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Properties

Label 35131.2.a.b
Level $35131$
Weight $2$
Character orbit 35131.a
Self dual yes
Analytic conductor $280.522$
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] = [35131,2,Mod(1,35131)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35131, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("35131.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 35131 = 19 \cdot 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35131.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,2,-2,-3,0,1,0,1,0,3,-4,-4,0,-6,4,-3,0,-1,6,2,0,0,0,4,0,-4, -2,-6,0,-4,0,6,0,-3,-2,-2,0,-8,0,-6,0,0,-6,-3,0,-3,8,-6,0,-6,8,12,0,-9, 0,-2,0,-6,12,1,0,1,-8,12,0,-4,6,0,0,-6,0,7,0,8,2,3,0,8,-12,-11,0,12,-4, 9,0,-12,0,-12,0,-4,0,-8,0,3,0,8,0,3,-8] 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: \(280.522447341\)
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)
 
\(f(q)\) \(=\) \( q + 2 q^{3} - 2 q^{4} - 3 q^{5} + q^{7} + q^{9} + 3 q^{11} - 4 q^{12} - 4 q^{13} - 6 q^{15} + 4 q^{16} - 3 q^{17} - q^{19} + 6 q^{20} + 2 q^{21} + 4 q^{25} - 4 q^{27} - 2 q^{28} - 6 q^{29} - 4 q^{31}+ \cdots + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(19\) \( +1 \)
\(43\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.