Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [20181,2,Mod(1,20181)] 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("20181.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20181, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 20181 = 3 \cdot 7 \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 20181.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-2,-1,2,4,2,1,0,1,-8,2,-2,1,-2,-4,-4,-4,-2,-7,8,-1,-4,-6,0, 11,-2,-1,2,0,8,0,8,-2,8,4,2,3,14,-1,0,2,2,5,4,4,12,4,4,1,-22,4,2,-2,2, 8,0,7,0,12,-8,-6,0,1,-8,4,4,-4,-8,6,-8,10,0,5,-6,-11,-14,2,2,0,-16,1,-4, -16,-2,-16,-10,0,0,-10,-8,1,-12,0,-8,-28,-8,5,-2,2,22] 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: \(161.146096319\)
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)
 
\(f(q)\) \(=\) \( q - 2 q^{2} - q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + q^{9} - 8 q^{10} + 2 q^{11} - 2 q^{12} + q^{13} - 2 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} - 2 q^{18} - 7 q^{19} + 8 q^{20} - q^{21} - 4 q^{22}+ \cdots + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(7\) \( -1 \)
\(31\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.