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Properties

Label 1444.3.c.d
Level $1444$
Weight $3$
Character orbit 1444.c
Analytic conductor $39.346$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1444,3,Mod(721,1444)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1444, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1444.721");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1444.c (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: \(39.3461501736\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{5} + 40 q^{7} - 104 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{5} + 40 q^{7} - 104 q^{9} - 64 q^{11} - 60 q^{17} + 100 q^{23} + 24 q^{25} - 144 q^{35} + 68 q^{39} - 16 q^{43} + 248 q^{45} + 180 q^{47} - 208 q^{49} - 532 q^{55} + 104 q^{61} - 1216 q^{63} - 484 q^{73} + 136 q^{77} + 460 q^{81} + 744 q^{83} + 32 q^{85} - 1296 q^{87} - 256 q^{93} + 804 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
721.1 0 − 5.75074i 0 6.82813 0 2.75886 0 −24.0710 0
721.2 0 − 5.26351i 0 0.413588 0 11.9368 0 −18.7045 0
721.3 0 − 4.89235i 0 −9.07521 0 11.2253 0 −14.9351 0
721.4 0 − 4.56439i 0 −0.176066 0 5.77972 0 −11.8337 0
721.5 0 − 4.28147i 0 −1.88757 0 1.12007 0 −9.33100 0
721.6 0 − 3.56718i 0 −2.91277 0 −2.95359 0 −3.72474 0
721.7 0 − 3.41116i 0 −9.09374 0 −4.38511 0 −2.63604 0
721.8 0 − 2.85365i 0 −4.24509 0 4.02162 0 0.856655 0
721.9 0 − 1.77829i 0 5.00808 0 3.79291 0 5.83769 0
721.10 0 − 0.650206i 0 4.27507 0 1.20044 0 8.57723 0
721.11 0 − 0.174362i 0 −0.292748 0 −5.22349 0 8.96960 0
721.12 0 − 0.0712756i 0 5.15832 0 −9.27347 0 8.99492 0
721.13 0 0.0712756i 0 5.15832 0 −9.27347 0 8.99492 0
721.14 0 0.174362i 0 −0.292748 0 −5.22349 0 8.96960 0
721.15 0 0.650206i 0 4.27507 0 1.20044 0 8.57723 0
721.16 0 1.77829i 0 5.00808 0 3.79291 0 5.83769 0
721.17 0 2.85365i 0 −4.24509 0 4.02162 0 0.856655 0
721.18 0 3.41116i 0 −9.09374 0 −4.38511 0 −2.63604 0
721.19 0 3.56718i 0 −2.91277 0 −2.95359 0 −3.72474 0
721.20 0 4.28147i 0 −1.88757 0 1.12007 0 −9.33100 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 721.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1444.3.c.d ✓ 24
19.b odd 2 1 inner 1444.3.c.d ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1444.3.c.d ✓ 24 1.a even 1 1 trivial
1444.3.c.d ✓ 24 19.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} + 160 T_{3}^{22} + 11011 T_{3}^{20} + 426612 T_{3}^{18} + 10221421 T_{3}^{16} + \cdots + 2085136 \) acting on \(S_{3}^{\mathrm{new}}(1444, [\chi])\). Copy content Toggle raw display