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Properties

Label 11011.2.a.f
Level $11011$
Weight $2$
Character orbit 11011.a
Self dual yes
Analytic conductor $87.923$
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] = [11011,2,Mod(1,11011)] 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("11011.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11011, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 11011 = 7 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 11011.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-2,-2,-3,0,-1,0,1,0,0,4,-1,0,6,4,6,0,7,6,2,0,3,0,4,0,4,2, 9,0,5,0,0,0,3,-2,2,0,2,0,6,0,1,0,-3,0,3,-8,1,0,-12,2,-9,0,0,0,-14,0,0, -12,10,0,-1,-8,3,0,14,-12,-6,0,-6,0,-11,0,-8,-14,0,0,1,-12,-11,0,-3,-4, -18,0,-18,0,15,0,1,-6,-10,0,-21,0,-1,0,0,-8] 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: \(87.9232776656\)
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)
 
\(f(q)\) \(=\) \( q - 2 q^{3} - 2 q^{4} - 3 q^{5} - q^{7} + q^{9} + 4 q^{12} - q^{13} + 6 q^{15} + 4 q^{16} + 6 q^{17} + 7 q^{19} + 6 q^{20} + 2 q^{21} + 3 q^{23} + 4 q^{25} + 4 q^{27} + 2 q^{28} + 9 q^{29} + 5 q^{31}+ \cdots - q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(7\) \( +1 \)
\(11\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.