## Results (1-50 of 262 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
175.1.c.a $$2$$ $$0.087$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{7}-iq^{8}-q^{9}-q^{11}+\cdots$$
175.1.d.a $$1$$ $$0.087$$ $$\Q$$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$1$$ $$q-q^{2}+q^{7}+q^{8}+q^{9}-q^{11}-q^{14}+\cdots$$
175.1.d.b $$1$$ $$0.087$$ $$\Q$$ $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$-1$$ $$q+q^{2}-q^{7}-q^{8}+q^{9}-q^{11}-q^{14}+\cdots$$
175.2.a.a $$1$$ $$1.397$$ $$\Q$$ None None $$-2$$ $$-1$$ $$0$$ $$1$$ $$+$$ $$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}-2q^{9}+\cdots$$
175.2.a.b $$1$$ $$1.397$$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$-1$$ $$+$$ $$q-q^{3}-2q^{4}-q^{7}-2q^{9}-3q^{11}+\cdots$$
175.2.a.c $$1$$ $$1.397$$ $$\Q$$ None None $$2$$ $$1$$ $$0$$ $$-1$$ $$-$$ $$q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}-2q^{9}+\cdots$$
175.2.a.d $$2$$ $$1.397$$ $$\Q(\sqrt{5})$$ None None $$-1$$ $$2$$ $$0$$ $$-2$$ $$-$$ $$q-\beta q^{2}+(2-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$$
175.2.a.e $$2$$ $$1.397$$ $$\Q(\sqrt{5})$$ None None $$1$$ $$-2$$ $$0$$ $$2$$ $$-$$ $$q+\beta q^{2}+(-2+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$$
175.2.a.f $$2$$ $$1.397$$ $$\Q(\sqrt{17})$$ None None $$1$$ $$1$$ $$0$$ $$2$$ $$-$$ $$q+\beta q^{2}+(1-\beta )q^{3}+(2+\beta )q^{4}-4q^{6}+\cdots$$
175.2.b.a $$2$$ $$1.397$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2q^{4}-iq^{7}+2q^{9}-3q^{11}+\cdots$$
175.2.b.b $$4$$ $$1.397$$ $$\Q(i, \sqrt{17})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots$$
175.2.b.c $$4$$ $$1.397$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2\beta _{1}-2\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$$
175.2.e.a $$2$$ $$1.397$$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$1$$ $$0$$ $$-1$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
175.2.e.b $$2$$ $$1.397$$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$-1$$ $$0$$ $$1$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
175.2.e.c $$4$$ $$1.397$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$2$$ $$2$$ $$0$$ $$-2$$ $$q+(1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots$$
175.2.e.d $$6$$ $$1.397$$ 6.0.1783323.2 None None $$-1$$ $$3$$ $$0$$ $$2$$ $$q-\beta _{1}q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots$$
175.2.e.e $$6$$ $$1.397$$ 6.0.1783323.2 None None $$1$$ $$-3$$ $$0$$ $$-2$$ $$q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots$$
175.2.f.a $$4$$ $$1.397$$ $$\Q(i, \sqrt{14})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-2\beta _{2}q^{4}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$$
175.2.f.b $$4$$ $$1.397$$ $$\Q(i, \sqrt{14})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+5\beta _{2}q^{4}-\beta _{1}q^{7}+3\beta _{3}q^{8}+\cdots$$
175.2.f.c $$4$$ $$1.397$$ $$\Q(i, \sqrt{10})$$ None None $$4$$ $$0$$ $$0$$ $$-4$$ $$q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{6}+\cdots$$
175.2.f.d $$8$$ $$1.397$$ 8.0.$$\cdots$$.1 $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(\beta _{1}+\beta _{3})q^{7}+\cdots$$
175.2.h.a $$4$$ $$1.397$$ $$\Q(\zeta_{10})$$ None None $$-5$$ $$-4$$ $$-5$$ $$-4$$ $$q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
175.2.h.b $$28$$ $$1.397$$ None None $$6$$ $$4$$ $$8$$ $$-28$$
175.2.h.c $$32$$ $$1.397$$ None None $$-3$$ $$-4$$ $$1$$ $$32$$
175.2.k.a $$8$$ $$1.397$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{3}q^{2}-\zeta_{24}^{4}q^{3}+(1-\zeta_{24}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots$$
175.2.k.b $$12$$ $$1.397$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{10}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots$$
175.2.n.a $$56$$ $$1.397$$ None None $$0$$ $$0$$ $$-6$$ $$0$$
175.2.o.a $$4$$ $$1.397$$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$4$$ $$0$$ $$10$$ $$q+(-1+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots$$
175.2.o.b $$4$$ $$1.397$$ $$\Q(\zeta_{12})$$ None None $$4$$ $$2$$ $$0$$ $$0$$ $$q+(1-\zeta_{12})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$$
175.2.o.c $$8$$ $$1.397$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{7}q^{2}+(-2\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots$$
175.2.o.d $$24$$ $$1.397$$ None None $$0$$ $$0$$ $$0$$ $$0$$
175.2.q.a $$144$$ $$1.397$$ None None $$-3$$ $$-3$$ $$-3$$ $$-22$$
175.2.s.a $$144$$ $$1.397$$ None None $$-16$$ $$0$$ $$0$$ $$-14$$
175.2.t.a $$144$$ $$1.397$$ None None $$-5$$ $$-5$$ $$-3$$ $$0$$
175.2.x.a $$288$$ $$1.397$$ None None $$-8$$ $$-24$$ $$-30$$ $$-10$$
175.3.c.a $$2$$ $$4.768$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{2}-5q^{4}+7iq^{7}-3iq^{8}-9q^{9}+\cdots$$
175.3.c.b $$4$$ $$4.768$$ $$\Q(i, \sqrt{21})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{2})q^{2}+(-5+3\beta _{3})q^{4}+7\beta _{2}q^{7}+\cdots$$
175.3.c.c $$4$$ $$4.768$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{6}+(-\beta _{1}+3\beta _{3})q^{7}+\cdots$$
175.3.c.d $$4$$ $$4.768$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+3q^{4}+\beta _{2}q^{6}-7\beta _{1}q^{7}+\cdots$$
175.3.c.e $$8$$ $$4.768$$ 8.0.$$\cdots$$.11 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{3}q^{3}+(-3+2\beta _{1})q^{4}+\cdots$$
175.3.d.a $$1$$ $$4.768$$ $$\Q$$ $$\Q(\sqrt{-7})$$ None $$3$$ $$0$$ $$0$$ $$7$$ $$q+3q^{2}+5q^{4}+7q^{7}+3q^{8}+9q^{9}+\cdots$$
175.3.d.b $$2$$ $$4.768$$ $$\Q(\sqrt{-10})$$ None None $$-6$$ $$0$$ $$0$$ $$6$$ $$q-3q^{2}+\beta q^{3}+5q^{4}-3\beta q^{6}+(3+2\beta )q^{7}+\cdots$$
175.3.d.c $$2$$ $$4.768$$ $$\Q(\sqrt{-5})$$ None None $$-4$$ $$0$$ $$0$$ $$4$$ $$q-2q^{2}+\beta q^{3}-2\beta q^{6}+(2-3\beta )q^{7}+\cdots$$
175.3.d.d $$2$$ $$4.768$$ $$\Q(\sqrt{21})$$ $$\Q(\sqrt{-7})$$ None $$-3$$ $$0$$ $$0$$ $$14$$ $$q+(-1-\beta )q^{2}+(2+3\beta )q^{4}+7q^{7}+\cdots$$
175.3.d.e $$2$$ $$4.768$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-4q^{4}-7iq^{7}+8q^{9}-13q^{11}+\cdots$$
175.3.d.f $$2$$ $$4.768$$ $$\Q(\sqrt{-5})$$ None None $$2$$ $$0$$ $$0$$ $$-14$$ $$q+q^{2}+\beta q^{3}-3q^{4}+\beta q^{6}-7q^{7}+\cdots$$
175.3.d.g $$2$$ $$4.768$$ $$\Q(\sqrt{21})$$ $$\Q(\sqrt{-7})$$ None $$3$$ $$0$$ $$0$$ $$-14$$ $$q+(1+\beta )q^{2}+(2+3\beta )q^{4}-7q^{7}+(13+\cdots)q^{8}+\cdots$$
175.3.d.h $$2$$ $$4.768$$ $$\Q(\sqrt{-10})$$ None None $$6$$ $$0$$ $$0$$ $$-6$$ $$q+3q^{2}+\beta q^{3}+5q^{4}+3\beta q^{6}+(-3+\cdots)q^{7}+\cdots$$
175.3.d.i $$4$$ $$4.768$$ 4.0.1163520.6 None None $$-4$$ $$0$$ $$0$$ $$4$$ $$q+(-1+\beta _{3})q^{2}-\beta _{1}q^{3}+(3-2\beta _{3})q^{4}+\cdots$$
175.3.d.j $$4$$ $$4.768$$ 4.0.1163520.6 None None $$4$$ $$0$$ $$0$$ $$-4$$ $$q+(1-\beta _{3})q^{2}-\beta _{1}q^{3}+(3-2\beta _{3})q^{4}+\cdots$$