↑

Properties

Label 28665.2.a.bx
Level $28665$
Weight $2$
Character orbit 28665.a
Self dual yes
Analytic conductor $228.891$
Dimension $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [28665,2,Mod(1,28665)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("28665.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28665, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 28665 = 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 28665.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,-1,0,-1,-2,0,0,0,0,1,4,0,-2,0,0,-3,2,0,9,1,0,3,-7,0,2,1,0, 0,-3,0,10,9,0,9,0,0,-16,-2,0,0,2,0,-3,-7,0,-4,-16,0,0,-1,0,1,-6,0,-4,0, 0,-1,5,0,0,-15,0,4,2,0,-14,-11,0,0,1,0,20,13,0,-7,0,0,-1,3,0,9,-7,0,-2, 4,0,-10,-3,0,0,11,0,3,-9,0,3,0,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(228.891177394\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{5}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 2 q - q^{2} - q^{4} - 2 q^{5} + q^{10} + 4 q^{11} - 2 q^{13} - 3 q^{16} + 2 q^{17} + 9 q^{19} + q^{20} + 3 q^{22} - 7 q^{23} + 2 q^{25} + q^{26} - 3 q^{29} + 10 q^{31} + 9 q^{32} + 9 q^{34} - 16 q^{37}+ \cdots + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.