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Properties

Label 20691.2.a.r
Level 2069120691
Weight 22
Character orbit 20691.a
Self dual yes
Analytic conductor 165.218165.218
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] = [20691,2,Mod(1,20691)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20691, 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("20691.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 20691=32⋅112⋅19 20691 = 3^{2} \cdot 11^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 20691.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,2,0,2,0,0,2,0,0,0,0,0,5,4,0,-4,-3,0,-1,0,0,0,-6,0,-5,10,0, 4,8,0,-2,-8,0,-6,0,0,-8,-2,0,0,2,0,-2,0,0,-12,4,0,-3,-10,0,10,-3,0,0,0, 0,16,-13,0,2,-4,0,-8,0,0,2,-6,0,0,-7,0,14,-16,0,-2,0,0,-11,0,0,4,-9,0, 0,-4,0,0,-13,0,10,-12,0,8,0,0,-18,-6,0,-10] 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: 165.218466822165.218466822
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+2q4+2q7+5q13+4q14−4q16−3q17−q19−6q23−5q25+10q26+4q28+8q29−2q31−8q32−6q34−8q37−2q38+2q41+⋯−6q98+O(q100) q + 2 q^{2} + 2 q^{4} + 2 q^{7} + 5 q^{13} + 4 q^{14} - 4 q^{16} - 3 q^{17} - q^{19} - 6 q^{23} - 5 q^{25} + 10 q^{26} + 4 q^{28} + 8 q^{29} - 2 q^{31} - 8 q^{32} - 6 q^{34} - 8 q^{37} - 2 q^{38} + 2 q^{41}+ \cdots - 6 q^{98}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
33 +1 +1
1111 +1 +1
1919 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.