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Properties

Label 28665.2.a.do
Level $28665$
Weight $2$
Character orbit 28665.a
Self dual yes
Analytic conductor $228.891$
Dimension $5$

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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 = [5,1,0,1,-5,0,0,6,0,-1,0,0,-5,0,0,5,5,0,0,-1,0,-7,-2,0,5,-1,0, 0,4,0,2,13,0,0,0,0,-12,14,0,-6,3,0,-15,1,0,-21,33,0,0,1,0,-1,23,0,0,0, 0,16,3,0,4,3,0,-2,5,0,-21,19,0,0,21,0,-13,-10,0,31,0,0,-14,-5,0,-6,29, 0,-5,-32,0,8,15,0,0,-34,0,43,0,0,-43,0,0,1] 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: \(5\)
Coefficient field: 5.5.70601.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 5x^{3} + 2x^{2} + 3x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 5 q + q^{2} + q^{4} - 5 q^{5} + 6 q^{8} - q^{10} - 5 q^{13} + 5 q^{16} + 5 q^{17} - q^{20} - 7 q^{22} - 2 q^{23} + 5 q^{25} - q^{26} + 4 q^{29} + 2 q^{31} + 13 q^{32} - 12 q^{37} + 14 q^{38} - 6 q^{40}+ \cdots - 43 q^{97}+O(q^{100}) \) 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.