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## Results (1-50 of 95 matches)

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Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3420.1.h.a $2$ $1.707$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q-\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{11}+(\zeta_{6}+\cdots)q^{17}+\cdots$$
3420.1.h.b $4$ $1.707$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{5}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{7}+(-\zeta_{12}+\cdots)q^{11}+\cdots$$
3420.1.u.a $8$ $1.707$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{24}q^{5}+(\zeta_{24}^{8}-\zeta_{24}^{10})q^{7}+(-\zeta_{24}+\cdots)q^{11}+\cdots$$
3420.1.u.b $8$ $1.707$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{24}^{7}q^{5}+(-\zeta_{24}^{8}+\zeta_{24}^{10})q^{7}+\cdots$$
3420.1.bh.a $2$ $1.707$ $$\Q(\sqrt{-3})$$ None $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$1$$ $$0$$ $$q-\zeta_{6}^{2}q^{5}-q^{11}-\zeta_{6}q^{19}-\zeta_{6}q^{25}+\cdots$$
3420.1.bn.a $16$ $1.707$ $$\Q(\zeta_{48})$$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{48}^{5}q^{2}+\zeta_{48}q^{3}+\zeta_{48}^{10}q^{4}+\cdots$$
3420.1.bn.b $16$ $1.707$ $$\Q(\zeta_{48})$$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{48}^{9}q^{2}+\zeta_{48}^{19}q^{3}+\zeta_{48}^{18}q^{4}+\cdots$$
3420.1.df.a $4$ $1.707$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$$
3420.1.df.b $4$ $1.707$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$$
3420.1.es.a $4$ $1.707$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$-4$$ $$q-\zeta_{12}^{2}q^{5}+(-1+\zeta_{12}^{3})q^{7}+q^{11}+\cdots$$
3420.1.es.b $4$ $1.707$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{12}^{2}q^{5}-q^{11}+(-\zeta_{12}+\zeta_{12}^{4}+\cdots)q^{13}+\cdots$$
3420.1.es.c $4$ $1.707$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$2$$ $$-4$$ $$q+\zeta_{12}^{2}q^{5}+(-1+\zeta_{12}^{3})q^{7}-q^{11}+\cdots$$
3420.1.fk.a $12$ $1.707$ $$\Q(\zeta_{36})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{36}^{5}q^{2}+\zeta_{36}^{10}q^{4}+\zeta_{36}q^{5}+\cdots$$
3420.1.fk.b $12$ $1.707$ $$\Q(\zeta_{36})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{36}^{3}q^{2}+\zeta_{36}^{6}q^{4}-\zeta_{36}q^{5}+\zeta_{36}^{9}q^{8}+\cdots$$
3420.2.a.a $1$ $27.309$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-4$$ $+$ $$q+q^{5}-4q^{7}-2q^{11}+6q^{13}+2q^{17}+\cdots$$
3420.2.a.b $1$ $27.309$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-2$$ $+$ $$q+q^{5}-2q^{7}-4q^{11}+2q^{17}+q^{19}+\cdots$$
3420.2.a.c $1$ $27.309$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-2$$ $-$ $$q+q^{5}-2q^{7}-4q^{13}+2q^{17}-q^{19}+\cdots$$
3420.2.a.d $1$ $27.309$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-2$$ $+$ $$q+q^{5}-2q^{7}+4q^{11}-4q^{13}-6q^{17}+\cdots$$
3420.2.a.e $1$ $27.309$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$2$$ $+$ $$q+q^{5}+2q^{7}-4q^{13}-6q^{17}+q^{19}+\cdots$$
3420.2.a.f $1$ $27.309$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$2$$ $-$ $$q+q^{5}+2q^{7}+6q^{13}-2q^{17}-q^{19}+\cdots$$
3420.2.a.g $2$ $27.309$ $$\Q(\sqrt{2})$$ None None $$0$$ $$0$$ $$-2$$ $$-4$$ $+$ $$q-q^{5}+(-2+2\beta )q^{7}+2q^{11}+(-2+\cdots)q^{13}+\cdots$$
3420.2.a.h $2$ $27.309$ $$\Q(\sqrt{3})$$ None None $$0$$ $$0$$ $$-2$$ $$4$$ $-$ $$q-q^{5}+2q^{7}-2\beta q^{11}+(-1+\beta )q^{13}+\cdots$$
3420.2.a.i $2$ $27.309$ $$\Q(\sqrt{13})$$ None None $$0$$ $$0$$ $$2$$ $$2$$ $-$ $$q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(1-\beta )q^{13}+\cdots$$
3420.2.a.j $3$ $27.309$ 3.3.404.1 None None $$0$$ $$0$$ $$-3$$ $$-2$$ $-$ $$q-q^{5}+(-1+\beta _{2})q^{7}+(1-\beta _{1}+2\beta _{2})q^{11}+\cdots$$
3420.2.a.k $3$ $27.309$ 3.3.1524.1 None None $$0$$ $$0$$ $$-3$$ $$0$$ $-$ $$q-q^{5}-\beta _{1}q^{7}+(1+\beta _{2})q^{11}+(2-\beta _{1}+\cdots)q^{13}+\cdots$$
3420.2.a.l $3$ $27.309$ 3.3.564.1 None None $$0$$ $$0$$ $$-3$$ $$2$$ $+$ $$q-q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{1})q^{11}+\cdots$$
3420.2.a.m $3$ $27.309$ 3.3.564.1 None None $$0$$ $$0$$ $$-3$$ $$4$$ $+$ $$q-q^{5}+(1-\beta _{2})q^{7}+(-2-\beta _{1}+\beta _{2})q^{11}+\cdots$$
3420.2.a.n $3$ $27.309$ 3.3.404.1 None None $$0$$ $$0$$ $$3$$ $$-2$$ $+$ $$q+q^{5}+(-1+\beta _{2})q^{7}+(-1+\beta _{1}-2\beta _{2})q^{11}+\cdots$$
3420.2.a.o $3$ $27.309$ 3.3.564.1 None None $$0$$ $$0$$ $$3$$ $$2$$ $-$ $$q+q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{1})q^{11}+\cdots$$
3420.2.e.a $16$ $27.309$ 16.0.$$\cdots$$.1 $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{5}+(-\beta _{11}+\beta _{12})q^{7}+(-\beta _{9}+\cdots)q^{11}+\cdots$$
3420.2.e.b $24$ $27.309$ None None $$0$$ $$0$$ $$0$$ $$0$$
3420.2.f.a $4$ $27.309$ $$\Q(\sqrt{-2}, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(3-\beta _{2})q^{11}+\cdots$$
3420.2.f.b $6$ $27.309$ 6.0.350464.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{4})q^{5}-\beta _{5}q^{7}+(1-\beta _{2})q^{11}+\cdots$$
3420.2.f.c $6$ $27.309$ 6.0.14077504.2 None None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\beta _{3}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-3-\beta _{1}+\cdots)q^{11}+\cdots$$
3420.2.f.d $8$ $27.309$ 8.0.796594176.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}-\beta _{5}q^{7}-\beta _{1}q^{11}-\beta _{5}q^{13}+\cdots$$
3420.2.f.e $10$ $27.309$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{7}q^{5}+\beta _{4}q^{7}+(-1+\beta _{5})q^{11}+\cdots$$
3420.2.f.f $12$ $27.309$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{5}+\beta _{5}q^{7}+\beta _{3}q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots$$
3420.2.j.a $24$ $27.309$ None None $$0$$ $$0$$ $$0$$ $$0$$
3420.2.t.a $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$-10$$ $$q+(-1+\zeta_{6})q^{5}-5q^{7}-6q^{11}+\zeta_{6}q^{13}+\cdots$$
3420.2.t.b $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$-8$$ $$q+(-1+\zeta_{6})q^{5}-4q^{7}+3q^{11}-6\zeta_{6}q^{13}+\cdots$$
3420.2.t.c $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$-6$$ $$q+(-1+\zeta_{6})q^{5}-3q^{7}+2q^{11}+\zeta_{6}q^{13}+\cdots$$
3420.2.t.d $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$-4$$ $$q+(-1+\zeta_{6})q^{5}-2q^{7}-2q^{11}+4\zeta_{6}q^{13}+\cdots$$
3420.2.t.e $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$4$$ $$q+(-1+\zeta_{6})q^{5}+2q^{7}-3q^{11}+6\zeta_{6}q^{13}+\cdots$$
3420.2.t.f $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$4$$ $$q+(-1+\zeta_{6})q^{5}+2q^{7}+q^{11}-6\zeta_{6}q^{13}+\cdots$$
3420.2.t.g $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$4$$ $$q+(-1+\zeta_{6})q^{5}+2q^{7}+6q^{11}+(5+\cdots)q^{17}+\cdots$$
3420.2.t.h $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$4$$ $$q+(-1+\zeta_{6})q^{5}+2q^{7}+6q^{11}+4\zeta_{6}q^{13}+\cdots$$
3420.2.t.i $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$8$$ $$q+(-1+\zeta_{6})q^{5}+4q^{7}+2q^{11}-6\zeta_{6}q^{13}+\cdots$$
3420.2.t.j $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$1$$ $$-4$$ $$q+(1-\zeta_{6})q^{5}-2q^{7}-3q^{11}+(-4+\cdots)q^{17}+\cdots$$
3420.2.t.k $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$1$$ $$-4$$ $$q+(1-\zeta_{6})q^{5}-2q^{7}+q^{11}-4\zeta_{6}q^{13}+\cdots$$
3420.2.t.l $2$ $27.309$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$1$$ $$-4$$ $$q+(1-\zeta_{6})q^{5}-2q^{7}+2q^{11}+(1-\zeta_{6})q^{17}+\cdots$$
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