↑

Properties

Label 1932.2.p.a
Level $1932$
Weight $2$
Character orbit 1932.p
Analytic conductor $15.427$
Analytic rank $0$
Dimension $48$
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] = [1932,2,Mod(1793,1932)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1932, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1932.1793");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1932.p (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: \(15.4270976705\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 4 q^{3} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q - 4 q^{3} + 4 q^{9} - 8 q^{13} + 72 q^{25} - 4 q^{27} + 40 q^{31} - 4 q^{39} - 48 q^{49} - 16 q^{55} + 24 q^{69} + 8 q^{73} + 24 q^{75} + 68 q^{81} + 40 q^{85} + 40 q^{87} - 4 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1793.1 0 −1.67713 − 0.432722i 0 −1.84151 0 − 1.00000i 0 2.62550 + 1.45146i 0
1793.2 0 −1.67713 − 0.432722i 0 1.84151 0 1.00000i 0 2.62550 + 1.45146i 0
1793.3 0 −1.67713 + 0.432722i 0 −1.84151 0 1.00000i 0 2.62550 − 1.45146i 0
1793.4 0 −1.67713 + 0.432722i 0 1.84151 0 − 1.00000i 0 2.62550 − 1.45146i 0
1793.5 0 −1.66715 − 0.469700i 0 −4.06580 0 1.00000i 0 2.55876 + 1.56612i 0
1793.6 0 −1.66715 − 0.469700i 0 4.06580 0 − 1.00000i 0 2.55876 + 1.56612i 0
1793.7 0 −1.66715 + 0.469700i 0 −4.06580 0 − 1.00000i 0 2.55876 − 1.56612i 0
1793.8 0 −1.66715 + 0.469700i 0 4.06580 0 1.00000i 0 2.55876 − 1.56612i 0
1793.9 0 −1.57587 − 0.718781i 0 −1.11772 0 − 1.00000i 0 1.96671 + 2.26541i 0
1793.10 0 −1.57587 − 0.718781i 0 1.11772 0 1.00000i 0 1.96671 + 2.26541i 0
1793.11 0 −1.57587 + 0.718781i 0 −1.11772 0 1.00000i 0 1.96671 − 2.26541i 0
1793.12 0 −1.57587 + 0.718781i 0 1.11772 0 − 1.00000i 0 1.96671 − 2.26541i 0
1793.13 0 −1.16163 − 1.28476i 0 −0.460794 0 − 1.00000i 0 −0.301214 + 2.98484i 0
1793.14 0 −1.16163 − 1.28476i 0 0.460794 0 1.00000i 0 −0.301214 + 2.98484i 0
1793.15 0 −1.16163 + 1.28476i 0 −0.460794 0 1.00000i 0 −0.301214 − 2.98484i 0
1793.16 0 −1.16163 + 1.28476i 0 0.460794 0 − 1.00000i 0 −0.301214 − 2.98484i 0
1793.17 0 −0.792229 − 1.54025i 0 −2.39968 0 − 1.00000i 0 −1.74475 + 2.44046i 0
1793.18 0 −0.792229 − 1.54025i 0 2.39968 0 1.00000i 0 −1.74475 + 2.44046i 0
1793.19 0 −0.792229 + 1.54025i 0 −2.39968 0 1.00000i 0 −1.74475 − 2.44046i 0
1793.20 0 −0.792229 + 1.54025i 0 2.39968 0 − 1.00000i 0 −1.74475 − 2.44046i 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1793.48
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1932.2.p.a ✓ 48
3.b odd 2 1 inner 1932.2.p.a ✓ 48
23.b odd 2 1 inner 1932.2.p.a ✓ 48
69.c even 2 1 inner 1932.2.p.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1932.2.p.a ✓ 48 1.a even 1 1 trivial
1932.2.p.a ✓ 48 3.b odd 2 1 inner
1932.2.p.a ✓ 48 23.b odd 2 1 inner
1932.2.p.a ✓ 48 69.c even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1932, [\chi])\).