
// Make newform 225.4.p.b in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_225_p();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_225_4_p_b();".
// 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_225_p();"
function MakeCharacter_225_p()
    N := 225;
    order := 12;
    char_gens := [101, 127];
    v := [10, 3];
    // 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_225_p_Hecke(Kf)
    return MakeCharacter_225_p();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_225_4_p_b();".
// 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_225_4_p_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_225_p();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<2,R![47176160719802692796416, 592584924614165381775360, 3721762088331344923852800, 15583153813955329130496000, 2255145046613629415194624, -162739108005261724335734784, 351607374452646396202844160, -769969679382859314159943680, 306580273877388824770510848, 1225525231472600194757689344, 757501213155877671198916608, 798231106018881792833716224, -86869520924710133043183616, -416583082437363474909831168, -63268177118179173103024128, -163196453034304655239799808, 23131495476873014750375168, 68813509751829985986489600, -1205016644683495819072512, 26532146224100349080478528, -2778339764503403609665488, -8023446571889778508140672, 2927592904959436874864256, -2073440924549324546642352, 300758800361856541295281, 333348469576113172558680, -164988929874813772354272, 89387865686524137415248, -12323532296745117923813, -11106219524874055373484, 6097911868727499579552, -2554646535481939602606, 427195730946375758583, 118877780893198534956, -67314368436456957912, 26991670135278170700, -4553621852471298746, -916135500546678084, 475795871298356058, -193353800235683616, 34251857657622313, 4719872497076136, -2094633674204166, 862994348925936, -156772699475235, -17243570075736, 6758068167252, -2819055717558, 526001902985, 44182339536, -14981572206, 6177415296, -1162171294, -71788860, 25455636, -9945624, 1833411, 73356, -25614, 9540, -1721, -36, 18, -6, 1]>],Snew);
    return Vf;
end function;