## Results (1-50 of 203 matches)

Label Dim $A$ Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.2.a.a $1$ $0.279$ $$\Q$$ None $$0$$ $$1$$ $$-1$$ $$1$$ $-$ $$q+q^{3}-2q^{4}-q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots$$
35.2.a.b $2$ $0.279$ $$\Q(\sqrt{17})$$ None $$-1$$ $$-1$$ $$2$$ $$-2$$ $-$ $$q-\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+q^{5}+\cdots$$
35.2.b.a $2$ $0.279$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+2iq^{2}-iq^{3}-2q^{4}+(-2-i)q^{5}+\cdots$$
35.2.e.a $4$ $0.279$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$-2$$ $$-2$$ $$2$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$$
35.2.f.a $4$ $0.279$ $$\Q(i, \sqrt{10})$$ None $$-4$$ $$0$$ $$0$$ $$4$$ $$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots$$
35.2.j.a $4$ $0.279$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
35.2.k.a $4$ $0.279$ $$\Q(\zeta_{12})$$ None $$-4$$ $$-2$$ $$-4$$ $$0$$ $$q+(-1+\zeta_{12})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$$
35.2.k.b $4$ $0.279$ $$\Q(\zeta_{12})$$ None $$2$$ $$-4$$ $$4$$ $$-10$$ $$q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots$$
35.3.c.a $1$ $0.954$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$-1$$ $$5$$ $$-7$$ $$q-q^{3}+4q^{4}+5q^{5}-7q^{7}-8q^{9}+\cdots$$
35.3.c.b $1$ $0.954$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$1$$ $$-5$$ $$7$$ $$q+q^{3}+4q^{4}-5q^{5}+7q^{7}-8q^{9}+\cdots$$
35.3.c.c $4$ $0.954$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{3}q^{3}-5q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots$$
35.3.d.a $2$ $0.954$ $$\Q(\sqrt{-5})$$ None $$-2$$ $$0$$ $$0$$ $$14$$ $$q-q^{2}+2\beta q^{3}-3q^{4}+\beta q^{5}-2\beta q^{6}+\cdots$$
35.3.d.b $2$ $0.954$ $$\Q(\sqrt{-5})$$ None $$4$$ $$0$$ $$0$$ $$-4$$ $$q+2q^{2}+\beta q^{3}-\beta q^{5}+2\beta q^{6}+(-2+\cdots)q^{7}+\cdots$$
35.3.g.a $12$ $0.954$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-4$$ $$-4$$ $$-8$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4}+\beta _{10}+\cdots)q^{4}+\cdots$$
35.3.h.a $12$ $0.954$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-2$$ $$-6$$ $$0$$ $$-2$$ $$q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots$$
35.3.i.a $12$ $0.954$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots$$
35.3.l.a $24$ $0.954$ None $$-2$$ $$-2$$ $$-4$$ $$-6$$
35.4.a.a $1$ $2.065$ $$\Q$$ None $$1$$ $$-8$$ $$-5$$ $$7$$ $-$ $$q+q^{2}-8q^{3}-7q^{4}-5q^{5}-8q^{6}+\cdots$$
35.4.a.b $2$ $2.065$ $$\Q(\sqrt{2})$$ None $$8$$ $$2$$ $$-10$$ $$-14$$ $+$ $$q+(4+\beta )q^{2}+(1-4\beta )q^{3}+(10+8\beta )q^{4}+\cdots$$
35.4.a.c $3$ $2.065$ 3.3.14360.1 None $$-3$$ $$2$$ $$15$$ $$21$$ $+$ $$q+(-1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\cdots$$
35.4.b.a $10$ $2.065$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-4+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$$
35.4.e.a $2$ $2.065$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$2$$ $$-5$$ $$-28$$ $$q-3\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
35.4.e.b $4$ $2.065$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$6$$ $$2$$ $$-10$$ $$22$$ $$q+(\beta _{1}-3\beta _{2}+\beta _{3})q^{2}+(1+3\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$$
35.4.e.c $10$ $2.065$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-1$$ $$8$$ $$25$$ $$-62$$ $$q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{3}-\beta _{5}+2\beta _{6}+\cdots)q^{3}+\cdots$$
35.4.f.a $4$ $2.065$ $$\Q(i, \sqrt{5})$$ None $$-8$$ $$0$$ $$0$$ $$-42$$ $$q+(-2-2\beta _{2})q^{2}+(1+2\beta _{1}+\beta _{2})q^{3}+\cdots$$
35.4.f.b $16$ $2.065$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$4$$ $$0$$ $$0$$ $$32$$ $$q+\beta _{7}q^{2}-\beta _{8}q^{3}+(-4\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots$$
35.4.j.a $20$ $2.065$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q-\beta _{1}q^{2}-\beta _{14}q^{3}+(-\beta _{2}-3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$$
35.4.k.a $40$ $2.065$ None $$-2$$ $$-6$$ $$-30$$ $$4$$
35.5.c.a $1$ $3.618$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$-17$$ $$25$$ $$49$$ $$q-17q^{3}+2^{4}q^{4}+5^{2}q^{5}+7^{2}q^{7}+\cdots$$
35.5.c.b $1$ $3.618$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$17$$ $$-25$$ $$-49$$ $$q+17q^{3}+2^{4}q^{4}-5^{2}q^{5}-7^{2}q^{7}+\cdots$$
35.5.c.c $2$ $3.618$ $$\Q(\sqrt{-6})$$ None $$0$$ $$-10$$ $$-10$$ $$-70$$ $$q+\beta q^{2}-5q^{3}+10q^{4}+(-5+10\beta )q^{5}+\cdots$$
35.5.c.d $2$ $3.618$ $$\Q(\sqrt{-6})$$ None $$0$$ $$10$$ $$10$$ $$70$$ $$q+\beta q^{2}+5q^{3}+10q^{4}+(5-10\beta )q^{5}+\cdots$$
35.5.c.e $8$ $3.618$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+3\beta _{3}q^{3}+(-22+\beta _{2})q^{4}+\cdots$$
35.5.d.a $12$ $3.618$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-6$$ $$0$$ $$0$$ $$-50$$ $$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(11-\beta _{1}+\cdots)q^{4}+\cdots$$
35.5.g.a $24$ $3.618$ None $$0$$ $$20$$ $$-48$$ $$0$$
35.5.h.a $20$ $3.618$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$6$$ $$-18$$ $$0$$ $$-54$$ $$q+(1+\beta _{1}+\beta _{3}+\beta _{4})q^{2}+(-1-\beta _{4}+\cdots)q^{3}+\cdots$$
35.5.i.a $28$ $3.618$ None $$0$$ $$0$$ $$-30$$ $$0$$
35.5.l.a $56$ $3.618$ None $$-2$$ $$-2$$ $$16$$ $$46$$
35.6.a.a $1$ $5.613$ $$\Q$$ None $$-8$$ $$1$$ $$25$$ $$49$$ $+$ $$q-8q^{2}+q^{3}+2^{5}q^{4}+5^{2}q^{5}-8q^{6}+\cdots$$
35.6.a.b $2$ $5.613$ $$\Q(\sqrt{65})$$ None $$1$$ $$3$$ $$-50$$ $$-98$$ $+$ $$q+\beta q^{2}+(3-3\beta )q^{3}+(-2^{4}+\beta )q^{4}+\cdots$$
35.6.a.c $3$ $5.613$ 3.3.577880.1 None $$-6$$ $$26$$ $$-75$$ $$147$$ $-$ $$q+(-2+\beta _{1})q^{2}+(9+\beta _{2})q^{3}+(38+2\beta _{2})q^{4}+\cdots$$
35.6.a.d $4$ $5.613$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None $$7$$ $$14$$ $$100$$ $$-196$$ $-$ $$q+(2-\beta _{1})q^{2}+(4-\beta _{1}+\beta _{3})q^{3}+(15+\cdots)q^{4}+\cdots$$
35.6.b.a $14$ $5.613$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$156$$ $$0$$ $$q-\beta _{4}q^{2}+\beta _{6}q^{3}+(-15+\beta _{1})q^{4}+\cdots$$
35.6.e.a $12$ $5.613$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$5$$ $$-20$$ $$150$$ $$-20$$ $$q+(1-\beta _{1}-\beta _{4})q^{2}+(\beta _{1}+\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots$$
35.6.e.b $16$ $5.613$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-3$$ $$2$$ $$-200$$ $$158$$ $$q-\beta _{1}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(\beta _{1}-5^{2}\beta _{2}+\cdots)q^{4}+\cdots$$
35.6.f.a $36$ $5.613$ None $$-4$$ $$0$$ $$0$$ $$-196$$
35.6.j.a $36$ $5.613$ None $$0$$ $$0$$ $$-12$$ $$0$$
35.6.k.a $72$ $5.613$ None $$-2$$ $$-6$$ $$60$$ $$190$$
35.7.c.a $1$ $8.052$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$-26$$ $$-125$$ $$343$$ $$q-26q^{3}+2^{6}q^{4}-5^{3}q^{5}+7^{3}q^{7}+\cdots$$
35.7.c.b $1$ $8.052$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$26$$ $$125$$ $$-343$$ $$q+26q^{3}+2^{6}q^{4}+5^{3}q^{5}-7^{3}q^{7}+\cdots$$