##### https://github.com/koffie/mdmagma

Tip revision:

**f69d0e06f67b9ac6f57e7d8e6ba3b3d69e650352**authored by**Maarten Derickx**on**02 November 2020, 22:43:35 UTC****Quickly lists all non cuspidal places up to diamond operators on X_1(N)** Tip revision:

**f69d0e0**rank_0_of_X_1(m,mn).txt

```
derickx@babbage:~/mdmagma$ magma
Magma V2.21-11 Fri Aug 19 2016 16:23:09 on babbage [Seed = 2355933278]
+-------------------------------------------------------------------+
| This copy of Magma has been made available through a |
| generous initiative of the |
| |
| Simons Foundation |
| |
| covering U.S. Colleges, Universities, Nonprofit Research entities,|
| and their students, faculty, and staff |
+-------------------------------------------------------------------+
Type ? for help. Type <Ctrl>-D to quit.
> load "rank_zero_of_X1mn.m";
Loading "rank_zero_of_X1mn.m"
> ms := [2,3,4,6];
> for m in ms do;
for> for n in [1..37] do;
for|for> x :=PostiveRankNewFactors(m,n);
for|for> if #x gt 0 then;
for|for|if> print m,n;
for|for|if> print x;
for|for|if> break;
for|for|if> end if;
for|for> end for;
for> end for;
2 22
[
Modular symbols space for Gamma_0(88) of weight 2 and dimension 1 over
Cyclotomic Field of order 10 and degree 4
]
3 11
[
Modular symbols space for Gamma_0(99) of weight 2 and dimension 1 over
Cyclotomic Field of order 10 and degree 4,
Modular symbols space for Gamma_0(99) of weight 2 and dimension 1 over
Cyclotomic Field of order 10 and degree 4
]
4 7
[
Modular symbols space for Gamma_0(112) of weight 2 and dimension 1 over
Cyclotomic Field of order 6 and degree 2,
Modular symbols space for Gamma_0(56) of weight 2 and dimension 1 over
Cyclotomic Field of order 6 and degree 2
]
6 6
[
Modular symbols space for Gamma_0(216) of weight 2 and dimension 1 over
Cyclotomic Field of order 6 and degree 2,
Modular symbols space for Gamma_0(216) of weight 2 and dimension 1 over
Cyclotomic Field of order 6 and degree 2
]
> %P
load "rank_zero_of_X1mn.m";
ms := [2,3,4,6];
for m in ms do;
for n in [1..37] do;
x :=PostiveRankNewFactors(m,n);
if #x gt 0 then;
print m,n;
print x;
break;
end if;
end for;
end for;
```