# Properties

 Label 15.e Modulus $15$ Conductor $15$ Order $4$ Real no Primitive yes Minimal yes Parity even

# Related objects

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(15, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([2,1]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(2,15))

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Basic properties

 Modulus: $$15$$ Conductor: $$15$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\sqrt{-1})$$ Fixed field: $$\Q(\zeta_{15})^+$$

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$11$$ $$13$$
$$\chi_{15}(2,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$-i$$
$$\chi_{15}(8,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$