Properties

Label 2205.4.a.j
Level $2205$
Weight $4$
Character orbit 2205.a
Self dual yes
Analytic conductor $130.099$
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] = [2205,4,Mod(1,2205)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2205, 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("2205.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.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: \(130.099211563\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 735)
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)
 
\(f(q)\) \(=\) \( q - q^{2} - 7 q^{4} - 5 q^{5} + 15 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - 7 q^{4} - 5 q^{5} + 15 q^{8} + 5 q^{10} - 10 q^{11} - 6 q^{13} + 41 q^{16} + 84 q^{17} - 48 q^{19} + 35 q^{20} + 10 q^{22} - 56 q^{23} + 25 q^{25} + 6 q^{26} + 232 q^{29} + 6 q^{31} - 161 q^{32} - 84 q^{34} - 48 q^{37} + 48 q^{38} - 75 q^{40} - 150 q^{41} - 426 q^{43} + 70 q^{44} + 56 q^{46} - 18 q^{47} - 25 q^{50} + 42 q^{52} + 58 q^{53} + 50 q^{55} - 232 q^{58} + 348 q^{59} - 882 q^{61} - 6 q^{62} - 167 q^{64} + 30 q^{65} - 182 q^{67} - 588 q^{68} + 524 q^{71} + 690 q^{73} + 48 q^{74} + 336 q^{76} - 1024 q^{79} - 205 q^{80} + 150 q^{82} + 384 q^{83} - 420 q^{85} + 426 q^{86} - 150 q^{88} - 246 q^{89} + 392 q^{92} + 18 q^{94} + 240 q^{95} - 1122 q^{97}+O(q^{100}) \) 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 0 −7.00000 −5.00000 0 0 15.0000 0 5.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(5\) \(1\)
\(7\) \(-1\)

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 2205.4.a.j 1
3.b odd 2 1 735.4.a.f yes 1
7.b odd 2 1 2205.4.a.m 1
21.c even 2 1 735.4.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
735.4.a.d 1 21.c even 2 1
735.4.a.f yes 1 3.b odd 2 1
2205.4.a.j 1 1.a even 1 1 trivial
2205.4.a.m 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2205))\):

\( T_{2} + 1 \) Copy content Toggle raw display
\( T_{11} + 10 \) Copy content Toggle raw display
\( T_{13} + 6 \) Copy content Toggle raw display
\( T_{17} - 84 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T + 5 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T + 10 \) Copy content Toggle raw display
$13$ \( T + 6 \) Copy content Toggle raw display
$17$ \( T - 84 \) Copy content Toggle raw display
$19$ \( T + 48 \) Copy content Toggle raw display
$23$ \( T + 56 \) Copy content Toggle raw display
$29$ \( T - 232 \) Copy content Toggle raw display
$31$ \( T - 6 \) Copy content Toggle raw display
$37$ \( T + 48 \) Copy content Toggle raw display
$41$ \( T + 150 \) Copy content Toggle raw display
$43$ \( T + 426 \) Copy content Toggle raw display
$47$ \( T + 18 \) Copy content Toggle raw display
$53$ \( T - 58 \) Copy content Toggle raw display
$59$ \( T - 348 \) Copy content Toggle raw display
$61$ \( T + 882 \) Copy content Toggle raw display
$67$ \( T + 182 \) Copy content Toggle raw display
$71$ \( T - 524 \) Copy content Toggle raw display
$73$ \( T - 690 \) Copy content Toggle raw display
$79$ \( T + 1024 \) Copy content Toggle raw display
$83$ \( T - 384 \) Copy content Toggle raw display
$89$ \( T + 246 \) Copy content Toggle raw display
$97$ \( T + 1122 \) Copy content Toggle raw display
show more
show less