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Properties

Label 42237.2.a.cw
Level $42237$
Weight $2$
Character orbit 42237.a
Self dual yes
Analytic conductor $337.264$
Dimension $22$

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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] = [42237,2,Mod(1,42237)] 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("42237.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42237, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 42237 = 3^{2} \cdot 13 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 42237.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [22,1,0,23,-9,0,8,9,0,-5,-7,0,-22,-6,0,33,-16,0,0,-14,0,-2,-13, 0,25,-1,0,18,5,0,-13,24,0,-4,-26,0,-41,0,0,13,-5,0,12,-12,0,11,-3,0,52, -24,0,-23,-18,0,-3,-34,0,11,28,0,13,-68,0,69,9,0,-67,-9,0,-14,12,0,35, 28,0,0,-20,0,-7,-40,0,-34,-23,0,38,41,0,-14,21,0,-8,-71,0,30,0,0,-58,-86, 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: \(337.264143017\)
Dimension: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + q^{2} + 23 q^{4} - 9 q^{5} + 8 q^{7} + 9 q^{8} - 5 q^{10} - 7 q^{11} - 22 q^{13} - 6 q^{14} + 33 q^{16} - 16 q^{17} - 14 q^{20} - 2 q^{22} - 13 q^{23} + 25 q^{25} - q^{26} + 18 q^{28} + 5 q^{29}+ \cdots - 86 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(13\) \( +1 \)
\(19\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.