Dear Loic,12I made a few minor changes to our paper. If you agree to these,3and Barry accepts the new version, then we are finally done.45Best,6William780. I changed9"images of $\rho$ and $\rho_0$ co\"\i ncide."10to11"images of $\rho$ and $\rho_0$ coincide."1213(For some reason you wrote "coincide" in a French way.)14151. I changed1617"Therefore there exists a field extension $K_2$ of degree18$d_2$ dividing $2d_K$ of $\B Q(\sqrt p)$, such that ..."1920to2122"Therefore, there exists an extension field $K_2$ of $\B Q(\sqrt p)$,23whose degree divides $2d_K$, such that ..."24252. I changed2627"Let us define $E$ over $\B Q$ so that $E$ has complex28multiplication over $K$."2930to3132"Since~$E$ is an elliptic curve over $\bar \B Q$ with complex33multiplication by a field of class number one, there is a model34for~$E$ that is defined over $\B Q$."35363. I changed3738"In this section we explain how we used39a computer to verify that the hypothesis of Proposition~1 are40satisfied for $p=11$ and $13 < p < 1000$."4142to4344"In this section we explain how we used45a computer to verify that the second hypothesis of Proposition~1 are46satisfied for $p=11$ and $13 < p < 1000$. (In the present paper,47this verification is only required for $p$ that are congruent to~$1$48modulo~$4$.)"49504. I deleted the word "be" from the following sentence:5152"Denote by $S_2(\Gamma_0(p);\B Z)$ be the set of modular forms "53^^^^54555. I deleted "as" in the following:5657"if we declare that $\B T_{\B C}$ as acts on $\B R^{2d} = \B C^d$ via"58596. I changed6061"over a relatively small prime finite field $\B F_\ell$ such62that~$\ell$ is congruent to~$1$ modulo $p-1$."6364to6566"over a relatively small finite field $\B F_\ell$ where~$\ell$ is67congruent to~$1$ modulo $p-1$."68697. I deleted the second "For each" in the following:7071"For each prime $p<1000$ different than $2,3,5,7, 13$, we72verified the existence of an ideal that satisfies the three conditions73given above, as follows. For each~$p$, we consider each ..."74758. I deleted "Finally" from the acknowledgement:7677"{\it Acknowledgment} : Finally we would like to thank Barry Mazur for78providing us several useful comments."7980becomes8182"{\it Acknowledgment}: We would like to thank Barry Mazur for83providing us several useful comments."8485Otherwise, it sounds like we thanked several people, and finally we are86thanking Barry.8788-- William89909192939495