Properties

Label 1440.2.a.m
Level $1440$
Weight $2$
Character orbit 1440.a
Self dual yes
Analytic conductor $11.498$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.4984578911\)
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

\(f(q)\) \(=\) \( q + q^{5} + 2 q^{7} + O(q^{10}) \) \( q + q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{17} + 4 q^{19} + q^{25} + 2 q^{29} + 8 q^{31} + 2 q^{35} - 4 q^{37} - 8 q^{41} + 8 q^{43} - 8 q^{47} - 3 q^{49} + 10 q^{53} + 2 q^{55} - 6 q^{59} + 2 q^{61} + 12 q^{67} + 12 q^{71} - 2 q^{73} + 4 q^{77} + 8 q^{79} - 4 q^{83} - 2 q^{85} - 12 q^{89} + 4 q^{95} + 10 q^{97} + O(q^{100}) \)

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.

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 1440.2.a.m yes 1
3.b odd 2 1 1440.2.a.e yes 1
4.b odd 2 1 1440.2.a.h yes 1
5.b even 2 1 7200.2.a.n 1
5.c odd 4 2 7200.2.f.u 2
8.b even 2 1 2880.2.a.l 1
8.d odd 2 1 2880.2.a.g 1
12.b even 2 1 1440.2.a.b 1
15.d odd 2 1 7200.2.a.m 1
15.e even 4 2 7200.2.f.h 2
20.d odd 2 1 7200.2.a.bn 1
20.e even 4 2 7200.2.f.i 2
24.f even 2 1 2880.2.a.v 1
24.h odd 2 1 2880.2.a.be 1
60.h even 2 1 7200.2.a.bo 1
60.l odd 4 2 7200.2.f.v 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1440.2.a.b 1 12.b even 2 1
1440.2.a.e yes 1 3.b odd 2 1
1440.2.a.h yes 1 4.b odd 2 1
1440.2.a.m yes 1 1.a even 1 1 trivial
2880.2.a.g 1 8.d odd 2 1
2880.2.a.l 1 8.b even 2 1
2880.2.a.v 1 24.f even 2 1
2880.2.a.be 1 24.h odd 2 1
7200.2.a.m 1 15.d odd 2 1
7200.2.a.n 1 5.b even 2 1
7200.2.a.bn 1 20.d odd 2 1
7200.2.a.bo 1 60.h even 2 1
7200.2.f.h 2 15.e even 4 2
7200.2.f.i 2 20.e even 4 2
7200.2.f.u 2 5.c odd 4 2
7200.2.f.v 2 60.l odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\):

\( T_{7} - 2 \)
\( T_{11} - 2 \)
\( T_{17} + 2 \)
\( T_{19} - 4 \)

Hecke characteristic polynomials

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