Sharedwww / merel-stein / lchizero.mOpen in CoCalc
Author: William A. Stein
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///////////////////////////////////////////////////////////
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// lchizero.m - MAGMA program //
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// //
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// Date: August, 1999 //
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// //
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// Author: William A. Stein (was@math.berkeley.edu) //
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///////////////////////////////////////////////////////////
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/*************************************************************
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* lchinz[p,i] = [divisors d of p-1 such that
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* L(A_{f_i},chi_d,1)=0, where
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* chi_d:(Z/pZ)^*-->C^* is one of the
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* conjugate characters of degree d.
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*
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* The computation was done using modular symbols.
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* We consider L(A_f,chi_d,1)=/=0 if the value
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* of a vector dual to f on the modular symbol
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* s = sum_{a in (Z/pZ)^*} chi_d(a) {0,-1/a}
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* is 0.
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*
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* This computation was done using the C++ program HECKE.
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*
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* The eigenforms in all tables are ordered in the same
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* way, which extends the ordering used by Cremona in his
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* tables of elliptic curves.
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* We sort the factors of $S_2(p)$ as follows.
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* First by dimension, with smallest dimension first.
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* Within each dimension, sort in binary order,
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* by the sign of the Atkin-Lehner involution
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* with - corresponding to 0 and + to 1.
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* Let $l$ be the smallest prime not equal to $p$.
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* Within each of the Atkin-Lehner classes, sort by
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* the magnitudes of the $K(f)/\Q$-trace of
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* $a_l$ breaking ties by letting the positive trace be first.
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* If there are still any ties, repeat the final step with the
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* next smallest prime not equal to $p$, etc.
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*************************************************************/
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LChiZero := [[] : i in [1..997]];
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LChiZero[11] := [[]];
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LChiZero[13] := [];
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LChiZero[17] := [[2]];
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LChiZero[19] := [[]];
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LChiZero[23] := [[]];
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LChiZero[29] := [[2]];
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LChiZero[31] := [[]];
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LChiZero[37] := [[1, 2, 6],[2]];
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LChiZero[41] := [[2]];
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LChiZero[43] := [[1],[]];
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LChiZero[47] := [[]];
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LChiZero[53] := [[1, 2],[2]];
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LChiZero[59] := [[]];
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LChiZero[61] := [[1, 2],[2]];
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LChiZero[67] := [[],[1],[]];
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LChiZero[71] := [[],[]];
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LChiZero[73] := [[2, 3, 6],[1, 2],[2]];
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LChiZero[79] := [[1],[]];
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LChiZero[83] := [[1],[]];
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LChiZero[89] := [[1, 2],[2],[2]];
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LChiZero[97] := [[1, 2],[2]];
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LChiZero[101] := [[1, 2, 4],[2]];
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LChiZero[103] := [[1],[]];
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LChiZero[107] := [[1],[]];
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LChiZero[109] := [[2],[1, 2],[2]];
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LChiZero[113] := [[2],[2],[1, 2],[2]];
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LChiZero[127] := [[1],[]];
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LChiZero[131] := [[1, 2],[]];
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LChiZero[137] := [[1, 2],[2]];
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LChiZero[139] := [[3],[1],[]];
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LChiZero[149] := [[1, 2],[2]];
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LChiZero[151] := [[1],[],[]];
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LChiZero[157] := [[1, 2],[2]];
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LChiZero[163] := [[1],[1],[]];
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LChiZero[167] := [[1],[]];
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LChiZero[173] := [[1, 2],[2]];
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LChiZero[179] := [[],[1],[]];
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LChiZero[181] := [[1, 2],[2]];
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LChiZero[191] := [[1],[]];
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LChiZero[193] := [[1, 2],[1, 2],[2]];
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LChiZero[197] := [[1, 2],[1, 2],[2]];
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LChiZero[199] := [[],[1],[]];
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LChiZero[211] := [[],[1],[1],[]];
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LChiZero[223] := [[1],[1],[]];
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LChiZero[227] := [[1],[],[],[1],[]];
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LChiZero[229] := [[1, 2, 3],[1, 2],[2]];
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LChiZero[233] := [[2],[1, 2],[2]];
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LChiZero[239] := [[1],[]];
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LChiZero[241] := [[1, 2],[2]];
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LChiZero[251] := [[1],[]];
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LChiZero[257] := [[1, 2],[2]];
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LChiZero[263] := [[1],[]];
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LChiZero[269] := [[1, 2],[1, 2],[2]];
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LChiZero[271] := [[1],[]];
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LChiZero[277] := [[1, 2],[2],[1, 2],[2]];
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LChiZero[281] := [[1, 2],[2]];
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LChiZero[283] := [[1],[]];
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LChiZero[293] := [[1, 2],[2]];
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LChiZero[307] := [[],[3],[],[],[],[],[1]];
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LChiZero[311] := [[1],[]];
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LChiZero[313] := [[2],[1, 2],[2]];
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LChiZero[317] := [[1, 2],[2]];
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LChiZero[331] := [[1],[1],[1],[]];
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LChiZero[337] := [[1, 2],[2]];
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LChiZero[347] := [[1],[1],[1],[]];
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LChiZero[349] := [[1, 2],[2]];
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LChiZero[353] := [[2, 4],[2],[1, 2],[2]];
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LChiZero[359] := [[1],[1, 2],[1],[]];
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LChiZero[367] := [[1],[]];
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LChiZero[373] := [[1, 2, 6],[1, 2],[2]];
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LChiZero[379] := [[1],[]];
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LChiZero[383] := [[1],[1],[]];
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LChiZero[389] := [[1, 2, 4],[1, 2],[1, 2],[1, 2],[2]];
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LChiZero[397] := [[1, 2],[2],[2],[2],[1, 2]];
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LChiZero[401] := [[1, 2],[2]];
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LChiZero[409] := [[1, 2],[2]];
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LChiZero[419] := [[1],[]];
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LChiZero[421] := [[1, 2],[2]];
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LChiZero[431] := [[1],[],[1],[],[1],[]];
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LChiZero[433] := [[1, 2],[2],[1, 2],[2]];
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LChiZero[439] := [[1],[1],[]];
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LChiZero[443] := [[1],[1],[2],[1],[]];
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LChiZero[449] := [[1, 2],[2]];
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LChiZero[457] := [[1, 2],[1, 2],[2]];
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LChiZero[461] := [[1, 2],[1, 2],[1, 2],[2]];
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LChiZero[463] := [[1],[]];
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LChiZero[467] := [[1, 2],[1],[]];
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LChiZero[479] := [[1],[]];
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LChiZero[487] := [[],[],[],[],[1]];
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LChiZero[491] := [[1],[1],[]];
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LChiZero[499] := [[1],[1],[]];
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LChiZero[503] := [[1],[],[],[],[1],[]];
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LChiZero[509] := [[1, 2],[2]];
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LChiZero[521] := [[1, 2],[2]];
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LChiZero[523] := [[1],[1],[]];
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LChiZero[541] := [[1, 2],[2]];
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LChiZero[547] := [[1],[1],[]];
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LChiZero[557] := [[1, 2],[2],[1, 2],[2]];
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LChiZero[563] := [[1],[1],[1],[1],[]];
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LChiZero[569] := [[1, 2],[2]];
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LChiZero[571] := [[],[1],[],[],[1],[],[1],[1],[]];
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LChiZero[577] := [[2],[2],[2],[2],[1, 2]];
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LChiZero[587] := [[1],[1],[]];
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LChiZero[593] := [[1, 2],[2, 8],[2],[1, 2],[2]];
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LChiZero[599] := [[1],[1],[]];
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LChiZero[601] := [[1, 2],[2]];
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LChiZero[607] := [[1],[1],[1],[]];
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LChiZero[613] := [[1, 2],[1, 2],[2]];
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LChiZero[617] := [[1, 2],[2]];
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LChiZero[619] := [[1],[]];
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LChiZero[631] := [[1],[]];
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LChiZero[641] := [[1, 2],[2]];
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LChiZero[643] := [[1, 3],[1],[]];
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LChiZero[647] := [[1],[1],[]];
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LChiZero[653] := [[1, 2],[1, 2],[2]];
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LChiZero[659] := [[1],[],[1],[]];
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LChiZero[661] := [[2],[1, 2],[2]];
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LChiZero[673] := [[2],[2],[2],[1, 2]];
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LChiZero[677] := [[1, 2],[1, 2],[1, 2],[2]];
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LChiZero[683] := [[],[1],[]];
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LChiZero[691] := [[1],[]];
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LChiZero[701] := [[2],[1, 2],[2]];
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LChiZero[709] := [[1, 2],[1, 2],[2]];
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LChiZero[719] := [[1],[1],[]];
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LChiZero[727] := [[1],[]];
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LChiZero[733] := [[2],[1, 2],[1, 2],[2]];
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LChiZero[739] := [[],[1],[1],[]];
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LChiZero[743] := [[1],[]];
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LChiZero[751] := [[1],[]];
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LChiZero[757] := [[1, 2],[2]];
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LChiZero[761] := [[1, 2],[1, 2],[2]];
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LChiZero[769] := [[1, 2],[2]];
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LChiZero[773] := [[1, 2],[1, 2],[2]];
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LChiZero[787] := [[1],[]];
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LChiZero[797] := [[1, 2],[2],[1, 2],[2]];
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LChiZero[809] := [[1, 2],[1, 2],[2]];
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LChiZero[811] := [[1],[1],[]];
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LChiZero[821] := [[1, 2],[2]];
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LChiZero[823] := [[1],[]];
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LChiZero[827] := [[1],[1],[1],[]];
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LChiZero[829] := [[1, 2],[1, 2],[2]];
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LChiZero[839] := [[1],[]];
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LChiZero[853] := [[1, 2],[2]];
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LChiZero[857] := [[1, 2],[2]];
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LChiZero[859] := [[1],[]];
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LChiZero[863] := [[1],[1],[]];
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LChiZero[877] := [[1, 2],[1, 2],[2]];
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LChiZero[881] := [[1, 2],[2]];
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LChiZero[883] := [[1],[]];
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LChiZero[887] := [[1],[1],[]];
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LChiZero[907] := [[1],[]];
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LChiZero[911] := [[1],[1],[]];
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LChiZero[919] := [[1],[1],[]];
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LChiZero[929] := [[1, 2],[1, 2],[2]];
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LChiZero[937] := [[1, 2],[2]];
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LChiZero[941] := [[1, 2],[2]];
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LChiZero[947] := [[1],[]];
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LChiZero[953] := [[1, 2],[2]];
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LChiZero[967] := [[1],[]];
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LChiZero[971] := [[1],[]];
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LChiZero[977] := [[1, 2],[2]];
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LChiZero[983] := [[1],[]];
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LChiZero[991] := [[1],[]];
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LChiZero[997] := [[1, 2],[1, 2],[1, 2],[1, 2],[1, 2],[1, 2],[1, 2],[2]];
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