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Properties

Label 24200.2.a.e
Level $24200$
Weight $2$
Character orbit 24200.a
Self dual yes
Analytic conductor $193.238$
Dimension $1$

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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 = [1,0,-2,0,0,0,4,0,1,0,0,0,-6,0,0,0,2,0,-4,0,-8,0,-6,0,0,0,4,0, 2,0,8,0,0,0,0,0,8,0,12,0,-6,0,12,0,0,0,-10,0,9,0,-4,0,0,0,0,0,8,0,-4,0, 10,0,4,0,0,0,-2,0,12,0,-8,0,2,0,0,0,0,0,-4,0,-11,0,-4,0,0,0,-4,0,-14,0, -24,0,-16,0,0,0,4,0,0,0] 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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - 2 q^{3} + 4 q^{7} + q^{9} - 6 q^{13} + 2 q^{17} - 4 q^{19} - 8 q^{21} - 6 q^{23} + 4 q^{27} + 2 q^{29} + 8 q^{31} + 8 q^{37} + 12 q^{39} - 6 q^{41} + 12 q^{43} - 10 q^{47} + 9 q^{49} - 4 q^{51} + 8 q^{57}+ \cdots + 4 q^{97}+O(q^{100}) \) 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.