## Results (1-50 of 53 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2023.1.c.a $$1$$ $$1.010$$ $$\Q$$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$-1$$ $$q-q^{2}-q^{7}+q^{8}+q^{9}-2q^{11}+q^{14}+\cdots$$
2023.1.c.b $$1$$ $$1.010$$ $$\Q$$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$1$$ $$q-q^{2}+q^{7}+q^{8}+q^{9}+2q^{11}-q^{14}+\cdots$$
2023.1.c.c $$3$$ $$1.010$$ $$\Q(\zeta_{18})^+$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$-3$$ $$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots$$
2023.1.c.d $$3$$ $$1.010$$ $$\Q(\zeta_{18})^+$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$3$$ $$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots$$
2023.1.c.e $$4$$ $$1.010$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-119})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$$
2023.1.d.a $$2$$ $$1.010$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-7})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-iq^{7}-q^{8}-q^{9}-iq^{11}-iq^{14}+\cdots$$
2023.1.d.b $$6$$ $$1.010$$ 6.0.419904.1 $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}+\beta _{4})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{7}+\cdots$$
2023.1.f.a $$4$$ $$1.010$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\zeta_{8}^{2}q^{9}+\cdots$$
2023.1.f.b $$8$$ $$1.010$$ 8.0.40960000.1 $$\Q(\sqrt{-119})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}-\beta _{5})q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots$$
2023.1.f.c $$12$$ $$1.010$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{2}+(-1+\beta _{6})q^{4}-\beta _{10}q^{7}+\cdots$$
2023.1.l.a $$8$$ $$1.010$$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{16}^{2}q^{2}-\zeta_{16}q^{7}-\zeta_{16}^{6}q^{8}+\zeta_{16}^{6}q^{9}+\cdots$$
2023.1.l.b $$16$$ $$1.010$$ 16.0.$$\cdots$$.1 $$\Q(\sqrt{-119})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{12}q^{2}-\beta _{1}q^{3}-\beta _{8}q^{4}+(-\beta _{10}+\cdots)q^{5}+\cdots$$
2023.1.l.c $$24$$ $$1.010$$ 24.0.$$\cdots$$.1 $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{21}q^{2}+(-\beta _{11}+\beta _{13}-\beta _{15})q^{4}+\cdots$$
2023.2.a.a $$1$$ $$16.154$$ $$\Q$$ None None $$-1$$ $$-3$$ $$-4$$ $$1$$ $$-$$ $$q-q^{2}-3q^{3}-q^{4}-4q^{5}+3q^{6}+q^{7}+\cdots$$
2023.2.a.b $$1$$ $$16.154$$ $$\Q$$ None None $$-1$$ $$3$$ $$4$$ $$-1$$ $$-$$ $$q-q^{2}+3q^{3}-q^{4}+4q^{5}-3q^{6}-q^{7}+\cdots$$
2023.2.a.c $$3$$ $$16.154$$ 3.3.148.1 None None $$-1$$ $$-1$$ $$-2$$ $$-3$$ $$+$$ $$q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$$
2023.2.a.d $$3$$ $$16.154$$ 3.3.148.1 None None $$-1$$ $$1$$ $$2$$ $$3$$ $$+$$ $$q-\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$$
2023.2.a.e $$4$$ $$16.154$$ 4.4.9301.1 None None $$-1$$ $$-2$$ $$-2$$ $$-4$$ $$+$$ $$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
2023.2.a.f $$4$$ $$16.154$$ 4.4.2225.1 None None $$3$$ $$-2$$ $$-4$$ $$-4$$ $$-$$ $$q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
2023.2.a.g $$4$$ $$16.154$$ 4.4.2225.1 None None $$3$$ $$2$$ $$4$$ $$4$$ $$-$$ $$q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
2023.2.a.h $$5$$ $$16.154$$ 5.5.240133.1 None None $$2$$ $$0$$ $$-4$$ $$-5$$ $$+$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
2023.2.a.i $$5$$ $$16.154$$ 5.5.240133.1 None None $$2$$ $$0$$ $$4$$ $$5$$ $$-$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{4})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$$
2023.2.a.j $$5$$ $$16.154$$ 5.5.453749.1 None None $$2$$ $$2$$ $$0$$ $$5$$ $$-$$ $$q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(2-\beta _{3})q^{4}+\cdots$$
2023.2.a.k $$9$$ $$16.154$$ 9.9.$$\cdots$$.1 None None $$-6$$ $$0$$ $$0$$ $$9$$ $$+$$ $$q+(-1-\beta _{5})q^{2}-\beta _{4}q^{3}+(1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$$
2023.2.a.l $$9$$ $$16.154$$ 9.9.$$\cdots$$.1 None None $$-6$$ $$0$$ $$0$$ $$-9$$ $$+$$ $$q+(-1-\beta _{5})q^{2}+\beta _{4}q^{3}+(1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$$
2023.2.a.m $$10$$ $$16.154$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$-4$$ $$-8$$ $$-10$$ $$+$$ $$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(2+\beta _{7}-\beta _{8})q^{4}+\cdots$$
2023.2.a.n $$10$$ $$16.154$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$4$$ $$8$$ $$10$$ $$-$$ $$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{7}-\beta _{8})q^{4}+\cdots$$
2023.2.a.o $$15$$ $$16.154$$ $$\mathbb{Q}[x]/(x^{15} - \cdots)$$ None None $$6$$ $$0$$ $$0$$ $$15$$ $$-$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{13})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$$
2023.2.a.p $$15$$ $$16.154$$ $$\mathbb{Q}[x]/(x^{15} - \cdots)$$ None None $$6$$ $$0$$ $$0$$ $$-15$$ $$-$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{13})q^{3}+(1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$
2023.2.a.q $$16$$ $$16.154$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-4$$ $$-8$$ $$-16$$ $$16$$ $$+$$ $$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
2023.2.a.r $$16$$ $$16.154$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-4$$ $$8$$ $$16$$ $$-16$$ $$-$$ $$q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
2023.4.a.a $$1$$ $$119.361$$ $$\Q$$ None None $$-1$$ $$2$$ $$-16$$ $$7$$ $$-$$ $$q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots$$
2023.4.a.b $$1$$ $$119.361$$ $$\Q$$ None None $$-1$$ $$6$$ $$20$$ $$7$$ $$-$$ $$q-q^{2}+6q^{3}-7q^{4}+20q^{5}-6q^{6}+\cdots$$
2023.4.a.c $$1$$ $$119.361$$ $$\Q$$ None None $$3$$ $$-1$$ $$6$$ $$-7$$ $$+$$ $$q+3q^{2}-q^{3}+q^{4}+6q^{5}-3q^{6}-7q^{7}+\cdots$$
2023.4.a.d $$1$$ $$119.361$$ $$\Q$$ None None $$3$$ $$1$$ $$-6$$ $$7$$ $$+$$ $$q+3q^{2}+q^{3}+q^{4}-6q^{5}+3q^{6}+7q^{7}+\cdots$$
2023.4.a.e $$3$$ $$119.361$$ 3.3.2429.1 None None $$-1$$ $$-5$$ $$19$$ $$21$$ $$-$$ $$q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$$
2023.4.a.f $$4$$ $$119.361$$ 4.4.68557.1 None None $$-2$$ $$7$$ $$9$$ $$-28$$ $$+$$ $$q+(-1-\beta _{2})q^{2}+(2+\beta _{1}+\beta _{3})q^{3}+\cdots$$
2023.4.a.g $$7$$ $$119.361$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$4$$ $$-5$$ $$-35$$ $$49$$ $$-$$ $$q+(1-\beta _{1})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots$$
2023.4.a.h $$9$$ $$119.361$$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$2$$ $$-11$$ $$3$$ $$-63$$ $$+$$ $$q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(4+\beta _{2})q^{4}+\cdots$$
2023.4.a.i $$11$$ $$119.361$$ $$\mathbb{Q}[x]/(x^{11} - \cdots)$$ None None $$-7$$ $$-2$$ $$2$$ $$-77$$ $$-$$ $$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
2023.4.a.j $$11$$ $$119.361$$ $$\mathbb{Q}[x]/(x^{11} - \cdots)$$ None None $$-7$$ $$2$$ $$-2$$ $$77$$ $$-$$ $$q+(-1+\beta _{1})q^{2}+\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
2023.4.a.k $$12$$ $$119.361$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$3$$ $$-3$$ $$12$$ $$84$$ $$+$$ $$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots$$
2023.4.a.l $$12$$ $$119.361$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$3$$ $$3$$ $$-12$$ $$-84$$ $$+$$ $$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots$$
2023.4.a.m $$13$$ $$119.361$$ $$\mathbb{Q}[x]/(x^{13} - \cdots)$$ None None $$0$$ $$-14$$ $$-20$$ $$91$$ $$-$$ $$q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots$$
2023.4.a.n $$13$$ $$119.361$$ $$\mathbb{Q}[x]/(x^{13} - \cdots)$$ None None $$0$$ $$14$$ $$20$$ $$-91$$ $$+$$ $$q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots$$
2023.4.a.o $$26$$ $$119.361$$ None None $$-8$$ $$-12$$ $$-40$$ $$182$$ $$-$$
2023.4.a.p $$26$$ $$119.361$$ None None $$-8$$ $$12$$ $$40$$ $$-182$$ $$+$$
2023.4.a.q $$33$$ $$119.361$$ None None $$-12$$ $$0$$ $$0$$ $$-231$$ $$-$$
2023.4.a.r $$33$$ $$119.361$$ None None $$-12$$ $$0$$ $$0$$ $$231$$ $$-$$
2023.4.a.s $$39$$ $$119.361$$ None None $$12$$ $$0$$ $$0$$ $$273$$ $$+$$