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Properties

Label 42237.2.a.be
Level $42237$
Weight $2$
Character orbit 42237.a
Self dual yes
Analytic conductor $337.264$
Dimension $3$

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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 = [3,2,0,2,-1,0,-5,6,0,8,3,0,3,-10,0,4,-1,0,0,18,0,-2,-8,0,4,2, 0,-12,6,0,-6,4,0,6,-7,0,-6,0,0,18,18,0,1,-18,0,-28,-3,0,-6,16,0,2,-12, 0,-21,-14,0,2,10,0,1,-8,0,4,-1,0,-2,8,0,-24,8,0,-23,-8,0,0,-1,0,2,16,0, 32,-28,0,9,18,0,-26,-20,0,-5,-20,0,24,0,0,12,18,0,20] 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: \(3\)
Coefficient field: 3.3.148.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q + 2 q^{2} + 2 q^{4} - q^{5} - 5 q^{7} + 6 q^{8} + 8 q^{10} + 3 q^{11} + 3 q^{13} - 10 q^{14} + 4 q^{16} - q^{17} + 18 q^{20} - 2 q^{22} - 8 q^{23} + 4 q^{25} + 2 q^{26} - 12 q^{28} + 6 q^{29} - 6 q^{31}+ \cdots + 18 q^{98}+O(q^{100}) \) 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.