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Properties

Label 11048.2.a.d
Level $11048$
Weight $2$
Character orbit 11048.a
Self dual yes
Analytic conductor $88.219$
Dimension $86$
CM no
Inner twists $1$

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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] = [11048,2,Mod(1,11048)] 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("11048.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11048, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 11048 = 2^{3} \cdot 1381 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 11048.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [86,0,7,0,-6,0,34,0,75,0,5,0,32,0,38,0,-5,0,39,0,2,0,42,0,86, 0,31,0,-10,0,63,0,30,0,16,0,30,0,59,0,-20,0,50,0,1,0,89,0,82,0,39,0,-11, 0,88,0,25,0,20,0,27,0,108,0,-18,0,68,0,-4,0,85,0,46,0,32,0,-14,0,88,0, 30,0,35,0,40,0,113,0,-24,0,60,0,21,0,87,0,71,0,50,0] 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: \(88.2187241531\)
Dimension: \(86\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 86 q + 7 q^{3} - 6 q^{5} + 34 q^{7} + 75 q^{9} + 5 q^{11} + 32 q^{13} + 38 q^{15} - 5 q^{17} + 39 q^{19} + 2 q^{21} + 42 q^{23} + 86 q^{25} + 31 q^{27} - 10 q^{29} + 63 q^{31} + 30 q^{33} + 16 q^{35} + 30 q^{37}+ \cdots + 50 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(1381\) \( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.