def CremonaModularSymbols(level, sign=0, cuspidal=False, verbose=0):
"""
Return the space of Cremona modular symbols with given level, sign, etc.
INPUT:
- ``level`` -- an integer >= 2 (at least 2, not just positive!)
- ``sign`` -- an integer either 0 (the default) or 1 or -1.
- ``cuspidal`` -- (default: False); if True, compute only the cuspidal subspace
- ``verbose`` -- (default: False): if True, print verbose information while creating space
EXAMPLES::
sage: M = CremonaModularSymbols(43); M
Cremona Modular Symbols space of dimension 7 for Gamma_0(43) of weight 2 with sign 0
sage: M = CremonaModularSymbols(43, sign=1); M
Cremona Modular Symbols space of dimension 4 for Gamma_0(43) of weight 2 with sign 1
sage: M = CremonaModularSymbols(43, cuspidal=True); M
Cremona Cuspidal Modular Symbols space of dimension 6 for Gamma_0(43) of weight 2 with sign 0
sage: M = CremonaModularSymbols(43, cuspidal=True, sign=1); M
Cremona Cuspidal Modular Symbols space of dimension 3 for Gamma_0(43) of weight 2 with sign 1
When run interactively, the following command will display verbose output::
sage: M = CremonaModularSymbols(43, verbose=1); M # not tested, since verbose output goes to stderr.
After 2-term relations, ngens = 22
predicted value of ngens = 22
ngens = 22
maxnumrel = 22
relation matrix has = 484 entries...
Finished 3-term relations: numrel = 17 ( maxnumrel = 22)
predicted value of ntriangles = 16 --WRONG!
Computing kernel...
rk = 7
About to compute cusps
ncusps = 2
About to compute matrix of delta
delta matrix done: size 2x7.
About to compute kernel of delta
done
Finished constructing homspace.
Cremona Modular Symbols space of dimension 7 for Gamma_0(43) of weight 2 with sign 0
The input must be valid or a ValueError is raised::
sage: M = CremonaModularSymbols(-1)
Traceback (most recent call last):
...
ValueError: the level (= -1) must be at least 2
sage: M = CremonaModularSymbols(0)
Traceback (most recent call last):
...
ValueError: the level (= 0) must be at least 2
The sign can only be 0 or 1 or -1::
sage: M = CremonaModularSymbols(10, sign = -2)
Traceback (most recent call last):
...
ValueError: sign (= -2) is not supported; use 0, +1 or -1
We do allow -1 as a sign (see #9476)::
sage: CremonaModularSymbols(10, sign = -1)
Cremona Modular Symbols space of dimension 0 for Gamma_0(10) of weight 2 with sign -1
"""
from homspace import ModularSymbols
return ModularSymbols(level=level, sign=sign, cuspidal=cuspidal, verbose=verbose)
