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Results tagged with computational-number-theory
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user 2481
Computational Number Theory is for explicit calculations or algorithms involving anything of interest to number theorists.
21
votes
What computer program for automorphic forms
The only CAS's that have built-in support for modular and automorphic forms, as far as I know, are Sage and Magma. [Edit: I had forgotten Pari/GP, which will introduce substantial modular forms functi …
- 37k
16
votes
Accepted
Computing an eigencuspform in $S_2(\Gamma_0(1776))$
I did the computation in Sage, and there is no such form $f$. There are 21 Galois orbits of newforms of level $\Gamma_0(1776)$ and trivial character, of which the largest has size 3, and none of the r …
- 37k
10
votes
Computing millions of coefficients of non self-dual modular forms
One shortcut you could use for computing the level 17 form you link to would be the following. There are exactly 8 Eisenstein series of weight 1 for $\Gamma_1(17)$ and they are all given by completely …
- 37k
8
votes
Coefficient field of a newform using Magma
Here is code in Sage which does what you're asking for:
sage: t = cputime()
....: f = Newforms(123, names='a')[3]
....: print(f.hecke_eigenvalue_field())
....: E = EllipticCurve('389a')
....: for p i …
- 37k
5
votes
Numerical evaluation of the Petersson product of elliptic modular forms
It's easy to reduce to the case of computing the Petersson product of a normalised new eigenform with itself. Here you can use the fact that the product is equal to the value at s=k of the symmetric s …