Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [25215,2,Mod(1,25215)] 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("25215.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25215, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 25215 = 3 \cdot 5 \cdot 41^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 25215.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,-1,1,-1,4,-3,1,1,0,1,-4,4,-1,-1,4,1,0,-1,-4,0,0,3,1,-4, -1,-4,-8,-1,-8,5,0,4,4,-1,-6,0,4,-3,0,-4,12,0,1,0,4,1,9,1,-4,4,-12,-1, 0,-12,0,-8,4,1,-14,-8,4,7,-4,0,12,-4,0,4,-8,-3,10,-6,-1,0,0,4,8,-1,1,0, 4,4,4,12,8,0,-8,1,-16,0,8,4,0,-5,12,9,0,-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: \(201.342788697\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} + 4 q^{7} - 3 q^{8} + q^{9} + q^{10} + q^{12} - 4 q^{13} + 4 q^{14} - q^{15} - q^{16} + 4 q^{17} + q^{18} - q^{20} - 4 q^{21} + 3 q^{24} + q^{25}+ \cdots + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( -1 \)
\(41\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.