Properties

Label 1911.4.a.f
Level $1911$
Weight $4$
Character orbit 1911.a
Self dual yes
Analytic conductor $112.753$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1911,4,Mod(1,1911)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1911, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1911.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1911.a (trivial)

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: yes
Analytic conductor: \(112.752650021\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + 3 q^{3} - 8 q^{4} + 12 q^{5} + 9 q^{9} - 36 q^{11} - 24 q^{12} - 13 q^{13} + 36 q^{15} + 64 q^{16} + 78 q^{17} - 74 q^{19} - 96 q^{20} - 96 q^{23} + 19 q^{25} + 27 q^{27} + 18 q^{29} + 214 q^{31} - 108 q^{33}+ \cdots - 324 q^{99}+O(q^{100}) \) 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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 3.00000 −8.00000 12.0000 0 0 0 9.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(7\) \( -1 \)
\(13\) \( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1911.4.a.f 1
7.b odd 2 1 39.4.a.a 1
21.c even 2 1 117.4.a.a 1
28.d even 2 1 624.4.a.g 1
35.c odd 2 1 975.4.a.e 1
56.e even 2 1 2496.4.a.f 1
56.h odd 2 1 2496.4.a.o 1
84.h odd 2 1 1872.4.a.m 1
91.b odd 2 1 507.4.a.c 1
91.i even 4 2 507.4.b.b 2
273.g even 2 1 1521.4.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
39.4.a.a 1 7.b odd 2 1
117.4.a.a 1 21.c even 2 1
507.4.a.c 1 91.b odd 2 1
507.4.b.b 2 91.i even 4 2
624.4.a.g 1 28.d even 2 1
975.4.a.e 1 35.c odd 2 1
1521.4.a.f 1 273.g even 2 1
1872.4.a.m 1 84.h odd 2 1
1911.4.a.f 1 1.a even 1 1 trivial
2496.4.a.f 1 56.e even 2 1
2496.4.a.o 1 56.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1911))\):

\( T_{2} \) Copy content Toggle raw display
\( T_{5} - 12 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 3 \) Copy content Toggle raw display
$5$ \( T - 12 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T + 36 \) Copy content Toggle raw display
$13$ \( T + 13 \) Copy content Toggle raw display
$17$ \( T - 78 \) Copy content Toggle raw display
$19$ \( T + 74 \) Copy content Toggle raw display
$23$ \( T + 96 \) Copy content Toggle raw display
$29$ \( T - 18 \) Copy content Toggle raw display
$31$ \( T - 214 \) Copy content Toggle raw display
$37$ \( T + 286 \) Copy content Toggle raw display
$41$ \( T - 384 \) Copy content Toggle raw display
$43$ \( T - 524 \) Copy content Toggle raw display
$47$ \( T + 300 \) Copy content Toggle raw display
$53$ \( T - 558 \) Copy content Toggle raw display
$59$ \( T + 576 \) Copy content Toggle raw display
$61$ \( T + 74 \) Copy content Toggle raw display
$67$ \( T - 38 \) Copy content Toggle raw display
$71$ \( T + 456 \) Copy content Toggle raw display
$73$ \( T - 682 \) Copy content Toggle raw display
$79$ \( T - 704 \) Copy content Toggle raw display
$83$ \( T - 888 \) Copy content Toggle raw display
$89$ \( T - 1020 \) Copy content Toggle raw display
$97$ \( T + 110 \) Copy content Toggle raw display
show more
show less