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Properties

Label 2448.2.o.d
Level $2448$
Weight $2$
Character orbit 2448.o
Analytic conductor $19.547$
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] = [2448,2,Mod(2447,2448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2448, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 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("2448.2447");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2448.o (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: \(19.5473784148\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 8 q^{13} + 16 q^{25} + 8 q^{49} + 8 q^{85}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2447.1 0 0 0 −3.75696 0 −3.40219 0 0 0
2447.2 0 0 0 −3.75696 0 3.40219 0 0 0
2447.3 0 0 0 −3.75696 0 3.40219 0 0 0
2447.4 0 0 0 −3.75696 0 −3.40219 0 0 0
2447.5 0 0 0 −1.52982 0 −3.07186 0 0 0
2447.6 0 0 0 −1.52982 0 3.07186 0 0 0
2447.7 0 0 0 −1.52982 0 3.07186 0 0 0
2447.8 0 0 0 −1.52982 0 −3.07186 0 0 0
2447.9 0 0 0 −0.738173 0 −0.994380 0 0 0
2447.10 0 0 0 −0.738173 0 0.994380 0 0 0
2447.11 0 0 0 −0.738173 0 0.994380 0 0 0
2447.12 0 0 0 −0.738173 0 −0.994380 0 0 0
2447.13 0 0 0 0.738173 0 0.994380 0 0 0
2447.14 0 0 0 0.738173 0 −0.994380 0 0 0
2447.15 0 0 0 0.738173 0 −0.994380 0 0 0
2447.16 0 0 0 0.738173 0 0.994380 0 0 0
2447.17 0 0 0 1.52982 0 3.07186 0 0 0
2447.18 0 0 0 1.52982 0 −3.07186 0 0 0
2447.19 0 0 0 1.52982 0 −3.07186 0 0 0
2447.20 0 0 0 1.52982 0 3.07186 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2447.24
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
17.b even 2 1 inner
51.c odd 2 1 inner
68.d odd 2 1 inner
204.h even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2448.2.o.d ✓ 24
3.b odd 2 1 inner 2448.2.o.d ✓ 24
4.b odd 2 1 inner 2448.2.o.d ✓ 24
12.b even 2 1 inner 2448.2.o.d ✓ 24
17.b even 2 1 inner 2448.2.o.d ✓ 24
51.c odd 2 1 inner 2448.2.o.d ✓ 24
68.d odd 2 1 inner 2448.2.o.d ✓ 24
204.h even 2 1 inner 2448.2.o.d ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2448.2.o.d ✓ 24 1.a even 1 1 trivial
2448.2.o.d ✓ 24 3.b odd 2 1 inner
2448.2.o.d ✓ 24 4.b odd 2 1 inner
2448.2.o.d ✓ 24 12.b even 2 1 inner
2448.2.o.d ✓ 24 17.b even 2 1 inner
2448.2.o.d ✓ 24 51.c odd 2 1 inner
2448.2.o.d ✓ 24 68.d odd 2 1 inner
2448.2.o.d ✓ 24 204.h even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{6} - 17T_{5}^{4} + 42T_{5}^{2} - 18 \) acting on \(S_{2}^{\mathrm{new}}(2448, [\chi])\). Copy content Toggle raw display