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Properties

Label 14079.2.a.e
Level $14079$
Weight $2$
Character orbit 14079.a
Self dual yes
Analytic conductor $112.421$
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] = [14079,2,Mod(1,14079)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14079, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("14079.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 14079 = 3 \cdot 13 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 14079.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,-1,2,-1,-4,3,1,-2,4,-1,-1,4,2,-1,2,-1,0,-2,-4,-4,0,3, -1,1,1,4,10,-2,-4,-5,4,-2,-8,-1,2,0,-1,6,-6,4,-12,-4,2,0,0,-1,9,1,2,1, -6,-1,8,-12,0,-10,-12,-2,-2,4,-4,7,-2,-4,8,-2,0,8,0,3,2,-2,-1,0,-16,1, -8,-2,1,6,4,4,4,12,10,12,2,-2,4,0,-4,0,0,-5,-10,-9,4,1] 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: \(112.421381006\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} - 4 q^{7} + 3 q^{8} + q^{9} - 2 q^{10} + 4 q^{11} - q^{12} - q^{13} + 4 q^{14} + 2 q^{15} - q^{16} + 2 q^{17} - q^{18} - 2 q^{20} - 4 q^{21} - 4 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) \) 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.