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## Results (1-50 of 135 matches)

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Label Dim $A$ Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
190.2.a.a $1$ $1.517$ $$\Q$$ None $$-1$$ $$-1$$ $$-1$$ $$-1$$ $+$ $$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$$
190.2.a.b $1$ $1.517$ $$\Q$$ None $$1$$ $$-3$$ $$-1$$ $$-5$$ $+$ $$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots$$
190.2.a.c $1$ $1.517$ $$\Q$$ None $$1$$ $$1$$ $$1$$ $$-1$$ $-$ $$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$$
190.2.a.d $2$ $1.517$ $$\Q(\sqrt{17})$$ None $$-2$$ $$-1$$ $$2$$ $$-1$$ $-$ $$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots$$
190.2.b.a $4$ $1.517$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots$$
190.2.b.b $6$ $1.517$ 6.0.5161984.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
190.2.e.a $2$ $1.517$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$1$$ $$2$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$$
190.2.e.b $2$ $1.517$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$1$$ $$4$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
190.2.e.c $4$ $1.517$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$2$$ $$1$$ $$-2$$ $$10$$ $$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots$$
190.2.f.a $4$ $1.517$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-4$$ $$-4$$ $$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+2\zeta_{8}^{2})q^{5}+\cdots$$
190.2.f.b $16$ $1.517$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{8}q^{2}+(\beta _{1}-\beta _{7}+\beta _{10}+\beta _{12})q^{3}+\cdots$$
190.2.i.a $20$ $1.517$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\beta _{2}-\beta _{13})q^{2}-\beta _{1}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$$
190.2.k.a $6$ $1.517$ $$\Q(\zeta_{18})$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots$$
190.2.k.b $12$ $1.517$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$6$$ $$q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$$
190.2.k.c $12$ $1.517$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$3$$ $$0$$ $$-6$$ $$q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots$$
190.2.k.d $18$ $1.517$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots$$
190.2.m.a $8$ $1.517$ $$\Q(\zeta_{24})$$ None $$0$$ $$12$$ $$4$$ $$-16$$ $$q+\zeta_{24}^{7}q^{2}+(2+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots$$
190.2.m.b $32$ $1.517$ None $$0$$ $$-12$$ $$0$$ $$24$$
190.2.p.a $60$ $1.517$ None $$0$$ $$0$$ $$0$$ $$0$$
190.2.r.a $120$ $1.517$ None $$0$$ $$0$$ $$0$$ $$-12$$
190.3.c.a $16$ $5.177$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{9}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots$$
190.3.d.a $20$ $5.177$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{4}q^{3}+2q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots$$
190.3.g.a $16$ $5.177$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-16$$ $$8$$ $$2$$ $$-10$$ $$q+(-1-\beta _{5})q^{2}+(-\beta _{2}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots$$
190.3.g.b $20$ $5.177$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$20$$ $$0$$ $$2$$ $$14$$ $$q+(1+\beta _{3})q^{2}-\beta _{2}q^{3}+2\beta _{3}q^{4}+\beta _{16}q^{5}+\cdots$$
190.3.h.a $4$ $5.177$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{1}q^{2}+2\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
190.3.h.b $36$ $5.177$ None $$0$$ $$0$$ $$4$$ $$0$$
190.3.j.a $32$ $5.177$ None $$0$$ $$-12$$ $$0$$ $$8$$
190.3.l.a $4$ $5.177$ $$\Q(\zeta_{12})$$ None $$-2$$ $$-6$$ $$8$$ $$32$$ $$q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+\cdots)q^{3}+\cdots$$
190.3.l.b $4$ $5.177$ $$\Q(\zeta_{12})$$ None $$2$$ $$6$$ $$10$$ $$8$$ $$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(3\zeta_{12}+\cdots)q^{3}+\cdots$$
190.3.l.c $36$ $5.177$ None $$-18$$ $$6$$ $$-10$$ $$-28$$
190.3.l.d $36$ $5.177$ None $$18$$ $$-6$$ $$-12$$ $$12$$
190.3.n.a $72$ $5.177$ None $$0$$ $$12$$ $$0$$ $$0$$
190.3.o.a $120$ $5.177$ None $$0$$ $$0$$ $$0$$ $$0$$
190.3.q.a $120$ $5.177$ None $$0$$ $$0$$ $$0$$ $$-18$$
190.3.q.b $120$ $5.177$ None $$0$$ $$0$$ $$0$$ $$-18$$
190.4.a.a $1$ $11.210$ $$\Q$$ None $$-2$$ $$-2$$ $$5$$ $$8$$ $+$ $$q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots$$
190.4.a.b $1$ $11.210$ $$\Q$$ None $$-2$$ $$2$$ $$5$$ $$-12$$ $-$ $$q-2q^{2}+2q^{3}+4q^{4}+5q^{5}-4q^{6}+\cdots$$
190.4.a.c $1$ $11.210$ $$\Q$$ None $$2$$ $$-4$$ $$5$$ $$-20$$ $-$ $$q+2q^{2}-4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots$$
190.4.a.d $2$ $11.210$ $$\Q(\sqrt{313})$$ None $$-4$$ $$1$$ $$10$$ $$-27$$ $+$ $$q-2q^{2}+\beta q^{3}+4q^{4}+5q^{5}-2\beta q^{6}+\cdots$$
190.4.a.e $2$ $11.210$ $$\Q(\sqrt{3})$$ None $$-4$$ $$2$$ $$-10$$ $$8$$ $+$ $$q-2q^{2}+(1+3\beta )q^{3}+4q^{4}-5q^{5}+\cdots$$
190.4.a.f $2$ $11.210$ $$\Q(\sqrt{34})$$ None $$4$$ $$0$$ $$-10$$ $$24$$ $+$ $$q+2q^{2}+\beta q^{3}+4q^{4}-5q^{5}+2\beta q^{6}+\cdots$$
190.4.a.g $3$ $11.210$ 3.3.126168.1 None $$-6$$ $$-1$$ $$-15$$ $$1$$ $-$ $$q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots$$
190.4.a.h $3$ $11.210$ 3.3.5468.1 None $$6$$ $$-9$$ $$-15$$ $$-11$$ $-$ $$q+2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$$
190.4.a.i $3$ $11.210$ 3.3.15357.1 None $$6$$ $$11$$ $$15$$ $$29$$ $+$ $$q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots$$
190.4.b.a $12$ $11.210$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$20$$ $$0$$ $$q+\beta _{8}q^{2}+(\beta _{8}-\beta _{9})q^{3}-4q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots$$
190.4.b.b $14$ $11.210$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\beta _{8}q^{2}+\beta _{3}q^{3}-4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$$
190.4.e.a $2$ $11.210$ $$\Q(\sqrt{-3})$$ None $$2$$ $$2$$ $$-5$$ $$-56$$ $$q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$$
190.4.e.b $2$ $11.210$ $$\Q(\sqrt{-3})$$ None $$2$$ $$2$$ $$5$$ $$64$$ $$q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$$
190.4.e.c $6$ $11.210$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$6$$ $$3$$ $$-15$$ $$36$$ $$q+2\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots$$
190.4.e.d $8$ $11.210$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$8$$ $$3$$ $$20$$ $$-82$$ $$q+(2+2\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$$
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