Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [14450,2,Mod(1,14450)] 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("14450.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14450, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 14450 = 2 \cdot 5^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 14450.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,0,1,-2,-1,-2,0,3,-1,-4,2,0,1,0,2,5,0,2,-3,-6,1,0,4, 5,-2,0,0,-2,-1,-3,0,0,-2,-2,-5,4,0,3,-2,-4,3,0,6,12,-1,-3,0,0,-4,6,-5, 0,2,-5,0,0,0,-2,2,4,1,0,3,-13,0,6,0,-12,2,-11,2,0,5,-6,-4,10,0,1,-3,-9, 2,0,4,0,-3,15,0,8,-6,2,-12,0,1,-2,3,-6,0] 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: \(115.383830921\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + q^{6} - 2 q^{7} - q^{8} - 2 q^{9} + 3 q^{11} - q^{12} - 4 q^{13} + 2 q^{14} + q^{16} + 2 q^{18} + 5 q^{19} + 2 q^{21} - 3 q^{22} - 6 q^{23} + q^{24} + 4 q^{26} + 5 q^{27}+ \cdots - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(5\) \( -1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.