# Eta products for S_6(Gamma0(24))

We're trying to find a basis for S_6(Gamma0(24)), and we would like it to be in terms of eta products. We have some eta products that we've worked out by hand, and we want to see which on them are linearly independent. We realize that SAGE has a built in function to find the basis of any space, but our professor has asked us to try and do it by hand a few times for practice.

The problem we're encountering is how to represent out eta products in SAGE. The EtaProduct(level, dict) function only recognizes eta products of a certain kind (the powers of eta have to sum to 0).

For example, if we enter EtaProduct(24, {2:12}) we get the following error : ValueError: sum r_d (=12) is not 0

We would also like to compute the Fourier expansion, to then check for linear independence.