Properties

Label 3520.2.a.n
Level $3520$
Weight $2$
Character orbit 3520.a
Self dual yes
Analytic conductor $28.107$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3520.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.1073415115\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{5} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{5} - 3 q^{9} - q^{11} - 2 q^{13} + 6 q^{17} - 4 q^{19} - 4 q^{23} + q^{25} - 6 q^{29} + 8 q^{31} + 2 q^{37} + 2 q^{41} + 4 q^{43} + 3 q^{45} + 12 q^{47} - 7 q^{49} + 2 q^{53} + q^{55} + 4 q^{59} + 10 q^{61} + 2 q^{65} - 16 q^{67} - 8 q^{71} + 14 q^{73} - 8 q^{79} + 9 q^{81} - 4 q^{83} - 6 q^{85} + 10 q^{89} + 4 q^{95} + 10 q^{97} + 3 q^{99}+O(q^{100}) \) 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.

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 0 0 −3.00000 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 3520.2.a.n 1
4.b odd 2 1 3520.2.a.p 1
8.b even 2 1 880.2.a.h 1
8.d odd 2 1 55.2.a.a 1
24.f even 2 1 495.2.a.a 1
24.h odd 2 1 7920.2.a.i 1
40.e odd 2 1 275.2.a.a 1
40.f even 2 1 4400.2.a.p 1
40.i odd 4 2 4400.2.b.n 2
40.k even 4 2 275.2.b.b 2
56.e even 2 1 2695.2.a.c 1
88.b odd 2 1 9680.2.a.r 1
88.g even 2 1 605.2.a.b 1
88.k even 10 4 605.2.g.c 4
88.l odd 10 4 605.2.g.a 4
104.h odd 2 1 9295.2.a.b 1
120.m even 2 1 2475.2.a.i 1
120.q odd 4 2 2475.2.c.f 2
264.p odd 2 1 5445.2.a.i 1
440.c even 2 1 3025.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.2.a.a 1 8.d odd 2 1
275.2.a.a 1 40.e odd 2 1
275.2.b.b 2 40.k even 4 2
495.2.a.a 1 24.f even 2 1
605.2.a.b 1 88.g even 2 1
605.2.g.a 4 88.l odd 10 4
605.2.g.c 4 88.k even 10 4
880.2.a.h 1 8.b even 2 1
2475.2.a.i 1 120.m even 2 1
2475.2.c.f 2 120.q odd 4 2
2695.2.a.c 1 56.e even 2 1
3025.2.a.f 1 440.c even 2 1
3520.2.a.n 1 1.a even 1 1 trivial
3520.2.a.p 1 4.b odd 2 1
4400.2.a.p 1 40.f even 2 1
4400.2.b.n 2 40.i odd 4 2
5445.2.a.i 1 264.p odd 2 1
7920.2.a.i 1 24.h odd 2 1
9295.2.a.b 1 104.h odd 2 1
9680.2.a.r 1 88.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3520))\):

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