
// Make newform 9025.2.a.ct in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_9025_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_9025_2_a_ct();".
// 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_9025_a();"
function MakeCharacter_9025_a()
    N := 9025;
    order := 1;
    char_gens := [5777, 3251];
    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_9025_a_Hecke(Kf)
    return MakeCharacter_9025_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_9025_2_a_ct();".
// 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_9025_2_a_ct( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_9025_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![19, 0, -783, 0, 10782, 0, -57610, 0, 133557, 0, -166671, 0, 125215, 0, -59871, 0, 18618, 0, -3743, 0, 468, 0, -33, 0, 1]>,<3,R![1539, 0, -55809, 0, 379557, 0, -1053622, 0, 1521996, 0, -1288617, 0, 683568, 0, -236172, 0, 54009, 0, -8116, 0, 771, 0, -42, 0, 1]>,<7,R![5000211, 0, -262504152, 0, 949207302, 0, -1151590949, 0, 717036678, 0, -267704640, 0, 64379316, 0, -10303185, 0, 1105830, 0, -78431, 0, 3516, 0, -90, 0, 1]>,<11,R![18981, 31158, -43137, -52480, 19323, 20499, -4355, -3315, 570, 237, -39, -6, 1]>,<29,R![-263169, 567891, 757431, -286713, -425574, -13797, 65511, 9369, -3600, -756, 45, 18, 1]>],Snew);
    return Vf;
end function;