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Properties

Label 24843.2.a.d
Level 2484324843
Weight 22
Character orbit 24843.a
Self dual yes
Analytic conductor 198.372198.372
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] = [24843,2,Mod(1,24843)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(24843, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("24843.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 24843=3⋅72⋅132 24843 = 3 \cdot 7^{2} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 24843.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-2,1,2,2,-2,0,0,1,-4,2,2,0,0,2,-4,0,-2,-1,4,0,-4,0,0,-1,0, 1,0,4,-4,-9,8,2,0,0,2,-3,2,0,0,10,0,5,4,2,0,6,-4,0,2,0,0,12,-2,4,0,-1, -8,12,4,10,18,0,-8,0,-4,5,0,0,0,6,0,3,6,-1,-2,0,0,-1,-8,1,-20,-6,0,0,-10, 4,0,-16,-4,0,0,-9,-12,-2,8,6,0,2,-2] 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: 198.372353741198.372353741
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−2q2+q3+2q4+2q5−2q6+q9−4q10+2q11+2q12+2q15−4q16−2q18−q19+4q20−4q22−q25+q27+4q29−4q30−9q31+⋯+2q99+O(q100) q - 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + q^{9} - 4 q^{10} + 2 q^{11} + 2 q^{12} + 2 q^{15} - 4 q^{16} - 2 q^{18} - q^{19} + 4 q^{20} - 4 q^{22} - q^{25} + q^{27} + 4 q^{29} - 4 q^{30} - 9 q^{31}+ \cdots + 2 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
33 −1 -1
77 +1 +1
1313 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.