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 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);
 
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")
 
Level: \( N \) \(=\) \( 28749 = 3 \cdot 7 \cdot 37^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 28749.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,1,-2,1,0,1,0,1,0,-1,-2,5,0,1,4,2,0,4,-2,1,0,4,0,-4,0,1,-2, -8,0,1,0,-1,0,1,-2,0,0,5,0,-10,0,6,2,1,0,-6,4,1,0,2,-10,-7,0,-1,0,4,0, -9,-2,2,0,1,-8,5,0,-13,-4,4,0,7,0,-14,0,-4,-8,-1,0,-12,4,1,0,14,-2,2,0, -8,0,-11,0,5,-8,1,0,4,0,-17,0,-1,8] 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: \(229.561920771\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-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)
 
\(f(q)\) \(=\) \( q + q^{3} - 2 q^{4} + q^{5} + q^{7} + q^{9} - q^{11} - 2 q^{12} + 5 q^{13} + q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{19} - 2 q^{20} + q^{21} + 4 q^{23} - 4 q^{25} + q^{27} - 2 q^{28} - 8 q^{29} + q^{31}+ \cdots - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(7\) \( -1 \)
\(37\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.