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Properties

Label 24843.2.a.bj
Level $24843$
Weight $2$
Character orbit 24843.a
Self dual yes
Analytic conductor $198.372$
Dimension $2$

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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] = [24843,2,Mod(1,24843)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(24843, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("24843.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 24843 = 3 \cdot 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 24843.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2,2,2,-4,2,0,6,2,0,4,2,0,0,-4,6,4,2,0,4,0,4,-4,6,2,0,2,0,-8, 0,8,-6,4,16,0,2,8,-8,0,-8,-4,0,0,4,-4,12,0,6,0,-14,4,0,-4,2,-8,0,0,0,8, 4,16,16,0,-14,0,4,0,28,-4,0,4,6,-8,8,2,-16,0,0,16,-12,2,8,8,0,4,-16,-8, 12,20,0,0,28,8,-8,-8,-6,-8,0,4,-30] 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: \(198.372353741\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{2}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + 6 q^{8} + 2 q^{9} + 4 q^{11} + 2 q^{12} - 4 q^{15} + 6 q^{16} + 4 q^{17} + 2 q^{18} + 4 q^{20} + 4 q^{22} - 4 q^{23} + 6 q^{24} + 2 q^{25} + 2 q^{27}+ \cdots + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.