Properties

Label 2420.2.a.b
Level $2420$
Weight $2$
Character orbit 2420.a
Self dual yes
Analytic conductor $19.324$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2420.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(19.3237972891\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 220)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{3} + q^{5} + 4 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{3} + q^{5} + 4 q^{7} + q^{9} + 4 q^{13} - 2 q^{15} + 4 q^{19} - 8 q^{21} - 6 q^{23} + q^{25} + 4 q^{27} + 6 q^{29} + 8 q^{31} + 4 q^{35} + 2 q^{37} - 8 q^{39} - 6 q^{41} - 8 q^{43} + q^{45} + 6 q^{47} + 9 q^{49} - 6 q^{53} - 8 q^{57} - 12 q^{59} - 2 q^{61} + 4 q^{63} + 4 q^{65} - 10 q^{67} + 12 q^{69} - 12 q^{71} + 16 q^{73} - 2 q^{75} - 8 q^{79} - 11 q^{81} - 12 q^{87} + 6 q^{89} + 16 q^{91} - 16 q^{93} + 4 q^{95} + 14 q^{97}+O(q^{100}) \) 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 −2.00000 0 1.00000 0 4.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(11\) \(-1\)

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 2420.2.a.b 1
4.b odd 2 1 9680.2.a.bb 1
11.b odd 2 1 220.2.a.a 1
33.d even 2 1 1980.2.a.a 1
44.c even 2 1 880.2.a.j 1
55.d odd 2 1 1100.2.a.e 1
55.e even 4 2 1100.2.b.a 2
88.b odd 2 1 3520.2.a.bd 1
88.g even 2 1 3520.2.a.d 1
132.d odd 2 1 7920.2.a.o 1
165.d even 2 1 9900.2.a.bd 1
165.l odd 4 2 9900.2.c.m 2
220.g even 2 1 4400.2.a.e 1
220.i odd 4 2 4400.2.b.f 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
220.2.a.a 1 11.b odd 2 1
880.2.a.j 1 44.c even 2 1
1100.2.a.e 1 55.d odd 2 1
1100.2.b.a 2 55.e even 4 2
1980.2.a.a 1 33.d even 2 1
2420.2.a.b 1 1.a even 1 1 trivial
3520.2.a.d 1 88.g even 2 1
3520.2.a.bd 1 88.b odd 2 1
4400.2.a.e 1 220.g even 2 1
4400.2.b.f 2 220.i odd 4 2
7920.2.a.o 1 132.d odd 2 1
9680.2.a.bb 1 4.b odd 2 1
9900.2.a.bd 1 165.d even 2 1
9900.2.c.m 2 165.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2420))\):

\( T_{3} + 2 \) Copy content Toggle raw display
\( T_{7} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 2 \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T - 4 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 4 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T - 4 \) Copy content Toggle raw display
$23$ \( T + 6 \) Copy content Toggle raw display
$29$ \( T - 6 \) Copy content Toggle raw display
$31$ \( T - 8 \) Copy content Toggle raw display
$37$ \( T - 2 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T + 8 \) Copy content Toggle raw display
$47$ \( T - 6 \) Copy content Toggle raw display
$53$ \( T + 6 \) Copy content Toggle raw display
$59$ \( T + 12 \) Copy content Toggle raw display
$61$ \( T + 2 \) Copy content Toggle raw display
$67$ \( T + 10 \) Copy content Toggle raw display
$71$ \( T + 12 \) Copy content Toggle raw display
$73$ \( T - 16 \) Copy content Toggle raw display
$79$ \( T + 8 \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T - 6 \) Copy content Toggle raw display
$97$ \( T - 14 \) Copy content Toggle raw display
show more
show less