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Properties

Label 42237.2.a.b
Level $42237$
Weight $2$
Character orbit 42237.a
Self dual yes
Analytic conductor $337.264$
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] = [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 = [1,1,0,-1,-3,0,5,-3,0,-3,0,0,1,5,0,-1,6,0,0,3,0,0,1,0,4,1,0,-5, 2,0,2,5,0,6,-15,0,-5,0,0,9,-2,0,-4,0,0,1,8,0,18,4,0,-1,9,0,0,-15,0,2,3, 0,-7,2,0,7,-3,0,14,-6,0,-15,5,0,0,-5,0,0,0,0,-15,3,0,-2,14,0,-18,-4,0, 0,-2,0,5,-1,0,8,0,0,5,18,0,-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: \(1\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{4} - 3 q^{5} + 5 q^{7} - 3 q^{8} - 3 q^{10} + q^{13} + 5 q^{14} - q^{16} + 6 q^{17} + 3 q^{20} + q^{23} + 4 q^{25} + q^{26} - 5 q^{28} + 2 q^{29} + 2 q^{31} + 5 q^{32} + 6 q^{34} - 15 q^{35}+ \cdots + 18 q^{98}+O(q^{100}) \) 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.