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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Try loading font information for U+msa on input line 13. (/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 13. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) Overfull \hbox (8.87912pt too wide) in paragraph at lines 26--34 \OT1/cmr/m/n/10 er-a-tor $\OML/cmm/m/it/10 T[]$ \OT1/cmr/m/n/10 to $\OML/cmm/m/ it/10 a[]$\OT1/cmr/m/n/10 . De-note by $\OML/cmm/m/it/10 A[]$ \OT1/cmr/m/n/10 t he op-ti-mal a-belian va-ri-ety quo-tien-t $\OML/cmm/m/it/10 J[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 =IJ[]\OT1/cmr/m/n/10 (\OM L/cmm/m/it/10 N\OT1/cmr/m/n/10 )$. [] Overfull \hbox (1.75488pt too wide) in paragraph at lines 56--59 []\OT1/cmr/m/n/10 The con-jec-ture is false when the lev-el is com-pos-ite. For ex-am-ple, let $\OML/cmm/m/it/10 E \OT1/cmr/m/n/10 =$\OT1/cmr/bx/n/10 33A\OT1/ cmr/m/n/10 ; [] [1 ] [2] LaTeX Font Info: Try loading font information for U+euf on input line 171. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 1995/01/05 v2.2e AMS font definitions ) [3] Overfull \hbox (24.2231pt too wide) in paragraph at lines 220--226 []\OT1/cmr/m/n/10 The max-i-mal fi-nite part of $\OML/cmm/m/it/10 A\OT1/cmr/m/n /10 [\OML/cmm/m/it/10 `\OT1/cmr/m/n/10 ]$ is $\OML/cmm/m/it/10 f[]\OT1/cmr/m/n/ 10 (^^H[][\OML/cmm/m/it/10 `\OT1/cmr/m/n/10 ])$, which is \OT1/cmr/m/it/10 big- ger \OT1/cmr/m/n/10 than $[](\OML/cmm/m/it/10 X=`X; ^^V[]\OT1/cmr/m/n/10 )$. [] [4] Overfull \hbox (2.33432pt too wide) in paragraph at lines 289--301 \OT1/cmr/m/n/10 (701;5), (733;61), (751;5), (761;5,19), (911;7), (919;3), (941; 5), (971;5), (1021;17), [] Overfull \hbox (6.55656pt too wide) in paragraph at lines 289--301 \OT1/cmr/m/n/10 (1091;5), (1279;3), (1289;7), (1291;5), (1297;3), (1321;11), (1 381;5,23), (1447;241), [] [5] Overfull \hbox (48.74657pt too wide) in paragraph at lines 390--390 [] \OT1/cmtt/m/n/10 Great. I'll try to send you a proof that in the "non-tou gh" cases, your[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 Please do, if possible; even a rough sketch will be very muc h appreciated.[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 390--390 [] \OT1/cmtt/m/n/10 cases can you tell me which have the property that the q- Eisenstein[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 390--390 [] \OT1/cmtt/m/n/10 quotient of the jacobian of X_0(p) is a simple abelian va riety, and which[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 390--390 [] \OT1/cmtt/m/n/10 not? When they split can you given the simple abelian va riety factors?[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 It appears that there are exactly two non-simple q-Eisenstei n quotients[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 (q odd) at level p<=2113. These just happen to be "tough". They occur at[] [] [6] Overfull \hbox (6.74693pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 J_0(N)^- for N<10000. As far as I can tell, he seems to cla im that[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 and 1999 cases; this is in direct contradiction with my comp utation.[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 (I've found another mistake in this table, so this doesn't m ean I'm wrong;[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 I'll email Armand.) The only example he lists in which the q-Eisenstein[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 quotient (q odd) is not simple is at level 3001. Here q=5 a nd n = 2*5^3,[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 Here is how I computed the torsion subgroup of each optimal quotient[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 the order of the image of 0-oo using modular symbols. Then I computed[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 In every case considered, I was lucky and the two bounds coi ncided.[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 390--390 []\OT1/cmtt/m/n/10 q-Eisenstein; however, it probably does within the range of conductors[] [] (refinedeisen.bbl [7]) [8] (refinedeisen.aux) ) Here is how much of TeX's memory you used: 3639 strings out of 10898 38792 string characters out of 72048 136381 words of memory out of 263001 6542 multiletter control sequences out of 10000+0 16256 words of font info for 65 fonts, out of 200000 for 1000 15 hyphenation exceptions out of 1000 30i,14n,24p,246b,415s stack positions out of 300i,100n,500p,30000b,4000s Output written on refinedeisen.dvi (8 pages, 25216 bytes).