Properties

Label 480.2.a.g
Level $480$
Weight $2$
Character orbit 480.a
Self dual yes
Analytic conductor $3.833$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 480.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.83281929702\)
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

\(f(q)\) \(=\) \( q + q^{3} + q^{5} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} + q^{5} + q^{9} + 2 q^{13} + q^{15} + 6 q^{17} + 4 q^{19} - 8 q^{23} + q^{25} + q^{27} - 2 q^{29} - 4 q^{31} + 10 q^{37} + 2 q^{39} + 2 q^{41} + 4 q^{43} + q^{45} - 8 q^{47} - 7 q^{49} + 6 q^{51} - 2 q^{53} + 4 q^{57} - 8 q^{59} - 2 q^{61} + 2 q^{65} + 12 q^{67} - 8 q^{69} - 8 q^{71} - 14 q^{73} + q^{75} + 12 q^{79} + q^{81} + 4 q^{83} + 6 q^{85} - 2 q^{87} - 14 q^{89} - 4 q^{93} + 4 q^{95} + 2 q^{97}+O(q^{100}) \) 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.

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
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(-1\)

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 480.2.a.g yes 1
3.b odd 2 1 1440.2.a.d 1
4.b odd 2 1 480.2.a.d 1
5.b even 2 1 2400.2.a.i 1
5.c odd 4 2 2400.2.f.g 2
8.b even 2 1 960.2.a.b 1
8.d odd 2 1 960.2.a.k 1
12.b even 2 1 1440.2.a.c 1
15.d odd 2 1 7200.2.a.ba 1
15.e even 4 2 7200.2.f.k 2
16.e even 4 2 3840.2.k.s 2
16.f odd 4 2 3840.2.k.n 2
20.d odd 2 1 2400.2.a.z 1
20.e even 4 2 2400.2.f.l 2
24.f even 2 1 2880.2.a.ba 1
24.h odd 2 1 2880.2.a.z 1
40.e odd 2 1 4800.2.a.s 1
40.f even 2 1 4800.2.a.cb 1
40.i odd 4 2 4800.2.f.v 2
40.k even 4 2 4800.2.f.o 2
60.h even 2 1 7200.2.a.z 1
60.l odd 4 2 7200.2.f.s 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
480.2.a.d 1 4.b odd 2 1
480.2.a.g yes 1 1.a even 1 1 trivial
960.2.a.b 1 8.b even 2 1
960.2.a.k 1 8.d odd 2 1
1440.2.a.c 1 12.b even 2 1
1440.2.a.d 1 3.b odd 2 1
2400.2.a.i 1 5.b even 2 1
2400.2.a.z 1 20.d odd 2 1
2400.2.f.g 2 5.c odd 4 2
2400.2.f.l 2 20.e even 4 2
2880.2.a.z 1 24.h odd 2 1
2880.2.a.ba 1 24.f even 2 1
3840.2.k.n 2 16.f odd 4 2
3840.2.k.s 2 16.e even 4 2
4800.2.a.s 1 40.e odd 2 1
4800.2.a.cb 1 40.f even 2 1
4800.2.f.o 2 40.k even 4 2
4800.2.f.v 2 40.i odd 4 2
7200.2.a.z 1 60.h even 2 1
7200.2.a.ba 1 15.d odd 2 1
7200.2.f.k 2 15.e even 4 2
7200.2.f.s 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(480))\):

\( T_{7} \) Copy content Toggle raw display
\( T_{11} \) Copy content Toggle raw display
\( T_{19} - 4 \) 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
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T - 6 \) Copy content Toggle raw display
$19$ \( T - 4 \) Copy content Toggle raw display
$23$ \( T + 8 \) Copy content Toggle raw display
$29$ \( T + 2 \) Copy content Toggle raw display
$31$ \( T + 4 \) Copy content Toggle raw display
$37$ \( T - 10 \) Copy content Toggle raw display
$41$ \( T - 2 \) Copy content Toggle raw display
$43$ \( T - 4 \) Copy content Toggle raw display
$47$ \( T + 8 \) Copy content Toggle raw display
$53$ \( T + 2 \) Copy content Toggle raw display
$59$ \( T + 8 \) Copy content Toggle raw display
$61$ \( T + 2 \) Copy content Toggle raw display
$67$ \( T - 12 \) Copy content Toggle raw display
$71$ \( T + 8 \) Copy content Toggle raw display
$73$ \( T + 14 \) Copy content Toggle raw display
$79$ \( T - 12 \) Copy content Toggle raw display
$83$ \( T - 4 \) Copy content Toggle raw display
$89$ \( T + 14 \) Copy content Toggle raw display
$97$ \( T - 2 \) Copy content Toggle raw display
show more
show less