## Results (34 matches)

Label Dim. $$A$$ Field CM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4100.2.a.a $$2$$ $$32.739$$ $$\Q(\sqrt{13})$$ None $$0$$ $$-2$$ $$0$$ $$3$$ $$+$$ $$q-q^{3}+(1+\beta )q^{7}-2q^{9}+(-3+2\beta )q^{11}+\cdots$$
4100.2.a.b $$2$$ $$32.739$$ $$\Q(\sqrt{5})$$ None $$0$$ $$2$$ $$0$$ $$1$$ $$-$$ $$q+q^{3}+(1-\beta )q^{7}-2q^{9}+(3-4\beta )q^{11}+\cdots$$
4100.2.a.c $$4$$ $$32.739$$ 4.4.25808.1 None $$0$$ $$-2$$ $$0$$ $$0$$ $$-$$ $$q+(\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots$$
4100.2.a.d $$4$$ $$32.739$$ 4.4.13068.1 None $$0$$ $$0$$ $$0$$ $$-1$$ $$+$$ $$q-\beta _{2}q^{3}+\beta _{1}q^{7}+(1-\beta _{1}+\beta _{3})q^{9}+\cdots$$
4100.2.a.e $$4$$ $$32.739$$ $$\Q(\sqrt{5}, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$-$$ $$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+\cdots$$
4100.2.a.f $$6$$ $$32.739$$ 6.6.3356224.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q-\beta _{4}q^{3}-\beta _{3}q^{7}+(-\beta _{1}+\beta _{2})q^{9}+\cdots$$
4100.2.a.g $$7$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None $$0$$ $$-3$$ $$0$$ $$0$$ $$+$$ $$q-\beta _{1}q^{3}+\beta _{4}q^{7}+(\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$$
4100.2.a.h $$7$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None $$0$$ $$-1$$ $$0$$ $$0$$ $$+$$ $$q-\beta _{1}q^{3}-\beta _{5}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$$
4100.2.a.i $$7$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None $$0$$ $$1$$ $$0$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}+\beta _{5}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$$
4100.2.a.j $$7$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}-\beta _{4}q^{7}+(\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$$
4100.2.a.k $$14$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}-\beta _{10}q^{7}+(2+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$$
4100.2.b.a $$2$$ $$32.739$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}-\beta q^{7}+q^{9}-3\beta q^{11}-2\beta q^{17}+\cdots$$
4100.2.b.b $$2$$ $$32.739$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}-\beta q^{7}+q^{9}+3\beta q^{11}-2\beta q^{17}+\cdots$$
4100.2.b.c $$4$$ $$32.739$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots$$
4100.2.b.d $$4$$ $$32.739$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots$$
4100.2.b.e $$4$$ $$32.739$$ 4.0.25088.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{3}q^{7}+\beta _{2}q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots$$
4100.2.b.f $$6$$ $$32.739$$ 6.0.36433296.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}-\beta _{4}q^{7}+(-2-\beta _{3})q^{9}-\beta _{5}q^{11}+\cdots$$
4100.2.b.g $$8$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{3}-\beta _{4}q^{7}+(-1-\beta _{3})q^{9}+\beta _{5}q^{11}+\cdots$$
4100.2.b.h $$10$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{9}q^{7}+(-1+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$$
4100.2.b.i $$10$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{9}q^{7}+(-1+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$$
4100.2.b.j $$16$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{3}+\beta _{11}q^{7}+(-1+\beta _{1})q^{9}+\cdots$$
4100.2.d.a $$4$$ $$32.739$$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots$$
4100.2.d.b $$4$$ $$32.739$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+(\beta _{1}+\beta _{3})q^{7}+2q^{9}+(3+4\beta _{2}+\cdots)q^{11}+\cdots$$
4100.2.d.c $$8$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{4}+\beta _{6})q^{3}+(\beta _{2}-\beta _{4}-\beta _{7})q^{7}+\cdots$$
4100.2.d.d $$8$$ $$32.739$$ 8.0.4569760000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots$$
4100.2.d.e $$8$$ $$32.739$$ 8.0.2732361984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}+\beta _{5}q^{7}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$$
4100.2.d.f $$14$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{11}q^{7}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots$$
4100.2.d.g $$14$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{7}q^{7}+(\beta _{2}+\beta _{3})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$$
4100.2.g.a $$4$$ $$32.739$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$-6$$ $$0$$ $$6$$ $$q+(-2-\beta _{2})q^{3}-3\beta _{2}q^{7}+(2+3\beta _{2}+\cdots)q^{9}+\cdots$$
4100.2.g.b $$4$$ $$32.739$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$6$$ $$0$$ $$-6$$ $$q+(2+\beta _{2})q^{3}+3\beta _{2}q^{7}+(2+3\beta _{2})q^{9}+\cdots$$
4100.2.g.c $$8$$ $$32.739$$ 8.0.629407744.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{5}q^{7}-\beta _{7}q^{9}+(-\beta _{2}-2\beta _{3}+\cdots)q^{11}+\cdots$$
4100.2.g.d $$12$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}-\beta _{8}q^{7}+(2-\beta _{3})q^{9}-\beta _{9}q^{11}+\cdots$$
4100.2.g.e $$16$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{3}-\beta _{7}q^{7}+(1-\beta _{6})q^{9}-\beta _{10}q^{11}+\cdots$$
4100.2.g.f $$20$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{3}q^{7}+(1-\beta _{2})q^{9}+(\beta _{13}+\cdots)q^{11}+\cdots$$