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Properties

Label 5544.2.f.a
Level $5544$
Weight $2$
Character orbit 5544.f
Analytic conductor $44.269$
Analytic rank $0$
Dimension $36$
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] = [5544,2,Mod(2969,5544)]
 
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, 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("5544.2969");
 
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.f (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: \(36\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 36 q - 4 q^{11} - 16 q^{17} - 28 q^{25} + 16 q^{29} + 16 q^{31} - 8 q^{35} - 8 q^{37} + 16 q^{41} - 36 q^{49} - 32 q^{55} - 32 q^{65} - 48 q^{67} + 8 q^{77} + 16 q^{83} + 48 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2969.1 0 0 0 − 4.21950i 0 1.00000i 0 0 0
2969.2 0 0 0 − 3.95003i 0 − 1.00000i 0 0 0
2969.3 0 0 0 − 3.80707i 0 − 1.00000i 0 0 0
2969.4 0 0 0 − 3.03961i 0 1.00000i 0 0 0
2969.5 0 0 0 − 3.03932i 0 − 1.00000i 0 0 0
2969.6 0 0 0 − 2.71772i 0 − 1.00000i 0 0 0
2969.7 0 0 0 − 2.53047i 0 1.00000i 0 0 0
2969.8 0 0 0 − 2.32977i 0 − 1.00000i 0 0 0
2969.9 0 0 0 − 2.19162i 0 − 1.00000i 0 0 0
2969.10 0 0 0 − 1.83965i 0 − 1.00000i 0 0 0
2969.11 0 0 0 − 1.60544i 0 1.00000i 0 0 0
2969.12 0 0 0 − 1.49136i 0 1.00000i 0 0 0
2969.13 0 0 0 − 1.46639i 0 1.00000i 0 0 0
2969.14 0 0 0 − 1.11210i 0 − 1.00000i 0 0 0
2969.15 0 0 0 − 0.941672i 0 1.00000i 0 0 0
2969.16 0 0 0 − 0.903908i 0 1.00000i 0 0 0
2969.17 0 0 0 − 0.478826i 0 1.00000i 0 0 0
2969.18 0 0 0 − 0.310116i 0 1.00000i 0 0 0
2969.19 0 0 0 0.310116i 0 − 1.00000i 0 0 0
2969.20 0 0 0 0.478826i 0 − 1.00000i 0 0 0
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2969.36
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
33.d 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.f.a ✓ 36
3.b odd 2 1 5544.2.f.b yes 36
11.b odd 2 1 5544.2.f.b yes 36
33.d even 2 1 inner 5544.2.f.a ✓ 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5544.2.f.a ✓ 36 1.a even 1 1 trivial
5544.2.f.a ✓ 36 33.d even 2 1 inner
5544.2.f.b yes 36 3.b odd 2 1
5544.2.f.b yes 36 11.b odd 2 1