## Results (1-50 of 163 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
693.1.h.a $4$ $0.346$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+\cdots$$
693.1.o.a $4$ $0.346$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}^{5}q^{6}+\cdots$$
693.1.bl.a $4$ $0.346$ $$\Q(\zeta_{12})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}-q^{3}+\zeta_{12}q^{6}-\zeta_{12}^{3}q^{7}+\cdots$$
693.1.bp.a $16$ $0.346$ $$\Q(\zeta_{40})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{2}+\zeta_{40}^{8}+\cdots)q^{4}+\cdots$$
693.1.br.a $4$ $0.346$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-7})$$ None $$2$$ $$0$$ $$0$$ $$-1$$ $$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$$
693.1.br.b $8$ $0.346$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(-\zeta_{20}^{2}+\zeta_{20}^{6}+\cdots)q^{4}+\cdots$$
693.2.a.a $1$ $5.534$ $$\Q$$ None None $$-1$$ $$0$$ $$2$$ $$-1$$ $-$ $$q-q^{2}-q^{4}+2q^{5}-q^{7}+3q^{8}-2q^{10}+\cdots$$
693.2.a.b $1$ $5.534$ $$\Q$$ None None $$0$$ $$0$$ $$-3$$ $$1$$ $-$ $$q-2q^{4}-3q^{5}+q^{7}+q^{11}-4q^{13}+\cdots$$
693.2.a.c $1$ $5.534$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-1$$ $+$ $$q-2q^{4}+q^{5}-q^{7}+q^{11}-4q^{13}+\cdots$$
693.2.a.d $1$ $5.534$ $$\Q$$ None None $$1$$ $$0$$ $$2$$ $$1$$ $-$ $$q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots$$
693.2.a.e $2$ $5.534$ $$\Q(\sqrt{5})$$ None None $$-3$$ $$0$$ $$-2$$ $$2$$ $+$ $$q+(-1-\beta )q^{2}+3\beta q^{4}-q^{5}+q^{7}+\cdots$$
693.2.a.f $2$ $5.534$ $$\Q(\sqrt{5})$$ None None $$-1$$ $$0$$ $$-2$$ $$2$$ $+$ $$q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots$$
693.2.a.g $2$ $5.534$ $$\Q(\sqrt{13})$$ None None $$-1$$ $$0$$ $$-2$$ $$-2$$ $+$ $$q-\beta q^{2}+(1+\beta )q^{4}-q^{5}-q^{7}-3q^{8}+\cdots$$
693.2.a.h $2$ $5.534$ $$\Q(\sqrt{5})$$ None None $$0$$ $$0$$ $$4$$ $$2$$ $-$ $$q-\beta q^{2}+3q^{4}+2q^{5}+q^{7}-\beta q^{8}+\cdots$$
693.2.a.i $2$ $5.534$ $$\Q(\sqrt{13})$$ None None $$1$$ $$0$$ $$2$$ $$-2$$ $-$ $$q+\beta q^{2}+(1+\beta )q^{4}+q^{5}-q^{7}+3q^{8}+\cdots$$
693.2.a.j $2$ $5.534$ $$\Q(\sqrt{21})$$ None None $$1$$ $$0$$ $$-6$$ $$2$$ $-$ $$q+\beta q^{2}+(3+\beta )q^{4}-3q^{5}+q^{7}+(5+\cdots)q^{8}+\cdots$$
693.2.a.k $2$ $5.534$ $$\Q(\sqrt{5})$$ None None $$3$$ $$0$$ $$2$$ $$2$$ $-$ $$q+(1+\beta )q^{2}+3\beta q^{4}+q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots$$
693.2.a.l $3$ $5.534$ 3.3.229.1 None None $$-2$$ $$0$$ $$-4$$ $$-3$$ $+$ $$q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots$$
693.2.a.m $3$ $5.534$ 3.3.837.1 None None $$0$$ $$0$$ $$0$$ $$-3$$ $-$ $$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$$
693.2.c.a $2$ $5.534$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}-5q^{4}+\beta q^{7}+3\beta q^{8}+(-2+\cdots)q^{11}+\cdots$$
693.2.c.b $4$ $5.534$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}-2\beta _{2}q^{8}+\cdots$$
693.2.c.c $4$ $5.534$ $$\Q(i, \sqrt{7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+q^{4}-\beta _{3}q^{7}+3\beta _{1}q^{8}+(2\beta _{1}+\cdots)q^{11}+\cdots$$
693.2.c.d $12$ $5.534$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ $$\Q(\sqrt{-231})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(-2+\beta _{1})q^{4}+\beta _{4}q^{5}+\beta _{6}q^{7}+\cdots$$
693.2.c.e $16$ $5.534$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+(-1+\beta _{4})q^{4}-\beta _{1}q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots$$
693.2.e.a $24$ $5.534$ None None $$0$$ $$0$$ $$0$$ $$8$$
693.2.g.a $24$ $5.534$ None None $$0$$ $$0$$ $$0$$ $$0$$
693.2.i.a $2$ $5.534$ $$\Q(\sqrt{-3})$$ None None $$-2$$ $$0$$ $$0$$ $$5$$ $$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots$$
693.2.i.b $2$ $5.534$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$0$$ $$4$$ $$-4$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$$
693.2.i.c $2$ $5.534$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-4$$ $$-5$$ $$q+(2-2\zeta_{6})q^{4}-4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
693.2.i.d $2$ $5.534$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$4$$ $$-5$$ $$q+(2-2\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
693.2.i.e $2$ $5.534$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$0$$ $$0$$ $$-4$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(-1-2\zeta_{6})q^{7}+\cdots$$
693.2.i.f $4$ $5.534$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$-2$$ $$0$$ $$-4$$ $$4$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
693.2.i.g $6$ $5.534$ 6.0.1783323.2 None None $$0$$ $$0$$ $$-2$$ $$2$$ $$q+(\beta _{3}-\beta _{5})q^{2}+(-1-\beta _{1}+\beta _{4}+\beta _{5})q^{4}+\cdots$$
693.2.i.h $6$ $5.534$ $$\Q(\zeta_{18})$$ None None $$0$$ $$0$$ $$6$$ $$0$$ $$q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$$
693.2.i.i $8$ $5.534$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$2$$ $$0$$ $$4$$ $$2$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{6})q^{4}+\cdots$$
693.2.i.j $10$ $5.534$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$2$$ $$0$$ $$-4$$ $$-1$$ $$q+\beta _{3}q^{2}+(-2-2\beta _{2}-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$$
693.2.i.k $12$ $5.534$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$-4$$ $$6$$ $$q+\beta _{6}q^{2}+(-2+2\beta _{4}-\beta _{8})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$$
693.2.i.l $12$ $5.534$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$4$$ $$6$$ $$q-\beta _{6}q^{2}+(-2+2\beta _{4}-\beta _{8})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$$
693.2.j.a $2$ $5.534$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$3$$ $$2$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
693.2.j.b $2$ $5.534$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$-3$$ $$3$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
693.2.j.c $2$ $5.534$ $$\Q(\sqrt{-3})$$ None None $$2$$ $$3$$ $$1$$ $$-1$$ $$q+(2-2\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$$
693.2.j.d $6$ $5.534$ 6.0.4406832.1 None None $$1$$ $$9$$ $$-1$$ $$-3$$ $$q+(-\beta _{3}+\beta _{5})q^{2}+(2-\beta _{4})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$$
693.2.j.e $12$ $5.534$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$-1$$ $$-1$$ $$12$$ $$-6$$ $$q+(-\beta _{4}+\beta _{8})q^{2}+(\beta _{2}-\beta _{8})q^{3}+(-2+\cdots)q^{4}+\cdots$$
693.2.j.f $18$ $5.534$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$-1$$ $$1$$ $$-6$$ $$-9$$ $$q-\beta _{1}q^{2}+\beta _{13}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$
693.2.j.g $20$ $5.534$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None None $$2$$ $$-8$$ $$-10$$ $$-10$$ $$q+\beta _{7}q^{2}+\beta _{4}q^{3}+(\beta _{7}+\beta _{12}-\beta _{13}+\cdots)q^{4}+\cdots$$
693.2.j.h $28$ $5.534$ None None $$-1$$ $$-2$$ $$-4$$ $$14$$
693.2.j.i $30$ $5.534$ None None $$-2$$ $$0$$ $$1$$ $$15$$
693.2.k.a $6$ $5.534$ $$\Q(\zeta_{18})$$ None None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots$$
693.2.k.b $74$ $5.534$ None None $$0$$ $$0$$ $$14$$ $$-1$$
693.2.k.c $80$ $5.534$ None None $$0$$ $$0$$ $$8$$ $$-1$$