↑

Properties

Label 27885.2.a.r
Level $27885$
Weight $2$
Character orbit 27885.a
Self dual yes
Analytic conductor $222.663$
Dimension $1$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [27885,2,Mod(1,27885)] 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("27885.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27885, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 27885 = 3 \cdot 5 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27885.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,-1,1,-1,-5,-3,1,1,1,1,0,-5,-1,-1,0,1,-6,-1,5,1,1,3,1, 0,-1,5,-1,-1,-3,5,-1,0,-5,-1,8,-6,0,-3,-5,5,-1,-1,1,1,-1,1,18,1,0,0,-9, -1,1,15,6,-1,0,1,8,-3,-5,7,0,-1,-2,0,-1,-5,-8,-3,11,8,-1,6,-5,0,10,-1, 1,-5,14,-5,0,-1,1,-3,14,1,0,-1,3,-1,-6,-5,12,18,1,-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: \(222.662846036\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 5 q^{14} - q^{15} - q^{16} + q^{18} - 6 q^{19} - q^{20} + 5 q^{21} + q^{22} + q^{23} + 3 q^{24}+ \cdots + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( -1 \)
\(11\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.