def set_info_for_web_newform(level=None,
weight=None,
character=None,
label=None,
**kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
info['label'] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(
level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, 'prec', default_prec, int)
bprec = my_get(info, 'bprec', default_display_bprec, int)
emf_logger.debug("PREC: {0}".format(prec))
emf_logger.debug("BITPREC: {0}".format(bprec))
try:
WNF = WebNewForm_cached(level=level,
weight=weight,
character=character,
label=label)
emf_logger.critical("defined webnewform for rendering!")
# if info.has_key('download') and info.has_key('tempfile'):
# WNF._save_to_file(info['tempfile'])
# info['filename']=str(weight)+'-'+str(level)+'-'+str(character)+'-'+label+'.sobj'
# return info
except IndexError as e:
WNF = None
info['error'] = e.message
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight,
character=character)
bread = [(EMF_TOP, url1)]
bread.append(("of level %s" % level, url2))
bread.append(("weight %s" % weight, url3))
if int(character) == 0:
bread.append(("trivial character", url4))
else:
bread.append(("\( %s \)" % (WNF.character.latex_name), url4))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character)
friends.append(
('\( S_{%s}(%s, %s)\)' %
(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if WNF.coefficient_field_label(check=True):
friends.append(('Number field ' + WNF.coefficient_field_label(),
WNF.coefficient_field_url()))
friends.append(
('Number field ' + WNF.base_field_label(), WNF.base_field_url()))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)",
WNF.character.url()))
if WNF.dimension == 0:
info['error'] = "This space is empty!"
# emf_logger.debug("WNF={0}".format(WNF))
#info['name'] = name
info['title'] = 'Modular Form ' + WNF.hecke_orbit_label
if 'error' in info:
return info
# info['name']=WNF._name
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if WNF.coefficient_field.absolute_degree() == 1:
rdeg = 1
else:
rdeg = WNF.coefficient_field.relative_degree()
if cdeg == 1:
info['satake'] = WNF.satake
info['qexp'] = WNF.q_expansion_latex(prec=10, name='a')
info['qexp_display'] = url_for(".get_qexp_latex",
level=level,
weight=weight,
character=character,
label=label)
# info['qexp'] = WNF.q_expansion_latex(prec=prec)
#c_pol_st = str(WNF.absolute_polynomial)
#b_pol_st = str(WNF.polynomial(type='base_ring',format='str'))
#b_pol_ltx = str(WNF.polynomial(type='base_ring',format='latex'))
#print "c=",c_pol_ltx
#print "b=",b_pol_ltx
if cdeg > 1: ## Field is QQ
if bdeg > 1 and rdeg > 1:
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = latex(p1)
lgc = p1.variables()[0]
c_pol_ltx = c_pol_ltx.replace(lgc, 'a')
z = p1.base_ring().gens()[0]
p2 = z.minpoly()
b_pol_ltx = latex(p2)
b_pol_ltx = b_pol_ltx.replace(latex(p2.variables()[0]), latex(z))
info['polynomial_st'] = 'where \({0}=0\) and \({1}=0\).'.format(
c_pol_ltx, b_pol_ltx)
else:
c_pol_ltx = latex(WNF.coefficient_field.relative_polynomial())
lgc = str(
latex(WNF.coefficient_field.relative_polynomial().variables()
[0]))
c_pol_ltx = c_pol_ltx.replace(lgc, 'a')
info['polynomial_st'] = 'where \({0}=0\)'.format(c_pol_ltx)
else:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg == 1:
info['is_rational'] = 1
else:
info['is_rational'] = 0
# info['q_exp_embeddings'] = WNF.print_q_expansion_embeddings()
# if(int(info['degree'])>1 and WNF.dimension()>1):
# s = 'One can embed it into \( \mathbb{C} \) as:'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# elif(int(info['degree'])>1):
# s = 'There are '+str(info['degree'])+' embeddings into \( \mathbb{C} \):'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# else:
# info['embeddings'] = ''
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF._embeddings[
'values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = []
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'],
list) and len(info['twist_info']) > 0:
info['is_minimal'] = info['twist_info'][0]
if (info['twist_info'][0]):
s = '- Is minimal<br>'
else:
s = '- Is a twist of lower level<br>'
properties2 = [('Twist info', s)]
else:
info['twist_info'] = 'Twist info currently not available.'
properties2 = [('Twist info', 'not available')]
args = list()
for x in range(5, 200, 10):
args.append({'digits': x})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm is None:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm is True:
s = '- Is a CM-form<br>'
else:
s = '- Is not a CM-form<br>'
properties2.append(('CM info', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev, dict) and len(alev.keys()) > 0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if (level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6', '')
if poly <> '':
d, monom, coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(d):
c = QQ(coeffs[i])
s = ""
if d > 1 and i > 0 and c > 0:
s = "+"
if c < 0:
s = "-"
if c.denominator() > 1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(
abs(c.numerator()), c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]
b = monom[i][1]
if a == 0 and b <> 0:
s += "E_6^{{ {0} }}".format(b)
elif b == 0 and a <> 0:
s += "E_4^{{ {0} }}".format(a)
else:
s += "E_4^{{ {0} }}E_6^{{ {1} }}".format(a, b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + \
'&label=' + str(label)
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if (label_other != label):
s = 'Modular form '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(
character) + str(label_other)
else:
s = s + str(level) + '.' + str(weight) + str(label_other)
url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label_other)
friends.append((s, url))
s = 'L-Function '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(character) + str(
label)
else:
s = s + str(level) + '.' + str(weight) + str(label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = '/L' + url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label)
if WNF.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_degree):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight == 2 and WNF.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_cn()
return info
def set_info_for_web_newform(level=None, weight=None, character=None, label=None, **kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info["level"] = level
info["weight"] = weight
info["character"] = character
info["label"] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, "prec", default_prec, int)
bprec = my_get(info, "bprec", default_display_bprec, int)
emf_logger.debug("PREC: {0}".format(prec))
emf_logger.debug("BITPREC: {0}".format(bprec))
try:
WNF = WebNewForm_cached(level=level, weight=weight, character=character, label=label)
emf_logger.critical("defined webnewform for rendering!")
# if info.has_key('download') and info.has_key('tempfile'):
# WNF._save_to_file(info['tempfile'])
# info['filename']=str(weight)+'-'+str(level)+'-'+str(character)+'-'+label+'.sobj'
# return info
except IndexError as e:
WNF = None
info["error"] = e.message
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight, character=character)
bread = [(EMF_TOP, url1)]
bread.append(("of level %s" % level, url2))
bread.append(("weight %s" % weight, url3))
if int(character) == 0:
bread.append(("trivial character", url4))
else:
bread.append(("\( %s \)" % (WNF.character.latex_name), url4))
info["bread"] = bread
properties2 = list()
friends = list()
space_url = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight, character=character)
friends.append(("\( S_{%s}(%s, %s)\)" % (WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if WNF.coefficient_field_label(check=True):
friends.append(("Number field " + WNF.coefficient_field_label(), WNF.coefficient_field_url()))
friends.append(("Number field " + WNF.base_field_label(), WNF.base_field_url()))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)", WNF.character.url()))
if WNF.dimension == 0:
info["error"] = "This space is empty!"
# emf_logger.debug("WNF={0}".format(WNF))
# info['name'] = name
info["title"] = "Modular Form " + WNF.hecke_orbit_label
if "error" in info:
return info
# info['name']=WNF._name
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if WNF.coefficient_field.absolute_degree() == 1:
rdeg = 1
else:
rdeg = WNF.coefficient_field.relative_degree()
if cdeg == 1:
info["satake"] = WNF.satake
info["qexp"] = WNF.q_expansion_latex(prec=10, name="a")
info["qexp_display"] = url_for(".get_qexp_latex", level=level, weight=weight, character=character, label=label)
# info['qexp'] = WNF.q_expansion_latex(prec=prec)
# c_pol_st = str(WNF.absolute_polynomial)
# b_pol_st = str(WNF.polynomial(type='base_ring',format='str'))
# b_pol_ltx = str(WNF.polynomial(type='base_ring',format='latex'))
# print "c=",c_pol_ltx
# print "b=",b_pol_ltx
if cdeg > 1: ## Field is QQ
if bdeg > 1 and rdeg > 1:
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = latex(p1)
lgc = p1.variables()[0]
c_pol_ltx = c_pol_ltx.replace(lgc, "a")
z = p1.base_ring().gens()[0]
p2 = z.minpoly()
b_pol_ltx = latex(p2)
b_pol_ltx = b_pol_ltx.replace(latex(p2.variables()[0]), latex(z))
info["polynomial_st"] = "where \({0}=0\) and \({1}=0\).".format(c_pol_ltx, b_pol_ltx)
else:
c_pol_ltx = latex(WNF.coefficient_field.relative_polynomial())
lgc = str(latex(WNF.coefficient_field.relative_polynomial().variables()[0]))
c_pol_ltx = c_pol_ltx.replace(lgc, "a")
info["polynomial_st"] = "where \({0}=0\)".format(c_pol_ltx)
else:
info["polynomial_st"] = ""
info["degree"] = int(cdeg)
if cdeg == 1:
info["is_rational"] = 1
else:
info["is_rational"] = 0
# info['q_exp_embeddings'] = WNF.print_q_expansion_embeddings()
# if(int(info['degree'])>1 and WNF.dimension()>1):
# s = 'One can embed it into \( \mathbb{C} \) as:'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# elif(int(info['degree'])>1):
# s = 'There are '+str(info['degree'])+' embeddings into \( \mathbb{C} \):'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# else:
# info['embeddings'] = ''
emf_logger.debug("PREC2: {0}".format(prec))
info["embeddings"] = WNF._embeddings["values"] # q_expansion_embeddings(prec, bprec,format='latex')
info["embeddings_len"] = len(info["embeddings"])
properties2 = []
if (ZZ(level)).is_squarefree():
info["twist_info"] = WNF.twist_info
if isinstance(info["twist_info"], list) and len(info["twist_info"]) > 0:
info["is_minimal"] = info["twist_info"][0]
if info["twist_info"][0]:
s = "- Is minimal<br>"
else:
s = "- Is a twist of lower level<br>"
properties2 = [("Twist info", s)]
else:
info["twist_info"] = "Twist info currently not available."
properties2 = [("Twist info", "not available")]
args = list()
for x in range(5, 200, 10):
args.append({"digits": x})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key("tau") and len(CM["tau"]) != 0:
info["CM_values"] = CM
info["is_cm"] = WNF.is_cm
if WNF.is_cm is None:
s = "- Unknown (insufficient data)<br>"
elif WNF.is_cm is True:
s = "- Is a CM-form<br>"
else:
s = "- Is not a CM-form<br>"
properties2.append(("CM info", s))
alev = WNF.atkin_lehner_eigenvalues()
info["atkinlehner"] = None
if isinstance(alev, dict) and len(alev.keys()) > 0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if level == 1:
poly = WNF.explicit_formulas.get("as_polynomial_in_E4_and_E6", "")
if poly != "":
d, monom, coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info["explicit_formulas"] = "\("
for i in range(d):
c = QQ(coeffs[i])
s = ""
if d > 1 and i > 0 and c > 0:
s = "+"
if c < 0:
s = "-"
if c.denominator() > 1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(abs(c.numerator()), c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]
b = monom[i][1]
if a == 0 and b != 0:
s += "E_6^{{ {0} }}".format(b)
elif b == 0 and a != 0:
s += "E_4^{{ {0} }}".format(a)
else:
s += "E_4^{{ {0} }}E_6^{{ {1} }}".format(a, b)
info["explicit_formulas"] += s
info["explicit_formulas"] += " \)"
cur_url = (
"?&level=" + str(level) + "&weight=" + str(weight) + "&character=" + str(character) + "&label=" + str(label)
)
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if label_other != label:
s = "Modular form "
if character:
s = s + str(level) + "." + str(weight) + "." + str(character) + str(label_other)
else:
s = s + str(level) + "." + str(weight) + str(label_other)
url = url_for(
"emf.render_elliptic_modular_forms",
level=level,
weight=weight,
character=character,
label=label_other,
)
friends.append((s, url))
s = "L-Function "
if character:
s = s + str(level) + "." + str(weight) + "." + str(character) + str(label)
else:
s = s + str(level) + "." + str(weight) + str(label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = "/L" + url_for(
"emf.render_elliptic_modular_forms", level=level, weight=weight, character=character, label=label
)
if WNF.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_degree):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight == 2 and WNF.coefficient_field_degree == 1:
llabel = str(level) + "." + label
s = "Elliptic curve isogeny class " + llabel
url = "/EllipticCurve/Q/" + llabel
friends.append((s, url))
info["properties2"] = properties2
info["friends"] = friends
info["max_cn"] = WNF.max_cn()
return info
