## Results (displaying all 40 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1175.1.b.a $$2$$ $$0.586$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-47})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}+q^{6}-iq^{7}-iq^{8}+\cdots$$
1175.1.b.b $$4$$ $$0.586$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-47})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots$$
1175.1.b.c $$8$$ $$0.586$$ 8.0.324000000.1 $$\Q(\sqrt{-47})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{3}+\beta _{5})q^{2}+(\beta _{3}+\beta _{7})q^{3}+\cdots$$
1175.1.d.a $$1$$ $$0.586$$ $$\Q$$ $$\Q(\sqrt{-47})$$ None $$-1$$ $$-1$$ $$0$$ $$-1$$ $$q-q^{2}-q^{3}+q^{6}-q^{7}+q^{8}+q^{14}+\cdots$$
1175.1.d.b $$1$$ $$0.586$$ $$\Q$$ $$\Q(\sqrt{-47})$$ None $$1$$ $$1$$ $$0$$ $$1$$ $$q+q^{2}+q^{3}+q^{6}+q^{7}-q^{8}+q^{14}+\cdots$$
1175.1.d.c $$2$$ $$0.586$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-47})$$ None $$1$$ $$1$$ $$0$$ $$1$$ $$q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$$
1175.1.d.d $$4$$ $$0.586$$ $$\Q(\zeta_{15})^+$$ $$\Q(\sqrt{-47})$$ None $$-1$$ $$-1$$ $$0$$ $$-1$$ $$q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
1175.1.d.e $$4$$ $$0.586$$ $$\Q(\zeta_{15})^+$$ $$\Q(\sqrt{-47})$$ None $$1$$ $$1$$ $$0$$ $$1$$ $$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$$
1175.2.a.a $$1$$ $$9.382$$ $$\Q$$ None None $$-2$$ $$-2$$ $$0$$ $$2$$ $$+$$ $$q-2q^{2}-2q^{3}+2q^{4}+4q^{6}+2q^{7}+\cdots$$
1175.2.a.b $$1$$ $$9.382$$ $$\Q$$ None None $$1$$ $$1$$ $$0$$ $$-1$$ $$+$$ $$q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots$$
1175.2.a.c $$1$$ $$9.382$$ $$\Q$$ None None $$1$$ $$1$$ $$0$$ $$-1$$ $$+$$ $$q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots$$
1175.2.a.d $$3$$ $$9.382$$ $$\Q(\zeta_{18})^+$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{6}+\cdots$$
1175.2.a.e $$3$$ $$9.382$$ $$\Q(\zeta_{18})^+$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{6}+\cdots$$
1175.2.a.f $$4$$ $$9.382$$ 4.4.1957.1 None None $$-1$$ $$0$$ $$0$$ $$-4$$ $$+$$ $$q-\beta _{3}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
1175.2.a.g $$5$$ $$9.382$$ 5.5.106069.1 None None $$4$$ $$5$$ $$0$$ $$5$$ $$-$$ $$q+(1+\beta _{4})q^{2}+(1-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$$
1175.2.a.h $$7$$ $$9.382$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$-1$$ $$-1$$ $$0$$ $$3$$ $$-$$ $$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{6}+\cdots$$
1175.2.a.i $$11$$ $$9.382$$ $$\mathbb{Q}[x]/(x^{11} - \cdots)$$ None None $$-4$$ $$-4$$ $$0$$ $$-12$$ $$+$$ $$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$$
1175.2.a.j $$11$$ $$9.382$$ $$\mathbb{Q}[x]/(x^{11} - \cdots)$$ None None $$4$$ $$4$$ $$0$$ $$12$$ $$-$$ $$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$$
1175.2.a.k $$13$$ $$9.382$$ $$\mathbb{Q}[x]/(x^{13} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(\beta _{5}+\cdots)q^{6}+\cdots$$
1175.2.a.l $$13$$ $$9.382$$ $$\mathbb{Q}[x]/(x^{13} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(\beta _{5}+\cdots)q^{6}+\cdots$$
1175.2.c.a $$2$$ $$9.382$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-2iq^{3}-2q^{4}+4q^{6}-2iq^{7}+\cdots$$
1175.2.c.b $$2$$ $$9.382$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}-iq^{7}+3iq^{8}+\cdots$$
1175.2.c.c $$2$$ $$9.382$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}-iq^{7}+3iq^{8}+\cdots$$
1175.2.c.d $$6$$ $$9.382$$ 6.0.419904.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots$$
1175.2.c.e $$8$$ $$9.382$$ 8.0.980441344.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(\beta _{3}-\beta _{7})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
1175.2.c.f $$10$$ $$9.382$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}+\beta _{6})q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1175.2.c.g $$14$$ $$9.382$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-1+\beta _{2})q^{4}+\cdots$$
1175.2.c.h $$26$$ $$9.382$$ None None $$0$$ $$0$$ $$0$$ $$0$$
1175.4.a.a $$3$$ $$69.327$$ 3.3.1101.1 None None $$5$$ $$5$$ $$0$$ $$45$$ $$+$$ $$q+(2+\beta _{2})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots$$
1175.4.a.b $$8$$ $$69.327$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$-3$$ $$-7$$ $$0$$ $$-39$$ $$-$$ $$q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(5+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$
1175.4.a.c $$8$$ $$69.327$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$3$$ $$10$$ $$0$$ $$15$$ $$-$$ $$q+\beta _{1}q^{2}+(2-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$$
1175.4.a.d $$10$$ $$69.327$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$-7$$ $$-8$$ $$0$$ $$-9$$ $$-$$ $$q+(-1+\beta _{1})q^{2}+(-1+\beta _{6})q^{3}+(4+\cdots)q^{4}+\cdots$$
1175.4.a.e $$13$$ $$69.327$$ $$\mathbb{Q}[x]/(x^{13} - \cdots)$$ None None $$3$$ $$10$$ $$0$$ $$19$$ $$+$$ $$q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(4+\beta _{2})q^{4}+\cdots$$
1175.4.a.f $$15$$ $$69.327$$ $$\mathbb{Q}[x]/(x^{15} - \cdots)$$ None None $$-7$$ $$-8$$ $$0$$ $$-13$$ $$+$$ $$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(5+\beta _{2})q^{4}+\cdots$$
1175.4.a.g $$18$$ $$69.327$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$-1$$ $$-7$$ $$0$$ $$-6$$ $$-$$ $$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$$
1175.4.a.h $$18$$ $$69.327$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$1$$ $$7$$ $$0$$ $$6$$ $$-$$ $$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$$
1175.4.a.i $$28$$ $$69.327$$ None None $$-1$$ $$-7$$ $$0$$ $$-6$$ $$+$$
1175.4.a.j $$28$$ $$69.327$$ None None $$1$$ $$7$$ $$0$$ $$6$$ $$+$$
1175.4.a.k $$35$$ $$69.327$$ None None $$-8$$ $$-12$$ $$0$$ $$-84$$ $$-$$
1175.4.a.l $$35$$ $$69.327$$ None None $$8$$ $$12$$ $$0$$ $$84$$ $$+$$