## Results (1-50 of 143 matches)

Label Dim $A$ Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
28.2.d.a $2$ $0.224$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots$$
28.2.e.a $2$ $0.224$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-3$$ $$-4$$ $$q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
28.2.f.a $4$ $0.224$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$-6$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots$$
28.3.b.a $2$ $0.763$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$10$$ $$q+\beta q^{3}-\beta q^{5}+(5-\beta )q^{7}-15q^{9}+\cdots$$
28.3.c.a $6$ $0.763$ 6.0.1539727.2 None $$-1$$ $$0$$ $$-4$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{3}q^{3}+(-\beta _{1}-\beta _{4})q^{4}+\cdots$$
28.3.g.a $12$ $0.763$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-2$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots$$
28.3.h.a $2$ $0.763$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$3$$ $$-14$$ $$q+(1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}-7q^{7}-6\zeta_{6}q^{9}+\cdots$$
28.4.a.a $1$ $1.652$ $$\Q$$ None $$0$$ $$-10$$ $$-8$$ $$-7$$ $-$ $$q-10q^{3}-8q^{5}-7q^{7}+73q^{9}-40q^{11}+\cdots$$
28.4.a.b $1$ $1.652$ $$\Q$$ None $$0$$ $$4$$ $$6$$ $$7$$ $+$ $$q+4q^{3}+6q^{5}+7q^{7}-11q^{9}-12q^{11}+\cdots$$
28.4.d.a $2$ $1.652$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ $$5$$ $$0$$ $$0$$ $$0$$ $$q+(3-\beta )q^{2}+(7-5\beta )q^{4}+(-7+14\beta )q^{7}+\cdots$$
28.4.d.b $8$ $1.652$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots$$
28.4.e.a $4$ $1.652$ $$\Q(\sqrt{-3}, \sqrt{37})$$ None $$0$$ $$0$$ $$14$$ $$24$$ $$q-\beta _{2}q^{3}+(7-7\beta _{1}-2\beta _{2}-2\beta _{3})q^{5}+\cdots$$
28.4.f.a $20$ $1.652$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{10}q^{3}-\beta _{14}q^{4}+\cdots$$
28.5.b.a $2$ $2.894$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-14$$ $$q-\zeta_{6}q^{3}-3\zeta_{6}q^{5}+(-7-7\zeta_{6})q^{7}+\cdots$$
28.5.c.a $12$ $2.894$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$3$$ $$0$$ $$24$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-3+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$$
28.5.g.a $28$ $2.894$ None $$2$$ $$0$$ $$-2$$ $$0$$
28.5.h.a $6$ $2.894$ 6.0.11337408.1 None $$0$$ $$9$$ $$-27$$ $$66$$ $$q+(2-\beta _{1}+\beta _{3})q^{3}+(-3-3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
28.6.a.a $1$ $4.491$ $$\Q$$ None $$0$$ $$-2$$ $$-96$$ $$49$$ $+$ $$q-2q^{3}-96q^{5}+7^{2}q^{7}-239q^{9}+\cdots$$
28.6.a.b $1$ $4.491$ $$\Q$$ None $$0$$ $$26$$ $$16$$ $$-49$$ $-$ $$q+26q^{3}+2^{4}q^{5}-7^{2}q^{7}+433q^{9}+\cdots$$
28.6.d.a $2$ $4.491$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ $$-11$$ $$0$$ $$0$$ $$0$$ $$q+(-5-\beta )q^{2}+(23+11\beta )q^{4}+(7^{2}+\cdots)q^{7}+\cdots$$
28.6.d.b $16$ $4.491$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$8$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{3})q^{2}-\beta _{2}q^{3}+(-3-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$$
28.6.e.a $2$ $4.491$ $$\Q(\sqrt{-3})$$ None $$0$$ $$19$$ $$-19$$ $$-140$$ $$q+19\zeta_{6}q^{3}+(-19+19\zeta_{6})q^{5}+(-133+\cdots)q^{7}+\cdots$$
28.6.e.b $4$ $4.491$ $$\Q(\sqrt{-3}, \sqrt{109})$$ None $$0$$ $$-28$$ $$-42$$ $$112$$ $$q+(-14+14\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-21\beta _{1}+\cdots)q^{5}+\cdots$$
28.6.f.a $36$ $4.491$ None $$0$$ $$0$$ $$-6$$ $$0$$
28.7.b.a $4$ $6.442$ 4.0.903168.1 None $$0$$ $$0$$ $$0$$ $$-28$$ $$q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-7-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$$
28.7.c.a $18$ $6.442$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$-5$$ $$0$$ $$-44$$ $$0$$ $$q+\beta _{3}q^{2}+(\beta _{3}-\beta _{4})q^{3}+(10-\beta _{1})q^{4}+\cdots$$
28.7.g.a $44$ $6.442$ None $$-6$$ $$0$$ $$-2$$ $$0$$
28.7.h.a $8$ $6.442$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$168$$ $$-452$$ $$q+\beta _{3}q^{3}+(28-14\beta _{1}-\beta _{5})q^{5}+(-11^{2}+\cdots)q^{7}+\cdots$$
28.8.a.a $2$ $8.747$ $$\Q(\sqrt{3529})$$ None $$0$$ $$-14$$ $$42$$ $$686$$ $+$ $$q+(-7-\beta )q^{3}+(21-3\beta )q^{5}+7^{3}q^{7}+\cdots$$
28.8.a.b $2$ $8.747$ $$\Q(\sqrt{1009})$$ None $$0$$ $$14$$ $$-294$$ $$-686$$ $-$ $$q+(7-\beta )q^{3}+(-147+11\beta )q^{5}-7^{3}q^{7}+\cdots$$
28.8.d.a $2$ $8.747$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ $$13$$ $$0$$ $$0$$ $$0$$ $$q+(7+\beta )q^{2}+(-37+13\beta )q^{4}+(7^{2}+\cdots)q^{7}+\cdots$$
28.8.d.b $24$ $8.747$ None $$-8$$ $$0$$ $$0$$ $$0$$
28.8.e.a $10$ $8.747$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$27$$ $$249$$ $$332$$ $$q+(5-5\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(7^{2}\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
28.8.f.a $52$ $8.747$ None $$-8$$ $$0$$ $$-6$$ $$0$$
28.9.b.a $6$ $11.407$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$2166$$ $$q-\beta _{1}q^{3}+(-3\beta _{1}-\beta _{2})q^{5}+(19^{2}-\beta _{1}+\cdots)q^{7}+\cdots$$
28.9.c.a $24$ $11.407$ None $$3$$ $$0$$ $$-336$$ $$0$$
28.9.g.a $60$ $11.407$ None $$2$$ $$0$$ $$-2$$ $$0$$
28.9.h.a $10$ $11.407$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$-81$$ $$-837$$ $$1526$$ $$q+(-11+5\beta _{1}+\beta _{3})q^{3}+(-57-55\beta _{1}+\cdots)q^{5}+\cdots$$
28.10.a.a $2$ $14.421$ $$\Q(\sqrt{4561})$$ None $$0$$ $$-224$$ $$1596$$ $$4802$$ $+$ $$q+(-112-\beta )q^{3}+(798+9\beta )q^{5}+7^{4}q^{7}+\cdots$$
28.10.a.b $2$ $14.421$ $$\Q(\sqrt{11209})$$ None $$0$$ $$-70$$ $$1554$$ $$-4802$$ $-$ $$q+(-35-\beta )q^{3}+(777-19\beta )q^{5}-7^{4}q^{7}+\cdots$$
28.10.d.a $2$ $14.421$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ $$5$$ $$0$$ $$0$$ $$0$$ $$q+(-6+17\beta )q^{2}+(-542+85\beta )q^{4}+\cdots$$
28.10.d.b $32$ $14.421$ None $$-24$$ $$0$$ $$0$$ $$0$$
28.10.e.a $12$ $14.421$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-966$$ $$7696$$ $$q+(\beta _{3}+\beta _{4})q^{3}+(-161+161\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$$
28.10.f.a $68$ $14.421$ None $$16$$ $$0$$ $$-6$$ $$0$$
28.11.b.a $6$ $17.790$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-15666$$ $$q+\beta _{1}q^{3}+(-5\beta _{1}-\beta _{2})q^{5}+(-2611+\cdots)q^{7}+\cdots$$
28.11.c.a $30$ $17.790$ None $$11$$ $$0$$ $$3116$$ $$0$$
28.11.g.a $76$ $17.790$ None $$10$$ $$0$$ $$-2$$ $$0$$
28.11.h.a $14$ $17.790$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$-243$$ $$3333$$ $$-8810$$ $$q+(-23+12\beta _{1}-\beta _{2})q^{3}+(160+158\beta _{1}+\cdots)q^{5}+\cdots$$
28.12.a.a $3$ $21.514$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$0$$ $$-100$$ $$4762$$ $$-50421$$ $-$ $$q+(-33-\beta _{1})q^{3}+(1585+7\beta _{1}-\beta _{2})q^{5}+\cdots$$
28.12.a.b $3$ $21.514$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$0$$ $$1132$$ $$4986$$ $$50421$$ $+$ $$q+(377-\beta _{1})q^{3}+(1662+\beta _{2})q^{5}+7^{5}q^{7}+\cdots$$