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Properties

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

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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 = [2,-2,0,2,2,0,2,-6,0,2,0,0,2,6,0,6,4,0,0,-6,0,-8,2,0,-4,-2,0, -14,8,0,8,6,0,-20,10,0,-6,0,0,-2,4,0,-8,16,0,10,4,0,4,12,0,2,-2,0,-8,2, 0,-16,-14,0,-6,0,0,-14,2,0,-24,36,0,2,14,0,4,-2,0,0,-16,0,10,6,0,20,8, 0,-12,0,0,-8,-24,0,2,-22,0,-4,0,0,-18,12,0,-20] 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: \(2\)
Coefficient field: \(\Q(\sqrt{2}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} - 6 q^{8} + 2 q^{10} + 2 q^{13} + 6 q^{14} + 6 q^{16} + 4 q^{17} - 6 q^{20} - 8 q^{22} + 2 q^{23} - 4 q^{25} - 2 q^{26} - 14 q^{28} + 8 q^{29} + 8 q^{31} + 6 q^{32}+ \cdots + 12 q^{98}+O(q^{100}) \) 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.