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Properties

Label 34272.2.a.dw
Level $34272$
Weight $2$
Character orbit 34272.a
Self dual yes
Analytic conductor $273.663$
Dimension $8$

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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] = [34272,2,Mod(1,34272)] 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("34272.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(34272, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 34272 = 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 34272.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,0,0,1,0,-8,0,0,0,-3,0,-5,0,0,0,8,0,1,0,0,0,9,0,13,0,0,0, -6,0,4,0,0,0,-1,0,2,0,0,0,-3,0,9,0,0,0,4,0,8,0,0,0,-14,0,15,0,0,0,-18, 0,-4,0,0,0,-33,0,8,0,0,0,24,0,-2,0,0,0,3,0,0,0,0,0,-16,0,1,0,0,0,-36,0, 5,0,0,0,45,0,18,0,0,0] 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: \(273.663297807\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} - 22x^{6} + 47x^{5} + 141x^{4} - 122x^{3} - 230x^{2} + 110x + 80 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 8 q + q^{5} - 8 q^{7} - 3 q^{11} - 5 q^{13} + 8 q^{17} + q^{19} + 9 q^{23} + 13 q^{25} - 6 q^{29} + 4 q^{31} - q^{35} + 2 q^{37} - 3 q^{41} + 9 q^{43} + 4 q^{47} + 8 q^{49} - 14 q^{53} + 15 q^{55} - 18 q^{59}+ \cdots + 18 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(7\) \( +1 \)
\(17\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.