added readme

README.txt

+Code to compute quinary orthogonal modular forms.
+
+Files:
+- quinary_module_l.sage: Sage file with the functions to compute the quinary omfs.
+- hypergeom.m: magma code to compute some hypergeometric motives.
+- genera_squarefree_2-2000.sobj: Sage sobj file, it is a dictionary with keys the squarefree numbers
+  in [2, 2000], for every D as before it has a list of quinary qf representative for every genus.
+
+Example:
+The following example shows how to compute de space of orthogonal modular forms
+in the case of trivial weight (d = 1), and non trivial weight (d = 167) for a lattice of
+discriminant 167.
+In the trivial weight case we choose a one dimensional Hecke eigenfunction and 
+compute some of the Tpk eigenvalues.
+We do the same for the non trivial weight case.
+
+sage: load('quinary_module_l.sage)
+sage: quins = load('genera_squarefree_2-2000.sobj')
+sage: qmod = quinary_module(quins[167][0])
+sage: qmod.decompose(d = 1)
+[Free module of degree 19 and rank 1 over Integer Ring
+ Echelon basis matrix:
+ [  1  10  60  20  30  30  60 120  30  20  30  10  60   5  20  10  30  30   5],
+ Free module of degree 19 and rank 1 over Integer Ring
+ Echelon basis matrix:
+ [ 0  0  1 -1 -1  1  0 -1  0 -1 -1  0  2  1 -1  0  0  1  0],
+ Free module of degree 19 and rank 2 over Integer Ring
+ Echelon basis matrix:
+ [ 0  0  1 -1  0 -1  0  0 -1  0  1  1  0  0  0  0  0  0  0]
+ [ 0  0  0  0  1  1  0 -2 -1  1 -1  1  1 -1 -2  0  0  2  0],
+ Free module of degree 19 and rank 15 over Integer Ring
+ Echelon basis matrix:
+ [ 1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1]
+ [ 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1]
+ [ 0  0  1  1  0  0  0  0  0  0  1  0  2  0  0  0  0  0 -5]
+ [ 0  0  0  2  0  0  0  0  0  0  0  1  6  0  0  0  0 -3 -6]
+ [ 0  0  0  0  1  0  0  0  0  0  0  0  2  0  0  0  0 -1 -2]
+ [ 0  0  0  0  0  1  0  0  0  0  1  0  0  0  0  0  0  0 -2]
+ [ 0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0 -1]
+ [ 0  0  0  0  0  0  0  2  0  0  0  0  0  0  1  0  0  2 -5]
+ [ 0  0  0  0  0  0  0  0  1  0  1  0  0  0  0  0  0  1 -3]
+ [ 0  0  0  0  0  0  0  0  0  1  0  0  3  0  1  0  0  0 -5]
+ [ 0  0  0  0  0  0  0  0  0  0  3 -1  0  0  0  0  0  3 -5]
+ [ 0  0  0  0  0  0  0  0  0  0  0  0 12 -1  0  0  0 -6 -5]
+ [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  3 -5]
+ [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0 -1]
+ [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0 -1]]
+sage: v = qmod.decompose()[1].0
+sage: for p in primes(14):
+....:     p, qmod.eigenvalue_tp_d(p, v, 1)
+....:     
+(2, -2)
+(3, 0)
+(5, -2)
+(7, 2)
+(11, -14)
+(13, -34)
+sage: for p in primes(6):
+....:     p, qmod.eigenvalue_tp2_d(p, v, 1)
+....:     
+(2, 2)
+(3, -17)
+(5, 16)
+sage: for p in primes(14):
+....:     p, qmod.eigenvalue_tp_d(p, v, 167)
+....:     
+(2, -8)
+(3, -10)
+(5, -4)
+(7, -14)
+(11, -22)
+(13, -4)
+sage: for p in primes(6):
+....:     p, qmod.eigenvalue_tp2_d(p, v, 167)
+....:     
+(2, 10)
+(3, 11)
+(5, -44)