LEVEL 13


GRITSENKO LIFTS
Number of wt 2 Gritsenko lifts: 0
Number of wt 4 Gritsenko lifts: 2


WEIGHT 4 CUSP FORMS
The weight 4 space of cusp forms (and the plus and minus parts) have dimensions:
     dim S4(K(13)) = 2
     dim S4(K(13))+ = 2
     dim S4(K(13))- = 0
Because wt 4 cusp forms have the same dimension as the space of wt 4 Gritsenko lifts, then the wt 4 cusp forms must all be plus forms.


PROVING UPPER BOUND ON NUMBER OF WEIGHT 2 NONLIFTS
We claim:
     At most number of wt 2 plus nonlifts: 0
     At most number of wt 2 minus nonlifts: 0
Because wt 4 cusp forms have the same dimension as the space of wt 4 Gritsenko lifts, then by theorem we have that
     dim H(2)+ = 0
which implies that
     dim S2(K(13)) = 0
and in particular there are no wt 2 nonlifts, plus or minus.