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Properties

Label 26862.2.a.j
Level $26862$
Weight $2$
Character orbit 26862.a
Self dual yes
Analytic conductor $214.494$
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] = [26862,2,Mod(1,26862)] 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("26862.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26862, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 26862 = 2 \cdot 3 \cdot 11^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 26862.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,1,2,-1,4,-1,1,-2,0,1,-4,-4,2,1,-2,-1,-8,2,4,0,4,-1,-1, 4,1,4,6,-2,0,-1,0,2,8,1,1,8,-4,-2,-6,-4,-8,0,2,-4,-6,1,9,1,-2,-4,0,-1, 0,-4,-8,-6,6,2,-8,0,4,1,-8,0,-12,-2,4,-8,2,-1,-4,-1,-1,-8,0,4,2,2,1,6, 0,4,-4,8,6,0,4,-2,-16,4,0,6,-16,-1,2,-9,0,-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: \(214.494149910\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - q^{8} + q^{9} - 2 q^{10} + q^{12} - 4 q^{13} - 4 q^{14} + 2 q^{15} + q^{16} - 2 q^{17} - q^{18} - 8 q^{19} + 2 q^{20} + 4 q^{21} + 4 q^{23}+ \cdots - 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(11\) \( +1 \)
\(37\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.