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Properties

Label 5544.2.v.b
Level $5544$
Weight $2$
Character orbit 5544.v
Analytic conductor $44.269$
Analytic rank $0$
Dimension $40$
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] = [5544,2,Mod(881,5544)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5544, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 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("5544.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5544 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5544.v (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: \(44.2690628806\)
Analytic rank: \(0\)
Dimension: \(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q + 24 q^{25} - 16 q^{37} - 64 q^{43} + 24 q^{49} + 16 q^{67} + 112 q^{79} - 32 q^{85} + 32 q^{91}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
881.1 0 0 0 −4.37297 0 −1.95148 + 1.78654i 0 0 0
881.2 0 0 0 −4.37297 0 −1.95148 − 1.78654i 0 0 0
881.3 0 0 0 −3.73699 0 1.51468 + 2.16927i 0 0 0
881.4 0 0 0 −3.73699 0 1.51468 − 2.16927i 0 0 0
881.5 0 0 0 −2.57534 0 0.102957 − 2.64375i 0 0 0
881.6 0 0 0 −2.57534 0 0.102957 + 2.64375i 0 0 0
881.7 0 0 0 −2.38559 0 2.60869 − 0.441264i 0 0 0
881.8 0 0 0 −2.38559 0 2.60869 + 0.441264i 0 0 0
881.9 0 0 0 −2.25014 0 −2.23397 + 1.41752i 0 0 0
881.10 0 0 0 −2.25014 0 −2.23397 − 1.41752i 0 0 0
881.11 0 0 0 −1.52190 0 1.79949 − 1.93954i 0 0 0
881.12 0 0 0 −1.52190 0 1.79949 + 1.93954i 0 0 0
881.13 0 0 0 −1.20022 0 2.61086 + 0.428234i 0 0 0
881.14 0 0 0 −1.20022 0 2.61086 − 0.428234i 0 0 0
881.15 0 0 0 −1.14395 0 −2.55967 − 0.669412i 0 0 0
881.16 0 0 0 −1.14395 0 −2.55967 + 0.669412i 0 0 0
881.17 0 0 0 −0.580557 0 −1.86645 − 1.87519i 0 0 0
881.18 0 0 0 −0.580557 0 −1.86645 + 1.87519i 0 0 0
881.19 0 0 0 −0.350902 0 −0.0251202 − 2.64563i 0 0 0
881.20 0 0 0 −0.350902 0 −0.0251202 + 2.64563i 0 0 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 881.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.b odd 2 1 inner
21.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5544.2.v.b ✓ 40
3.b odd 2 1 inner 5544.2.v.b ✓ 40
7.b odd 2 1 inner 5544.2.v.b ✓ 40
21.c even 2 1 inner 5544.2.v.b ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5544.2.v.b ✓ 40 1.a even 1 1 trivial
5544.2.v.b ✓ 40 3.b odd 2 1 inner
5544.2.v.b ✓ 40 7.b odd 2 1 inner
5544.2.v.b ✓ 40 21.c even 2 1 inner