Degree of freedom in Wilk's Theorem

The data: Y_i is poisson(lambda), and and let xi be corresponding values of an explanatory variable x.

I have hypothesis: H0: lambda_i = lambda,

H_full: lambda_i free to be different for i = 1,....,n,

and H_linear: lambda_i = b0+b1*x_i.

So I derive the generalized log likelihood ratio statistics, but not sure how to determine the degree of freedom for H_0 v.s H_full, and H_linear v.s. H_0. In general, I don't know what is the dimension of these hypothesis.