
// Make newform 925.2.o.d in Magma, downloaded from the LMFDB on 10 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_925_o();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_925_2_o_d();".
// 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_925_o();"
function MakeCharacter_925_o()
    N := 925;
    order := 6;
    char_gens := [852, 76];
    v := [3, 2];
    // 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_925_o_Hecke(Kf)
    return MakeCharacter_925_o();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_925_2_o_d();".
// 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_925_2_o_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_925_o();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![6561, 0, -215622, 0, 5018881, 0, -51230306, 0, 360019094, 0, -1548506356, 0, 4743883865, 0, -9681710274, 0, 14488778922, 0, -16488324024, 0, 14832271844, 0, -10735417537, 0, 6355291830, 0, -3097850866, 0, 1251462007, 0, -419175677, 0, 116564168, 0, -26802435, 0, 5080526, 0, -785338, 0, 97803, 0, -9531, 0, 700, 0, -35, 0, 1]>],Snew);
    return Vf;
end function;