Let $p=5$ and $\omega_5$ the Teichimuller character. Let $\theta=(\frac{\cdot}{-51})$ be the quadratic character mod $-51$. For any $k \geq 2$ fixed, let $\chi_k=\theta\cdot\omega_5^{2-k}$ and $S_k^{\mathrm{ord}}(\Gamma_0(255), \chi_k)$ the space of the ordinary cuspforms. Could anyone can teach me how to use sage to compute the Eisenstein component of $S_k^{\mathrm{ord}}(\Gamma_0(255), \chi_k)$ and the Fourier coefficient of one of that cuspforms? If it have Eisenstein componet, what value could $k$ take?
From William Stein's book, I learn to compute the basis of $S_k^{\mathrm{ord}}(\Gamma_0(141), \chi_k)$ when $p=3$ because at that time $\chi_k$ is a quadratic character and check the Fourier coefficients to identify the congruence.