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Properties

Label 22542.2.a.x
Level $22542$
Weight $2$
Character orbit 22542.a
Self dual yes
Analytic conductor $179.999$
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] = [22542,2,Mod(1,22542)] 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("22542.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22542, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 22542 = 2 \cdot 3 \cdot 13 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 22542.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,1,1,0,1,2,1,1,0,2,1,-1,2,0,1,0,1,-8,0,2,2,0,1,-5,-1,1,2, 6,0,-6,1,2,0,0,1,-4,-8,-1,0,-4,2,-4,2,0,0,-8,1,-3,-5,0,-1,-6,1,0,2,-8, 6,-8,0,2,-6,2,1,0,2,-8,0,0,0,6,1,-12,-4,-5,-8,4,-1,-4,0,1,-4,-12,2,0,-4, 6,2,6,0,-2,0,-6,-8,0,1,0,-3,2,-5] 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: \(179.998776236\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} + q^{9} + 2 q^{11} + q^{12} - q^{13} + 2 q^{14} + q^{16} + q^{18} - 8 q^{19} + 2 q^{21} + 2 q^{22} + q^{24} - 5 q^{25} - q^{26} + q^{27}+ \cdots + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(13\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.