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Properties

Label 11048.2.a.b
Level $11048$
Weight $2$
Character orbit 11048.a
Self dual yes
Analytic conductor $88.219$
Dimension $78$
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 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")
 
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);
 
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 = [78,0,0,0,-19,0,-15,0,50,0,-8,0,-46,0,13,0,-40,0,-42,0,-31,0, 24,0,55,0,-9,0,-25,0,-1,0,-57,0,-8,0,-52,0,21,0,-56,0,-27,0,-71,0,36,0, 35,0,-15,0,-25,0,-1,0,-38,0,-33,0,-65,0,-30,0,-40,0,-68,0,-72,0,72,0,-76, 0,-54,0,-58,0,7,0,-2,0,-45,0,-69,0,-11,0,-92,0,-54,0,-16,0,59,0,-88,0, -56,0] 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: \(78\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 78 q - 19 q^{5} - 15 q^{7} + 50 q^{9} - 8 q^{11} - 46 q^{13} + 13 q^{15} - 40 q^{17} - 42 q^{19} - 31 q^{21} + 24 q^{23} + 55 q^{25} - 9 q^{27} - 25 q^{29} - q^{31} - 57 q^{33} - 8 q^{35} - 52 q^{37} + 21 q^{39}+ \cdots - 56 q^{99}+O(q^{100}) \) 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.