OFFSET
1,1
COMMENTS
These primes are sometimes called SL_2(Z)-Buzzard-irregular.
LINKS
Kevin Buzzard, Questions about slopes of modular forms, Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), 15 pp. See also.
PROG
(Magma)
irregularprimesuptoN:=function(N);
testlist:=function(L);
if #L ge 2 then
return true;
elif (L[1] ne []) and L[1][1][1] gt 0 then
return true;
else
return false;
end if;
end function;
irregularlist:=function(p);
L:=[];
kp:=Integers()! ((p+3)/2);
exists(L[1]){[p] : k in [k : k in [2..kp]| IsEven(k)] | testlist([*ValuationsOfRoots(HeckePolynomial(CuspForms(Gamma0(1), k), p), p)*]) };
return L;
end function;
P:=[p : p in [4..N] | IsPrime(p)];
L:=[];
for p in P do
L:=L cat irregularlist(p);
end for;
return L;
end function;
CROSSREFS
KEYWORD
nonn
AUTHOR
Chris Birkbeck, Sep 13 2021
STATUS
approved