↑

Properties

Label 11094.2.a.q
Level $11094$
Weight $2$
Character orbit 11094.a
Self dual yes
Analytic conductor $88.586$
Dimension $1$

Related objects

Downloads

Learn more

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,-1,1,5,1,1,-1,1,1,-3,5,-1,1,0,1,7,-1,5,1,-4,1,-4,-3, 1,5,3,-1,-2,1,1,0,-5,1,-2,7,-3,-1,8,5,0,1,-1,-4,7,1,18,-4,0,-3,-12,1,-1, 5,7,3,12,-1,-4,-2,5,1,3,1,6,0,-4,-5,8,1,0,-2,-4,7,5,-3,-10,-1,1,8,-3,5, 0,0,3,1,14,-1,-15,-4,-2,7,-7,1,-7,18,1,-4] 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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 5 q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} - 3 q^{13} + 5 q^{14} - q^{15} + q^{16} + q^{18} + 7 q^{19} - q^{20} + 5 q^{21} + q^{22} - 4 q^{23}+ \cdots + q^{99}+O(q^{100}) \) 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.