Properties

Label 567.4.a.b
Level $567$
Weight $4$
Character orbit 567.a
Self dual yes
Analytic conductor $33.454$
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] = [567,4,Mod(1,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("567.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 567.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: \(33.4540829733\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - 7 q^{4} + 14 q^{5} - 7 q^{7} - 15 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} - 7 q^{4} + 14 q^{5} - 7 q^{7} - 15 q^{8} + 14 q^{10} + 47 q^{11} - 86 q^{13} - 7 q^{14} + 41 q^{16} + 9 q^{17} - 131 q^{19} - 98 q^{20} + 47 q^{22} + 12 q^{23} + 71 q^{25} - 86 q^{26} + 49 q^{28} + 260 q^{29} - 54 q^{31} + 161 q^{32} + 9 q^{34} - 98 q^{35} - 246 q^{37} - 131 q^{38} - 210 q^{40} - 383 q^{41} - 169 q^{43} - 329 q^{44} + 12 q^{46} - 96 q^{47} + 49 q^{49} + 71 q^{50} + 602 q^{52} - 300 q^{53} + 658 q^{55} + 105 q^{56} + 260 q^{58} - 429 q^{59} - 380 q^{61} - 54 q^{62} - 167 q^{64} - 1204 q^{65} - 155 q^{67} - 63 q^{68} - 98 q^{70} - 72 q^{71} + 117 q^{73} - 246 q^{74} + 917 q^{76} - 329 q^{77} - 526 q^{79} + 574 q^{80} - 383 q^{82} - 576 q^{83} + 126 q^{85} - 169 q^{86} - 705 q^{88} + 278 q^{89} + 602 q^{91} - 84 q^{92} - 96 q^{94} - 1834 q^{95} - 201 q^{97} + 49 q^{98}+O(q^{100}) \) 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 14.0000 0 −7.00000 −15.0000 0 14.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 567.4.a.b 1
3.b odd 2 1 567.4.a.a 1
9.c even 3 2 189.4.f.a 2
9.d odd 6 2 63.4.f.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
63.4.f.a 2 9.d odd 6 2
189.4.f.a 2 9.c even 3 2
567.4.a.a 1 3.b odd 2 1
567.4.a.b 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(567))\). 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
$5$ \( T - 14 \) Copy content Toggle raw display
$7$ \( T + 7 \) Copy content Toggle raw display
$11$ \( T - 47 \) Copy content Toggle raw display
$13$ \( T + 86 \) Copy content Toggle raw display
$17$ \( T - 9 \) Copy content Toggle raw display
$19$ \( T + 131 \) Copy content Toggle raw display
$23$ \( T - 12 \) Copy content Toggle raw display
$29$ \( T - 260 \) Copy content Toggle raw display
$31$ \( T + 54 \) Copy content Toggle raw display
$37$ \( T + 246 \) Copy content Toggle raw display
$41$ \( T + 383 \) Copy content Toggle raw display
$43$ \( T + 169 \) Copy content Toggle raw display
$47$ \( T + 96 \) Copy content Toggle raw display
$53$ \( T + 300 \) Copy content Toggle raw display
$59$ \( T + 429 \) Copy content Toggle raw display
$61$ \( T + 380 \) Copy content Toggle raw display
$67$ \( T + 155 \) Copy content Toggle raw display
$71$ \( T + 72 \) Copy content Toggle raw display
$73$ \( T - 117 \) Copy content Toggle raw display
$79$ \( T + 526 \) Copy content Toggle raw display
$83$ \( T + 576 \) Copy content Toggle raw display
$89$ \( T - 278 \) Copy content Toggle raw display
$97$ \( T + 201 \) Copy content Toggle raw display
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