## Results (50 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
729.1.f.a $6$ $0.364$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{18}q^{4}-\zeta_{18}^{8}q^{7}-\zeta_{18}^{4}q^{13}+\cdots$$
729.2.a.a $6$ $5.821$ 6.6.1397493.1 None None $$-3$$ $$0$$ $$-6$$ $$0$$ $+$ $$q+(-\beta _{1}-\beta _{5})q^{2}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots$$
729.2.a.b $6$ $5.821$ 6.6.7459857.1 None None $$-3$$ $$0$$ $$3$$ $$6$$ $-$ $$q+(-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$
729.2.a.c $6$ $5.821$ $$\Q(\zeta_{36})^+$$ None None $$0$$ $$0$$ $$0$$ $$-12$$ $+$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$$
729.2.a.d $6$ $5.821$ 6.6.1397493.1 None None $$3$$ $$0$$ $$6$$ $$0$$ $-$ $$q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots$$
729.2.a.e $6$ $5.821$ 6.6.7459857.1 None None $$3$$ $$0$$ $$-3$$ $$6$$ $-$ $$q+(\beta _{1}+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$
729.2.c.a $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$-3$$ $$0$$ $$3$$ $$-6$$ $$q+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{6})q^{2}+(-1+\cdots)q^{4}+\cdots$$
729.2.c.b $12$ $5.821$ 12.0.$$\cdots$$.1 None None $$-3$$ $$0$$ $$-6$$ $$0$$ $$q+(\beta _{6}+\beta _{8}-\beta _{10})q^{2}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$
729.2.c.c $12$ $5.821$ $$\Q(\zeta_{36})$$ None None $$0$$ $$0$$ $$0$$ $$12$$ $$q+(-\zeta_{36}^{7}-\zeta_{36}^{8}+\zeta_{36}^{10})q^{2}-\zeta_{36}^{11}q^{4}+\cdots$$
729.2.c.d $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$3$$ $$0$$ $$-3$$ $$-6$$ $$q+(\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{9})q^{2}+(-1+\cdots)q^{4}+\cdots$$
729.2.c.e $12$ $5.821$ 12.0.$$\cdots$$.1 None None $$3$$ $$0$$ $$6$$ $$0$$ $$q+(-\beta _{6}-\beta _{8}+\beta _{10})q^{2}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
729.2.e.a $6$ $5.821$ $$\Q(\zeta_{18})$$ None None $$-6$$ $$0$$ $$-3$$ $$-9$$ $$q+(-1-\zeta_{18}+\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$$
729.2.e.b $6$ $5.821$ $$\Q(\zeta_{18})$$ None None $$-3$$ $$0$$ $$-6$$ $$9$$ $$q+(-1+\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{4}+\cdots)q^{2}+\cdots$$
729.2.e.c $6$ $5.821$ $$\Q(\zeta_{18})$$ None None $$-3$$ $$0$$ $$3$$ $$0$$ $$q+(\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+\cdots$$
729.2.e.d $6$ $5.821$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{18}^{5}q^{4}+5\zeta_{18}^{4}q^{7}+2\zeta_{18}^{2}q^{13}+\cdots$$
729.2.e.e $6$ $5.821$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{18}^{5}q^{4}-4\zeta_{18}^{4}q^{7}-7\zeta_{18}^{2}q^{13}+\cdots$$
729.2.e.f $6$ $5.821$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{18}^{5}q^{4}-\zeta_{18}^{4}q^{7}+5\zeta_{18}^{2}q^{13}+\cdots$$
729.2.e.g $6$ $5.821$ $$\Q(\zeta_{18})$$ None None $$3$$ $$0$$ $$6$$ $$9$$ $$q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots$$
729.2.e.h $6$ $5.821$ $$\Q(\zeta_{18})$$ None None $$3$$ $$0$$ $$-3$$ $$0$$ $$q+(-\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots$$
729.2.e.i $6$ $5.821$ $$\Q(\zeta_{18})$$ None None $$6$$ $$0$$ $$3$$ $$-9$$ $$q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{4}+\cdots$$
729.2.e.j $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$-6$$ $$0$$ $$6$$ $$-3$$ $$q+(-1-\beta _{6}-\beta _{7}+\beta _{11})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$$
729.2.e.k $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$-3$$ $$0$$ $$-6$$ $$6$$ $$q+(-\beta _{5}-\beta _{7}+\beta _{10})q^{2}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$$
729.2.e.l $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$-3$$ $$0$$ $$12$$ $$-3$$ $$q+\beta _{2}q^{2}+(-2\beta _{1}-\beta _{2}+\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$$
729.2.e.m $12$ $5.821$ $$\Q(\zeta_{36})$$ None None $$0$$ $$0$$ $$0$$ $$6$$ $$q+(-\zeta_{36}^{2}+\zeta_{36}^{7}-\zeta_{36}^{9}+\zeta_{36}^{11})q^{2}+\cdots$$
729.2.e.n $12$ $5.821$ $$\Q(\zeta_{36})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{36}^{8}q^{2}+(-\zeta_{36}^{2}+\zeta_{36}^{7})q^{4}+\cdots$$
729.2.e.o $12$ $5.821$ $$\Q(\zeta_{36})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{36}^{8}q^{2}+(-\zeta_{36}^{2}+\zeta_{36}^{7})q^{4}+\cdots$$
729.2.e.p $12$ $5.821$ 12.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+4\beta _{5}q^{4}+\beta _{11}q^{5}-2\beta _{7}q^{7}+\cdots$$
729.2.e.q $12$ $5.821$ $$\Q(\zeta_{36})$$ None None $$0$$ $$0$$ $$0$$ $$-12$$ $$q+\zeta_{36}^{9}q^{2}+(1+\zeta_{36}-\zeta_{36}^{4})q^{4}+\cdots$$
729.2.e.r $12$ $5.821$ $$\Q(\zeta_{36})$$ None None $$0$$ $$0$$ $$0$$ $$6$$ $$q+(-\zeta_{36}^{9}+\zeta_{36}^{10})q^{2}+(1+\zeta_{36}^{3}+\cdots)q^{4}+\cdots$$
729.2.e.s $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$3$$ $$0$$ $$-12$$ $$-3$$ $$q+(1-\beta _{5}+\beta _{6}+\beta _{10}-\beta _{11})q^{2}+(\beta _{1}+\cdots)q^{4}+\cdots$$
729.2.e.t $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$3$$ $$0$$ $$6$$ $$6$$ $$q+(\beta _{1}+\beta _{2}+\beta _{5}-\beta _{6}-\beta _{8})q^{2}+(1+\cdots)q^{4}+\cdots$$
729.2.e.u $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$6$$ $$0$$ $$-6$$ $$-3$$ $$q+(\beta _{1}+\beta _{5}-\beta _{6}-\beta _{8})q^{2}+(-1+2\beta _{1}+\cdots)q^{4}+\cdots$$
729.2.g.a $144$ $5.821$ None None $$-9$$ $$0$$ $$-9$$ $$9$$
729.2.g.b $144$ $5.821$ None None $$-9$$ $$0$$ $$-9$$ $$9$$
729.2.g.c $144$ $5.821$ None None $$9$$ $$0$$ $$9$$ $$9$$
729.2.g.d $144$ $5.821$ None None $$9$$ $$0$$ $$9$$ $$9$$
729.2.i.a $1404$ $5.821$ None None $$54$$ $$0$$ $$54$$ $$-54$$
729.2.k.a $12960$ $5.821$ None None $$-162$$ $$-162$$ $$-162$$ $$-162$$
729.3.b.a $30$ $19.864$ None None $$0$$ $$0$$ $$0$$ $$0$$
729.3.b.b $36$ $19.864$ None None $$0$$ $$0$$ $$0$$ $$0$$
729.4.a.a $12$ $43.012$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$-6$$ $$0$$ $$-12$$ $$-42$$ $-$ $$q+(-1+\beta _{1})q^{2}+(3+\beta _{2}+\beta _{3})q^{4}+\cdots$$
729.4.a.b $12$ $43.012$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$6$$ $$0$$ $$12$$ $$-42$$ $-$ $$q+(1-\beta _{1})q^{2}+(3+\beta _{2}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$$
729.4.a.c $24$ $43.012$ None None $$-6$$ $$0$$ $$-30$$ $$0$$ $-$
729.4.a.d $24$ $43.012$ None None $$6$$ $$0$$ $$30$$ $$0$$ $+$
729.4.a.e $30$ $43.012$ None None $$0$$ $$0$$ $$0$$ $$84$$ $+$
729.6.a.a $24$ $116.920$ None None $$-12$$ $$0$$ $$-33$$ $$294$$ $-$
729.6.a.b $24$ $116.920$ None None $$12$$ $$0$$ $$33$$ $$294$$ $-$
729.6.a.c $42$ $116.920$ None None $$-12$$ $$0$$ $$-150$$ $$0$$ $+$
729.6.a.d $42$ $116.920$ None None $$0$$ $$0$$ $$0$$ $$-588$$ $+$
729.6.a.e $42$ $116.920$ None None $$12$$ $$0$$ $$150$$ $$0$$ $-$