## Results (displaying matches 1-50 of at least 1000) Next

Label Dim. $$A$$ Field CM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2.8.a.a $$1$$ $$0.625$$ $$\Q$$ None $$-8$$ $$12$$ $$-210$$ $$1016$$ $$+$$ $$q-8q^{2}+12q^{3}+2^{6}q^{4}-210q^{5}+\cdots$$
3.8.a.a $$1$$ $$0.937$$ $$\Q$$ None $$6$$ $$-27$$ $$390$$ $$-64$$ $$+$$ $$q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots$$
5.8.a.a $$1$$ $$1.562$$ $$\Q$$ None $$-14$$ $$-48$$ $$125$$ $$-1644$$ $$-$$ $$q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots$$
5.8.a.b $$2$$ $$1.562$$ $$\Q(\sqrt{19})$$ None $$20$$ $$20$$ $$-250$$ $$-100$$ $$+$$ $$q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots$$
5.8.b.a $$2$$ $$1.562$$ $$\Q(\sqrt{-29})$$ None $$0$$ $$0$$ $$150$$ $$0$$ $$q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots$$
6.8.a.a $$1$$ $$1.874$$ $$\Q$$ None $$8$$ $$27$$ $$-114$$ $$-1576$$ $$+$$ $$q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-114q^{5}+\cdots$$
7.8.a.a $$1$$ $$2.187$$ $$\Q$$ None $$-6$$ $$-42$$ $$-84$$ $$343$$ $$-$$ $$q-6q^{2}-42q^{3}-92q^{4}-84q^{5}+252q^{6}+\cdots$$
7.8.a.b $$2$$ $$2.187$$ $$\Q(\sqrt{865})$$ None $$-3$$ $$94$$ $$330$$ $$-686$$ $$+$$ $$q+(-1-\beta )q^{2}+(46+2\beta )q^{3}+(89+3\beta )q^{4}+\cdots$$
7.8.c.a $$8$$ $$2.187$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$6$$ $$-28$$ $$-252$$ $$672$$ $$q+(-1+2\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(-6+\cdots)q^{3}+\cdots$$
8.8.a.a $$1$$ $$2.499$$ $$\Q$$ None $$0$$ $$-84$$ $$-82$$ $$-456$$ $$-$$ $$q-84q^{3}-82q^{5}-456q^{7}+4869q^{9}+\cdots$$
8.8.a.b $$1$$ $$2.499$$ $$\Q$$ None $$0$$ $$44$$ $$430$$ $$-1224$$ $$+$$ $$q+44q^{3}+430q^{5}-1224q^{7}-251q^{9}+\cdots$$
8.8.b.a $$6$$ $$2.499$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$6$$ $$0$$ $$0$$ $$-688$$ $$q+(1+\beta _{1})q^{2}+\beta _{4}q^{3}+(19+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$$
9.8.a.a $$1$$ $$2.811$$ $$\Q$$ None $$-6$$ $$0$$ $$-390$$ $$-64$$ $$-$$ $$q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots$$
9.8.a.b $$2$$ $$2.811$$ $$\Q(\sqrt{10})$$ None $$0$$ $$0$$ $$0$$ $$520$$ $$+$$ $$q+\beta q^{2}+232q^{4}-2^{4}\beta q^{5}+260q^{7}+\cdots$$
9.8.c.a $$12$$ $$2.811$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-9$$ $$24$$ $$-180$$ $$-84$$ $$q+(-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$$
10.8.a.a $$1$$ $$3.124$$ $$\Q$$ None $$8$$ $$28$$ $$125$$ $$104$$ $$+$$ $$q+8q^{2}+28q^{3}+2^{6}q^{4}+5^{3}q^{5}+224q^{6}+\cdots$$
10.8.b.a $$4$$ $$3.124$$ $$\Q(i, \sqrt{31})$$ None $$0$$ $$0$$ $$60$$ $$0$$ $$q-\beta _{1}q^{2}+(3\beta _{1}-\beta _{3})q^{3}-2^{6}q^{4}+(15+\cdots)q^{5}+\cdots$$
11.8.a.a $$2$$ $$3.436$$ $$\Q(\sqrt{15})$$ None $$-8$$ $$-6$$ $$-470$$ $$-1228$$ $$-$$ $$q+(-4+\beta )q^{2}+(-3-6\beta )q^{3}+(-52+\cdots)q^{4}+\cdots$$
11.8.a.b $$4$$ $$3.436$$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None $$0$$ $$-35$$ $$537$$ $$170$$ $$+$$ $$q-\beta _{2}q^{2}+(-9-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$$
11.8.c.a $$24$$ $$3.436$$ None $$3$$ $$36$$ $$-72$$ $$68$$
12.8.a.a $$1$$ $$3.749$$ $$\Q$$ None $$0$$ $$-27$$ $$-378$$ $$-832$$ $$-$$ $$q-3^{3}q^{3}-378q^{5}-832q^{7}+3^{6}q^{9}+\cdots$$
12.8.a.b $$1$$ $$3.749$$ $$\Q$$ None $$0$$ $$27$$ $$270$$ $$1112$$ $$+$$ $$q+3^{3}q^{3}+270q^{5}+1112q^{7}+3^{6}q^{9}+\cdots$$
12.8.b.a $$4$$ $$3.749$$ $$\Q(\sqrt{3}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(-3\beta _{2}+3\beta _{3})q^{3}+(88+4\beta _{1}+\cdots)q^{4}+\cdots$$
12.8.b.b $$8$$ $$3.749$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-41+\beta _{2}+\cdots)q^{4}+\cdots$$
13.8.a.a $$1$$ $$4.061$$ $$\Q$$ None $$10$$ $$-73$$ $$-295$$ $$1373$$ $$-$$ $$q+10q^{2}-73q^{3}-28q^{4}-295q^{5}+\cdots$$
13.8.a.b $$2$$ $$4.061$$ $$\Q(\sqrt{337})$$ None $$-19$$ $$45$$ $$-353$$ $$-2009$$ $$-$$ $$q+(-9-\beta )q^{2}+(21+3\beta )q^{3}+(37+19\beta )q^{4}+\cdots$$
13.8.a.c $$4$$ $$4.061$$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None $$15$$ $$80$$ $$258$$ $$1692$$ $$+$$ $$q+(4-\beta _{1})q^{2}+(21-2\beta _{1}+\beta _{2})q^{3}+\cdots$$
13.8.b.a $$6$$ $$4.061$$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$-56$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-9-\beta _{2})q^{3}+(-22-\beta _{4}+\cdots)q^{4}+\cdots$$
13.8.c.a $$16$$ $$4.061$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-9$$ $$-28$$ $$384$$ $$196$$ $$q+(-1-\beta _{1}-\beta _{2})q^{2}+(-4-4\beta _{2}+\cdots)q^{3}+\cdots$$
13.8.e.a $$14$$ $$4.061$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$-3$$ $$26$$ $$0$$ $$-2772$$ $$q+\beta _{2}q^{2}+(4+4\beta _{3}-\beta _{4}-\beta _{6})q^{3}+\cdots$$
14.8.a.a $$1$$ $$4.373$$ $$\Q$$ None $$-8$$ $$-82$$ $$448$$ $$-343$$ $$+$$ $$q-8q^{2}-82q^{3}+2^{6}q^{4}+448q^{5}+\cdots$$
14.8.a.b $$1$$ $$4.373$$ $$\Q$$ None $$8$$ $$-66$$ $$-400$$ $$-343$$ $$-$$ $$q+8q^{2}-66q^{3}+2^{6}q^{4}-20^{2}q^{5}+\cdots$$
14.8.a.c $$2$$ $$4.373$$ $$\Q(\sqrt{1969})$$ None $$16$$ $$70$$ $$126$$ $$686$$ $$+$$ $$q+8q^{2}+(35-\beta )q^{3}+2^{6}q^{4}+(63+9\beta )q^{5}+\cdots$$
14.8.c.a $$4$$ $$4.373$$ $$\Q(\sqrt{-3}, \sqrt{2389})$$ None $$-16$$ $$56$$ $$238$$ $$168$$ $$q+(-8+8\beta _{1})q^{2}+(28\beta _{1}-\beta _{2})q^{3}+\cdots$$
14.8.c.b $$4$$ $$4.373$$ $$\Q(\sqrt{-3}, \sqrt{949})$$ None $$16$$ $$-56$$ $$14$$ $$-1848$$ $$q+8\beta _{1}q^{2}+(-28+28\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$$
15.8.a.a $$1$$ $$4.686$$ $$\Q$$ None $$-22$$ $$27$$ $$-125$$ $$-420$$ $$-$$ $$q-22q^{2}+3^{3}q^{3}+356q^{4}-5^{3}q^{5}+\cdots$$
15.8.a.b $$1$$ $$4.686$$ $$\Q$$ None $$-13$$ $$-27$$ $$-125$$ $$1380$$ $$+$$ $$q-13q^{2}-3^{3}q^{3}+41q^{4}-5^{3}q^{5}+\cdots$$
15.8.a.c $$2$$ $$4.686$$ $$\Q(\sqrt{601})$$ None $$7$$ $$54$$ $$250$$ $$1304$$ $$+$$ $$q+(4-\beta )q^{2}+3^{3}q^{3}+(38-7\beta )q^{4}+\cdots$$
15.8.b.a $$8$$ $$4.686$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$-444$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-83-\beta _{4})q^{4}+\cdots$$
15.8.e.a $$24$$ $$4.686$$ None $$0$$ $$24$$ $$0$$ $$1344$$
16.8.a.a $$1$$ $$4.998$$ $$\Q$$ None $$0$$ $$-44$$ $$430$$ $$1224$$ $$+$$ $$q-44q^{3}+430q^{5}+1224q^{7}-251q^{9}+\cdots$$
16.8.a.b $$1$$ $$4.998$$ $$\Q$$ None $$0$$ $$-12$$ $$-210$$ $$-1016$$ $$-$$ $$q-12q^{3}-210q^{5}-1016q^{7}-2043q^{9}+\cdots$$
16.8.a.c $$1$$ $$4.998$$ $$\Q$$ None $$0$$ $$84$$ $$-82$$ $$456$$ $$+$$ $$q+84q^{3}-82q^{5}+456q^{7}+4869q^{9}+\cdots$$
16.8.e.a $$26$$ $$4.998$$ None $$-2$$ $$-2$$ $$-2$$ $$0$$
17.8.a.a $$1$$ $$5.311$$ $$\Q$$ None $$-2$$ $$18$$ $$-10$$ $$-902$$ $$-$$ $$q-2q^{2}+18q^{3}-124q^{4}-10q^{5}+\cdots$$
17.8.a.b $$3$$ $$5.311$$ 3.3.694349.1 None $$1$$ $$-86$$ $$-198$$ $$-1558$$ $$-$$ $$q+\beta _{2}q^{2}+(-28-\beta _{1}-2\beta _{2})q^{3}+(78+\cdots)q^{4}+\cdots$$
17.8.a.c $$6$$ $$5.311$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$15$$ $$40$$ $$-184$$ $$2064$$ $$+$$ $$q+(2+\beta _{1})q^{2}+(6+\beta _{1}+\beta _{4})q^{3}+(78+\cdots)q^{4}+\cdots$$
17.8.b.a $$10$$ $$5.311$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$-18$$ $$0$$ $$0$$ $$0$$ $$q+(-2+\beta _{2})q^{2}+\beta _{1}q^{3}+(69-2\beta _{2}+\cdots)q^{4}+\cdots$$
17.8.c.a $$20$$ $$5.311$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$24$$ $$384$$ $$392$$ $$q+\beta _{1}q^{2}+(1-\beta _{6}+\beta _{8})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots$$
17.8.d.a $$36$$ $$5.311$$ None $$-4$$ $$-4$$ $$0$$ $$-4$$
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