1) Return all graded homework 

2) Clarify current homework assignment:
     * All problems from dimension formulas chapter 
       and one linear algebra problem: 
          Exercise 7.1 (not easy).
       Should have more linalg exercises but too late.
     * Working together on homework is OK (I should
       have mentioned this earlier...)

3) Current plan for rest of quarter:

[] (may 15) Higher Weight Modular Symbols 1: basic definitions; 
            how to compute:
             Sections 8.1 -- 8.2
[] (may 17) Higher Weight Modular Symbols 2: Hecke operators on them
             Sections 8.3
[] (may 19) Higher Weight Modular Symbols 3: using to compute modular forms
             Sections 8.4 -- 8.6

[] (may 22) Newforms 1: Atkin-Lehner-Li theory
             Sections 9.1 -- 9.3
[] (may 24) Newforms 2: Computing (and storing!) systems of eigenvalues
             Section 9.4
[] (may 26) Special Values of L-functions using modular symbols
             Sections 10.1-10.4

[] (may 29 -- memorial day holiday)
[] (may 31) Enumeration of all elliptic curves of given conductor 
            (Cremona's program):
             Sections 10.6-10.7
[] (june 2) Sturm's bound: Congruences between modular forms and gen. 
            Hecke algebras
             Chapter 11

4) Quick demo of multi-modular linear algebra implemented in SAGE
   (verbose).

sage: A = MatrixSpace(QQ, 5).random_element()
sage: set_verbose(2)
sage: A.echelon_form()
verbose 1 (4072: matrix.py, echelon_form) height_guess=64
verbose 1 (4072: matrix.py, echelon_form) p=20011
sage: A = MatrixSpace(QQ, 5,10).random_element()
sage: A.echelon_form()
verbose 1 (4072: matrix.py, echelon_form) height_guess=4096
verbose 1 (4072: matrix.py, echelon_form) p=20011
verbose 1 (4072: matrix.py, echelon_form) p=20021
verbose 1 (4072: matrix.py, echelon_form) start rr
verbose 1 (4072: matrix.py, echelon_form) done (time = 0.0)
 _5 = 
[     1      0      0      0      0 -17/12  13/24   -7/8    5/8   5/12]
[     0      1      0      0      0   -1/4    1/8   -9/8    3/8   -3/4]
[     0      0      1      0      0    7/6 -11/12    1/4   -7/4   -1/6]
[     0      0      0      1      0    7/9   -4/9   -1/3   -2/3   -1/9]
[     0      0      0      0      1  11/36  17/72  29/24   1/24   1/36]
sage: A = MatrixSpace(QQ, 50,100).random_element()
sage: E = A.echelon_form()
sage: A.echelon_form(height_guess=1)

Note -- time dominated by rational reconstruction; there is a trick...
sage: A = MatrixSpace(QQ, 40,30).random_element()
sage: K = A.kernel()
sage: K.dimension()
sage: K.basis()[0]

sage: A = MatrixSpace(QQ, 50).random_element()
sage: A.charpoly()
sage: A = ModularSymbols(389).T(2).matrix()
sage: A.parent()
sage: A.charpoly()

5) New chapter: modular symbols of higher weight.