## Results (displaying matches 1-50 of 291) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
768.1.e.a $$1$$ $$0.383$$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{6})$$ $$0$$ $$-1$$ $$0$$ $$0$$ $$q-q^{3}+q^{9}+2q^{19}+q^{25}-q^{27}+\cdots$$
768.1.e.b $$1$$ $$0.383$$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{6})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q+q^{3}+q^{9}-2q^{19}+q^{25}+q^{27}+\cdots$$
768.1.e.c $$2$$ $$0.383$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-iq^{11}+q^{25}+iq^{27}+\cdots$$
768.1.i.a $$4$$ $$0.383$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{3}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots$$
768.1.i.b $$4$$ $$0.383$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots$$
768.2.a.a $$1$$ $$6.133$$ $$\Q$$ None None $$0$$ $$-1$$ $$-2$$ $$2$$ $$+$$ $$q-q^{3}-2q^{5}+2q^{7}+q^{9}-4q^{13}+\cdots$$
768.2.a.b $$1$$ $$6.133$$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$-4$$ $$+$$ $$q-q^{3}-4q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$$
768.2.a.c $$1$$ $$6.133$$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$4$$ $$-$$ $$q-q^{3}+4q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots$$
768.2.a.d $$1$$ $$6.133$$ $$\Q$$ None None $$0$$ $$-1$$ $$2$$ $$-2$$ $$-$$ $$q-q^{3}+2q^{5}-2q^{7}+q^{9}+4q^{13}+\cdots$$
768.2.a.e $$1$$ $$6.133$$ $$\Q$$ None None $$0$$ $$1$$ $$-2$$ $$-2$$ $$+$$ $$q+q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{13}+\cdots$$
768.2.a.f $$1$$ $$6.133$$ $$\Q$$ None None $$0$$ $$1$$ $$0$$ $$-4$$ $$+$$ $$q+q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$$
768.2.a.g $$1$$ $$6.133$$ $$\Q$$ None None $$0$$ $$1$$ $$0$$ $$4$$ $$-$$ $$q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$$
768.2.a.h $$1$$ $$6.133$$ $$\Q$$ None None $$0$$ $$1$$ $$2$$ $$2$$ $$-$$ $$q+q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{13}+\cdots$$
768.2.a.i $$2$$ $$6.133$$ $$\Q(\sqrt{2})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$+$$ $$q-q^{3}+\beta q^{5}-\beta q^{7}+q^{9}-4q^{11}+\cdots$$
768.2.a.j $$2$$ $$6.133$$ $$\Q(\sqrt{3})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$-$$ $$q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots$$
768.2.a.k $$2$$ $$6.133$$ $$\Q(\sqrt{3})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$-$$ $$q+q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots$$
768.2.a.l $$2$$ $$6.133$$ $$\Q(\sqrt{2})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$-$$ $$q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+4q^{11}+\cdots$$
768.2.c.a $$2$$ $$6.133$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-1+\beta )q^{3}+2\beta q^{5}-2\beta q^{7}+(-1+\cdots)q^{9}+\cdots$$
768.2.c.b $$2$$ $$6.133$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-1-\beta )q^{3}+2\beta q^{5}-2\beta q^{7}+(-1+\cdots)q^{9}+\cdots$$
768.2.c.c $$2$$ $$6.133$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-1-\beta )q^{3}+(-1+2\beta )q^{9}+6q^{11}+\cdots$$
768.2.c.d $$2$$ $$6.133$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta )q^{3}+(-1+2\beta )q^{9}-6q^{11}+\cdots$$
768.2.c.e $$2$$ $$6.133$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1-\beta )q^{3}+2\beta q^{5}+2\beta q^{7}+(-1+\cdots)q^{9}+\cdots$$
768.2.c.f $$2$$ $$6.133$$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta )q^{3}+2\beta q^{5}+2\beta q^{7}+(-1+\cdots)q^{9}+\cdots$$
768.2.c.g $$4$$ $$6.133$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}-3q^{9}+\zeta_{12}^{3}q^{13}+\cdots$$
768.2.c.h $$4$$ $$6.133$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{3}+(1+\zeta_{8}^{3})q^{9}+(\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{11}+\cdots$$
768.2.c.i $$4$$ $$6.133$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+3q^{9}+\cdots$$
768.2.c.j $$4$$ $$6.133$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}-\beta _{1}q^{5}-\beta _{3}q^{7}+3q^{9}-2\beta _{2}q^{11}+\cdots$$
768.2.d.a $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+iq^{3}+2iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots$$
768.2.d.b $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+iq^{3}-2q^{7}-q^{9}-4iq^{11}-6iq^{13}+\cdots$$
768.2.d.c $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-iq^{3}+4iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots$$
768.2.d.d $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2iq^{5}-q^{9}+4iq^{11}-2iq^{13}+\cdots$$
768.2.d.e $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2iq^{5}-q^{9}-4iq^{11}-2iq^{13}+\cdots$$
768.2.d.f $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+iq^{3}+4iq^{5}+2q^{7}-q^{9}+4iq^{11}+\cdots$$
768.2.d.g $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q-iq^{3}+2q^{7}-q^{9}+4iq^{11}-6iq^{13}+\cdots$$
768.2.d.h $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$8$$ $$q-iq^{3}+2iq^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots$$
768.2.f.a $$4$$ $$6.133$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\zeta_{8}^{2})q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}q^{7}+\cdots$$
768.2.f.b $$4$$ $$6.133$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$-2$$ $$-4$$ $$0$$ $$q+(-1+\beta _{3})q^{3}+(-2-\beta _{1}+\beta _{3})q^{5}+\cdots$$
768.2.f.c $$4$$ $$6.133$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$-2$$ $$4$$ $$0$$ $$q+(-1-\beta _{1})q^{3}+(2+\beta _{1}-\beta _{3})q^{5}+\cdots$$
768.2.f.d $$4$$ $$6.133$$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{7}+3q^{9}+\zeta_{12}^{3}q^{13}+\cdots$$
768.2.f.e $$4$$ $$6.133$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$2$$ $$-4$$ $$0$$ $$q+(1-\beta _{3})q^{3}+(-2-\beta _{1}+\beta _{3})q^{5}+\cdots$$
768.2.f.f $$4$$ $$6.133$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$2$$ $$4$$ $$0$$ $$q+(1+\beta _{1})q^{3}+(2+\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$
768.2.f.g $$4$$ $$6.133$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\zeta_{8}^{2})q^{3}-\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+(-1+\cdots)q^{9}+\cdots$$
768.2.j.a $$4$$ $$6.133$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\zeta_{8}q^{3}+(-2+2\zeta_{8}^{2})q^{5}+(3\zeta_{8}+3\zeta_{8}^{3})q^{7}+\cdots$$
768.2.j.b $$4$$ $$6.133$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{3}q^{3}+(\zeta_{8}+\zeta_{8}^{3})q^{7}-\zeta_{8}^{2}q^{9}+\cdots$$
768.2.j.c $$4$$ $$6.133$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{3}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}-\zeta_{8}^{2}q^{9}+\cdots$$
768.2.j.d $$4$$ $$6.133$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\zeta_{8}q^{3}+(2-2\zeta_{8}^{2})q^{5}+(3\zeta_{8}+3\zeta_{8}^{3})q^{7}+\cdots$$
768.2.j.e $$8$$ $$6.133$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\zeta_{24}q^{3}+(-1+\zeta_{24}^{2}-\zeta_{24}^{6})q^{5}+\cdots$$
768.2.j.f $$8$$ $$6.133$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$8$$ $$0$$ $$q-\zeta_{24}q^{3}+(1-\zeta_{24}^{2}+\zeta_{24}^{6})q^{5}+\cdots$$
768.2.k.a $$4$$ $$6.133$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{5}+\cdots$$
768.2.k.b $$4$$ $$6.133$$ $$\Q(\zeta_{8})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{5}+\cdots$$
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