Properties

Label 28665.2.a.ft
Level $28665$
Weight $2$
Character orbit 28665.a
Self dual yes
Analytic conductor $228.891$
Dimension $24$

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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] = [28665,2,Mod(1,28665)] 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("28665.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28665, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 28665 = 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 28665.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,-4,0,28,24,0,0,-12,0,-4,-16,0,24,0,0,32,-8,0,-24,28,0,0,-40, 0,24,-4,0,0,-16,0,-16,-28,0,-24,0,0,8,-12,0,-12,0,0,16,-40,0,4,-8,0,0, -4,0,28,-24,0,-16,0,0,-8,0,0,-24,-20,0,44,24,0,-24,-24,0,0,-72,0,-8,-80, 0,-48,0,0,8,32,0,0,16,0,-8,-40,0,0,-8,0,0,-80,0,16,-24,0,-24,0,0,28] 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: \(228.891177394\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{2} + 28 q^{4} + 24 q^{5} - 12 q^{8} - 4 q^{10} - 16 q^{11} + 24 q^{13} + 32 q^{16} - 8 q^{17} - 24 q^{19} + 28 q^{20} - 40 q^{23} + 24 q^{25} - 4 q^{26} - 16 q^{29} - 16 q^{31} - 28 q^{32} - 24 q^{34}+ \cdots - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( -1 \)
\(7\) \( +1 \)
\(13\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.