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
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:
Here are the actual files:
- 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.
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Last modified: Sat Aug 11 10:54:12 -0500 2001