↑

Properties

Label 24200.2.a.dz
Level $24200$
Weight $2$
Character orbit 24200.a
Self dual yes
Analytic conductor $193.238$
Dimension $8$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [24200,2,Mod(1,24200)] 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("24200.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(24200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 24200 = 2^{3} \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 24200.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,0,0,0,0,2,0,8,0,0,0,0,0,0,0,14,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,18,0,0,0,0,0,0,0,-18,0,-10,0,0,0, 48,0,0,0,0,0,22,0,-4,0,24,0,0,0,0,0,0,0,-20,0,24,0,0,0,-18,0,16,0,4,0, 0,0,0,0,0,0,0,0] 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: \(193.237972891\)
Dimension: \(8\)
Coefficient field: 8.8.149886671104.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 15x^{6} + 64x^{4} - 68x^{2} + 16 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: not computed

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 8 q + 2 q^{7} + 8 q^{9} + 14 q^{17} + 16 q^{43} + 18 q^{49} - 18 q^{57} - 10 q^{59} + 48 q^{63} + 22 q^{69} - 4 q^{71} + 24 q^{73} - 20 q^{81} + 24 q^{83} - 18 q^{87} + 16 q^{89} + 4 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(5\) \( -1 \)
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.