| All data as a single tar gzipped file [103MB] |
DESCRIPTION: This is arithmetic data about (at least) 76582 newforms f of weight 2 on Gamma 0(N) attached to a newform of level N, for a large number of N. The point of this table is to give you a quick view of what level N "looks like" for many N. For each newform f, we list the following data:
| Level | The level N of the newform f. |
|---|---|
| Galois Conjugacy Class | We order the isogeny classes in lexicographic order by the trace q-expansion of any representative newform. This entry is a number between 1 and the number of isogeny classes. |
| Degree | The degree of the field generated by the Fourier coefficients of the newform f. |
| Atkin-Lehner Eigenvalues | The eigenvalues of the Atkin-Lehner involutions Wq on f, ordered by prime divisor of the level (where q is a power of the ith prime that divides the level). |
| Refined Parity of Order of Vanishing at s=1 | An integer that is congruent modulo 2 to the order of vanishing of L(f,s) at s=1. If this integer is 0, then L(f,1) is definitely (provably) nonzero. If this integer is 1, then L(f,s) vanishes to odd order at s=1. If this integer is 2, then L(f,s) vanishes to even order at s=1, and L(f,1) is definitely (provably) zero. |
| Characteristic Polynomials | The characteristic polynomials of the coefficients a2, a3, ..., a19 of the newform f. These are helpful in determining whether two newforms are congruent, and deciding what field f is defined over. |
The reason I created this table was to make a table of data about probable congruences, modular degrees, probable visibility, etc., for abelian varieties attached to newforms. However, you might find this data useful for many other purposes.
How to use in MAGMA: The data files are MAGMA-readable. You must initialize an empty array called "data" before reading them in.
> data := []
> load "389"; // etc. for any other levels you want.
> data[389];
... data about level 389 ...