↑

Properties

Label 38720.2.a.ba
Level $38720$
Weight $2$
Character orbit 38720.a
Self dual yes
Analytic conductor $309.181$
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] = [38720,2,Mod(1,38720)] 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("38720.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(38720, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 38720 = 2^{6} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38720.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,0,-1,0,3,0,-2,0,0,0,0,0,1,0,8,0,8,0,-3,0,0,0,1,0,5,0, -2,0,-6,0,0,0,-3,0,0,0,0,0,5,0,1,0,2,0,5,0,2,0,-8,0,-8,0,0,0,-8,0,-10, 0,-7,0,-6,0,0,0,-7,0,0,0,14,0,-16,0,-1,0,0,0,-10,0,1,0,-12,0,-8,0,2,0, 9,0,0,0,6,0,-8,0,12,0,0,0] 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: \(309.180756626\)
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)
 
\(f(q)\) \(=\) \( q - q^{3} - q^{5} + 3 q^{7} - 2 q^{9} + q^{15} + 8 q^{17} + 8 q^{19} - 3 q^{21} + q^{25} + 5 q^{27} - 2 q^{29} - 6 q^{31} - 3 q^{35} + 5 q^{41} + q^{43} + 2 q^{45} + 5 q^{47} + 2 q^{49} - 8 q^{51}+ \cdots + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( +1 \)
\(11\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.