Properties

Label 2880.2.a.d
Level $2880$
Weight $2$
Character orbit 2880.a
Self dual yes
Analytic conductor $22.997$
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] = [2880,2,Mod(1,2880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("2880.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.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: \(22.9969157821\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 160)
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)
 
\(f(q)\) \(=\) \( q - q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{5} - 2 q^{7} - 4 q^{11} + 6 q^{13} - 2 q^{17} - 8 q^{19} + 6 q^{23} + q^{25} - 2 q^{29} + 4 q^{31} + 2 q^{35} - 2 q^{37} + 10 q^{41} + 2 q^{43} + 2 q^{47} - 3 q^{49} + 2 q^{53} + 4 q^{55} - 2 q^{61} - 6 q^{65} + 6 q^{67} + 12 q^{71} + 10 q^{73} + 8 q^{77} - 8 q^{79} - 10 q^{83} + 2 q^{85} + 6 q^{89} - 12 q^{91} + 8 q^{95} + 10 q^{97}+O(q^{100}) \) 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
0 0 0 −1.00000 0 −2.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)

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 2880.2.a.d 1
3.b odd 2 1 320.2.a.e 1
4.b odd 2 1 2880.2.a.o 1
8.b even 2 1 1440.2.a.i 1
8.d odd 2 1 1440.2.a.l 1
12.b even 2 1 320.2.a.b 1
15.d odd 2 1 1600.2.a.e 1
15.e even 4 2 1600.2.c.f 2
24.f even 2 1 160.2.a.b yes 1
24.h odd 2 1 160.2.a.a 1
40.e odd 2 1 7200.2.a.l 1
40.f even 2 1 7200.2.a.bp 1
40.i odd 4 2 7200.2.f.w 2
40.k even 4 2 7200.2.f.g 2
48.i odd 4 2 1280.2.d.h 2
48.k even 4 2 1280.2.d.b 2
60.h even 2 1 1600.2.a.t 1
60.l odd 4 2 1600.2.c.c 2
120.i odd 2 1 800.2.a.i 1
120.m even 2 1 800.2.a.a 1
120.q odd 4 2 800.2.c.b 2
120.w even 4 2 800.2.c.a 2
168.e odd 2 1 7840.2.a.e 1
168.i even 2 1 7840.2.a.w 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
160.2.a.a 1 24.h odd 2 1
160.2.a.b yes 1 24.f even 2 1
320.2.a.b 1 12.b even 2 1
320.2.a.e 1 3.b odd 2 1
800.2.a.a 1 120.m even 2 1
800.2.a.i 1 120.i odd 2 1
800.2.c.a 2 120.w even 4 2
800.2.c.b 2 120.q odd 4 2
1280.2.d.b 2 48.k even 4 2
1280.2.d.h 2 48.i odd 4 2
1440.2.a.i 1 8.b even 2 1
1440.2.a.l 1 8.d odd 2 1
1600.2.a.e 1 15.d odd 2 1
1600.2.a.t 1 60.h even 2 1
1600.2.c.c 2 60.l odd 4 2
1600.2.c.f 2 15.e even 4 2
2880.2.a.d 1 1.a even 1 1 trivial
2880.2.a.o 1 4.b odd 2 1
7200.2.a.l 1 40.e odd 2 1
7200.2.a.bp 1 40.f even 2 1
7200.2.f.g 2 40.k even 4 2
7200.2.f.w 2 40.i odd 4 2
7840.2.a.e 1 168.e odd 2 1
7840.2.a.w 1 168.i even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2880))\):

\( T_{7} + 2 \) Copy content Toggle raw display
\( T_{11} + 4 \) Copy content Toggle raw display
\( T_{13} - 6 \) Copy content Toggle raw display
\( T_{17} + 2 \) Copy content Toggle raw display
\( T_{19} + 8 \) Copy content Toggle raw display

Hecke characteristic polynomials

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