## Results (1-50 of 269 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.1.k.a $4$ $0.262$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-35})$$ $$\Q(\sqrt{105})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots$$
525.1.p.a $4$ $0.262$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
525.1.u.a $2$ $0.262$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-1$$ $$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$$
525.1.u.b $2$ $0.262$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$1$$ $$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$$
525.1.be.a $8$ $0.262$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+\cdots$$
525.2.a.a $1$ $4.192$ $$\Q$$ None None $$-1$$ $$-1$$ $$0$$ $$-1$$ $+$ $$q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots$$
525.2.a.b $1$ $4.192$ $$\Q$$ None None $$-1$$ $$1$$ $$0$$ $$-1$$ $+$ $$q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots$$
525.2.a.c $1$ $4.192$ $$\Q$$ None None $$1$$ $$-1$$ $$0$$ $$1$$ $+$ $$q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots$$
525.2.a.d $1$ $4.192$ $$\Q$$ None None $$1$$ $$-1$$ $$0$$ $$1$$ $-$ $$q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots$$
525.2.a.e $2$ $4.192$ $$\Q(\sqrt{5})$$ None None $$-3$$ $$-2$$ $$0$$ $$2$$ $+$ $$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots$$
525.2.a.f $2$ $4.192$ $$\Q(\sqrt{13})$$ None None $$-1$$ $$-2$$ $$0$$ $$-2$$ $+$ $$q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots$$
525.2.a.g $2$ $4.192$ $$\Q(\sqrt{5})$$ None None $$0$$ $$2$$ $$0$$ $$-2$$ $-$ $$q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-q^{7}-\beta q^{8}+\cdots$$
525.2.a.h $2$ $4.192$ $$\Q(\sqrt{13})$$ None None $$1$$ $$2$$ $$0$$ $$2$$ $-$ $$q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+q^{7}+\cdots$$
525.2.a.i $2$ $4.192$ $$\Q(\sqrt{5})$$ None None $$3$$ $$2$$ $$0$$ $$-2$$ $-$ $$q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots$$
525.2.a.j $3$ $4.192$ 3.3.148.1 None None $$-1$$ $$3$$ $$0$$ $$3$$ $-$ $$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$$
525.2.a.k $3$ $4.192$ 3.3.148.1 None None $$1$$ $$-3$$ $$0$$ $$-3$$ $-$ $$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$$
525.2.b.a $2$ $4.192$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-3q^{6}+(-2+\cdots)q^{7}+\cdots$$
525.2.b.b $2$ $4.192$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+3q^{6}+(-2+\cdots)q^{7}+\cdots$$
525.2.b.c $2$ $4.192$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-5$$ $$q+(1-2\zeta_{6})q^{3}+2q^{4}+(-2-\zeta_{6})q^{7}+\cdots$$
525.2.b.d $2$ $4.192$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$5$$ $$q+(1-2\zeta_{6})q^{3}+2q^{4}+(3-\zeta_{6})q^{7}+\cdots$$
525.2.b.e $4$ $4.192$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$-1$$ $$0$$ $$8$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots$$
525.2.b.f $4$ $4.192$ $$\Q(\sqrt{5}, \sqrt{-7})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+2q^{4}+(\beta _{1}-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$$
525.2.b.g $4$ $4.192$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$1$$ $$0$$ $$8$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots$$
525.2.b.h $8$ $4.192$ 8.0.$$\cdots$$.7 None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{2}q^{2}-\beta _{7}q^{3}+(-2+\beta _{4})q^{4}+\beta _{3}q^{6}+\cdots$$
525.2.b.i $8$ $4.192$ 8.0.$$\cdots$$.7 None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\beta _{3}q^{2}+\beta _{1}q^{3}+(-2+\beta _{4})q^{4}-\beta _{5}q^{6}+\cdots$$
525.2.b.j $8$ $4.192$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{2}-\zeta_{24}^{3}q^{3}-q^{4}+(\zeta_{24}^{2}+\cdots)q^{6}+\cdots$$
525.2.d.a $2$ $4.192$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}+iq^{7}+3iq^{8}+\cdots$$
525.2.d.b $2$ $4.192$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}+iq^{7}+3iq^{8}+\cdots$$
525.2.d.c $4$ $4.192$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{1}q^{3}-3q^{4}+\beta _{3}q^{6}-\beta _{1}q^{7}+\cdots$$
525.2.d.d $4$ $4.192$ $$\Q(i, \sqrt{13})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots$$
525.2.d.e $4$ $4.192$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots$$
525.2.g.a $4$ $4.192$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{3}-2q^{4}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots$$
525.2.g.b $4$ $4.192$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+q^{4}-3q^{6}+(-\zeta_{12}+\cdots)q^{7}+\cdots$$
525.2.g.c $4$ $4.192$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}-\zeta_{12}q^{3}+q^{4}+3q^{6}+(-\zeta_{12}+\cdots)q^{7}+\cdots$$
525.2.g.d $8$ $4.192$ 8.0.303595776.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{4}-\beta _{5})q^{2}-\beta _{1}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$$
525.2.g.e $8$ $4.192$ 8.0.303595776.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots$$
525.2.g.f $16$ $4.192$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}-\beta _{8}q^{6}+\cdots$$
525.2.i.a $2$ $4.192$ $$\Q(\sqrt{-3})$$ None None $$-2$$ $$1$$ $$0$$ $$1$$ $$q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
525.2.i.b $2$ $4.192$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$-1$$ $$0$$ $$-1$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
525.2.i.c $2$ $4.192$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$0$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(-2-\zeta_{6})q^{7}+\cdots$$
525.2.i.d $2$ $4.192$ $$\Q(\sqrt{-3})$$ None None $$1$$ $$1$$ $$0$$ $$1$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
525.2.i.e $2$ $4.192$ $$\Q(\sqrt{-3})$$ None None $$2$$ $$1$$ $$0$$ $$5$$ $$q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
525.2.i.f $4$ $4.192$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$-2$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
525.2.i.g $4$ $4.192$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$-2$$ $$0$$ $$2$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{3}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$$
525.2.i.h $8$ $4.192$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$-2$$ $$4$$ $$0$$ $$2$$ $$q+(-1-\beta _{1}-\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots$$
525.2.i.i $8$ $4.192$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$-1$$ $$4$$ $$0$$ $$1$$ $$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots$$
525.2.i.j $8$ $4.192$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$1$$ $$-4$$ $$0$$ $$-1$$ $$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots$$
525.2.i.k $8$ $4.192$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$2$$ $$-4$$ $$0$$ $$-2$$ $$q+(1+\beta _{1}+\beta _{3}-\beta _{4})q^{2}-\beta _{4}q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$$
525.2.j.a $16$ $4.192$ 16.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{10}+\beta _{13}-\beta _{15})q^{2}+\beta _{7}q^{3}+\cdots$$
525.2.j.b $24$ $4.192$ None None $$0$$ $$4$$ $$0$$ $$0$$