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Properties

Label 34848.2.a.ez
Level $34848$
Weight $2$
Character orbit 34848.a
Self dual yes
Analytic conductor $278.263$
Dimension $4$

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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] = [34848,2,Mod(1,34848)] 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("34848.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(34848, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 34848 = 2^{5} \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 34848.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,-6,0,0,0,0,0,0,0,-4,0,0,0,-2,0,0,0,0,0,0,0,-6,0,0,0, 16,0,0,0,0,0,0,0,12,0,0,0,-8,0,0,0,0,0,0,0,-8,0,0,0,6,0,0,0,0,0,0,0,-10, 0,0,0,26,0,0,0,0,0,0,0,-16,0,0,0,0,0,0,0,0,0,0,0,-12,0,0,0,-24,0,0,0,0, 0,0,0,58,0,0,0] 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: \(278.262680964\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{20})^+\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 5x^{2} + 5 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: not computed

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 4 q - 6 q^{5} - 4 q^{13} - 2 q^{17} - 6 q^{25} + 16 q^{29} + 12 q^{37} - 8 q^{41} - 8 q^{49} + 6 q^{53} - 10 q^{61} + 26 q^{65} - 16 q^{73} - 12 q^{85} - 24 q^{89} + 58 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.