## Results (39 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3724.1.e.a $$1$$ $$1.859$$ $$\Q$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-2q^{5}+q^{9}-q^{11}+q^{17}-q^{19}+\cdots$$
3724.1.e.b $$1$$ $$1.859$$ $$\Q$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-q^{5}+q^{9}+2q^{11}-q^{17}+q^{19}+\cdots$$
3724.1.e.c $$1$$ $$1.859$$ $$\Q$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+q^{5}+q^{9}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots$$
3724.1.e.d $$1$$ $$1.859$$ $$\Q$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+q^{5}+q^{9}+2q^{11}+q^{17}-q^{19}+\cdots$$
3724.1.e.e $$1$$ $$1.859$$ $$\Q$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+2q^{5}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$$
3724.1.n.a $$4$$ $$1.859$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{6}+\cdots$$
3724.1.bb.a $$4$$ $$1.859$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$$
3724.1.bb.b $$4$$ $$1.859$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$$
3724.1.bc.a $$2$$ $$1.859$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots$$
3724.1.bc.b $$2$$ $$1.859$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots$$
3724.1.bc.c $$2$$ $$1.859$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}-\zeta_{6}^{2}q^{17}+\cdots$$
3724.1.bc.d $$2$$ $$1.859$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots$$
3724.1.bk.a $$4$$ $$1.859$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{4}q^{6}+\cdots$$
3724.1.bv.a $$12$$ $$1.859$$ $$\Q(\zeta_{21})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$1$$ $$q+(-\zeta_{42}-\zeta_{42}^{5})q^{5}-\zeta_{42}^{17}q^{7}+\cdots$$
3724.1.dj.a $$12$$ $$1.859$$ $$\Q(\zeta_{21})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$-2$$ $$q+(-\zeta_{42}-\zeta_{42}^{3})q^{5}-\zeta_{42}^{9}q^{7}-\zeta_{42}^{11}q^{9}+\cdots$$
3724.1.dj.b $$12$$ $$1.859$$ $$\Q(\zeta_{21})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$1$$ $$q+(\zeta_{42}^{8}-\zeta_{42}^{17})q^{5}+\zeta_{42}^{16}q^{7}+\cdots$$
3724.2.a.a $$1$$ $$29.736$$ $$\Q$$ None None $$0$$ $$-2$$ $$1$$ $$0$$ $$-$$ $$q-2q^{3}+q^{5}+q^{9}+5q^{11}+4q^{13}+\cdots$$
3724.2.a.b $$1$$ $$29.736$$ $$\Q$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$+$$ $$q+2q^{5}-3q^{9}+4q^{11}-4q^{13}-6q^{17}+\cdots$$
3724.2.a.c $$2$$ $$29.736$$ $$\Q(\sqrt{3})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$+$$ $$q+(-1+\beta )q^{3}+(1-2\beta )q^{9}+(-3+2\beta )q^{11}+\cdots$$
3724.2.a.d $$2$$ $$29.736$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-1$$ $$4$$ $$0$$ $$+$$ $$q-\beta q^{3}+(1+2\beta )q^{5}+(-2+\beta )q^{9}+\cdots$$
3724.2.a.e $$2$$ $$29.736$$ $$\Q(\sqrt{21})$$ None None $$0$$ $$1$$ $$-6$$ $$0$$ $$+$$ $$q+\beta q^{3}-3q^{5}+(2+\beta )q^{9}+(-1-\beta )q^{11}+\cdots$$
3724.2.a.f $$2$$ $$29.736$$ $$\Q(\sqrt{3})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$+$$ $$q+(1+\beta )q^{3}+(1+2\beta )q^{9}+(-3-2\beta )q^{11}+\cdots$$
3724.2.a.g $$2$$ $$29.736$$ $$\Q(\sqrt{5})$$ None None $$0$$ $$3$$ $$2$$ $$0$$ $$-$$ $$q+(1+\beta )q^{3}+q^{5}+(-1+3\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$$
3724.2.a.h $$3$$ $$29.736$$ 3.3.404.1 None None $$0$$ $$-2$$ $$-3$$ $$0$$ $$+$$ $$q+(-1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots$$
3724.2.a.i $$3$$ $$29.736$$ 3.3.733.1 None None $$0$$ $$1$$ $$-2$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots$$
3724.2.a.j $$3$$ $$29.736$$ 3.3.404.1 None None $$0$$ $$2$$ $$3$$ $$0$$ $$+$$ $$q+(1-\beta _{1})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+(1+\cdots)q^{9}+\cdots$$
3724.2.a.k $$5$$ $$29.736$$ 5.5.11350832.1 None None $$0$$ $$-2$$ $$0$$ $$0$$ $$+$$ $$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$$
3724.2.a.l $$5$$ $$29.736$$ 5.5.11350832.1 None None $$0$$ $$2$$ $$0$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$$
3724.2.a.m $$7$$ $$29.736$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$-$$ $$q-\beta _{1}q^{3}-\beta _{6}q^{5}+(2-\beta _{4}+\beta _{5})q^{9}+\cdots$$
3724.2.a.n $$7$$ $$29.736$$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}+\beta _{6}q^{5}+(2-\beta _{4}+\beta _{5})q^{9}+\cdots$$
3724.2.a.o $$8$$ $$29.736$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$+$$ $$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots$$
3724.2.a.p $$8$$ $$29.736$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots$$
3724.2.g.a $$2$$ $$29.736$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-2q^{3}+q^{9}-3q^{11}-2q^{13}-3\zeta_{6}q^{17}+\cdots$$
3724.2.g.b $$2$$ $$29.736$$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+2q^{3}+q^{9}-3q^{11}+2q^{13}+3\zeta_{6}q^{17}+\cdots$$
3724.2.g.c $$4$$ $$29.736$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}-2\beta _{3})q^{5}-3q^{9}+(-2-\beta _{2}+\cdots)q^{11}+\cdots$$
3724.2.g.d $$4$$ $$29.736$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}-\beta _{3})q^{5}-3q^{9}+5q^{11}+(4\beta _{1}+\cdots)q^{17}+\cdots$$
3724.2.g.e $$8$$ $$29.736$$ 8.0.3288334336.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{5}-3q^{9}-2q^{11}-\beta _{1}q^{13}+\cdots$$
3724.2.g.f $$16$$ $$29.736$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{3}+\beta _{9}q^{5}+(3+\beta _{4})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots$$
3724.2.g.g $$32$$ $$29.736$$ None None $$0$$ $$0$$ $$0$$ $$0$$