Properties

Label 4032.2.i.c
Level $4032$
Weight $2$
Character orbit 4032.i
Analytic conductor $32.196$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $16$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4032,2,Mod(1889,4032)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4032.1889");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4032.i (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: \(32.1956820950\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q - 80 q^{25} - 16 q^{49}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1889.1 0 0 0 1.77767i 0 −2.39248 1.12962i 0 0 0
1889.2 0 0 0 1.77767i 0 −2.39248 + 1.12962i 0 0 0
1889.3 0 0 0 1.21807i 0 0.355387 2.62177i 0 0 0
1889.4 0 0 0 1.21807i 0 0.355387 + 2.62177i 0 0 0
1889.5 0 0 0 1.77767i 0 −2.39248 1.12962i 0 0 0
1889.6 0 0 0 1.77767i 0 −2.39248 + 1.12962i 0 0 0
1889.7 0 0 0 3.91870i 0 2.03709 1.68827i 0 0 0
1889.8 0 0 0 3.91870i 0 2.03709 + 1.68827i 0 0 0
1889.9 0 0 0 1.21807i 0 0.355387 + 2.62177i 0 0 0
1889.10 0 0 0 1.21807i 0 0.355387 2.62177i 0 0 0
1889.11 0 0 0 1.77767i 0 2.39248 1.12962i 0 0 0
1889.12 0 0 0 1.77767i 0 2.39248 + 1.12962i 0 0 0
1889.13 0 0 0 3.91870i 0 2.03709 1.68827i 0 0 0
1889.14 0 0 0 3.91870i 0 2.03709 + 1.68827i 0 0 0
1889.15 0 0 0 3.91870i 0 2.03709 + 1.68827i 0 0 0
1889.16 0 0 0 3.91870i 0 2.03709 1.68827i 0 0 0
1889.17 0 0 0 3.91870i 0 −2.03709 1.68827i 0 0 0
1889.18 0 0 0 3.91870i 0 −2.03709 + 1.68827i 0 0 0
1889.19 0 0 0 1.77767i 0 −2.39248 + 1.12962i 0 0 0
1889.20 0 0 0 1.77767i 0 −2.39248 1.12962i 0 0 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1889.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
4.b odd 2 1 inner
7.b odd 2 1 inner
8.b even 2 1 inner
8.d odd 2 1 inner
12.b even 2 1 inner
21.c even 2 1 inner
24.f even 2 1 inner
24.h odd 2 1 inner
28.d even 2 1 inner
56.e even 2 1 inner
56.h odd 2 1 inner
84.h odd 2 1 inner
168.e odd 2 1 inner
168.i even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4032.2.i.c 48
3.b odd 2 1 inner 4032.2.i.c 48
4.b odd 2 1 inner 4032.2.i.c 48
7.b odd 2 1 inner 4032.2.i.c 48
8.b even 2 1 inner 4032.2.i.c 48
8.d odd 2 1 inner 4032.2.i.c 48
12.b even 2 1 inner 4032.2.i.c 48
21.c even 2 1 inner 4032.2.i.c 48
24.f even 2 1 inner 4032.2.i.c 48
24.h odd 2 1 inner 4032.2.i.c 48
28.d even 2 1 inner 4032.2.i.c 48
56.e even 2 1 inner 4032.2.i.c 48
56.h odd 2 1 inner 4032.2.i.c 48
84.h odd 2 1 inner 4032.2.i.c 48
168.e odd 2 1 inner 4032.2.i.c 48
168.i even 2 1 inner 4032.2.i.c 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4032.2.i.c 48 1.a even 1 1 trivial
4032.2.i.c 48 3.b odd 2 1 inner
4032.2.i.c 48 4.b odd 2 1 inner
4032.2.i.c 48 7.b odd 2 1 inner
4032.2.i.c 48 8.b even 2 1 inner
4032.2.i.c 48 8.d odd 2 1 inner
4032.2.i.c 48 12.b even 2 1 inner
4032.2.i.c 48 21.c even 2 1 inner
4032.2.i.c 48 24.f even 2 1 inner
4032.2.i.c 48 24.h odd 2 1 inner
4032.2.i.c 48 28.d even 2 1 inner
4032.2.i.c 48 56.e even 2 1 inner
4032.2.i.c 48 56.h odd 2 1 inner
4032.2.i.c 48 84.h odd 2 1 inner
4032.2.i.c 48 168.e odd 2 1 inner
4032.2.i.c 48 168.i even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(4032, [\chi])\):

\( T_{5}^{6} + 20T_{5}^{4} + 76T_{5}^{2} + 72 \) Copy content Toggle raw display
\( T_{47}^{6} - 128T_{47}^{4} + 3520T_{47}^{2} - 4608 \) Copy content Toggle raw display