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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.
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
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 …
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
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
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