Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [35322,2,Mod(1,35322)] 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("35322.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35322, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 35322 = 2 \cdot 3 \cdot 7 \cdot 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35322.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,1,-2,-1,-1,-1,1,2,4,1,6,1,-2,1,-2,-1,4,-2,-1,-4,8,-1, -1,-6,1,-1,0,2,0,-1,4,2,2,1,10,-4,6,2,6,1,4,4,-2,-8,0,1,1,1,-2,6,6,-1, -8,1,4,0,4,-2,-6,0,-1,1,-12,-4,4,-2,8,-2,8,-1,-10,-10,-1,4,-4,-6,0,-2, 1,-6,-4,-1,4,-4,0,-4,6,2,-6,8,0,0,-8,-1,14,-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: \(282.047590020\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 2 q^{10} + 4 q^{11} + q^{12} + 6 q^{13} + q^{14} - 2 q^{15} + q^{16} - 2 q^{17} - q^{18} + 4 q^{19} - 2 q^{20} - q^{21}+ \cdots + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(7\) \( +1 \)
\(29\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.