def set_info_for_navigation(info, is_set, sbar):
r"""
Set information for the navigation page.
"""
(friends, lifts) = sbar
## We always print the list of weights
info['initial_list_of_weights'] = print_list_of_weights()
# ajax_more2(print_list_of_weights,{'kstart':[0,10,25,50],'klen':[15,15,15]},text=['<<','>>'])
## And the list of characters if we know the level.
if(is_set['level']):
s = "<option value=" + str(0) + ">Trivial character</option>"
D = DirichletGroup(info['level'])
if(is_set['weight'] and is_even(info['weight'])):
if(is_fundamental_discriminant(info['level'])):
x = kronecker_character(info['level'])
xi = D.list().index(x)
s = s + "<option value=" + str(xi) + ">Kronecker character</option>"
for x in D:
if(is_set['weight'] and is_even(info['weight']) and x.is_odd()):
continue
if(is_set['weight'] and is_odd(info['weight']) and x.is_even()):
continue
xi = D.list().index(x)
# s=s+"<option value="+str(xi)+">\(\chi_{"+str(xi)+"}\)</option>"
s = s + "<option value=" + str(xi) + ">" + str(xi) + "</option>"
info['list_of_characters'] = s
friends.append(('L-function', '/Lfunction/ModularForm/GL2/Q/holomorphic/'))
lifts.append(('Half-Integral Weight Forms', '/ModularForm/Mp2/Q'))
lifts.append(('Siegel Modular Forms', '/ModularForm/GSp4/Q'))
return (info, lifts)
def set_info_for_navigation(info, is_set, sbar):
r"""
Set information for the navigation page.
"""
(friends, lifts) = sbar
## We always print the list of weights
info['initial_list_of_weights'] = print_list_of_weights()
# ajax_more2(print_list_of_weights,{'kstart':[0,10,25,50],'klen':[15,15,15]},text=['<<','>>'])
## And the list of characters if we know the level.
if (is_set['level']):
s = "<option value=" + str(0) + ">Trivial character</option>"
D = DirichletGroup(info['level'])
if (is_set['weight'] and is_even(info['weight'])):
if (is_fundamental_discriminant(info['level'])):
x = kronecker_character(info['level'])
xi = D.list().index(x)
s = s + "<option value=" + str(
xi) + ">Kronecker character</option>"
for x in D:
if (is_set['weight'] and is_even(info['weight']) and x.is_odd()):
continue
if (is_set['weight'] and is_odd(info['weight']) and x.is_even()):
continue
xi = D.list().index(x)
# s=s+"<option value="+str(xi)+">\(\chi_{"+str(xi)+"}\)</option>"
s = s + "<option value=" + str(xi) + ">" + str(xi) + "</option>"
info['list_of_characters'] = s
friends.append(('L-function', '/Lfunction/ModularForm/GL2/Q/holomorphic/'))
lifts.append(('Half-Integral Weight Forms', '/ModularForm/Mp2/Q'))
lifts.append(('Siegel Modular Forms', '/ModularForm/GSp4/Q'))
return (info, lifts)
def print_list_of_characters(level=1, weight=2):
r"""
Prints a list of characters compatible with the weight and level.
"""
emf_logger.debug("print_list_of_chars")
D = DirichletGroup(level)
res = list()
for j in range(len(D.list())):
if D.list()[j].is_even() and is_even(weight):
res.append(j)
if D.list()[j].is_odd() and is_odd(weight):
res.append(j)
s = ""
for j in res:
s += "\(\chi_{" + str(j) + "}\)"
return s
def print_list_of_characters(level=1, weight=2):
r"""
Prints a list of characters compatible with the weight and level.
"""
emf_logger.debug("print_list_of_chars")
D = DirichletGroup(level)
res = list()
for j in range(len(D.list())):
if D.list()[j].is_even() and is_even(weight):
res.append(j)
if D.list()[j].is_odd() and is_odd(weight):
res.append(j)
s = ""
for j in res:
s += "\(\chi_{" + str(j) + "}\)"
return s
def _Weyl_law_consts(self):
r"""
Compute constants for the Weyl law on self._G
OUTPUT:
- tuple of real numbers
EXAMPLES::
sage: M=MaassWaveForms(MySubgroup(Gamma0(1)))
sage: M._Weyl_law_consts()
(0, 2/pi, (log(pi) - log(2) + 2)/pi, 0, -2)
"""
import mpmath
pi=mpmath.fp.pi
ix=Integer(self._G.index())
nc=Integer(len(self._G.cusps()))
if(self._G.is_congruence()):
lvl=Integer(self._G.level())
else:
lvl=0
n2=Integer(self._G.nu2())
n3=Integer(self._G.nu3())
c1=ix/Integer(12)
c2=Integer(2)*nc/pi
c3=nc*(Integer(2)-ln(Integer(2))+ln(pi))/pi
if(lvl<>0):
A=1
for q in divisors(lvl):
num_prim_dc=0
DG=DirichletGroup(q)
for chi in DG.list():
if(chi.is_primitive()):
num_prim_dc=num_prim_dc+1
for m in divisors(lvl):
if(lvl % (m*q) == 0 and m % q ==0 ):
fak=(q*lvl)/gcd(m,lvl/m)
A=A*Integer(fak)**num_prim_dc
c4=-ln(A)/pi
else:
c4=Integer(0)
# constant term
c5=-ix/144+n2/8+n3*2/9-nc/4-1
return (c1,c2,c3,c4,c5)
def set_table(info, is_set, make_link=True): # level_min,level_max,weight=2,chi=0,make_link=True):
r"""
make a bunch of html tables with information about spaces of modular forms
with parameters in the given ranges.
Should use database in the future...
"""
D = 0
rowlen = 10 # split into rows of this length...
rowlen0 = rowlen
rowlen1 = rowlen
characters = dict()
if('level_min' in info):
level_min = int(info['level_min'])
else:
level_min = 1
if('level_max' in info):
level_max = int(info['level_max'])
else:
level_max = 50
if (level_max - level_min + 1) < rowlen:
rowlen0 = level_max - level_min + 1
if(info['list_chars'] != '0'):
char1 = 1
else:
char1 = 0
if(is_set['weight']):
weight = int(info['weight'])
else:
weight = 2
## setup the table
# print "char11=",char1
tbl = dict()
if(char1 == 1):
tbl['header'] = 'Dimension of \( S_{' + str(weight) + '}(N,\chi_{n})\)'
else:
tbl['header'] = 'Dimension of \( S_{' + str(weight) + '}(N)\)'
tbl['headersv'] = list()
tbl['headersh'] = list()
tbl['corner_label'] = ""
tbl['data'] = list()
tbl['data_format'] = 'html'
tbl['class'] = "dimension_table"
tbl['atts'] = "border=\"0\" class=\"data_table\""
num_rows = ceil(QQ(level_max - level_min + 1) / QQ(rowlen0))
print "num_rows=", num_rows
for i in range(1, rowlen0 + 1):
tbl['headersh'].append(i + level_min - 1)
for r in range(num_rows):
tbl['headersv'].append(r * rowlen0)
print "level_min=", level_min
print "level_max=", level_max
print "char=", char1
for r in range(num_rows):
row = list()
for k in range(1, rowlen0 + 1):
row.append("")
# print "row nr. ",r
for k in range(1, rowlen0 + 1):
N = level_min - 1 + r * rowlen0 + k
s = "<a name=\"#" + str(N) + "\"></a>"
# print "col ",k,"=",N
if(N > level_max or N < 1):
continue
if(char1 == 0):
d = dimension_cusp_forms(N, weight)
print "d=", d
if(make_link):
url = "?weight=" + str(weight) + "&level=" + str(N) + "&character=0"
row.append(s + "<a target=\"mainWindow\" href=\"" + url + "\">" + str(d) + "</a>")
else:
row.append(s + str(d))
# print "dim(",N,weight,")=",d
else:
D = DirichletGroup(N)
print "D=", D
s = "<a name=\"#" + str(N) + "\"></a>"
small_tbl = dict()
# small_tbl['header']='Dimension of \( S_{'+str(weight)+'}(N)\)'
small_tbl['headersv'] = ['\( d \)']
small_tbl['headersh'] = list()
small_tbl['corner_label'] = "\( n \)"
small_tbl['data'] = list()
small_tbl['atts'] = "border=\"1\" padding=\"1\""
small_tbl['data_format'] = 'html'
row1 = list()
# num_small_rows = ceil(QQ(level_max) / QQ(rowlen))
ii = 0
for chi in range(0, len(D.list())):
x = D[chi]
S = CuspForms(x, weight)
d = S.dimension()
if(d == 0):
continue
small_tbl['headersh'].append(chi)
if(make_link):
url = "?weight=" + str(weight) + "&level=" + str(N) + "&character=" + str(chi)
row1.append("<a target=\"mainWindow\" href=\"" + url + "\">" + str(d) + "</a>")
else:
row1.append(d)
ii = ii + 1
print "d=", d
if(ii > rowlen1 and len(row1) > 0):
## we make a new table since we may not have regularly dstributed labels
# print "Break line! Make new table!"
small_tbl['data'].append(row1)
s = s + html_table(small_tbl)
small_tbl['headersh'] = list()
small_tbl['data'] = list()
row1 = list()
ii = 0
if(len(row1) > 0):
small_tbl['data'].append(row1)
if(len(row1) > 0 or len(small_tbl['data']) > 0):
# print "small_tbl=",small_tbl
ss = html_table(small_tbl)
# print "ss=",ss
s = s + ss
# s=s+"\( \chi_{"+str(chi)+"}\) :"+str(d)
# print N,k,chi,d
# print s
else:
s = "All spaces are zero-dimensional!"
row.append(s)
print "row=", row
tbl['data'].append(row)
s = html_table(tbl)
s = s + "\n <br> \(N=" + str(rowlen0) + "\cdot row+col\)"
print "Whole table=", s
## ugly solution. but we have latex in the data fields...
ss = re.sub('texttt', '', s)
info['popup_table'] = ss
# info['sidebar']=set_sidebar([navigation,parents,siblings,friends,lifts])
return info
def set_table(
info,
is_set,
make_link=True): # level_min,level_max,weight=2,chi=0,make_link=True):
r"""
make a bunch of html tables with information about spaces of modular forms
with parameters in the given ranges.
Should use database in the future...
"""
D = 0
rowlen = 10 # split into rows of this length...
rowlen0 = rowlen
rowlen1 = rowlen
characters = dict()
if ('level_min' in info):
level_min = int(info['level_min'])
else:
level_min = 1
if ('level_max' in info):
level_max = int(info['level_max'])
else:
level_max = 50
if (level_max - level_min + 1) < rowlen:
rowlen0 = level_max - level_min + 1
if (info['list_chars'] != '0'):
char1 = 1
else:
char1 = 0
if (is_set['weight']):
weight = int(info['weight'])
else:
weight = 2
## setup the table
# print "char11=",char1
tbl = dict()
if (char1 == 1):
tbl['header'] = 'Dimension of \( S_{' + str(weight) + '}(N,\chi_{n})\)'
else:
tbl['header'] = 'Dimension of \( S_{' + str(weight) + '}(N)\)'
tbl['headersv'] = list()
tbl['headersh'] = list()
tbl['corner_label'] = ""
tbl['data'] = list()
tbl['data_format'] = 'html'
tbl['class'] = "dimension_table"
tbl['atts'] = "border=\"0\" class=\"data_table\""
num_rows = ceil(QQ(level_max - level_min + 1) / QQ(rowlen0))
print "num_rows=", num_rows
for i in range(1, rowlen0 + 1):
tbl['headersh'].append(i + level_min - 1)
for r in range(num_rows):
tbl['headersv'].append(r * rowlen0)
print "level_min=", level_min
print "level_max=", level_max
print "char=", char1
for r in range(num_rows):
row = list()
for k in range(1, rowlen0 + 1):
row.append("")
# print "row nr. ",r
for k in range(1, rowlen0 + 1):
N = level_min - 1 + r * rowlen0 + k
s = "<a name=\"#" + str(N) + "\"></a>"
# print "col ",k,"=",N
if (N > level_max or N < 1):
continue
if (char1 == 0):
d = dimension_cusp_forms(N, weight)
print "d=", d
if (make_link):
url = "?weight=" + str(weight) + "&level=" + str(
N) + "&character=0"
row.append(s + "<a target=\"mainWindow\" href=\"" + url +
"\">" + str(d) + "</a>")
else:
row.append(s + str(d))
# print "dim(",N,weight,")=",d
else:
D = DirichletGroup(N)
print "D=", D
s = "<a name=\"#" + str(N) + "\"></a>"
small_tbl = dict()
# small_tbl['header']='Dimension of \( S_{'+str(weight)+'}(N)\)'
small_tbl['headersv'] = ['\( d \)']
small_tbl['headersh'] = list()
small_tbl['corner_label'] = "\( n \)"
small_tbl['data'] = list()
small_tbl['atts'] = "border=\"1\" padding=\"1\""
small_tbl['data_format'] = 'html'
row1 = list()
# num_small_rows = ceil(QQ(level_max) / QQ(rowlen))
ii = 0
for chi in range(0, len(D.list())):
x = D[chi]
S = CuspForms(x, weight)
d = S.dimension()
if (d == 0):
continue
small_tbl['headersh'].append(chi)
if (make_link):
url = "?weight=" + str(weight) + "&level=" + str(
N) + "&character=" + str(chi)
row1.append("<a target=\"mainWindow\" href=\"" + url +
"\">" + str(d) + "</a>")
else:
row1.append(d)
ii = ii + 1
print "d=", d
if (ii > rowlen1 and len(row1) > 0):
## we make a new table since we may not have regularly dstributed labels
# print "Break line! Make new table!"
small_tbl['data'].append(row1)
s = s + html_table(small_tbl)
small_tbl['headersh'] = list()
small_tbl['data'] = list()
row1 = list()
ii = 0
if (len(row1) > 0):
small_tbl['data'].append(row1)
if (len(row1) > 0 or len(small_tbl['data']) > 0):
# print "small_tbl=",small_tbl
ss = html_table(small_tbl)
# print "ss=",ss
s = s + ss
# s=s+"\( \chi_{"+str(chi)+"}\) :"+str(d)
# print N,k,chi,d
# print s
else:
s = "All spaces are zero-dimensional!"
row.append(s)
print "row=", row
tbl['data'].append(row)
s = html_table(tbl)
s = s + "\n <br> \(N=" + str(rowlen0) + "\cdot row+col\)"
print "Whole table=", s
## ugly solution. but we have latex in the data fields...
ss = re.sub('texttt', '', s)
info['popup_table'] = ss
# info['sidebar']=set_sidebar([navigation,parents,siblings,friends,lifts])
return info
