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All Siegel modular form data currently in the database has been computed using rigorous algorithms that do not depend on any unproved assumptions or conjectures.

In addition to using mathematically rigorous algorithms whenever possible, we have performed a variety of consistency checks intended to catch any errors in the software packages used to compute modular forms data, or any errors that might have been introduced during post-processing. The following checks have been performed:

  • All newforms of weight $(k,j) = (3,0)$ and level $N$ for which there exists a prime $p$ with $p \parallel N$ have been independently computed using two different code packages. One package using [Pari/GP] and another independent package written in C. By comparing the results of these computations we have verified that the decompositions of each newspace $S_{3,0}^{\rm new}(K(N))$ into Galois orbits agree (with matching coefficient fields), that the first 100 coefficients of the trace forms for each Galois orbit agree, and for newforms of dimension $d \le 13$, that there is an automorphism of the coefficient field that relates the sequences of algebraic eigenvalues $(a_1,\ldots,a_{100})$ computed by both packages.

For all newforms of weight $(k,j) = (3,0), (3,2), (4,0)$ and squarefree level $N$ we have verified that the dimensions agree with known dimension formulas [MR:3638279] [arXiv:2208.13578].

Knowl status:
  • Review status: beta
  • Last edited by Shiva Chidambaram on 2023-11-16 15:25:35
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Not referenced anywhere at the moment.

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