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Properties

Label 920.3.k.a
Level $920$
Weight $3$
Character orbit 920.k
Analytic conductor $25.068$
Analytic rank $0$
Dimension $48$
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] = [920,3,Mod(321,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("920.321");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 920.k (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: \(25.0681843211\)
Analytic rank: \(0\)
Dimension: \(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 128 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 128 q^{9} + 8 q^{23} - 240 q^{25} + 72 q^{29} + 32 q^{31} - 40 q^{35} - 96 q^{39} - 104 q^{41} + 128 q^{47} - 344 q^{49} + 80 q^{55} + 248 q^{59} + 292 q^{69} + 208 q^{71} + 224 q^{73} - 288 q^{77} + 184 q^{81} - 48 q^{87} - 672 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
321.1 0 −5.52295 0 2.23607i 0 3.78203i 0 21.5030 0
321.2 0 −5.52295 0 − 2.23607i 0 − 3.78203i 0 21.5030 0
321.3 0 −5.43932 0 − 2.23607i 0 − 7.73868i 0 20.5862 0
321.4 0 −5.43932 0 2.23607i 0 7.73868i 0 20.5862 0
321.5 0 −4.25033 0 2.23607i 0 − 7.64554i 0 9.06530 0
321.6 0 −4.25033 0 − 2.23607i 0 7.64554i 0 9.06530 0
321.7 0 −3.94362 0 − 2.23607i 0 13.6497i 0 6.55217 0
321.8 0 −3.94362 0 2.23607i 0 − 13.6497i 0 6.55217 0
321.9 0 −3.88236 0 − 2.23607i 0 0.578647i 0 6.07274 0
321.10 0 −3.88236 0 2.23607i 0 − 0.578647i 0 6.07274 0
321.11 0 −3.73180 0 − 2.23607i 0 − 9.98391i 0 4.92630 0
321.12 0 −3.73180 0 2.23607i 0 9.98391i 0 4.92630 0
321.13 0 −2.45185 0 − 2.23607i 0 0.852420i 0 −2.98844 0
321.14 0 −2.45185 0 2.23607i 0 − 0.852420i 0 −2.98844 0
321.15 0 −1.88263 0 2.23607i 0 13.3901i 0 −5.45570 0
321.16 0 −1.88263 0 − 2.23607i 0 − 13.3901i 0 −5.45570 0
321.17 0 −1.73513 0 2.23607i 0 − 1.69715i 0 −5.98931 0
321.18 0 −1.73513 0 − 2.23607i 0 1.69715i 0 −5.98931 0
321.19 0 −1.73033 0 − 2.23607i 0 1.02507i 0 −6.00597 0
321.20 0 −1.73033 0 2.23607i 0 − 1.02507i 0 −6.00597 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 321.48
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 920.3.k.a ✓ 48
4.b odd 2 1 1840.3.k.e 48
23.b odd 2 1 inner 920.3.k.a ✓ 48
92.b even 2 1 1840.3.k.e 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
920.3.k.a ✓ 48 1.a even 1 1 trivial
920.3.k.a ✓ 48 23.b odd 2 1 inner
1840.3.k.e 48 4.b odd 2 1
1840.3.k.e 48 92.b even 2 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(920, [\chi])\).