Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [27945,2,Mod(1,27945)] 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("27945.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27945, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 27945 = 3^{5} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27945.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,2,0,2,-1,0,-2,0,0,-2,-1,0,-3,-4,0,-4,5,0,-4,-2,0,-2,1,0,1, -6,0,-4,4,0,-8,-8,0,10,2,0,2,-8,0,0,-2,0,-8,-2,0,2,6,0,-3,2,0,-6,-3,0, 1,0,0,8,12,0,-12,-16,0,-8,3,0,-4,10,0,4,-2,0,-5,4,0,-8,2,0,4,4,0,-4,9, 0,-5,-16,0,0,-2,0,6,2,0,12,4,0,8,-6,0,2] 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: \(223.141948448\)
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)
 
\(f(q)\) \(=\) \( q + 2 q^{2} + 2 q^{4} - q^{5} - 2 q^{7} - 2 q^{10} - q^{11} - 3 q^{13} - 4 q^{14} - 4 q^{16} + 5 q^{17} - 4 q^{19} - 2 q^{20} - 2 q^{22} + q^{23} + q^{25} - 6 q^{26} - 4 q^{28} + 4 q^{29} - 8 q^{31}+ \cdots - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( +1 \)
\(23\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.