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Properties

Label 24200.2.a.dx
Level $24200$
Weight $2$
Character orbit 24200.a
Self dual yes
Analytic conductor $193.238$
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] = [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,-1,0,0,0,6,0,19,0,0,0,-12,0,0,0,-2,0,-6,0,6,0,-10,0,0,0, -13,0,8,0,19,0,0,0,0,0,-12,0,-21,0,-3,0,8,0,0,0,-10,0,22,0,-7,0,-28,0, 0,0,-25,0,25,0,10,0,64,0,0,0,2,0,18,0,25,0,-38,0,0,0,0,0,-38,0,32,0,28, 0,0,0,-15,0,12,0,8,0,15,0,0,0,-21,0,0,0] 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: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 21x^{6} + 15x^{5} + 140x^{4} - 60x^{3} - 295x^{2} + 50x + 100 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 8 q - q^{3} + 6 q^{7} + 19 q^{9} - 12 q^{13} - 2 q^{17} - 6 q^{19} + 6 q^{21} - 10 q^{23} - 13 q^{27} + 8 q^{29} + 19 q^{31} - 12 q^{37} - 21 q^{39} - 3 q^{41} + 8 q^{43} - 10 q^{47} + 22 q^{49} - 7 q^{51}+ \cdots - 21 q^{97}+O(q^{100}) \) 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.