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Properties

Label 23104.2.a.r
Level 2310423104
Weight 22
Character orbit 23104.a
Self dual yes
Analytic conductor 184.486184.486
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] = [23104,2,Mod(1,23104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23104, 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("23104.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 23104=26⋅192 23104 = 2^{6} \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 23104.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,0,0,0,4,0,-2,0,3,0,2,0,0,0,-6,0,0,0,-4,0,6,0,-5,0,5,0, 0,0,2,0,-3,0,0,0,-10,0,-2,0,-9,0,-4,0,0,0,0,0,9,0,6,0,6,0,0,0,0,0,9,0, 4,0,-8,0,0,0,7,0,-6,0,-6,0,-1,0,5,0,12,0,-4,0,1,0,3,0,0,0,0,0,-6,0,8,0, -2,0,0,0,-17,0,-6,0] 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: 184.486368830184.486368830
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+4q7−2q9+3q11+2q13−6q17−4q21+6q23−5q25+5q27+2q31−3q33−10q37−2q39−9q41−4q43+9q49+6q51+6q53+⋯−6q99+O(q100) q - q^{3} + 4 q^{7} - 2 q^{9} + 3 q^{11} + 2 q^{13} - 6 q^{17} - 4 q^{21} + 6 q^{23} - 5 q^{25} + 5 q^{27} + 2 q^{31} - 3 q^{33} - 10 q^{37} - 2 q^{39} - 9 q^{41} - 4 q^{43} + 9 q^{49} + 6 q^{51} + 6 q^{53}+ \cdots - 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 −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.