Properties

Label 24.10.a.c
Level $24$
Weight $10$
Character orbit 24.a
Self dual yes
Analytic conductor $12.361$
Analytic rank $0$
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] = [24,10,Mod(1,24)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(24, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("24.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 24.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: \(12.3608600679\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
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)
 
\(f(q)\) \(=\) \( q + 81 q^{3} + 614 q^{5} + 2184 q^{7} + 6561 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 81 q^{3} + 614 q^{5} + 2184 q^{7} + 6561 q^{9} + 4940 q^{11} + 69934 q^{13} + 49734 q^{15} + 376978 q^{17} + 780884 q^{19} + 176904 q^{21} + 1764632 q^{23} - 1576129 q^{25} + 531441 q^{27} - 3212226 q^{29} - 342880 q^{31} + 400140 q^{33} + 1340976 q^{35} - 19744506 q^{37} + 5664654 q^{39} - 15882390 q^{41} - 22575764 q^{43} + 4028454 q^{45} + 48948528 q^{47} - 35583751 q^{49} + 30535218 q^{51} + 52342550 q^{53} + 3033160 q^{55} + 63251604 q^{57} + 77057660 q^{59} + 13045726 q^{61} + 14329224 q^{63} + 42939476 q^{65} - 280727164 q^{67} + 142935192 q^{69} - 88554680 q^{71} - 59105654 q^{73} - 127666449 q^{75} + 10788960 q^{77} - 415337264 q^{79} + 43046721 q^{81} + 42806932 q^{83} + 231464492 q^{85} - 260190306 q^{87} - 803465958 q^{89} + 152735856 q^{91} - 27773280 q^{93} + 479462776 q^{95} + 674417762 q^{97} + 32411340 q^{99}+O(q^{100}) \) 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 81.0000 0 614.000 0 2184.00 0 6561.00 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)

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 24.10.a.c 1
3.b odd 2 1 72.10.a.c 1
4.b odd 2 1 48.10.a.c 1
8.b even 2 1 192.10.a.d 1
8.d odd 2 1 192.10.a.k 1
12.b even 2 1 144.10.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
24.10.a.c 1 1.a even 1 1 trivial
48.10.a.c 1 4.b odd 2 1
72.10.a.c 1 3.b odd 2 1
144.10.a.f 1 12.b even 2 1
192.10.a.d 1 8.b even 2 1
192.10.a.k 1 8.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 614 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(24))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 81 \) Copy content Toggle raw display
$5$ \( T - 614 \) Copy content Toggle raw display
$7$ \( T - 2184 \) Copy content Toggle raw display
$11$ \( T - 4940 \) Copy content Toggle raw display
$13$ \( T - 69934 \) Copy content Toggle raw display
$17$ \( T - 376978 \) Copy content Toggle raw display
$19$ \( T - 780884 \) Copy content Toggle raw display
$23$ \( T - 1764632 \) Copy content Toggle raw display
$29$ \( T + 3212226 \) Copy content Toggle raw display
$31$ \( T + 342880 \) Copy content Toggle raw display
$37$ \( T + 19744506 \) Copy content Toggle raw display
$41$ \( T + 15882390 \) Copy content Toggle raw display
$43$ \( T + 22575764 \) Copy content Toggle raw display
$47$ \( T - 48948528 \) Copy content Toggle raw display
$53$ \( T - 52342550 \) Copy content Toggle raw display
$59$ \( T - 77057660 \) Copy content Toggle raw display
$61$ \( T - 13045726 \) Copy content Toggle raw display
$67$ \( T + 280727164 \) Copy content Toggle raw display
$71$ \( T + 88554680 \) Copy content Toggle raw display
$73$ \( T + 59105654 \) Copy content Toggle raw display
$79$ \( T + 415337264 \) Copy content Toggle raw display
$83$ \( T - 42806932 \) Copy content Toggle raw display
$89$ \( T + 803465958 \) Copy content Toggle raw display
$97$ \( T - 674417762 \) Copy content Toggle raw display
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