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,-5,1,-2,0,-4,1,-3,-5,0,1,0,-2,-2,0,-5,-4,-8,1,0, -3,-5,-5,0,0,5,1,-4,0,0,-2,-12,-2,-3,0,10,-5,4,-4,0,-8,2,1,18,0,0,-3,1, -5,0,-5,-2,0,0,0,-2,5,10,1,0,-4,-8,0,-8,0,-5,-2,4,-12,0,-2,20,-3,17,0, 1,10,16,-5,0,4,0,-4,-6,0,15,-8,5,2,0,1,16,18,8,0] 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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} - 5 q^{7} + q^{8} - 2 q^{9} - 4 q^{11} + q^{12} - 3 q^{13} - 5 q^{14} + q^{16} - 2 q^{18} - 2 q^{19} - 5 q^{21} - 4 q^{22} - 8 q^{23} + q^{24} - 3 q^{26} - 5 q^{27}+ \cdots + 8 q^{99}+O(q^{100}) \) 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.