
// Make newform 6034.2.a.r in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6034_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_r();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
// To make the character of type GrpDrchElt, type "MakeCharacter_6034_a();"
function MakeCharacter_6034_a()
    N := 6034;
    order := 1;
    char_gens := [1725, 869];
    v := [1, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_6034_a_Hecke(Kf)
    return MakeCharacter_6034_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_r();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_6034_2_a_r( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6034_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![21632, 218592, -372288, -6427184, 135688, 56108360, -3382836, -217799170, 48267444, 438145567, -148974663, -505238365, 211641649, 361049593, -173191775, -167782285, 90284416, 51783942, -31519940, -10534577, 7533280, 1336254, -1234337, -85102, 136027, -1213, -9610, 638, 392, -43, -7, 1]>,<5,R![639529984, 6106176512, 1264796624, -39696514368, -24141618640, 99506646668, 69450782787, -133378133551, -92715498295, 112118447446, 71280010953, -64905053233, -34668988621, 27206798942, 11101232317, -8417293845, -2336787124, 1918515848, 303488150, -317121113, -17934385, 36968472, -1018928, -2902985, 287851, 141011, -23833, -3427, 943, 6, -15, 1]>,<11,R![17135117778944, -110381404067840, 208827694061312, 7846591807456, -428440614772488, 313667381587080, 264759762033401, -355858024050527, -45784288677030, 184054964714428, -19476819477436, -55646995669212, 12630560459118, 10799638613957, -3334588626817, -1402635078150, 531931541004, 123139577228, -56442567405, -7125603622, 4121449591, 244915106, -208240442, -2760413, 7154782, -147301, -159480, 7412, 2078, -139, -12, 1]>],Snew);
    return Vf;
end function;