This dataset contains normalized complex Hecke eigenvalues $a_n/n^{(k-1)/2}$ and Satake angles $\theta_p$ for embedded newforms.
There are currently 14,417,694 embedded newforms (arising from 281,965 newforms), with odd weight ranging from $1$ to $181$ and even weight ranging from $2$ to $316$. The stored levels vary by weight, and for each newform we store either 2000, 4000, or 6000 Hecke eigenvalues (and corresponding Satake angles). The main difference between this dataset and the internal mf_hecke_cc table within the LMFDB is that this dataset stores more eigenvalues (the internal table only has $n$ up to 100).
File and data format
Each text file starts with a header line follwed by a blank line; the remainder of the file contains one line per embedded newform, and each line has the following format.| label | The label of the embedded newform. |
| dual_label | The label for the dual |
| embedding_root | A pair [a,b] giving the image $a + bi$ of the generator for the coefficient field under this embedding. If unknown (which will occur when the degree of the coefficient field is larger than $20$), the string None is recorded instead. |
| an_normalized | A list of pairs [cn, dn] so that the Hecke eigenvalue $a_n = n^{(k-1)/2} (c_n + d_n i)$. Here $k$ is the weight and the list starts at $n=1$. |
| angles | The list of Satake angles $\theta_p$ for good primes $p$. For $p$ dividing the level, the string NULL is recorded instead. |
Download
Specify both a weight $k$ and a level $N$ to download the file containing data for the embedded newforms in $S_k^{\mathrm{new}}(\Gamma_1(N)),$ or provide one to get a page showing the available options for the other. Alternatively, you may give the full label to get just the data for one embedded modular form.