↑

Properties

Label 14641.2.a.i
Level $14641$
Weight $2$
Character orbit 14641.a
Self dual yes
Analytic conductor $116.909$
Dimension $90$

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] = [14641,2,Mod(1,14641)] 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("14641.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
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")
 
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 = [90,10,-10,88,-22,-2,2,36,78,-1,0,-28,-1,-50,-47,84,-28,54,-17, -75,-62,0,-67,6,82,-71,-55,-2,-31,-2,-73,17,0,-57,2,52,-32,-72,-2,3,-61, -62,0,0,-79,-2,-116,-33,58,-51,10,1,-69,4,0,-148,-12,-31,-135,-116,27, -97,2,76,153,0,-55,-137,-103,-70,-157,168,46,3,-37,-38,0,-72,10,-183,62, 28,-6,-48,93,-90,-18,0,-121,-210,-114,-164,-75,-46,-6,-197,-12,102,0,81] 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: \(90\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 90 q + 10 q^{2} - 10 q^{3} + 88 q^{4} - 22 q^{5} - 2 q^{6} + 2 q^{7} + 36 q^{8} + 78 q^{9} - q^{10} - 28 q^{12} - q^{13} - 50 q^{14} - 47 q^{15} + 84 q^{16} - 28 q^{17} + 54 q^{18} - 17 q^{19} - 75 q^{20}+ \cdots + 102 q^{98}+O(q^{100}) \) 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.