
// Make newform 115.2.g.c in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_115_g();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_115_2_g_c();".
// 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_115_g();"
function MakeCharacter_115_g()
    N := 115;
    order := 11;
    char_gens := [47, 51];
    v := [11, 9];
    // 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_115_g_Hecke(Kf)
    return MakeCharacter_115_g();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_115_2_g_c();".
// 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_115_2_g_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_115_g();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![529, 85928, 4370449, -109239055, 550352032, -16163871, 11183657950, 15275378257, 35522299230, 29399782541, 58569363108, 44697286636, 71897780237, 33436233997, 53181336668, 8102114267, 26004989070, -15914833083, 8872359820, -12845544607, 8465681966, 1295560056, 6604070729, 1805242847, 2063795999, 111085, 327288896, 261824350, 275684456, 61654971, 28100233, 12096827, 12497589, 5062088, 1799080, 438389, 517741, 199581, 181775, 76133, 46911, 19471, 7749, 2684, 965, 399, 179, 66, 23, 5, 1]>],Snew);
    return Vf;
end function;