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Properties

Label 16272.2.a.cy
Level $16272$
Weight $2$
Character orbit 16272.a
Self dual yes
Analytic conductor $129.933$
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] = [16272,2,Mod(1,16272)] 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("16272.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16272, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 16272 = 2^{4} \cdot 3^{2} \cdot 113 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16272.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [7,0,0,0,3,0,-4,0,0,0,-5,0,5,0,0,0,10,0,-7,0,0,0,2,0,18,0,0,0, 8,0,-24,0,0,0,-5,0,17,0,0,0,2,0,-11,0,0,0,15,0,27,0,0,0,5,0,-12,0,0,0, 11,0,21,0,0,0,-19,0,3,0,0,0,-2,0,10,0,0,0,-6,0,-16,0,0,0,-7,0,1,0,0,0, -3,0,-37,0,0,0,20,0,29,0,0,0] 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: \(129.932574169\)
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: \( x^{7} - 3x^{6} - 22x^{5} + 56x^{4} + 158x^{3} - 342x^{2} - 364x + 696 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 7 q + 3 q^{5} - 4 q^{7} - 5 q^{11} + 5 q^{13} + 10 q^{17} - 7 q^{19} + 2 q^{23} + 18 q^{25} + 8 q^{29} - 24 q^{31} - 5 q^{35} + 17 q^{37} + 2 q^{41} - 11 q^{43} + 15 q^{47} + 27 q^{49} + 5 q^{53} - 12 q^{55}+ \cdots + 29 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(113\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.