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Properties

Label 2592.3.h.a
Level $2592$
Weight $3$
Character orbit 2592.h
Analytic conductor $70.627$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2592,3,Mod(1457,2592)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2592, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2592.1457");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2592.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(70.6268845222\)
Analytic rank: \(0\)
Dimension: \(44\)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q - 4 q^{7} + 144 q^{25} - 4 q^{31} + 144 q^{49} - 92 q^{55} - 8 q^{73} - 4 q^{79} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1457.1 0 0 0 −8.56180 0 −7.51600 0 0 0
1457.2 0 0 0 −8.56180 0 −7.51600 0 0 0
1457.3 0 0 0 −7.97647 0 11.2970 0 0 0
1457.4 0 0 0 −7.97647 0 11.2970 0 0 0
1457.5 0 0 0 −7.29297 0 −0.974251 0 0 0
1457.6 0 0 0 −7.29297 0 −0.974251 0 0 0
1457.7 0 0 0 −6.95397 0 4.59069 0 0 0
1457.8 0 0 0 −6.95397 0 4.59069 0 0 0
1457.9 0 0 0 −5.81548 0 −0.726764 0 0 0
1457.10 0 0 0 −5.81548 0 −0.726764 0 0 0
1457.11 0 0 0 −3.79077 0 −11.4149 0 0 0
1457.12 0 0 0 −3.79077 0 −11.4149 0 0 0
1457.13 0 0 0 −3.28777 0 −9.88862 0 0 0
1457.14 0 0 0 −3.28777 0 −9.88862 0 0 0
1457.15 0 0 0 −3.06253 0 −1.44096 0 0 0
1457.16 0 0 0 −3.06253 0 −1.44096 0 0 0
1457.17 0 0 0 −1.38604 0 −1.12598 0 0 0
1457.18 0 0 0 −1.38604 0 −1.12598 0 0 0
1457.19 0 0 0 −1.32371 0 9.78668 0 0 0
1457.20 0 0 0 −1.32371 0 9.78668 0 0 0
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1457.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
8.b even 2 1 inner
24.h odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2592.3.h.a 44
3.b odd 2 1 inner 2592.3.h.a 44
4.b odd 2 1 648.3.h.a 44
8.b even 2 1 inner 2592.3.h.a 44
8.d odd 2 1 648.3.h.a 44
9.c even 3 1 288.3.n.a 44
9.c even 3 1 864.3.n.a 44
9.d odd 6 1 288.3.n.a 44
9.d odd 6 1 864.3.n.a 44
12.b even 2 1 648.3.h.a 44
24.f even 2 1 648.3.h.a 44
24.h odd 2 1 inner 2592.3.h.a 44
36.f odd 6 1 72.3.j.a ✓ 44
36.f odd 6 1 216.3.j.a 44
36.h even 6 1 72.3.j.a ✓ 44
36.h even 6 1 216.3.j.a 44
72.j odd 6 1 288.3.n.a 44
72.j odd 6 1 864.3.n.a 44
72.l even 6 1 72.3.j.a ✓ 44
72.l even 6 1 216.3.j.a 44
72.n even 6 1 288.3.n.a 44
72.n even 6 1 864.3.n.a 44
72.p odd 6 1 72.3.j.a ✓ 44
72.p odd 6 1 216.3.j.a 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
72.3.j.a ✓ 44 36.f odd 6 1
72.3.j.a ✓ 44 36.h even 6 1
72.3.j.a ✓ 44 72.l even 6 1
72.3.j.a ✓ 44 72.p odd 6 1
216.3.j.a 44 36.f odd 6 1
216.3.j.a 44 36.h even 6 1
216.3.j.a 44 72.l even 6 1
216.3.j.a 44 72.p odd 6 1
288.3.n.a 44 9.c even 3 1
288.3.n.a 44 9.d odd 6 1
288.3.n.a 44 72.j odd 6 1
288.3.n.a 44 72.n even 6 1
648.3.h.a 44 4.b odd 2 1
648.3.h.a 44 8.d odd 2 1
648.3.h.a 44 12.b even 2 1
648.3.h.a 44 24.f even 2 1
864.3.n.a 44 9.c even 3 1
864.3.n.a 44 9.d odd 6 1
864.3.n.a 44 72.j odd 6 1
864.3.n.a 44 72.n even 6 1
2592.3.h.a 44 1.a even 1 1 trivial
2592.3.h.a 44 3.b odd 2 1 inner
2592.3.h.a 44 8.b even 2 1 inner
2592.3.h.a 44 24.h odd 2 1 inner