
// Make newform 6897.2.a.bq in Magma, downloaded from the LMFDB on 14 December 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_6897_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6897_2_a_bq();".
// 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_6897_a();"
function MakeCharacter_6897_a()
    N := 6897;
    order := 1;
    char_gens := [2300, 970, 3631];
    v := [1, 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_6897_a_Hecke( : Kf := Kf)
    return MakeCharacter_6897_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6897_2_a_bq();".
// 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_6897_2_a_bq( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6897_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-880, 14760, -42064, -108736, 353633, 429960, -958690, -814322, 1355868, 833567, -1154228, -504274, 625319, 191153, -221698, -46761, 51941, 7391, -7958, -730, 766, 41, -42, -1, 1]>,<5,R![-5403584, -8939328, 49165416, 53128212, -182124249, -95819674, 326019701, 43770771, -287360757, 22395999, 135343491, -27672739, -36207442, 10764035, 5595708, -2179098, -476412, 253054, 17183, -16940, 324, 607, -45, -9, 1]>,<7,R![-312840000, 3341988000, -579689600, -8671928380, 2678100311, 9241182176, -3206314577, -5357339442, 1926273956, 1887129897, -682424190, -425684489, 152754994, 62920843, -22282546, -6112812, 2133438, 383927, -132148, -14912, 5070, 324, -109, -3, 1]>,<13,R![747556864, 6048634880, 10192720896, -23529582080, -80354010368, -39387611392, 79773632256, 84894732064, -10969092912, -42574858568, -9832406172, 7065040124, 2826700057, -505274444, -319644765, 14326285, 19586282, 116999, -713355, -17309, 15581, 394, -190, -3, 1]>],Snew);
    return Vf;
end function;