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Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3240.1.p.a $$1$$ $$1.617$$ $$\Q$$ $$\Q(\sqrt{-10})$$ None $$-1$$ $$0$$ $$-1$$ $$-1$$ $$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$$
3240.1.p.b $$1$$ $$1.617$$ $$\Q$$ $$\Q(\sqrt{-10})$$ None $$-1$$ $$0$$ $$-1$$ $$1$$ $$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$$
3240.1.p.c $$1$$ $$1.617$$ $$\Q$$ $$\Q(\sqrt{-10})$$ None $$1$$ $$0$$ $$1$$ $$-1$$ $$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$$
3240.1.p.d $$1$$ $$1.617$$ $$\Q$$ $$\Q(\sqrt{-10})$$ None $$1$$ $$0$$ $$1$$ $$1$$ $$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$$
3240.1.p.e $$2$$ $$1.617$$ $$\Q(\sqrt{3})$$ $$\Q(\sqrt{-10})$$ None $$-2$$ $$0$$ $$2$$ $$0$$ $$q-q^{2}+q^{4}+q^{5}-\beta q^{7}-q^{8}-q^{10}+\cdots$$
3240.1.p.f $$2$$ $$1.617$$ $$\Q(\sqrt{3})$$ $$\Q(\sqrt{-10})$$ None $$2$$ $$0$$ $$-2$$ $$0$$ $$q+q^{2}+q^{4}-q^{5}-\beta q^{7}+q^{8}-q^{10}+\cdots$$
3240.1.v.a $$2$$ $$1.617$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-q^{5}+q^{11}+iq^{19}+(-1-i)q^{23}+\cdots$$
3240.1.v.b $$2$$ $$1.617$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+q^{5}-q^{11}+iq^{19}+(1+i)q^{23}+\cdots$$
3240.1.z.a $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-15})$$ None $$-2$$ $$0$$ $$-1$$ $$0$$ $$q-q^{2}+q^{4}+\zeta_{6}^{2}q^{5}-q^{8}-\zeta_{6}^{2}q^{10}+\cdots$$
3240.1.z.b $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-10})$$ None $$-1$$ $$0$$ $$-1$$ $$-1$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$$
3240.1.z.c $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-10})$$ None $$-1$$ $$0$$ $$-1$$ $$1$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$$
3240.1.z.d $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-15})$$, $$\Q(\sqrt{-10})$$ $$\Q(\sqrt{6})$$ $$-1$$ $$0$$ $$1$$ $$0$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots$$
3240.1.z.e $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-15})$$ None $$-1$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots$$
3240.1.z.f $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-15})$$, $$\Q(\sqrt{-10})$$ $$\Q(\sqrt{6})$$ $$1$$ $$0$$ $$-1$$ $$0$$ $$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots$$
3240.1.z.g $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-15})$$ None $$1$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots$$
3240.1.z.h $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-10})$$ None $$1$$ $$0$$ $$1$$ $$-1$$ $$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$$
3240.1.z.i $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-10})$$ None $$1$$ $$0$$ $$1$$ $$1$$ $$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$$
3240.1.z.j $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-15})$$ None $$2$$ $$0$$ $$1$$ $$0$$ $$q+q^{2}+q^{4}-\zeta_{6}^{2}q^{5}+q^{8}-\zeta_{6}^{2}q^{10}+\cdots$$
3240.1.z.k $$4$$ $$1.617$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-10})$$ None $$-2$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{5}+\cdots$$
3240.1.z.l $$4$$ $$1.617$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-10})$$ None $$2$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\cdots$$
3240.1.bh.a $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-30})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+q^{8}+\cdots$$
3240.1.bh.b $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-30})$$ None $$-1$$ $$0$$ $$1$$ $$0$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots$$
3240.1.bh.c $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-30})$$ None $$1$$ $$0$$ $$-1$$ $$0$$ $$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots$$
3240.1.bh.d $$2$$ $$1.617$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-30})$$ None $$1$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-q^{8}+\cdots$$
3240.1.bh.e $$4$$ $$1.617$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$$
3240.1.bh.f $$4$$ $$1.617$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$-6$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+(-1+\cdots)q^{7}+\cdots$$
3240.1.bh.g $$4$$ $$1.617$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots$$
3240.1.bh.h $$4$$ $$1.617$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-15})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{10})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$$
3240.1.bh.i $$4$$ $$1.617$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$6$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}+(1+\cdots)q^{7}+\cdots$$
3240.1.bn.a $$8$$ $$1.617$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{7}q^{5}-\zeta_{24}^{2}q^{7}+(\zeta_{24}^{5}-\zeta_{24}^{11}+\cdots)q^{11}+\cdots$$
3240.1.bq.a $$4$$ $$1.617$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{12}^{2}q^{5}-\zeta_{12}^{4}q^{11}+\zeta_{12}^{3}q^{19}+\cdots$$
3240.1.bq.b $$4$$ $$1.617$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}^{2}q^{5}+\zeta_{12}^{4}q^{11}+\zeta_{12}^{3}q^{19}+\cdots$$
3240.1.bv.a $$8$$ $$1.617$$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}-\zeta_{24}q^{5}+(-1+\cdots)q^{7}+\cdots$$
3240.1.bv.b $$8$$ $$1.617$$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}-\zeta_{24}^{9}q^{5}+\cdots$$
3240.1.bv.c $$8$$ $$1.617$$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}-\zeta_{24}^{5}q^{5}+\cdots$$
3240.2.a.a $$1$$ $$25.872$$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-2$$ $$+$$ $$q-q^{5}-2q^{7}+3q^{11}-2q^{17}+q^{19}+\cdots$$
3240.2.a.b $$1$$ $$25.872$$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$0$$ $$+$$ $$q-q^{5}-5q^{11}+3q^{17}+5q^{19}+6q^{23}+\cdots$$
3240.2.a.c $$1$$ $$25.872$$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$0$$ $$+$$ $$q-q^{5}+q^{11}-7q^{19}+6q^{23}+q^{25}+\cdots$$
3240.2.a.d $$1$$ $$25.872$$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-2$$ $$+$$ $$q+q^{5}-2q^{7}-3q^{11}+2q^{17}+q^{19}+\cdots$$
3240.2.a.e $$1$$ $$25.872$$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$0$$ $$+$$ $$q+q^{5}-q^{11}-7q^{19}-6q^{23}+q^{25}+\cdots$$
3240.2.a.f $$1$$ $$25.872$$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$0$$ $$-$$ $$q+q^{5}+5q^{11}-3q^{17}+5q^{19}-6q^{23}+\cdots$$
3240.2.a.g $$2$$ $$25.872$$ $$\Q(\sqrt{3})$$ None None $$0$$ $$0$$ $$-2$$ $$-2$$ $$+$$ $$q-q^{5}+(-1+\beta )q^{7}+(2+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$$
3240.2.a.h $$2$$ $$25.872$$ $$\Q(\sqrt{57})$$ None None $$0$$ $$0$$ $$-2$$ $$1$$ $$-$$ $$q-q^{5}+\beta q^{7}+(-3+\beta )q^{11}+(2+\beta )q^{13}+\cdots$$
3240.2.a.i $$2$$ $$25.872$$ $$\Q(\sqrt{33})$$ None None $$0$$ $$0$$ $$-2$$ $$1$$ $$-$$ $$q-q^{5}+\beta q^{7}+(1-\beta )q^{11}-\beta q^{13}+\cdots$$
3240.2.a.j $$2$$ $$25.872$$ $$\Q(\sqrt{6})$$ None None $$0$$ $$0$$ $$-2$$ $$2$$ $$+$$ $$q-q^{5}+(1+\beta )q^{7}-2q^{17}+(-2-2\beta )q^{19}+\cdots$$
3240.2.a.k $$2$$ $$25.872$$ $$\Q(\sqrt{3})$$ None None $$0$$ $$0$$ $$-2$$ $$4$$ $$-$$ $$q-q^{5}+(2+\beta )q^{7}+(2+2\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$$
3240.2.a.l $$2$$ $$25.872$$ $$\Q(\sqrt{3})$$ None None $$0$$ $$0$$ $$2$$ $$-2$$ $$+$$ $$q+q^{5}+(-1+\beta )q^{7}+(-2-\beta )q^{11}+\cdots$$
3240.2.a.m $$2$$ $$25.872$$ $$\Q(\sqrt{33})$$ None None $$0$$ $$0$$ $$2$$ $$1$$ $$-$$ $$q+q^{5}+\beta q^{7}+(-1+\beta )q^{11}-\beta q^{13}+\cdots$$
3240.2.a.n $$2$$ $$25.872$$ $$\Q(\sqrt{57})$$ None None $$0$$ $$0$$ $$2$$ $$1$$ $$-$$ $$q+q^{5}+\beta q^{7}+(3-\beta )q^{11}+(2+\beta )q^{13}+\cdots$$
3240.2.a.o $$2$$ $$25.872$$ $$\Q(\sqrt{6})$$ None None $$0$$ $$0$$ $$2$$ $$2$$ $$-$$ $$q+q^{5}+(1+\beta )q^{7}+2q^{17}+(-2-2\beta )q^{19}+\cdots$$
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