Properties

Label 28749.2.a.a
Level 2874928749
Weight 22
Character orbit 28749.a
Self dual yes
Analytic conductor 229.562229.562
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] = [28749,2,Mod(1,28749)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28749, 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("28749.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 28749=37372 28749 = 3 \cdot 7 \cdot 37^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 28749.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,-1,2,1,-1,3,1,-2,4,1,-2,1,-2,-1,-2,-1,-4,-2,1,-4,0,-3, -1,2,-1,1,-10,2,0,-5,-4,2,-2,-1,0,4,2,6,-6,-1,-8,-4,2,0,0,1,1,1,2,2,14, 1,8,-3,4,10,8,2,14,0,-1,7,-4,4,-12,2,0,2,8,3,10,0,1,4,-4,-2,-4,-2,1,6, 12,-1,-4,8,10,12,14,-2,2,0,0,0,-8,5,-6,-1,4,1] 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: 229.561920771229.561920771
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) == qq2q3q4+2q5+q6q7+3q8+q92q10+4q11+q122q13+q142q15q162q17q184q192q20+q21++4q99+O(q100) q - q^{2} - q^{3} - q^{4} + 2 q^{5} + q^{6} - q^{7} + 3 q^{8} + q^{9} - 2 q^{10} + 4 q^{11} + q^{12} - 2 q^{13} + q^{14} - 2 q^{15} - q^{16} - 2 q^{17} - q^{18} - 4 q^{19} - 2 q^{20} + q^{21}+ \cdots + 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
33 +1 +1
77 +1 +1
3737 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.