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Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1040.1.l.a $2$ $0.519$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-65})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta q^{3}-q^{5}+q^{9}-\beta q^{11}+q^{13}+\cdots$$
1040.1.l.b $2$ $0.519$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-65})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta q^{3}+q^{5}+q^{9}+\beta q^{11}-q^{13}+\cdots$$
1040.1.bf.a $2$ $0.519$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{5}-iq^{9}-iq^{13}+(-1+i)q^{17}+\cdots$$
1040.1.cb.a $4$ $0.519$ $$\Q(\zeta_{8})$$ None $$\Q(\sqrt{65})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$$
1040.1.ce.a $2$ $0.519$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-q^{5}-iq^{9}+q^{13}+(1-i)q^{17}+q^{25}+\cdots$$
1040.1.cx.a $2$ $0.519$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}-\zeta_{6}q^{13}+(1+\zeta_{6}+\cdots)q^{17}+\cdots$$
1040.1.cx.b $2$ $0.519$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-1+\cdots)q^{17}+\cdots$$
1040.1.ea.a $4$ $0.519$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{12}^{4}q^{5}-\zeta_{12}q^{9}-\zeta_{12}^{2}q^{13}+\cdots$$
1040.1.ez.a $4$ $0.519$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}-\zeta_{12}q^{13}+(-\zeta_{12}^{3}+\cdots)q^{17}+\cdots$$
1040.2.a.a $1$ $8.304$ $$\Q$$ None None $$0$$ $$-2$$ $$-1$$ $$-2$$ $-$ $$q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$$
1040.2.a.b $1$ $8.304$ $$\Q$$ None None $$0$$ $$-2$$ $$-1$$ $$4$$ $-$ $$q-2q^{3}-q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots$$
1040.2.a.c $1$ $8.304$ $$\Q$$ None None $$0$$ $$-2$$ $$1$$ $$0$$ $+$ $$q-2q^{3}+q^{5}+q^{9}-2q^{11}+q^{13}+\cdots$$
1040.2.a.d $1$ $8.304$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$0$$ $+$ $$q-q^{5}-3q^{9}+4q^{11}-q^{13}-6q^{17}+\cdots$$
1040.2.a.e $1$ $8.304$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$0$$ $-$ $$q+q^{5}-3q^{9}+q^{13}+2q^{17}+8q^{19}+\cdots$$
1040.2.a.f $1$ $8.304$ $$\Q$$ None None $$0$$ $$2$$ $$-1$$ $$4$$ $-$ $$q+2q^{3}-q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots$$
1040.2.a.g $1$ $8.304$ $$\Q$$ None None $$0$$ $$2$$ $$1$$ $$4$$ $-$ $$q+2q^{3}+q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots$$
1040.2.a.h $2$ $8.304$ $$\Q(\sqrt{3})$$ None None $$0$$ $$-2$$ $$-2$$ $$-4$$ $+$ $$q+(-1+\beta )q^{3}-q^{5}-2q^{7}+(1-2\beta )q^{9}+\cdots$$
1040.2.a.i $2$ $8.304$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-2$$ $$-2$$ $$0$$ $+$ $$q+(-1-\beta )q^{3}-q^{5}+(3+2\beta )q^{9}+(-3+\cdots)q^{11}+\cdots$$
1040.2.a.j $2$ $8.304$ $$\Q(\sqrt{2})$$ None None $$0$$ $$0$$ $$2$$ $$-4$$ $+$ $$q+\beta q^{3}+q^{5}+(-2-2\beta )q^{7}-q^{9}+\cdots$$
1040.2.a.k $2$ $8.304$ $$\Q(\sqrt{6})$$ None None $$0$$ $$0$$ $$2$$ $$-4$$ $-$ $$q+\beta q^{3}+q^{5}-2q^{7}+3q^{9}+(2+\beta )q^{11}+\cdots$$
1040.2.a.l $2$ $8.304$ $$\Q(\sqrt{3})$$ None None $$0$$ $$2$$ $$-2$$ $$0$$ $-$ $$q+(1+\beta )q^{3}-q^{5}+2\beta q^{7}+(1+2\beta )q^{9}+\cdots$$
1040.2.a.m $2$ $8.304$ $$\Q(\sqrt{3})$$ None None $$0$$ $$2$$ $$-2$$ $$0$$ $-$ $$q+(1+\beta )q^{3}-q^{5}-2\beta q^{7}+(1+2\beta )q^{9}+\cdots$$
1040.2.a.n $2$ $8.304$ $$\Q(\sqrt{2})$$ None None $$0$$ $$4$$ $$2$$ $$4$$ $-$ $$q+(2+\beta )q^{3}+q^{5}+2q^{7}+(3+4\beta )q^{9}+\cdots$$
1040.2.a.o $3$ $8.304$ 3.3.564.1 None None $$0$$ $$-2$$ $$3$$ $$2$$ $-$ $$q+(-1-\beta _{2})q^{3}+q^{5}+(1+\beta _{1})q^{7}+\cdots$$
1040.2.d.a $2$ $8.304$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-i)q^{5}-4iq^{7}+3q^{9}+2q^{11}+\cdots$$
1040.2.d.b $6$ $8.304$ 6.0.3534400.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{4})q^{3}+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots$$
1040.2.d.c $6$ $8.304$ 6.0.350464.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$$
1040.2.d.d $6$ $8.304$ 6.0.350464.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$$
1040.2.d.e $6$ $8.304$ 6.0.350464.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}+\beta _{4})q^{3}+(\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$$
1040.2.d.f $10$ $8.304$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\beta _{9}q^{3}+\beta _{2}q^{5}-\beta _{4}q^{7}+(-4-\beta _{5}+\cdots)q^{9}+\cdots$$
1040.2.f.a $2$ $8.304$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1-i)q^{5}-q^{9}+iq^{11}+\cdots$$
1040.2.f.b $2$ $8.304$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1+i)q^{5}-q^{9}-iq^{11}+(-3+\cdots)q^{13}+\cdots$$
1040.2.f.c $4$ $8.304$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$0$$ $$-3$$ $$2$$ $$q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$$
1040.2.f.d $4$ $8.304$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$0$$ $$3$$ $$-2$$ $$q-\beta _{2}q^{3}+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$$
1040.2.f.e $8$ $8.304$ 8.0.$$\cdots$$.3 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{4}q^{5}+(-\beta _{4}+\beta _{7})q^{7}+\cdots$$
1040.2.f.f $10$ $8.304$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$0$$ $$-3$$ $$-2$$ $$q-\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$$
1040.2.f.g $10$ $8.304$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$0$$ $$3$$ $$2$$ $$q-\beta _{3}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$$
1040.2.k.a $2$ $8.304$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-2q^{3}-iq^{5}+q^{9}+(2+3i)q^{13}+\cdots$$
1040.2.k.b $6$ $8.304$ 6.0.350464.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots$$
1040.2.k.c $6$ $8.304$ 6.0.9144576.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots$$
1040.2.k.d $6$ $8.304$ 6.0.5089536.1 None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\beta _{1})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$$
1040.2.k.e $8$ $8.304$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$$
1040.2.q.a $2$ $8.304$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$-2$$ $$3$$ $$q+(-3+3\zeta_{6})q^{3}-q^{5}+3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$$
1040.2.q.b $2$ $8.304$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$2$$ $$3$$ $$q+(-3+3\zeta_{6})q^{3}+q^{5}+3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$$
1040.2.q.c $2$ $8.304$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-2$$ $$-2$$ $$-1$$ $$q+(-2+2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$$
1040.2.q.d $2$ $8.304$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-2$$ $$-3$$ $$q+(-1+\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$$
1040.2.q.e $2$ $8.304$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-2$$ $$-3$$ $$q+(-1+\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$$
1040.2.q.f $2$ $8.304$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-2$$ $$5$$ $$q+(-1+\zeta_{6})q^{3}-q^{5}+5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$$
1040.2.q.g $2$ $8.304$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$2$$ $$-3$$ $$q+(-1+\zeta_{6})q^{3}+q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$$
1040.2.q.h $2$ $8.304$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$2$$ $$-3$$ $$q+q^{5}-3\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-3+3\zeta_{6})q^{11}+\cdots$$
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