
// Make newform 805.2.u.d in Magma, downloaded from the LMFDB on 07 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_805_u();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_805_2_u_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_805_u();"
function MakeCharacter_805_u()
    N := 805;
    order := 11;
    char_gens := [162, 346, 281];
    v := [11, 11, 7];
    // 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_805_u_Hecke(Kf)
    return MakeCharacter_805_u();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_805_2_u_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_805_2_u_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_805_u();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![279841, 1533042, 2453180897, 65293996752, 3091757584941, 23472767325240, 550595335836313, 8412487225191749, 59150234364955334, 227560446492346880, 608877254246882622, 1150507610946286204, -1367041019592600128, -59814872870636992081, 176923010415686379232, -88928776665201502631, 417572336410133721655, -4239188294170528351631, 11918953754846889854061, -13715472529378746397685, 24376869364150376487588, -102529652505168838225987, 298702163137890235771528, -552264091050439499382895, 843371263154140861009181, -1648633959768413198358598, 3552360114198695285020631, -5854218805949301104070338, 8011531420291314111989313, -9647217248209206448976383, 12647905985896844540557173, -16963305128205778345186994, 19110407478883448504895866, -7273861083058470688578936, 3508264153346459596796205, -9850248075967140856120030, 14993367391292637047023251, 5602399081902913451884405, 19348915680575786376516895, -57360104653646653072629576, 102169030538861433413622870, -64618372265083679032600519, 42466076051344801198380570, 2048992491671618593701563, 30305033860080619784621782, -22126235336919896501902201, 59922819273180200092561014, -28477050562696398919107578, 42347103583136667090736767, -3590593271882694790440319, 20543368686832262296169995, 1354944930407670577914337, 19550332626221831523344335, -5314569044321606097710301, 20183637121762589265587215, -5483899167479573179366531, 14146034189737030252275511, -2195327399544156853772761, 8127194127132155007622112, -172382266212923621521590, 4899175001606142512689724, 595022288522828557386894, 2968941674992947211901304, 809272177370571698860819, 1637094448479396952797564, 654184437333106763717904, 818697373232795166091914, 382706116957407197399420, 374374339355759035086201, 178525866457925139709226, 154852822147388037682306, 70994783429891185662634, 57227287069273633731101, 24837112968455454468606, 18975243193490968444158, 7708813225899289096373, 5674790817658260467948, 2123787916670182298748, 1531903850459532068655, 522550888760044277750, 375685865146743052812, 115961618246133056178, 84749654092195073116, 23999110459668654644, 18017272548234984210, 4823626575755917224, 3742054793352434638, 956849335738751256, 783714505829178793, 184911229566900435, 162746217944080161, 33999082590474148, 32298275131584312, 5942049692005955, 6083310505102776, 972995870516105, 1100547920037089, 150436604214479, 192087185417871, 22824137124445, 32997877997178, 3148236981869, 5529686032261, 407009230516, 892803815209, 50242161657, 147130826392, 3701963298, 24237657471, -12865603, 3631144886, -59397176, 508913484, -14174633, 68040131, -1866247, 9045356, -488969, 1275845, -126860, 176730, -20565, 21395, -2080, 2292, -213, 253, -29, 23, -2, 1]>],Snew);
    return Vf;
end function;