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Properties

Label 22898.2.a.w
Level $22898$
Weight $2$
Character orbit 22898.a
Self dual yes
Analytic conductor $182.841$
Dimension $6$

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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] = [22898,2,Mod(1,22898)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22898, 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("22898.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 22898 = 2 \cdot 107^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 22898.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,-6,-3,6,0,3,6,-6,3,0,-6,-3,9,-6,-3,6,9,-3,3,0,-15,6,-12,3, -6,-9,-12,6,-9,3,-3,-6,-12,-9,6,3,-33,-3,-6,0,18,15,18,-6,-15,12,12,-3, -12,6,-15,9,-9,12,12,-6,3,9,-12,-3,30,3,-3,6,-15,12,-36,9,0,-6,-21,-3, 12,33,-6,3,-12,6,30,0,6,-18,-6,-15,21,-18,18,6,-39,15,30,-12,42,-12,9, 3,3,12,0,-6] 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: \(182.841450548\)
Dimension: \(6\)
Coefficient field: 6.6.1397493.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1 \) Copy content Toggle raw display
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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q - 6 q^{2} - 3 q^{3} + 6 q^{4} + 3 q^{6} + 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{11} - 3 q^{12} + 9 q^{13} - 6 q^{14} - 3 q^{15} + 6 q^{16} + 9 q^{17} - 3 q^{18} + 3 q^{19} - 15 q^{21} + 6 q^{22} - 12 q^{23}+ \cdots + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(107\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.