Properties

Label 1083.2.a.c
Level $1083$
Weight $2$
Character orbit 1083.a
Self dual yes
Analytic conductor $8.648$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1083,2,Mod(1,1083)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1083, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1083.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1083 = 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1083.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: \(8.64779853890\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 57)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} - q^{6} + q^{7} - 3 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} - q^{3} - q^{4} - q^{6} + q^{7} - 3 q^{8} + q^{9} - 2 q^{11} + q^{12} + 5 q^{13} + q^{14} - q^{16} - 4 q^{17} + q^{18} - q^{21} - 2 q^{22} - 4 q^{23} + 3 q^{24} - 5 q^{25} + 5 q^{26} - q^{27} - q^{28} - 8 q^{29} - 3 q^{31} + 5 q^{32} + 2 q^{33} - 4 q^{34} - q^{36} + 3 q^{37} - 5 q^{39} - 12 q^{41} - q^{42} - q^{43} + 2 q^{44} - 4 q^{46} - 6 q^{47} + q^{48} - 6 q^{49} - 5 q^{50} + 4 q^{51} - 5 q^{52} + 4 q^{53} - q^{54} - 3 q^{56} - 8 q^{58} + 10 q^{59} - 13 q^{61} - 3 q^{62} + q^{63} + 7 q^{64} + 2 q^{66} + 11 q^{67} + 4 q^{68} + 4 q^{69} + 6 q^{71} - 3 q^{72} - 11 q^{73} + 3 q^{74} + 5 q^{75} - 2 q^{77} - 5 q^{78} + q^{79} + q^{81} - 12 q^{82} + q^{84} - q^{86} + 8 q^{87} + 6 q^{88} - 6 q^{89} + 5 q^{91} + 4 q^{92} + 3 q^{93} - 6 q^{94} - 5 q^{96} + 2 q^{97} - 6 q^{98} - 2 q^{99}+O(q^{100}) \) 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
1.00000 −1.00000 −1.00000 0 −1.00000 1.00000 −3.00000 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(19\) \( +1 \)

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 1083.2.a.c 1
3.b odd 2 1 3249.2.a.c 1
19.b odd 2 1 1083.2.a.b 1
19.c even 3 2 57.2.e.a 2
57.d even 2 1 3249.2.a.f 1
57.h odd 6 2 171.2.f.a 2
76.g odd 6 2 912.2.q.a 2
228.m even 6 2 2736.2.s.j 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
57.2.e.a 2 19.c even 3 2
171.2.f.a 2 57.h odd 6 2
912.2.q.a 2 76.g odd 6 2
1083.2.a.b 1 19.b odd 2 1
1083.2.a.c 1 1.a even 1 1 trivial
2736.2.s.j 2 228.m even 6 2
3249.2.a.c 1 3.b odd 2 1
3249.2.a.f 1 57.d even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\):

\( T_{2} - 1 \) Copy content Toggle raw display
\( T_{5} \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T + 1 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T + 2 \) Copy content Toggle raw display
$13$ \( T - 5 \) Copy content Toggle raw display
$17$ \( T + 4 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T + 4 \) Copy content Toggle raw display
$29$ \( T + 8 \) Copy content Toggle raw display
$31$ \( T + 3 \) Copy content Toggle raw display
$37$ \( T - 3 \) Copy content Toggle raw display
$41$ \( T + 12 \) Copy content Toggle raw display
$43$ \( T + 1 \) Copy content Toggle raw display
$47$ \( T + 6 \) Copy content Toggle raw display
$53$ \( T - 4 \) Copy content Toggle raw display
$59$ \( T - 10 \) Copy content Toggle raw display
$61$ \( T + 13 \) Copy content Toggle raw display
$67$ \( T - 11 \) Copy content Toggle raw display
$71$ \( T - 6 \) Copy content Toggle raw display
$73$ \( T + 11 \) Copy content Toggle raw display
$79$ \( T - 1 \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T + 6 \) Copy content Toggle raw display
$97$ \( T - 2 \) Copy content Toggle raw display
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