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%I #39 Sep 08 2022 08:46:26
%S 59,79,107,131,139,151,173,193,223,229,257,263,269,277,283,307,313,
%T 331,353,379,419,463,479,491,499,577,599,601,647,653,701,719,761,769,
%U 811,839,853,883,907,1049,1051,1061,1063,1069,1087,1117,1123,1129,1181,1187,1229,1231
%N Primes for which there exists a level 1 modular form of weight less than or equal to (p+3)/2 which is not ordinary (meaning the p-adic valuation of its a_p eigenvalue is not zero).
%C These primes are sometimes called SL_2(Z)-Buzzard-irregular.
%H Kevin Buzzard, <a href="http://www.numdam.org/item/AST_2005__298__1_0/">Questions about slopes of modular forms</a>, Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), 15 pp. See <a href="https://www.ma.imperial.ac.uk/~buzzard/maths/research/papers/conjs.pdf">also</a>.
%o (Magma)
%o irregularprimesuptoN:=function(N);
%o testlist:=function(L);
%o if #L ge 2 then
%o return true;
%o elif (L[1] ne []) and L[1][1][1] gt 0 then
%o return true;
%o else
%o return false;
%o end if;
%o end function;
%o irregularlist:=function(p);
%o L:=[];
%o kp:=Integers()! ((p+3)/2);
%o exists(L[1]){[p] : k in [k : k in [2..kp]| IsEven(k)] | testlist([*ValuationsOfRoots(HeckePolynomial(CuspForms(Gamma0(1),k),p),p)*]) };
%o return L;
%o end function;
%o P:=[p : p in [4..N] | IsPrime(p)];
%o L:=[];
%o for p in P do
%o L:=L cat irregularlist(p);
%o end for;
%o return L;
%o end function;
%Y Cf. A000040.
%K nonn
%O 1,1
%A _Chris Birkbeck_, Sep 13 2021
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