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Properties

Label 28224.2.a.et
Level 2822428224
Weight 22
Character orbit 28224.a
Self dual yes
Analytic conductor 225.370225.370
Dimension 11

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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] = [28224,2,Mod(1,28224)] 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("28224.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28224, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 28224=26⋅32⋅72 28224 = 2^{6} \cdot 3^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 28224.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,2,0,0,0,0,0,-4,0,-2,0,0,0,2,0,4,0,0,0,-8,0,-1,0,0,0, 6,0,8,0,0,0,0,0,-6,0,0,0,-6,0,4,0,0,0,0,0,0,0,0,0,-2,0,-8,0,0,0,4,0,-2, 0,0,0,-4,0,-4,0,0,0,8,0,-10,0,0,0,0,0,8,0,0,0,-4,0,4,0,0,0,-6,0,0,0,0, 0,8,0,-2,0,0,0] 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: 225.369774665225.369774665
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: not computed
Fricke sign: −1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

qq-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)f(q) == q+2q5−4q11−2q13+2q17+4q19−8q23−q25+6q29+8q31−6q37−6q41+4q43−2q53−8q55+4q59−2q61−4q65−4q67+8q71+⋯−2q97+O(q100) q + 2 q^{5} - 4 q^{11} - 2 q^{13} + 2 q^{17} + 4 q^{19} - 8 q^{23} - q^{25} + 6 q^{29} + 8 q^{31} - 6 q^{37} - 6 q^{41} + 4 q^{43} - 2 q^{53} - 8 q^{55} + 4 q^{59} - 2 q^{61} - 4 q^{65} - 4 q^{67} + 8 q^{71}+ \cdots - 2 q^{97}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 −1 -1
33 −1 -1
77 −1 -1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.