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Properties

Label 5796.2.p.a
Level $5796$
Weight $2$
Character orbit 5796.p
Analytic conductor $46.281$
Analytic rank $0$
Dimension $48$
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] = [5796,2,Mod(3725,5796)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5796, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5796.3725");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5796.p (of order \(2\), degree \(1\), 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: \(46.2812930115\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 16 q^{13} + 48 q^{25} - 32 q^{31} - 48 q^{49} - 16 q^{55} - 16 q^{73} - 80 q^{85}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3725.1 0 0 0 −4.21550 0 1.00000i 0 0 0
3725.2 0 0 0 −4.21550 0 − 1.00000i 0 0 0
3725.3 0 0 0 −3.71379 0 1.00000i 0 0 0
3725.4 0 0 0 −3.71379 0 − 1.00000i 0 0 0
3725.5 0 0 0 −2.91840 0 1.00000i 0 0 0
3725.6 0 0 0 −2.91840 0 − 1.00000i 0 0 0
3725.7 0 0 0 −2.84983 0 − 1.00000i 0 0 0
3725.8 0 0 0 −2.84983 0 1.00000i 0 0 0
3725.9 0 0 0 −2.58292 0 1.00000i 0 0 0
3725.10 0 0 0 −2.58292 0 − 1.00000i 0 0 0
3725.11 0 0 0 −2.52995 0 − 1.00000i 0 0 0
3725.12 0 0 0 −2.52995 0 1.00000i 0 0 0
3725.13 0 0 0 −2.38433 0 − 1.00000i 0 0 0
3725.14 0 0 0 −2.38433 0 1.00000i 0 0 0
3725.15 0 0 0 −1.46900 0 1.00000i 0 0 0
3725.16 0 0 0 −1.46900 0 − 1.00000i 0 0 0
3725.17 0 0 0 −1.46646 0 − 1.00000i 0 0 0
3725.18 0 0 0 −1.46646 0 1.00000i 0 0 0
3725.19 0 0 0 −0.794278 0 − 1.00000i 0 0 0
3725.20 0 0 0 −0.794278 0 1.00000i 0 0 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3725.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
23.b odd 2 1 inner
69.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5796.2.p.a ✓ 48
3.b odd 2 1 inner 5796.2.p.a ✓ 48
23.b odd 2 1 inner 5796.2.p.a ✓ 48
69.c even 2 1 inner 5796.2.p.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5796.2.p.a ✓ 48 1.a even 1 1 trivial
5796.2.p.a ✓ 48 3.b odd 2 1 inner
5796.2.p.a ✓ 48 23.b odd 2 1 inner
5796.2.p.a ✓ 48 69.c even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(5796, [\chi])\).