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Properties

Label 5184.2.c.m
Level $5184$
Weight $2$
Character orbit 5184.c
Analytic conductor $41.394$
Analytic rank $0$
Dimension $24$
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] = [5184,2,Mod(5183,5184)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("5184.5183");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.c (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: \(41.3944484078\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 288)
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
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{25} - 24 q^{49} + 24 q^{73} - 24 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5183.1 0 0 0 − 3.93668i 0 − 1.11004i 0 0 0
5183.2 0 0 0 − 3.93668i 0 1.11004i 0 0 0
5183.3 0 0 0 − 3.47695i 0 − 3.60624i 0 0 0
5183.4 0 0 0 − 3.47695i 0 3.60624i 0 0 0
5183.5 0 0 0 − 2.09855i 0 − 0.165946i 0 0 0
5183.6 0 0 0 − 2.09855i 0 0.165946i 0 0 0
5183.7 0 0 0 − 1.94263i 0 − 3.01875i 0 0 0
5183.8 0 0 0 − 1.94263i 0 3.01875i 0 0 0
5183.9 0 0 0 − 0.459724i 0 − 4.94568i 0 0 0
5183.10 0 0 0 − 0.459724i 0 4.94568i 0 0 0
5183.11 0 0 0 − 0.155928i 0 − 0.403315i 0 0 0
5183.12 0 0 0 − 0.155928i 0 0.403315i 0 0 0
5183.13 0 0 0 0.155928i 0 − 0.403315i 0 0 0
5183.14 0 0 0 0.155928i 0 0.403315i 0 0 0
5183.15 0 0 0 0.459724i 0 − 4.94568i 0 0 0
5183.16 0 0 0 0.459724i 0 4.94568i 0 0 0
5183.17 0 0 0 1.94263i 0 − 3.01875i 0 0 0
5183.18 0 0 0 1.94263i 0 3.01875i 0 0 0
5183.19 0 0 0 2.09855i 0 − 0.165946i 0 0 0
5183.20 0 0 0 2.09855i 0 0.165946i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5183.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
4.b odd 2 1 inner
12.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5184.2.c.m 24
3.b odd 2 1 inner 5184.2.c.m 24
4.b odd 2 1 inner 5184.2.c.m 24
8.b even 2 1 2592.2.c.c 24
8.d odd 2 1 2592.2.c.c 24
9.c even 3 1 576.2.s.g 24
9.c even 3 1 1728.2.s.g 24
9.d odd 6 1 576.2.s.g 24
9.d odd 6 1 1728.2.s.g 24
12.b even 2 1 inner 5184.2.c.m 24
24.f even 2 1 2592.2.c.c 24
24.h odd 2 1 2592.2.c.c 24
36.f odd 6 1 576.2.s.g 24
36.f odd 6 1 1728.2.s.g 24
36.h even 6 1 576.2.s.g 24
36.h even 6 1 1728.2.s.g 24
72.j odd 6 1 288.2.s.a ✓ 24
72.j odd 6 1 864.2.s.a 24
72.l even 6 1 288.2.s.a ✓ 24
72.l even 6 1 864.2.s.a 24
72.n even 6 1 288.2.s.a ✓ 24
72.n even 6 1 864.2.s.a 24
72.p odd 6 1 288.2.s.a ✓ 24
72.p odd 6 1 864.2.s.a 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
288.2.s.a ✓ 24 72.j odd 6 1
288.2.s.a ✓ 24 72.l even 6 1
288.2.s.a ✓ 24 72.n even 6 1
288.2.s.a ✓ 24 72.p odd 6 1
576.2.s.g 24 9.c even 3 1
576.2.s.g 24 9.d odd 6 1
576.2.s.g 24 36.f odd 6 1
576.2.s.g 24 36.h even 6 1
864.2.s.a 24 72.j odd 6 1
864.2.s.a 24 72.l even 6 1
864.2.s.a 24 72.n even 6 1
864.2.s.a 24 72.p odd 6 1
1728.2.s.g 24 9.c even 3 1
1728.2.s.g 24 9.d odd 6 1
1728.2.s.g 24 36.f odd 6 1
1728.2.s.g 24 36.h even 6 1
2592.2.c.c 24 8.b even 2 1
2592.2.c.c 24 8.d odd 2 1
2592.2.c.c 24 24.f even 2 1
2592.2.c.c 24 24.h odd 2 1
5184.2.c.m 24 1.a even 1 1 trivial
5184.2.c.m 24 3.b odd 2 1 inner
5184.2.c.m 24 4.b odd 2 1 inner
5184.2.c.m 24 12.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(5184, [\chi])\):

\( T_{5}^{12} + 36T_{5}^{10} + 438T_{5}^{8} + 2092T_{5}^{6} + 3585T_{5}^{4} + 744T_{5}^{2} + 16 \) Copy content Toggle raw display
\( T_{7}^{12} + 48T_{7}^{10} + 726T_{7}^{8} + 3848T_{7}^{6} + 4281T_{7}^{4} + 696T_{7}^{2} + 16 \) Copy content Toggle raw display
\( T_{11}^{12} - 66T_{11}^{10} + 1671T_{11}^{8} - 20524T_{11}^{6} + 128079T_{11}^{4} - 381426T_{11}^{2} + 413449 \) Copy content Toggle raw display