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Properties

Label 24843.2.a.ez
Level $24843$
Weight $2$
Character orbit 24843.a
Self dual yes
Analytic conductor $198.372$
Dimension $24$

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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 = [24,7,24,25,0,7,0,18,24,2,16,25,0,0,0,31,-2,7,26,-5,0,15,-12, 18,16,0,24,0,3,2,45,43,16,26,0,25,52,-8,0,-7,-5,0,-9,51,0,32,-2,31,0,63, -2,0,34,7,-1,0,26,9,-5,-5,-11,54,0,36,0,15,34,0,-12,0,45,18,19,-37,16, 72,0,0,8,-25,24,-4,-12,0,80,-13,3,42,-21,2,0,16,45,-26,-26,43,32,0,16, -25] 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: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 7 q^{2} + 24 q^{3} + 25 q^{4} + 7 q^{6} + 18 q^{8} + 24 q^{9} + 2 q^{10} + 16 q^{11} + 25 q^{12} + 31 q^{16} - 2 q^{17} + 7 q^{18} + 26 q^{19} - 5 q^{20} + 15 q^{22} - 12 q^{23} + 18 q^{24} + 16 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 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.