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Properties

Label 5148.2.p.a
Level $5148$
Weight $2$
Character orbit 5148.p
Analytic conductor $41.107$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5148,2,Mod(2573,5148)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5148, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5148.2573");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5148.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: \(41.1069869606\)
Analytic rank: \(0\)
Dimension: \(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 56 q + 72 q^{25} + 72 q^{49} + 32 q^{55} + 48 q^{91}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2573.1 0 0 0 −4.24278 0 1.98844 0 0 0
2573.2 0 0 0 −4.24278 0 −1.98844 0 0 0
2573.3 0 0 0 −4.24278 0 −1.98844 0 0 0
2573.4 0 0 0 −4.24278 0 1.98844 0 0 0
2573.5 0 0 0 −3.40820 0 −0.847800 0 0 0
2573.6 0 0 0 −3.40820 0 0.847800 0 0 0
2573.7 0 0 0 −3.40820 0 0.847800 0 0 0
2573.8 0 0 0 −3.40820 0 −0.847800 0 0 0
2573.9 0 0 0 −2.26527 0 4.54395 0 0 0
2573.10 0 0 0 −2.26527 0 −4.54395 0 0 0
2573.11 0 0 0 −2.26527 0 −4.54395 0 0 0
2573.12 0 0 0 −2.26527 0 4.54395 0 0 0
2573.13 0 0 0 −2.26470 0 −3.98215 0 0 0
2573.14 0 0 0 −2.26470 0 3.98215 0 0 0
2573.15 0 0 0 −2.26470 0 3.98215 0 0 0
2573.16 0 0 0 −2.26470 0 −3.98215 0 0 0
2573.17 0 0 0 −1.50333 0 −0.372487 0 0 0
2573.18 0 0 0 −1.50333 0 0.372487 0 0 0
2573.19 0 0 0 −1.50333 0 0.372487 0 0 0
2573.20 0 0 0 −1.50333 0 −0.372487 0 0 0
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2573.56
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
11.b odd 2 1 inner
13.b even 2 1 inner
33.d even 2 1 inner
39.d odd 2 1 inner
143.d odd 2 1 inner
429.e even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5148.2.p.a ✓ 56
3.b odd 2 1 inner 5148.2.p.a ✓ 56
11.b odd 2 1 inner 5148.2.p.a ✓ 56
13.b even 2 1 inner 5148.2.p.a ✓ 56
33.d even 2 1 inner 5148.2.p.a ✓ 56
39.d odd 2 1 inner 5148.2.p.a ✓ 56
143.d odd 2 1 inner 5148.2.p.a ✓ 56
429.e even 2 1 inner 5148.2.p.a ✓ 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5148.2.p.a ✓ 56 1.a even 1 1 trivial
5148.2.p.a ✓ 56 3.b odd 2 1 inner
5148.2.p.a ✓ 56 11.b odd 2 1 inner
5148.2.p.a ✓ 56 13.b even 2 1 inner
5148.2.p.a ✓ 56 33.d even 2 1 inner
5148.2.p.a ✓ 56 39.d odd 2 1 inner
5148.2.p.a ✓ 56 143.d odd 2 1 inner
5148.2.p.a ✓ 56 429.e even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(5148, [\chi])\).