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Properties

Label 24200.2.a.ee
Level $24200$
Weight $2$
Character orbit 24200.a
Self dual yes
Analytic conductor $193.238$
Dimension $10$

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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 = [10,0,4,0,0,0,-2,0,8,0,0,0,2,0,0,0,-4,0,-12,0,-10,0,-2,0,0,0, 16,0,-18,0,-6,0,0,0,0,0,-12,0,16,0,0,0,6,0,0,0,10,0,18,0,-16,0,-10,0,0, 0,-4,0,-2,0,-2,0,-38,0,0,0,4,0,18,0,4,0,-16,0,0,0,0,0,-40,0,6,0,0,0,0, 0,-16,0,-6,0,12,0,-18,0,0,0,-12,0,0,0] 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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{9} - 11x^{8} + 52x^{7} + 28x^{6} - 208x^{5} - 9x^{4} + 330x^{3} - 20x^{2} - 180x - 2 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 10 q + 4 q^{3} - 2 q^{7} + 8 q^{9} + 2 q^{13} - 4 q^{17} - 12 q^{19} - 10 q^{21} - 2 q^{23} + 16 q^{27} - 18 q^{29} - 6 q^{31} - 12 q^{37} + 16 q^{39} + 6 q^{43} + 10 q^{47} + 18 q^{49} - 16 q^{51} - 10 q^{53}+ \cdots - 12 q^{97}+O(q^{100}) \) 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.