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Comments. 05-31-0212Most are small stylistic comments; the ones with nontrivial3mathematical content are set off by *'s.45* page 1: Change "with which are associated modular forms" to6"which are associated to modular forms". It sounds less awkard7and exhibits better parallelism with the second part of the sentence.89* page 1, last para: change "are congruent modulo some q" to10"are congruent modulo a maximal ideal q of odd residue characteristic".11Otherwise it is not true that L(g,s) is forced to vanish to order >= 2.12Also, say that f and g are forms for Gamma_0. Alternatively, say13"It turns out, under additional hypothesis, that this forces..."1415* page 1, last para: change "in each case q appears in the" to16"in each case q divides the numerator".1718* page 2, last para of intro: change "whose existence we cannot prove19theoretically" to "whose existence we do not prove theoretically."20You or I might very well eventually be able to prove them, so it's21not right to say that we "cannot prove" them. All we can see is22that we do not, in the present paper, prove them.2324* page 2. There is a single occurence of \ldots on this page,25in the Hodge filtration, and it would be better replaced by a \cdots.2627* page 3, first line: I don't like starting sentences with symbols.28An easy fix would be to replace '"finite part". D_p is' by29'"finite part", D_p is', i.e., replace the first period by a comma.3031* page 3, line 5: The subscript on B_dR should be in roman face, but32is italicized here. Elsewhere in our paper it is correctly typeset33in roman.3435* page 3, line 10, "Let H_f^1...":36This should not be a new paragraph.3738* page 4, in the displayed definition of ord_{\lambda}(c_p(j))39the lambda have turned into q's in two places.4041* page 5, Lemma 4.3: some comments:42a) The notation "I_p" was only introduced in the proof43of Lemma 4.2. Since it is used repeatedly, it might44be better to introduce it before the statement of45Lemma 4.2.46b) You use dim a lot, and it's not very ambiguous.47Nonetheless, it might be nice to say what you view48the base field that you're taking dimensions as being.49It's O/q I assume.50c) * First sentence of proof: I don't see why it suffices51to prove that equality. *5253* Section 5: I don't remember checking that none of our q divide Phi(N).54I just checked that now and it's OK. I'm sure you checked it.5556* page 7: Replace "This is analogous to the remark at the end of57Section 3 of \cite{CM}. It shows that" by "This is analogous to the58remark at the end of Section 3 of \cite{CM}, which shows that".5960* page 8: Case 2 of the proof, two comments:61a) I would replace "First we must show that" by62"First we show that". It is more efficient. Also,63maybe there is a way to prove this that doesn't first64begin by showing that H^0 is q-divisible, so maybe65we don't absolutely have to proceed in that manner.66b) * You say that equality of dimensions would imply that67a certain map is injective. Doesn't this assume that68H^0(I_p, T_q'(k/2)) = 0, and if so, how do we know this? *6970* Did we ever check the hypothesis to Theorem 6.1, that71"for all p|N, p=/=-w_p (mod q), with p=/=-1(mod q) if p^2|N"?72I just checked, and amazingly there are no examples (N,q) such73that a divisor p of N satisfies p = +/-1 (mod q).7475* Page 10, replace "then by $|\mbox{\rm Tr}(a_p(g))|$ for~$p$ not76dividing" by "then by the sequence of absolute values $|\mbox{\rm77Tr}(a_p(g))|)$, for~$p$ not dividing"7879* Page 11, replace "standard part of the MAGMA V2.8 (see \cite{magma})."80by "standard part of MAGMA (see \cite{magma})." That is, delete81"the" before MAGMA and the version, which is wrong by now anyways.8283* Page 11, replace "X^{\frac{k}{2}-1}Y^{k-2-(\frac{k}{2}-1)}" in the84middle of the page by "X^{\frac{k}{2}-1}Y^{\frac{k}{2}-1}".8586* Page 11, in "For the two examples \nf{581k4} and \nf{684k4K}, the square"87we forgot part of one of the labels; it should be \nf{581k4E}.8889* Page 12: Everyone on this page the spacing in expressions like90"between $g=$\nf{81k4A}" looks bad. You can put the \nf macro91in math mode like so: "$g=\nf{81k4A}$", which looks better.9293* Page 12: Lots of modq's which should be "mod q"'s. I.e., there94is missing space between mod and q. Instead of typesetting this95with "$\bmod{ \qq}$", instead try "$\bmod{\,\qq}$".9697I still haven't computed the decomposition of q in each Fourier field.98It's coming up.99