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

Label Dim. $$A$$ Field CM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1.12.a.a $$1$$ $$0.768$$ $$\Q$$ None $$-24$$ $$252$$ $$4830$$ $$-16744$$ $$+$$ $$q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}+\cdots$$
3.12.a.a $$1$$ $$2.305$$ $$\Q$$ None $$78$$ $$-243$$ $$-5370$$ $$-27760$$ $$+$$ $$q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots$$
4.12.a.a $$1$$ $$3.073$$ $$\Q$$ None $$0$$ $$-516$$ $$-10530$$ $$49304$$ $$-$$ $$q-516q^{3}-10530q^{5}+49304q^{7}+\cdots$$
5.12.a.a $$1$$ $$3.842$$ $$\Q$$ None $$34$$ $$-792$$ $$3125$$ $$-17556$$ $$-$$ $$q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots$$
5.12.a.b $$2$$ $$3.842$$ $$\Q(\sqrt{151})$$ None $$-20$$ $$-220$$ $$-6250$$ $$57900$$ $$+$$ $$q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots$$
5.12.b.a $$4$$ $$3.842$$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None $$0$$ $$0$$ $$-300$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-18-\beta _{2})q^{4}+\cdots$$
6.12.a.a $$1$$ $$4.610$$ $$\Q$$ None $$-32$$ $$-243$$ $$5766$$ $$72464$$ $$+$$ $$q-2^{5}q^{2}-3^{5}q^{3}+2^{10}q^{4}+5766q^{5}+\cdots$$
6.12.a.b $$1$$ $$4.610$$ $$\Q$$ None $$-32$$ $$243$$ $$-11730$$ $$-50008$$ $$-$$ $$q-2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}-11730q^{5}+\cdots$$
6.12.a.c $$1$$ $$4.610$$ $$\Q$$ None $$32$$ $$243$$ $$3630$$ $$32936$$ $$+$$ $$q+2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}+3630q^{5}+\cdots$$
7.12.a.a $$2$$ $$5.378$$ $$\Q(\sqrt{3369})$$ None $$-54$$ $$120$$ $$-13500$$ $$33614$$ $$-$$ $$q+(-3^{3}-\beta )q^{2}+(60+6\beta )q^{3}+(2050+\cdots)q^{4}+\cdots$$
7.12.a.b $$3$$ $$5.378$$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$77$$ $$-140$$ $$5026$$ $$-50421$$ $$+$$ $$q+(26+\beta _{2})q^{2}+(-47-11\beta _{1}+10\beta _{2})q^{3}+\cdots$$
7.12.c.a $$12$$ $$5.378$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$22$$ $$-244$$ $$-8782$$ $$-504$$ $$q+(4-\beta _{1}-4\beta _{2})q^{2}+(\beta _{1}-40\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$$
8.12.a.a $$1$$ $$6.147$$ $$\Q$$ None $$0$$ $$-36$$ $$-3490$$ $$-55464$$ $$-$$ $$q-6^{2}q^{3}-3490q^{5}-55464q^{7}-175851q^{9}+\cdots$$
8.12.a.b $$2$$ $$6.147$$ $$\Q(\sqrt{109})$$ None $$0$$ $$56$$ $$7868$$ $$91056$$ $$+$$ $$q+(28+\beta )q^{3}+(3934-12\beta )q^{5}+(45528+\cdots)q^{7}+\cdots$$
8.12.b.a $$10$$ $$6.147$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$22$$ $$0$$ $$0$$ $$-33616$$ $$q+(2+\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(43+2\beta _{1}+\cdots)q^{4}+\cdots$$
9.12.a.a $$1$$ $$6.915$$ $$\Q$$ None $$-78$$ $$0$$ $$5370$$ $$-27760$$ $$-$$ $$q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots$$
9.12.a.b $$1$$ $$6.915$$ $$\Q$$ None $$24$$ $$0$$ $$-4830$$ $$-16744$$ $$-$$ $$q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots$$
9.12.a.c $$2$$ $$6.915$$ $$\Q(\sqrt{70})$$ None $$0$$ $$0$$ $$0$$ $$116200$$ $$+$$ $$q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots$$
9.12.c.a $$20$$ $$6.915$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$-33$$ $$-12$$ $$-7230$$ $$8512$$ $$q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$$
10.12.a.a $$1$$ $$7.683$$ $$\Q$$ None $$-32$$ $$-12$$ $$3125$$ $$-14176$$ $$-$$ $$q-2^{5}q^{2}-12q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots$$
10.12.a.b $$1$$ $$7.683$$ $$\Q$$ None $$-32$$ $$738$$ $$-3125$$ $$25574$$ $$+$$ $$q-2^{5}q^{2}+738q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots$$
10.12.a.c $$1$$ $$7.683$$ $$\Q$$ None $$32$$ $$-318$$ $$-3125$$ $$-70714$$ $$-$$ $$q+2^{5}q^{2}-318q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots$$
10.12.a.d $$2$$ $$7.683$$ $$\Q(\sqrt{1969})$$ None $$64$$ $$604$$ $$6250$$ $$14092$$ $$+$$ $$q+2^{5}q^{2}+(302-\beta )q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots$$
10.12.b.a $$6$$ $$7.683$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$0$$ $$0$$ $$530$$ $$0$$ $$q-\beta _{2}q^{2}+(\beta _{1}+3\beta _{2})q^{3}-2^{10}q^{4}+\cdots$$
11.12.a.a $$3$$ $$8.452$$ 3.3.202533.1 None $$0$$ $$-393$$ $$-7305$$ $$-5082$$ $$-$$ $$q-\beta _{1}q^{2}+(-131-2\beta _{1}-4\beta _{2})q^{3}+\cdots$$
11.12.a.b $$5$$ $$8.452$$ $$\mathbb{Q}[x]/(x^{5} - \cdots)$$ None $$32$$ $$160$$ $$-8398$$ $$79040$$ $$+$$ $$q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots$$
11.12.c.a $$40$$ $$8.452$$ None $$11$$ $$-276$$ $$6038$$ $$55440$$
12.12.a.a $$1$$ $$9.220$$ $$\Q$$ None $$0$$ $$-243$$ $$9990$$ $$-86128$$ $$-$$ $$q-3^{5}q^{3}+9990q^{5}-86128q^{7}+3^{10}q^{9}+\cdots$$
12.12.a.b $$1$$ $$9.220$$ $$\Q$$ None $$0$$ $$243$$ $$2862$$ $$9128$$ $$+$$ $$q+3^{5}q^{3}+2862q^{5}+9128q^{7}+3^{10}q^{9}+\cdots$$
12.12.b.a $$20$$ $$9.220$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(99+\beta _{2})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots$$
13.12.a.a $$5$$ $$9.988$$ $$\mathbb{Q}[x]/(x^{5} - \cdots)$$ None $$-41$$ $$-496$$ $$-2542$$ $$-36296$$ $$-$$ $$q+(-8-\beta _{1})q^{2}+(-99-2\beta _{1}-\beta _{4})q^{3}+\cdots$$
13.12.a.b $$6$$ $$9.988$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$55$$ $$476$$ $$3312$$ $$-4176$$ $$+$$ $$q+(9+\beta _{1})q^{2}+(80-2\beta _{1}+\beta _{4})q^{3}+\cdots$$
13.12.b.a $$12$$ $$9.988$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$-488$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-41-\beta _{2})q^{3}+(-2^{10}+\cdots)q^{4}+\cdots$$
13.12.c.a $$24$$ $$9.988$$ None $$31$$ $$-244$$ $$-10436$$ $$-2928$$
13.12.e.a $$22$$ $$9.988$$ None $$-3$$ $$242$$ $$0$$ $$128496$$
14.12.a.a $$1$$ $$10.757$$ $$\Q$$ None $$-32$$ $$-396$$ $$7350$$ $$16807$$ $$-$$ $$q-2^{5}q^{2}-396q^{3}+2^{10}q^{4}+7350q^{5}+\cdots$$
14.12.a.b $$1$$ $$10.757$$ $$\Q$$ None $$32$$ $$-90$$ $$-7480$$ $$-16807$$ $$-$$ $$q+2^{5}q^{2}-90q^{3}+2^{10}q^{4}-7480q^{5}+\cdots$$
14.12.a.c $$2$$ $$10.757$$ $$\Q(\sqrt{153169})$$ None $$-64$$ $$350$$ $$266$$ $$-33614$$ $$+$$ $$q-2^{5}q^{2}+(175-\beta )q^{3}+2^{10}q^{4}+(133+\cdots)q^{5}+\cdots$$
14.12.a.d $$2$$ $$10.757$$ $$\Q(\sqrt{352969})$$ None $$64$$ $$-350$$ $$3738$$ $$33614$$ $$+$$ $$q+2^{5}q^{2}+(-175-\beta )q^{3}+2^{10}q^{4}+\cdots$$
14.12.c.a $$8$$ $$10.757$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-128$$ $$266$$ $$7504$$ $$-42224$$ $$q+(-2^{5}+2^{5}\beta _{2})q^{2}+(67\beta _{2}-\beta _{3})q^{3}+\cdots$$
14.12.c.b $$8$$ $$10.757$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$128$$ $$-266$$ $$3808$$ $$110328$$ $$q+2^{5}\beta _{2}q^{2}+(-67+\beta _{1}+67\beta _{2})q^{3}+\cdots$$
15.12.a.a $$1$$ $$11.525$$ $$\Q$$ None $$-56$$ $$-243$$ $$3125$$ $$27984$$ $$-$$ $$q-56q^{2}-3^{5}q^{3}+1088q^{4}+5^{5}q^{5}+\cdots$$
15.12.a.b $$2$$ $$11.525$$ $$\Q(\sqrt{1609})$$ None $$-22$$ $$486$$ $$-6250$$ $$-10864$$ $$-$$ $$q+(-11-\beta )q^{2}+3^{5}q^{3}+(-318+22\beta )q^{4}+\cdots$$
15.12.a.c $$2$$ $$11.525$$ $$\Q(\sqrt{1801})$$ None $$-13$$ $$-486$$ $$-6250$$ $$7784$$ $$+$$ $$q+(-6-\beta )q^{2}-3^{5}q^{3}+(-1562+13\beta )q^{4}+\cdots$$
15.12.a.d $$3$$ $$11.525$$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$-1$$ $$729$$ $$9375$$ $$-14608$$ $$+$$ $$q-\beta _{1}q^{2}+3^{5}q^{3}+(1585+3\beta _{1}+\beta _{2})q^{4}+\cdots$$
15.12.b.a $$12$$ $$11.525$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$2556$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1359+\beta _{1})q^{4}+\cdots$$
15.12.e.a $$40$$ $$11.525$$ None $$0$$ $$504$$ $$0$$ $$31504$$
16.12.a.a $$1$$ $$12.293$$ $$\Q$$ None $$0$$ $$-252$$ $$4830$$ $$16744$$ $$-$$ $$q-252q^{3}+4830q^{5}+16744q^{7}+\cdots$$
16.12.a.b $$1$$ $$12.293$$ $$\Q$$ None $$0$$ $$36$$ $$-3490$$ $$55464$$ $$+$$ $$q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\cdots$$
16.12.a.c $$1$$ $$12.293$$ $$\Q$$ None $$0$$ $$516$$ $$-10530$$ $$-49304$$ $$-$$ $$q+516q^{3}-10530q^{5}-49304q^{7}+\cdots$$
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