## Results (41 matches)

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
869.1.j.a $$20$$ $$0.434$$ $$\Q(\zeta_{50})$$ $$\Q(\sqrt{-79})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$$
869.2.a.a $$1$$ $$6.939$$ $$\Q$$ None None $$-2$$ $$1$$ $$1$$ $$-2$$ $$+$$ $$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots$$
869.2.a.b $$1$$ $$6.939$$ $$\Q$$ None None $$-1$$ $$-2$$ $$2$$ $$4$$ $$-$$ $$q-q^{2}-2q^{3}-q^{4}+2q^{5}+2q^{6}+4q^{7}+\cdots$$
869.2.a.c $$1$$ $$6.939$$ $$\Q$$ None None $$1$$ $$-1$$ $$1$$ $$1$$ $$+$$ $$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots$$
869.2.a.d $$1$$ $$6.939$$ $$\Q$$ None None $$1$$ $$1$$ $$1$$ $$-5$$ $$+$$ $$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-5q^{7}+\cdots$$
869.2.a.e $$11$$ $$6.939$$ $$\mathbb{Q}[x]/(x^{11} - \cdots)$$ None None $$-3$$ $$-3$$ $$-8$$ $$-7$$ $$+$$ $$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{7}+\beta _{8})q^{4}+\cdots$$
869.2.a.f $$11$$ $$6.939$$ $$\mathbb{Q}[x]/(x^{11} - \cdots)$$ None None $$1$$ $$-9$$ $$-8$$ $$-3$$ $$+$$ $$q+\beta _{1}q^{2}+(-1-\beta _{7})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
869.2.a.g $$18$$ $$6.939$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$4$$ $$8$$ $$-3$$ $$10$$ $$-$$ $$q+\beta _{1}q^{2}-\beta _{15}q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$$
869.2.a.h $$21$$ $$6.939$$ None None $$0$$ $$7$$ $$6$$ $$10$$ $$-$$
869.2.b.a $$10$$ $$6.939$$ 10.0.$$\cdots$$.1 $$\Q(\sqrt{-79})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{8}q^{2}+(-2+\beta _{1}+\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots$$
869.2.b.b $$68$$ $$6.939$$ None None $$0$$ $$0$$ $$-4$$ $$0$$
869.2.e.a $$66$$ $$6.939$$ None None $$0$$ $$-3$$ $$0$$ $$-4$$
869.2.e.b $$66$$ $$6.939$$ None None $$0$$ $$1$$ $$0$$ $$2$$
869.2.f.a $$4$$ $$6.939$$ $$\Q(\zeta_{10})$$ None None $$-3$$ $$-1$$ $$-3$$ $$-5$$ $$q+(-1+\zeta_{10}^{3})q^{2}+(-\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots$$
869.2.f.b $$132$$ $$6.939$$ None None $$2$$ $$4$$ $$16$$ $$8$$
869.2.f.c $$176$$ $$6.939$$ None None $$-1$$ $$-9$$ $$-19$$ $$3$$
869.2.i.a $$156$$ $$6.939$$ None None $$0$$ $$-6$$ $$-2$$ $$0$$
869.2.l.a $$8$$ $$6.939$$ 8.0.484000000.9 None None $$10$$ $$0$$ $$14$$ $$0$$ $$q+(2+\beta _{2}+\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}-\beta _{4}+\cdots)q^{3}+\cdots$$
869.2.l.b $$40$$ $$6.939$$ $$\Q(\sqrt{-79})$$ None $$0$$ $$0$$ $$0$$ $$0$$
869.2.l.c $$264$$ $$6.939$$ None None $$-20$$ $$0$$ $$-20$$ $$0$$
869.2.m.a $$408$$ $$6.939$$ None None $$0$$ $$-4$$ $$0$$ $$1$$
869.2.m.b $$408$$ $$6.939$$ None None $$0$$ $$0$$ $$0$$ $$-13$$
869.2.n.a $$8$$ $$6.939$$ $$\Q(\zeta_{15})$$ None None $$-3$$ $$-1$$ $$-2$$ $$4$$ $$q+(\zeta_{15}^{2}+\zeta_{15}^{5})q^{2}+(1-\zeta_{15}+\zeta_{15}^{3}+\cdots)q^{3}+\cdots$$
869.2.n.b $$616$$ $$6.939$$ None None $$2$$ $$-2$$ $$-1$$ $$-7$$
869.2.q.a $$936$$ $$6.939$$ None None $$0$$ $$-26$$ $$-22$$ $$0$$
869.2.r.a $$624$$ $$6.939$$ None None $$-5$$ $$-9$$ $$-3$$ $$-15$$
869.2.u.a $$792$$ $$6.939$$ None None $$0$$ $$-1$$ $$0$$ $$11$$
869.2.u.b $$792$$ $$6.939$$ None None $$0$$ $$3$$ $$0$$ $$-9$$
869.2.v.a $$3744$$ $$6.939$$ None None $$-37$$ $$-33$$ $$-33$$ $$-45$$
869.2.w.a $$1872$$ $$6.939$$ None None $$0$$ $$-46$$ $$-50$$ $$0$$
869.2.z.a $$3744$$ $$6.939$$ None None $$-55$$ $$-39$$ $$-33$$ $$-65$$
869.2.bc.a $$7488$$ $$6.939$$ None None $$-77$$ $$-75$$ $$-75$$ $$-75$$
869.2.bf.a $$7488$$ $$6.939$$ None None $$-125$$ $$-69$$ $$-75$$ $$-115$$
869.4.a.a $$44$$ $$51.273$$ None None $$-2$$ $$-16$$ $$-32$$ $$-70$$ $$-$$
869.4.a.b $$46$$ $$51.273$$ None None $$-8$$ $$-24$$ $$-30$$ $$-98$$ $$-$$
869.4.a.c $$52$$ $$51.273$$ None None $$-2$$ $$26$$ $$28$$ $$70$$ $$+$$
869.4.a.d $$54$$ $$51.273$$ None None $$8$$ $$18$$ $$30$$ $$98$$ $$+$$
869.6.a.a $$76$$ $$139.374$$ None None $$-16$$ $$-79$$ $$-174$$ $$-686$$ $$+$$
869.6.a.b $$78$$ $$139.374$$ None None $$4$$ $$-48$$ $$-131$$ $$-490$$ $$+$$
869.6.a.c $$84$$ $$139.374$$ None None $$16$$ $$47$$ $$126$$ $$686$$ $$-$$
869.6.a.d $$86$$ $$139.374$$ None None $$4$$ $$78$$ $$169$$ $$490$$ $$-$$