Properties

Label 8820.2.a.c
Level $8820$
Weight $2$
Character orbit 8820.a
Self dual yes
Analytic conductor $70.428$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q - q^{5} + O(q^{10}) \) \( q - q^{5} - 4q^{11} + 2q^{17} + 6q^{19} - 6q^{23} + q^{25} - 2q^{31} + 2q^{37} + 2q^{41} + 4q^{43} + 8q^{47} - 10q^{53} + 4q^{55} + 4q^{59} + 2q^{61} + 12q^{67} - 8q^{71} - 8q^{73} - 8q^{79} - 4q^{83} - 2q^{85} + 10q^{89} - 6q^{95} + 4q^{97} + O(q^{100}) \)

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

\( T_{11} + 4 \)
\( T_{13} \)
\( T_{17} - 2 \)
\( T_{31} + 2 \)

Hecke characteristic polynomials

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