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Properties

Label 2835.506
Modulus $2835$
Conductor $567$
Order $54$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2835, base_ring=CyclotomicField(54)) M = H._module chi = DirichletCharacter(H, M([25,0,18]))
 
Copy content gp:[g,chi] = znchar(Mod(506, 2835))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2835.506");
 

Basic properties

Modulus: \(2835\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(567\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(54\)
Copy content comment:Order
 
Copy content sage:chi.multiplicative_order()
 
Copy content gp:charorder(g,chi)
 
Copy content magma:Order(chi);
 
Real: no
Copy content comment:Whether the character is real
 
Copy content sage:chi.multiplicative_order() <= 2
 
Copy content gp:charorder(g,chi) <= 2
 
Copy content magma:Order(chi) le 2;
 
Primitive: no, induced from \(\chi_{567}(506,\cdot)\)
Copy content comment:If the character is primitive
 
Copy content sage:chi.is_primitive()
 
Copy content gp:#znconreyconductor(g,chi)==1
 
Copy content magma:IsPrimitive(chi);
 
Minimal: yes
Parity: odd
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Galois orbit 2835.ek

\(\chi_{2835}(191,\cdot)\) \(\chi_{2835}(221,\cdot)\) \(\chi_{2835}(506,\cdot)\) \(\chi_{2835}(536,\cdot)\) \(\chi_{2835}(821,\cdot)\) \(\chi_{2835}(851,\cdot)\) \(\chi_{2835}(1136,\cdot)\) \(\chi_{2835}(1166,\cdot)\) \(\chi_{2835}(1451,\cdot)\) \(\chi_{2835}(1481,\cdot)\) \(\chi_{2835}(1766,\cdot)\) \(\chi_{2835}(1796,\cdot)\) \(\chi_{2835}(2081,\cdot)\) \(\chi_{2835}(2111,\cdot)\) \(\chi_{2835}(2396,\cdot)\) \(\chi_{2835}(2426,\cdot)\) \(\chi_{2835}(2711,\cdot)\) \(\chi_{2835}(2741,\cdot)\)

Copy content comment:Galois orbit
 
Copy content sage:chi.galois_orbit()
 
Copy content gp:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 
Copy content magma:order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Related number fields

Field of values: \(\Q(\zeta_{27})\)
Fixed field: Number field defined by a degree 54 polynomial

Values on generators

\((1541,1702,2026)\) → \((e\left(\frac{25}{54}\right),1,e\left(\frac{1}{3}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(8\)\(11\)\(13\)\(16\)\(17\)\(19\)\(22\)\(23\)
\( \chi_{ 2835 }(506, a) \) \(-1\)\(1\)\(e\left(\frac{7}{54}\right)\)\(e\left(\frac{7}{27}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{19}{54}\right)\)\(e\left(\frac{19}{27}\right)\)\(e\left(\frac{14}{27}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{13}{27}\right)\)\(e\left(\frac{41}{54}\right)\)
Copy content comment:Value of chi at x
 
Copy content sage:chi(x)
 
Copy content gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
 
Copy content magma:chi(x)
 
\( \chi_{ 2835 }(506,a) \;\) at \(\;a = \) e.g. 2