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Properties

Label 22898.2.a.bf
Level $22898$
Weight $2$
Character orbit 22898.a
Self dual yes
Analytic conductor $182.841$
Dimension $45$

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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 = [45,45,0,45,-9,0,-18,45,63,-9,-9,0,-9,-18,-18,45,-27,63,-9,-9, -18,-9,-18,0,54,-9,-27,-18,-54,-18,-36,45,-63,-27,-18,63,-27,-9,-63,-9, -27,-18,-63,-9,-45,-18,-27,0,45,54,-18,-9,-45,-27,-27,-18,-9,-54,-9,-18, -27,-36,-81,45,-45,-63,-63,-27,-54,-18,-18,63,-99,-27,-54,-9,-45,-63,0, -9,117,-27,-72,-18,-18,-63,-27,-9,-63,-45,-63,-18,-9,-27,-90,0,-108,45, -117,54] 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: \(45\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 45 q + 45 q^{2} + 45 q^{4} - 9 q^{5} - 18 q^{7} + 45 q^{8} + 63 q^{9} - 9 q^{10} - 9 q^{11} - 9 q^{13} - 18 q^{14} - 18 q^{15} + 45 q^{16} - 27 q^{17} + 63 q^{18} - 9 q^{19} - 9 q^{20} - 18 q^{21} - 9 q^{22}+ \cdots - 117 q^{99}+O(q^{100}) \) 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.