
// Make newform 99.2.m.b in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_99_m();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_99_2_m_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_99_m();"
function MakeCharacter_99_m()
    N := 99;
    order := 15;
    char_gens := [56, 46];
    v := [5, 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_99_m_Hecke(Kf)
    return MakeCharacter_99_m();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_99_2_m_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_99_2_m_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_99_m();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![9150625, 52408125, 55614625, 231904750, 2236990075, 5717356100, 10276015885, 23541117060, 20956992101, -9404806289, 56794056873, 138906178653, 200502250666, 684048611446, 699016793241, 265524696543, 2023505496350, 2577779465638, 806449622388, 3122082312715, 106114949263, -7800174102356, 138990664100, 6980806209788, -1759571479187, -3800021940005, 125939385642, -141935090574, 1770504896229, 3112283399200, -335949900071, -2850669945390, -1378184732645, 630012441574, 1181021420257, 659884319097, -206251567270, -594192638268, -175373150822, 147351235374, 138430074305, 20397833220, -29788885082, -27299729607, -3740354569, 8550872393, 3531552152, -1105464304, -752017280, -122424610, 19375926, 99281839, 41893853, -28113973, -15995862, 3987900, 2597742, 140689, 60857, -201363, -97690, 47090, 18853, -5509, -1644, 80, -78, 112, 76, -19, -14, 1, 1]>],Snew);
    return Vf;
end function;