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Properties

Label 15840.2.a.cc
Level $15840$
Weight $2$
Character orbit 15840.a
Self dual yes
Analytic conductor $126.483$
Dimension $3$

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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] = [15840,2,Mod(1,15840)] 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("15840.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 15840 = 2^{5} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 15840.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,0,0,0,3,0,-2,0,0,0,3,0,-2,0,0,0,0,0,6,0,0,0,4,0,3,0,0,0,12, 0,0,0,0,0,-2,0,-6,0,0,0,0,0,2,0,0,0,8,0,-1,0,0,0,2,0,3,0,0,0,12,0,-18, 0,0,0,-2,0,0,0,0,0,16,0,-2,0,0,0,-2,0,14,0,0,0,0,0,0,0,0,0,14,0,-8,0,0, 0,6,0,6,0,0,0] 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: \(126.483036802\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q + 3 q^{5} - 2 q^{7} + 3 q^{11} - 2 q^{13} + 6 q^{19} + 4 q^{23} + 3 q^{25} + 12 q^{29} - 2 q^{35} - 6 q^{37} + 2 q^{43} + 8 q^{47} - q^{49} + 2 q^{53} + 3 q^{55} + 12 q^{59} - 18 q^{61} - 2 q^{65}+ \cdots + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(5\) \( -1 \)
\(11\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.