Properties

Label 16.b
Modulus $16$
Conductor $8$
Order $2$
Real yes
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(16, base_ring=CyclotomicField(2))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,1]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(9,16))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(16\)
Conductor: \(8\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from 8.b
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q\)
Fixed field: \(\Q(\sqrt{2}) \)

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\)
\(\chi_{16}(9,\cdot)\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)