We evaluate the action of Hecke operators on Siegel Eisenstein series of degree 2, square-free level N and arbitrary character, without using knowledge of their Fourier coefficients. From this we construct a basis of simultaneous eigenforms for the full Hecke algebra, and we compute their eigenvalues. As well, we obtain Hecke relations amond the Eisenstein series. Using these Hecke relations in the case that the character is trivial, we generate a basis for the space of Eisenstein series from one of the Eisenstein series.
|Translated title of the contribution||Hecke eigenvalues and relations for degree 2 Siegel Eisenstein series of square-free level|
|Number of pages||24|
|Journal||Journal of Number Theory|
|Publication status||Published - Nov 2012|
- Siegel modular form
- Eisenstein series
- Hecke operators