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Properties

Label 39326.2.a.n
Level $39326$
Weight $2$
Character orbit 39326.a
Self dual yes
Analytic conductor $314.020$
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] = [39326,2,Mod(1,39326)] 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("39326.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(39326, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 39326 = 2 \cdot 7 \cdot 53^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39326.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,3,1,1,3,-1,1,6,1,6,3,1,-1,3,1,6,6,-3,1,-3,6,0,3,-4,1,9,-1, 6,3,2,1,18,6,-1,6,-6,-3,3,1,-10,-3,8,6,6,0,-12,3,1,-4,18,1,0,9,6,-1,-9, 6,4,3,1,2,-6,1,1,18,2,6,0,-1,3,6,2,-6,-12,-3,-6,3,13,1,9,-10,-12,-3,6, 8,18,6,-4,6,-1,0,6,-12,-3,3,16,1,36,-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: \(314.019690989\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + 3 q^{3} + q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} + 6 q^{9} + q^{10} + 6 q^{11} + 3 q^{12} + q^{13} - q^{14} + 3 q^{15} + q^{16} + 6 q^{17} + 6 q^{18} - 3 q^{19} + q^{20} - 3 q^{21}+ \cdots + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(7\) \( +1 \)
\(53\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.