[was@modular 04-07-02__cong_prime]$ [was@modular 04-07-02__cong_prime]$ Magma V2.8-10     Sun Apr  7 2002 01:08:16 on modular  [Seed = 1489733183]
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Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
> M := ModularSymbols(1,390,GF(389),+1);
> S := CS(M);
> f3 := HeckePolynomial(S,3);
> Discriminant(f3);
0
> S;
Modular symbols space of level 1, weight 390, and dimension 32
> factor(f3);
[
<x + 2, 1>,
<x + 78, 1>,
<x + 129, 1>,
<x + 184, 2>,
<x + 225, 1>,
<x + 231, 1>,
<x + 289, 1>,
<x^2 + 4*x + 2, 1>,
<x^2 + 76*x + 361, 1>,
<x^2 + 158*x + 64, 1>,
<x^2 + 340*x + 91, 1>,
<x^5 + 262*x^4 + 158*x^3 + 229*x^2 + 309*x + 243, 1>,
<x^11 + 172*x^10 + 287*x^9 + 36*x^8 + 226*x^7 + 24*x^6 + 92*x^5 + 212*x^4 + 213*x^3 + 311*x^2 + 72*x + 229, 1>
]
1
> time f5 := HeckePolynomial(S,5);
Time: 1.540
>  Discriminant(f5);
0
> time f7 := HeckePolynomial(S,7);
Time: 2.640
> f7;
x^32 + 2*x^31 + 262*x^30 + 105*x^29 + 84*x^28 + 29*x^27 + 189*x^26 + 309*x^25 + 94*x^24 + 235*x^23 + 179*x^22 + 185*x^21 + 241*x^20 + 104*x^19 + 123*x^18 + 219*x^17 + 20*x^16 + 329*x^15 + 229*x^14 + 54*x^13 + 346*x^12 + 103*x^11 + 36*x^10 + 180*x^9 + 385*x^8 + 338*x^7 + 41*x^6 + 348*x^5 + 349*x^4 + 142*x^3 + 169*x^2 + 13*x + 336
> factor(f7);
[
<x + 1, 3>,
<x + 5, 1>,
<x + 27, 1>,
<x + 183, 1>,
<x + 318, 1>,
<x + 328, 1>,
<x + 341, 2>,
<x^2 + 2*x + 382, 1>,
<x^2 + 61*x + 93, 1>,
<x^2 + 122*x + 35, 1>,
<x^5 + 46*x^4 + 15*x^3 + 14*x^2 + 156*x + 293, 1>,
<x^11 + 170*x^10 + 314*x^9 + 62*x^8 + 114*x^7 + 149*x^6 + 357*x^5 + 242*x^4 + 164*x^3 + 109*x^2 + 256*x + 58, 1>
]
1
> time f2 := HeckePolynomial(S,2);
Time: 0.410
> factor(f2);
[
<x + 2, 1>,
<x + 56, 1>,
<x + 135, 1>,
<x + 158, 1>,
<x + 175, 2>,
<x + 315, 1>,
<x + 342, 1>,
<x^2 + 387, 1>,
<x^2 + 97*x + 164, 1>,
<x^2 + 231*x + 64, 1>,
<x^2 + 286*x + 63, 1>,
<x^5 + 88*x^4 + 196*x^3 + 113*x^2 + 168*x + 349, 1>,
<x^11 + 276*x^10 + 182*x^9 + 13*x^8 + 298*x^7 + 316*x^6 + 213*x^5 + 248*x^4 + 108*x^3 + 283*x^2 + x + 101, 1>
]
1
>