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LaTeX Font Info: Try loading font information for U+msa on input line 386. (/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 386. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) [1 ] [2 ] (./current.toc) \tf@toc=\write5 \openout5 = `current.toc'. [3] [4 ] LaTeX Warning: Citation `sage' on page 5 undefined on input line 408. LaTeX Warning: Citation `stein:hecke' on page 5 undefined on input line 413. LaTeX Warning: Citation `magma' on page 5 undefined on input line 413. LaTeX Warning: Citation `cremona:algs' on page 5 undefined on input line 425. LaTeX Warning: Citation `cohen:course_ant' on page 5 undefined on input line 42 7. [5] LaTeX Warning: Citation `serre:arithmetic' on page 6 undefined on input line 47 0. [6] Chapter 1. LaTeX Font Info: Try loading font information for U+euf on input line 515. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Warning: Citation `serre:arithmetic' on page 7 undefined on input line 55 2. LaTeX Font Info: Try loading font information for OMS+cmr on input line 552. (/usr/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 552. [7 ] [8] LaTeX Warning: Citation `serre:arithmetic' on page 9 undefined on input line 67 9. [9] [10] [11] LaTeX Font Info: Try loading font information for OMS+cmss on input line 867 . LaTeX Font Info: No file OMScmss.fd. on input line 867. LaTeX Font Warning: Font shape `OMS/cmss/m/n' undefined (Font) using `OMS/cmsy/m/n' instead (Font) for symbol `textbullet' on input line 867. [12] LaTeX Warning: Citation `serre:arithmetic' on page 13 undefined on input line 9 42. Overfull \hbox (12.34515pt too wide) detected at line 953 \OML/cmm/m/it/10 G[]\OT1/cmr/m/n/10 (\OMS/cmss/m/n/10 ^^@\OT1/cmr/m/n/10 1\OML/ cmm/m/it/10 =z\OT1/cmr/m/n/10 ) = [] [] = [] [] = \OML/cmm/m/it/10 z[] [] [] \O T1/cmr/m/n/10 = \OML/cmm/m/it/10 z[]G[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 z\OT1/ cmr/m/n/10 )\OML/cmm/m/it/10 : [] [13] Overfull \hbox (3.35062pt too wide) in paragraph at lines 984--987 \OT1/cmr/m/n/10 The dis-crim-i-nant of the cu-bic $4\OML/cmm/m/it/10 x[] \OMS/c mss/m/n/10 ^^@ \OT1/cmr/m/n/10 60\OML/cmm/m/it/10 G[]\OT1/cmr/m/n/10 (\OML/cmm/ m/it/10 ![]=![]\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 x \OMS/cmss/m/n/10 ^^@ \OT1/cm r/m/n/10 140\OML/cmm/m/it/10 G[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 ![]=![]\OT1/c mr/m/n/10 )$ is $16^^A(\OML/cmm/m/it/10 ![]=![]\OT1/cmr/m/n/10 )$, [] LaTeX Warning: Citation `serre:arithmetic' on page 14 undefined on input line 1 016. [14] LaTeX Warning: Citation `serre:arithmetic' on page 15 undefined on input line 1 083. [15] LaTeX Warning: Citation `serre:arithmetic' on page 16 undefined on input line 1 135. LaTeX Warning: Citation `serre:arithmetic' on page 16 undefined on input line 1 178. [16] [17] LaTeX Warning: Citation `lang:modular' on page 18 undefined on input line 1324. [18] [19] [20] [21] LaTeX Warning: Citation `serre:arithmetic' on page 22 undefined on input line 1 652. [22] LaTeX Warning: Citation `buzzard:t2' on page 23 undefined on input line 1769. LaTeX Warning: Citation `farmer-james:maeda' on page 23 undefined on input line 1769. [23] LaTeX Warning: Citation `MR1413578' on page 24 undefined on input line 1815. Overfull \hbox (3.26103pt too wide) in paragraph at lines 1834--1841 []\OT1/cmr/m/n/10 The rest of this book is about meth-ods for com-put-ing sub-s paces of $\OML/cmm/m/it/10 M[]\OT1/cmr/m/n/10 (^^@[](\OML/cmm/m/it/10 N\OT1/cmr /m/n/10 ))$ [] [24] [25] [26 ] Chapter 2. [27] Overfull \hbox (0.52818pt too wide) in paragraph at lines 2022--2028 []\OT1/cmr/m/n/10 The di-a-mond bracket ac-tion is sim-ply the ac-tion of $^^@[ ](\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 ^^@[](\O ML/cmm/m/it/10 N\OT1/cmr/m/n/10 ) [] (\U/msb/m/n/10 Z\OML/cmm/m/it/10 =N\U/msb/ m/n/10 Z\OT1/cmr/m/n/10 )[]$ [] [28] [29] LaTeX Warning: Citation `cohen:course_ant' on page 30 undefined on input line 2 133. LaTeX Warning: Citation `cohen:course_ant' on page 30 undefined on input line 2 144. LaTeX Warning: Citation `cohen:course_ant' on page 30 undefined on input line 2 148. [30] [31] LaTeX Warning: Citation `shoup:lower' on page 32 undefined on input line 2311. LaTeX Warning: Citation `nechaev:lower' on page 32 undefined on input line 2311 . LaTeX Warning: Citation `gordon:dlog' on page 32 undefined on input line 2314. LaTeX Warning: Citation `gordon:dlp' on page 32 undefined on input line 2319. [32] LaTeX Warning: Citation `cohen:course_ant' on page 33 undefined on input line 2 382. LaTeX Warning: Citation `cohen:course_ant' on page 33 undefined on input line 2 386. [33] LaTeX Warning: Citation `hijikata:trace' on page 34 undefined on input line 246 8. [34] [35] [36] LaTeX Font Warning: Font shape `OT1/cmss/m/it' in size <10> not available (Font) Font shape `OT1/cmss/m/sl' tried instead on input line 2669 . [37] [38] [39] [40 ] Chapter 3. Overfull \hbox (15.75899pt too wide) in paragraph at lines 2874--2877 []\OT1/cmr/bx/n/10 Definition 3.1.1 \OT1/cmr/m/n/10 (Gen-er-al-ized Bernoulli N um-ber)\OT1/cmr/bx/n/10 . []\OT1/cmr/m/n/10 De-fine the []\OT1/cmr/m/it/10 gen- er-al-ized Bernoulli [] [41] Underfull \vbox (badness 10000) has occurred while \output is active [] [42] LaTeX Warning: Citation `miyake' on page 43 undefined on input line 3000. [43] Overfull \hbox (9.05328pt too wide) in paragraph at lines 3066--3069 []\OT1/cmr/bx/n/10 Example 3.2.6. []\OT1/cmr/m/n/10 The fol-low-ing is a ba-sis of Eisen-stein se-ries $\OML/cmm/m/it/10 E[]$ \OT1/cmr/m/n/10 for $\OML/cmm/m/ it/10 E[]\OT1/cmr/m/n/10 (^^@[](13))$. [] Underfull \vbox (badness 1024) has occurred while \output is active [] [44] LaTeX Warning: Citation `shimura:intro' on page 45 undefined on input line 3105 . [45] [46 ] Chapter 4. LaTeX Warning: Citation `shimura:intro' on page 47 undefined on input line 3182 . LaTeX Warning: Citation `cohen-oesterle:dimensions' on page 47 undefined on inp ut line 3183. [47] LaTeX Warning: Citation `shimura:intro' on page 48 undefined on input line 3201 . LaTeX Warning: Citation `miyake' on page 48 undefined on input line 3202. LaTeX Warning: Citation `diamond-im' on page 48 undefined on input line 3207. Overfull \hbox (6.45883pt too wide) in paragraph at lines 3255--3267 [] [] [48] LaTeX Warning: Citation `lang:modular' on page 49 undefined on input line 3284. LaTeX Warning: Citation `atkin-lehner' on page 49 undefined on input line 3299. LaTeX Warning: Citation `winnie:newforms' on page 49 undefined on input line 33 19. Overfull \hbox (4.75533pt too wide) in paragraph at lines 3321--3327 \OT1/cmr/m/n/10 through $\OML/cmm/m/it/10 M[]\OT1/cmr/m/n/10 (^^@[](\OML/cmm/m/ it/10 N[]\OT1/cmr/m/n/10 ))$. Thus in the def-i-ni-tion of $\OML/cmm/m/it/10 M[ ]\OT1/cmr/m/n/10 (^^@[](\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 ))[]$ and $\OML/cmm/m /it/10 M[]\OT1/cmr/m/n/10 (^^@[](\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 ))[]$, [] [49] [50] LaTeX Warning: Citation `csirik-wetherell-zieve:g0' on page 51 undefined on inp ut line 3436. [51] [52] Overfull \hbox (6.45883pt too wide) in paragraph at lines 3522--3534 [] [] LaTeX Warning: Citation `cohen-oesterle:dimensions' on page 53 undefined on inp ut line 3547. Underfull \vbox (badness 1292) has occurred while \output is active [] [53] Overfull \hbox (25.14609pt too wide) in paragraph at lines 3589--3592 []\OT1/cmr/m/n/10 The for-mula can be used to com-pute $[] \OML/cmm/m/it/10 M[] \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N; "\OT1/cmr/m/n/10 )$, $[] \OML/cmm/m/it/10 S[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N; "\OT1/cmr/m/n/10 )$, and $[] \OML/cmm/m /it/10 E[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N; "\OT1/cmr/m/n/10 )$ [] [54] LaTeX Warning: Citation `cohen-oesterle:dimensions' on page 55 undefined on inp ut line 3689. [55] Overfull \hbox (2.00069pt too wide) in paragraph at lines 3701--3703 []\OT1/cmr/m/n/10 Fill in the el-e-men-tary num-ber the-ory de-tails of the pro of of Al-go-rithm []4.3.1[]. [] [56] Chapter 5. LaTeX Warning: Citation `cohen:course_ant' on page 57 undefined on input line 3 752. [57 ] Overfull \hbox (28.37373pt too wide) in paragraph at lines 3874--3874 [] \OT1/cmtt/m/n/9 # Add -A[i,c] times start_row to the i-th row[] [] Overfull \hbox (4.74901pt too wide) in paragraph at lines 3874--3874 [] \OT1/cmtt/m/n/9 # in order to clear the leading e ntry of[] [] Overfull \hbox (23.64879pt too wide) in paragraph at lines 3874--3874 [] \OT1/cmtt/m/n/9 A.add_multiple_of_row(start_row, -A[i,c], i)[] [] Underfull \vbox (badness 10000) has occurred while \output is active [] [58] [59] [60] Overfull \hbox (18.92384pt too wide) in paragraph at lines 3988--3988 [] \OT1/cmtt/m/n/9 q = U[2]//V[2] # // means divide and take the in teger part[] [] LaTeX Warning: Citation `knuth2' on page 61 undefined on input line 4001. LaTeX Warning: Citation `knuth2' on page 61 undefined on input line 4009. [61] [62] [63] [64] LaTeX Warning: Citation `cohen:course_ant' on page 65 undefined on input line 4 232. [65] [66] [67] LaTeX Warning: Citation `cohen:course_ant' on page 68 undefined on input line 4 427. LaTeX Warning: Citation `cohen:course_ant' on page 68 undefined on input line 4 435. [68] [69] [70] [71] [72 ] Chapter 6. LaTeX Warning: Citation `merel:1585' on page 73 undefined on input line 4676. Underfull \vbox (badness 1558) has occurred while \output is active [] [73] [74] LaTeX Warning: Reference `sec:msff' on page 75 undefined on input line 4805. [75] [76] LaTeX Warning: Citation `mtt' on page 77 undefined on input line 4890. LaTeX Warning: Citation `merel:1585' on page 77 undefined on input line 4927. LaTeX Warning: Citation `sokurov:shimura' on page 77 undefined on input line 49 30. LaTeX Warning: Citation `math252' on page 77 undefined on input line 4932. LaTeX Warning: Citation `manin:parabolic' on page 77 undefined on input line 49 33. LaTeX Warning: Citation `merel:1585' on page 77 undefined on input line 4938. [77] LaTeX Warning: Reference `ch:modsymcomp' on page 78 undefined on input line 499 3. [78] LaTeX Warning: Citation `cremona:gammaone' on page 79 undefined on input line 5 010. LaTeX Warning: Citation `cremona:algs' on page 79 undefined on input line 5068. [79] [80] Overfull \hbox (3.07326pt too wide) detected at line 5182 \OT1/cmr/m/n/10 ^^A[] = [] [] [81] LaTeX Warning: Citation `merel:1585' on page 82 undefined on input line 5297. LaTeX Warning: Citation `mazur:symboles' on page 82 undefined on input line 529 7. [82] LaTeX Warning: Citation `merel:1585' on page 83 undefined on input line 5308. [83] LaTeX Warning: Citation `cremona:algs' on page 84 undefined on input line 5405. [84] LaTeX Warning: Citation `basmaji:thesis' on page 85 undefined on input line 543 7. [85] LaTeX Warning: Citation `merel:1585' on page 86 undefined on input line 5525. [86] Overfull \hbox (5.65291pt too wide) in paragraph at lines 5569--5572 []\OT1/cmr/bx/n/10 Remark 6.5.1. []\OT1/cmr/m/n/10 The in-te-gra-tion pair-ing is re-lated to spe-cial val-ues of $\OML/cmm/m/it/10 L$\OT1/cmr/m/n/10 -functio ns. [] LaTeX Warning: Citation `knapp:elliptic' on page 87 undefined on input line 557 9. Overfull \hbox (33.85875pt too wide) has occurred while \output is active [][]\OT1/cmr/m/sl/10 6.5. THE PAIRING BETWEEN MODULAR SYMBOLS AND MODULAR FORM S \OT1/cmr/m/n/10 87 [] [87] LaTeX Warning: Citation `merel:1585' on page 88 undefined on input line 5636. LaTeX Warning: Citation `merel:1585' on page 88 undefined on input line 5651. Overfull \hbox (3.33667pt too wide) in paragraph at lines 5690--5690 [] [] [88] Overfull \hbox (33.85875pt too wide) has occurred while \output is active [][]\OT1/cmr/m/sl/10 6.5. THE PAIRING BETWEEN MODULAR SYMBOLS AND MODULAR FORM S \OT1/cmr/m/n/10 89 [] [89] LaTeX Warning: Citation `cremona:algs' on page 90 undefined on input line 5758. Overfull \hbox (3.91318pt too wide) in paragraph at lines 5757--5761 []\OT1/cmr/bx/n/10 Remark 6.5.6 \OT1/cmr/m/n/10 (WARN-ING)\OT1/cmr/bx/n/10 . [] \OT1/cmr/m/n/10 No-tice the $\OMS/cmss/m/n/10 ^^@$ \OT1/cmr/m/n/10 sign in fron t of $\OMS/cmss/m/n/10 ^^@\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X ; \OMS/cmss/m/n/10 ^^@\OML/cmm/m/it/10 Y\OT1/cmr/m/n/10 )\OMS/cmss/m/n/10 f^^@\ OML/cmm/m/it/10 ; \OMS/cmss/m/n/10 ^^@\OML/cmm/m/it/10 ^^L\OMS/cmss/m/n/10 g$ [] [90] LaTeX Warning: Citation `cremona:algs' on page 91 undefined on input line 5812. LaTeX Warning: Citation `cremona:algs' on page 91 undefined on input line 5816. [91] Overfull \hbox (8.79385pt too wide) in paragraph at lines 5877--5880 []\OT1/cmss/m/n/10 We have $[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 u; v; N\OT1/cmr /m/n/10 ) = [](\OML/cmm/m/it/10 g; v\OT1/cmr/m/n/10 )$\OT1/cmss/m/n/10 , so if $[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g; v\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 > \ OT1/cmr/m/n/10 1$\OT1/cmss/m/n/10 , then $\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 u; v\OT1/cmr/m/n/10 ) \OMS/cmss/m/n/10 62 \U/msb/m/n/10 P[]\OT1/cmr/m/n/10 (\U/msb /m/n/10 Z\OML/cmm/m/it/10 =N\U/msb/m/n/10 Z\OT1/cmr/m/n/10 )$\OT1/cmss/m/n/10 . [] [92] LaTeX Warning: Reference `alg:p1list' on page 93 undefined on input line 5940. LaTeX Warning: Reference `alg:p1list' on page 93 undefined on input line 5953. LaTeX Warning: Reference `alg:p1list' on page 93 undefined on input line 5959. Overfull \hbox (25.0241pt too wide) in paragraph at lines 5975--5975 [] \OT1/cmtt/m/n/9 for c in range(1,N): # iterate c such that 1 <= c < N:[] [] Overfull \hbox (6.12431pt too wide) in paragraph at lines 5975--5975 [] \OT1/cmtt/m/n/9 for d in xrange(2,N): # 2 <= d < N[] [] [93] [94] Underfull \vbox (badness 10000) has occurred while \output is active [] [95] Overfull \hbox (14.54114pt too wide) detected at line 6141 \OML/cmm/m/it/10 x[] \OT1/cmr/m/n/10 = (0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)\ OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0 )\OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)\OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/ 10 2)\OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/m/ n/10 3)\OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/ m/n/10 4)\OML/cmm/m/it/10 ; [] Overfull \hbox (17.5134pt too wide) detected at line 6149 \OML/cmm/m/it/10 x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 5)\ OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 6 )\OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 7)\OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/ 10 8)\OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/m/ n/10 9)\OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1\OML/cmm/m/it/10 ; \OT1/cmr/ m/n/10 10)\OML/cmm/m/it/10 : [] [96] LaTeX Warning: Reference `example:m4_1' on page 97 undefined on input line 6210 . [97] Overfull \hbox (11.99197pt too wide) detected at line 6324 [] [] [98] Overfull \hbox (13.01974pt too wide) detected at line 6347 [] [] [99] [100] Overfull \hbox (43.711pt too wide) detected at line 6477 [] [] [101] LaTeX Warning: Reference `alg:p1list' on page 102 undefined on input line 6518. Overfull \hbox (22.36095pt too wide) detected at line 6523 \OML/cmm/m/it/10 x[] \OT1/cmr/m/n/10 = (0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)\ OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0)\OML/c mm/m/it/10 ; \OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)\OML/cmm/m/ it/10 ; \OT1/cmr/m/n/10 (1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2)\OML/cmm/m/it/10 ; [] ; \OT1/cmr/m/n/10 (501\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 7)\OML/cmm/m/it/ 10 ; \OT1/cmr/m/n/10 (668\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 (668\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 3)\OML/cmm/m/it/10 ; \ OT1/cmr/m/n/10 (668\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 5)\OML/cmm/m/it/10 ; x[] \OT1/cmr/m/n/10 = (1002\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1) [] LaTeX Warning: Reference `alg:twoterm' on page 102 undefined on input line 6563 . [102] Overfull \hbox (99.24791pt too wide) in paragraph at lines 6713--6713 [] \OT1/cmtt/m/n/9 >>> rels = set([((0,3), (1,-1)), ((1,1), (3,1)), ((2, 1),(3,1)), ((4,1),(5,-1))])[] [] Overfull \hbox (4.74901pt too wide) in paragraph at lines 6713--6713 [] \OT1/cmtt/m/n/9 # all xi equal to free[t[0]] must now equal t o zero.[] [] Underfull \vbox (badness 10000) has occurred while \output is active [] [103] Overfull \vbox (213.0pt too high) has occurred while \output is active [] [104] LaTeX Warning: Reference `sec:periods' on page 105 undefined on input line 6743 . LaTeX Warning: Reference `sec:findall' on page 105 undefined on input line 6748 . LaTeX Warning: Citation `birch:bsd' on page 105 undefined on input line 6755. LaTeX Warning: Citation `manin:parabolic' on page 105 undefined on input line 6 757. LaTeX Warning: Citation `merel:1585' on page 105 undefined on input line 6762. LaTeX Warning: Citation `sokurov:shimura' on page 105 undefined on input line 6 763. LaTeX Warning: Citation `cremona:algs' on page 105 undefined on input line 6767 . LaTeX Warning: Citation `cremona:gammaone' on page 105 undefined on input line 6770. LaTeX Warning: Citation `basmaji:thesis' on page 105 undefined on input line 67 74. LaTeX Warning: Citation `stein:phd' on page 105 undefined on input line 6778. LaTeX Warning: Citation `agashe:phd' on page 105 undefined on input line 6781. LaTeX Warning: Citation `martin:thesis' on page 105 undefined on input line 678 1. LaTeX Warning: Citation `lemelin:dominic' on page 105 undefined on input line 6 783. LaTeX Warning: Citation `frey-muller' on page 105 undefined on input line 6786. [105] LaTeX Warning: Citation `dembele' on page 106 undefined on input line 6794. LaTeX Warning: Citation `darmon-pollack' on page 106 undefined on input line 68 03. LaTeX Warning: Citation `mtt' on page 106 undefined on input line 6818. [106] Chapter 7. LaTeX Warning: Citation `atkin-lehner' on page 107 undefined on input line 6874 . LaTeX Warning: Citation `winnie:newforms' on page 107 undefined on input line 6 874. LaTeX Warning: Reference `eqn:decomp' on page 107 undefined on input line 6883. [107 ] LaTeX Warning: Reference `ex:onlyold' on page 108 undefined on input line 6919. LaTeX Warning: Citation `winnie:newforms' on page 108 undefined on input line 6 952. [108] LaTeX Warning: Reference `eqn:eigenexp' on page 109 undefined on input line 699 8. LaTeX Warning: Reference `eqn:decomp' on page 109 undefined on input line 7033. LaTeX Warning: Reference `prop:eigncoeffs' on page 109 undefined on input line 7037. LaTeX Warning: Citation `merel:1585' on page 109 undefined on input line 7047. LaTeX Warning: Reference `alg:modsympresent' on page 109 undefined on input lin e 7053. Overfull \hbox (1.1528pt too wide) in paragraph at lines 7052--7057 []\OT1/cmss/m/n/10 [Compute [] [109] LaTeX Warning: Reference `alg:merelqexp' on page 110 undefined on input line 70 83. LaTeX Warning: Reference `alg:merelqexp' on page 110 undefined on input line 70 85. [110] LaTeX Warning: Reference `alg:proj' on page 111 undefined on input line 7162. [111] LaTeX Warning: Reference `alg:ap:gen' on page 112 undefined on input line 7200. LaTeX Warning: Reference `alg:ap:gen' on page 112 undefined on input line 7204. [112] LaTeX Warning: Reference `alg:eigsys' on page 113 undefined on input line 7286. LaTeX Warning: Reference `alg:eigsys' on page 113 undefined on input line 7311. LaTeX Warning: Reference `alg:proj' on page 113 undefined on input line 7314. [113] LaTeX Warning: Citation `mfd' on page 114 undefined on input line 7392. [114] Chapter 8. LaTeX Warning: Citation `cremona:algs' on page 115 undefined on input line 7454 . [115 ] LaTeX Warning: Citation `shimura:surles' on page 116 undefined on input line 75 22. [116] LaTeX Warning: Reference `eqn:extpair' on page 117 undefined on input line 7568 . Overfull \hbox (4.25626pt too wide) in paragraph at lines 7589--7589 []\OT1/cmr/bx/n/14.4 Numerically Ap-prox-i-mat-ing Pe-riod In-te-grals [] [117] LaTeX Warning: Citation `cremona:algs' on page 118 undefined on input line 7634 . LaTeX Warning: Citation `cremona:algs' on page 118 undefined on input line 7663 . LaTeX Warning: Reference `modsym-errorterm' on page 118 undefined on input line 7675. [118] LaTeX Warning: Reference `eqn:intsum' on page 119 undefined on input line 7682. LaTeX Warning: Reference `lem:intexp' on page 119 undefined on input line 7682. LaTeX Warning: Reference `modsym-errorterm' on page 119 undefined on input line 7684. LaTeX Warning: Citation `manin:parabolic' on page 119 undefined on input line 7 699. LaTeX Warning: Reference `eqn:erroreqn' on page 119 undefined on input line 771 2. LaTeX Warning: Citation `stein-verrill:transportable' on page 119 undefined on input line 7789. LaTeX Warning: Reference `fig:trans' on page 119 undefined on input line 7795. [119] [120] [121] Overfull \hbox (17.47293pt too wide) in paragraph at lines 7811--7811 []\OT1/cmr/bx/n/14.4 Speeding Con-ver-gence Us-ing the Atkin-Lehner [] LaTeX Warning: Citation `cremona:periods' on page 122 undefined on input line 7 846. Overfull \hbox (8.49567pt too wide) in paragraph at lines 7862--7862 [] [] LaTeX Warning: Reference `modsym-errorterm' on page 122 undefined on input line 7866. Underfull \hbox (badness 10000) in paragraph at lines 7866--7869 [] Overfull \hbox (29.2303pt too wide) in paragraph at lines 7883--7883 [] [] [122] LaTeX Warning: Reference `sec:numper' on page 123 undefined on input line 7918. LaTeX Warning: Reference `wntrick' on page 123 undefined on input line 7922. LaTeX Warning: Reference `wntrick' on page 123 undefined on input line 7926. LaTeX Warning: Reference `ch:periods' on page 123 undefined on input line 7939. LaTeX Warning: Reference `ex:funceqn' on page 123 undefined on input line 7939. Overfull \hbox (25.24976pt too wide) has occurred while \output is active [][]\OT1/cmr/m/sl/10 8.4. SPEEDING CONVERGENCE USING THE ATKIN-LEHNER OPERATOR \OT1/cmr/m/n/10 123 [] [123] LaTeX Warning: Citation `cohen:course_ant' on page 124 undefined on input line 7960. LaTeX Warning: Citation `cremona:algs' on page 124 undefined on input line 7960 . LaTeX Warning: Reference `eqn:lone' on page 124 undefined on input line 7962. LaTeX Warning: Citation `cremona:algs' on page 124 undefined on input line 7962 . [124] LaTeX Warning: Reference `modsym-errorterm' on page 125 undefined on input line 8004. LaTeX Warning: Reference `wntrick' on page 125 undefined on input line 8004. LaTeX Warning: Reference `wntrick' on page 125 undefined on input line 8024. LaTeX Warning: Citation `cremona:algs' on page 125 undefined on input line 8031 . LaTeX Warning: Citation `wiles:fermat' on page 125 undefined on input line 8091 . LaTeX Warning: Citation `breuil-conrad-diamond-taylor' on page 125 undefined on input line 8091. LaTeX Warning: Citation `taylor-wiles:fermat' on page 125 undefined on input li ne 8091. LaTeX Warning: Citation `cremona:algs' on page 125 undefined on input line 8094 . [125] Overfull \hbox (34.09412pt too wide) in paragraph at lines 8104--8117 []\OT1/cmss/m/n/10 [Find Ra-tio-nal Eigenspaces] []Find the two-dimensional eig enspaces $\OML/cmm/m/it/10 V$ \OT1/cmss/m/n/10 in $\U/msb/m/n/10 M[]\OT1/cmr/m/ n/10 (^^@[](\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 ))[]$ [] LaTeX Warning: Reference `alg:eigsys' on page 126 undefined on input line 8119. LaTeX Warning: Reference `step:rateigen' on page 126 undefined on input line 81 21. LaTeX Warning: Reference `step:ratnew' on page 126 undefined on input line 8125 . LaTeX Warning: Reference `sec:computephi' on page 126 undefined on input line 8 131. LaTeX Warning: Reference `step:tau' on page 126 undefined on input line 8150. [126] LaTeX Warning: Reference `thm:sturm' on page 127 undefined on input line 8172. LaTeX Warning: Citation `cremona:periods' on page 127 undefined on input line 8 184. LaTeX Warning: Citation `cremona:algs' on page 127 undefined on input line 8194 . LaTeX Warning: Citation `cremona-lingham' on page 127 undefined on input line 8 201. LaTeX Warning: Citation `tate:antwerpiv' on page 127 undefined on input line 82 06. LaTeX Warning: Citation `cremona:algs' on page 127 undefined on input line 8206 . LaTeX Warning: Citation `silverman:aec' on page 127 undefined on input line 822 1. [127] LaTeX Warning: Citation `cremona-lingham' on page 128 undefined on input line 8 238. LaTeX Warning: Citation `empirical' on page 128 undefined on input line 8252. LaTeX Warning: Citation `empirical' on page 128 undefined on input line 8258. LaTeX Warning: Citation `empirical' on page 128 undefined on input line 8264. LaTeX Warning: Reference `sec:wntrick' on page 128 undefined on input line 8281 . [128] LaTeX Warning: Citation `empirical' on page 129 undefined on input line 8314. LaTeX Warning: Reference `table:vols' on page 129 undefined on input line 8329. LaTeX Warning: Reference `table:cmcurves' on page 129 undefined on input line 8 370. LaTeX Warning: Reference `table:cmcurves' on page 129 undefined on input line 8 372. [129] Overfull \hbox (41.68187pt too wide) in paragraph at lines 8381--8399 [] [] LaTeX Warning: Citation `cremona:algs' on page 130 undefined on input line 8404 . [130] LaTeX Warning: Citation `cremona:algs' on page 131 undefined on input line 8436 . [131] [132 ] Chapter 9. LaTeX Warning: Citation `serre:arithmetic' on page 133 undefined on input line 8516. [133] LaTeX Warning: Citation `sturm:cong' on page 134 undefined on input line 8551. LaTeX Warning: Citation `sturm:cong' on page 134 undefined on input line 8552. LaTeX Warning: Reference `eqn:sturm1' on page 134 undefined on input line 8589. LaTeX Warning: Reference `eqn:sturm2' on page 134 undefined on input line 8589. LaTeX Warning: Reference `lem:jform' on page 134 undefined on input line 8595. [134] [135] LaTeX Warning: Reference `eqn:sturm_crt' on page 136 undefined on input line 87 20. LaTeX Warning: Reference `eqn:sturm:ords' on page 136 undefined on input line 8 739. Package amsmath Warning: Foreign command \over; (amsmath) \frac or \genfrac should be used instead (amsmath) on input line 8809. [136] LaTeX Warning: Reference `thm:sturm' on page 137 undefined on input line 8821. LaTeX Warning: Citation `sturm:cong' on page 137 undefined on input line 8826. LaTeX Warning: Citation `buzzard-stein:artin' on page 137 undefined on input li ne 8853. LaTeX Warning: Citation `buzzard-stein:artin' on page 137 undefined on input li ne 8876. Overfull \hbox (2.19801pt too wide) in paragraph at lines 8881--8881 []\OT1/cmr/bx/n/14.4 Generating the Hecke Al-ge-bra as a $\U/msb/m/n/14.4 Z$\OT 1/cmr/bx/n/14.4 -module [] LaTeX Warning: Citation `lario-schoof' on page 137 undefined on input line 8883 . [137] Overfull \hbox (5.38551pt too wide) in paragraph at lines 8891--8896 \OT1/cmr/m/it/10 where $\OML/cmm/m/it/10 m \OT1/cmr/m/n/10 = [[][](\U/msb/m/n/1 0 Z\OT1/cmr/m/n/10 ) : ^^@]$\OT1/cmr/m/it/10 . Then the Hecke al-ge-bra $\U/msb /m/n/10 T \OT1/cmr/m/n/10 = \U/msb/m/n/10 Z\OT1/cmr/m/n/10 [[] \OML/cmm/m/it/10 ; T[]; []\OT1/cmr/m/n/10 ] \OMS/cmss/m/n/10 ^^Z []\OT1/cmr/m/n/10 (\OML/cmm/m/ it/10 S[]\OT1/cmr/m/n/10 (^^@))$ [] LaTeX Warning: Reference `thm:sturm' on page 138 undefined on input line 8918. LaTeX Warning: Reference `eqn:perfectR' on page 138 undefined on input line 892 1. LaTeX Warning: Reference `thm:heckegen' on page 138 undefined on input line 893 3. No file current.bbl. No file current.ind. [138] (./current.aux) LaTeX Font Warning: Some font shapes were not available, defaults substituted. LaTeX Warning: There were undefined references. LaTeX Warning: There were multiply-defined labels. ) Here is how much of TeX's memory you used: 6148 strings out of 94501 74960 string characters out of 1176788 292875 words of memory out of 1000000 9206 multiletter control sequences out of 10000+50000 27560 words of font info for 109 fonts, out of 500000 for 2000 580 hyphenation exceptions out of 8191 27i,19n,30p,447b,441s stack positions out of 1500i,500n,5000p,200000b,5000s Output written on current.dvi (138 pages, 597240 bytes).