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Properties

Label 23520.2.a.f
Level 2352023520
Weight 22
Character orbit 23520.a
Self dual yes
Analytic conductor 187.808187.808
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] = [23520,2,Mod(1,23520)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23520, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 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("23520.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 23520=25⋅3⋅5⋅72 23520 = 2^{5} \cdot 3 \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 23520.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,0,-1,0,0,0,1,0,-2,0,2,0,1,0,0,0,-4,0,0,0,0,0,1,0,-1,0, -4,0,-6,0,2,0,0,0,-8,0,-2,0,-10,0,10,0,-1,0,6,0,0,0,0,0,10,0,2,0,4,0,12, 0,-14,0,0,0,-2,0,6,0,0,0,-16,0,-2,0,-1,0,0,0,0,0,1,0,0,0,0,0,4,0,-10,0, 0,0,6,0,4,0,2,0,-2,0] 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: 187.808145554187.808145554
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−q3−q5+q9−2q11+2q13+q15−4q19+q25−q27−4q29−6q31+2q33−8q37−2q39−10q41+10q43−q45+6q47+10q53+⋯−2q99+O(q100) q - q^{3} - q^{5} + q^{9} - 2 q^{11} + 2 q^{13} + q^{15} - 4 q^{19} + q^{25} - q^{27} - 4 q^{29} - 6 q^{31} + 2 q^{33} - 8 q^{37} - 2 q^{39} - 10 q^{41} + 10 q^{43} - q^{45} + 6 q^{47} + 10 q^{53}+ \cdots - 2 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 +1 +1
33 +1 +1
55 +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.