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,-2,0,0,1,1,-2,0,1,0,2,-1,0,2,0,-6,-1,0,-1, -5,2,3,0,-5,-1,0,0,0,-2,8,1,1,0,-6,-2,10,0,0,6,3,1,-3,0,0,1,3,5,0,-2,-1, -3,3,0,-11,5,-4,1,0,0,-2,0,-6,0,-9,2,11,-8,0,-1,0,-1,-8,0,1,6,12,2,0,-10, 3,0,15,0,2,-6,-5,-3,0,-1,-7,3,0,0] 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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{6} + 2 q^{7} - q^{8} - 2 q^{9} + q^{12} + q^{13} - 2 q^{14} + q^{16} + 2 q^{18} - q^{19} + 2 q^{21} - 6 q^{23} - q^{24} - q^{26} - 5 q^{27} + 2 q^{28} + 3 q^{29}+ \cdots + 3 q^{98}+O(q^{100}) \) 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.