↑

Properties

Label 22898.2.a.g
Level $22898$
Weight $2$
Character orbit 22898.a
Self dual yes
Analytic conductor $182.841$
Dimension $1$

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] = [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 = [1,1,1,1,4,1,2,1,-2,4,-3,1,-1,2,4,1,-6,-2,1,4,2,-3,-7,1,11,-1, -5,2,-6,4,-4,1,-3,-6,8,-2,-9,1,-1,4,-5,2,-12,-3,-8,-7,8,1,-3,11,-6,-1, 7,-5,-12,2,1,-6,6,4,1,-4,-4,1,-4,-3,10,-6,-7,8,-6,-2,4,-9,11,1,-6,-1,-7, 4,1,-5,4,2,-24,-12,-6,-3,-15,-8,-2,-7,-4,8,4,1,6,-3,6,11] 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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} + 2 q^{7} + q^{8} - 2 q^{9} + 4 q^{10} - 3 q^{11} + q^{12} - q^{13} + 2 q^{14} + 4 q^{15} + q^{16} - 6 q^{17} - 2 q^{18} + q^{19} + 4 q^{20} + 2 q^{21}+ \cdots + 6 q^{99}+O(q^{100}) \) 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.