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Properties

Label 14641.2.a.c
Level $14641$
Weight $2$
Character orbit 14641.a
Self dual yes
Analytic conductor $116.909$
Dimension $35$

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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] = [14641,2,Mod(1,14641)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14641, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("14641.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 14641 = 11^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 14641.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [35,-4,-5,28,-2,6,4,-9,32,-2,0,-23,-4,14,-19,10,-24,-8,-1,-3, -50,0,-29,30,5,-12,-50,17,-18,47,-18,-62,0,-6,46,-20,2,-20,39,56,-23,-7, 11,0,-14,58,-27,-65,-21,-47,36,60,-40,60,0,-50,40,3,-20,14,-68,-62,52, -31,-13,0,4,-58,1,-13,-57,15,26,24,-75,26,0,44,40,-46,-45,-75,53,-86,-1, -33,71,0,-73,-70,-19,1,27,17,71,-61,-51,36,0,-26] 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: \(116.908973599\)
Dimension: \(35\)
Twist minimal: not computed
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.

\(\operatorname{Tr}(f)(q) = \) \( 35 q - 4 q^{2} - 5 q^{3} + 28 q^{4} - 2 q^{5} + 6 q^{6} + 4 q^{7} - 9 q^{8} + 32 q^{9} - 2 q^{10} - 23 q^{12} - 4 q^{13} + 14 q^{14} - 19 q^{15} + 10 q^{16} - 24 q^{17} - 8 q^{18} - q^{19} - 3 q^{20} - 50 q^{21}+ \cdots + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.