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Properties

Label 15800.2.a.z
Level $15800$
Weight $2$
Character orbit 15800.a
Self dual yes
Analytic conductor $126.164$
Dimension $22$

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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 = [22,0,-4,0,0,0,-1,0,24,0,4,0,5,0,0,0,-2,0,14,0,9,0,-13,0,0,0, -19,0,8,0,24,0,-6,0,0,0,5,0,7,0,18,0,-5,0,0,0,-16,0,37,0,17,0,29,0,0,0, -18,0,15,0,18,0,11,0,0,0,-20,0,16,0,18,0,5,0,0,0,43,0,22,0,46,0,5,0,0, 0,-52,0,15,0,13,0,29,0,0,0,-1,0,37,0] 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: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 4 q^{3} - q^{7} + 24 q^{9} + 4 q^{11} + 5 q^{13} - 2 q^{17} + 14 q^{19} + 9 q^{21} - 13 q^{23} - 19 q^{27} + 8 q^{29} + 24 q^{31} - 6 q^{33} + 5 q^{37} + 7 q^{39} + 18 q^{41} - 5 q^{43} - 16 q^{47}+ \cdots + 37 q^{99}+O(q^{100}) \) 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.