https://cst.temple.edu/sites/cst/files/theses1/bao.pdf
Note that in the case p = 2, an explicit basis of M2k( 0(2)) is given by f(E 2)aEb 4j2a + 4b = 2kg; where E 2(z) = E2(z) 2E(2z) and E2(z); E4(z) is Eisenstein series of weight 2 and 4 respectively (see page 56 of [14]). One checks that S10( 0(2)) is one dimensional and the Fourier expansion of