530$ $$\Q(\sqrt{2})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $+$ $$q+q^{3}+\beta q^{5}+q^{9}-4q^{11}-\beta q^{13}+\cdots$$
3072.2.a.f $2$ $24.530$ $$\Q(\sqrt{2})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $-$ $$q+q^{3}+2\beta q^{5}+3\beta q^{7}+q^{9}-4q^{11}+\cdots$$
3072.2.a.g $2$ $24.530$ $$\Q(\sqrt{2})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $+$ $$q+q^{3}-\beta q^{7}+q^{9}+\beta q^{13}-6q^{17}+\cdots$$
3072.2.a.h $2$ $24.530$ $$\Q(\sqrt{2})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $-$ $$q+q^{3}+\beta q^{5}-2\beta q^{7}+q^{9}-3\beta q^{13}+\cdots$$
3072.2.a.i $4$ $24.530$ 4.4.4352.1 None None $$0$$ $$-4$$ $$-4$$ $$4$$ $+$ $$q-q^{3}+(-1-\beta _{3})q^{5}+(1+\beta _{2})q^{7}+\cdots$$
3072.2.a.j $4$ $24.530$ $$\Q(\zeta_{16})^+$$ None None $$0$$ $$-4$$ $$0$$ $$-8$$ $+$ $$q-q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-2-\beta _{3})q^{7}+\cdots$$
3072.2.a.k $4$ $24.530$ $$\Q(\sqrt{2}, \sqrt{5})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $+$ $$q-q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$$
3072.2.a.l $4$ $24.530$ $$\Q(\zeta_{24})^+$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $-$ $$q-q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots$$
3072.2.a.m $4$ $24.530$ $$\Q(\zeta_{16})^+$$ None None $$0$$ $$-4$$ $$0$$ $$8$$ $-$ $$q-q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(2-\beta _{3})q^{7}+\cdots$$
3072.2.a.n $4$ $24.530$ 4.4.4352.1 None None $$0$$ $$-4$$ $$4$$ $$-4$$ $-$ $$q-q^{3}+(1+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+\cdots$$
3072.2.a.o $4$ $24.530$ 4.4.4352.1 None None $$0$$ $$4$$ $$-4$$ $$-4$$ $+$ $$q+q^{3}+(-1-\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+\cdots$$
3072.2.a.p $4$ $24.530$ $$\Q(\zeta_{16})^+$$ None None $$0$$ $$4$$ $$0$$ $$-8$$ $+$ $$q+q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-2+\beta _{3})q^{7}+\cdots$$
3072.2.a.q $4$ $24.530$ $$\Q(\sqrt{2}, \sqrt{5})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $-$ $$q+q^{3}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$$
3072.2.a.r $4$ $24.530$ $$\Q(\zeta_{24})^+$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $-$ $$q+q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots$$
3072.2.a.s $4$ $24.530$ $$\Q(\zeta_{16})^+$$ None None $$0$$ $$4$$ $$0$$ $$8$$ $-$ $$q+q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2+\beta _{3})q^{7}+q^{9}+\cdots$$
3072.2.a.t $4$ $24.530$ 4.4.4352.1 None None $$0$$ $$4$$ $$4$$ $$4$$ $-$ $$q+q^{3}+(1+\beta _{3})q^{5}+(1+\beta _{2})q^{7}+q^{9}+\cdots$$
3072.2.d.a $4$ $24.530$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}-q^{9}-\zeta_{8}^{2}q^{13}+\cdots$$
3072.2.d.b $4$ $24.530$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-q^{9}+4\zeta_{8}q^{11}+\cdots$$
3072.2.d.c $4$ $24.530$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{7}-q^{9}+\cdots$$
3072.2.d.d $4$ $24.530$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{3}+2\zeta_{8}^{2}q^{5}+3\zeta_{8}^{3}q^{7}-q^{9}+\cdots$$
3072.2.d.e $8$ $24.530$ $$\Q(\zeta_{16})$$ None None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots$$
3072.2.d.f $8$ $24.530$ 8.0.18939904.2 None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$$
3072.2.d.g $8$ $24.530$ 8.0.40960000.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{6}q^{5}+(\beta _{2}-\beta _{7})q^{7}-q^{9}+\cdots$$
3072.2.d.h $8$ $24.530$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{3}+(-\zeta_{24}^{2}-\zeta_{24}^{7})q^{5}+\zeta_{24}^{3}q^{7}+\cdots$$
3072.2.d.i $8$ $24.530$ 8.0.18939904.2 None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(1-\beta _{1})q^{7}+\cdots$$
3072.2.d.j $8$ $24.530$ $$\Q(\zeta_{16})$$ None None $$0$$ $$0$$ $$0$$ $$16$$ $$q-\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(2-\zeta_{16}^{5}+\cdots)q^{7}+\cdots$$