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Properties

Label 24843.2.a.dz
Level $24843$
Weight $2$
Character orbit 24843.a
Self dual yes
Analytic conductor $198.372$
Dimension $12$

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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 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);
 
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")
 
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 = [12,0,-12,10,0,0,0,0,12,14,0,-10,0,0,0,-6,0,0,0,0,0,-14,-32,0, 20,0,-12,0,10,-14,0,0,0,0,0,10,0,-48,0,42,0,0,-26,0,0,0,0,6,0,0,0,0,-36, 0,26,0,0,0,0,0,52,26,0,4,0,14,0,0,32,0,0,0,0,-76,-20,0,0,0,8,0,12,28,0, 0,0,0,-10,32,0,14,0,-40,0,-6,-56,0,0,0,0,4] 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: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 16x^{10} + 88x^{8} - 197x^{6} + 172x^{4} - 36x^{2} + 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 12 q - 12 q^{3} + 10 q^{4} + 12 q^{9} + 14 q^{10} - 10 q^{12} - 6 q^{16} - 14 q^{22} - 32 q^{23} + 20 q^{25} - 12 q^{27} + 10 q^{29} - 14 q^{30} + 10 q^{36} - 48 q^{38} + 42 q^{40} - 26 q^{43} + 6 q^{48}+ \cdots - 56 q^{95}+O(q^{100}) \) 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.