Slope Computations for small prime and weight

As explained in "Where the Slopes Are" (which is available in either pdf format or dvi format), the files contain, for primes less than 100, slope sequences for forms of weight k, level p, and trivial character. For each prime, I indicate below the largest weight computed.

The notes and slides from a seminar talk discussing these computations are also available in either dvi format or pdf format. The talk is more informal than the paper.

This paper has now appeared:

"Where the Slopes Are," Journal of the Ramanujan Mathematical Society, 16 (2001), 75--99.

The observations discussed in the paper and the talk include:

In every case the slope is less than (k-1)/2.
In almost all cases the slope is less than (k-1)/(p+1). The known exceptional cases are indicated by asterisks in the table. In this range, they occur only for p = 59 and p = 79. See note on exceptional slopes.
In almost all cases the slope is an integer. Again, the only exceptional cases in this range occur for p = 59 and p = 79. See note on exceptional slopes.

Here are the actual files:

p = 2; maximum weight 500.
p = 3; maximum weight 500.
p = 5; maximum weight 500.
p = 7; maximum weight 500.
p = 11; maximum weight 500.
p = 13; maximum weight 500.
p = 17; maximum weight 500.
p = 19; maximum weight 500.
p = 23; maximum weight 500.
p = 29; maximum weight 500.
p = 31; maximum weight 500.
p = 37; maximum weight 500.
p = 41; maximum weight 500.
p = 43; maximum weight 500.
p = 47; maximum weight 500.
p = 53; maximum weight 500.
p = 59; maximum weight 500, plus k=826, 886.
p = 61; maximum weight 500.
p = 67; maximum weight 500.
p = 71; maximum weight 500.
p = 73; maximum weight 500.
p = 79; maximum weight 500.
p = 83; maximum weight 500.
p = 89; maximum weight 500.
p = 97; maximum weight 500.

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Fernando Q. Gouvêa ---- fqgouvea@colby.edu

Last modified: Sat Aug 11 10:54:12 -0500 2001