Properties

Label 8820.2.a.u
Level $8820$
Weight $2$
Character orbit 8820.a
Self dual yes
Analytic conductor $70.428$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8820.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(70.4280545828\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1260)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{5}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{5} + 4 q^{13} + 6 q^{17} - 2 q^{19} - 6 q^{23} + q^{25} - 2 q^{31} + 2 q^{37} + 6 q^{41} - 4 q^{43} + 6 q^{53} + 12 q^{59} + 10 q^{61} + 4 q^{65} - 4 q^{67} - 12 q^{71} + 4 q^{73} + 8 q^{79} + 12 q^{83} + 6 q^{85} + 6 q^{89} - 2 q^{95} - 8 q^{97}+O(q^{100}) \) 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 0 0 1.00000 0 0 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 8820.2.a.u 1
3.b odd 2 1 8820.2.a.h 1
7.b odd 2 1 1260.2.a.d 1
21.c even 2 1 1260.2.a.j yes 1
28.d even 2 1 5040.2.a.e 1
35.c odd 2 1 6300.2.a.i 1
35.f even 4 2 6300.2.k.i 2
84.h odd 2 1 5040.2.a.w 1
105.g even 2 1 6300.2.a.h 1
105.k odd 4 2 6300.2.k.j 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1260.2.a.d 1 7.b odd 2 1
1260.2.a.j yes 1 21.c even 2 1
5040.2.a.e 1 28.d even 2 1
5040.2.a.w 1 84.h odd 2 1
6300.2.a.h 1 105.g even 2 1
6300.2.a.i 1 35.c odd 2 1
6300.2.k.i 2 35.f even 4 2
6300.2.k.j 2 105.k odd 4 2
8820.2.a.h 1 3.b odd 2 1
8820.2.a.u 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8820))\):

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