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Properties

Label 40898.2.a.bk
Level $40898$
Weight $2$
Character orbit 40898.a
Self dual yes
Analytic conductor $326.572$
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] = [40898,2,Mod(1,40898)] 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("40898.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40898, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 40898 = 2 \cdot 11^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 40898.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,1,-1,-1,3,1,-2,-1,0,-1,0,3,1,1,-3,-2,0,-1,-3,0,4,-1,-4, 0,5,3,0,1,8,1,0,-3,-3,-2,7,0,0,-1,-8,-3,1,0,2,4,7,-1,2,-4,3,0,-6,5,0,3, 0,0,-10,1,8,8,-6,1,0,0,-8,-3,-4,-3,-7,-2,-16,7,4,0,0,0,-10,-1,1,-8,4,-3, 3,1,0,0,0,2,0,4,-8,7,0,-1,-8,2,0,-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: \(326.572174187\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 3 q^{7} + q^{8} - 2 q^{9} - q^{10} - q^{12} + 3 q^{14} + q^{15} + q^{16} - 3 q^{17} - 2 q^{18} - q^{20} - 3 q^{21} + 4 q^{23} - q^{24} - 4 q^{25}+ \cdots + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(11\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.