## Results (1-50 of 117 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
688.1.b.a $1$ $0.343$ $$\Q$$ $$\Q(\sqrt{-43})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{9}+q^{11}-q^{13}-q^{17}+q^{23}+\cdots$$
688.1.b.b $2$ $0.343$ $$\Q(\sqrt{-2})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}-\beta q^{5}-\beta q^{7}-q^{9}+q^{11}+\cdots$$
688.1.r.a $4$ $0.343$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{3}q^{11}+\cdots$$
688.2.a.a $1$ $5.494$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$2$$ $+$ $$q-2q^{5}+2q^{7}-3q^{9}-q^{11}-q^{13}+\cdots$$
688.2.a.b $1$ $5.494$ $$\Q$$ None None $$0$$ $$2$$ $$-4$$ $$0$$ $+$ $$q+2q^{3}-4q^{5}+q^{9}-3q^{11}-5q^{13}+\cdots$$
688.2.a.c $1$ $5.494$ $$\Q$$ None None $$0$$ $$2$$ $$0$$ $$4$$ $-$ $$q+2q^{3}+4q^{7}+q^{9}+3q^{11}-q^{13}+\cdots$$
688.2.a.d $2$ $5.494$ $$\Q(\sqrt{2})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $+$ $$q+(-2+\beta )q^{3}+\beta q^{5}-\beta q^{7}+(3-4\beta )q^{9}+\cdots$$
688.2.a.e $2$ $5.494$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-1$$ $$-3$$ $$0$$ $+$ $$q-\beta q^{3}+(-1-\beta )q^{5}+(-2+4\beta )q^{7}+\cdots$$
688.2.a.f $2$ $5.494$ $$\Q(\sqrt{2})$$ None None $$0$$ $$0$$ $$4$$ $$4$$ $-$ $$q+\beta q^{3}+(2-\beta )q^{5}+(2-\beta )q^{7}-q^{9}+\cdots$$
688.2.a.g $2$ $5.494$ $$\Q(\sqrt{21})$$ None None $$0$$ $$1$$ $$3$$ $$-4$$ $-$ $$q+\beta q^{3}+(1+\beta )q^{5}-2q^{7}+(2+\beta )q^{9}+\cdots$$
688.2.a.h $2$ $5.494$ $$\Q(\sqrt{3})$$ None None $$0$$ $$2$$ $$-2$$ $$2$$ $-$ $$q+(1+\beta )q^{3}+(-1+\beta )q^{5}+(1-\beta )q^{7}+\cdots$$
688.2.a.i $3$ $5.494$ 3.3.229.1 None None $$0$$ $$-3$$ $$1$$ $$-6$$ $+$ $$q+(-1+\beta _{1})q^{3}-\beta _{2}q^{5}-2q^{7}+(1+\cdots)q^{9}+\cdots$$
688.2.a.j $5$ $5.494$ 5.5.7998268.1 None None $$0$$ $$1$$ $$1$$ $$-2$$ $-$ $$q+\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{2}-\beta _{4})q^{7}+\cdots$$
688.2.g.a $2$ $5.494$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-4$$ $$0$$ $$-4$$ $$q-2q^{3}-2\zeta_{6}q^{5}-2q^{7}+q^{9}-\zeta_{6}q^{11}+\cdots$$
688.2.g.b $2$ $5.494$ $$\Q(\sqrt{-43})$$ $$\Q(\sqrt{-43})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-3q^{9}-\beta q^{11}+3q^{13}-5q^{17}-\beta q^{23}+\cdots$$
688.2.g.c $2$ $5.494$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$4$$ $$0$$ $$4$$ $$q+2q^{3}+2\zeta_{6}q^{5}+2q^{7}+q^{9}-\zeta_{6}q^{11}+\cdots$$
688.2.g.d $4$ $5.494$ $$\Q(\sqrt{-3}, \sqrt{-43})$$ $$\Q(\sqrt{-43})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-3q^{9}+(-\beta _{1}-\beta _{3})q^{11}+(-2+\beta _{2}+\cdots)q^{13}+\cdots$$
688.2.g.e $12$ $5.494$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+\beta _{8}q^{5}+\beta _{10}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$$
688.2.i.a $2$ $5.494$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$-1$$ $$1$$ $$q+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+\zeta_{6}q^{7}+\cdots$$
688.2.i.b $2$ $5.494$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$1$$ $$5$$ $$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+5\zeta_{6}q^{7}+\cdots$$
688.2.i.c $2$ $5.494$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-3$$ $$-1$$ $$q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots$$
688.2.i.d $2$ $5.494$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$1$$ $$3$$ $$q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots$$
688.2.i.e $4$ $5.494$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$0$$ $$-3$$ $$2$$ $$-4$$ $$q+(-1-\beta _{1}-\beta _{3})q^{3}+(2-2\beta _{1}+2\beta _{3})q^{5}+\cdots$$
688.2.i.f $4$ $5.494$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None None $$0$$ $$1$$ $$-3$$ $$3$$ $$q+\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{5}+(2+\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$$
688.2.i.g $8$ $5.494$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$0$$ $$-1$$ $$0$$ $$-4$$ $$q+(\beta _{4}-\beta _{6})q^{3}+\beta _{5}q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots$$
688.2.i.h $8$ $5.494$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$0$$ $$3$$ $$0$$ $$-2$$ $$q+(1-\beta _{1}+\beta _{2})q^{3}-\beta _{5}q^{5}+(\beta _{4}+\beta _{7})q^{7}+\cdots$$
688.2.i.i $10$ $5.494$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$5$$ $$2$$ $$-4$$ $$q+(1-\beta _{1}+\beta _{7})q^{3}+(\beta _{1}-\beta _{6})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
688.2.j.a $172$ $5.494$ None None $$0$$ $$0$$ $$0$$ $$0$$
688.2.k.a $168$ $5.494$ None None $$0$$ $$0$$ $$0$$ $$0$$
688.2.o.a $2$ $5.494$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-3$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots$$
688.2.o.b $2$ $5.494$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-3$$ $$1$$ $$q+(1-\zeta_{6})q^{3}+(-1-\zeta_{6})q^{5}+\zeta_{6}q^{7}+\cdots$$
688.2.o.c $6$ $5.494$ 6.0.1714608.1 None None $$0$$ $$-3$$ $$3$$ $$-3$$ $$q+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots$$
688.2.o.d $6$ $5.494$ 6.0.3636603.4 None None $$0$$ $$-1$$ $$0$$ $$2$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{7}+\cdots$$
688.2.o.e $6$ $5.494$ 6.0.3636603.4 None None $$0$$ $$1$$ $$0$$ $$-2$$ $$q+(\beta _{1}+\beta _{2}-\beta _{4})q^{3}+(-\beta _{1}-\beta _{4})q^{7}+\cdots$$
688.2.o.f $6$ $5.494$ 6.0.1714608.1 None None $$0$$ $$3$$ $$3$$ $$3$$ $$q-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots$$
688.2.o.g $16$ $5.494$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{3}+\beta _{4}q^{5}+(-\beta _{9}-\beta _{10})q^{7}+\cdots$$
688.2.u.a $6$ $5.494$ $$\Q(\zeta_{14})$$ None None $$0$$ $$-8$$ $$-3$$ $$-4$$ $$q+(-2+2\zeta_{14}+\zeta_{14}^{3}+\zeta_{14}^{5})q^{3}+\cdots$$
688.2.u.b $6$ $5.494$ $$\Q(\zeta_{14})$$ None None $$0$$ $$-2$$ $$-3$$ $$0$$ $$q+(-\zeta_{14}^{3}-\zeta_{14}^{5})q^{3}+(-\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{5}+\cdots$$
688.2.u.c $6$ $5.494$ $$\Q(\zeta_{14})$$ None None $$0$$ $$3$$ $$2$$ $$16$$ $$q+(1-\zeta_{14}+2\zeta_{14}^{4})q^{3}-2\zeta_{14}^{2}q^{5}+\cdots$$
688.2.u.d $12$ $5.494$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$6$$ $$-3$$ $$4$$ $$q+(\beta _{6}+\beta _{9})q^{3}+(-1+\beta _{3}+\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots$$
688.2.u.e $12$ $5.494$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$10$$ $$3$$ $$0$$ $$q+(1-\beta _{10})q^{3}+(-1+\beta _{1}-\beta _{2}-2\beta _{3}+\cdots)q^{5}+\cdots$$
688.2.u.f $18$ $5.494$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$0$$ $$-2$$ $$-3$$ $$8$$ $$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7}+\cdots)q^{3}+\cdots$$
688.2.u.g $30$ $5.494$ None None $$0$$ $$-6$$ $$1$$ $$4$$
688.2.u.h $36$ $5.494$ None None $$0$$ $$6$$ $$1$$ $$0$$
688.2.x.a $344$ $5.494$ None None $$-8$$ $$-2$$ $$-2$$ $$0$$
688.2.y.a $344$ $5.494$ None None $$0$$ $$-6$$ $$-6$$ $$-12$$
688.2.bb.a $36$ $5.494$ None None $$0$$ $$0$$ $$0$$ $$0$$
688.2.bb.b $96$ $5.494$ None None $$0$$ $$0$$ $$0$$ $$0$$
688.2.bg.a $12$ $5.494$ $$\Q(\zeta_{21})$$ None None $$0$$ $$-8$$ $$3$$ $$1$$ $$q+(-1-\zeta_{21}^{7}+\zeta_{21}^{9})q^{3}+(1-\zeta_{21}+\cdots)q^{5}+\cdots$$
688.2.bg.b $24$ $5.494$ None None $$0$$ $$6$$ $$3$$ $$-3$$