Properties

Label 39326.2.a.bk
Level $39326$
Weight $2$
Character orbit 39326.a
Self dual yes
Analytic conductor $314.020$
Dimension $7$

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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 = [7,-7,1,7,3,-1,-7,-7,6,-3,-3,1,1,7,2,7,4,-6,15,3,-1,3,4,-1,26, -1,-11,-7,11,-2,11,-7,26,-4,-3,6,-13,-15,11,-3,-16,1,-7,-3,23,-4,-6,1, 7,-26,19,1,0,11,1,7,29,-11,-11,2,12,-11,-6,7,-22,-26,-8,4,-15,3,19,-6, 8,13,45,15,3,-11,-16,3,23,16,-17,-1,23,7,-17,3,1,-23,-1,4,46,6,8,-1,-6, -7,5,26] 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: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 13x^{5} + 15x^{4} + 32x^{3} - 42x^{2} + 6x + 4 \) 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.

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