def render_modlmf_webpage(**args):
C = getDBConnection()
data = None
if 'label' in args:
lab = args.get('label')
data = C.mod_l_eigenvalues.modlmf.find_one({'label': lab })
if data is None:
t = "mod ℓ modular form search error"
bread = [('mod ℓ Modular Forms', url_for(".modlmf_render_webpage"))]
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label for a mod ℓ modular form in the database." % (lab)),"error")
return render_template("modlmf-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
info = {}
info.update(data)
info['friends'] = []
bread=[('Modular Forms', "/ModularForm"),('GL(2)',""),('mod ℓ', url_for(".modlmf_render_webpage")), ('%s' % data['label'], ' ')]
credit = modlmf_credit
f = C.mod_l_eigenvalues.modlmf.find_one({'characteristic':data['characteristic'], 'deg' : data['deg'], 'level' : data['level'],'conductor' : data['conductor'],'min_weight': data['min_weight'], 'dirchar' : data['dirchar'], 'atkinlehner': data['atkinlehner'],'n_coeffs': data['n_coeffs'],'coeffs': data['coeffs']})
for m in ['characteristic','deg','level','conductor','min_weight', 'n_coeffs']:
info[m]=int(f[m])
for m in ['coeffs', 'atkinlehner']:
info[m]=f[m]
info['dirchar']=str(f['dirchar'])
if f['deg'] == int(1):
info['field']=str('𝔽<sub>%s</sub>' %f['characteristic'])
else:
try:
pol=str(conway_polynomial(f['characteristic'], f['deg']))
info['field']=str('𝔽<sub>%s<sup>%s</sup></sub>𝔽<sub>%s</sub>[x]/(%s)' %(str(f['characteristic']), str(f['deg']), str(f['characteristic']), pol))
except:
info['field']=""
ncoeff=int(round(50/f['deg']))
if f['coeffs'] != "":
coeff=[f['coeffs'][i] for i in range(ncoeff+1)]
info['q_exp']=my_latex(print_q_expansion(coeff))
info['q_exp_display'] = url_for(".q_exp_display", label=f['label'], number="")
p_range=prime_range(100)
info['table_list']=[[p_range[i], f['coeffs'][p_range[i]]] for i in range(len(p_range))]
info['download_q_exp'] = [
(i, url_for(".render_modlmf_webpage_download", label=info['label'], lang=i)) for i in ['gp', 'magma','sage']]
t = "mod ℓ Modular Form "+info['label']
info['properties'] = [
('Field characteristic', '%s' %info['characteristic']),
('Field degree', '%s' %info['deg']),
('Level', '%s' %info['level']),
('Conductor', '%s' %info['conductor']),
('Minimal weight', '%s' %info['min_weight']),
('Label', '%s' %info['label'])]
return render_template("modlmf-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list())
def render_modlmf_webpage(**args):
C = getDBConnection()
data = None
if 'label' in args:
lab = args.get('label')
data = C.mod_l_eigenvalues.modlmf.find_one({'label': lab })
if data is None:
t = "Mod ℓ modular form search error"
bread = [('mod ℓ Modular Forms', url_for(".modlmf_render_webpage"))]
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label for a mod ℓ modular form in the database." % (lab)),"error")
return render_template("modlmf-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
info = {}
info.update(data)
info['friends'] = []
bread=[('Modular Forms', "/ModularForm"),('mod ℓ', url_for(".modlmf_render_webpage")), ('%s' % data['label'], ' ')]
credit = modlmf_credit
f = C.mod_l_eigenvalues.modlmf.find_one({'characteristic':data['characteristic'], 'deg' : data['deg'], 'level' : data['level'],'weight_grading': data['weight_grading'], 'reducible' : data['reducible'], 'cuspidal_lift': data['cuspidal_lift'], 'dirchar' : data['dirchar'], 'atkinlehner': data['atkinlehner'],'n_coeffs': data['n_coeffs'],'coeffs': data['coeffs'], 'ordinary': data['ordinary'],'min_theta_weight': data['min_theta_weight'], 'theta_cycle' : data['theta_cycle']})
for m in ['characteristic','deg','level','weight_grading', 'n_coeffs', 'min_theta_weight', 'ordinary']:
info[m]=int(f[m])
info['atkinlehner']=f['atkinlehner']
info['dirchar']=str(f['dirchar'])
info['label']=str(f['label'])
if f['reducible']:
info['reducible']=f['reducible']
info['cuspidal_lift']=f['cuspidal_lift']
info['cuspidal_lift_weight']=int(f['cuspidal_lift'][0])
info['cuspidal_lift_orbit']=str(f['cuspidal_lift'][1])
if f['cuspidal_lift'][2]=='x':
info['cuspidal_hecke_field']=1
else:
info['cuspidal_hecke_field']=latex(f['cuspidal_lift'][2])
info['cuspidal_lift_gen']=f['cuspidal_lift'][3]
if f['theta_cycle']:
info['theta_cycle']=f['theta_cycle']
info['coeffs']=[str(s).replace('x','a').replace('*','') for s in f['coeffs']]
if f['deg'] != int(1):
try:
pol=str(conway_polynomial(f['characteristic'], f['deg'])).replace('x','a').replace('*','')
info['field']= pol
except:
info['field']=""
ncoeff=int(round(20/f['deg']))
av_coeffs=min(f['n_coeffs'],100)
info['av_coeffs']=int(av_coeffs)
if f['coeffs'] != "":
coeff=[info['coeffs'][i] for i in range(ncoeff+1)]
info['q_exp']=my_latex(print_q_expansion(coeff))
info['q_exp_display'] = url_for(".q_exp_display", label=f['label'], number="")
p_range=prime_range(av_coeffs)
info['table_list']=[[p_range[i], info['coeffs'][p_range[i]]] for i in range(len(p_range))]
info['download_q_exp'] = [
(i, url_for(".render_modlmf_webpage_download", label=info['label'], lang=i)) for i in ['gp', 'magma','sage']]
t = "Mod "+str(info['characteristic'])+" Modular Form "+info['label']
info['properties'] = [
('Label', '%s' %info['label']),
('Field characteristic', '%s' %info['characteristic']),
('Field degree', '%s' %info['deg']),
('Level', '%s' %info['level']),
('Weight grading', '%s' %info['weight_grading'])]
return render_template("modlmf-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list())
def render_modlmf_webpage(**args):
C = getDBConnection()
data = None
if 'label' in args:
lab = args.get('label')
data = C.mod_l_eigenvalues.modlmf.find_one({'label': lab})
if data is None:
t = "Mod ℓ modular form search error"
bread = [('mod ℓ Modular Forms',
url_for(".modlmf_render_webpage"))]
flash(
Markup(
"Error: <span style='color:black'>%s</span> is not a valid label for a mod ℓ modular form in the database."
% (lab)), "error")
return render_template("modlmf-error.html",
title=t,
properties=[],
bread=bread,
learnmore=learnmore_list())
info = {}
info.update(data)
info['friends'] = []
bread = [('Modular Forms', "/ModularForm"),
('mod ℓ', url_for(".modlmf_render_webpage")),
('%s' % data['label'], ' ')]
credit = modlmf_credit
f = C.mod_l_eigenvalues.modlmf.find_one({
'characteristic':
data['characteristic'],
'deg':
data['deg'],
'level':
data['level'],
'weight_grading':
data['weight_grading'],
'reducible':
data['reducible'],
'cuspidal_lift':
data['cuspidal_lift'],
'dirchar':
data['dirchar'],
'atkinlehner':
data['atkinlehner'],
'n_coeffs':
data['n_coeffs'],
'coeffs':
data['coeffs'],
'ordinary':
data['ordinary'],
'min_theta_weight':
data['min_theta_weight'],
'theta_cycle':
data['theta_cycle']
})
for m in [
'characteristic', 'deg', 'level', 'weight_grading', 'n_coeffs',
'min_theta_weight', 'ordinary'
]:
info[m] = int(f[m])
info['atkinlehner'] = f['atkinlehner']
info['dirchar'] = str(f['dirchar'])
info['label'] = str(f['label'])
if f['reducible']:
info['reducible'] = f['reducible']
info['cuspidal_lift'] = f['cuspidal_lift']
info['cuspidal_lift_weight'] = int(f['cuspidal_lift'][0])
info['cuspidal_lift_orbit'] = str(f['cuspidal_lift'][1])
if f['cuspidal_lift'][2] == 'x':
info['cuspidal_hecke_field'] = 1
else:
info['cuspidal_hecke_field'] = latex(f['cuspidal_lift'][2])
info['cuspidal_lift_gen'] = f['cuspidal_lift'][3]
if f['theta_cycle']:
info['theta_cycle'] = f['theta_cycle']
info['coeffs'] = [
str(s).replace('x', 'a').replace('*', '') for s in f['coeffs']
]
if f['deg'] != int(1):
try:
pol = str(conway_polynomial(f['characteristic'],
f['deg'])).replace('x', 'a').replace(
'*', '')
info['field'] = pol
except:
info['field'] = ""
ncoeff = int(round(20 / f['deg']))
av_coeffs = min(f['n_coeffs'], 100)
info['av_coeffs'] = int(av_coeffs)
if f['coeffs'] != "":
coeff = [info['coeffs'][i] for i in range(ncoeff + 1)]
info['q_exp'] = my_latex(print_q_expansion(coeff))
info['q_exp_display'] = url_for(".q_exp_display",
label=f['label'],
number="")
p_range = prime_range(av_coeffs)
info['table_list'] = [[p_range[i], info['coeffs'][p_range[i]]]
for i in range(len(p_range))]
info['download_q_exp'] = [(i,
url_for(".render_modlmf_webpage_download",
label=info['label'],
lang=i))
for i in ['gp', 'magma', 'sage']]
t = "Mod " + str(
info['characteristic']) + " Modular Form " + info['label']
info['properties'] = [('Label', '%s' % info['label']),
('Field characteristic',
'%s' % info['characteristic']),
('Field degree', '%s' % info['deg']),
('Level', '%s' % info['level']),
('Weight grading', '%s' % info['weight_grading'])]
return render_template("modlmf-single.html",
info=info,
credit=credit,
title=t,
bread=bread,
properties2=info['properties'],
learnmore=learnmore_list())
def render_rep_galois_modl_webpage(**args):
C = getDBConnection()
data = None
if 'label' in args:
lab = args.get('label')
data = C.mod_l_galois.reps.find_one({'label': lab })
if data is None:
t = "Mod ℓ Galois representations Search Error"
bread = [('Representations', "/Representation"),("mod ℓ", url_for(".rep_galois_modl_render_webpage"))]
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid label for a mod ℓ Galois representation in the database." % (lab)),"error")
return render_template("rep_galois_modl-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
info = {}
info.update(data)
info['friends'] = []
bread = [('Representations', "/Representation"),("mod ℓ", url_for(".rep_galois_modl_render_webpage")), ('%s' % data['label'], ' ')]
credit = rep_galois_modl_credit
f = C.mod_l_galois.reps.find_one({'base_field':data['base_field'],'rep_type':data['rep_type'],'image_type':data['image_type'],'image_label':data['image_label'],'image_at':data['image_at'], 'projective_type':data['projective_type'],'projective_label':data['projective_label'],'poly_ker':data['poly_ker'],'poly_proj_ker':data['poly_proj_ker'], 'related_objects':data['related_objects'],'dim':data['dim'],'field_char':data['field_char'],'field_deg':data['field_deg'],'conductor':data['conductor'], 'weight': data['weight'],'abs_irr':data['abs_irr'],'image_order':data['image_order'],'degree_proj_field':data['degree_proj_field'], 'primes_conductor':data['primes_conductor'],'bad_prime_list':data['bad_prime_list'],'good_prime_list':data['good_prime_list']})
for m in ['base_field','image_type','image_label','image_at','projective_type','projective_label','related_objects', 'label']:
info[m]=str(f[m])
for m in ['dim','field_char','field_deg','conductor','weight','abs_irr','image_order','degree_proj_field']:
info[m]=int(f[m])
info['primes_conductor']=[int(i) for i in f['primes_conductor']]
for m in ['poly_ker','poly_proj_ker']:
info[m]=str(f[m]).replace("*", "").strip('(').strip(')')
if f['rep_type'] =="symp":
info['rep_type']="Symplectic"
elif f['rep_type'] =="orth":
info['rep_type']="Orthogonal"
else:
info['rep_type']="Linear"
if info['field_deg'] > int(1):
try:
pol=str(conway_polynomial(f['characteristic'], f['deg'])).replace("*", "")
info['field_str']=str('$\mathbb{F}_%s \cong \mathbb{F}_%s[a]$ where $a$ satisfies: $%s=0$' %(str(f['field_char']), str(f['field_char']), pol))
except:
info['field_str']=""
info['bad_prime_list']=[]
info['good_prime_list']=[]
for n in f['bad_prime_list']:
try:
n1=[int(n[0]), str(n[1]), str(n[2]), int(n[3]), int(n[4])]
except:
n1=[int(n[0]), str(n[1]), str(n[2]), str(n[3]), str(n[4])]
info['bad_prime_list'].append(n1)
info['len_good']=[int(i+1) for i in range(len(f['good_prime_list'][0][1]))]
for n in f['good_prime_list']:
try:
n1=[int(n[0]), [str(m) for m in n[1]], str(n[2]), int(n[3]), int(n[4])]
except:
n1=[int(n[0]), [str(m) for m in n[1]], str(n[2]), str(n[3]), str(n[4])]
info['good_prime_list'].append(n1)
info['download_list'] = [
(i, url_for(".render_rep_galois_modl_webpage_download", label=info['label'], lang=i)) for i in ['gp', 'magma','sage']]
t = "Mod ℓ Galois representation "+info['label']
info['properties'] = [
('Label', '%s' %info['label']),
('Dimension', '%s' %info['dim']),
('Field characteristic', '%s' %info['field_char']),
('Conductor', '%s' %info['conductor']),]
return render_template("rep_galois_modl-single.html", info=info, credit=credit, title=t, bread=bread, properties2=info['properties'], learnmore=learnmore_list())
def render_rep_galois_modl_webpage(**args):
data = None
if 'label' in args:
lab = args.get('label')
data = db.modlgal_reps.lookup(lab)
if data is None:
t = "Mod ℓ Galois representations Search Error"
bread = [('Representations', "/Representation"),("mod ℓ", url_for(".rep_galois_modl_render_webpage"))]
flash_error("%s is not a valid label for a mod ℓ Galois representation in the database.", lab)
return render_template("rep_galois_modl-error.html", title=t, properties=[], bread=bread, learnmore=learnmore_list())
info = {}
info.update(data)
info['friends'] = []
bread = [('Representations', "/Representation"),("mod ℓ", url_for(".rep_galois_modl_render_webpage")), ('%s' % data['label'], ' ')]
credit = rep_galois_modl_credit
for m in ['base_field','image_type','image_label','image_at','projective_type','projective_label','related_objects', 'label']:
info[m]=str(data[m])
for m in ['dim','field_char','field_deg','conductor','weight','abs_irr','image_order','degree_proj_field']:
info[m]=int(data[m])
info['primes_conductor']=[int(i) for i in data['primes_conductor']]
for m in ['poly_ker','poly_proj_ker']:
info[m]=str(data[m]).replace("*", "").strip('(').strip(')')
if data['rep_type'] =="symp":
info['rep_type']="Symplectic"
elif data['rep_type'] =="orth":
info['rep_type']="Orthogonal"
else:
info['rep_type']="Linear"
if info['field_deg'] > int(1):
try:
pol=str(conway_polynomial(data['characteristic'], data['deg'])).replace("*", "")
info['field_str']=str(r'$\mathbb{F}_%s \cong \mathbb{F}_%s[a]$ where $a$ satisfies: $%s=0$' %(str(data['field_char']), str(data['field_char']), pol))
except:
info['field_str']=""
info['bad_prime_list']=[]
info['good_prime_list']=[]
for n in data['bad_prime_list']:
try:
n1=[int(n[0]), str(n[1]), str(n[2]), int(n[3]), int(n[4])]
except:
n1=[int(n[0]), str(n[1]), str(n[2]), str(n[3]), str(n[4])]
info['bad_prime_list'].append(n1)
info['len_good']=[int(i+1) for i in range(len(data['good_prime_list'][0][1]))]
for n in data['good_prime_list']:
try:
n1=[int(n[0]), [str(m) for m in n[1]], str(n[2]), int(n[3]), int(n[4])]
except:
n1=[int(n[0]), [str(m) for m in n[1]], str(n[2]), str(n[3]), str(n[4])]
info['good_prime_list'].append(n1)
info['download_list'] = [
(i, url_for(".render_rep_galois_modl_webpage_download", label=info['label'], lang=i)) for i in ['gp', 'magma','sage']]
t = "Mod ℓ Galois representation "+info['label']
info['properties'] = [
('Label', '%s' %info['label']),
('Dimension', '%s' %info['dim']),
('Field characteristic', '%s' %info['field_char']),
('Conductor', '%s' %info['conductor']),]
return render_template("rep_galois_modl-single.html", info=info, credit=credit, title=t, bread=bread, properties=info['properties'], learnmore=learnmore_list(), KNOWL_ID='gal.modl.%s'%info['label'])
