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Properties

Label 5472.2.e.f
Level $5472$
Weight $2$
Character orbit 5472.e
Analytic conductor $43.694$
Analytic rank $0$
Dimension $24$
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] = [5472,2,Mod(5167,5472)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5472, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("5472.5167");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5472.e (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: \(43.6941399860\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 1368)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{19} - 40 q^{25} - 72 q^{49} + 80 q^{73}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5167.1 0 0 0 − 2.55248i 0 3.08957i 0 0 0
5167.2 0 0 0 2.55248i 0 − 3.08957i 0 0 0
5167.3 0 0 0 − 3.10261i 0 4.34495i 0 0 0
5167.4 0 0 0 3.10261i 0 − 4.34495i 0 0 0
5167.5 0 0 0 − 3.10261i 0 − 4.34495i 0 0 0
5167.6 0 0 0 3.10261i 0 4.34495i 0 0 0
5167.7 0 0 0 − 2.55248i 0 3.08957i 0 0 0
5167.8 0 0 0 2.55248i 0 − 3.08957i 0 0 0
5167.9 0 0 0 − 1.96435i 0 1.25539i 0 0 0
5167.10 0 0 0 1.96435i 0 − 1.25539i 0 0 0
5167.11 0 0 0 − 1.96435i 0 − 1.25539i 0 0 0
5167.12 0 0 0 1.96435i 0 1.25539i 0 0 0
5167.13 0 0 0 − 2.55248i 0 − 3.08957i 0 0 0
5167.14 0 0 0 2.55248i 0 3.08957i 0 0 0
5167.15 0 0 0 − 3.10261i 0 − 4.34495i 0 0 0
5167.16 0 0 0 3.10261i 0 4.34495i 0 0 0
5167.17 0 0 0 − 1.96435i 0 − 1.25539i 0 0 0
5167.18 0 0 0 1.96435i 0 1.25539i 0 0 0
5167.19 0 0 0 − 1.96435i 0 1.25539i 0 0 0
5167.20 0 0 0 1.96435i 0 − 1.25539i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5167.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
8.d odd 2 1 inner
19.b odd 2 1 inner
24.f even 2 1 inner
57.d even 2 1 inner
152.b even 2 1 inner
456.l odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5472.2.e.f 24
3.b odd 2 1 inner 5472.2.e.f 24
4.b odd 2 1 1368.2.e.f ✓ 24
8.b even 2 1 1368.2.e.f ✓ 24
8.d odd 2 1 inner 5472.2.e.f 24
12.b even 2 1 1368.2.e.f ✓ 24
19.b odd 2 1 inner 5472.2.e.f 24
24.f even 2 1 inner 5472.2.e.f 24
24.h odd 2 1 1368.2.e.f ✓ 24
57.d even 2 1 inner 5472.2.e.f 24
76.d even 2 1 1368.2.e.f ✓ 24
152.b even 2 1 inner 5472.2.e.f 24
152.g odd 2 1 1368.2.e.f ✓ 24
228.b odd 2 1 1368.2.e.f ✓ 24
456.l odd 2 1 inner 5472.2.e.f 24
456.p even 2 1 1368.2.e.f ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1368.2.e.f ✓ 24 4.b odd 2 1
1368.2.e.f ✓ 24 8.b even 2 1
1368.2.e.f ✓ 24 12.b even 2 1
1368.2.e.f ✓ 24 24.h odd 2 1
1368.2.e.f ✓ 24 76.d even 2 1
1368.2.e.f ✓ 24 152.g odd 2 1
1368.2.e.f ✓ 24 228.b odd 2 1
1368.2.e.f ✓ 24 456.p even 2 1
5472.2.e.f 24 1.a even 1 1 trivial
5472.2.e.f 24 3.b odd 2 1 inner
5472.2.e.f 24 8.d odd 2 1 inner
5472.2.e.f 24 19.b odd 2 1 inner
5472.2.e.f 24 24.f even 2 1 inner
5472.2.e.f 24 57.d even 2 1 inner
5472.2.e.f 24 152.b even 2 1 inner
5472.2.e.f 24 456.l odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(5472, [\chi])\):

\( T_{5}^{6} + 20T_{5}^{4} + 125T_{5}^{2} + 242 \) Copy content Toggle raw display
\( T_{7}^{6} + 30T_{7}^{4} + 225T_{7}^{2} + 284 \) Copy content Toggle raw display