The following two images are the ideal low pass filter in the frequency domain. As you can see, the origin (low frequency component), can pass through this filter while the high frequency are blocked. The white value coresponds to 1, the black value coresponds to 0. 
And corespondingly, its spatial domain representation is (2d sinc function):
However, there is a thing that said: "for the spatial domain, the radius of centre component and number of cycle per unit distance from the origin are inversely proportional to the cutoff frequency of the ideal low pass filter".
So when you increase the cutoff frequency, you skretch in frequency domain, but you compress in spatial domain; how does the "number of cycle per unit distance from the origin" decrease? It should increase.
The larger the cutoff frequency, you approach the ideal spectrum. If you define the number of cycle "sidelobes" within a particular surface of interest "let us say centered in the origin" then you gain in resolution "The main lobe become narrower" and you suppressed some among of sidelobes ("cycles") when you compress within large cutoff interval. But to rely see this suppression (decrease), the surface of interest have to be large enough. I think this should affect also nearby sidelobes (cycle close to the main lobe).