Properties

Label 1080.6.a.b
Level $1080$
Weight $6$
Character orbit 1080.a
Self dual yes
Analytic conductor $173.215$
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] = [1080,6,Mod(1,1080)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1080.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1080.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: \(173.214525398\)
Analytic rank: \(1\)
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)
 
\(f(q)\) \(=\) \( q + 25 q^{5} - 234 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + 25 q^{5} - 234 q^{7} + 347 q^{11} - 33 q^{13} + 237 q^{17} + 1496 q^{19} - 2811 q^{23} + 625 q^{25} - 5513 q^{29} + 2911 q^{31} - 5850 q^{35} + 5602 q^{37} + 4716 q^{41} + 10479 q^{43} + 5963 q^{47} + 37949 q^{49} - 17964 q^{53} + 8675 q^{55} + 30372 q^{59} - 35530 q^{61} - 825 q^{65} - 12476 q^{67} + 7520 q^{71} + 36378 q^{73} - 81198 q^{77} - 22727 q^{79} + 46254 q^{83} + 5925 q^{85} - 58832 q^{89} + 7722 q^{91} + 37400 q^{95} - 145906 q^{97}+O(q^{100}) \) 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 25.0000 0 −234.000 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 1080.6.a.b yes 1
3.b odd 2 1 1080.6.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1080.6.a.a 1 3.b odd 2 1
1080.6.a.b yes 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(1080))\):

\( T_{7} + 234 \) Copy content Toggle raw display
\( T_{11} - 347 \) 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
$5$ \( T - 25 \) Copy content Toggle raw display
$7$ \( T + 234 \) Copy content Toggle raw display
$11$ \( T - 347 \) Copy content Toggle raw display
$13$ \( T + 33 \) Copy content Toggle raw display
$17$ \( T - 237 \) Copy content Toggle raw display
$19$ \( T - 1496 \) Copy content Toggle raw display
$23$ \( T + 2811 \) Copy content Toggle raw display
$29$ \( T + 5513 \) Copy content Toggle raw display
$31$ \( T - 2911 \) Copy content Toggle raw display
$37$ \( T - 5602 \) Copy content Toggle raw display
$41$ \( T - 4716 \) Copy content Toggle raw display
$43$ \( T - 10479 \) Copy content Toggle raw display
$47$ \( T - 5963 \) Copy content Toggle raw display
$53$ \( T + 17964 \) Copy content Toggle raw display
$59$ \( T - 30372 \) Copy content Toggle raw display
$61$ \( T + 35530 \) Copy content Toggle raw display
$67$ \( T + 12476 \) Copy content Toggle raw display
$71$ \( T - 7520 \) Copy content Toggle raw display
$73$ \( T - 36378 \) Copy content Toggle raw display
$79$ \( T + 22727 \) Copy content Toggle raw display
$83$ \( T - 46254 \) Copy content Toggle raw display
$89$ \( T + 58832 \) Copy content Toggle raw display
$97$ \( T + 145906 \) Copy content Toggle raw display
show more
show less