## Results (1-50 of 310 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
448.1.l.a $2$ $0.224$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-iq^{9}+(1+i)q^{11}+iq^{25}+\cdots$$
448.1.r.a $4$ $0.224$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots$$
448.1.bf.a $8$ $0.224$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{5}q^{7}-\zeta_{16}^{3}q^{8}+\cdots$$
448.2.a.a $1$ $3.577$ $$\Q$$ None None $$0$$ $$-2$$ $$0$$ $$-1$$ $-$ $$q-2q^{3}-q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots$$
448.2.a.b $1$ $3.577$ $$\Q$$ None None $$0$$ $$-2$$ $$0$$ $$1$$ $+$ $$q-2q^{3}+q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$$
448.2.a.c $1$ $3.577$ $$\Q$$ None None $$0$$ $$-2$$ $$4$$ $$1$$ $-$ $$q-2q^{3}+4q^{5}+q^{7}+q^{9}-8q^{15}+\cdots$$
448.2.a.d $1$ $3.577$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$-1$$ $+$ $$q-2q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots$$
448.2.a.e $1$ $3.577$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$1$$ $+$ $$q-2q^{5}+q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots$$
448.2.a.f $1$ $3.577$ $$\Q$$ None None $$0$$ $$2$$ $$0$$ $$-1$$ $-$ $$q+2q^{3}-q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$$
448.2.a.g $1$ $3.577$ $$\Q$$ None None $$0$$ $$2$$ $$0$$ $$1$$ $-$ $$q+2q^{3}+q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots$$
448.2.a.h $1$ $3.577$ $$\Q$$ None None $$0$$ $$2$$ $$4$$ $$-1$$ $-$ $$q+2q^{3}+4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots$$
448.2.a.i $2$ $3.577$ $$\Q(\sqrt{5})$$ None None $$0$$ $$-2$$ $$-2$$ $$-2$$ $+$ $$q+(-1-\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots$$
448.2.a.j $2$ $3.577$ $$\Q(\sqrt{5})$$ None None $$0$$ $$2$$ $$-2$$ $$2$$ $-$ $$q+(1+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots$$
448.2.b.a $2$ $3.577$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}-2iq^{5}-q^{7}-q^{9}-iq^{11}+\cdots$$
448.2.b.b $2$ $3.577$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+2iq^{5}+q^{7}-q^{9}-iq^{11}+\cdots$$
448.2.b.c $4$ $3.577$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{12}q^{3}-\zeta_{12}q^{5}-q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots$$
448.2.b.d $4$ $3.577$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{12}q^{3}+\zeta_{12}q^{5}+q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots$$
448.2.e.a $8$ $3.577$ 8.0.629407744.1 $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+(-3-\beta _{7})q^{9}+\cdots$$
448.2.e.b $8$ $3.577$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{2}q^{3}+\zeta_{24}^{6}q^{5}-\zeta_{24}^{4}q^{7}+\cdots$$
448.2.f.a $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-4$$ $$0$$ $$-4$$ $$q-2q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots$$
448.2.f.b $2$ $3.577$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{7}-3q^{9}-2\beta q^{11}-2\beta q^{23}+\cdots$$
448.2.f.c $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$4$$ $$0$$ $$4$$ $$q+2q^{3}+2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots$$
448.2.f.d $8$ $3.577$ $$\Q(\zeta_{16})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{4}q^{7}+\cdots$$
448.2.i.a $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$-1$$ $$-4$$ $$q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$
448.2.i.b $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-1$$ $$-4$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
448.2.i.c $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$3$$ $$4$$ $$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
448.2.i.d $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-1$$ $$4$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
448.2.i.e $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$3$$ $$-4$$ $$q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$
448.2.i.f $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$-1$$ $$4$$ $$q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
448.2.i.g $4$ $3.577$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$-2$$ $$2$$ $$4$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+(2\beta _{1}-\beta _{2}+2\beta _{3})q^{5}+\cdots$$
448.2.i.h $4$ $3.577$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{1}q^{3}+3\beta _{2}q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$$
448.2.i.i $4$ $3.577$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1-\zeta_{12}^{2})q^{5}+\cdots$$
448.2.i.j $4$ $3.577$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$2$$ $$2$$ $$-4$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+\cdots$$
448.2.j.a $4$ $3.577$ $$\Q(i, \sqrt{7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{7}+3\beta _{1}q^{9}+(-2+2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$$
448.2.j.b $4$ $3.577$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2})q^{7}-3\beta _{1}q^{9}+\cdots$$
448.2.j.c $4$ $3.577$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots$$
448.2.j.d $16$ $3.577$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{6}q^{3}+\beta _{5}q^{5}+(-1+\beta _{13})q^{7}+\cdots$$
448.2.m.a $2$ $3.577$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+2i)q^{5}+iq^{7}+3iq^{9}+(-1+\cdots)q^{11}+\cdots$$
448.2.m.b $2$ $3.577$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$4$$ $$-4$$ $$0$$ $$q+(2-2i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots$$
448.2.m.c $8$ $3.577$ 8.0.214798336.3 None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\beta _{4}q^{3}+\beta _{1}q^{5}+\beta _{5}q^{7}+(-\beta _{5}-\beta _{7})q^{9}+\cdots$$
448.2.m.d $12$ $3.577$ 12.0.$$\cdots$$.1 None None $$0$$ $$-4$$ $$4$$ $$0$$ $$q+\beta _{6}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5})q^{5}-\beta _{3}q^{7}+\cdots$$
448.2.p.a $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-3$$ $$-4$$ $$q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$$
448.2.p.b $2$ $3.577$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-3$$ $$4$$ $$q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
448.2.p.c $4$ $3.577$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None None $$0$$ $$0$$ $$6$$ $$0$$ $$q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$$
448.2.p.d $4$ $3.577$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$6$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1+\zeta_{12}^{2})q^{5}+\cdots$$
448.2.p.e $16$ $3.577$ 16.0.$$\cdots$$.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{14}q^{3}+\beta _{13}q^{5}+\beta _{9}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots$$
448.2.q.a $8$ $3.577$ 8.0.12960000.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}+\beta _{7})q^{3}+\beta _{6}q^{5}+(2\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots$$
448.2.q.b $12$ $3.577$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$-6$$ $$0$$ $$q-\beta _{5}q^{3}+(\beta _{6}-\beta _{7})q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots$$
448.2.q.c $12$ $3.577$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$6$$ $$0$$ $$q-\beta _{5}q^{3}+(-\beta _{6}+\beta _{7})q^{5}+(-\beta _{4}+\beta _{10}+\cdots)q^{7}+\cdots$$
448.2.t.a $8$ $3.577$ 8.0.49787136.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{3}+\beta _{6}q^{5}+(\beta _{5}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots$$