# Learn more about

## Results (45 matches)

Download to
Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
103.1.b.a $$2$$ $$0.051$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-103})$$ None $$-1$$ $$0$$ $$0$$ $$-1$$ $$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots$$
103.2.a.a $$2$$ $$0.822$$ $$\Q(\sqrt{5})$$ None None $$-3$$ $$-2$$ $$-3$$ $$-2$$ $$+$$ $$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots$$
103.2.a.b $$6$$ $$0.822$$ 6.6.6999257.1 None None $$4$$ $$0$$ $$3$$ $$-2$$ $$-$$ $$q+(1-\beta _{1})q^{2}+(-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots$$
103.2.c.a $$16$$ $$0.822$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-1$$ $$-4$$ $$3$$ $$-5$$ $$q-\beta _{1}q^{2}+\beta _{12}q^{3}+(-1+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$$
103.2.e.a $$112$$ $$0.822$$ None None $$-15$$ $$-11$$ $$-11$$ $$-5$$
103.2.g.a $$256$$ $$0.822$$ None None $$-33$$ $$-30$$ $$-37$$ $$-29$$
103.3.b.a $$5$$ $$2.807$$ 5.5.33153125.1 $$\Q(\sqrt{-103})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(4+\beta _{1}+\beta _{4})q^{4}+(-4\beta _{1}+\cdots)q^{7}+\cdots$$
103.3.b.b $$12$$ $$2.807$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{2}-\beta _{1}q^{3}+(1+\beta _{8})q^{4}+\beta _{2}q^{5}+\cdots$$
103.3.d.a $$32$$ $$2.807$$ None None $$-1$$ $$0$$ $$-3$$ $$5$$
103.3.f.a $$272$$ $$2.807$$ None None $$-15$$ $$-17$$ $$-17$$ $$-17$$
103.3.h.a $$512$$ $$2.807$$ None None $$-33$$ $$-34$$ $$-31$$ $$-39$$
103.4.a.a $$10$$ $$6.077$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$-11$$ $$-8$$ $$-30$$ $$-33$$ $$-$$ $$q+(-1-\beta _{1})q^{2}+(-1-\beta _{6})q^{3}+(3+\cdots)q^{4}+\cdots$$
103.4.a.b $$15$$ $$6.077$$ $$\mathbb{Q}[x]/(x^{15} - \cdots)$$ None None $$9$$ $$10$$ $$30$$ $$23$$ $$+$$ $$q+(1-\beta _{1})q^{2}+(1+\beta _{9})q^{3}+(5-\beta _{1}+\cdots)q^{4}+\cdots$$
103.4.c.a $$50$$ $$6.077$$ None None $$-1$$ $$4$$ $$-3$$ $$13$$
103.4.e.a $$400$$ $$6.077$$ None None $$-15$$ $$-19$$ $$-17$$ $$-7$$
103.4.g.a $$800$$ $$6.077$$ None None $$-33$$ $$-38$$ $$-31$$ $$-47$$
103.5.b.a $$5$$ $$10.647$$ 5.5.33153125.1 $$\Q(\sqrt{-103})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(2^{4}+6\beta _{2}-\beta _{3})q^{4}+(11\beta _{2}+\cdots)q^{7}+\cdots$$
103.5.b.b $$28$$ $$10.647$$ None None $$-2$$ $$0$$ $$0$$ $$28$$
103.5.d.a $$68$$ $$10.647$$ None None $$-1$$ $$0$$ $$-3$$ $$69$$
103.5.f.a $$528$$ $$10.647$$ None None $$-15$$ $$-17$$ $$-17$$ $$-45$$
103.5.h.a $$1088$$ $$10.647$$ None None $$-33$$ $$-34$$ $$-31$$ $$-103$$
103.6.a.a $$19$$ $$16.520$$ $$\mathbb{Q}[x]/(x^{19} - \cdots)$$ None None $$-21$$ $$-38$$ $$-147$$ $$-206$$ $$+$$ $$q+(-1-\beta _{1})q^{2}+(-2-\beta _{7})q^{3}+(14+\cdots)q^{4}+\cdots$$
103.6.a.b $$24$$ $$16.520$$ None None $$19$$ $$16$$ $$153$$ $$186$$ $$-$$
103.6.c.a $$84$$ $$16.520$$ None None $$-1$$ $$-20$$ $$-9$$ $$139$$
103.6.e.a $$688$$ $$16.520$$ None None $$-15$$ $$5$$ $$-23$$ $$3$$
103.6.g.a $$1344$$ $$16.520$$ None None $$-33$$ $$-14$$ $$-25$$ $$-173$$
103.7.b.a $$5$$ $$23.696$$ 5.5.33153125.1 $$\Q(\sqrt{-103})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}+\beta _{3})q^{2}+(2^{6}-19\beta _{1}-4\beta _{4})q^{4}+\cdots$$
103.7.b.b $$46$$ $$23.696$$ None None $$-2$$ $$0$$ $$0$$ $$-810$$
103.8.a.a $$27$$ $$32.176$$ None None $$-41$$ $$-68$$ $$-555$$ $$-1518$$ $$-$$
103.8.a.b $$32$$ $$32.176$$ None None $$39$$ $$94$$ $$945$$ $$1226$$ $$+$$
103.9.b.a $$5$$ $$41.960$$ 5.5.33153125.1 $$\Q(\sqrt{-103})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(6\beta _{2}-\beta _{3})q^{2}+(2^{8}-65\beta _{1}+14\beta _{4})q^{4}+\cdots$$
103.9.b.b $$64$$ $$41.960$$ None None $$-2$$ $$0$$ $$0$$ $$-5152$$
103.10.a.a $$36$$ $$53.049$$ None None $$-81$$ $$-170$$ $$-5172$$ $$-5297$$ $$+$$
103.10.a.b $$41$$ $$53.049$$ None None $$79$$ $$316$$ $$2328$$ $$13911$$ $$-$$
103.11.b.a $$1$$ $$65.442$$ $$\Q$$ $$\Q(\sqrt{-103})$$ None $$-39$$ $$0$$ $$0$$ $$242$$ $$q-39q^{2}+497q^{4}+242q^{7}+20553q^{8}+\cdots$$
103.11.b.b $$4$$ $$65.442$$ 4.4.1326125.1 $$\Q(\sqrt{-103})$$ None $$39$$ $$0$$ $$0$$ $$-242$$ $$q+(17+17\beta _{2}-5\beta _{3})q^{2}+(2^{10}+195\beta _{1}+\cdots)q^{4}+\cdots$$
103.11.b.c $$80$$ $$65.442$$ None None $$-2$$ $$0$$ $$0$$ $$56700$$
103.12.a.a $$44$$ $$79.139$$ None None $$-137$$ $$-992$$ $$-21435$$ $$-103218$$ $$-$$
103.12.a.b $$49$$ $$79.139$$ None None $$183$$ $$466$$ $$16065$$ $$31238$$ $$+$$
103.14.a.a $$53$$ $$110.448$$ None None $$-321$$ $$-2318$$ $$-88497$$ $$-350426$$ $$+$$
103.14.a.b $$58$$ $$110.448$$ None None $$319$$ $$2056$$ $$99003$$ $$590766$$ $$-$$
103.16.a.a $$61$$ $$146.974$$ None None $$-857$$ $$-3932$$ $$-439140$$ $$-3190353$$ $$-$$
103.16.a.b $$66$$ $$146.974$$ None None $$423$$ $$9190$$ $$498360$$ $$3397991$$ $$+$$
103.18.a.a $$70$$ $$188.719$$ None None $$-753$$ $$-23762$$ $$-2234097$$ $$-22054742$$ $$+$$
103.18.a.b $$75$$ $$188.719$$ None None $$1807$$ $$15604$$ $$2453403$$ $$24063666$$ $$-$$
Download to