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Properties

Label 15800.2.a.be
Level $15800$
Weight $2$
Character orbit 15800.a
Self dual yes
Analytic conductor $126.164$
Dimension $29$

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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] = [15800,2,Mod(1,15800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15800, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("15800.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 15800 = 2^{3} \cdot 5^{2} \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 15800.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [29,0,6,0,0,0,12,0,29,0,-4,0,22,0,0,0,8,0,-2,0,8,0,6,0,0,0,18, 0,28,0,-10,0,16,0,0,0,20,0,-12,0,2,0,12,0,0,0,18,0,27,0,-4,0,4,0,0,0,20, 0,-16,0,40,0,32,0,0,0,58,0,50,0,-26,0,48,0,0,0,34,0,29,0,29,0,18,0,0,0, 58,0,-4,0,-8,0,28,0,0,0,56,0,-16,0] 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: \(126.163635194\)
Dimension: \(29\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 29 q + 6 q^{3} + 12 q^{7} + 29 q^{9} - 4 q^{11} + 22 q^{13} + 8 q^{17} - 2 q^{19} + 8 q^{21} + 6 q^{23} + 18 q^{27} + 28 q^{29} - 10 q^{31} + 16 q^{33} + 20 q^{37} - 12 q^{39} + 2 q^{41} + 12 q^{43} + 18 q^{47}+ \cdots - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( -1 \)
\(79\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.