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Properties

Label 22898.2.a.d
Level $22898$
Weight $2$
Character orbit 22898.a
Self dual yes
Analytic conductor $182.841$
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] = [22898,2,Mod(1,22898)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22898, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("22898.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 22898 = 2 \cdot 107^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 22898.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,2,1,-3,-2,0,-1,1,3,0,2,4,0,-6,1,-6,-1,-2,-3,0,0,3,-2,4, -4,-4,0,6,6,0,-1,0,6,0,1,2,2,8,3,-3,0,-9,0,-3,-3,9,2,-7,-4,-12,4,12,4, 0,0,-4,-6,9,-6,-10,0,0,1,-12,0,9,-6,6,0,6,-1,0,-2,8,-2,0,-8,1,-3,-11,3, 6,0,18,9,12,0,-15,3,0,3,0,-9,6,-2,0,7,0,4] 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: \(182.841450548\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + 2 q^{3} + q^{4} - 3 q^{5} - 2 q^{6} - q^{8} + q^{9} + 3 q^{10} + 2 q^{12} + 4 q^{13} - 6 q^{15} + q^{16} - 6 q^{17} - q^{18} - 2 q^{19} - 3 q^{20} + 3 q^{23} - 2 q^{24} + 4 q^{25} - 4 q^{26}+ \cdots + 7 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(107\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.