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Properties

Label 24843.2.a.s
Level $24843$
Weight $2$
Character orbit 24843.a
Self dual yes
Analytic conductor $198.372$
Dimension $1$

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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 = [1,1,1,-1,1,1,0,-3,1,1,-2,-1,0,0,1,-1,7,1,6,-1,0,-2,-6,-3,-4, 0,1,0,-1,1,-4,5,-2,7,0,-1,1,6,0,-3,-9,0,6,2,1,-6,-6,-1,0,-4,7,0,-9,1,-2, 0,6,-1,0,-1,-1,-4,0,7,0,-2,-2,-7,-6,0,6,-3,-11,1,-4,-6,0,0,-4,-1,1,-9, 14,0,7,6,-1,6,14,1,0,6,-4,-6,6,5,2,0,-2,4] 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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 3 q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} - q^{16} + 7 q^{17} + q^{18} + 6 q^{19} - q^{20} - 2 q^{22} - 6 q^{23} - 3 q^{24} - 4 q^{25}+ \cdots - 2 q^{99}+O(q^{100}) \) 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.