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A347804
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).
0
59, 79, 107, 131, 139, 151, 173, 193, 223, 229, 257, 263, 269, 277, 283, 307, 313, 331, 353, 379, 419, 463, 479, 491, 499, 577, 599, 601, 647, 653, 701, 719, 761, 769, 811, 839, 853, 883, 907, 1049, 1051, 1061, 1063, 1069, 1087, 1117, 1123, 1129, 1181, 1187, 1229, 1231
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
Cf. A000040.
Sequence in context: A212266 A322919 A026050 * A304356 A283146 A068209
KEYWORD
nonn
AUTHOR
Chris Birkbeck, Sep 13 2021
STATUS
approved