
// Make newform 6025.2.a.k in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6025_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6025_2_a_k();".
// 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_6025_a();"
function MakeCharacter_6025_a()
    N := 6025;
    order := 1;
    char_gens := [2652, 2176];
    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_6025_a_Hecke(Kf)
    return MakeCharacter_6025_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6025_2_a_k();".
// 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_6025_2_a_k( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6025_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-2031, -6975, 44432, 88382, -345133, -343234, 1134175, 585214, -1947527, -484928, 1954583, 170313, -1224320, 21791, 496308, -44543, -131976, 18654, 22815, -4099, -2465, 515, 151, -35, -4, 1]>,<3,R![-688, -5816, 127549, 225683, -1298053, -1857649, 4139978, 5926968, -5548432, -9029002, 3128561, 7203316, -391888, -3255137, -364634, 870086, 196424, -137037, -44773, 11683, 5451, -356, -346, -15, 9, 1]>],Snew);
    return Vf;
end function;