Properties

Label 64.24.a.a
Level $64$
Weight $24$
Character orbit 64.a
Self dual yes
Analytic conductor $214.531$
Analytic rank $1$
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] = [64,24,Mod(1,64)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(64, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 24, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("64.1");
 
S:= CuspForms(chi, 24);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 64.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: \(214.530583901\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2)
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)
 
\(f(q)\) \(=\) \( q - 505908 q^{3} + 90135570 q^{5} - 6872255096 q^{7} + 161799725637 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 505908 q^{3} + 90135570 q^{5} - 6872255096 q^{7} + 161799725637 q^{9} - 965328798588 q^{11} - 542359999142 q^{13} - 45600305947560 q^{15} + 82083537265266 q^{17} + 555748551616700 q^{19} + 34\!\cdots\!68 q^{21}+ \cdots - 15\!\cdots\!56 q^{99}+O(q^{100}) \) 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 −505908. 0 9.01356e7 0 −6.87226e9 0 1.61800e11 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 64.24.a.a 1
4.b odd 2 1 64.24.a.c 1
8.b even 2 1 16.24.a.a 1
8.d odd 2 1 2.24.a.a 1
24.f even 2 1 18.24.a.d 1
40.e odd 2 1 50.24.a.a 1
40.k even 4 2 50.24.b.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2.24.a.a 1 8.d odd 2 1
16.24.a.a 1 8.b even 2 1
18.24.a.d 1 24.f even 2 1
50.24.a.a 1 40.e odd 2 1
50.24.b.a 2 40.k even 4 2
64.24.a.a 1 1.a even 1 1 trivial
64.24.a.c 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 505908 \) acting on \(S_{24}^{\mathrm{new}}(\Gamma_0(64))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 505908 \) Copy content Toggle raw display
$5$ \( T - 90135570 \) Copy content Toggle raw display
$7$ \( T + 6872255096 \) Copy content Toggle raw display
$11$ \( T + 965328798588 \) Copy content Toggle raw display
$13$ \( T + 542359999142 \) Copy content Toggle raw display
$17$ \( T - 82083537265266 \) Copy content Toggle raw display
$19$ \( T - 555748551616700 \) Copy content Toggle raw display
$23$ \( T + 6508638190765032 \) Copy content Toggle raw display
$29$ \( T - 12\!\cdots\!90 \) Copy content Toggle raw display
$31$ \( T + 11\!\cdots\!52 \) Copy content Toggle raw display
$37$ \( T - 61\!\cdots\!34 \) Copy content Toggle raw display
$41$ \( T + 15\!\cdots\!38 \) Copy content Toggle raw display
$43$ \( T - 83\!\cdots\!32 \) Copy content Toggle raw display
$47$ \( T + 13\!\cdots\!96 \) Copy content Toggle raw display
$53$ \( T + 41\!\cdots\!22 \) Copy content Toggle raw display
$59$ \( T + 74\!\cdots\!80 \) Copy content Toggle raw display
$61$ \( T - 27\!\cdots\!98 \) Copy content Toggle raw display
$67$ \( T - 17\!\cdots\!76 \) Copy content Toggle raw display
$71$ \( T - 27\!\cdots\!68 \) Copy content Toggle raw display
$73$ \( T - 43\!\cdots\!62 \) Copy content Toggle raw display
$79$ \( T + 35\!\cdots\!40 \) Copy content Toggle raw display
$83$ \( T + 22\!\cdots\!28 \) Copy content Toggle raw display
$89$ \( T - 33\!\cdots\!10 \) Copy content Toggle raw display
$97$ \( T - 92\!\cdots\!06 \) Copy content Toggle raw display
show more
show less