↑

Properties

Label 2070.2.h.a
Level $2070$
Weight $2$
Character orbit 2070.h
Analytic conductor $16.529$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2070,2,Mod(2069,2070)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2070.2069");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2070.h (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: \(16.5290332184\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{16} - 4 q^{23} + 8 q^{31} - 24 q^{32} - 16 q^{35} + 4 q^{46} + 16 q^{47} + 56 q^{49} - 8 q^{55} - 8 q^{62} + 24 q^{64} + 16 q^{70} - 40 q^{77} + 64 q^{85} - 4 q^{92} - 16 q^{94} - 8 q^{95} - 56 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2069.1 −1.00000 0 1.00000 −2.21324 − 0.318667i 0 −2.37249 −1.00000 0 2.21324 + 0.318667i
2069.2 −1.00000 0 1.00000 −2.21324 + 0.318667i 0 −2.37249 −1.00000 0 2.21324 − 0.318667i
2069.3 −1.00000 0 1.00000 −2.15114 − 0.610392i 0 4.98705 −1.00000 0 2.15114 + 0.610392i
2069.4 −1.00000 0 1.00000 −2.15114 + 0.610392i 0 4.98705 −1.00000 0 2.15114 − 0.610392i
2069.5 −1.00000 0 1.00000 −1.50764 − 1.65137i 0 −4.08561 −1.00000 0 1.50764 + 1.65137i
2069.6 −1.00000 0 1.00000 −1.50764 + 1.65137i 0 −4.08561 −1.00000 0 1.50764 − 1.65137i
2069.7 −1.00000 0 1.00000 −1.28449 − 1.83032i 0 1.16069 −1.00000 0 1.28449 + 1.83032i
2069.8 −1.00000 0 1.00000 −1.28449 + 1.83032i 0 1.16069 −1.00000 0 1.28449 − 1.83032i
2069.9 −1.00000 0 1.00000 −1.06271 − 1.96739i 0 1.69360 −1.00000 0 1.06271 + 1.96739i
2069.10 −1.00000 0 1.00000 −1.06271 + 1.96739i 0 1.69360 −1.00000 0 1.06271 − 1.96739i
2069.11 −1.00000 0 1.00000 −0.649505 − 2.13966i 0 2.14311 −1.00000 0 0.649505 + 2.13966i
2069.12 −1.00000 0 1.00000 −0.649505 + 2.13966i 0 2.14311 −1.00000 0 0.649505 − 2.13966i
2069.13 −1.00000 0 1.00000 0.649505 − 2.13966i 0 −2.14311 −1.00000 0 −0.649505 + 2.13966i
2069.14 −1.00000 0 1.00000 0.649505 + 2.13966i 0 −2.14311 −1.00000 0 −0.649505 − 2.13966i
2069.15 −1.00000 0 1.00000 1.06271 − 1.96739i 0 −1.69360 −1.00000 0 −1.06271 + 1.96739i
2069.16 −1.00000 0 1.00000 1.06271 + 1.96739i 0 −1.69360 −1.00000 0 −1.06271 − 1.96739i
2069.17 −1.00000 0 1.00000 1.28449 − 1.83032i 0 −1.16069 −1.00000 0 −1.28449 + 1.83032i
2069.18 −1.00000 0 1.00000 1.28449 + 1.83032i 0 −1.16069 −1.00000 0 −1.28449 − 1.83032i
2069.19 −1.00000 0 1.00000 1.50764 − 1.65137i 0 4.08561 −1.00000 0 −1.50764 + 1.65137i
2069.20 −1.00000 0 1.00000 1.50764 + 1.65137i 0 4.08561 −1.00000 0 −1.50764 − 1.65137i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2069.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
15.d odd 2 1 inner
23.b odd 2 1 inner
345.h even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2070.2.h.a ✓ 24
3.b odd 2 1 2070.2.h.b yes 24
5.b even 2 1 2070.2.h.b yes 24
15.d odd 2 1 inner 2070.2.h.a ✓ 24
23.b odd 2 1 inner 2070.2.h.a ✓ 24
69.c even 2 1 2070.2.h.b yes 24
115.c odd 2 1 2070.2.h.b yes 24
345.h even 2 1 inner 2070.2.h.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2070.2.h.a ✓ 24 1.a even 1 1 trivial
2070.2.h.a ✓ 24 15.d odd 2 1 inner
2070.2.h.a ✓ 24 23.b odd 2 1 inner
2070.2.h.a ✓ 24 345.h even 2 1 inner
2070.2.h.b yes 24 3.b odd 2 1
2070.2.h.b yes 24 5.b even 2 1
2070.2.h.b yes 24 69.c even 2 1
2070.2.h.b yes 24 115.c odd 2 1