## Results (1-50 of 54 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
644.1.h.a $1$ $0.321$ $$\Q$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-161})$$ $$\Q(\sqrt{23})$$ $$1$$ $$0$$ $$0$$ $$-1$$ $$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}+2q^{11}+\cdots$$
644.1.h.b $1$ $0.321$ $$\Q$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-161})$$ $$\Q(\sqrt{23})$$ $$1$$ $$0$$ $$0$$ $$1$$ $$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{9}-2q^{11}+\cdots$$
644.1.h.c $2$ $0.321$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-161})$$ None $$-2$$ $$0$$ $$0$$ $$-2$$ $$q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}-q^{7}+\cdots$$
644.1.h.d $2$ $0.321$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-161})$$ None $$-2$$ $$0$$ $$0$$ $$2$$ $$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+q^{7}+\cdots$$
644.1.r.a $10$ $0.321$ $$\Q(\zeta_{22})$$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$-1$$ $$q+\zeta_{22}^{6}q^{2}-\zeta_{22}q^{4}-\zeta_{22}^{9}q^{7}-\zeta_{22}^{7}q^{8}+\cdots$$
644.1.r.b $10$ $0.321$ $$\Q(\zeta_{22})$$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$1$$ $$q+\zeta_{22}^{4}q^{2}+\zeta_{22}^{8}q^{4}+\zeta_{22}^{9}q^{7}+\cdots$$
644.2.a.a $1$ $5.142$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$1$$ $+$ $$q-q^{3}+q^{7}-2q^{9}-2q^{11}-3q^{13}+\cdots$$
644.2.a.b $1$ $5.142$ $$\Q$$ None None $$0$$ $$1$$ $$-2$$ $$-1$$ $+$ $$q+q^{3}-2q^{5}-q^{7}-2q^{9}-2q^{11}+\cdots$$
644.2.a.c $5$ $5.142$ 5.5.8580816.1 None None $$0$$ $$1$$ $$4$$ $$5$$ $-$ $$q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$$
644.2.a.d $5$ $5.142$ 5.5.6963152.1 None None $$0$$ $$3$$ $$2$$ $$-5$$ $-$ $$q+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots$$
644.2.c.a $36$ $5.142$ None None $$1$$ $$0$$ $$0$$ $$-36$$
644.2.c.b $36$ $5.142$ None None $$1$$ $$0$$ $$0$$ $$36$$
644.2.d.a $16$ $5.142$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{3}+\beta _{2}q^{5}+\beta _{8}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$$
644.2.f.a $4$ $5.142$ $$\Q(i, \sqrt{14})$$ None None $$-4$$ $$-4$$ $$0$$ $$0$$ $$q+(-1+\beta _{2})q^{2}-q^{3}-2\beta _{2}q^{4}-2\beta _{2}q^{5}+\cdots$$
644.2.f.b $4$ $5.142$ $$\Q(i, \sqrt{14})$$ None None $$-4$$ $$4$$ $$0$$ $$0$$ $$q+(-1+\beta _{2})q^{2}+q^{3}-2\beta _{2}q^{4}+2\beta _{2}q^{5}+\cdots$$
644.2.f.c $80$ $5.142$ None None $$8$$ $$0$$ $$0$$ $$0$$
644.2.i.a $14$ $5.142$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None None $$0$$ $$-3$$ $$-2$$ $$6$$ $$q+\beta _{10}q^{3}+(-\beta _{2}-\beta _{11})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$$
644.2.i.b $14$ $5.142$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None None $$0$$ $$5$$ $$2$$ $$4$$ $$q+(1-\beta _{1}-\beta _{7})q^{3}+(-\beta _{3}-\beta _{5})q^{5}+\cdots$$
644.2.k.a $176$ $5.142$ None None $$0$$ $$0$$ $$0$$ $$0$$
644.2.m.a $32$ $5.142$ None None $$0$$ $$0$$ $$0$$ $$0$$
644.2.p.a $184$ $5.142$ None None $$0$$ $$0$$ $$0$$ $$0$$
644.2.q.a $60$ $5.142$ None None $$0$$ $$-4$$ $$-11$$ $$6$$
644.2.q.b $60$ $5.142$ None None $$0$$ $$0$$ $$7$$ $$-6$$
644.2.t.a $20$ $5.142$ 20.0.$$\cdots$$.2 $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{13})q^{2}+(-\beta _{10}-\beta _{19})q^{4}+\cdots$$
644.2.t.b $20$ $5.142$ 20.0.$$\cdots$$.2 $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{13})q^{2}+(-\beta _{10}-\beta _{19})q^{4}+\cdots$$
644.2.t.c $880$ $5.142$ None None $$-22$$ $$0$$ $$0$$ $$0$$
644.2.v.a $160$ $5.142$ None None $$0$$ $$0$$ $$0$$ $$0$$
644.2.w.a $360$ $5.142$ None None $$-1$$ $$0$$ $$0$$ $$-36$$
644.2.w.b $360$ $5.142$ None None $$-1$$ $$0$$ $$0$$ $$36$$
644.2.y.a $320$ $5.142$ None None $$0$$ $$0$$ $$6$$ $$-2$$
644.2.z.a $1840$ $5.142$ None None $$-11$$ $$0$$ $$-22$$ $$0$$
644.2.bc.a $320$ $5.142$ None None $$0$$ $$0$$ $$0$$ $$0$$
644.2.be.a $1840$ $5.142$ None None $$-7$$ $$0$$ $$-54$$ $$0$$
644.3.b.a $28$ $17.548$ None None $$0$$ $$0$$ $$0$$ $$-14$$
644.3.g.a $24$ $17.548$ None None $$0$$ $$-4$$ $$0$$ $$0$$
644.3.l.a $64$ $17.548$ None None $$0$$ $$0$$ $$0$$ $$0$$
644.3.o.a $60$ $17.548$ None None $$0$$ $$-6$$ $$0$$ $$22$$
644.4.a.a $6$ $37.997$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None None $$0$$ $$-6$$ $$-10$$ $$42$$ $-$ $$q+(-1+\beta _{1})q^{3}+(-2-\beta _{1}-\beta _{4})q^{5}+\cdots$$
644.4.a.b $6$ $37.997$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None None $$0$$ $$2$$ $$0$$ $$-42$$ $-$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}-7q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$$
644.4.a.c $10$ $37.997$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$0$$ $$10$$ $$70$$ $+$ $$q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}+7q^{7}+(12+\beta _{2}+\cdots)q^{9}+\cdots$$
644.4.a.d $10$ $37.997$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$8$$ $$20$$ $$-70$$ $+$ $$q+(1-\beta _{1})q^{3}+(2-\beta _{4})q^{5}-7q^{7}+(12+\cdots)q^{9}+\cdots$$
644.4.d.a $48$ $37.997$ None None $$0$$ $$0$$ $$0$$ $$0$$
644.4.i.a $44$ $37.997$ None None $$0$$ $$-12$$ $$-10$$ $$-38$$
644.4.i.b $44$ $37.997$ None None $$0$$ $$12$$ $$10$$ $$-6$$
644.4.m.a $96$ $37.997$ None None $$0$$ $$0$$ $$0$$ $$0$$
644.5.b.a $60$ $66.570$ None None $$0$$ $$0$$ $$0$$ $$-2$$
644.5.g.a $48$ $66.570$ None None $$0$$ $$20$$ $$0$$ $$0$$
644.6.a.a $12$ $103.287$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-25$$ $$-64$$ $$-588$$ $+$ $$q+(-2-\beta _{1})q^{3}+(-5+\beta _{5})q^{5}-7^{2}q^{7}+\cdots$$
644.6.a.b $12$ $103.287$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-15$$ $$-14$$ $$588$$ $+$ $$q+(-1-\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+7^{2}q^{7}+\cdots$$
644.6.a.c $16$ $103.287$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$-7$$ $$36$$ $$-784$$ $-$ $$q-\beta _{1}q^{3}+(2-\beta _{3})q^{5}-7^{2}q^{7}+(102+\cdots)q^{9}+\cdots$$