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Properties

Label 33282.2.a.ee
Level $33282$
Weight $2$
Character orbit 33282.a
Self dual yes
Analytic conductor $265.758$
Dimension $40$

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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] = [33282,2,Mod(1,33282)] 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("33282.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33282, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 33282 = 2 \cdot 3^{2} \cdot 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 33282.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [40,40,0,40,24,0,0,40,0,24,0,0,2,0,0,40,0,0,0,24,0,0,0,0,60,2, 0,0,24,0,-22,40,0,0,0,0,0,0,0,24,0,0,0,0,0,0,0,0,90,60,0,2,0,0,0,0,0,24, 0,0,0,-22,0,40,84,0,8,0,0,0,52,0,0,0,0,0,124,0,-14,24,0,0,0,0,0,0,0,0, 170,0,0,0,0,0,0,0,28,90,0,60] 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: \(265.758108007\)
Dimension: \(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 40 q^{2} + 40 q^{4} + 24 q^{5} + 40 q^{8} + 24 q^{10} + 2 q^{13} + 40 q^{16} + 24 q^{20} + 60 q^{25} + 2 q^{26} + 24 q^{29} - 22 q^{31} + 40 q^{32} + 24 q^{40} + 90 q^{49} + 60 q^{50} + 2 q^{52}+ \cdots + 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(43\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.