↑

Properties

Label 33856.2.a.s
Level $33856$
Weight $2$
Character orbit 33856.a
Self dual yes
Analytic conductor $270.342$
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] = [33856,2,Mod(1,33856)] 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("33856.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33856, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 33856 = 2^{6} \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 33856.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,-2,0,0,0,-3,0,0,0,-6,0,0,0,-2,0,0,0,0,0,0,0,-1,0,0,0, 10,0,0,0,0,0,0,0,-2,0,0,0,10,0,0,0,6,0,0,0,-7,0,0,0,14,0,0,0,0,0,0,0,-10, 0,0,0,12,0,0,0,0,0,0,0,-6,0,0,0,0,0,0,0,9,0,0,0,4,0,0,0,-10,0,0,0,0,0, 0,0,-18,0,0,0] 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: \(270.341521083\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: not computed

$q$-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)
 
\(f(q)\) \(=\) \( q - 2 q^{5} - 3 q^{9} - 6 q^{13} - 2 q^{17} - q^{25} + 10 q^{29} - 2 q^{37} + 10 q^{41} + 6 q^{45} - 7 q^{49} + 14 q^{53} - 10 q^{61} + 12 q^{65} - 6 q^{73} + 9 q^{81} + 4 q^{85} - 10 q^{89} - 18 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(23\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.