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Properties

Label 39326.2.a.q
Level $39326$
Weight $2$
Character orbit 39326.a
Self dual yes
Analytic conductor $314.020$
Dimension $2$

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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 = [2,2,2,2,0,2,2,2,0,0,-8,2,2,2,4,2,-10,0,-2,0,2,-8,-2,2,-6,2,2, 2,-2,4,-12,2,-4,-10,0,0,2,-2,18,0,12,2,-12,-8,8,-2,4,2,2,-6,-14,2,0,2, 4,2,-14,-2,4,4,16,-12,0,2,16,-4,20,-10,-14,0,-2,0,16,2,-6,-2,-8,18,-14, 0,-2,12,18,2,-4,-12,-14,-8,12,8,2,-2,-12,4,-12,2,-6,2,8,-6] 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: \(2\)
Coefficient field: \(\Q(\sqrt{2}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} + 2 q^{8} - 8 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} + 4 q^{15} + 2 q^{16} - 10 q^{17} - 2 q^{19} + 2 q^{21} - 8 q^{22} - 2 q^{23} + 2 q^{24} - 6 q^{25}+ \cdots + 8 q^{99}+O(q^{100}) \) 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.