## Results (1-50 of 223 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.1.f.a $1$ $0.489$ $$\Q$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$-1$$ $$-1$$ $$0$$ $$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$$
980.1.f.b $1$ $0.489$ $$\Q$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$1$$ $$1$$ $$0$$ $$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$$
980.1.f.c $1$ $0.489$ $$\Q$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$-1$$ $$1$$ $$0$$ $$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$$
980.1.f.d $1$ $0.489$ $$\Q$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$1$$ $$-1$$ $$0$$ $$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$$
980.1.f.e $4$ $0.489$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{8}+\cdots$$
980.1.j.a $8$ $0.489$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{4}q^{4}+\zeta_{16}^{5}q^{5}+\cdots$$
980.1.l.a $4$ $0.489$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}-q^{11}-\zeta_{8}q^{13}+\cdots$$
980.1.n.a $2$ $0.489$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$-1$$ $$1$$ $$0$$ $$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}+q^{13}+\cdots$$
980.1.n.b $2$ $0.489$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-q^{13}+\cdots$$
980.1.p.a $2$ $0.489$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$-1$$ $$1$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$$
980.1.p.b $2$ $0.489$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$1$$ $$1$$ $$0$$ $$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$$
980.1.p.c $8$ $0.489$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots$$
980.1.w.a $8$ $0.489$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{5}q^{5}+\zeta_{24}^{4}q^{11}+\cdots$$
980.1.y.a $16$ $0.489$ $$\Q(\zeta_{48})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{48}^{2}q^{2}+\zeta_{48}^{4}q^{4}+\zeta_{48}^{5}q^{5}+\cdots$$
980.1.ba.a $6$ $0.489$ $$\Q(\zeta_{14})$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$5$$ $$-1$$ $$-1$$ $$q-\zeta_{14}q^{2}+(1+\zeta_{14}^{6})q^{3}+\zeta_{14}^{2}q^{4}+\cdots$$
980.1.ba.b $6$ $0.489$ $$\Q(\zeta_{14})$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$-5$$ $$-1$$ $$1$$ $$q+\zeta_{14}q^{2}+(-1-\zeta_{14}^{6})q^{3}+\zeta_{14}^{2}q^{4}+\cdots$$
980.1.bq.a $12$ $0.489$ $$\Q(\zeta_{21})$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$8$$ $$1$$ $$-1$$ $$q-\zeta_{42}^{4}q^{2}+(\zeta_{42}^{3}+\zeta_{42}^{7})q^{3}+\zeta_{42}^{8}q^{4}+\cdots$$
980.1.bq.b $12$ $0.489$ $$\Q(\zeta_{21})$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$-8$$ $$1$$ $$1$$ $$q+\zeta_{42}^{4}q^{2}+(-\zeta_{42}^{3}-\zeta_{42}^{7})q^{3}+\cdots$$
980.2.a.a $1$ $7.825$ $$\Q$$ None None $$0$$ $$-3$$ $$-1$$ $$0$$ $-$ $$q-3q^{3}-q^{5}+6q^{9}-2q^{11}-6q^{13}+\cdots$$
980.2.a.b $1$ $7.825$ $$\Q$$ None None $$0$$ $$-3$$ $$1$$ $$0$$ $-$ $$q-3q^{3}+q^{5}+6q^{9}-5q^{11}+3q^{13}+\cdots$$
980.2.a.c $1$ $7.825$ $$\Q$$ None None $$0$$ $$-1$$ $$-1$$ $$0$$ $+$ $$q-q^{3}-q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots$$
980.2.a.d $1$ $7.825$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$0$$ $-$ $$q-q^{3}+q^{5}-2q^{9}-q^{11}+5q^{13}+\cdots$$
980.2.a.e $1$ $7.825$ $$\Q$$ None None $$0$$ $$-1$$ $$1$$ $$0$$ $-$ $$q-q^{3}+q^{5}-2q^{9}+6q^{11}-2q^{13}+\cdots$$
980.2.a.f $1$ $7.825$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$0$$ $+$ $$q+q^{3}-q^{5}-2q^{9}-q^{11}-5q^{13}+\cdots$$
980.2.a.g $1$ $7.825$ $$\Q$$ None None $$0$$ $$1$$ $$-1$$ $$0$$ $-$ $$q+q^{3}-q^{5}-2q^{9}+6q^{11}+2q^{13}+\cdots$$
980.2.a.h $1$ $7.825$ $$\Q$$ None None $$0$$ $$2$$ $$1$$ $$0$$ $-$ $$q+2q^{3}+q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots$$
980.2.a.i $1$ $7.825$ $$\Q$$ None None $$0$$ $$3$$ $$1$$ $$0$$ $-$ $$q+3q^{3}+q^{5}+6q^{9}-2q^{11}+6q^{13}+\cdots$$
980.2.a.j $2$ $7.825$ $$\Q(\sqrt{2})$$ None None $$0$$ $$-2$$ $$2$$ $$0$$ $+$ $$q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-1+\cdots)q^{11}+\cdots$$
980.2.a.k $2$ $7.825$ $$\Q(\sqrt{2})$$ None None $$0$$ $$2$$ $$-2$$ $$0$$ $-$ $$q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-1+2\beta )q^{11}+\cdots$$
980.2.c.a $8$ $7.825$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}^{2}q^{2}-2q^{4}-\zeta_{16}^{4}q^{5}+2\zeta_{16}^{2}q^{8}+\cdots$$
980.2.c.b $8$ $7.825$ 8.0.3317760000.3 $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{6}q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots$$
980.2.c.c $16$ $7.825$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(-\beta _{8}-\beta _{10}-\beta _{12})q^{3}+\cdots$$
980.2.c.d $32$ $7.825$ None None $$0$$ $$0$$ $$0$$ $$0$$
980.2.c.e $48$ $7.825$ None None $$0$$ $$0$$ $$0$$ $$0$$
980.2.e.a $2$ $7.825$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-i)q^{5}+3q^{9}+2iq^{13}-2iq^{17}+\cdots$$
980.2.e.b $2$ $7.825$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+3iq^{3}+(2+i)q^{5}-6q^{9}+3q^{11}+\cdots$$
980.2.e.c $4$ $7.825$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots$$
980.2.e.d $4$ $7.825$ $$\Q(\sqrt{-5}, \sqrt{-21})$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-4+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots$$
980.2.e.e $4$ $7.825$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}-q^{11}-\beta _{2}q^{13}+\cdots$$
980.2.e.f $4$ $7.825$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None None $$0$$ $$0$$ $$1$$ $$0$$ $$q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots$$
980.2.g.a $32$ $7.825$ None None $$-4$$ $$0$$ $$0$$ $$0$$
980.2.g.b $48$ $7.825$ None None $$8$$ $$0$$ $$0$$ $$0$$
980.2.i.a $2$ $7.825$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$-1$$ $$0$$ $$q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$$
980.2.i.b $2$ $7.825$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$1$$ $$0$$ $$q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$$
980.2.i.c $2$ $7.825$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-2$$ $$-1$$ $$0$$ $$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
980.2.i.d $2$ $7.825$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$$
980.2.i.e $2$ $7.825$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$$
980.2.i.f $2$ $7.825$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots$$
980.2.i.g $2$ $7.825$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots$$
980.2.i.h $2$ $7.825$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$$