## Results (1-50 of 15755 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
23.1.b.a $$1$$ $$0.011$$ $$\Q$$ $$\Q(\sqrt{-23})$$ None $$-1$$ $$-1$$ $$0$$ $$0$$ $$q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots$$
31.1.b.a $$1$$ $$0.015$$ $$\Q$$ $$\Q(\sqrt{-31})$$ None $$-1$$ $$0$$ $$-1$$ $$-1$$ $$q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots$$
39.1.d.a $$1$$ $$0.019$$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-39})$$ $$\Q(\sqrt{13})$$ $$0$$ $$-1$$ $$0$$ $$0$$ $$q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$$
44.1.d.a $$1$$ $$0.022$$ $$\Q$$ $$\Q(\sqrt{-11})$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots$$
47.1.b.a $$2$$ $$0.023$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-47})$$ None $$-1$$ $$-1$$ $$0$$ $$-1$$ $$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$$
52.1.j.a $$2$$ $$0.026$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-1})$$ None $$-1$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$$
55.1.d.a $$1$$ $$0.027$$ $$\Q$$ $$\Q(\sqrt{-11})$$, $$\Q(\sqrt{-55})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$-1$$ $$0$$ $$q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots$$
56.1.h.a $$1$$ $$0.028$$ $$\Q$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-14})$$ $$\Q(\sqrt{2})$$ $$-1$$ $$0$$ $$0$$ $$-1$$ $$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots$$
57.1.h.a $$2$$ $$0.028$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-2$$ $$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots$$
59.1.b.a $$1$$ $$0.029$$ $$\Q$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$-1$$ $$-1$$ $$-1$$ $$q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots$$
63.1.d.a $$1$$ $$0.031$$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{21})$$ $$0$$ $$0$$ $$0$$ $$-1$$ $$q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots$$
68.1.d.a $$1$$ $$0.034$$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-17})$$ $$\Q(\sqrt{17})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots$$
68.1.f.a $$2$$ $$0.034$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$$
71.1.b.a $$3$$ $$0.035$$ $$\Q(\zeta_{14})^+$$ $$\Q(\sqrt{-71})$$ None $$-1$$ $$-1$$ $$-1$$ $$0$$ $$q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
72.1.p.a $$2$$ $$0.036$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-2})$$ None $$-1$$ $$-1$$ $$0$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$$
76.1.c.a $$1$$ $$0.038$$ $$\Q$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$-1$$ $$q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$$
77.1.j.a $$4$$ $$0.038$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-7})$$ None $$-2$$ $$0$$ $$0$$ $$-1$$ $$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$$
79.1.b.a $$2$$ $$0.039$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-79})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots$$
80.1.h.a $$1$$ $$0.040$$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$-1$$ $$0$$ $$q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots$$
83.1.b.a $$1$$ $$0.041$$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$-1$$ $$0$$ $$-1$$ $$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$$
84.1.p.a $$2$$ $$0.042$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-1$$ $$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots$$
87.1.d.a $$1$$ $$0.043$$ $$\Q$$ $$\Q(\sqrt{-87})$$ None $$-1$$ $$1$$ $$0$$ $$-1$$ $$q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots$$
87.1.d.b $$1$$ $$0.043$$ $$\Q$$ $$\Q(\sqrt{-87})$$ None $$1$$ $$-1$$ $$0$$ $$-1$$ $$q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots$$
88.1.l.a $$4$$ $$0.044$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-2})$$ None $$-1$$ $$-2$$ $$0$$ $$0$$ $$q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$$
93.1.l.a $$4$$ $$0.046$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-2$$ $$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$$
95.1.d.a $$1$$ $$0.047$$ $$\Q$$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-95})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$1$$ $$0$$ $$q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots$$
95.1.d.b $$2$$ $$0.047$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$$
99.1.h.a $$2$$ $$0.049$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-11})$$ None $$0$$ $$-1$$ $$1$$ $$0$$ $$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots$$
100.1.j.a $$4$$ $$0.050$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-1})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$$
11.2.a.a $$1$$ $$0.088$$ $$\Q$$ None None $$-2$$ $$-1$$ $$1$$ $$-2$$ $$-$$ $$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots$$
13.2.e.a $$2$$ $$0.104$$ $$\Q(\sqrt{-3})$$ None None $$-3$$ $$-2$$ $$0$$ $$0$$ $$q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
14.2.a.a $$1$$ $$0.112$$ $$\Q$$ None None $$-1$$ $$-2$$ $$0$$ $$1$$ $$-$$ $$q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots$$
15.2.a.a $$1$$ $$0.120$$ $$\Q$$ None None $$-1$$ $$-1$$ $$1$$ $$0$$ $$-$$ $$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots$$
16.2.e.a $$2$$ $$0.128$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$-2$$ $$0$$ $$q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots$$
17.2.a.a $$1$$ $$0.136$$ $$\Q$$ None None $$-1$$ $$0$$ $$-2$$ $$4$$ $$-$$ $$q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots$$
17.2.d.a $$4$$ $$0.136$$ $$\Q(\zeta_{8})$$ None None $$-4$$ $$-4$$ $$0$$ $$-4$$ $$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$$
18.2.c.a $$2$$ $$0.144$$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$-3$$ $$0$$ $$-2$$ $$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
19.2.a.a $$1$$ $$0.152$$ $$\Q$$ None None $$0$$ $$-2$$ $$3$$ $$-1$$ $$-$$ $$q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots$$
19.2.e.a $$6$$ $$0.152$$ $$\Q(\zeta_{18})$$ None None $$-6$$ $$-3$$ $$-6$$ $$0$$ $$q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots$$
20.2.a.a $$1$$ $$0.160$$ $$\Q$$ None None $$0$$ $$-2$$ $$-1$$ $$2$$ $$-$$ $$q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots$$
20.2.e.a $$2$$ $$0.160$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$-4$$ $$0$$ $$q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots$$
21.2.a.a $$1$$ $$0.168$$ $$\Q$$ None None $$-1$$ $$1$$ $$-2$$ $$-1$$ $$-$$ $$q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$$
21.2.e.a $$2$$ $$0.168$$ $$\Q(\sqrt{-3})$$ None None $$-2$$ $$-1$$ $$2$$ $$-5$$ $$q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots$$
21.2.g.a $$2$$ $$0.168$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$0$$ $$1$$ $$q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots$$
22.2.c.a $$4$$ $$0.176$$ $$\Q(\zeta_{10})$$ None None $$-1$$ $$-4$$ $$-6$$ $$2$$ $$q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$$
23.2.a.a $$2$$ $$0.184$$ $$\Q(\sqrt{5})$$ None None $$-1$$ $$0$$ $$-2$$ $$2$$ $$-$$ $$q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$$
23.2.c.a $$10$$ $$0.184$$ $$\Q(\zeta_{22})$$ None None $$-7$$ $$-7$$ $$-3$$ $$-5$$ $$q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots$$
24.2.a.a $$1$$ $$0.192$$ $$\Q$$ None None $$0$$ $$-1$$ $$-2$$ $$0$$ $$-$$ $$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$$
24.2.d.a $$2$$ $$0.192$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots$$
24.2.f.a $$2$$ $$0.192$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots$$