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Properties

Label 2736.2.d.b
Level $2736$
Weight $2$
Character orbit 2736.d
Analytic conductor $21.847$
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] = [2736,2,Mod(2015,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.2015");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.d (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: \(21.8470699930\)
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
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{25} - 32 q^{37} - 32 q^{49} + 8 q^{73} + 40 q^{85} + 16 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2015.1 0 0 0 − 2.95877i 0 − 0.569970i 0 0 0
2015.2 0 0 0 − 2.95877i 0 0.569970i 0 0 0
2015.3 0 0 0 − 2.62670i 0 − 0.815178i 0 0 0
2015.4 0 0 0 − 2.62670i 0 0.815178i 0 0 0
2015.5 0 0 0 − 2.30935i 0 − 4.59902i 0 0 0
2015.6 0 0 0 − 2.30935i 0 4.59902i 0 0 0
2015.7 0 0 0 − 2.03314i 0 − 3.00897i 0 0 0
2015.8 0 0 0 − 2.03314i 0 3.00897i 0 0 0
2015.9 0 0 0 − 1.28244i 0 − 4.16899i 0 0 0
2015.10 0 0 0 − 1.28244i 0 4.16899i 0 0 0
2015.11 0 0 0 − 1.11119i 0 − 1.19380i 0 0 0
2015.12 0 0 0 − 1.11119i 0 1.19380i 0 0 0
2015.13 0 0 0 1.11119i 0 − 1.19380i 0 0 0
2015.14 0 0 0 1.11119i 0 1.19380i 0 0 0
2015.15 0 0 0 1.28244i 0 − 4.16899i 0 0 0
2015.16 0 0 0 1.28244i 0 4.16899i 0 0 0
2015.17 0 0 0 2.03314i 0 − 3.00897i 0 0 0
2015.18 0 0 0 2.03314i 0 3.00897i 0 0 0
2015.19 0 0 0 2.30935i 0 − 4.59902i 0 0 0
2015.20 0 0 0 2.30935i 0 4.59902i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2015.24
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 2736.2.d.b ✓ 24
3.b odd 2 1 inner 2736.2.d.b ✓ 24
4.b odd 2 1 inner 2736.2.d.b ✓ 24
12.b even 2 1 inner 2736.2.d.b ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2736.2.d.b ✓ 24 1.a even 1 1 trivial
2736.2.d.b ✓ 24 3.b odd 2 1 inner
2736.2.d.b ✓ 24 4.b odd 2 1 inner
2736.2.d.b ✓ 24 12.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} + 28T_{5}^{10} + 305T_{5}^{8} + 1632T_{5}^{6} + 4440T_{5}^{4} + 5696T_{5}^{2} + 2704 \) acting on \(S_{2}^{\mathrm{new}}(2736, [\chi])\). Copy content Toggle raw display