↑

Properties

Label 1020.2.bp.b
Level $1020$
Weight $2$
Character orbit 1020.bp
Analytic conductor $8.145$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1020,2,Mod(121,1020)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1020, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1020.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1020.bp (of order \(8\), degree \(4\), 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: \(8.14474100617\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{7} - 24 q^{17} - 8 q^{19} - 32 q^{23} + 32 q^{29} + 16 q^{31} + 16 q^{33} + 16 q^{37} + 8 q^{39} + 32 q^{41} - 48 q^{43} - 24 q^{49} + 8 q^{51} + 56 q^{53} - 32 q^{57} + 24 q^{59} + 8 q^{61} - 8 q^{63} + 64 q^{67} - 16 q^{69} - 16 q^{71} + 16 q^{73} - 24 q^{77} - 24 q^{79} + 24 q^{83} + 8 q^{85} + 24 q^{87} - 80 q^{91} + 8 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
121.1 0 −0.923880 + 0.382683i 0 0.382683 + 0.923880i 0 −0.0317349 + 0.0766149i 0 0.707107 − 0.707107i 0
121.2 0 −0.923880 + 0.382683i 0 0.382683 + 0.923880i 0 1.34509 − 3.24734i 0 0.707107 − 0.707107i 0
121.3 0 −0.923880 + 0.382683i 0 0.382683 + 0.923880i 0 −0.479268 + 1.15705i 0 0.707107 − 0.707107i 0
121.4 0 0.923880 − 0.382683i 0 −0.382683 − 0.923880i 0 1.94612 − 4.69835i 0 0.707107 − 0.707107i 0
121.5 0 0.923880 − 0.382683i 0 −0.382683 − 0.923880i 0 −0.539198 + 1.30174i 0 0.707107 − 0.707107i 0
121.6 0 0.923880 − 0.382683i 0 −0.382683 − 0.923880i 0 −1.65522 + 3.99607i 0 0.707107 − 0.707107i 0
661.1 0 −0.382683 − 0.923880i 0 −0.923880 + 0.382683i 0 3.91808 + 1.62292i 0 −0.707107 + 0.707107i 0
661.2 0 −0.382683 − 0.923880i 0 −0.923880 + 0.382683i 0 0.155576 + 0.0644419i 0 −0.707107 + 0.707107i 0
661.3 0 −0.382683 − 0.923880i 0 −0.923880 + 0.382683i 0 −1.05999 − 0.439061i 0 −0.707107 + 0.707107i 0
661.4 0 0.382683 + 0.923880i 0 0.923880 − 0.382683i 0 −1.99749 − 0.827389i 0 −0.707107 + 0.707107i 0
661.5 0 0.382683 + 0.923880i 0 0.923880 − 0.382683i 0 −1.42564 − 0.590521i 0 −0.707107 + 0.707107i 0
661.6 0 0.382683 + 0.923880i 0 0.923880 − 0.382683i 0 3.82368 + 1.58382i 0 −0.707107 + 0.707107i 0
841.1 0 −0.382683 + 0.923880i 0 −0.923880 − 0.382683i 0 3.91808 − 1.62292i 0 −0.707107 − 0.707107i 0
841.2 0 −0.382683 + 0.923880i 0 −0.923880 − 0.382683i 0 0.155576 − 0.0644419i 0 −0.707107 − 0.707107i 0
841.3 0 −0.382683 + 0.923880i 0 −0.923880 − 0.382683i 0 −1.05999 + 0.439061i 0 −0.707107 − 0.707107i 0
841.4 0 0.382683 − 0.923880i 0 0.923880 + 0.382683i 0 −1.99749 + 0.827389i 0 −0.707107 − 0.707107i 0
841.5 0 0.382683 − 0.923880i 0 0.923880 + 0.382683i 0 −1.42564 + 0.590521i 0 −0.707107 − 0.707107i 0
841.6 0 0.382683 − 0.923880i 0 0.923880 + 0.382683i 0 3.82368 − 1.58382i 0 −0.707107 − 0.707107i 0
961.1 0 −0.923880 − 0.382683i 0 0.382683 − 0.923880i 0 −0.0317349 − 0.0766149i 0 0.707107 + 0.707107i 0
961.2 0 −0.923880 − 0.382683i 0 0.382683 − 0.923880i 0 1.34509 + 3.24734i 0 0.707107 + 0.707107i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 121.6
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.d even 8 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1020.2.bp.b ✓ 24
17.d even 8 1 inner 1020.2.bp.b ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1020.2.bp.b ✓ 24 1.a even 1 1 trivial
1020.2.bp.b ✓ 24 17.d even 8 1 inner