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Properties

Label 39326.2.a.bb
Level $39326$
Weight $2$
Character orbit 39326.a
Self dual yes
Analytic conductor $314.020$
Dimension $4$

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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 = [4,-4,1,4,3,-1,4,-4,7,-3,11,1,5,-4,-18,4,2,-7,9,3,1,-11,-2,-1, 1,-5,7,4,5,18,-15,-4,-16,-2,3,7,-5,-9,-11,-3,4,-1,-9,11,-3,2,-10,1,4,-1, 11,5,0,-7,27,-4,21,-5,-1,-18,-22,15,7,4,16,16,-2,2,-7,-3,-33,-7,-6,5,-29, 9,11,11,-28,3,20,-4,-17,1,-9,9,3,-11,-9,3,5,-2,-12,10,-12,-1,-4,-4,11, 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: \(314.019690989\)
Dimension: \(4\)
Coefficient field: 4.4.399092.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 9x^{2} + 5x + 6 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - 4 q^{8} + 7 q^{9} - 3 q^{10} + 11 q^{11} + q^{12} + 5 q^{13} - 4 q^{14} - 18 q^{15} + 4 q^{16} + 2 q^{17} - 7 q^{18} + 9 q^{19} + 3 q^{20}+ \cdots + 11 q^{99}+O(q^{100}) \) 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.