
// Make newform 6025.2.a.q in Magma, downloaded from the LMFDB on 19 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_q();".
// 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_q();".
// 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_q( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6025_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-1841449, 0, 253747673, 0, -11048999599, 0, 246600093167, 0, -3347928632631, 0, 30102827385462, 0, -188619534316924, 0, 853420033729989, 0, -2869118751033410, 0, 7348305618226927, 0, -14657139407177186, 0, 23207180266409698, 0, -29643685863938922, 0, 30962239017889419, 0, -26738120901916055, 0, 19262822001973205, 0, -11659801004464039, 0, 5962518254403338, 0, -2586334768112999, 0, 954149188357074, 0, -299791605458853, 0, 80227735479551, 0, -18262935623253, 0, 3526528911581, 0, -575036837699, 0, 78658767871, 0, -8942833038, 0, 834250271, 0, -62721100, 0, 3703934, 0, -165314, 0, 5239, 0, -105, 0, 1]>,<3,R![-262144, 0, 427458560, 0, -205383271424, 0, 25065997794048, 0, -694711423478400, 0, 8946772746282784, 0, -66896479216104868, 0, 324172362551821723, 0, -1088648472382646107, 0, 2652688601395438532, 0, -4851750003869321520, 0, 6837974115572824246, 0, -7583350541906939117, 0, 6730631661084317217, 0, -4847349419559818779, 0, 2864728646698489331, 0, -1401937186470610276, 0, 572213681375369233, 0, -195867996919823148, 0, 56450378559249545, 0, -13732700879671325, 0, 2822873756638367, 0, -490103514744246, 0, 71723508271990, 0, -8813266070021, 0, 903840699455, 0, -76685465974, 0, 5316206015, 0, -295883613, 0, 12889773, 0, -423019, 0, 9828, 0, -144, 0, 1]>],Snew);
    return Vf;
end function;