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Properties

Label 22253.2.a.e
Level $22253$
Weight $2$
Character orbit 22253.a
Self dual yes
Analytic conductor $177.691$
Dimension $1$

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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] = [22253,2,Mod(1,22253)] 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("22253.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22253, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 22253 = 7 \cdot 11 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 22253.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,-2,-3,0,-1,0,-2,0,1,2,-4,0,3,4,0,0,2,6,1,0,-3,0,4,0,5, 2,6,0,-5,0,-1,0,3,4,-11,0,4,0,-6,0,8,-2,6,0,0,-4,1,0,0,8,-6,0,-3,0,-2, 0,-9,-6,10,0,2,-8,12,0,5,0,3,0,-9,0,-2,0,-4,-4,-1,0,10,-12,1,0,12,-2,0, 0,-6,0,-3,0,4,6,5,0,-6,0,1,0,-2,-8] 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: \(177.691099618\)
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)
 
\(f(q)\) \(=\) \( q - q^{3} - 2 q^{4} - 3 q^{5} - q^{7} - 2 q^{9} + q^{11} + 2 q^{12} - 4 q^{13} + 3 q^{15} + 4 q^{16} + 2 q^{19} + 6 q^{20} + q^{21} - 3 q^{23} + 4 q^{25} + 5 q^{27} + 2 q^{28} + 6 q^{29} - 5 q^{31}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(7\) \( +1 \)
\(11\) \( -1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.