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Properties

Label 2496.2.m.d
Level $2496$
Weight $2$
Character orbit 2496.m
Analytic conductor $19.931$
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] = [2496,2,Mod(2209,2496)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2496, 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("2496.2209");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2496.m (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: \(19.9306603445\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{9} - 32 q^{17} + 56 q^{25} - 104 q^{49} + 32 q^{65} + 24 q^{81}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2209.1 0 − 1.00000i 0 −3.70616 0 − 2.74796i 0 −1.00000 0
2209.2 0 − 1.00000i 0 3.70616 0 2.74796i 0 −1.00000 0
2209.3 0 1.00000i 0 −3.70616 0 2.74796i 0 −1.00000 0
2209.4 0 1.00000i 0 3.70616 0 − 2.74796i 0 −1.00000 0
2209.5 0 − 1.00000i 0 −1.25094 0 − 1.81503i 0 −1.00000 0
2209.6 0 − 1.00000i 0 1.25094 0 1.81503i 0 −1.00000 0
2209.7 0 1.00000i 0 −1.25094 0 1.81503i 0 −1.00000 0
2209.8 0 1.00000i 0 1.25094 0 − 1.81503i 0 −1.00000 0
2209.9 0 − 1.00000i 0 −3.70616 0 − 2.74796i 0 −1.00000 0
2209.10 0 − 1.00000i 0 3.70616 0 2.74796i 0 −1.00000 0
2209.11 0 1.00000i 0 −3.70616 0 2.74796i 0 −1.00000 0
2209.12 0 1.00000i 0 3.70616 0 − 2.74796i 0 −1.00000 0
2209.13 0 − 1.00000i 0 −1.25094 0 − 1.81503i 0 −1.00000 0
2209.14 0 − 1.00000i 0 1.25094 0 1.81503i 0 −1.00000 0
2209.15 0 1.00000i 0 −1.25094 0 1.81503i 0 −1.00000 0
2209.16 0 1.00000i 0 1.25094 0 − 1.81503i 0 −1.00000 0
2209.17 0 − 1.00000i 0 −2.58834 0 4.81190i 0 −1.00000 0
2209.18 0 − 1.00000i 0 2.58834 0 − 4.81190i 0 −1.00000 0
2209.19 0 1.00000i 0 −2.58834 0 − 4.81190i 0 −1.00000 0
2209.20 0 1.00000i 0 2.58834 0 4.81190i 0 −1.00000 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2209.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
8.b even 2 1 inner
8.d odd 2 1 inner
13.b even 2 1 inner
52.b odd 2 1 inner
104.e even 2 1 inner
104.h odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2496.2.m.d ✓ 24
4.b odd 2 1 inner 2496.2.m.d ✓ 24
8.b even 2 1 inner 2496.2.m.d ✓ 24
8.d odd 2 1 inner 2496.2.m.d ✓ 24
13.b even 2 1 inner 2496.2.m.d ✓ 24
52.b odd 2 1 inner 2496.2.m.d ✓ 24
104.e even 2 1 inner 2496.2.m.d ✓ 24
104.h odd 2 1 inner 2496.2.m.d ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2496.2.m.d ✓ 24 1.a even 1 1 trivial
2496.2.m.d ✓ 24 4.b odd 2 1 inner
2496.2.m.d ✓ 24 8.b even 2 1 inner
2496.2.m.d ✓ 24 8.d odd 2 1 inner
2496.2.m.d ✓ 24 13.b even 2 1 inner
2496.2.m.d ✓ 24 52.b odd 2 1 inner
2496.2.m.d ✓ 24 104.e even 2 1 inner
2496.2.m.d ✓ 24 104.h 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 \(S_{2}^{\mathrm{new}}(2496, [\chi])\):

\( T_{5}^{6} - 22T_{5}^{4} + 124T_{5}^{2} - 144 \) Copy content Toggle raw display
\( T_{7}^{6} + 34T_{7}^{4} + 276T_{7}^{2} + 576 \) Copy content Toggle raw display