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Package hyperref Info: Link coloring OFF on input line 2533. \c@Item=\count113 \c@Hfootnote=\count114 ) *hyperref using driver hypertex* (/usr/share/texmf/tex/latex/hyperref/hypertex.def File: hypertex.def 2003/01/22 v6.73n Hyperref driver for HyperTeX specials ) \c@theorem=\count115 \tf@default=\write4 \idxtitle@default=\toks36 \openout4 = `257.idx'. index.sty> Writing index file 257.idx (./257.aux LaTeX Warning: Label `alg:decomp:factor' multiply defined. ) \openout1 = `257.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 381. LaTeX Font Info: ... okay on input line 381. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 381. LaTeX Font Info: ... okay on input line 381. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 381. LaTeX Font Info: ... okay on input line 381. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 381. LaTeX Font Info: ... okay on input line 381. 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LaTeX Font Info: Try loading font information for U+msa on input line 383. (/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 383. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) [1 ] [2] (./257.toc [3 ] [4]) \tf@toc=\write5 \openout5 = `257.toc'. [5] [6 ] [7] Overfull \hbox (2.15204pt too wide) in paragraph at lines 466--471 \OT1/cmr/m/n/10 help-ful in find-ing the al-go-rithms in Chap-ter []2[][]. \OT1 /cmr/bx/n/10 Noam Elkies: \OT1/cmr/m/n/10 Re-marks through- [] LaTeX Font Info: Try loading font information for OMS+cmr on input line 473. (/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 473. [8] Chapter 1. LaTeX Font Info: Try loading font information for U+euf on input line 498. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 2002/01/19 v2.2g AMS font definitions ) [9 ] [10] Overfull \hbox (12.34515pt too wide) detected at line 631 \OML/cmm/m/it/10 G[]\OT1/cmr/m/n/10 (\OMS/cmsy/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 : [] Overfull \hbox (3.35062pt too wide) in paragraph at lines 660--663 []\OT1/cmr/m/n/10 The dis-crim-i-nant of the cu-bic $4\OML/cmm/m/it/10 x[] \OMS /cmsy/m/n/10 ^^@ \OT1/cmr/m/n/10 60\OML/cmm/m/it/10 G[]\OT1/cmr/m/n/10 (\OML/cm m/m/it/10 ![]=![]\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 x \OMS/cmsy/m/n/10 ^^@ \OT1/ cmr/m/n/10 140\OML/cmm/m/it/10 G[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 ![]=![]\OT1 /cmr/m/n/10 )$ is $16^^A(\OML/cmm/m/it/10 ![]=![]\OT1/cmr/m/n/10 )$, [] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] Overfull \hbox (36.14932pt too wide) has occurred while \output is active [][]\OT1/cmr/m/sl/10 1.6. CAN ONE COMPUTE THE COEFFICIENTS OF $\OT1/cmr/m/n/10 ^^A$ \OT1/cmr/m/sl/10 IN POLYNOMIAL TIME? \OT1/cmr/m/n/10 21 [] [21] [22] Chapter 2. [23 ] LaTeX Font Info: Try loading font information for OMS+cmss on input line 154 4. LaTeX Font Info: No file OMScmss.fd. on input line 1544. LaTeX Font Warning: Font shape `OMS/cmss/m/n' undefined (Font) using `OMS/cmsy/m/n' instead (Font) for symbol `textsection' on input line 1544. [24] [25] Overfull \hbox (6.08577pt too wide) in paragraph at lines 1642--1646 [] \OT1/cmss/m/n/10 Given a Dirich-let char-ac-ter $\OML/cmm/m/it/10 "$ \OT1/cm ss/m/n/10 mod-ulo $\OML/cmm/m/it/10 N$\OT1/cmss/m/n/10 , rep-re-sented by a lis t $\OT1/cmr/m/n/10 [\OML/cmm/m/it/10 "\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g[]\OT1 /cmr/m/n/10 )\OML/cmm/m/it/10 ; "\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g[]\OT1/cmr/ m/n/10 )\OML/cmm/m/it/10 ; [] ; "\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g[]\OT1/cmr/ m/n/10 )]$\OT1/cmss/m/n/10 , [] [26] [27] [28] [29] [30] [31] [32] 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 2151 . [33] [34] [35] [36] Chapter 3. [37 ] Underfull \hbox (badness 10000) in paragraph at lines 2395--2396 [] Overfull \hbox (42.19318pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 38 \OT1/cmr/m/sl/10 CHAPTER 3. MODULAR FORMS AND EISENSTEI N SERIES OF HIGHER LEVEL [] [38] Overfull \hbox (0.52818pt too wide) in paragraph at lines 2463--2469 [][]\OT1/cmr/m/n/10 The di-a-mond bracket ac-tion is sim-ply the ac-tion of $^^ @[](\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 ^^@[]( \OML/cmm/m/it/10 N\OT1/cmr/m/n/10 ) [] (\U/msb/m/n/10 Z\OML/cmm/m/it/10 =N\U/ms b/m/n/10 Z\OT1/cmr/m/n/10 )[]$ [] [39] Overfull \hbox (42.19318pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 40 \OT1/cmr/m/sl/10 CHAPTER 3. MODULAR FORMS AND EISENSTEI N SERIES OF HIGHER LEVEL [] [40] [41] Overfull \hbox (42.19318pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 42 \OT1/cmr/m/sl/10 CHAPTER 3. MODULAR FORMS AND EISENSTEI N SERIES OF HIGHER LEVEL [] [42] Overfull \hbox (9.05328pt too wide) in paragraph at lines 2723--2725 \OT1/cmr/bx/n/10 Example 3.3.6. []\OT1/cmr/m/n/10 The fol-low-ing is a ba-sis o f Eisen-stein se-ries $\OML/cmm/m/it/10 E[]$ \OT1/cmr/m/n/10 for $\OML/cmm/m/it /10 E[]\OT1/cmr/m/n/10 (^^@[](13))$. [] [43] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2751--2751 [] \OT1/cmtt/m/n/10 + (3*zeta_12^2 - 2)*q^3 + O(q^4)[] [] Overfull \hbox (42.19318pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 44 \OT1/cmr/m/sl/10 CHAPTER 3. MODULAR FORMS AND EISENSTEI N SERIES OF HIGHER LEVEL [] [44] Chapter 4. [45 ] Overfull \hbox (30.66539pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 46 \OT1/cmr/m/sl/10 CHAPTER 4. COMPUTING DIMENSIONS OF SPA CES OF MODULAR FORMS [] [46] Overfull \hbox (6.45883pt too wide) in paragraph at lines 2885--2897 [][] [] [47] Overfull \hbox (4.75533pt too wide) in paragraph at lines 2951--2957 \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 $\OML/cmm/m /it/10 M[]\OT1/cmr/m/n/10 (^^@[](\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 ))[]$, [] Overfull \hbox (30.66539pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 48 \OT1/cmr/m/sl/10 CHAPTER 4. COMPUTING DIMENSIONS OF SPA CES OF MODULAR FORMS [] [48] [49] Underfull \hbox (badness 10000) in paragraph at lines 3101--3105 [] Overfull \hbox (30.66539pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 50 \OT1/cmr/m/sl/10 CHAPTER 4. COMPUTING DIMENSIONS OF SPA CES OF MODULAR FORMS [] [50] Overfull \hbox (6.45883pt too wide) in paragraph at lines 3147--3159 [][] [] Underfull \vbox (badness 1292) has occurred while \output is active [] [51] Overfull \hbox (25.14609pt too wide) in paragraph at lines 3214--3217 [][]\OT1/cmr/m/n/10 The for-mula can be used to com-pute $[] \OML/cmm/m/it/10 M []\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N; "\OT1/cmr/m/n/10 )$, $[] \OML/cmm/m/it/1 0 S[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N; "\OT1/cmr/m/n/10 )$, and $[] \OML/cmm /m/it/10 E[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N; "\OT1/cmr/m/n/10 )$ [] Overfull \hbox (30.66539pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 52 \OT1/cmr/m/sl/10 CHAPTER 4. COMPUTING DIMENSIONS OF SPA CES OF MODULAR FORMS [] [52] [53] Overfull \hbox (2.00069pt too wide) in paragraph at lines 3326--3328 [][]\OT1/cmr/m/n/10 Fill in the el-e-men-tary num-ber the-ory de-tails of the p roof of Al-go-rithm []4.3.1[][]. [] Overfull \hbox (30.66539pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 54 \OT1/cmr/m/sl/10 CHAPTER 4. COMPUTING DIMENSIONS OF SPA CES OF MODULAR FORMS [] [54] Chapter 5. [55 ] Overfull \hbox (38.24666pt too wide) in paragraph at lines 3468--3468 [] \OT1/cmtt/m/n/10 # Add -A[i,c] times start_row to the i-th row[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 3468--3468 [] \OT1/cmtt/m/n/10 # in order to clear the leading entry of[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 3468--3468 [] \OT1/cmtt/m/n/10 A.add_multiple_of_row(start_row, -A[i,c], i)[] [] [56] [57] [58] Overfull \hbox (27.74675pt too wide) in paragraph at lines 3581--3581 [] \OT1/cmtt/m/n/10 q = U[2]//V[2] # // means divide and take the i nteger part[] [] [59] [60] [61] Overfull \hbox (5.4972pt too wide) in paragraph at lines 3782--3782 [][]\OT1/cmtt/m/n/10 http://magma.maths.usyd.edu.au/users/allan/gb/faugere_f4. ps.gz[] [] [62] [63] [64 ] Chapter 6. Underfull \vbox (badness 1558) has occurred while \output is active [] [65] [66] LaTeX Warning: Reference `sec:msff' on page 67 undefined on input line 3994. [67] [68] [69] LaTeX Warning: Reference `ch:modsymcomp' on page 70 undefined on input line 418 2. [70] [71] [72] Overfull \hbox (3.07326pt too wide) detected at line 4371 \OT1/cmr/m/n/10 ^^A[] = [] [] [73] [74] [75] [76] [77] [78] Overfull \hbox (5.65291pt too wide) in paragraph at lines 4757--4760 \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 -functions . [] 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 79 [] [79] Overfull \hbox (3.33667pt too wide) in paragraph at lines 4878--4878 [] [] [80] 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 81 [] [81] Overfull \hbox (13.9266pt too wide) in paragraph at lines 4945--4949 \OT1/cmr/bx/n/10 Remark 6.5.6 (WARN-ING). []\OT1/cmr/m/n/10 No-tice the $\OMS/c mss/m/n/10 ^^@$ \OT1/cmr/m/n/10 sign in front of $\OMS/cmss/m/n/10 ^^@\OML/cmm/ m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X; \OMS/cmss/m/n/10 ^^@\OML/cmm/m/it /10 Y\OT1/cmr/m/n/10 )\OMS/cmss/m/n/10 f^^@\OML/cmm/m/it/10 ^^K; \OMS/cmss/m/n/ 10 ^^@\OML/cmm/m/it/10 ^^L\OMS/cmss/m/n/10 g$ [] [82] [83] Overfull \hbox (8.79385pt too wide) in paragraph at lines 5063--5065 [][]\OT1/cmss/m/n/10 We have $[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 u; v; N\OT1/c mr/m/n/10 ) = [](\OML/cmm/m/it/10 g; v\OT1/cmr/m/n/10 )$\OT1/cmss/m/n/10 , so i f $[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g; v\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 > \OT1/cmr/m/n/10 1$\OT1/cmss/m/n/10 , then $\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 u ; v\OT1/cmr/m/n/10 ) \OMS/cmss/m/n/10 62 \U/msb/m/n/10 P[]\OT1/cmr/m/n/10 (\U/m sb/m/n/10 Z\OML/cmm/m/it/10 =N\U/msb/m/n/10 Z\OT1/cmr/m/n/10 )$\OT1/cmss/m/n/10 . [] [84] Overfull \hbox (3.04187pt too wide) in paragraph at lines 5121--5122 \OT1/cmr/bx/n/10 Remark 6.6.2. []\OT1/cmr/m/n/10 Al-lan Steel and the au-thor j ointly came up with Al-go-rithm []6.6.1[][]. [] Overfull \hbox (2.43726pt too wide) in paragraph at lines 5138--5142 \OT1/cmss/m/n/10 up $\U/msb/m/n/10 P[]\OT1/cmr/m/n/10 (\U/msb/m/n/10 Z\OML/cmm/ m/it/10 =N\U/msb/m/n/10 Z\OT1/cmr/m/n/10 )$\OT1/cmss/m/n/10 . In the fol-low-in g code, we name Al-go-rithm []6.6.1[][] \OT1/cmtt/m/n/10 p1[]normalize\OT1/cmss /m/n/10 . [] Overfull \hbox (31.74696pt too wide) in paragraph at lines 5155--5155 [] \OT1/cmtt/m/n/10 for c in range(1,N): # iterate c such that 1 < = c < N:[] [] [85] Overfull \hbox (10.74715pt too wide) in paragraph at lines 5155--5155 [] \OT1/cmtt/m/n/10 for d in xrange(2,N): # 2 <= d < N[] [] Overfull \hbox (0.24724pt too wide) in paragraph at lines 5162--5162 [][] \OT1/cmtt/m/n/10 lst = list(set(lst)) # Python trick remove duplica tes.[] [] [86] Underfull \vbox (badness 10000) has occurred while \output is active [] [87] Overfull \hbox (14.54114pt too wide) detected at line 5320 \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 5328 \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 : [] [88] [89] Overfull \hbox (11.99197pt too wide) detected at line 5503 [] [] [90] Overfull \hbox (13.01974pt too wide) detected at line 5526 [] [] [91] [92] Overfull \hbox (43.711pt too wide) detected at line 5656 [] [] [93] Overfull \hbox (22.36095pt too wide) detected at line 5702 \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 `' on page 94 undefined on input line 5728. [94] Overfull \hbox (6.74693pt too wide) in paragraph at lines 5892--5892 [] \OT1/cmtt/m/n/10 3*x0 - x1 = 0, x1 + x3 = 0, x2 + x3 = 0, x4 - x5 = 0[] [] Overfull \hbox (116.99597pt too wide) in paragraph at lines 5892--5892 [] \OT1/cmtt/m/n/10 >>> rels = set([((0,3), (1,-1)), ((1,1), (3,1)), ((2 ,1),(3,1)), ((4,1),(5,-1))])[] [] [95] Overfull \hbox (11.99689pt too wide) in paragraph at lines 5892--5892 [] \OT1/cmtt/m/n/10 # all xi equal to free[t[0]] must now equal to zero.[] [] [96] LaTeX Warning: Reference `sec:degen' on page 97 undefined on input line 5911. [97] [98] [99] [100 ] Chapter 7. [101] Overfull \hbox (98.02443pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 102 \OT1/cmr/m/sl/10 CHAPTER 7. USING MODULAR SYMBOLS TO C OMPUTE SPACES OF MODULAR FORMS [] [102] [103] Overfull \hbox (98.02443pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 104 \OT1/cmr/m/sl/10 CHAPTER 7. USING MODULAR SYMBOLS TO C OMPUTE SPACES OF MODULAR FORMS [] [104] [105] Overfull \hbox (98.02443pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 106 \OT1/cmr/m/sl/10 CHAPTER 7. USING MODULAR SYMBOLS TO C OMPUTE SPACES OF MODULAR FORMS [] [106] [107] Overfull \hbox (1.69481pt too wide) in paragraph at lines 6532--6544 [][]\OT1/cmss/m/n/10 [Compute Pro-jec-tion] As de-scribed in Sec-tion []7.3.1[] [], com-pute the $\U/msb/m/n/10 T$\OT1/cmss/m/n/10 -equivariant [] Overfull \hbox (98.02443pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 108 \OT1/cmr/m/sl/10 CHAPTER 7. USING MODULAR SYMBOLS TO C OMPUTE SPACES OF MODULAR FORMS [] [108] [109] Overfull \hbox (98.02443pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 110 \OT1/cmr/m/sl/10 CHAPTER 7. USING MODULAR SYMBOLS TO C OMPUTE SPACES OF MODULAR FORMS [] [110] Chapter 8. Overfull \hbox (17.58359pt too wide) in paragraph at lines 6656--6659 \OT1/cmss/m/n/10 Given a new-form $\OML/cmm/m/it/10 f$ \OT1/cmss/m/n/10 in $\OM L/cmm/m/it/10 S[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N; "\OT1/cmr/m/n/10 )$\OT1/c mss/m/n/10 , this al-go-rithm ap-prox-i-mates the pe-riod map $\OML/cmm/m/it/10 M[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N; "\OT1/cmr/m/n/10 ) \OMS/cmss/m/n/10 ! [] [111 ] [112 ] Chapter 9. [113] Overfull \hbox (18.7914pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 114 \OT1/cmr/m/sl/10 CHAPTER 9. MODULAR CURVES AND MODULAR ABELIAN VARIETIES [] [114 ] Chapter 10. Overfull \hbox (11.80632pt too wide) in paragraph at lines 6695--6695 []\OT1/cmr/bx/n/14.4 Congruences and Re-duc-tion Mod-ulo a Prime [] [115] [116] Chapter 11. Overfull \hbox (17.24684pt too wide) in paragraph at lines 6831--6831 []\OT1/cmtt/m/n/10 >>> t2.charpoly() # call in more ``object-orient ed'' way.[] [] [117 ] Overfull \hbox (14.6942pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 118 \OT1/cmr/m/sl/10 CHAPTER 11. SOFTWARE FOR COMPUTING WI TH MODULAR FORMS [] [118] LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <9> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 6846. [119 ] Overfull \hbox (14.6942pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 120 \OT1/cmr/m/sl/10 CHAPTER 11. SOFTWARE FOR COMPUTING WI TH MODULAR FORMS [] [120] [121] Overfull \hbox (14.6942pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 122 \OT1/cmr/m/sl/10 CHAPTER 11. SOFTWARE FOR COMPUTING WI TH MODULAR FORMS [] [122] [123] (./257.bbl Overfull \hbox (14.6942pt too wide) has occurred while \output is active [][]\OT1/cmr/m/n/10 124 \OT1/cmr/m/sl/10 CHAPTER 11. SOFTWARE FOR COMPUTING WI TH MODULAR FORMS [] [124] Underfull \hbox (badness 10000) in paragraph at lines 20--23 [][]\OT1/cmr/m/n/10 Jacques Bas-maji, \OT1/cmr/m/it/10 Ein al-go-rith-mus zur b erech-nung von [] Underfull \hbox (badness 10000) in paragraph at lines 20--23 \OT1/cmr/m/it/10 hecke-operatoren und an-wen-dun-gen auf mod-u-lare kur-ven\OT1 /cmr/m/n/10 , [] Underfull \hbox (badness 10000) in paragraph at lines 20--23 \OT1/cmtt/m/n/10 http://modular.fas.harvard.edu/scans/papers/basmaji/ [] [125 ] Overfull \hbox (48.44151pt too wide) in paragraph at lines 63--66 \OT1/cmtt/m/n/10 http://modular.fas.harvard.edu/mcs/archive/spring2004/dembele. html\OT1/cmr/m/n/10 . [] Underfull \hbox (badness 5862) in paragraph at lines 72--74 [][]\OT1/cmr/m/n/10 Denis Diderot, \OT1/cmr/m/it/10 P^^Seriodes de formes mod-u -laires de poids 1\OT1/cmr/m/n/10 , [] Underfull \hbox (badness 10000) in paragraph at lines 72--74 \OT1/cmtt/m/n/10 http://modular.fas.harvard.edu/scans/papers/diderot/ [] [126] [127]) (./257.ind) [128] (./257.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: 5666 strings out of 95755 67648 string characters out of 1194952 288141 words of memory out of 1000001 8556 multiletter control sequences out of 10000+50000 22916 words of font info for 89 fonts, out of 500000 for 1000 14 hyphenation exceptions out of 1000 27i,19n,30p,443b,468s stack positions out of 1500i,500n,5000p,200000b,5000s Output written on 257.dvi (128 pages, 504796 bytes).