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Properties

Label 24843.2.a.ef
Level $24843$
Weight $2$
Character orbit 24843.a
Self dual yes
Analytic conductor $198.372$
Dimension $16$

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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 = [16,0,-16,20,0,0,0,0,16,-8,0,-20,0,0,0,28,-20,0,0,-12,0,16,-8, 0,16,0,-16,0,-4,8,0,-20,0,32,0,20,0,-36,0,-48,0,0,16,40,0,4,-8,-28,0,0, 20,0,-8,0,-24,0,0,-12,-12,12,-40,-16,0,56,0,-16,12,-52,8,0,-32,0,-8,16, -16,32,0,0,28,-108,16,0,4,0,16,-32,4,32,44,-8,0,-32,0,-24,-12,20,0,0,0, 12] 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: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 26 x^{14} + 269 x^{12} - 4 x^{11} - 1418 x^{10} + 68 x^{9} + 4039 x^{8} - 388 x^{7} - 6016 x^{6} + \cdots + 7 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 16 q - 16 q^{3} + 20 q^{4} + 16 q^{9} - 8 q^{10} - 20 q^{12} + 28 q^{16} - 20 q^{17} - 12 q^{20} + 16 q^{22} - 8 q^{23} + 16 q^{25} - 16 q^{27} - 4 q^{29} + 8 q^{30} - 20 q^{32} + 32 q^{34} + 20 q^{36}+ \cdots + 20 q^{96}+O(q^{100}) \) 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.