↑

Properties

Label 35557.2.a.b
Level $35557$
Weight $2$
Character orbit 35557.a
Self dual yes
Analytic conductor $283.924$
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] = [35557,2,Mod(1,35557)] 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("35557.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35557, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 35557 = 31^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35557.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-2,3,2,-2,-6,-1,0,6,4,5,6,2,2,-6,-4,0,-12,0,-4,-3,-10,-2,0, -1,-4,9,-2,-6,12,0,8,15,0,2,12,1,0,6,0,-9,6,-2,10,-12,4,-9,-12,-6,2,0, 4,-1,-18,-10,0,0,12,8,-12,8,0,-6,-8,-4,-30,8,0,-6,-4,9,0,1,-2,-3,0,-5, -12,-4,8,9,18,15,-6,0,4,-18,0,-4,24,-2,-4,0,18,0,24,4,12,30,-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: \(283.924074467\)
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)
 
\(f(q)\) \(=\) \( q - 2 q^{2} + 3 q^{3} + 2 q^{4} - 2 q^{5} - 6 q^{6} - q^{7} + 6 q^{9} + 4 q^{10} + 5 q^{11} + 6 q^{12} + 2 q^{13} + 2 q^{14} - 6 q^{15} - 4 q^{16} - 12 q^{18} - 4 q^{20} - 3 q^{21} - 10 q^{22} - 2 q^{23}+ \cdots + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(31\) \( -1 \)
\(37\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.