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Properties

Label 11094.2.a.b
Level $11094$
Weight $2$
Character orbit 11094.a
Self dual yes
Analytic conductor $88.586$
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] = [11094,2,Mod(1,11094)] 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("11094.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11094, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 11094 = 2 \cdot 3 \cdot 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 11094.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,-2,1,2,-1,1,2,-4,-1,2,-2,2,1,-2,-1,4,-2,-2,4,2,1,-1, -2,-1,2,-10,-2,-4,-1,4,2,-4,1,8,-4,-2,2,6,2,0,-4,-2,-2,2,-1,-3,1,2,2,-12, 1,8,-2,-4,10,4,2,8,4,2,1,-4,-4,4,-2,-2,4,0,-1,-10,-8,1,4,-8,2,-8,-2,1, -6,8,-2,4,0,10,4,-6,2,4,2,4,-2,-8,1,14,3,-4,-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: \(88.5860360024\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - q^{8} + q^{9} + 2 q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - 2 q^{14} + 2 q^{15} + q^{16} - 2 q^{17} - q^{18} + 4 q^{19} - 2 q^{20} - 2 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(43\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.