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Properties

Label 28665.2.a.s
Level $28665$
Weight $2$
Character orbit 28665.a
Self dual yes
Analytic conductor $228.891$
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] = [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 = [1,-1,0,-1,1,0,0,3,0,-1,3,0,1,0,0,-1,-3,0,-6,-1,0,-3,-7,0,1,-1, 0,0,10,0,-4,-5,0,3,0,0,5,6,0,3,-1,0,-8,-3,0,7,-6,0,0,-1,0,-1,10,0,3,0, 0,-10,9,0,-2,4,0,7,1,0,11,3,0,0,0,0,-15,-5,0,6,0,0,5,-1,0,1,4,0,-3,8,0, 9,-7,0,0,7,0,6,-6,0,7,0,0,-1] 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: \(1\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{4} + q^{5} + 3 q^{8} - q^{10} + 3 q^{11} + q^{13} - q^{16} - 3 q^{17} - 6 q^{19} - q^{20} - 3 q^{22} - 7 q^{23} + q^{25} - q^{26} + 10 q^{29} - 4 q^{31} - 5 q^{32} + 3 q^{34} + 5 q^{37}+ \cdots + 7 q^{97}+O(q^{100}) \) 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.