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Properties

Label 11466.2.a.q
Level $11466$
Weight $2$
Character orbit 11466.a
Self dual yes
Analytic conductor $91.556$
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] = [11466,2,Mod(1,11466)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11466, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("11466.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 11466 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 11466.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,0,0,0,-1,0,0,3,0,-1,0,0,1,0,0,-2,0,0,-3,3,0,-5,1,0, 0,0,0,-5,-1,0,0,0,0,-7,2,0,0,3,0,8,3,0,-3,-3,0,0,5,0,-1,12,0,0,0,0,0,6, 0,1,5,0,1,0,0,5,0,0,0,-12,0,-11,7,0,-2,0,0,-1,0,0,-3,12,0,0,-8,0,-3,-18, 0,0,3,0,3,0,0,-17,0,0,-5] 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: \(91.5564709576\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{8} + 3 q^{11} - q^{13} + q^{16} - 2 q^{19} - 3 q^{22} + 3 q^{23} - 5 q^{25} + q^{26} - 5 q^{31} - q^{32} - 7 q^{37} + 2 q^{38} + 3 q^{41} + 8 q^{43} + 3 q^{44} - 3 q^{46}+ \cdots - 17 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(7\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.