Properties

Label 5880.2.a.ba
Level $5880$
Weight $2$
Character orbit 5880.a
Self dual yes
Analytic conductor $46.952$
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] = [5880,2,Mod(1,5880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5880, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("5880.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5880 = 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5880.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: \(46.9520363885\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 840)
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)
 
\(f(q)\) \(=\) \( q + q^{3} - q^{5} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} - q^{5} + q^{9} + 4 q^{11} + 5 q^{13} - q^{15} - 6 q^{17} + 5 q^{19} + 2 q^{23} + q^{25} + q^{27} - 2 q^{29} + 9 q^{31} + 4 q^{33} - 11 q^{37} + 5 q^{39} + 8 q^{41} + q^{43} - q^{45} - 6 q^{47} - 6 q^{51} - 4 q^{53} - 4 q^{55} + 5 q^{57} - 6 q^{59} + 14 q^{61} - 5 q^{65} - q^{67} + 2 q^{69} + 12 q^{71} - 11 q^{73} + q^{75} + q^{79} + q^{81} + 4 q^{83} + 6 q^{85} - 2 q^{87} - 18 q^{89} + 9 q^{93} - 5 q^{95} + 18 q^{97} + 4 q^{99}+O(q^{100}) \) 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 1.00000 0 −1.00000 0 0 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(7\) \(-1\)

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 5880.2.a.ba 1
7.b odd 2 1 5880.2.a.q 1
7.d odd 6 2 840.2.bg.b 2
21.g even 6 2 2520.2.bi.h 2
28.f even 6 2 1680.2.bg.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
840.2.bg.b 2 7.d odd 6 2
1680.2.bg.c 2 28.f even 6 2
2520.2.bi.h 2 21.g even 6 2
5880.2.a.q 1 7.b odd 2 1
5880.2.a.ba 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5880))\):

\( T_{11} - 4 \) Copy content Toggle raw display
\( T_{13} - 5 \) Copy content Toggle raw display
\( T_{17} + 6 \) Copy content Toggle raw display
\( T_{19} - 5 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 1 \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 4 \) Copy content Toggle raw display
$13$ \( T - 5 \) Copy content Toggle raw display
$17$ \( T + 6 \) Copy content Toggle raw display
$19$ \( T - 5 \) Copy content Toggle raw display
$23$ \( T - 2 \) Copy content Toggle raw display
$29$ \( T + 2 \) Copy content Toggle raw display
$31$ \( T - 9 \) Copy content Toggle raw display
$37$ \( T + 11 \) Copy content Toggle raw display
$41$ \( T - 8 \) Copy content Toggle raw display
$43$ \( T - 1 \) Copy content Toggle raw display
$47$ \( T + 6 \) Copy content Toggle raw display
$53$ \( T + 4 \) Copy content Toggle raw display
$59$ \( T + 6 \) Copy content Toggle raw display
$61$ \( T - 14 \) Copy content Toggle raw display
$67$ \( T + 1 \) Copy content Toggle raw display
$71$ \( T - 12 \) Copy content Toggle raw display
$73$ \( T + 11 \) Copy content Toggle raw display
$79$ \( T - 1 \) Copy content Toggle raw display
$83$ \( T - 4 \) Copy content Toggle raw display
$89$ \( T + 18 \) Copy content Toggle raw display
$97$ \( T - 18 \) Copy content Toggle raw display
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