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Properties

Label 20070.2.a.bh
Level 2007020070
Weight 22
Character orbit 20070.a
Self dual yes
Analytic conductor 160.260160.260
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] = [20070,2,Mod(1,20070)] 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("20070.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20070, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 20070=2⋅32⋅5⋅223 20070 = 2 \cdot 3^{2} \cdot 5 \cdot 223
Weight: k k == 2 2
Character orbit: [χ][\chi] == 20070.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,0,1,1,0,1,1,0,1,0,0,2,1,0,1,3,0,-5,1,0,0,0,0,1,2,0,1,-5, 0,0,1,0,3,1,0,-5,-5,0,1,-10,0,-8,0,0,0,-10,0,-6,1,0,2,4,0,0,1,0,-5,-13, 0,-11,0,0,1,2,0,3,3,0,1,8,0,8,-5,0,-5,0,0,-13,1,0,-10,-11,0,3,-8,0,0,-10, 0,2,0,0,-10,-5,0,7,-6,0,1] 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: 160.259756857160.259756857
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+q2+q4+q5+q7+q8+q10+2q13+q14+q16+3q17−5q19+q20+q25+2q26+q28−5q29+q32+3q34+q35−5q37+⋯−6q98+O(q100) q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + 2 q^{13} + q^{14} + q^{16} + 3 q^{17} - 5 q^{19} + q^{20} + q^{25} + 2 q^{26} + q^{28} - 5 q^{29} + q^{32} + 3 q^{34} + q^{35} - 5 q^{37}+ \cdots - 6 q^{98}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 −1 -1
33 +1 +1
55 −1 -1
223223 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.