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).

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

Table of n, a(n) for n=1..52.

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

Adjacent sequences: A347801 A347802 A347803 * A347805 A347806 A347807

Keyword

nonn

Author

Chris Birkbeck, Sep 13 2021

Status

approved