## Results (1-50 of 244 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
675.1.c.a $1$ $0.337$ $$\Q$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+q^{4}-q^{7}+2q^{13}+q^{16}-q^{19}+\cdots$$
675.1.c.b $1$ $0.337$ $$\Q$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q+q^{4}+q^{7}-2q^{13}+q^{16}-q^{19}+\cdots$$
675.1.c.c $2$ $0.337$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{8}-q^{16}-iq^{17}+q^{19}+\cdots$$
675.1.d.a $2$ $0.337$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-q^{4}-iq^{7}-iq^{13}+q^{16}+q^{19}+\cdots$$
675.1.g.a $4$ $0.337$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+2\beta _{2}q^{4}-\beta _{3}q^{8}-q^{16}+\cdots$$
675.1.g.b $4$ $0.337$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{4}-\beta _{1}q^{7}-q^{16}-\beta _{2}q^{19}+\cdots$$
675.1.o.a $8$ $0.337$ $$\Q(\zeta_{20})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\zeta_{20}-\zeta_{20}^{5})q^{2}+(-1+\zeta_{20}^{2}+\cdots)q^{4}+\cdots$$
675.2.a.a $1$ $5.390$ $$\Q$$ None None $$-2$$ $$0$$ $$0$$ $$3$$ $-$ $$q-2q^{2}+2q^{4}+3q^{7}+2q^{11}+5q^{13}+\cdots$$
675.2.a.b $1$ $5.390$ $$\Q$$ None None $$-1$$ $$0$$ $$0$$ $$0$$ $+$ $$q-q^{2}-q^{4}+3q^{8}-5q^{11}+5q^{13}+\cdots$$
675.2.a.c $1$ $5.390$ $$\Q$$ None None $$-1$$ $$0$$ $$0$$ $$0$$ $-$ $$q-q^{2}-q^{4}+3q^{8}+5q^{11}-5q^{13}+\cdots$$
675.2.a.d $1$ $5.390$ $$\Q$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $-$ $$q-2q^{4}-4q^{7}+5q^{13}+4q^{16}+8q^{19}+\cdots$$
675.2.a.e $1$ $5.390$ $$\Q$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $+$ $$q-2q^{4}+q^{7}-5q^{13}+4q^{16}-7q^{19}+\cdots$$
675.2.a.f $1$ $5.390$ $$\Q$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $-$ $$q-2q^{4}+4q^{7}-5q^{13}+4q^{16}+8q^{19}+\cdots$$
675.2.a.g $1$ $5.390$ $$\Q$$ None None $$1$$ $$0$$ $$0$$ $$0$$ $+$ $$q+q^{2}-q^{4}-3q^{8}-5q^{11}-5q^{13}+\cdots$$
675.2.a.h $1$ $5.390$ $$\Q$$ None None $$1$$ $$0$$ $$0$$ $$0$$ $-$ $$q+q^{2}-q^{4}-3q^{8}+5q^{11}+5q^{13}+\cdots$$
675.2.a.i $1$ $5.390$ $$\Q$$ None None $$2$$ $$0$$ $$0$$ $$3$$ $-$ $$q+2q^{2}+2q^{4}+3q^{7}-2q^{11}+5q^{13}+\cdots$$
675.2.a.j $2$ $5.390$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-15})$$ None $$-3$$ $$0$$ $$0$$ $$0$$ $+$ $$q+(-1-\beta )q^{2}+3\beta q^{4}+(-1-4\beta )q^{8}+\cdots$$
675.2.a.k $2$ $5.390$ $$\Q(\sqrt{13})$$ None None $$-1$$ $$0$$ $$0$$ $$-2$$ $+$ $$q-\beta q^{2}+(1+\beta )q^{4}+(-2+2\beta )q^{7}+\cdots$$
675.2.a.l $2$ $5.390$ $$\Q(\sqrt{2})$$ None None $$0$$ $$0$$ $$0$$ $$-6$$ $+$ $$q+\beta q^{2}-3q^{7}-2\beta q^{8}-3\beta q^{11}-3q^{13}+\cdots$$
675.2.a.m $2$ $5.390$ $$\Q(\sqrt{2})$$ None None $$0$$ $$0$$ $$0$$ $$6$$ $-$ $$q+\beta q^{2}+3q^{7}-2\beta q^{8}+3\beta q^{11}+3q^{13}+\cdots$$
675.2.a.n $2$ $5.390$ $$\Q(\sqrt{7})$$ None None $$0$$ $$0$$ $$0$$ $$-6$$ $-$ $$q+\beta q^{2}+5q^{4}-3q^{7}+3\beta q^{8}+2\beta q^{11}+\cdots$$
675.2.a.o $2$ $5.390$ $$\Q(\sqrt{7})$$ None None $$0$$ $$0$$ $$0$$ $$6$$ $-$ $$q+\beta q^{2}+5q^{4}+3q^{7}+3\beta q^{8}-2\beta q^{11}+\cdots$$
675.2.a.p $2$ $5.390$ $$\Q(\sqrt{13})$$ None None $$1$$ $$0$$ $$0$$ $$-2$$ $-$ $$q+\beta q^{2}+(1+\beta )q^{4}+(-2+2\beta )q^{7}+\cdots$$
675.2.a.q $2$ $5.390$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-15})$$ None $$3$$ $$0$$ $$0$$ $$0$$ $-$ $$q+(1+\beta )q^{2}+3\beta q^{4}+(1+4\beta )q^{8}+(5+\cdots)q^{16}+\cdots$$
675.2.b.a $2$ $5.390$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-2q^{4}+3iq^{7}-2q^{11}-5iq^{13}+\cdots$$
675.2.b.b $2$ $5.390$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-2q^{4}-3iq^{7}+2q^{11}+5iq^{13}+\cdots$$
675.2.b.c $2$ $5.390$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+3iq^{8}-5q^{11}+5iq^{13}+\cdots$$
675.2.b.d $2$ $5.390$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+3iq^{8}+5q^{11}-5iq^{13}+\cdots$$
675.2.b.e $2$ $5.390$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+4iq^{7}+5iq^{13}+4q^{16}+\cdots$$
675.2.b.f $2$ $5.390$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+iq^{7}+5iq^{13}+4q^{16}+7q^{19}+\cdots$$
675.2.b.g $4$ $5.390$ $$\Q(i, \sqrt{7})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-5q^{4}+3\beta _{1}q^{7}-3\beta _{3}q^{8}+\cdots$$
675.2.b.h $4$ $5.390$ $$\Q(i, \sqrt{13})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$$
675.2.b.i $4$ $5.390$ $$\Q(i, \sqrt{13})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(2\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$$
675.2.e.a $2$ $5.390$ $$\Q(\sqrt{-3})$$ None None $$-1$$ $$0$$ $$0$$ $$-3$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{7}+\cdots$$
675.2.e.b $6$ $5.390$ 6.0.954288.1 None None $$-1$$ $$0$$ $$0$$ $$5$$ $$q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots$$
675.2.e.c $8$ $5.390$ 8.0.1223810289.2 None None $$-2$$ $$0$$ $$0$$ $$-1$$ $$q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}+\beta _{6})q^{4}+\cdots$$
675.2.e.d $8$ $5.390$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-2\zeta_{24}^{3}+\cdots)q^{7}+\cdots$$
675.2.e.e $8$ $5.390$ 8.0.1223810289.2 None None $$2$$ $$0$$ $$0$$ $$1$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}+\beta _{6})q^{4}+\cdots$$
675.2.f.a $4$ $5.390$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+2\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots$$
675.2.f.b $4$ $5.390$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots$$
675.2.f.c $4$ $5.390$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{4}+2\beta _{1}q^{7}-3\beta _{3}q^{13}-4q^{16}+\cdots$$
675.2.f.d $4$ $5.390$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{4}-\beta _{1}q^{7}-\beta _{3}q^{13}-4q^{16}+\cdots$$
675.2.f.e $4$ $5.390$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots$$
675.2.f.f $4$ $5.390$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}-2\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots$$
675.2.f.g $8$ $5.390$ 8.0.$$\cdots$$.8 None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{7}+\cdots$$
675.2.f.h $8$ $5.390$ 8.0.3317760000.9 $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(3\beta _{1}+\beta _{2})q^{4}+(-3\beta _{3}-\beta _{5}+\cdots)q^{8}+\cdots$$
675.2.f.i $8$ $5.390$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$$
675.2.h.a $40$ $5.390$ None None $$-2$$ $$0$$ $$-3$$ $$-2$$
675.2.h.b $40$ $5.390$ None None $$0$$ $$0$$ $$0$$ $$20$$
675.2.h.c $40$ $5.390$ None None $$0$$ $$0$$ $$0$$ $$-12$$